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STUDIES OF HYPERPOLARIZED 3He
RELAXATION AT GLASS SURFACES
by
Richard Emil Jacob
A dissertation submitted to the faculty ofThe University of Utah
in partial fulfillment of the requirements for the degree of
Doctor of Philosophy
Department of Physics
The University of Utah
May 2003
Copyright c© Richard Emil Jacob 2003
All Rights Reserved
THE UNIVERSITY OF UTAH GRADUATE SCHOOL
SUPERVISORY COMMITTEE APPROVAL
of a dissertation submitted by
Richard Emil Jacob
This dissertation has been read by each member of the following supervisory committeeand by majority vote has been found to be satisfactory.
Chair: David C. Ailion
Carleton DeTar
Dennis Parker
Brian T. Saam
Clayton Williams
THE UNIVERSITY OF UTAH GRADUATE SCHOOL
FINAL READING APPROVAL
To the Graduate Council of The University of Utah:
I have read the dissertation of Richard Emil Jacob in itsfinal form and have found that (1) its format, citations, and bibliographicstyle are consistent and acceptable; (2) its illustrative materials includingfigures, tables, and charts are in place; and (3) the final manuscript issatisfactory to the Supervisory Committee and is ready for submission toThe Graduate School.
Date David C. AilionChair, Supervisory Committee
Approved for the Major Department
Z. Valy VardenyChair
Approved for the Graduate Council
David S. ChapmanDean of The Graduate School
ABSTRACT
Enormous nonequilibrium nuclear polarizations, of order 10%, can be achieved
in certain noble-gas nuclei via spin-exchange optical pumping (SEOP). Applications
of such hyperpolarized (HP) gases depend critically on the ability to maximize and
maintain the polarization. Both the polarization level and longitudinal relaxation
time are limited by relaxive interactions between the gas and glass vessels, or cells,
that contain the gas. An understanding of the interactions is critical to consistent
production of nonrelaxive cells. Magnetic resonance image quality and sensitivity,
using HP gas as the signal source, benefit greatly from maximally polarized gas.
This thesis addresses nuclear longitudinal relaxation mechanisms of 3He on glass
surfaces.
Much information about the glass–3He interactions can be obtained by measuring
3He polarization loss by periodically sampling a 3He free induction decay signal using
a pulse nuclear magnetic resonance spectrometer. Over time, the initial amplitude
of the signal decays with a characteristic time constant T1. The HP 3He T1’s are
very sensitive to surface relaxation mechanisms because of the high mobility of the
gas.
Wall relaxation is a very complicated, multivariable problem. We show that
relaxation in bare Pyrex glass is mainly due to 3He dissolving into the glass and
interacting with paramagnetic Fe3+ ions in a predictable way. We describe the first
experimentally confirmed predictive model of relaxation rates of 3He in bare-glass
cells. However, once Rb metal is added to a cell for SEOP, the relaxation interactions
change significantly. Our data suggest that, when Rb is present, interactions with
Fe3+ ions no longer contribute significantly to relaxation so that other mechanisms
take over.
One surprising and significant mechanism in Rb-coated cells is interactions of the
3He with magnetic particles. We found that the 3He T1’s can be reduced significantly
due solely to exposure of a cell to a high (several thousand Gauss) magnetic field,
an effect termed T1 hysteresis. The magnetized cells can be degaussed to restore the
original T1. We present a model that predicts approximately 104 magnetic sites on
the surface of a typical spherical 50 cm3 cell, or a few sites per square millimeter.
This astonishingly low site density underscores the sensitivity to surfaces of 3He
relaxation measurements. The model also predicts a linear dependence of T1 on
pressure at a given temperature, which we confirm experimentally.
v
to Dad
who showed me the roads to take
and
to Connie
who kept me on them
It is a profound and necessary truth that the deep things in science
are not found because they are useful;
they are found because it was possible to find them.
– Robert Oppenheimer
CONTENTS
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv
CHAPTERS
1. INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Hyperpolarized Noble Gases . . . . . . . . . . . . . . . . . . . . . . 11.1.1 Overview of Polarized Gas . . . . . . . . . . . . . . . . . . . 11.1.2 Uses of Polarized Gas . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Background and History . . . . . . . . . . . . . . . . . . . . . . . . 21.2.1 Spin-exchange and Optical Pumping . . . . . . . . . . . . . . 21.2.2 Current Issues . . . . . . . . . . . . . . . . . . . . . . . . . . 21.2.3 Basic Physics of Spin-exchange Optical Pumping . . . . . . . 31.2.4 3He Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . 61.2.5 Spin-exchange Vessels . . . . . . . . . . . . . . . . . . . . . . 8
1.3 Thesis Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10
2. NMR SPECTROMETER AND TECHNIQUES . . . . . . . . . . . . . . 13
2.1 100 kHz Pulse NMR Spectrometer . . . . . . . . . . . . . . . . . . . 132.1.1 The Applied Field . . . . . . . . . . . . . . . . . . . . . . . . 132.1.2 The Spectrometer . . . . . . . . . . . . . . . . . . . . . . . . 142.1.3 The NMR Coil . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2 T1 Measurement Techniques . . . . . . . . . . . . . . . . . . . . . . 16
3. WALL RELAXATION OF 3HE IN SPIN-EXCHANGE CELLS . 18
3.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 203.4 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 213.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 233.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 303.7 Addendum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
4. 3HE SPIN-EXCHANGE CELLSFOR MRI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32
4.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 324.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 344.4 Wall Relaxation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 354.5 Cell Fabrication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 374.6 Cell Preparation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 404.7 Cell Filling System . . . . . . . . . . . . . . . . . . . . . . . . . . . 444.8 The Polarizer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474.9 Experimental Results . . . . . . . . . . . . . . . . . . . . . . . . . . 50
4.9.1 T1 Measurements . . . . . . . . . . . . . . . . . . . . . . . . 504.9.2 Polarimetry . . . . . . . . . . . . . . . . . . . . . . . . . . . 524.9.3 Overall Performance . . . . . . . . . . . . . . . . . . . . . . . 55
4.10 Transit Time of 3He in the Capillary . . . . . . . . . . . . . . . . . . 564.11 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 594.12 Addendum . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5. MAGNETIC FIELD DEPENDENCE OF 3HE RELAXATION . . 63
5.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
5.3.1 High-field Hysteresis . . . . . . . . . . . . . . . . . . . . . . . 645.3.2 Low-field Hysteresis . . . . . . . . . . . . . . . . . . . . . . . 65
5.4 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665.5 Results/Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.5.1 High-field Hysteresis . . . . . . . . . . . . . . . . . . . . . . . 695.5.2 Low-field Hysteresis . . . . . . . . . . . . . . . . . . . . . . . 75
5.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
6. FUNDAMENTAL MECHANISMS OF 3HE RELAXATION ONGLASS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
6.1 Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 796.2 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.3 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 806.4 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
6.4.1 T > Room Temperature . . . . . . . . . . . . . . . . . . . . 816.4.2 T < Room Temperature . . . . . . . . . . . . . . . . . . . . 87
6.5 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 896.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 90
6.6.1 T > Room Temperature . . . . . . . . . . . . . . . . . . . . 906.6.2 T < Room Temperature . . . . . . . . . . . . . . . . . . . . 92
6.7 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93ix
7. 3HE RELAXATION IN BARE AND RB-COATED GLASS . . . . 95
7.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 957.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
7.3.1 Aluminosilicate Glass . . . . . . . . . . . . . . . . . . . . . . 967.3.2 Quartz Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . 997.3.3 Rb-coated Pyrex Glass . . . . . . . . . . . . . . . . . . . . . 101
7.4 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1017.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.5.1 Aluminosilicate Glass . . . . . . . . . . . . . . . . . . . . . . 1037.5.1.1 T > Room Remperature . . . . . . . . . . . . . . . 1037.5.1.2 T < Room Temperature . . . . . . . . . . . . . . . 104
7.5.2 Quartz . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1057.5.3 Pyrex Glass . . . . . . . . . . . . . . . . . . . . . . . . . . . 107
7.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 113
8. CELL RINSING . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
8.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1148.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1148.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1158.4 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1178.5 Results/Discussion . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
8.5.1 Reducing-agent Rinse . . . . . . . . . . . . . . . . . . . . . . 1188.5.2 Rb Rinses . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1198.5.3 Acid Rinses . . . . . . . . . . . . . . . . . . . . . . . . . . . 122
8.5.3.1 HF Rinse . . . . . . . . . . . . . . . . . . . . . . . . 1228.5.3.2 Aqua Regia Rinse . . . . . . . . . . . . . . . . . . . 1248.5.3.3 HF and HCl Rinse . . . . . . . . . . . . . . . . . . 1258.5.3.4 Intervening HCl Rinse . . . . . . . . . . . . . . . . 127
8.5.4 Potassium Rinse . . . . . . . . . . . . . . . . . . . . . . . . . 1298.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129
9. MRI OF FLOWING POLARIZED 3HE . . . . . . . . . . . . . . . . . . . . . 131
9.1 Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1319.2 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1319.3 Theory . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1339.4 Experimental . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1359.5 Results and Discussion . . . . . . . . . . . . . . . . . . . . . . . . . 1379.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140
APPENDIX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 141
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147
x
LIST OF FIGURES
1.1 Depopulation optical pumping . . . . . . . . . . . . . . . . . . . . . . . . 4
2.1 100 kHz NMR spectrometer . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.1 T1 hysteresis of cell 5A . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
3.2 T1 pressure dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
3.3 Rb dependence . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
4.1 A Pyrex valved spin-exchange cell for generating hyperpolarized 3He . . 38
4.2 Diagram of a cell manifold . . . . . . . . . . . . . . . . . . . . . . . . . . 40
4.3 The oil-free high-vacuum system used for cell fabrication . . . . . . . . . 41
4.4 Gas-handling system used to fill cells with 3He . . . . . . . . . . . . . . . 45
4.5 Polarization and decay transients . . . . . . . . . . . . . . . . . . . . . . 48
4.6 Relaxation rates for several cells . . . . . . . . . . . . . . . . . . . . . . . 51
4.7 Polarimetry free-induction decays . . . . . . . . . . . . . . . . . . . . . . 54
5.1 A sketch of a typical hysteresis loop showing the relationship betweenmagnetic moment M and applied field H . . . . . . . . . . . . . . . . 66
5.2 Gas transfer manifold . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.3 T1 hysteresis loop of an aluminosilicate cell . . . . . . . . . . . . . . . . . 70
5.4 A T1 hysteresis loop of a bare (no Rb) Pyrex cell . . . . . . . . . . . . . 71
5.5 A T1 hysteresis loop of Pyrex cell 9A . . . . . . . . . . . . . . . . . . . . 72
5.6 A T1 hysteresis loop of Pyrex cell 10A . . . . . . . . . . . . . . . . . . . 73
5.7 A T1 hysteresis loop of Pyrex cell 18A . . . . . . . . . . . . . . . . . . . 73
5.8 Low-field T1 hysteresis . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
6.1 Temperature dependent relaxation rates for three bare (no Rb) Pyrexcells above room temperature . . . . . . . . . . . . . . . . . . . . . . 91
6.2 Relaxation rate vs 1000/T for two bare Pyrex cells at ≈4 amagats . . . . 92
7.1 Relaxation rate vs. 1000/T for two bare aluminosilicate (GE-180) cellsfor T ≤ 300 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
7.2 Relaxation rate vs. 1000/T for two bare aluminosilicate (GE-180) cellsfor T ≥ 300 K . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
7.3 Relaxation rate vs. 1000/T for two bare quartz (GE fused silica) cells at≈ 4 atm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 106
7.4 Wall T−11 measurements of several spin-exchange cells for T > 295 K . . 107
8.1 Cells rinsed with a chemical reducing agent . . . . . . . . . . . . . . . . 119
8.2 Relaxation rates for three different cells before and after Rb is rinsed out 120
8.3 Relaxation rates for cell 11A when bare (new, no Rb), with Rb, and withthe Rb rinsed out . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
8.4 T1 hysteresis of HF-rinsed cells . . . . . . . . . . . . . . . . . . . . . . . 122
8.5 An AFM image of an untreated Pyrex sample . . . . . . . . . . . . . . . 123
8.6 An AFM image of a Pyrex sample rinsed with a 10% HF solution forseveral minutes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124
8.7 T1 hysteresis of cells rinsed with aqua regia . . . . . . . . . . . . . . . . . 125
8.8 T1 hysteresis of cells rinsed with HF and HCl . . . . . . . . . . . . . . . 126
8.9 Atomic force microscopy of a bare Pyrex sample rinsed with HCl . . . . 127
8.10 T1 hysteresis of Rb and HCl rinsed cells . . . . . . . . . . . . . . . . . . 128
9.1 The velocity and diffusion sensitive gradient sequence used to makeimages in Fig. 9.3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
9.2 Experimental set-up for MRI flow imaging . . . . . . . . . . . . . . . . . 136
9.3 Velocity map (left) and ADC map (right) for flowing HP 3He through atube . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137
xii
9.4 Visualization of real-time MRI of 3He flowing through a tube . . . . . . . 139
A.1 Box 1 of the intermediate-field spectrometer . . . . . . . . . . . . . . . . 142
A.2 Box 2 of the intermediate-field spectrometer . . . . . . . . . . . . . . . . 143
A.3 Box 3 of the intermediate-field spectrometer . . . . . . . . . . . . . . . . 145
A.4 Intermediate field spectrometer pulse generator and low-pass filter sec-tion details . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 146
xiii
ACKNOWLEDGEMENTS
The individual most responsible for my success and progress as a graduate student
is my adviser, Brian Saam. He had an undying patience for my incessant questions,
hair-brained ideas, and myriad mistakes. And the fact that we were both new to
the game – I was his first graduate student – meant we were in it together. I learned
good experimental practices, some plumbing, some electronics, a little squash, and
how to make my hands and brain do things I never thought possible. It was only
one year after we entered a completely empty room we called a laboratory that we
found a ground-breaking and critically important new phenomenon which led to my
first publication: a Letter to the Physical Review. I will always have fond memories
of the time we spent together doing, talking, and thinking physics.
David Ailion was very helpful in getting me through the Common Exam orals
and in setting up my committee. He and Gernot Laicher introduced me to NMR
and took me on as a student prior to Brian’s arrival. Several others made important
contributions to the research, namely: Steve “Just Drill The Hole” Morgan, who
helped build the vacuum systems and acquire data; Ben Anger, who put together
the intermediate-field spectrometer and took the initial goofy field-dependence data;
and Ryan Stapley, who helped take data one summer. The guys in the machine shop,
Bob Fernelius, Jack Pitts, and Ed Munford, sure helped make my job easier. Mark
Conradi, Thad Walker, and Will Happer made significant intangible contributions,
mostly through conversations with Brian. Jason Leawoods was instrumental in
making the PRL complete, and continues to have good ideas for finding out more
about T1 hysteresis. The CPL was motivated by the brilliant thinking and cooper-
ation of Bas Driehuys, and the flow images would not have been possible without
Kevin Minard and the facilities at PNNL. Finally, Janice Kyle’s expert glassblowing
contributed significantly to all of our incredible cell-making success.
Thanks to my folks for always showing support and interest in whatever I did.
Just knowing they expected a lot was great motivation to achieve a lot. And knowing
that I would finally accomplish something that Kris, John (though it’s just a matter
of time), and Becky have not accomplished was additional motivation. They really
help me live up to my potential. And Scott and Dawnette Palmer provided a great
stress relief valve through evenings of games and watching ASU football (go Devils!).
My dear wife, Connie, to whom I have been married for over seven years, has
been incredibly patient and understanding over the five and a half years of graduate
school. She supported the family both financially and emotionally. She gave me the
encouragement, and shoulder, I often needed. The fact that she has stayed with me
astonishes me, and the prospect of being together forever elates me. I am, indeed,
a lucky man.
xv
CHAPTER 1
INTRODUCTION
1.1 Hyperpolarized Noble Gases
1.1.1 Overview of Polarized Gas
Enormous nonequilibrium nuclear polarizations (of order 10%) can be achieved
in certain noble-gas nuclei, specifically 129Xe and 3He. Gases with such polarizations
are referred to as hyperpolarized (HP), because the net magnetization of a sample
is several orders of magnitude higher than at thermal equilibrium in a several-Tesla
magnetic field. These polarizations can be achieved through optical pumping meth-
ods, either spin-exchange optical pumping (SEOP) [1] or metastability-exchange
optical pumping (MEOP) [2]. The former requires an alkali metal intermediary, and
the latter polarizes the 3He nuclei directly. Both MEOP and SEOP allow for the
polarization of large quantities of gas (∼ 1 atm·L) to sufficiently high polarizations
(≥ 50%). This dissertation deals exclusively with 3He polarized via SEOP.
1.1.2 Uses of Polarized Gas
HP gas has several applications in physics, chemistry, and biomedicine. These
include the determination of the neutron spin-structure function by scattering po-
larized electrons from targets of highly polarized 3He [3], studies of fundamental
symmetries [4, 5], neutron polarizers and spin filters [6], and studies of surface inter-
actions [7]. An exciting, recent application is magnetic resonance imaging (MRI) of
2
lung air spaces [8, 9]. Pulmonary MRI in humans requires a large volume (≈ 0.5 L)
of polarized gas, and recent developments in high power, low cost, diode-array lasers
has allowed for production of liter quantities of HP 3He making such experiments
feasible.
1.2 Background and History
1.2.1 Spin-exchange and Optical Pumping
The term “optical pumping” refers to the use of light to produce a nonequilibrium
energy level population of a system, such as the electron spin distribution of alkali
metal atoms. A Nobel prize was awarded in 1966 for the pioneering optical pumping
work of A. Kastler [10]. “Spin-exchange” is a process of angular momentum transfer
from optically pumped alkali metal atoms to nuclei of noble gas atoms. The first
successful demonstration of large, nonequilibrium polarizations in noble gas nuclei
attained via SEOP was published in 1961 by M. Bouchiat, et al. [11]. Optical
pumping is a photon-limited process; thus the exclusive availability of discharge
lamps and low-power lasers initially limited the quantities and applications of HP
gas. Within the last 10 years, developments in inexpensive, high-power, efficient
diode-array lasers have helped open the flood gates of polarized gas research, since
they made polarizing liter quantities of 3He possible. See [1, 12] for thorough reviews
of optical pumping.
1.2.2 Current Issues
As research in HP gas has progressed, many interesting physics problems have
arisen. This is a good sign, indicating a realm of physics gaining the interest of a
growing number of researchers. Several of the problems have affected, and arisen
3
from, my research on HP 3He. One issue is the production of the glass cells used
for SEOP. 3He relaxes to thermal equilibrium mainly through interactions with
the cell walls. Consistently making cells with long lifetimes has proven frustrating
and problematic, and some groups have developed elaborate methods of preparing
cells. Through the production of dozens of cells, we have developed successful
protocols for consistently making quality cells. Another problem is that a basic
understanding of the relaxation interactions between 3He and the glass is lacking, as
is an understanding of exactly what the 3He is interacting with. Studies of cell-wall
relaxation have been the crux of my research. Closely related to wall relaxation is
the problem that I (very unexpectedly) discovered involving ferromagnetic inclusions
in the glass. We would like to know exactly where these inclusions come from, how
much magnetic material is present, and, most especially, how to eliminate them. An
exciting consequence of this discovery is the possibility of a new application of HP
3He: an ultra-sensitive probe for surface magnetism.
1.2.3 Basic Physics of Spin-exchange Optical Pumping
SEOP is a two-step process that involves an alkali metal and circularly-polarized
laser light [1]. The first step, optical pumping, polarizes the valence electrons of
the alkali-metal vapor, typically Rb. A sufficient Rb vapor pressure is achieved by
heating the cell to 160–180C [13]. The circularly polarized laser light is resonant
with the transition from the 5S1/2 ground state to the 5P1/2 excited state. Allowed
transitions of the valence electron are from the m = ±1/2 to the m = ∓1/2 sublevels,
obeying the ∆m = ±1 selection rule for σ± light. Pressure broadening of the
absorption line allows for use of a laser with a broad linewidth (1 - 2 nm fwhm), such
as a diode-array. For example, as depicted in Fig. 1.1, left-circularly polarized (σ+)
light will excite the m = −1/2 (spin-down) sublevel to the m = +1/2 (spin-up)
4
50% 50%
5P1/2
5S1/2
collisional mixing
m=-1/2 m=1/2
σ+
Figure 1.1. Depopulation optical pumping. The interaction between left-circularlypolarized (σ+) light and alkali-metal atoms causes the m = −1/2 sublevel to bedepleted into the m = +1/2 sublevel. The ∆m = +1 selection rule causes the spinsin the m = +1/2 state to be invisible to the laser light.
sublevel with the absorption of +h of angular momentum per atom. Collisional
mixing in the excited state causes relaxation from the 5P1/2 state to both m sublevels
of the 5S1/2 state to occur with equal probability; thus an average of two photons are
required to polarize an atom. The m = +1/2 sublevel, transparent to left-circularly
polarized light, will increase in population until global saturation is reached, which
occurs on a time scale of 10’s of microseconds. Various relaxation mechanisms,
such as Rb–3He spin-rotation interactions or dipolar Rb–Rb interactions, cause Rb
polarization loss on the time scale of milliseconds, so the laser must remain on
continuously to maintain saturation. This process is termed “depopulation optical
pumping.”
The second step, spin-exchange, is the process of spin angular momentum trans-
fer from the alkali-metal electron to the nucleus of the noble gas. The angular
momentum is collisionally transferred via a Fermi contact interaction, leaving the
now-unpolarized alkali metal free to scatter another photon or two and continue the
5
SEOP process. The binary collisions between the 3He and Rb last about 10−12 s
and the spin-exchange cross section is quite small, ≈ 1 barn; thus spin-exchange is
an inherently slow process; the characteristic spin-exchange time is typically 4–6 h.
Equation (1.1) describes the time dependence of the 3He polarization under SEOP
conditions:
PHe(t) = 〈PA〉 γse
γse + Γ
[1− e−(γse+Γ)t
], (1.1)
where 〈PA〉 is the time- and volume-averaged alkali-metal electron polarization,
γse is the spin-exchange rate, and Γ is the 3He relaxation rate. Based on direct
Rb polarization measurements by other researchers, we estimate that the 〈PA〉is maintained at ≈ 100% in our cells [14]; thus the long time limit (t → ∞) of
3He polarization depends on the fraction γse/(γse + Γ). Since binary collisions are
responsible for Rb–3He spin exchange, the spin-exchange rate may be written:
γse = [Rb] 〈σv〉 , (1.2)
where [Rb] is the Rb number density, which is strongly temperature dependent,
and 〈σv〉 is the velocity-averaged spin-exchange cross section, which is weakly tem-
perature dependent. Since a macroscopic amount of Rb is in our cells, we can
approximate [Rb] by using the saturated vapor-pressure curve [13]:
[Rb] =10(10.55−4132/T )
kBT, (1.3)
6
where T is the temperature and kB is Boltzman’s constant. By increasing the
temperature, [Rb] can be increased dramatically in our temperature regime; thus
PHe should be easily maximized. However, SEOP is a photon-limited process: if [Rb]
is increased beyond the capacity of the laser to maintain uniform Rb polarization
in a given volume, then 〈PA〉 may drop well below 100%. Thus, 〈PA〉 γse can
be optimized, but the optimal value is essentially fixed. Hence, the final 3He
polarization is largely determined by the 3He relaxation rate Γ.
1.2.4 3He Relaxation
The 3He polarization decays to thermal equilibrium with a characteristic time
constant T1. The longitudinal relaxation rate T−11 of 3He (Γ ≡ T−1
1 ) is characterized
by:
1
T1
=1
T1 dd
+1
T1 G
+1
T1 wall
. (1.4)
T1 dd is the dipole-dipole relaxation rate due to interactions between colliding 3He
atoms and is given by [15]:
1
T1 dd
=[3He]
744hours−1, (1.5)
where [3He] is the 3He density in amagats (an amagat is defined as the measured
density per density at 0C and 1 atm). For a given 3He density, this relaxation rate
is fixed. At 8 atm of 3He pressure, T1 dd = 100 hours.
T1 G is relaxation due to diffusion in external magnetic field gradients [16]:
7
1
T1 G
= D(∇B
B
)2
, (1.6)
where D is the 3He diffusion coefficient, B is the mean longitudinal external field,
and ∇B is the external field gradient transverse to B. Equation (1.6) is valid in
the limiting case when the time required for a spin to diffuse across the cell is much
longer than the Larmor period. This condition was easily met in all of our cells. In a
homogeneous magnetic field, such as one created by a carefully adjusted Helmholtz
pair, T1 G is negligible (often as long as several thousands of hours at high 3He
pressure).
T1 wall is relaxation due to interactions with the cell wall, and depends on several
factors, including surface-to-volume ratio and concentration of relaxation sites in the
glass. Wall relaxation varies widely from cell to cell and ranges from several minutes
to several hundreds of hours. Thus it alone often limits maximum polarization and
determines the overall T−11 . The most basic model of surface relaxation assumes
ballistic collisions of the 3He with the surface. This essentially means that the 3He
interacts with a relaxive surface site for a time much shorter than the relaxation
time at that site. A cell containing N total atoms should have a measured relaxation
time given by:
1
T1 wall
=n
N× 1
Ts
, (1.7)
where Ts is the relaxation time for atoms under the influence of relaxation sites and
n is the number of atoms interacting with relaxation sites. That is, n is the number
of atoms within a characteristic distance δ of the surface such that δ = vts, where
v is a mean thermal velocity and ts is the surface–atom interaction time (≈ 10−13 s
at room temperature [17]). Therefore,
8
n =A
VNδ, (1.8)
where A/V is the surface to volume ratio of the cell. By substituting Eq. (1.8) into
Eq. (1.7), the relaxation time becomes:
1
T1 wall
=A
Vvη, (1.9)
where η = ts/Ts is the relaxivity, which is defined as the probability to relax per
surface encounter. In the ballistic limit ts ¿ Ts, and η is typically on the order of
10−6 for glass (Ts was estimated to be ≈ 10−7 s in glass [18]). The wall relaxation
time given in Eq. (1.9) is independent of the 3He number density and external
magnetic field strength, and is weakly dependent on temperature since v ∝ √T . In
reality, however, wall relaxation is not so simple. The bulk of this thesis addresses
the complexities of wall relaxation, including the effects of external magnetic fields,
temperature dependence, the effects of the presence of Rb, and history of cell
exposure to magnetic fields. By understanding wall relaxation mechanisms and
learning to minimize them, we can achieve the goal of consistent production of
reliable, long-lifetime spin-exchange cells.
1.2.5 Spin-exchange Vessels
The special vessels, or cells, used to contain HP gas must meet the following crite-
ria: they must be alkali-metal resistant, heat resistant (up to ∼ 200C), transparent
to laser light, able to withstand high pressures (∼ 15 atm), able to hold a quantity
of gas comparable to an average adult’s tidal volume (≈ 0.5 atm·L), and refillable
9
without affecting the relaxation properties. All of these conditions are best met by
using glass. Pyrex (Corning glass number 7740) is our glass of choice because it is
robust, easily worked by any glass blower, inexpensive, and readily available. As
discussed in Sec. 1.2.4, the characteristics of the cell walls are critical in determining
the maximum level of polarization and the rate at which the gas will relax. Most
of the work presented in this thesis addresses understanding and minimizing 3He
relaxation mechanisms in Pyrex spin-exchange cells.
Much work, mostly trial-and-error, has been done to consistently fabricate cells
that have long lifetimes or to apply various nonrelaxive coatings to cells. Important
contributions were made by Fitzsimmons et al. [19] in their study of relaxation
mechanisms in bare cells of various glass types. They determined that adsorption
(sticking) and absorption (permeation) of 3He contributes significantly to relaxation,
and they proposed some phenomenological theories that supported their findings.
To date, it is considered by many to be the definitive work on 3He relaxation. Timisit
et al. [17] investigated relaxation in several types of glass vessels that contained only
3He, as well as vessels that had been treated by irradiation or that contained various
materials, such as pieces of brass or silicon. Many of the results were inconsistent
but demonstrated the unique sensitivity of 3He relaxation to different surfaces. Heil
et al. [20] showed that coating storage cells (cells used to hold HP gas that are not
necessarily used for spin exchange) with various metals, especially Cs, resulted in
very long relaxation times compared to those of bare glass. Hsu et al. [21] used a
sol-gel coating to produce SEOP cells with lifetimes approaching the bulk dipole-
dipole limit [see Eq. (1.5)]. The technique was very tedious and time consuming.
For the most part, production of long-lifetime cells has proven inconsistent, with
much lore and tradition dictating techniques used to fabricate and prepare cells.
10
1.3 Thesis Summary
Three chapters of this thesis have been either published as articles (Chapters 3
and 4) or have been submitted for publication (Chapter 6). The other chapters, in
the interest of uniformity, were written in the same format. Thus, each chapter
should read like a self-contained document. The advantage of this is that the
chapters need not be read in any particular order. The drawback is that there
is some repetition of background information, especially in the introduction of each
chapter, although the reader may find this periodic review of concepts helpful.
Chapter 2 is a brief overview of the equipment and methods we used to make
T1 measurements. The high, field-independent nuclear polarization and relaxation
times of 10’s of hours require nonconventional approaches to NMR detection and T1
measurements.
Chapter 3 is an article published in the 1 October 2001 issue of Physical Review
Letters as an introduction to “T1 hysteresis.” T1 hysteresis is an effect characterized
by the dependence of measured 3He relaxation rates on the history of a cell’s
exposure to large magnetic fields (of order several thousand Gauss). We found
that the T1 of a cell can decrease dramatically solely due to exposure to a magnetic
field, and that the original T1 can be restored by degaussing the cell, a process of
rotating the cell in a slowly decreasing magnetic field. We attribute the effect to
magnetic inclusions in the glass, and we present a model for 3He relaxation due to
interactions with such inclusions.
Chapter 4 is an article published in the 1 August 2002 issue of the Journal of
Applied Physics. There has always been a lack of definite, proven techniques for
the consistent and reliable production of long-lifetime (∼ 40 h) spin-exchange cells
that can be routinely used to produce 3He polarized to 40% or more. We have been
very successful in reaching this “40/40” benchmark, and this chapter outlines our
11
protocols with specifications of our apparatus and procedures. This was the first
paper in the literature to provide a detailed discussion of successful cell fabrication
techniques. The contribution to the measured relaxation time due to diffusion in
the cell capillary is also discussed.
Chapter 5 addresses external magnetic field dependence of 3He relaxation. The
model derived in Chapter 3 predicts that T−11 is proportional to the square of a
site’s magnetic moment. This dependence is qualitatively seen in an aluminosilicate
cell that contains Rb and in a bare Pyrex cell. But in Pyrex cells coated with
Rb, a different dependence altogether is observed: a strong field dependence that
is independent of the size of the moments. This chapter describes this unusual and
unexpected behavior.
Chapter 6 is a manuscript submitted for publication to Chemical Physics Letters.
In this chapter we continue to use 3He as a surface probe to determine relaxation
mechanisms in bare (containing no Rb) glass cells. For the first time, we develop a
theory which accurately predicts the surface relaxation rate of 3Hein glass. In bare
Pyrex, above about 200 K, 3He relaxes mainly due to interactions with Fe3+ ions
while dissolved in the glass. At lower temperatures, adsorption to the cell wall is
the major cause of relaxation.
Chapter 7, a follow up to Chapter 6, extends the investigation of relaxation on
bare Pyrex. We show that the theory outlined in Chapter 6 is applicable to bare
aluminosilicate and bare quartz, but not to Pyrex cells containing Rb for SEOP.
Theory dictates that we should be able to achieve at least 80% 3He polarization for
a cell with a 40 h T1, but 50% is as high as has been reported. We show that this
polarization deficit is probably not due to increases in the wall relaxation rate at
the high spin-exchange temperatures (≈ 180C), as has been hypothesized.
Chapter 8 discusses effects of rinsing cells with acids or alkali metals. In an
attempt to eliminate the magnetic inclusions, we rinsed the cells with various acids
12
to dissolve the sites. We found that cells rinsed with acid are typically not very good,
and they tend exhibit T1 hysteresis more strongly than other cells. Atomic force
microscopy images of acid-rinsed Pyrex samples reveal increases in surface-to-volume
ratio due to etching. We also rinsed the Rb out of a few cells to learn about surface
chemistry that takes place between the Rb and the glass. We found that these rinsed
cells still show T1 hysteresis, whereas cells never exposed to Rb do not. As in other
chapters, we are essentially using the polarized 3He as a surface probe to determine
cell relaxation characteristics.
Chapter 9 discusses preliminary results of novel 3He flow MRI experiments done
in conjunction with the Virtual Lung project at Pacific Northwest National Lab-
oratory. This work was possible largely because of the success we have realized
in making long-lifetime cells. The project uses a computational fluid dynamics
model to predict particulate deposition and long-term disease progression in the
human respiratory system. As part of model validation, measurements of gas flow in
physiologically relevant phantoms must be made. The preliminary results described
in this chapter demonstrate the feasibility of HP 3He flow measurements, but there
are some limitations due to the high diffusivity of the gas.
CHAPTER 2
NMR SPECTROMETER AND
TECHNIQUES
2.1 100 kHz Pulse NMR Spectrometer
2.1.1 The Applied Field
All of the 3He T1 relaxation data, except where noted in Chapter 5, were taken
using home-built 100 kHz pulse NMR spectrometers and a ≈ 30 G magnetic field
provided by a Helmholtz pair. We constructed multiple spectrometers, each using
a different Helmholtz pair. The Helmholtz pair used during spin-exchange optical
pumping (SEOP) is ≈ 44 cm in diameter and ≈ 22 cm separation, has 200 turns of
14 AWG wire, and consumes about 80 W, which is dissipated to air. A second set
is attached to a wheeled cart for portability. It is conveniently made from ≈ 42 cm
diameter bicycle rims with ≈ 21 cm separation. Its 110 turns of 14 AWG wire
consume about 140 W, which is dissipated to air. The third set, also made from
bicycle rims, is ≈ 56 cm diameter and ≈ 28 cm separation. Its 115 turns of 12 AWG
wire consume about 180 W, also dissipated to air. We note that the third pair
typically runs very warm, and if a higher field were desired from it, water cooling
would be necessary. We found that using bicycle rims for coil forms is very cost and
time effective, but the channel depth is insufficient to hold many more than about
100 turns of 14 AWG wire.
14
2.1.2 The Spectrometer
The 100 kHz spectrometer is described in detail with circuit diagrams in Ref. [22].
It consists of three sections: the pulse generator, the transmitter, and the receiver.
The receiver consists of a duplexer, several amplifier stages, and a phase-sensitive
detector. The receiver amplifiers and duplexer are contained within one chassis box
and the other components within another box. Both boxes are grounded to the line
ground.
Figure 2.1 shows a block diagram of the spectrometer. The pulse generator
provides a 100 kHz pulse that can be continuously varied from 10 µs to 10 ms.
A pushbutton switch initiates the pulse sequence by enabling a digital gate. The
transmitter uses a 1 MHz crystal oscillator and ÷10 circuitry to obtain the 100 kHz
NMR frequency. The gate, whose duration is determined by the pulse generator
circuitry, controls the transmission of the pulse by opening an analog IC switch.
A switch at the RF amplifier allows the pulse amplitude to be switched between
≈ 3.5 V and ≈ 15.0 V. A typical pulse is 10 µs and 3.5 V. We estimate such a pulse
to result in a < 5 flip angle. The pulse length or amplitude can be increased if
necessary to provide stronger signal as the polarization diminishes. This is never
done during a single T1 measurement, only between different measurements.
A single NMR coil is used to transmit the RF pulse and to receive the NMR
signal. The duplexer consists of a cross diode gate, which conducts during the RF
pulse, and a tunable parallel LC circuit. Here Q ≈ 70, so the impedance is about
25 kΩ at the NMR frequency. The large Q is a result of the large inductance of the
NMR coil. An additional diode gate to ground protects the receiver circuit during
the RF pulse. During the free induction decay (FID), the diode gates channel the
signal to the receiver amplifiers. Four switchable operational amplifiers in series
provide a minimum of 44 dB and a maximum of 104 dB of gain. Phase-sensitive
15
pulse generator
100 kHz frequency generator
analog switch
RF amplifier
diode gates
receiver amplifier stages
phase
detector
audio-frequency amplifier
signal out to scope
gate 100 kHz
L
C
tuning circuit
TRANSMITTER
RECEIVER100 kHz in
from frequency generator
NMR
probe
Figure 2.1. 100 kHz NMR spectrometer. See [22] for a detailed description andcircuit diagrams of the spectrometer.
16
detection takes place by switching an analog switch at the resonant frequency, which
selects between the signal and its inverse, resulting in an audio-frequency signal. One
additional gain stage that can provide 0 dB or 20 dB of gain precedes the output.
The resulting FID can be viewed on an oscilloscope; typical signal amplitudes with
a total of 44 dB of gain and a sample of ≈ 40% polarized 3He are ∼ 5 V. Typical
noise levels are ∼ 20 mV. The enormous signal-to-noise ratio allows us to omit some
commonly used filtering techniques, such as quarter-wave cables.
2.1.3 The NMR Coil
Our NMR coils were constructed such that they would fit easily around the cell
stems, which are typically 6 mm o.d. The coils were wound on a form made from
plastic that can withstand the ∼ 200C operating temperature of the polarizing
oven. About 200 turns of copper Litz wire (25 strands of individually insulated
44 AWG wire) over a length of about 5 mm were used for the coils. Typical coil
inductances are approximately 600 µH. It is important that the RF pulse not have
a measurable affect on the total polarization of the cell, in order to be sure that the
measured T1 is accurate. We estimate that the coil was sensitive to about 0.25 cm3
of the ≈ 50 cm3 total cell volume, or about 0.5% of the cell volume. Thus, even
very large flip angles, up to 90, had only a small effect on the total polarization of
the cell, although such flip angles were always avoided when possible.
2.2 T1 Measurement Techniques
All data were taken using a single transmit/receive NMR coil placed around a
cell stem in order to minimize the volume of gas excited, thereby minimizing the
polarization loss with each pulse. The coil forms also provided convenient holders
17
for the cells during measurements. Very small flip angles, typically < 5, were used,
resulting in negligible polarization loss. Cells were carefully positioned at the center
of the Helmholtz field to minimize relaxation due to diffusion through field gradients.
Because of the highly nonequilibrium state of the gas, relaxation rate measure-
ments were made by sampling the initial FID height at different times and fitting
the data to S(t) = S(0) exp(−t/T1) to extract T−11 . Several T1 measurements could
typically be made on a single polarization of gas.
CHAPTER 3
WALL RELAXATION OF 3He IN
SPIN-EXCHANGE CELLS
3.1 Preface
This chapter is an article that was published in the 1 October 2001 print edition
of Physical Review Letters, and it describes T1 hysteresis, the effect that launched
my thesis research. I first noticed the effect on 11 October 2000 when I was making
polarization measurements on cell 5B by placing it in a ≈ 1 T magnetic field (see Sec.
4.9.2). The 3He relaxation time in the cell had been measured to be about 10 h, so
the trip to and from the magnet should have resulted in a negligible polarization loss.
To my surprise, upon returning from the electromagnet I was unable to detect any
NMR signal. An innocent yet foretelling comment was recorded in the lab notebook
that night at 10:00 pm: “Has T1 changed?” Over the following week, three other
cells were affected in a similar way after high-field exposure: the 3He relaxation
times appeared to immediately and inexplicably decrease. Finally, I began careful,
systematic tests using cell 5A and was able to determine with little doubt that
exposure to a high magnetic field was solely responsible for the sudden decrease in
the measured relaxation times in the cells.
At this point we were concerned that the changes would be permanent and that
our cells were doomed to ruin. Further experiment proved, however, that we could
degauss the cells and restore the original relaxation times. After discussing the
19
results with collaborators, namely M. Conradi and W. Happer, we were convinced
that this discovery was very significant. I must admit that there was some luck
involved. Both cells 5A and 5B, the first cells whose polarizations I attempted
to measure, were rinsed with hydrofluoric acid (HF) prior to being attached to a
manifold for Rb distillation. As we later learned, cells rinsed with acid, especially
HF, tend to show T1 hysteresis more strongly than unrinsed cells (see Chapter 8).
This fortunate coincidence made it easy for me to see the factor of 20–100 changes
in T1 that were occurring in cells 5A and 5B after the polarization measurements.
There are some important points that are not brought forward in the paper. One
is the fact that 3He does not relax at the surface of glass in the simple way described
in Sec. 1.2.4, even though a short correlation time is assumed. This is most pointedly
demonstrated by the pressure dependence discussed in Sec. 3.5 where a magnetized
cell shows a linear dependence of T−11 on pressure (at a constant temperature)
while the same cell has no such dependence when degaussed; the simple model
predicts no pressure dependence whatsoever. Another point is that these results
may affect all SEOP researchers, not just the few who periodically expose their cells
to high magnetic fields. The exquisite sensitivity of the relaxation rate to the wall
characteristics and the dependence of T1 on the square of a magnetic site’s moment
[see Eq. (3.1)] imply that the effect may be present in cells exposed to low fields
(≈ 30 G), such as those used during polarization. In fact, at the time this paper was
published, we had seen differences in T1’s as large as a factor of 2 in unmagnetized
cells depending only on orientation in a 30 G field (see Sec. 5.5.2).
My coauthors on this paper were S. Morgan, an undergraduate who assisted
in some of the data acquisition, J. Leawoods, who, at our request, independently
confirmed T1 hysteresis in cells made by his group at Washington University, and
B. Saam, my advisor.
20
3.2 Abstract
The 3He longitudinal spin-relaxation rate T−11 is crucial for production of highly
polarized 3He by spin-exchange optical pumping. We show that T−11 is increased by
a factor of 2–20 solely by exposure of spin-exchange cells to a few-kG magnetic field.
The original T−11 can be restored by degaussing the cell. The effect is attributed
to magnetic surface sites and has been observed in both Pyrex and aluminosilicate-
glass cells. Our results both advance the understanding of wall relaxation and
demonstrate the use of 3He as an extremely sensitive probe of surface magnetism.
3.3 Introduction
Large nonequilibrium nuclear polarizations can be obtained in certain noble-gas
isotopes by spin exchange with an optically pumped and polarized Rb vapor [1].
Polarizations O(0.1) are routinely achieved for liter-quantities (STP) of 3He and
129Xe at 350–450 K in applied magnetic fields B0 = O(10) G. These hyperpolarized
(HP) gases have been studied and applied in diverse scientific realms [23, 24, 25],
perhaps most dramatically as the signal source in magnetic resonance imaging (MRI)
of the lung air space [9]. Indeed, we are concerned here with HP 3He as prepared
for most MRI experiments, where one requires large (≥ 40 cm3) valved glass vessels
(cells) which can be repeatedly polarized, emptied, and refilled with 3He to pressures
approaching 10 atm.
The production and subsequent storage of highly polarized gas depends crucially
on the nuclear spin-lattice relaxation rate T−11 , which shorts out the delivery of an-
gular momentum by Rb–3He spin exchange. Since the characteristic spin-exchange
time for Rb–3He is at least several hours [26], a stable T1 of many tens of hours
is required to generate and preserve substantial magnetization. T−11 is usually
dominated by interactions with the cell surface (wall relaxation). Bulk relaxation
21
from 3He–3He collisions [15] also contributes at sufficiently high pressure (greater
than several atm). Despite decades of research, relatively little is known about
the nature of 3He wall relaxation at most surfaces. This has generally led to
irreproducibility in cell fabrication. Several types of glass have been tried with
varying degrees of success [19, 27, 28], but documented fabrication protocols yielding
consistent results are generally lacking, especially for large-volume valved cells.
In this Letter we present evidence that magnetic sites, showing remanence and
hysteresis, significantly affect, if not dominate, wall relaxation in spin-exchange cells.
We demonstrate that large reversible changes in T−11 , and hence in the corresponding
surface relaxation sites, are induced in such cells solely by exposing them to a large
(∼ 10 kG) magnetic field, and that this effect (termed “T1 hysteresis”) is correlated
with the presence of Rb in these cells. The presence of Rb is also strongly correlated
with reduced wall relaxation rates (by as much as an order of magnitude) compared
to bare-wall glass cells. Our results represent the first explicit evidence of the nature
of a surface-relaxation mechanism for 3He in spin-exchange cells. Further study of
this mechanism will likely yield vital information for the efficient and reproducible
production of highly polarized 3He by spin exchange.
3.4 Experimental
Our valved Pyrex cells have 10 cm of 0.5–1.0 mm i.d. capillary separating the
valve (glass stem with o-rings) from the ≈ 50 cm3 main chamber. Each cell was
attached to a glass manifold and baked (except for the valve) under high vacuum
(base pressure 2 × 10−8 Torr) for 2–4 days at ∼ 400C. Rb metal (100–300 mg;
> 99.93% pure) was then distilled in prior to flame-sealing each cell under vacuum
from the manifold. A separate gas-handling system was used to fill and refill the cells
with 3He to 8 atm at room temperature [29]. A sidearm protruding from the valve
22
body, normally used for gas filling and dispensing, defines two physical orientations
of a cell with respect to an applied magnetic field; these are termed “north” and
“south” according to whether the sidearm points to the north or south pole of the
magnet.
All relaxation measurements were made at room temperature using 100 kHz
NMR detection at H0 ≈ 30 G (see Chapter 2) . Very low flip angles were used to
generate large-amplitude free induction decays (FIDs) with neglible loss of longitu-
dinal magnetization. The initial height of the FID was recorded as a function of
time and fit to an exponential decay to extract T−11 .
The basic experimental sequence consisted of three pairs of T−11 measurements
made with the cell oriented north and then south (or vice versa). Each measurement
pair was made with no intermediate removal of the cell from the 30 G field, no
heating, and no exposure to laser light; the cell was simply rotated 180 about
its capillary axis and a new T−11 measurement was initiated. The first pair was
performed after the cell was fabricated and filled for the first time (before any
exposure to high field); the second pair was done after the cell was magnetized north
or south, i.e., exposed for ≈ 30 s to the 10 kG field of an iron-core electromagnet
in the specified orientation (n.b., the word “magnetize” here refers to the cell walls
and not to the 3He spins); the third pair was made after the cell was degaussed. A
magnetized cell is degaussed by rotating it at ≈ 1 Hz about the capillary axis in
the field of the electromagnet as the field is gradually lowered from 10 kG to the
electromagnet’s remanent field (≈ 30 G). The rotation is maintained as the cell is
slowly withdrawn from the magnet. The second and third pairs of measurements
were repeated after magnetizing the cell in the opposite cell orientation.
23
3.5 Results and Discussion
We have performed this sequence of measurements on 20 cells (40 cells as of
October 2002). All cells we have examined show significant and consistent increases
(factors of 2 to 20) in wall relaxation rate due solely to exposure to the 10 kG field.
All cells previously exposed to the 10 kG field show a nearly complete restoration
of the original relaxation rate after being degaussed. In addition, all magnetized
cells show a consistent dependence of T−11 on physical orientation (north or south)
in the 30 G field; this change is typically ≈ 20%, but factors of 2–3 have been
observed. Cells that have been magnetized north (south) at 10 kG have a larger
T−11 oriented north (south) with respect to the 30 G measurement field. These
results are reproducible over several exposures to the 10 kG field, several degaussing
procedures, several refills with 3He, and several repolarizations. Figure 3.1 is a plot
of relaxation rate vs. chronological history of magnetic-field exposure for a single
representative cell demonstrating all of the described effects. The initial lifetimes
vary among the cells from 10s of minutes to 10s of hours, but the qualitative behavior
shown in Figure 3.1 is the same for all.
We performed a number of checks to confirm that high-field exposure is the sole
and direct cause of the change in T−11 observed before and after magnetizing or
degaussing a cell. For most cells, several measurements are possible without need of
repolarizing the gas. In many cases, all that transpires between radically different
T−11 measurements at 30 G is that a cell is transported in a portable solenoid back
and forth from the 30 G Helmholtz coils to the electromagnet in order to be exposed
to the 10 kG field. We have verified that a partial or sloppy degaussing procedure
(e.g., slowly removing the rotating cell from the magnet without turning down the
field) only partially restores the original T−11 . One of us (J.C.L.) has observed T1
hysteresis in two valved Pyrex cells fabricated and filled using a different glass blower,
24
0.0
0.2
0.4
0.6
0.8
1.0
1.2
un
mag
n.
deg
aussed
mag
n. n
orth
mag
n. so
uth
mag
n. n
orth
deg
aussed
mag
n. so
uth
UnmagnetizedDegaussedMeasured NorthMeasured South
T1-1
(h
ou
rs-1
)
chronological order
Figure 3.1. T1 hysteresis of cell 5A. Relaxation rates at 30 G are plotted vs. thechronological history of intervening exposure to a 10 kG field for a single cell. Thecell was both magnetized and measured in each of two physical orientations, labeled“north” and “south.” Mere exposure to the large field increased the rate by about20 times. Rates were slightly greater when the magnetizing and measuring fieldswere in the same direction with respect to the cell’s orientation.
vacuum system, and filling system. The effect has also been observed unambiguously
in two aluminosilicate-glass cells, one of GE-180 (General Electric) and one of 1720
(Corning). The 1720 cell is a sealed 8 cm3 spherical cell containing 3.5 atm 3He (at
295 K) and has no valves or capillaries; it was prepared by a third research group.
Our results point to the existence of magnetic sites at or near the glass surface
of our spin-exchange cells. These sites are a major source of wall relaxation for cells
exposed to fields greater than several hundred Gauss. This conclusion is supported
by the data in Fig. 3.1, which shows that wall-relaxation rates T−11 in our cells
have all of the basic characteristics of magnetic hysteresis, including remanence,
orientation dependence, and the ability to be degaussed.
25
Previously, wall relaxation has almost always been ascribed to isolated para-
magnetic impurities at or near the surface [17, 19], but such a mechanism has
never been explicitly experimentally demonstrated. Surface paramagnetism may
well dominate relaxation in bare-wall cells, but it would not show the hysteresis,
reversibility upon degaussing, and orientation dependence of T−11 that we observe
in our Rb-coated cells. The large fractional change in T−11 for cells with a broad
range of initial lifetimes (tens of minutes to tens of hours) suggests that the size
and/or concentration of magnetic sites may be responsible for the wide variation in
relaxation rates that is often observed with spin exchange cells. Indeed, the data
in Fig. 3.1 actually understate the effect of T1 hysteresis on many of the cells with
longer initial lifetimes, since these also have a significant bulk contribution to the
wall rate (about 0.01 h−1 at 8 atm [15]), regardless of whether the cell is magnetized.
When a cell is first fabricated and Rb distilled in, the domains in each magnetic
site are randomly oriented, or perhaps slightly aligned. Exposure to the 10 kG field
aligns the domains and produces a large enhancement of the magnetic moment of
each site. A remanent magnetization exists in the cell after it has been removed to
30 G, where an increased T−11 is then measured. When the domains are randomized
by degaussing, the magnetic moment of each site is reduced, and T−11 returns to its
original value. We propose that the 3He spins relax by interacting with these sites
while diffusing near the cell surface. We assume N sites having magnetic moment µ
and radius R. In the weak-collision limit [30], where the interaction time τ is much
shorter than the 3He Larmor period at 30 G, the longitudinal relaxation rate for one
site is M2τ , where the second moment M2 ≈ (γµ)2/R6. Using τ = R2/6D, where
D is the diffusion coefficient, we obtain for the whole cell:
1
T1
=Nπγ2µ2
9RDV, (3.1)
26
where γ is the 3He gyromagnetic ratio, V is the cell volume, and we have factored
in the fraction of spins interacting with sites (≈ 2πR3N/3V ). This analysis assumes
that the mean free path λ for 3He atoms is much smaller than R (λ ≈ 24 nm at 8
atm [31]).
Equation (3.1) suggests a linear pressure dependence of T−11 through 1/D. We
have investigated this dependence by measuring T1 after each of several releases of
a known quantity of polarized gas from the cell. Prior to each measurement, the
capillary entrance to the cell was blocked by maneuvering a small bead of Rb metal
over the opening. Our results from one cell supporting the weak-collision theory are
shown in Fig. 3.2. By contrast, the limit τ À (γB0)−1 would produce an inverse
0.000
0.005
0.010
0.015
0.020
0.025
0.030
3 4 5 6 7 8
T1 magnetized
T1 degaussed
Wal
l T1-1
(h
ou
rs-1
)
Pressure (atm)
Figure 3.2. T1 pressure dependence. The appropriate He–He relaxation rate hasbeen subtracted from all data shown to yield the wall relaxation rate as a functionof pressure. The wall rate increases linearly with pressure when the cell is magnetized(supporting the weak-collision theory), but there is no pressure dependence after thecell has been degaussed.
27
linear dependence on pressure [16]. An upper limit on R can thus be calculated
from R2 = 6D/γB0 and yields R = 10 µm for 3He at 8 atm, where we have used
D = 0.23 cm2/s [32]. Since R must be at least several times λ (or else there is no
pressure dependence whatsoever), we place a lower limit on R of ≈ 0.1 µm.
For example, if the sites were metallic iron (see below), and we use V = 50 cm3,
R = 0.25 µm, and a magnetized T1 of 5 h, we obtain N = 4×104 sites. Here, we have
used the density of iron to obtain an estimate of 5.6× 109 atoms per site and have
assumed that each atom contributes one Bohr magneton at full magnetization. This
number of atoms is reasonable for producing the multidomain structure necessary
to generate T1 hysteresis.
Our hypothesis for the cause of the orientation dependence is that the 30 G mea-
surement field causes a slight deviation from the zero-field remanent magnetization
of the cell, thus slightly increasing or decreasing the magnetic moments (and hence
relaxivity) of the sites. The orientation dependence of T−11 we observe at 30 G is
consistent with this picture in all cells we have tested.
We have also investigated the dependence of wall relaxation and T1 hysteresis on
the presence of Rb in the cell. Two additional cells, otherwise identical to the others,
were prepared using the same protocol except that Rb distillation was omitted.
HP 3He was transferred to these bare-wall cells from another room-temperature
spin-exchange cell, and the measurement sequence described above was perfomed.
The bare cells exhibited no T1 hysteresis. We then remounted the cells to the high
vacuum system and distilled in the usual amount of Rb so as to visibly coat most
of the cell surface. Again, HP 3He was transferred from another spin-exchange cell,
and the standard measurement sequence was performed. Not only did T−11 decrease
significantly after the introduction of Rb, but T1 hysteresis was also observed; see
Fig. 3.3.
28
0.01
0.1
1
un
mag
n.
mag
n.
deg
aussed
un
mag
n.
mag
n.
deg
aussed
T1-1
(h
ou
rs-1
)
chronological order
no Rb
Rb
Figure 3.3. Rb dependence. Relaxation rate is plotted vs. the chronological historyof preparation of a single cell. This cell was tested before and after introducing Rbmetal. For all measurements, hyperpolarized 3He was transferred in from anotherspin-exchange cell. Rb both greatly reduces the wall relaxation rate and gives riseto T1 hysteresis.
The data of Fig. 3.3 suggest that the presence of Rb both inhibits wall relaxation
and gives rise to T1 hysteresis. The former conclusion is in line with earlier work [19,
20], and we have confirmed the effect using the same cell, thus reducing uncertainties
associated with cell-to-cell variation. We can speculate at present only about how
the Rb (itself or in a compound) beneficially affects the cell walls: it may, for
example, chemically neutralize paramagnetic sites. It may also act as a physical
barrier to surface sites or to helium permeation of the glass. It is further apparent
that Rb plays a role in creating magnetic sites, perhaps by acting as a reducing agent
on ionic iron impurities in the glass, catalyzing the formation of ferromagnetic iron
oxides or metallic iron. Alternatively, the 1 g Rb ampules we use [33] have Fe, Ni,
29
and Co impurities at the ≈ 10 ppm level, although these levels may be reduced
by distillation. The characteristic applied field at which cells become magnetized is
about 500 G, with saturation occurring at 1–2 kG – reasonable numbers for iron or
iron oxide impurities. The bare-wall cells we measured had T1’s between 5 h and
12 h, comparable to or longer than T1’s measured for most of the Rb-coated cells
when magnetized. It is therefore not likely that the sites are resident initially in the
glass and that the Rb is simply removing a more dominant nonhysteretic mechanism.
We have initiated studies of Rb-coated Pyrex using ESR, SQUID, and the magneto-
optical Kerr effect [34], in order to look for an independent confirmation of magnetic
hysteresis as well as to better quantify the size, concentration, and chemical identity
of the sites. Results so far are negative. However, we note that ESR and SQUID
suffer from decreased filling factor compared with our measurements, which are
exquisitely sensitive to the surface alone.
Our understanding of both T1 hysteresis and the importance of the Rb coating has
allowed us to make substantial progress toward reproducible fabrication of Pyrex
spin-exchange vessels. Early research suggested that the helium permeability of
Pyrex glass leads to large wall relaxation rates [19]. More recently, Hsu, et al.
[21] showed that long T1’s were possible even for simple Rb-coated Pyrex. Pyrex
remains attractive for spin-exchange cells despite its difficulties because it is rugged,
inexpensive, ubiquitous, and easy to work compared with most other glasses. Most
of our cells have T1 > 30 h when degaussed. Several cells have T1 > 60 h, from
which one infers wall relaxation times > 150 h using the bulk relaxation rate at
8 atm [15]. Absent exposure to high field, we find these T1 values to change very
little as the cells are repeatedly heated to 160–180C, exposed to the 40 W laser,
and repeatedly refilled with gas. We routinely produce 3He polarizations > 40% in
these cells; they are robust and well suited to the MRI experiments for which they
30
were designed.
3.6 Conclusion
We conclude that 3He T1 hysteresis is a robust, reproducible, and consistent
effect which should be observable to some degree in almost all spin-exchange cells.
The effect is observed only in the presence of the Rb needed for optical pumping
and may be due to ferromagnetic impurities which are either in the Rb itself or
are catalyzed by Rb at the glass surface. Our results suggest an approach to
making reproducible spin-exchange cells that greatly narrows the search for effective
fabrication techniques to those that are likely to affect the size, concentration,
and magnetic moment of the sites responsible for this effect. Our results also
demonstrate the first use of hyperpolarized 3He as an extremely sensitive probe
of surface magnetism.
We acknowledge helpful discussions with M.S. Conradi, P.A. Fedders, R.V. Cham-
berlin, and W. Happer, and the glass-blowing of J. Kyle. This work was supported
by a grant from the Whitaker Foundation.
3.7 Addendum
Although, at the time this paper was submitted, we strongly felt that the mag-
netic sites originated in the glass, we had little evidence. Later experiments provided
strong circumstantial evidence, but nothing conclusive, in support of our hypothesis.
Two of these experiments are discussed in Sec. 8.5.1 and Sec. 8.5.2, in which cells
are rinsed with a chemical reducing agent and rinsed of their Rb, respectively. All
of these rinsed cells, which contained no Rb, showed T1 hysteresis.
Further evidence against the sites originating with the Rb was found in two
independent Rb distillation experiments. In one experiment, a manifold was pre-
31
pared with the section containing the Rb reservoirs and retort bent down from the
horizontal at about a 30 angle. This forced the first two distillation steps to be done
up-hill, which prevented globs of Rb from flowing up the tube, as is common during
distillation. The idea was to prevent any clusters of iron that might be present in the
Rb from riding such globs, entering the cells, and causing T1 hysteresis. However,
the cells still showed T1 hysteresis, providing evidence that the sites do not originate
in the Rb, and were of shorter than average lifetime. The distillation process in this
experiment required excessive heating of the manifold, which caused some visible
Rb-glass reactions (i.e., visible orange and black stains formed inside the glass) and
required much more time than usual. Because there were no apparent benefits of
this distillation method, it has not been repeated.
The second experiment used a locally strong magnetic field (≈ 4 kG over an area
of ≈ 1 cm2) placed around the cell manifold during Rb distillation. The field was
created by two permanent-magnet discs attached to a steel U channel facing each
other with a 1.5 cm separation. If iron clusters were present in the Rb, the magnetic
field could have two effects during distillation as the Rb passed through the field:
it could trap iron particles that are present in the Rb, or it could magnetize iron
particles as they pass through. If the former occurred, then the cell should not
exhibit T1 hysteresis. If the latter, then the cell would start out magnetized with an
initial relaxation time that could be improved with degaussing. The cells showed
neither behavior, suggesting again that the sites originate in the glass.
CHAPTER 4
3He SPIN-EXCHANGE CELLS
FOR MRI
4.1 Preface
This chapter is an article that was published in the 1 August 2002 print edition
of the Journal of Applied Physics. This paper was motivated by our unprecedented
success at making long-lifetime spin-exchange cells, and the fact that there were
no previous publications detailing cell-making procedures. This chapter contains
specific information about the equipment involved in producing and filling the cells.
Most of the equipment designs and procedural protocols were based on work done
by my advisor, B. Saam, while he was a postdoctoral researcher at Washington
University in St. Louis. A few of my most significant contributions include the
following: the transition to spherical cells from oblong cells, the introduction of
the oven for cell baking, and the refinement of cell preparation protocols. We have
found that our spherical cells tend to have longer lifetimes than our oblong cells.
This may be due to the higher surface-to-volume ratio of spherical cells, however
we have no direct proof. The oven has greatly reduced bake-out set up time and
potential damage to manifolds due to over handling. Cell preparation protocols have
always been based on some degree of lore or legend. Through trial and error and the
production of many quality cells, we have established a protocol that results in good
cells routinely and reliably. Unfortunately, we still have not been able to decisively
33
pinpoint exactly what step(s) determine the cells’ quality. However, through my
work in producing about three dozen cells, we have been able to gather evidence
that a cell’s relaxation properties are set during cell preparation or introduction of
Rb. My coauthors were S. Morgan, an undergraduate assistant who did much of
the equipment assembly, and B. Saam.
4.2 Abstract
We present a protocol for the consistent fabrication of glass cells to provide hyper-
polarized (HP) 3He for pulmonary magnetic resonance imaging (MRI). The method
for producing HP 3He is spin-exchange optical pumping (SEOP). The valved cells
must hold of order 1 atm·L of gas at up to 15 atm pressure. Because characteristic
spin-exchange times are several hours, the longitudinal nuclear relaxation time T1
for 3He must be several 10s of hours and robust with respect to repeated refilling
and repolarization. Collisions with the cell wall are a significant and often dominant
cause of relaxation. Consistent control of wall relaxation through cell fabrication
procedures has historically proven difficult. With the help of the discovery of an
important mechanism for wall relaxation that involves magnetic surface sites in the
glass, and with the further confirmation of the importance of Rb metal to long
wall-relaxation times, we have developed a successful protocol for fabrication of 3He
spin-exchange cells from inexpensive and easily worked borosilicate (Pyrex) glass.
The cells are prepared under vacuum using a high-vacuum oil-free turbomolecular
pumping station, and they are sealed off under vacuum after ≥ 100 mg of distilled
Rb metal is driven in. Filling of cells with the requisite 3He–N2 mixture is done on an
entirely separate gas-handling system. Our cells can be refilled and the gas repolar-
ized indefinitely with no significant change in their wall properties. Relaxation data
are presented for about 30 cells; the majority of these reach a “40/40” benchmark:
34
T1 > 40 h, and 3He polarizations reach or exceed 40%. Typical polarization times
range from 12–20 h; 20% polarization can be achieved in 3–5 h.
4.3 Introduction
The past decade has witnessed vigorous progress in the study of HP noble
gases and their application to a broad range of problems in physics, chemistry,
and biomedicine. Advances are coming in areas as varied as neutron polarizers
[28], measurements of fundamental symmetries [35], NMR at surfaces [36, 37], and
magnetic resonance imaging of the lung air space [9, 38]. In HP gases, enormous
nonequilibrium nuclear spin polarizations (of order 0.1) can be attained at room
temperature in ordinary magnetic fields via optical pumping techniques [1, 39],
greatly enhancing the NMR sensitivity of these nuclei. We are concerned here with
SEOP [1] of 3He gas for application to pulmonary MRI. The advent of relatively
inexpensive high-power diode-array lasers has paved the way in particular for MRI
and other applications requiring large quantities (of order 1 atm·L) of polarized gas,
since the quantity is essentially limited by the available laser power.
HP 3He is produced (and often stored) inside a glass spin-exchange cell containing
3He at several or more atmospheres, 50–100 mbar N2 (a fluorescence-quenching gas
necessary for efficient optical pumping [12]), and a macroscopic amount of alkali
metal (typically Rb). The cell is heated to 160–200C to obtain the optimal Rb
vapor density. The laser light, circularly polarized at a frequency corresponding to
the D1 atomic transition in Rb (795 nm) and colinear with a small magnetic field
(of order 10 G) is trained on the cell, thus polarizing the valence electron of the Rb
atoms. The polarization is thence collisionally transferred to the 3He nuclei.
In this paper we present a protocol for the consistent fabrication of spin-exchange
cells which will provide liter quantities of highly polarized 3He for pulmonary MRI.
35
These cells must (1) hold a quantity of gas comparable to an average adult’s tidal
volume (≈ 0.5 atm·L), (2) be transparent to 795 nm laser light, (3) withstand
pressures of up to 15 atm at 200C (making efficient use of the spectrally broad
diode-laser array by suitably broadening the Rb absorption line [40]), and (4) be
valved and refillable for repeated use without altering important cell characteristics
(mainly the longitudinal nuclear relaxation rate at the cell surface).
4.4 Wall Relaxation
Controlling longitudinal nuclear spin relaxation is critical to optimizing both the
polarization and the useful storage time of the gas for applications. In MRI, for
example, polarization is directly related to image quality for a given amount of 3He,
and the gas often needs to be transported some distance to the MRI scanner without
significant polarization loss.
The noble-gas polarization transient PN(t) during optical pumping is given by:
PN(t) = 〈PA〉 γse
γse + Γ[1− e−(γse+Γ)t], (4.1)
where 〈PA〉 is the time- and volume-averaged alkali-metal electron polarization, γse
is the spin-exchange rate, and Γ is the 3He longitudinal relaxation rate, with the
corresponding relaxation time T1 ≡ 1/Γ. Since typical spin-exchange times are 5–
10 h, T1 must be several tens of hours to obtain noble-gas polarizations approaching
〈PA〉, which can normally be kept close to unity [14].
Contributions to Γ come from bulk He-He binary collisions, gas diffusion through
ambient gradients, and from wall collisions. The bulk rate is linear with the 3He
density and is usually only significant for cells above several atm; for our room-
temperature 8 atm cells it is 0.010 h−1 [15]. The Helmholtz coils we use for
36
SEOP (see Sec. 4.8) provide adequate field homogeneity so that the rate due to
diffusion [16, 41] for cells of the size and pressure discussed here is negligible. The
wall relaxation rate thus practically dictates the quality of a 3He spin-exchange
cell, and efforts have been made for more than thirty years to understand and
control it. Various glass types, surface treatments, surface coatings, and bakeout
procedures have been tried. The results vary widely among research groups and are
usually inconsistent and irreproducible. Paradoxically, consistently long polarization
lifetimes seem especially difficult to achieve for larger-volume cells, where one would
expect a lower surface-to-volume ratio to yield generally slower rates.
Work to understand and control 3He wall relaxation has generally proceeded
from the assumption that the major source of such relaxation is paramagnetic
impurities on the glass surface. In early work [17, 19], bare borosilicate (Pyrex)
and aluminosilicate glass surfaces (such as Corning 1720) were studied. These
workers used metastability exchange optical pumping [39], which does not require
an alkali-metal intermediary to produce HP 3He. A local maximum in T1 (at about
130 K) as a function of temperature in Pyrex [19] suggested the importance of
helium permeability, which brings the 3He into close and prolonged contact with
the surface. (Quartz is even more permeable than Pyrex [42], so much so that most
quartz cells would leak substantial fractions of their helium to the atmosphere in
days or weeks.) Lower permeabilities and overall better results generally led the
community toward the use of aluminosilicates [15, 28, 43], although these glasses
are generally more difficult and expensive to procure and are more difficult for a
glass blower to work than borosilicates. Good results were, however, reported for
sealed cells using Corning 7056, a high-alkali borosilicate glass with much lower
helium permeability than Pyrex [27]. An excellent review of the results of many
groups using various glasses and coatings for pumping and for storage cells is given
37
in Ref. [44].
We have chosen to continue working with Pyrex, due to its robustness, worka-
bility, and easy availability. Moreover, the presence of Rb (which surely coats the
cell walls to some degree) chemically alters the surface and inhibits wall relaxation
relative to bare Pyrex [19, 21, 44]; see Sec. 4.9.1. Indeed, in Ref. [19] there was
only one cell tested which contained Rb, and that cell had the longest T1 of all in
that work by a large margin. T1’s in the hundreds of hours have been observed in
HP 3He storage cells with macroscopic coatings of Rb and Cs metal [20]. These
developments, coupled with the discovery of a previously unknown relaxation mech-
anism involving magnetic surface sites [45] and some trial-and-error testing, have
led to our consistent achievement of two benchmarks, T1 = 40 h and PN = 40%, for
large-volume Pyrex 3He spin-exchange cells.
4.5 Cell Fabrication
Our cells are made of standard borosilicate glass (Pyrex), but we have also
experimented with quartz and aluminosilicate glasses. The cell body is either
spherical (≈ 4.5 cm i.d.) or cylindrical with rounded ends (≈ 3 cm i.d. × 5.5 cm
long). The typical total volumes are 50 cm3 and 35 cm3, respectively; see Fig. 4.1.
Recently, we have gone exclusively to spherical cells, as it is easier to produce a
surface of uniform thickness, thus minimizing lensing of the incident laser light.
The spherical cells generally yield longer T1’s and higher polarizations, although the
reasons for this are not clear. We use 32 mm heavy-wall tubing which is “reblown”
to the specified inner diameter, creating a freshly exposed inner surface. The cells
are shaped by blowing the glass on a lathe; cylindrical cells require the additional
use of a graphite shaping paddle on the outer surface. A capillary tube, valve, and
stem are then attached.
38
Figure 4.1. A Pyrex valved spin-exchange cell for generating hyperpolarized 3He.The spherical cell body shown here has a volume of ≈ 50 cm3. The capillary allowsthe o-rings in the valve to sit outside the ovens involved both with the initial bakeout(see Sec. 4.6) and with optical pumping (see Sec. 4.8). The penny is shown for scale.
The valve is a right-angle, high-vacuum, all-glass valve [46]. Perpendicular to
the valve is attached a threaded glass side arm [47], through which polarized gas is
dispensed and by which the cell is attached to a separate gas-handling system (see
Sec. 4.7) for filling with 3He. The valve is attached to the cell via a 10 cm length
of glass capillary, which consists of a 6 cm length of 0.5 mm i.d. tubing in series
with a 4 cm length of 1 mm i.d. tubing. The wider end is attached to the cell body
and helps to prevent the Rb metal from clogging the capillary; the narrow portion
is attached to the valve. The gas must pass through the capillary during cell filling
and dispensing, so it cannot be impractically narrow. The capillary allows the valve
to be kept outside of the oven during optical pumping and suitably lengthens the
transit time of a 3He atom from the cell body to the ≈ 1 cm3 volume near the valve.
Because of the unknown relaxation characteristics of the valve materials and the fact
that the valve cannot be baked out well, it is assumed that all 3He atoms that enter
39
the valve volume relax completely. The capillary plays a measureable role in wall
relaxation of our long-lifetime cells. By measuring T1 before and after maneuvering
a bead of Rb in the cell to block the capillary, we have estimated its contribution
to be Γcap = 0.002–0.004 h−1 at 8 atm pressure; see Sec. 4.10.
A 4 cm length of 6 mm standard-wall tubing (the “stem”) is attached opposite
to the capillary and connects the cell to a glass manifold for initial evacuation and
baking; see Sec. 4.6. After the cell is flame-sealed away from the manifold, the stem
accommodates an NMR coil for monitoring the production and decay of HP 3He;
see Sec. 4.8.
The manifold is basically a long tube (primarily 12 mm o.d. Pyrex) connecting
the high vacuum system on one end to an open vertical retort on the other end. The
retort, which is 15 mm o.d., accommodates a prescored 1 g ampule of 99.93% pure
Rb metal [33]. The cells (usually two at a time) are attached orthogonally to the
manifold by their stems; see Fig. 4.2. The manifold includes two small reservoirs
used in the Rb distillation process between the retort and the cells. A u-tube liquid
nitrogen (LN2) trap is located between the high-vacuum port and the cells. The
LN2 trap provides additional cryopumping of the manifold, limits backstreaming
contamination, and prevents Rb from migrating to the high-vacuum system.
The cells are fabricated and attached to the manifold by our chemistry depart-
ment’s glass blower. The completed manifold is annealed at 560C with a soaking
time (time for which the glass is held at the maximum temperature) of ≈ 10 min.
The manifold is then allowed to cool slowly for about 45 min. Upon removal from
the annealing oven, the open ends are covered with a self-sealing wax film to help
prevent ambient moisture or other contaminants from entering and adsorbing to the
inner surfaces of the manifold.
40
retort
reservoirscells
capillary
valveside arm
section bakedin oven
B
LN2trap
A
to high-vacsystem
stem
Figure 4.2. Diagram of a cell manifold. The glass manifold with two cells attached,as it appears just before being connected to the high-vacuum system (Fig. 4.3).The top of the retort is flame-sealed after a Rb ampule is dropped in. The cellsare attached to the manifold at a 55 angle out of the page. Constrictions in themanifold and stems allow for easy pull-off. Manifolds are labeled by numbers andcells by letters, starting with the furthest upstream.
4.6 Cell Preparation
The purpose of careful cell preparation is to remove impurities adsorbed to the
surface of the glass and to prevent contaminants from entering. To accomplish this,
the cells are baked under vacuum using an oil-free high-vacuum system; see Fig. 4.3.
The construction is stainless steel with copper-gasketed or swaged connecting seals
and packless, bellows-sealed valves [48]. The vacuum pump is a turbomolecular
drag pump backed by a diaphragm pump [49]. With the cell manifold attached,
the system reaches a base pressure of ≤ 4× 10−8 mbar, monitored at the inlet
by a combination cold-cathode/Pirani full-range gauge [50]. Connected opposite
the gauge is a residual gas analyzer (RGA) [51], which also functions as a helium
leak detector. The gauge and RGA are downstream from the 38 mm stainless
steel right-angle main valve. Upstream of this valve are large- and small-bottle
41
compressionseal
to large-bottlemanifold
RGAfull-range
gauge
pressuresensor
to dryroughing
pumpto small-bottlemanifold
to turbopump
mainvalve
to glassmanifold
Figure 4.3. The oil-free high-vacuum system used for cell fabrication. The glassmanifold (Fig. 4.2) is attached via the compression-seal fitting at right. Theconstruction is stainless steel with packless bellows-sealed valves. Nitrogen purgegas is provided as needed through the connection to the large-bottle manifold.
gas-handling manifolds, an additional diaphragm roughing pump [52], and a port for
connecting the system to the glass manifold via a 12.7 mm o-ring compression-seal
fitting. A 0–1.3 bar capacitance manometer [53] and a solid-state pressure sensor
[54] are used for fine and coarse monitoring of upstream pressures. High-purity
nitrogen, used as a purge gas, is available through the large-bottle manifold; the
attached gas-handling manifolds are generally used for making permanently sealed
spin-exchange cells and will not otherwise be described here.
The completed manifold with cells is attached to the vacuum system at the
manifold port. This is done while purging the system with research-grade nitrogen
gas to help prevent water vapor and oxygen from entering the manifold and vacuum
system. The valve stems, with lightly greased ethylene-propylene (alkali-metal
resistant) o-rings [55], are then seated, and the cell valves are closed. An ampule
42
of Rb is opened in the flow of N2 from the retort and is dropped, open end down,
into the retort. The purge gas is turned off, and the retort is flame-sealed shut.
With the manifold now sealed from the external environment, it is evacuated with
the roughing pump, opened to the turbo pump, and tested for leaks with the RGA.
Minor leaks can often be repaired on the spot, while more serious problems may
have to be sent back to the glass blower. Finally, with the manifold sealed and
leak-tight, LN2 is added to the dewar surrounding the trap.
The manifold is then baked continuously at about 400C for 2–4 days. We now
use a home-built, insulated, steel-walled oven designed especially for these manifolds.
We previously wrapped the manifold in heating tape and aluminum foil. The oven
heats stably and uniformly (within a few degrees), avoiding hot spots that can
develop from the use of heating tape; it also greatly reduces set-up time and the
risk of damaging the delicate manifold due to overhandling. The cells are attached
to the manifold at a 55 angle from vertical (see Fig. 4.2) to allow the valves to
protrude laterally through a cut-out in the oven (to avoid damaging the o-rings).
The oven is blanketed by 25 mm thick ceramic fiber insulation [56], which is covered
with high-temperature silica cloth [57]. This blanket keeps the valves near room
temperature, even though they are only a few centimeters from the oven. Heat is
provided by a 1.8 kW, 120 VAC ceramic strip heater [58] located on the oven floor,
which is controlled by a 2 kW, 120 VAC solid-state dimmer switch. A 50 VAC
input is sufficient to maintain the baking temperature. The retort and distillation
reservoirs also protrude out of the oven; these are wrapped in heating tape and
aluminum foil, which can be removed as necessary as Rb distillation progresses.
Temperatures are monitored with type-E thermocouples placed both in the oven
and on the manifold under the heater tape and foil.
After about 24 h of baking, the Rb metal is liquified for the first time by brief
43
exposure to a flame, which allows any trapped gases to escape and be pumped
away. After allowing the retort to cool, Rb is distilled from the retort to the first
reservoir. First, the foil and heat tape are unwrapped from the retort to 3 cm
beyond the first distillation reservoir, and this section is allowed to cool. The Rb
is then “chased,” i.e., heated and evaporated with a cool methane-oxygen flame
(not so cool that carbon deposits, which inhibit visibility, are left on the glass),
driving it into but not beyond the first reservoir. The idea here is to volatilize all
of the Rb that is eventually to be chased into the reservoir, leaving less volatile
contaminants in the retort. The flame is not held in one spot on the glass long
enough to produce any orange sodium glare; this avoids softening of the glass or
its reaction with Rb. Effective chasing requires 30–45 min and benefits from some
practice. When completed, contaminants (e.g., Rb oxides and RbOH) and about
10–20% of the Rb metal are left behind in the retort, which is then flame-sealed
away from the manifold.
After 12–24 h of further baking, Rb is chased to the second reservoir by a similar
procedure. The cells are allowed to bake for yet another 12–24 h before the oven is
turned off and allowed to cool completely. Rb is then chased into the cells, starting
with the one closest to the retort (cell “A”). The capillary is kept hot during this step
so that it will not become clogged with Rb. After 100–300 mg of Rb is distilled in,
the cell is flame-sealed from the manifold. The process is repeated for the remaining
cell(s), working downstream.
We have found a difference in convenience only, and not in cell quality, with
the introduction of the baking oven. We also find no difference in the case where
the Rb is distilled into all of the cells in one step before they are each sealed
from the manifold. We note that the amount of Rb distilled in does matter;
amounts significantly less than about 100 mg generally result in cells with poor
44
wall characteristics. The relationship between Rb and wall relaxation is discussed
further in Sec. 4.9.1. The baking time and temperature have not been optimized
experimentally, but those we use seem reasonable based on the ideas that (1) we
wish to bake as hot as possible without approaching the annealing point of the glass
and (2) the base vacuum pressure and RGA spectrum change very little after a
day or so of baking. Our ability to consistently produce quality cells has compelled
us not to experiment much with our bakeout parameters or other aspects of the
fabrication protocol.
4.7 Cell Filling System
A separate, home-built vacuum and gas-handling system is used to fill and refill
cells; see Fig. 4.4. This system is similar to one built previously by Saam and
Conradi [9]. It is constructed of 6.4 mm o.d., 4.8 mm i.d. stainless steel tubing with
weld and swage fittings. The packed, nonrotating-stem valves [59] are labeled by
letters, as shown in Fig. 4.4. The system, built vertically on two large aluminum
plates affixed to a relay rack, is divided into an upper gas-handling and purification
manifold and a lower vacuum manifold; these are connected at two points by valves
(I) and (G). The vacuum manifold has a dial gauge and a thermocouple gauge to
monitor pressure. Below valve (M) is a u-tube LN2 trap followed by a 150 L/min
rotating-vane mechanical pump. The pump has a Micromaze [60] trap at the inlet
to further inhibit oil backstreaming.
The upper manifold is essentially a fill path from the gas bottle to the cell. When
new, the lecture bottle contains 25 atm·L of research-grade 3He (99.99% pure) mixed
with 2% nitrogen, at a total pressure of 55.4 bar. The ≈ 3 cm3 volume bounded
by the bottle valve and valve (J) is the charging volume used for a new bottle. As
the gas is used up and the bottle pressure decreases, the ≈ 12 cm3 charging volume
45
A B C D
EF G H I
J
K L M
to cell
N2 line
purifiers
N2 line
tocollectionbottle
to LN2 trap andmechanicalvacuum pump
high-pressuregauge
vacuumgauge
t.c.gauge
3Hebottle
upperpanel
lowerpanel
Figure 4.4. Gas-handling system used to fill cells with 3He. This system iscompletely separate from the high-vacuum system (Fig. 4.3) used for bakeout andRb distillation. Cells can be refilled indefinitely with no change in the 3He wallrelaxation time. The valves and bottle are all mounted to two vertical plates ona relay rack. The dashed line marks the boundary between the upper and lowerplates. Open squares represent auxiliary ports. The collection bottle is used to save3He that would otherwise be discarded after cell filling.
up to valve (H) is employed. The gas is conducted through a purifier [61] bounded
by valves (B) and (C), and then to the cell through a 1 m length of 1.6 mm i.d.
stainless steel (ss) capillary tubing. The flexible ss capillary provides stress relief for
the cell and a low dead volume for filling. The cell is placed in a secure wooden box
(mounted to the side of the relay rack) with its glass capillary and valve protruding.
It is attached, using the compression-seal fitting on the side arm, to the ss capillary
tube via a custom-built tee connector. The other outlet of the tee is exhausted to
46
room air through a flow meter and one-way pressure-relief valve. Because of the low
conductance of the ss capillary, a N2 purge line with purifier is provided and used
in addition to evacuation to keep the system clean. The two identical gas purifiers
discussed here are designed for use with nitrogen but are also adequate for use with
noble gases.
Initially, the cell (with its valve closed) is attached to the tee connector with the
compression seal loose. A N2 purge is passed through the capillary at ≈ 0.2 L/min
for ≈ 20 min. After the purge, the compression seal is tightened, valve (A) is closed,
and the fill line is evacuated through valve (G). The system remains under vacuum
for tens of minutes to hours. A series of at least three backfill/evacuate sequences
(closing valve (G), filling the ss capillary and cell side arm with purge gas, then
re-evacuating) is completed to help remove room air that may have entered when
the cell was attached.
When the evacuation procedure is complete, valve (G) is closed, and the cell
valve is opened in preparation for filling. The cells are filled in a series of charges.
At the start of each charge, all valves except the cell valve are closed. The bottle is
opened to the charging volume and closed again immediately. The valves (H), (C),
and (B) are successively opened until the pressure measured by the 0–200 psig dial
gauge equilibrates. Valves are opened gradually, so that the gas can be metered;
this is particularly important in opening valves (C) and (B), since the purifier is
effective only at flow rates below 0.2 L/min. In our system, staying below this rate
is assured by watching the pressure gauge and keeping the rate of change in pressure
below about 2 psi/s. At equilibrium, all valves except the cell valve are closed again.
This procedure is repeated until the desired cell pressure is reached; we typically
fill cells to 8 atm (absolute pressure). When the desired final pressure is reached,
the cell valve is closed, and all other valves in the filling path are closed to preserve
47
the gas contained therein for future use. The filling path from the bottle to valve
(B) is evacuated and pumped on only occasionally, such as when the 3He bottle is
replaced. The remaining 3He is collected into a large ballast volume (an otherwise
empty gas cylinder) for recycling.
4.8 The Polarizer
The polarizer consists mostly of an aluminum-frame cart (≈ 2 m long, 0.6 m deep,
and 1 m high) with a top surface for mounting optical components and shelving
below. The cart has a built-in 45 cm dia. Helmholtz pair (200 turns of 14 AWG
wire per coil), which produces a 30 G field when driven in parallel with 12 V at 8 A.
A welded aluminum box covered with fiberboard insulation serves as an oven. It
is located at the center of the Helmholtz pair and is heated by air forced through a
filament-heater pipe [62] attached to the cart. The temperature is maintained to a
few tenths of a degree with a resistive temperature detector (RTD) and controller
[63]. A cradle at the center of the oven holds the cell body; the capillary protrudes
out one side of the oven to avoid heating the valve. The top plate and the top half
of the side plate above the capillary are welded together and can be removed as a
unit for internal access. Round windows (5 cm dia.) are located on four sides–for
laser entry, laser exit, on top, and laterally opposite the capillary. The latter two
are for monitoring fluorescence from the cell during SEOP. Window glass (6.4 mm
thick) is used throughout, double-paned for extra insulation except at the laser-
entrance window. (Laser transmittance through this window could be improved by
a few percent by using an optical flat, anti-reflection coated for 795 nm.) The oven
temperature is typically set for 160C, although based on the characteristic time we
observe to polarize cells (Fig. 4.5), the actual cell temperature is 170–180C, where
the saturated vapor density of Rb is about 2.5–4.5×1014 cm−3 [13]; see Sec. 4.9.2.
48
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
0 500 1000 1500 2000 2500 3000
TIME (min)
T1 = 60 ± 2 h
Ch 1: 200 mVolt 2.5 ms
(b)
0
1
2
3
4
5
6
0 200 400 600 800 1000 1200 1400 1600
SIG
NA
L (
Vo
lts)
TIME (min)
(γse
+ Γ)-1= 10.0 ± 0.2 h
(a)
Figure 4.5. Polarization and decay transients. (a) Typical 3He polarization transientfor cell 8A at 8 atm in a 30 G magnetic field. The curve is a best fit to Eq. (4.1),yielding the characteristic “spin-up” time of 10 h. Although the oven temperaturewas set to 160C, the spin-up time corresponds to 170–180C. The temperatureincrease is due to the laser heating of the cell. (b) Subsequent room-temperaturedecay transient at 30 G for the same cell, measuring the combined wall and bulkrelaxation rates. The line is a best fit to a single exponential decay. One deduces awall-relaxation time for this cell of ≈ 150 h, since the bulk time is ≈ 100 h. Inset:A typical 3He FID acquired at 30 G (100 kHz); the inital FID amplitude providesthe data for spin-up and spin-down measurements.
49
The temperature difference is caused by the large laser power: the N2 gas in the cell
heats up due to increased collisional de-excitation of Rb atoms [64]. The laser and
optics train are mounted on optical rail to one side of the coils and oven. The laser
is a 795 nm, 40 W diode array [65] with a fwhm linewidth of about 1.7 nm. The
laser is resonant with the 795 nm D1 transition in Rb (see Sec. 1.2.3). It is mounted
to an aluminum block which is water-cooled by a closed-loop refrigerator [66] with
built-in temperature control to a few tenths of a degree. Cylindrical optics are used
to collimate the fast and slow axes separately. A 76 mm dia. mica quarter-wave plate
[67] circularly polarizes the light just before it enters the oven. Rubidium-vapor
absorption is monitored by a PC plug-in miniature spectrometer [68] with 0.3 nm
resolution coupled by a fiber optic to the light emerging from the laser exit window.
When the laser is at the proper frequency, the computer displays the laser line
with a central dip corresponding to absorption by the vapor. Laser fluorescence is
visually monitored with surveillance-system cameras and a small tv monitor. The
cameras are sensitive in the near-infrared and are equipped with interference filters
[69] for the Rb D2 resonance (780 nm). The D1 and D2 states are mixed after a Rb
atom absorbs a photon [12]; monitoring D2 fluorescence thus effectively separates
fluorescence from laser scatter. The beam profile can then be matched to the cell
dimensions by adjusting lens positions.
The 3He polarization is monitored by a home-built 100 kHz pulse NMR spectro-
meter [22]; the multiturn coil (inductance L ≈ 800 µH, quality factor Q ≈ 50) is
placed around the stem of the cell inside the oven. The aluminum walls of the oven
are grounded and provide adequate rf shielding. Figure 4.5 shows samples of a free
induction decay (FID), polarization transient (“spin-up”), and room-temperature
decay transient (“spin-down”) for 3He in a typical 8 atm cell.
50
4.9 Experimental Results
4.9.1 T1 Measurements
All measurements of the longitudinal relaxation time T1 for our cells were made
at room temperature and at 30 G, unless otherwise indicated. These are relevant
conditions for HP-gas production, since high fields are not necessary to generate
the polarization, and a 30 G Helmholtz pair is inexpensive and portable. Very low
flip angles (< 5) were used to generate a FID at appropriate time intervals with
negligible loss of polarization. The initial height S of the FID was recorded as a
function of time and fit to S(t) = S(0) exp(−t/T1) to extract T1. (The thermal
equilibrium signal is negligible for our conditions.)
We have recently discovered that T1 at 30 G is dramatically reduced (factors of
2–20) solely by intervening exposure of a cell to a large magnetic field (of order
0.1 T or greater). The original T1 can be restored by demagnetizing or degaussing
the cell, i.e., rotating it at about 1 Hz in a field which is gradually reduced to
zero from about 1 T. (Magnetizing and degaussing were conveniently done in a 1 T
iron-core electromagnet.) The effect, termed “T1 hysteresis,” is due to multidomain
magnetic sites at or near the glass surface. These sites become magnetized in a
large field and have a significant remanent magnetization when the cell is returned
to 30 G, leading to a stronger interaction with colliding 3He spins and a shorter
T1. The effect has been observed in borosilicate, aluminosilicate, and quartz glasses
and is correlated with the presence of the Rb necessary for SEOP. Indeed, the effect
should be observable to some degree in almost all spin-exchange cells. The details
of T1 hysteresis are discussed in Chapter 3.
We have consistently produced cells with T1’s in excess of 40 h. The measured
T1’s are generally robust and reproducible (to 10% or so), although the cell is refilled
several times and/or repeatedly exposed to the 40 W laser at temperatures of 160–
51
200C. The results of T1 measurements on many of our cells are shown in Fig. 4.6.
The wall relaxation rate Γw is shown for each cell before exposure to a high field
(unmagnetized), magnetized, and degaussed. The bulk contribution (0.010 h−1 at
8 atm [15]) has been subtracted from the data. T1 hysteresis occurs to some degree
for all cells over a broad range of initial unmagnetized lifetimes (a few hundred
minutes to tens of hours), indicating that the variation in rates from cell to cell may
be due to differences in the size and/or concentration of magnetic sites. In any case,
10-3
10-2
10-1
100
101
CELL DESIGNATION
UnmagnetizedMagnetizedDegaussed
WA
LL
RE
LA
XA
TIO
N R
AT
E
Γ w (
h-1
)
5A 6A 7B 10B8B 9B 15B14B12B11B5B 7A 8A 11A9A 10A 15A14A12A
Figure 4.6. Relaxation rates for several cells. The wall relaxation rate Γw at30 G plotted vs. cell designation for 19 of approximately 30 3He spin-exchangecells fabricated in our laboratory. These cells all contain Rb, except for 12A and12B, which contain potassium. The manifolds are numbered chronologically; “A”and “B” refer to a pair of cells made on the same manifold (Fig. 2). The bulk3He–3He relaxation rate of 0.010 h−1 for 8 atm has been subtracted for each cell.Prior to being magnetized at 1 T or after degaussing, most cells have Γw ≈ 0.01 h−1
or smaller, meaning a measured T1 ≥ 50 h.
52
it is necessary to avoid exposure of most cells to large magnetic fields (the onset of
T1 hysteresis occurs at a few hundred gauss [45]) or to degauss them before they are
used for SEOP.
In addition to its crucial role in optical pumping, the presence of alkali metal in
SEOP cells inhibits wall relaxation while simultaneously giving rise to T1 hysteresis
[45]. Almost all of the cells represented in Fig. 4.6 contain Rb (cells 12A and
12B contain potassium). We also made several otherwise identical cells containing
no alkali metal. Polarized 3He was then introduced in order to measure T1 on
bare Pyrex. For these cells T1 was typically less than 10 h, and no hysteresis was
observed. The Rb may be chemically neutralizing paramagnetic sites or inhibiting
permeation of 3He into the glass; see Sec. 4.4 and Refs. [17, 19]. At the same time,
the Rb introduces T1 hysteresis, presumably by creating magnetic sites. Our current
working hypothesis is that the Rb acts as a reducing agent, converting iron ions and
oxides to multidomain metallic iron. Section 8.5.1 explores this possibility further.
4.9.2 Polarimetry
Using our benchmark T1 of 40 h, the measured Rb–3He spin-exchange rate at
180C [26, 70], the saturated vapor pressure curve for Rb [13], and Eq. (4.1), the
theoretical limit of attainable 3He polarization is about 80%, given 〈PRb〉 = 100%.
We estimate (and other research groups have shown directly [14]) that 〈PRb〉 can be
maintained at nearly 100% under these conditions with a diode-array laser such as
the one we use; yet there are no reports in the literature of 3He polarizations above
about 50%. This polarization deficit remains unexplained at present.
We measure the absolute polarization of HP 3He by comparing the NMR signal
from the 3He cell to a proton signal provided by a water sample in thermal equi-
librium. The water sample has a geometry similar to the 3He cell and contains a
53
sufficient amount of dissolved CuSO4 to reduce the proton T1 to less than 100 ms.
The comparison is done at a common NMR frequency, high enough for sufficient
proton signal. Since the proton polarization can be calculated, and the spin densities
of both samples are known, the 3He polarization can be determined by measuring
the ratio of NMR signals from the two samples. (The polarization is independent of
applied field for hyperpolarized gases.) In the low-flip-angle limit, the signal ratio
S3/S1 is given by [22]
S3
S1
=P3
P1
n3
n1
γ23
γ21
, (4.2)
where P is polarization, γ is gyromagnetic ratio, n is spin density, and the subscripts
“3” and “1” refer to 3He and protons, respectively. The spin density for the 3He cell
can be calculated from the pressure measured when it is filled. When solved for P3
using water, Eq.(4.2) can be expressed
P3 = (3.76× 10−4)f
p
S3
S1
, (4.3)
where f is the common NMR frequency in Megahertz, and p is the cell pressure
in atmospheres at room temperature. For our cells, S3/S1 is typically 40–50 dB.
Fig. 4.7 shows a pair of FID’s at 32.5 MHz on the same oscilloscope voltage scale.
The 3He FID is a single acquisition from an 8 atm cell with 50 dB attenuation in the
signal line; the proton FID is four averaged signals with no signal-line attenuation.
Using Eq. (4.3) and factoring in the slight difference in the two FID amplitudes, the
3He polarization is P3 = 50 ± 4%. The uncertainty comes from the measurement
of the proton FID height and from small losses in transporting the cell from the
polarizer to the electromagnet.
54
>
Ch 1: 100 mVolt 1 ms
dY: 487 mVolt
(a)
1 >
Ch 1: 100 mVolt 1 ms
dY: 503 mVolt
(b)
Figure 4.7. Polarimetry free-induction decays. Two FID’s acquired at 32.5 MHzusing the exact same NMR equipment and settings; only the field is different.The flip angle is < 10 in both cases. The peak-to-peak voltage of the first fulloscillation is marked by the solid horizontal cursor lines. (a) Four averaged waterproton signals acquired at 0.763 T. (b) A single acquisition at 1.00 T from an 8 atm3He cell with 50 dB of signal-line attenuation relative to (a). Using Eq. (4.3), the(field-independent) 3He polarization is 50 ± 4%. The transverse coherence timeis dominated by field gradients and is longer in (b) because of the better fieldhomogeneity in the electromagnet at higher fields.
55
4.9.3 Overall Performance
We now routinely fabricate SEOP cells that reach a “40/40” benchmark: 3He
polarization ≥ 40% and a 8 atm relaxation time T1 ≥ 40 h. The maximum
polarization is achieved in 12–20 h in about 0.5 atm·L of gas, although polarizations
as high as 20% are achieved in 3–5 h. The system can be left to run overnight
unattended in order to achieve maximum polarization. The apparatus described
here cost $35–40k to build; about $15k of that total was spent on the high-vacuum
system.
A few other research groups and at least one company, Amersham Health (AH),
have put some effort into high-volume, high-throughput devices to generate HP
3He. With the exception of Gentile et al. [44], there are few details of these systems
described in the open literature. Recent papers from the University of Virginia
group describe the AH system (which also uses SEOP but is not yet commercially
available) as capable of up to 35% polarization in ≈ 1 atm·L of gas after several
hours [38, 71]. Our system is roughly comparable, although our spin-exchange rates
are typically somewhat lower. We note that while we have yet to use our system
for human studies, the group at Washington University has obtained the necessary
FDA exemption for a system very similar to ours.
Groups at NIST in Gaithersburg, MD and at Mainz University in Germany have
employed the technique of metastability exchange optical pumping (MEOP) [39].
The Mainz group can produce ≈ 1 atm·L of 55% polarized 3He in about 2 h [6].
As with all MEOP systems, the gas must be compressed from a few Torr up to
atmospheric pressure with minimal polarization loss. A two-stage titanium piston
compressor is employed for this purpose. The disadvantages of this system are its
size, complexity, and nonportability. Our system is portable enough to have been
recently driven from Salt Lake City to Richland, Washington for collaborative MRI
56
experiments at Pacific Northwest National Laboratory. At NIST, a compact and
portable device for gas compression involving a modified diaphragm pump has been
developed. For MRI applications, it is expected to produce ≈ 1 atm·L of 20%
polarized gas in about 2 h [44]. We achieve substantially higher final polarization
than the NIST system at the expense of considerable pumping time.
4.10 Transit Time of 3He in the Capillary
As discussed in Sec. 4.5, the valve on our refillable 3He spin-exchange cells is
separated from the cell body by a glass capillary tube (see Fig. 4.1), so that the
potentially relaxive components of the valve are isolated from the bulk gas. Here we
calculate Γcap, the 3He relaxation rate due to the capillary and valve. The analysis
here is based in part on notes from discussions with both H.L. Middleton and M.S.
Conradi. We assume a capillary of length L, radius r, and cross section A = πr2.
We assume that the diffusion time, both across the cell and between the cell and the
valve, is short compared to the polarization lifetime T1, that T1 is dominated by wall
relaxation, and that the cell has a uniform relaxivity η, so that the wall-relaxation
rate Γw is given everywhere by
Γw = ηS
V, (4.4)
where S/V is the surface to volume ratio, equal to 2/r for the cylindrical capillary.
We consider the case in which the magnetization M0 in the cell body may be
considered constant. We note that it is quite possible that η in the capillary is larger
than in the body (due, for example, to the low conductance during the bakeout or
to the capillary coming from a different batch of Pyrex). We deal with this possible
57
difference below. In the capillary, the diffusion equation for 3He magnetization M(x)
in one dimension is:
∂M(x)
∂t= D
∂2M(x)
∂x2+ Q(x), (4.5)
where D is the diffusion coefficient of 3He atoms in the cell and Q(x) is a source
term. Under steady-state conditions with Q(x) = −ΓwM(x) and using Eq. (4.4) we
obtain:
d2
dx2M(x) =
ηS
DVM(x) =
2η
DrM(x), (4.6)
The general solution to Eq. (4.6) is
M(x) = C sinh(qx) + K cosh(qx), (4.7)
where
q2 = 2η/Dr. (4.8)
We assume that the valve at x = 0 instantly relaxes all spins with which it comes
in contact. The boundary conditions are thus M(0) = 0 and M(L) = M0. Hence,
we must have K = 0, and the particular solution is
M(x) =M0
sinh(qL)sinh qx. (4.9)
58
The flux of magnetic moment J(x) through a plane of constant x in the capillary
is thus
J(x) = −DdM(x)
dx= − DM0q
sinh(qL)cosh(qx), (4.10)
and the total magnetic moment per unit time flowing into the cell at the capillary
opening is
AJ(L) = −πr2DM0q coth(qL). (4.11)
Hence, the effective relaxation rate due to the capillary and valve is
Γcap = −AJ(L)
M0Vc
=πr2Dq coth(qL)
Vc
, (4.12)
where Vc is the cell volume. In our case, η is usually small, and in the limit qL ¿ 1,
Γcap =πr2D
VcL. (4.13)
Note that in this limit, Γcap is independent of η, and a modest increase in η in the
capillary compared to the cell body would be irrelevant.
Based on T1 = 40 h for a spherical cell 4.5 cm in diameter, we estimate η ≈5 × 10−6 cm/s. For an 8 atm cell, D = 0.23 cm2/s for 3He at 295 K [32]. Using
r = 0.025 cm and L = 6 cm for the narrow portion of the capillary and Eq. (4.8),
we obtain qL = 0.25. Using Eq. (4.13), we calculate Γcap ≈ 0.008 h−1. This number
59
is a factor of 2–4 greater than the measured range for Γcap given in Sec. 4.5 for our
cells. The discrepancy has at least two potential sources: the additional 4 cm of
1 mm i.d. capillary in our cells was not included in this calculation, and the valve
may not be perfectly relaxing (i.e., we may have M(0) > 0).
4.11 Conclusion
We have developed a successful protocol for fabrication of large-volume, valved
3He spin-exchange cells for MRI from inexpensive and easily-worked Pyrex glass. We
have identified an important mechanism for wall relaxation that has been directly
confirmed experimentally by studies of T1 hysteresis, and we have confirmed the im-
portance of Rb metal (in amounts of order 100 mg or more) for long wall-relaxation
times.
We have yet to reach the ultimate goal of understanding the physics of the cell
fabrication process at each step, but we have detailed here some progress away
from cell-making “voodoo.” The filling of cells has been separated from the rest of
the process and is done on a separate gas-handling system. Cell properties are
determined and, so far as we know, fixed by one or more of the earlier steps
(glass blowing, evacuation, baking, and Rb distillation). Once sealed from the
high-vacuum system, cells can be refilled indefinitely with no significant change
in their wall properties. Based on the comparative previous experience of one of us
(B.T.S.) with several cell-fabrication systems, we can make an educated guess that
the important elements of cell-preparation include the clean, oil-free turbomolecular
pump, the u-tube LN2 trap included on the glass manifold, and the multistage
distillation of the Rb metal into the cells. Our vacuum system does not qualify as
UHV and is not entirely metal-sealed, although the stainless-steel construction and
60
good vacuum practice (e.g., keeping air and water out of the system at all possible
times) presumably help to further minimize contaminants in the manifold.
The discovery of T1 hysteresis has opened the door to learning more about cell
fabrication by finally providing a concrete lead as to the dominant mechanism
involved in glass-surface relaxation of 3He. The detection of magnetism in Rb-coated
glass with a second method (ESR or vibrating-sample magnetometry, for example)
would confirm the effect and, in conjunction with further NMR measurements,
potentially allow better determination of the chemical identity, size, concentration,
and magnetic moment of the magnetic sites. It may eventually prove possible to
eliminate the sites altogether, perhaps improving T1 still further and making cells
even more robust in high-field environments, such as in or near an MRI magnet.
We gratefully acknowledge many useful discussions with M.S. Conradi and J.C.
Leawoods at Washington University, as well as the expert glass blowing of J. Kyle.
This work was supported by a grant from the Whitaker Foundation.
4.12 Addendum
As discussed in this paper, much attention is paid to cleanliness during cell
preparation: the baking under high vacuum and high temperatures, the three-step
Rb distillation process, and the separate 3He filling system with gas purifiers all
help prevent cell contamination. It is well established that gaseous oxygen can relax
3He very rapidly [72], but relatively little is known about relaxation properties of
rubidium oxides. It has always been assumed in cell preparation “lore” that clean,
pristine cells have the best chance at long lifetimes. Recent evidence, however,
suggests that oxidized Rb could be beneficial [73]. Heil et al. [6] show that the
relaxation rate of 3He interacting with a substrate is strongly dependent on the
substrate’s work function. Qualitatively this makes sense, Heil et al. argue, because
61
substances with low work functions have loosely bound electrons which repel the
He atoms more effectively than a substance with a higher work functions. This is
a possible explanation of the relatively long lifetimes observed in Rb and Cs coated
cells. Alkali metals have comparatively low work functions, and alkali oxides can
have even lower work functions. For example, Rb oxide at room temperature has a
work function of about 0.9–1.2 eV [74], which is substantially lower than the 2.26 eV
for metallic Rb [75]. An alkali oxide layer may, therefore, be quite beneficial in a
spin-exchange cell, as long as a sufficient Rb vapor can be achieved for SEOP.
We are conducting experiments in which we add oxygen to spin-exchange cells and
investigate the effects on 3He relaxation rates. These experiments are ongoing at the
time of this writing, but preliminary results indicate that relaxation rates actually
improved somewhat by adding oxygen. However, T1 hysteresis is not eliminated, as
we hoped that the iron sites would oxidize and become nonmagnetic. Any oxygen
added to a cell reacts rapidly with the Rb. Depending on how much oxygen is added,
we have observed Rb turn, in progression, slightly dark, then a dark-bronze colored
liquid, then a very dark brown solid, and finally a yellowish solid. Cells with Rb in
all conditions except the last can be optically pumped because enough metallic Rb
remains to provide sufficient vapor pressure.
One example is cell 11A′, which is discussed in Sec. 8.5.3. This cell had a
relaxation time of ≈ 40 h prior to the introduction of oxygen. The cell was opened at
the valve to release the 3He, then it was attached to an oxygen bottle. About 5 psi of
oxygen was added to the cell. All of the visible metallic Rb turned dark brown and
solid at room temperature; the oxidized Rb does not melt at SEOP temperatures.
We then attached the cell to the high vacuum system (see Fig. 4.3) with the cell
valve open and evacuated any excess oxygen over several days. After filling the cell
with 3He we measured a relaxation time of about 52 h. After subtracting dipolar
62
He–He relaxation, 0.01 h−1 at 8 atm and room temperature [see Eq. (1.5)], this cell
showed an increase in the wall relaxation time of about 60%. This significant increase
indicates a promising technique for improving wall relaxation times in existing cells.
Further investigations should include quantifying the amount of oxygen required
to optimize a cell’s relaxation rate, investigating long-term behavior of the cells,
and investigations of applied field and temperature dependence. By quantifying
and optimizing the amount of oxygen needed, a step could be easily added to the
cell preparation protocol. Long-term cell behavior could be influenced by the ability
of the Rb to getter oxygen or water vapor that might leech in from the glass. We
typically rely on the Rb to neutralize such otherwise harmful contaminants that
cannot be removed during baking or evacuating or that might be inadvertently
introduced during cell filling. If insufficient Rb remains to take care of this task,
then oxygenated cells may have a limited useful lifetime or may require periodic
evacuation, both undesirable. Finally, studies of temperature and field dependence
of T−11 in oxygenated cells may provide clues about the nature of the Rb-oxide–3He
interactions.
CHAPTER 5
MAGNETIC FIELD DEPENDENCE
OF 3He RELAXATION
5.1 Abstract
An observed external magnetic field dependence of measured 3He relaxation
rates is characterized by a dramatic increase in T−11 with decreasing external field
magnitude and is inconsistent with a previous relaxation model. The effect is
observed only in Pyrex spin-exchange cells (cells containing Rb for spin-exchange
optical pumping). This field dependence is not observed in aluminosilicate or quartz
spin-exchange cells or in bare (containing no Rb) Pyrex cells. The effect could
be caused by the 3He remaining near relaxation centers much longer than the
typical ballistic interaction time of ≈ 10−12 s, but possible reasons for the very
long interaction times are not given. In all cells measured at high fields, local T−11
minima at coercive fields and an asymptotic approach to a maximum value of T−11 at
high fields is expected and observed. The lack of the dramatic increase in measured
T−11 ’s in aluminosilicate and quartz is the only qualitative difference that we have
observed in 3He relaxation in different types of glass.
5.2 Introduction
There have been few attempts in the past to investigate field-dependent nuclear
relaxation of 3He in glass vessels [19, 76]. These attempts have generally been at
64
low, positive external fields (≈ 0 to 430 G) with bare, sealed cells at low pressures
(generally a few Torr). A slight field dependence in measured relaxation rates was
observed, but no attempts at an explanation were made. In [19], observed field
dependent relaxation in bare cells was attributed to paramagnetic centers, the major
cause of relaxation in bare cells (see Chapter 6 for a detailed discussion of 3He
relaxation in bare cells). In Chapter 3 we showed that ferromagnetic sites are largely
responsible for 3He relaxation in cells containing an alkali metal for spin-exchange
optical pumping (SEOP) and that such sites appeared to be absent in bare cells.
We studied the dependence of T−11 on high external fields, in the relatively broad
field range of −2000 G to +2000 G. In this chapter we show that Pyrex cells that
contain Rb demonstrate a strong field dependence independent of the size of the
magnetic sites’ moments. This effect is absent in aluminosilicate and quartz spin-
exchange cells and in bare Pyrex cells. We also show that bare Pyrex cells appear
to demonstrate field dependence characteristic of the presence of magnetic sites.
The possibility of observable T1 hysteresis at low fields (on the order of tens of
Gauss) is more pertinent to most HP gas researchers than effects due to high fields.
All spin-exchange cells are exposed to low fields for optical pumping or polarized
gas storage, whereas few researchers expose cells to higher fields. If field-dependent
effects appear in such fields, then T1 hysteresis will have broader importance. For
example, careful attention may have to be paid to the orientation of a cell during
polarization and HP gas storage.
5.3 Theory
5.3.1 High-field Hysteresis
As discussed in Chapter 3, T1 hysteresis is characterized by a sometimes dramatic
increase in T−11 measured at low field (≈ 30 G) due solely to intervening exposure
65
of the cell to a several-kG magnetic field. The original T−11 can be restored by
degaussing the cell by rotating it in a gradually decreasing magnetic field. In Chapter
3 we proposed that N spherical, magnetic sites of moment µ at or near the surface
of the cell are the main source of relaxation in magnetized cells. We presented a
model for magnetic-site relaxation (relaxation due only to interactions of 3He with
the sites) of 3He in spin-exchange cells; see Eq. (3.1). According to this model, T−11
should be directly related to the cell pressure (at a given temperature) through the
gas diffusion coefficient D and inversely related to the square of the moment of a
site, µ2. We experimentally demonstrated the former relationship in Chapter 3, so
in this chapter we attempt to demonstrate the latter.
The total magnetization M , the magnetic moment per unit volume, of a typical
ferromagnetic substance is a multivalued function of the applied external magnetic
field H, best described graphically by a hysteresis loop (see Fig. 5.1). If the model
for relaxation in Eq. (3.1) is correct, then the field-dependence of T−11 should look
qualitatively like the square of the hysteresis loop (that is, M2 vs. H). Notably, there
should be local T−11 minima at the coercive fields, where the net magnetization is zero
for a nonzero applied field, and T−11 should “saturate,” or asymptotically approach a
maximum value, as the magnetization saturates at large positive or negative fields.
5.3.2 Low-field Hysteresis
If low-field (≈ ± 30 G) T1 hysteresis is observable in unmagnetized or degaussed
cells, the field dependence of the measured T−11 ’s should behave similarly to that
described above, except saturation will be absent, and the coercive field may be too
small to measure without the relaxation being affected by field gradients [see Eq.
(1.6)]. However, the 60 G change in field may be too small to cause any measurable
T1 hysteresis if the loop between −30 and +30 G is very narrow or is a straight line.
66
M
H
coercive fields
Figure 5.1. A sketch of a typical hysteresis loop showing the relationship betweenmagnetic moment M and applied field H. Of note are the coercive fields: nonzeroapplied fields at which the net magnetization is zero. Also, the magnetizationapproaches saturation values as the magnitude of the external field becomes large.Different ferromagnetic materials have different characteristic hysteresis loops.
In this case, if a cell is perfectly degaussed and if a 30 G field is strong enough to
change the magnetization, then a plot of T−11 vs. applied field would be single-valued
parabolic function with a minimum at H = 0 (where M = 0).
5.4 Experimental
Most cells studied were Pyrex, ≈ 50 cm3, spherical, valved, and prepared ac-
cording to our cell-making protocols (see Chapter 4). The aluminosilicate cell
(GE-180) used was ≈ 40 cm3, cylindrical with rounded ends, valved, and prepared
by collaborators at Washington University. All cells contained ≈ 8 amagats of 3He,
except for the bare Pyrex cell which contained ≈ 4 amagats of 3He.
The high-field measurements were made in an electromagnet. The electromagnet
has automatic field reversal capabilities, but field spikes that occurred during field
reversal forced us to use a different procedure. To reverse the field we reversed
67
the cell orientation by lowering the field to zero, removing the cell, rotating the
cell 180 degrees in earth’s field, and replacing it. This avoided rotating the cell in
the magnet’s ≈ 60 G remanent field. The best method for making field-dependent
measurements is to measure relaxation rates at the fields of interest without field
cycling (or cycling the field to and from a measurement field). This insures that
measurements are made on only one hysteresis loop and at the right position on
the loop. This necessitated the design and construction of an NMR spectrometer
(see the Appendix) which has the capability of measuring 3He NMR in the range of
−3000 G to +3000 G (a cell side-arm pointing to the magnet’s north pole defines
a positive field). A low-Q probe consisting of a series LC resonator in series with
a 50 Ω resistor was used for NMR detection. The coil, which accomodates the cell
stem (see Fig. 4.1), was placed in a fixed position in the magnet such that the body
of the cell was in the center of the magnet. Very small flip angles were used to
minimize polarization destruction. Because intervening polarization of the gas was
necessary to complete a loop, each cell was degaussed prior to reintroduction to the
field. This helped assure that we would find our way back to the same hysteresis
loop each time.
The measurements made on the bare Pyrex cell were made possible by trans-
ferring polarized gas into it from a spin-exchange cell of similar size. This was
done on a special gas-transfer manifold (see Fig. 5.2). The manifold is made of
1 mm i.d. Pyrex capillary tubing, to minimize the volume, with two ports where
cells attach, a valved port to attach the vacuum system, and a valved port for a
pressure sensor. The cell ports are separated by about 5 cm to to allow the cells
to be adjacent to each other. The manifold is positioned in a Helmholtz pair such
that the cell bodies are on the longitudinal axis of the coils and the entire manifold
is in a nonzero field. This helps prevent 3He relaxation due to field gradients during
68
X
X
to pressure
sensorto vacuum
system/purge gas
valve
valve
to cell
to cell
Figure 5.2. Gas transfer manifold. This manifold, made of 1 mm capillary Pyrextubing, is used to transfer polarized gas from a spin-exchange cell to a bare cell.Either cell can be in either position.
the transfer procedure. The cells attach via o-ring compression fittings. After the
cells are attached, the manifold is evacuated. It is then backfilled with nitrogen
and evacuated in sequence several times to help remove moisture and oxygen. After
about 20 minutes of pulling vacuum, the vacuum-system port valve is closed, the
valve of the cell into which gas will be transferred is opened, and the high-pressure
cell is opened. After equilibrium is reached, usually after a few seconds, both cell
valves are closed and the cells can be removed.
As with the high-field measurements, the low-field measurements were preceded
by degaussing the cells. To avoid any intervening exposure to high magnetic fields
and to assure thorough degaussing, we used a tuned, 60 Hz series LC circuit,
controlled by a variable AC transformer, capable of producing fields up to ≈ 1400 G.
Four 35 µF 440 V capacitors in a series/parallel configuration provide a total of
35 µF capacitance. The inductor cavity is ≈ 10 cm in diameter and ≈ 7.6 cm long,
69
large enough to easily accommodate our cells, and has an inductance of 200 mH.
The highest degaussing field used was ≈ 100 G, with the idea of avoiding exposure
of the cell to any field significantly higher than the maximum 30 G field at which
measurements would be made while still using a field high enough to assure thorough
degaussing. The low-field hysteresis measurements were made in a Helmholtz coil
using the 100 kHz pulse NMR spectrometer described in Chapter 2 and a coil on the
cell stem. Very small flip angles were used to avoid polarization destruction. Field
reversal was accomplished by reversing the cell orientation in zero field. All low-field
data were taken at 100 kHz, so the field was cycled along a hysteresis loop each time
data were acquired. The entire cycle took about one minute, so an insignificant
amount of time was spent away from the field of interest.
5.5 Results/Discussion
5.5.1 High-field Hysteresis
Measurements of an aluminosilicate (GE-180) spin-exchange cell (Fig. 5.3) show a
behavior which is qualitatively consistent with the field-dependence of T−11 through
µ given in Eq. (3.1). This figure shows a symmetric, closed loop with local minima
at the coercive fields of ≈ ±200 G, as expected. The initial measurement is at a
low, positive field with the cell degaussed (M ≈ 0 and H ≈ 0). As the external
field increases to +2000 G, the T−11 increases and gradually approaches saturation.
Hysteretic changes in T−11 consistent with ferromagnetism can be seen as the field is
decreased from +2000 G through zero to −2000 G and back up again to +2000 G.
Unfortunately, a quantitative assessment of the relationship between T1 and H is
not possible due to the unknown nature of the hysteresis of the magnetic inclusions.
We note that the relaxation rates measured at the coercive fields are lower than the
initial rate when the cell was degaussed. This may indicate that storing polarized
70
0.03
0.04
0.05
0.06
0.07
0.08
0.09
0.1
-2000 -1500 -1000 -500 0 500 1000 1500 2000
T1-1
(h
ou
rs-1
)
Field (Gauss)
Figure 5.3. T1 hysteresis loop of an aluminosilicate cell. The relaxation rate isplotted vs external field. The solid line with arrows was added to help guide theeye. The data were taken at the fields of interest with no field cycling. Notice thelocal minima at the coercive fields (≈ ±200 G). These results are consistent withthe model in Chapter 3.
gas in a magnetized cell at the coercive field may be better than storing it in a
degaussed cell at low field.
Measurements were also made on a bare Pyrex cell, as shown in Fig. 5.4. Polarized
gas was transferred into the cell from a high-pressure (≈ 8 atm) spin-exchange cell, as
discussed in Sec. 5.4. This cell behaves qualitatively similar to the aluminosilicate
cell (Fig. 5.3), with the T−11 approaching saturation at higher external fields and
local minima at coercive fields. Several transfers of gas were required to complete
the loop, and duplicate measurements at were made to check consistency before and
after the cell was refilled. We found that the wall rate was not completely consistent.
This is most evident for the −600 G measurements made on the return path from
−2000 G: the two points connected by the vertical line were made at the same field
and position on the loop but with different charges of gas. This offset in measured
71
0.06
0.08
0.10
0.12
0.14
0.16
0.18
0.20
-2000 -1000 0 1000 2000
T1-1
(h
ou
rs-1
)
Field (Gauss)
Figure 5.4. A T1 hysteresis loop of a bare (no Rb) Pyrex cell. The relaxation ratesare plotted vs. external field. The solid line with arrows was added to help guidethe eye. The data were taken at the fields of interest with no field cycling. Noticethe local minima at the coercive fields (≈ ±200 G). These data are qualitativelyconsistent with the aluminosilicate results and with the model in Chapter 3.
rates merely breaks symmetry in the plot but makes it difficult to state definitively
whether the data in Fig. 5.4 form a hysteretic loop. However, the bare Pyrex cell
shows evidence of the presence of ferromagnetism due to the local T−11 minima at
or near the coercive fields. This is apparently contrary to the results presented in
Chapter 3, where we showed that the relaxation rates of a bare cell measured at
30 G before and after exposure to a 1.0 T magnetic field did not change (see Fig.
3.3). Because both cells had about the same T1 when unmagnetized and measured
at low field, it is unlikely that T1 hysteresis was being masked by other relaxation
mechanisms in one cell and not the other. Further evidence is required for us to
draw any conclusions about the nature of bare-cell T1 hysteresis.
Similar experiments were conducted using three Pyrex spin-exchange cells (cells
containing Rb for optical pumping). The results show a very different behavior.
72
Figures 5.5, 5.6, and 5.7 show symmetric, closed loops of T−11 vs. external field, as
with the aluminosilicate and bare Pyrex cells. However, each cell shows a significant
field dependence that appears independent of the size of the magnetic moments:
as the magnitude of the field, thus the magnetization of the sites, decreases, T−11
increases dramatically until the external field passes through zero. Then the T−11
drops precipitously as the coercive field is approached, where each cell shows a local
T−11 minimum, as expected. This field-dependent effect is not accounted for in the
model, and is the only qualitative behavioral difference between different types of
glass that we have observed with 3He T−11 measurements. This is a very surprising
result, because a field dependence to the surface relaxation should only occur at fields
where the correlation time for the interaction is of the order of the Larmor period.
0
0.1
0.2
0.3
0.4
0.5
0.6
-2000 -1500 -1000 -500 0 500 1000 1500 2000
T1-1
(h
ou
rs-1
)
Field (Gauss)
Figure 5.5. A T1 hysteresis loop of Pyrex cell 9A. The relaxation rate is plotted vsthe external field. The data were taken at the fields of interest with no field cycling.The solid line with arrows is added to guide the eye. Local minima are presentat the coercive fields, as expected, but the strong field dependence of T−1
1 as theexternal field approaches zero from saturation is unexpected and unexplained.
73
0.0
0.2
0.4
0.6
0.8
1.0
-2000 -1500 -1000 -500 0 500 1000 1500 2000
T1-1
(h
ou
rs-1
)
Field (Gauss)
Figure 5.6. A T1 hysteresis loop of Pyrex cell 10A.
0.00
0.05
0.10
0.15
0.20
0.25
0.30
0.35
-2000 -1500 -1000 -500 0 500 1000 1500 2000
T1-1
(h
ou
rs-1
)
Field (Gauss)
Figure 5.7. A T1 hysteresis loop of Pyrex cell 18A. This particular cell was rinsedwith a 5% HF solution and a 37% HCl solution prior to Rb distillation, as discussedin Sec. 8.5.3.
74
Thus, we currently have no satisfactory explanation for the observed phenomenon
that is consistent with previous models.
We would expect the correlation time to be the collision time with the wall, which
should be much shorter than the Larmor period at any of our fields of interest. If
the field of a relaxation site is dipolar, then the general form of relaxation would
have the form [30]:
1
T1
∝ τ
1 + ω2τ 2, (5.1)
where ω is the Larmor frequency, which is proportional to the external field, and τ is
the correlation time. The relaxation models we develop and verify in Chapter 3 and
Chapter 6 assume ω2τ 2 ¿ 1, which is easily the case with 100 kHz Larmor frequency
(at ≈ 30 G) and a correlation time on the order of 10−12 s [17]. The dramatic field
dependence shown in Figs. 5.5, 5.6, and 5.7 implies that the same assumption is not
valid here. This is troubling, because pressure-dependence measurements supported
Eq. (3.1). A long correlation time would mean that the relaxation mechanism in
the presence of a magnetic site would be due to 3He diffusion through the field
gradient caused by that site. As given in Eq. (1.6), T−11 due to field gradients is
directly proportional to the diffusion coefficient which varies inversely with pressure.
Thus, the long correlation-time limit would result in opposite pressure dependence
than was observed in Chapter 3. Also troubling is the fact that the strange field
dependence was observed only in Rb-coated Pyrex, and not bare Pyrex, Rb-coated
quartz, or Rb-coated aluminosilicate.
One difference between Pyrex and aluminosilicate glasses is the permeability to
helium: Pyrex is about 104 to 105 times more permeable at room temperature [77].
If the 3He is able to permeate the glass and remain in the vicinity of a magnetic
75
site for much longer than a typical adsorption interaction (≈ 10−12 s [17]) then
a field dependence such as that observed would be explained. However, there
are several problems. First, temperature-dependence studies detailed in Chapter
7 suggest that the presence of Rb in the cells reduces permeability significantly
when compared to that of bare Pyrex. Second, the bare Pyrex cell did not show
the same field dependence as seen in the Rb-coated Pyrex. Third, quartz is more
permeable than Pyrex by an order of magnitude at room temperature [77]; thus we
expected to see the effect even more strongly than in Pyrex. However, preliminary
measurements strongly indicated that quartz spin-exchange cells do not show the
same field dependence as the Pyrex spin-exchange cells. Fourth, we can think of no
way of explaining how the 3He might remain in the vicinity of a relaxation site long
enough to cause the effect. Since the effect has thus far been observed only in Pyrex
cells containing Rb, then it is likely that a chemical interaction between the Pyrex
and Rb is somehow responsible. Clearly, this remains an open question warranting
further study.
5.5.2 Low-field Hysteresis
Other researchers have reported seeing changes in T−11 with variations of cell
orientation in low field (tens of Gauss) for unmagnetized or degaussed cells [73, 78].
We measured the relaxation rates for two cells at various fields in the range of +30 G
to −30 G (see Fig. 5.8). Cell 20B was never exposed to a high magnetic field, so its
T1 hysteresis properties are not known. Cell 14A was used as a control, since it is
not affected by T1 hysteresis to a significant degree (<10%, see Fig. 4.6). Both cells
had the same size, shape, and gas pressure. An incomplete loop was acquired for
each cell: cell 20B was measured at various fields from +30 G to −30 G and back
up to −5 G, and cell 14A was measured at +30 G, +5 G, −5 G, and −30 G. The
76
0.01
0.1
-30 -20 -10 0 10 20 30
14A
20B
T1-1
(h
ou
rs-1
)
Field (Gauss)
Figure 5.8. Low-field T1 hysteresis. A plot of T−11 vs applied magnetic field for
two cells. Cell 20B has never been exposed to a large magnetic field, and cell 14Bwas degaussed. The data were corrected for bulk He–He relaxation. Field cyclingwas employed with all data taken at +30 G. Cell 20B was measured from +30 Gto −30 G and back up to −5 G; multiple data points were acquired at +5 G toassure consistency in measurements due to intervening polarization of the gas. Cell20B shows strong field dependence while cell 14A shows almost no field dependence.Cell 14A was used as a control because it was known to not exhibit significant T1
hysteresis effects.
large increase in T−11 seen in cell 20B cannot be attributed to gradient relaxation,
because cell 14B did not show similar behavior. If gradient relaxation dominated at
±5 G, then both cells would be expected to have similar T−11 ’s at those fields.
There are three characteristics of Fig. 5.8 that we wish to address. First, there
is a significant difference between the measured rates at +30 G and −30 G for cell
20B. Second, cell 14B does not show the same strong field dependence that 20B
shows. Third, the low-field data lack evidence of a coercive field.
First, we seek an explanation for why cell 20B had such different measured rates
at +30 G and −30 G. If the cell was thoroughly degaussed and if no measurable
77
hysteresis was present, then there should be no difference between the magnitude
of M at ±30 G, so the measured rates should be the same. However, the rate
increase from −30 G and +30 G was about a factor of 2, which implies that the
cell was not completely degaussed. Reasons for this are not clear. Either we did
not do a thorough job of degaussing (although cell 20B was never exposed to a
static field above 30 G) or there are magnetic sites that have some slight permanent
magnetization. We have looked at other unmagnetized and degaussed cells at ±30 G
with mixed results. Some have shown a difference between the two fields and others
have not. This wide variation between different cells makes it difficult to draw any
conclusions.
Second, the large increase in rate seen in cell 20B (Fig. 5.8) as the magnitude of
the field was lowered toward 0 G is similar to the rate increases seen in the high-field
measurements of Rb-coated Pyrex (see Figs. 5.5, 5.6, and 5.7). In contrast, cell
14B showed very little change. Since cell 14B showed only slight T1 hysteresis, we
hypothesize that cell 14B simply lacks a sufficient number of magnetic sites to make
the effect measurable.
Third, it is clear that there is a field-dependent relaxation mechanism at low fields
in some cells, although the results of low-field hysteresis are qualitatively different
from the high-field results. The most significant difference is the lack of local T−11
minima at coercive fields. This may be due to two things: the corresponding
hysteresis loop does not cross the H axis, or the lack of any hysteresis. First, we
assumed that at low fields the magnetization in the cells would have hysteresis loops
centered about the origin of the M vs. H plot. However, it is possible that even a
degaussed cell has some degree of remanent magnetization, the origins of which are
not clear. This would place the hysteresis loop above, or below, the horizontal (H)
axis so that the loop would never cross the axis for a sufficiently low range of fields.
78
Second, M may be a nearly single-valued function of H between ± 30 G, meaning
that the hysteresis loop may be very narrow or even linear, resulting in virtually
no change in T−11 at fields of a given magnitude. Because T1 measurements of cell
20B showed only a field dependence with a lack of hysteresis, both possibilities may
hold.
We note that if the M vs. H dependence for degaussed cells in the range of ±30 G
is linear or nearly linear, then we should see a T1 field dependence that is parabolic,
according to the relationship T−11 ∝ µ2 given in Eq. (3.1). The very strong field
dependence observed is opposite this, implying that the actual field dependence is
much stronger.
5.6 Conclusion
We observed a very strong field dependence of T1 values measured in Rb-coated
Pyrex cells at fields between ±2000 G that is independent of the size of the moments
of the magnetic sites. This dependence is not explained by the model developed in
Chapter 3. We did, however, observe field dependence in Rb-coated aluminosilicate
and bare Pyrex that was qualitatively consistent with the model. This is the first
qualitative difference between different types of glass that we have observed using
T1 measurements of 3He relaxation. We also observed field-dependent effects in
Rb-coated Pyrex at low fields similar to those observed at high fields, with the
exception that no coercive fields or definite hysteresis were observed. The cause of
the unexpected field dependence in the Rb-coated Pyrex is indicative of very long
interaction times between the 3He atoms and the relaxation sites. These times would
have to be many orders of magnitude longer than the ballistic collision time. The
cause of such long interaction times is currently a mystery.
CHAPTER 6
FUNDAMENTAL MECHANISMS OF3He RELAXATION ON GLASS
6.1 Preface
This chapter is a manuscript submitted to Chemical Physics Letters in September
2002. This paper presents the first experimentally verified model of 3He relaxation
in bare (containing no Rb) glass, an important step in understanding relaxation
mechanisms in alkali-coated glass. Two significant points make this paper strong.
First, the theoretical prediction of T−11 temperature dependence is confirmed inde-
pendently by two different research groups using cells of different surface to volume
ratio, different 3He pressures, and measurement fields of different strength. These
aspects support the universality of the results for all bare Pyrex cells. Second, we
show that physical properties of the glass alone determine the relaxation rate of the
gas. Follow-up work has shown that the theory is general enough to extend to other
types of glass, and, more importantly, that the presence of an alkali metal in the
cells changes the fundamental relaxation mechanisms, a fact that was not previously
appreciated (see Chapter 7).
My coauthors are B. Driehuys, of Amersham Health, and B. Saam, my advisor.
Much of the theory in this paper was based on derivations by B. Driehuys, with my
refinements and explanatory text. I also compiled the numerical predictions and
analyzed the data.
80
6.2 Abstract
We present a model of 3He relaxation on the surface of borosilicate glass which
accurately predicts observed relaxation rates and their temperature dependence.
Above room temperature 3He dissolves into Pyrex, where interactions with Fe3+ ions
result in a relaxation time of ≈ 1 ms. Gas exchange across the glass surface of an
enclosed vessel leads to T−11 = A/V × (3.9± 1.4)× 10−2 cm/h at room temperature,
where A/V is the surface-to-volume ratio. The activation energy for relaxation is
13.7 ± 0.7 kJ/mol and is dominated by the activation energy of 3He diffusion in
glass. This is the first successful confirmation of predicted 3He relaxation rates in
glass vessels.
6.3 Introduction
Spin-exchange optical pumping (SEOP) [1] and metastability-exchange optical
pumping (MEOP) [2] are common methods of producing very high, nonequilibrium
nuclear polarization in certain noble gas nuclei. The gas is typically polarized
and/or stored in glass vessels, or cells. Workers in the field have long attempted to
determine a quantitative and predictive model of 3He surface relaxation on glass.
Since 3He surface relaxation has proven to be a very complex problem, understanding
even a single model system would be critical progress. The ultimate goal is a
better understanding of 3He relaxation in spin-exchange cells (cells containing an
alkali metal), where magnetic inclusions in the glass can dominate relaxation [45].
Researchers who use bare glass cells of all types, and Pyrex in particular, as storage
cells for polarized gas research may find these results especially pertinent.
Previous measurements of 3He relaxation as a function of temperature on glass
surfaces have been made in bare (containing no Rb or surface coatings), sealed
Pyrex, aluminosilicate, and quartz cells [19, 76]. For Pyrex, Fitzsimmons et al.
81
provided significant insight into 3He relaxation mechanisms by showing that adsorp-
tion dominates relaxation below about 130 K and absorption dominates at higher
temperatures. They derived and verified a model for adsorption-based relaxation.
However, a quantitative understanding of the absorption regime, which is relevant
for most practical experiments, has eluded researchers. In this paper we provide
a theory valid for all bare Pyrex cells which accurately predicts the measured
rates for dissolution-dominated relaxation. We show that such relaxation can be
characterized by an Arrhenius relation with a relaxivity %0 and the appropriate
activation energy EA:
1
T1
=A
V%0 exp
(− EA
R T
), (6.1)
where A/V is the surface to volume ratio.
6.4 Theory
6.4.1 T > Room Temperature
Our model for relaxation of polarized 3He is based on the solubility, diffusivity,
and intrinsic relaxation of 3He in the glass. We assume that all relaxation is due to
interactions of 3He with paramagnetic impurities in the glass, and that the number
of 3He atoms in the gas is much greater than the number of dissolved atoms. The
net flow of magnetization is from the gas to the glass in the −ξ direction, while
ξ = 0 represents the glass-gas interface. In the limit of weakly-relaxing walls [79],
the polarization may be assumed uniform in the gas and continuous across the
glass–gas interface.
The diffusion equation in the glass is
82
∂
∂tM(ξ) = Db(T )
∂2
∂ξ2M(ξ) + Q(ξ), (6.2)
where Db(T ) is the temperature-dependent diffusion coefficient of the helium in
the bulk glass, M(ξ) is the 3He magnetization, and Q(ξ) is a source term. The
magnetization loss is
∂
∂tM(ξ) = − 1
T1
M(ξ), (6.3)
where T1 is the measured relaxation time. The source term represents the magneti-
zation destroyed while in the dissolved phase:
Q(ξ) = − 1
T1 b(T )M(ξ), (6.4)
where T1 b(T ) is the temperature-dependent relaxation time of the dissolved gas.
From the above assumptions, T1 À T1 b. Equation (6.2) becomes:
Db(T )∂2
∂ξ2M(ξ) − 1
T1 b(T )M(ξ) ≈ 0. (6.5)
The general solution to Eq. (6.5) is
M(ξ) = S(T ) M0 exp(ξ/λ), (6.6)
83
where M0 is the gas-phase magnetization, S(T ) is the Ostwald solubility (Suckow [80]
refers to the Bunsen solubility1, which we will use in later calculations), and λ =√
Db(T ) T1 b(T ) represents a characteristic penetration depth of magnetization in
the glass. We note that solubility is usually calculated from measurements of
permeability K and diffusivity, since S = K/D.
The observed rate I at which total magnetic moment leaves the gas phase and
enters the dissolved phase is
I = −M0 V
T1
, (6.7)
where V is the cell volume. This rate is also the flux of total magnetic moment at
the interface multiplied by the interface area A:
I = −A Db∂
∂ξM(ξ) = −A
√√√√ Db(T )
T1 b(T )M0 S(T ). (6.8)
Equating (6.7) and (6.8) gives a prediction for the relaxation rate of polarized 3He in
a bare glass cell entirely in terms of the cell geometry and the bulk glass properties:
1
T1
=AS(T )
V
√√√√ Db(T )
T1 b(T ). (6.9)
A similar equation was partially derived by Deaton et al. in their study of 3He
relaxation on polymer surfaces [81].
1The Ostwald solubility is the volume of gas dissolved in a unit volume of a liquid at a specifiedtemperature and pressure. Bunsen solubility is the Ostwald solubility measured at STP.
84
The general form of relaxation due to dipolar interactions in the bulk [30] is
1
T1 b
=6
15
Mr6
τc
1 + ω2τ 2c
, (6.10)
where r is the separation, τc is the correlation time of the interaction, ω is the
3He Larmor frequency, and M = γ2gas γ2
e h2 S(S+1), where γgas and γe are the
gyromagnetic ratios for 3He and electrons, respectively. Mazitov et al. showed that
3He relaxation in bulk borosilicate glass depends most strongly on interactions with
Fe3+ ions (spin S = 5/2), which have a correlation time τFe for electron spin flips
of approximately 8× 10−9 s at room temperature [18]. To consider the effect of all
Fe3+ ions on a 3He nucleus, the expression in Eq. (6.10) must be integrated from
the distance of closest approach a through all space:
1
T1 b
=∫ ∞
a
6
15
Mr6
τc
1 + ω2τ 2c
N 4πr2 dr, (6.11)
where N is the density of Fe3+ ions in the glass. Since τc ≈ τFe, Eq. (6.11) becomes:
1
T1 b
=24π
45
N Ma3
τFe
1 + ω2 τ 2Fe
. (6.12)
Our measurements are made at low fields (see Sec. 6.5). Since ω2 τ 2Fe ¿ 1 we can
simplify Eq. (6.12) to:
1
T1 b
≈ 24π
45
N Ma3
τFe. (6.13)
85
Combining Eqs. (6.9) and (6.13) gives:
1
T1
=A
V
√24π
45
N Ma3
S(T )√
τFe(T ) D(T ). (6.14)
The temperature dependence of S(T ), Db(T ), and τFe(T ) can be characterized by
Arrhenius relations [18, 80]:
S(T ) = S0 exp(− ES
R T
), (6.15)
Db(T ) = D0 exp(−ED
R T
), (6.16)
τFe(T ) = τ0 exp(−EFe
R T
), (6.17)
where ES, ED, and EFe are molar activation energies for solubility, diffusion, and
Fe3+ electron spin flips, respectively, R is the universal gas constant, and T is the
absolute temperature. The subscript 0 indicates an asymptotic (T →∞) value. By
substituting Eqs. (6.15), (6.16), and (6.17) into Eq. (6.14) we have:
1
T1
=A
V
√24 π
45
N Ma3
S0
√τ0 D0 exp
(− EA
R T
)=
A
V%0 exp
(− EA
R T
), (6.18)
where we have defined %0 as the relaxivity and the total activation energy as
EA = ES +1
2(EFe + ED). (6.19)
86
We are primarily interested in relaxation in Pyrex, a borosilicate glass made by
Corning, because it is commonly used for spin-exchange cells. To calculate the
relaxation rate predicted by (6.18) for Pyrex we use the values obtained from bulk
glass measurements shown in Table 6.1. τ0 was calculated using Eq. (6.17) and
values for EFe and τFe. Based on [18] and a discussion with Mazitov, we assume
a 10% uncertainty for τ0 and N . As Shelby [82] points out, there is generally
poor agreement in reported activation energies for permeation of He in Pyrex,
ranging from 21.8 kJ/mol to 31.4 kJ/mol, and similar discrepancies exist for diffusion
measurements. Bulk-glass activation energies reported in [80] were used in Table 6.1
rather than measurements by several other workers (see, for example, [77, 82, 83])
because the former measurements were made on Duran, a borosilicate glass made
Table 6.1.Important values for Eq. (6.18) for Pyrex glass.
Variable Value Uncertainty Units Ref
D0 7.0× 10−4 0.6× 10−4 cm2/s [80]
ED 27.8 0.5 kJ/mol [80]
S0 6.3× 10−3 0.6× 10−3 cm3 STP/cm3 [80]
ES 1.5 0.6 kJ/mol [80]
τFe(295K) 0.77× 10−8 s [18]
τ0 1.9× 10−9 10% s
EFe −3.4 0.3 kJ/mol [18]
N 8× 1018 10% cm−3 [18]
a 5 A [18]
87
by Schott which is very similar to Pyrex, and because an uncertainty was given
with each of the measured values. From Eq. (6.13) we estimate the relaxation time
in bulk glass as T1 b ≈ 1 ms, therefore the magnetization penetration depth λ is
≈ 30 nm.
Inserting relevant values into Eq. (6.18) gives the relaxivity:
%0 = (10 ± 2) cm/h. (6.20)
Equation (6.19) gives the activation energy:
EA = 13.7± 0.7 kJ/mol, (6.21)
which is dominated by the activation energy of 3He diffusion in glass. We then
calculate an expected room temperature relaxation rate:
1
T1
=[A
V(3.9 ± 1.4)× 10−2
]h−1. (6.22)
Equation (6.22) predicts that bare Pyrex is of marginal utility for polarized 3He
storage, a fact that has been verified by several investigators [17, 19, 20]. As
discussed in Sec. 6.6.1, this situation changes drastically for cells containing alkali
metals.
6.4.2 T < Room Temperature
At lower temperatures the 3He lacks sufficient kinetic energy to overcome the
potential barrier for dissolution. For example, 13.7 kJ/mol of kinetic energy is
88
required for the 3He to overcome the potential barrier of dissolution relaxation,
whereas only 1.7 kJ/mol is available at 200 K. Relaxation mechanisms with negative
activation energies, such as adsorption to the cell wall, will begin to dominate the
measured T−11 as the temperature decreases. Although typical sticking times are only
≈ 10−13 s at room temperature [17], there is no potential barrier to overcome, since
the interaction is slightly attractive. Fitzsimmons et al. [19] derive an expression
for relaxation in a cell where adsorption dominates:
T1 =N
n(tad + Tad), (6.23)
where N is the total number of gas atoms in the cell, n is the total number of
gas atoms adsorbed to the surface at any instant, tad is the average adsorbed-atom
sticking time, and Tad is the relaxation time of an adsorbed atom. The number of
adsorbed atoms is assumed much less than N , and is given by n = N v A tad/(4 V ),
where v is the mean thermal velocity of the 3He atoms. They show that Tad À tad
and that Tad = tad/2 W , where W is the probability of an adsorbed atom relaxing.
W is proportional to t2ad, and tad follows an Arrhenius relation with activation energy
Ead. Thus Eq. (6.23) becomes:
1
T1 ad
=A
Vκ0 exp
(−2Ead
R T
) √T , (6.24)
where κ0 = W√
2 R/NA mπ, the 3He mass is m and NA is Avogadro’s number.
Muller [84] reports an activation energy of He adsorption on glass of
Ead = −0.96 ± 0.19 kJ/mol. (6.25)
89
This was independently confirmed by Fitzsimmons et al. [19] by observing nuclear
spin-relaxation of polarized 3He in low-pressure, sealed cells at various temperatures
below room temperature.
By assuming that a 3He atom will only relax in a collision with a Fe3+ ion at the
surface, we can approximate W and find κ0. The Fe3+ concentration is about one
part in 104 by volume [18], and Timsit et al. estimate that an average of 106 collisions
are required to relax a 3He atom [17]. Therefore, κ0 ≈ 3× 10−2 cm h−1 K−1/2.
6.5 Experimental
All measurements were made on spherical, valved, bare Pyrex cells. Cells pre-
pared at Utah were ≈ 50 cm3 and contained ≈ 4 amagats of 3He, and the cell
prepared at Amersham Health (AH) was ≈ 180 cm3 and contained ≈ 1 amagat of
3He. The Utah cells were prepared by baking under vacuum for ≈ 48 hours at up
to 400C. (Procedures used at Utah for cell fabrication and a detailed description
of the cells can be found in Chapter 4.) Polarized gas was transferred into an
evacuated cell from a similar, higher-pressure spin-exchange cell by connecting the
cells, opening the valves, and allowing the pressure to equilibrate. The gas could
not be polarized in the cells directly because bare cells, as we define them, do
not contain Rb. All Utah T−11 measurements were made at ≈ 30 G using 100
kHz pulse NMR (see Chapter 2) and very small flip angles to excite only a small
fraction of the gas. The AH measurements were made at ≈ 7 G (24 kHz). The
initial heights of the free-induction decays acquired at appropriate time intervals
were fit to a single exponential to extract T−11 . Several T−1
1 measurements could
be made on a single charge of gas with intervening changes in temperature. The
above-room-temperature measurements were done in a forced-air oven typically used
for SEOP. The temperature was maintained to a few tenths of a degree by a resistive
90
temperature detector and controller. The measurements below room temperature
were done in an insulated cylinder connected to a liquid nitrogen dewar. The desired
temperature was reached by boiling off the liquid nitrogen at a specific rate with
submerged heating tape powered by a variable AC transformer. The temperature
was monitored with a thermocouple and maintained to within a few degrees. In all
cases the cell valve was kept at room temperature to prevent o-ring failure.
6.6 Results and Discussion
6.6.1 T > Room Temperature
Relaxation rates of three bare Pyrex cells, labelled 19A, 19B, and PXX05, were
measured at various temperatures between 298 K and 473 K (see Fig. 6.1). By
comparing the average curve fit results of the three cells to Eq. (6.18) we find that
EA = 14.7 ± 0.3 kJ/mol and %0 = (36 ± 4) cm/h (represented by the solid line
in Fig. 6.1). This equates to a room-temperature relaxation rate of
1
T1
=[A
V× (9.6 ± 1.6)× 10−2
]h−1. (6.26)
Our results are in excellent agreement with the predicted value of EA = (13.7
± 0.7) kJ/mol and in good agreement with %0 = (10 ± 2) cm/h (represented in
Fig. 6.1 by the dashed line), providing strong evidence that the model, Eq. (6.18),
accounts for the majority of relaxation in this temperature range. The discrepancy
in the intercepts in Fig. 6.1 is directly related to the discrepancy in %0. We note,
however, that the experimental value of %0 was obtained by assuming a perfectly
smooth cells surface (minimum value of A/V ). It is not difficult to imagine that the
actual A/V is larger by a factor of two or more, which would bring the measured
91
0.01
0.1
1
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
19A
19B
PXX05
theory
V/A
T1-1
(cm
ho
urs
-1)
1000/T (K-1)
Figure 6.1. Temperature dependent relaxation rates for three bare (no Rb) Pyrexcells above room temperature. Equation (6.18) is also plotted using (6.20) and(6.21). Cells 19A and 19B were prepared and measured by the group at Utah,and cell PXX05 was prepared and measured at Amersham Health. Cells 19Aand 19B were ≈ 50 cm3 and ≈ 4 amagats, and cell PXX05 was ≈ 180 cm3 and≈ 1 amagat. Rates were measured at temperatures between 298 K and 473 K.Bulk He–He relaxation was subtracted from the data. The data were fit to anArrhenius relation with % and EA as free parameters. The resulting activationenergy is EA = 14.7 ± 0.3 kJ/mol. Differences in the slopes represent a differencein EA, whereas differences in the intercept could be due to an underestimation inA/V , since we assumed a smooth, spherical surface.
%0 into much closer agreement with theory. In addition, slight differences in glass
composition [85] or thermal history [86] could lead to variations in N or D0 beyond
the quoted errors we assumed. Differences in the relaxivity might lead to nonlinear
behavior in Fig. 6.1 or to a slope different from that predicted. The theory accounts
only for absorption relaxation, thus Eq. (6.22) represents a lower limit for T−11 at
room temperature.
We have also studied the temperature-dependent relaxation of 3He in several
Pyrex cells containing Rb metal. In stark contrast to bare cells, we found that
92
diffusion-based relaxation is absent but that an adsorption-based relaxation model
seems much more appropriate for the longest-lifetime cells. This suggests that the
Rb strongly inhibits dissolution in spin-exchange cells leaving other relatively weak
mechanisms to dominate relaxation.
6.6.2 T < Room Temperature
To investigate adsorption-based relaxation, we measured 3He relaxation in a
temperature range of 95 K to 175 K. Figure 6.2 shows T−11 vs. 1000/T for two
of the cells discussed in Section 6.6.1. Results of a global fit of the data to Eq.
(6.24) give Ead = −0.63± 0.03 kJ/mol and κ0 = (1.6± 0.1)× 10−3 cm h−1 K(−1/2).
0.01
0.1
1
10
5 6 7 8 9 10 11
19A rate
19B rate
theory
T1-1
(h
ou
rs-1
)
1000/T (K-1)
Figure 6.2. Relaxation rate vs 1000/T for two bare Pyrex cells at ≈4 amagats.These are two of the same cells shown in Fig. 6.1 but with a different charge of gas.The dashed line is a plot of Eq. (6.24) using (6.25) and κ0. Temperatures rangedfrom about 95 K to 175 K. The data, with bulk He–He relaxation subtracted,were fit to Eq. (6.24). The results from a global fit give an activation energyof Ead = −0.63 ± 0.03 kJ/mol, somewhat weaker than reported in [19, 84] of−0.96± 0.19 kJ/mol.
93
There is good agreement between our value of κ0 and the predicted value of 3× 10−2
cm h−1 K(−1/2), although our value is somewhat lower. This could be a result of
fewer Fe3+ ions on the glass surface than anticipated, and suggests the possibility
of using polarized 3He to measure Fe3+ ion surface concentration in various types of
glass. The activation energy we found was somewhat weaker (closer to zero) than
that reported by Fitzsimmons et al. [19] and Muller [84] of −0.96 ± 0.19 kJ/mol.
We note that Fitzsimmons et al. found a local minimum in T−11 of 3He relaxation
in bare Pyrex at about 120 K, reflecting the transition between adsorption- and
absorption-dominated relaxation. We clearly observed adsorption behavior up to
about 170 K and a local minimum at about 200 K. We have no direct explanation
for the discrepancy, but we point out that the relevant data in Ref. [19] carry large
error bars, particularly near the T−11 minimum; in addition the curves used to fit
their data are at least somewhat speculative.
6.7 Conclusion
This work represents the first successful quantitative verification of predicted
3He relaxation phenomena in bare Pyrex glass. We conclude that we have identified
the correct relaxation mechanism for bare Pyrex, that our theoretical calculation
represents a lower bound on T−11 , and that experimental values will be larger as A/V
departs from an ideally smooth surface. The relaxation is dominated by interactions
of dissolved 3He with Fe3+ ions in the glass. We have experimentally verified the
predicted activation energy of dissolution-based relaxation, which depends on the
activation energies of 3He solution, diffusion, and Fe3+ electron spin flips. By
comparing these results to the results of similar studies of vessels containing Rb,
we will gain further insight to the relaxation mechanisms in spin-exchange cells.
94
This will lead to more consistent production of quality vessels and more efficient use
of the spin-polarized gas.
We acknowledge helpful discussions with R. K. Mazitov, M. Conradi, and W.
Happer, and we are grateful for the expert glassblowing of J. Kyle. This work was
funded in part by Amersham Health.
CHAPTER 7
3He RELAXATION IN BARE AND
Rb-COATED GLASS
7.1 Abstract
By studying the temperature dependence of 3He relaxation in various cells, we
show that 3He relaxes in cells containing an alkali metal for spin-exchange optical
pumping by a different mechanism than in bare vessels, containing no alkali metal.
Dissolution into the glass and adsorption to the glass provide dominant relaxation
mechanisms in bare Pyrex vessels, but dissolution-dominated relaxation is virtually
nonexistent in the presence of Rb. Thus, lower than expected polarizations (50% vs.
80%) cannot be attributed to increased wall relaxation rates at high temperatures
required for spin-exchange. In addition, we observe that adsorption relaxation is
dominate in bare aluminosilicate cells at our temperatures of interest. By contrast,
adsorption relaxation is dominate in bare quartz vessels only at temperatures above
about 120 K.
7.2 Introduction
3He wall relaxation times in spin-exchange cells can vary from 10s of minutes to
100s of hours, and very little is understood about the wall relaxation mechanisms.
By studying the temperature dependence of relaxation rates in bare glass (no alkali
metal or surface coatings) we hope to better understand wall relaxation mechanisms
96
and the role that alkali metals play in inhibiting relaxation. Bare Pyrex has already
been investigated (see Chapter 6), so in this chapter we show results of similar
studies on bare aluminosilicate, bare quartz, and Rb-coated Pyrex. The ultimate
goal is to apply an understanding of the basic physics of 3He wall relaxation to the
consistent fabrication of long-lifetime spin-exchange cells.
The 3He polarization during optical pumping is given by Eq. (1.1). We estimate
that 〈PA〉 can be maintained at near 100% under our SEOP conditions [14]. Using
a measured spin-exchange rate at 180C [26] and the saturated vapor pressure curve
for Rb [13], the maximum attainable 3He polarization in a typical 40 h cell is about
80%. There are no reports in the literature of 3He polarizations achieved with
SEOP over about 50%. This polarization deficit remains unexplained at present,
but it has been speculated that it may be due to increased wall relaxation times at
spin-exchange temperatures. We show in Chapter 6 that relaxation rates in bare
Pyrex do, in fact, increase exponentially with increasing temperature. In this paper
we show that the same phenomenon does not occur in spin-exchange cells and cannot
account for the polarization deficit.
7.3 Theory
7.3.1 Aluminosilicate Glass
In the quest to find a suitable glass for the consistent and reliable production of
spin-exchange cells, much attention has been paid to aluminosilicate glass because
of its low permeability. Aluminosilicate glass is several orders of magnitude less
permeable to He than Pyrex [77] but suffers from lower availability and workability.
In spite of the low permeability, only limited success in making long-lifetime cells has
been realized with little evidence that it can be used to consistently produce spin-
exchange cells with lower relaxation rates than Pyrex. Aluminosilicate is greatly
97
advantageous in some applications that require low-boron, low-permeability glass
[87].
We can apply the relaxation model derived for bare glass in Chapter 6 to bare
aluminosilicate cells. The very high activation energy of diffusion (see Table 7.1)
should cause the room-temperature relaxation rate to be quite small. Applying
permeation and diffusion measurements made on Supremax glass (an aluminosilicate
glass) shown in Table 7.1 to Eq. (6.19), we calculate an activation energy EA =
29.6 ± 1.1 kJ/mol. Assuming an iron content similar to Pyrex [18, 88] and a cell
with A/V = 1, we approximate a room-temperature relaxation rate of 5× 10−5 h−1,
about 103 times smaller than bare Pyrex. Such relaxation rates have not been
observed in aluminosilicate cells, although the rates are generally somewhat lower
than bare Pyrex. Gentile et al. reported a relaxation time in a bare, 40 cm3, sealed
GE-180 cell of 6 h and in 1720 (Corning) as high as 72 h [44]. Other workers have
Table 7.1.Important values for Eqn. (6.18) for aluminosilicate glass.
Variable Value Uncertainty Units Ref
D0 1.8× 10−3 0.3× 10−3 cm2/s [80]
ED 56.9 1.0 kJ/mol [80]
S0 3.1× 10−3 0.5× 10−3 cm3 STP/cm3 [80]
ES 2.8 1.0 kJ/mol [80]
τFe(295K) 0.77× 10−8 s [18]
τ0 1.9× 10−9 10% s
EFe −3.4 0.3 kJ/mol [18]
98
reported times in 1720 ranging from about 6 h to about 30 h [17, 19, 76]. It is likely
that another, undetermined relaxation mechanism masks any absorption relaxation
that occurs at room temperature, thus causing the lower than expected relaxation
times. However, it has been shown that GE-180 cells that contain Rb can have very
long lifetimes: a 0.85 atm cell had a measured lifetime of 840 h [87].
The activation energy of adsorption of He on alumonosilicate should be similar
to that of Pyrex, as the principal constituent of both glasses is SiO2. Because of
the much higher EA for aluminosilicate, we anticipate that the transition tempera-
ture between absorption and adsorption relaxation, reflected as a minimum of the
relaxation rate in a plot of T−11 vs. temperature, should occur at a somewhat higher
temperature than the ≈ 200 K for Pyrex. By adding Eqs. (6.18) and (6.24) we have
a general equation for relaxation at all temperatures:
1
T1
(T ) =A
V%0 exp
(− EA
R T
)+ κ0 exp
(−2Ead
R T
)√T . (7.1)
By setting the first derivative of Eq. (7.1) with respect to T equal to zero then solving
for T , we can predict the transition temperature between absorption and adsorption
relaxation. By using the same value of %0 for aluminosilicate that was calculated
for Pyrex, since S0, D0 and N are approximately the same (GE-180 contains 0.02%
iron oxide by weight [88], which is approximately the same concentration as Pyrex,
if not slightly lower [18]), and using the measured values of Ead and κ0 in Pyrex,
we estimate that the transition temperature for aluminosilicate to be ≈ 300 K.
This temperature may be too high for us to clearly see absorption relaxation in our
temperature range, but adsorption relaxation should be easily observed.
99
7.3.2 Quartz Glass
Quartz glass is about an order of magnitude more permeable to He than Pyrex
at room temperature [83], but the iron content is far lower. To predict relaxation in
quartz, we can assume two limits: no contribution to relaxation from iron (iron-free
quartz) and iron-dominated relaxation (enough iron in the glass to dominate relax-
ation). In the zero-iron-content limit, the dominant bulk-glass relaxation mechanism
T1 b will be from interactions with unpaired electrons from broken SiO2 bonds, which
have a spin-flip correlation time of about 1.6× 10−7 s [18]. The correlation time
for diffusion is τD = r2/6D(T ) ≈ 4× 10−9 s at room temperature, where r is the
average jump distance of≈ 2.5 A [18] and D(T ) was measured to be about 2.2× 10−8
cm2/s at room temperature [89]. The 3He relaxation would be dominated by the
mechanism with the shorter correlation time: 3He diffusion in the glass. Using Eq.
(6.9), it can be shown that T−11 would depend only on the temperature-dependent
3He solubility S(T ). The activation energy of solution in quartz is negative (see
Table 7.2), implying that the relaxation rate of 3He in quartz would decrease with
increasing temperature for all temperatures. In the second limit, the correlation time
for Fe3+ electron spin flips would dominate relaxation and the expression derived for
Pyrex glass would be applicable. Using values shown in Table 7.2, we calculate the
activation energy EA = 7.2 ± 0.4 kJ/mol and a room-temperature relaxation rate
of approximately 3× 10−2 h−1 for a cell with A/V = 1. The resulting temperature
dependence for absorption relaxation would be qualitatively similar to that of Pyrex.
GE fused silica, the glass we used, has an iron content of 0.2 ppm by weight [90]. If,
due to the low, but nonzero, iron content, we are in a regime where both mechanisms
contribute to T1 b then we would expect to see an activation energy somewhere
between ES and EA.
Assuming that Ead will be similar for quartz and Pyrex and that the limit in
100
Table 7.2.Important values for Eqn. (6.18) for fused silica.
Variable Value Uncertainty Units Ref
D0 3.0× 10−4 cm2/s [89]
ED 23.4 0.2 kJ/mol [89]
S0 7.3× 10−3 cm3 STP/cm3 [89]
ES -2.9 0.3 kJ/mol [89]
τFe(295K) 0.77× 10−8 s [18]
τ0 1.9× 10−9 10% s
EFe −3.4 0.3 kJ/mol [18]
which iron dominates relaxation is correct, then we would expect to see a transition
between absorption and adsorption relaxation at a temperature somewhat lower
than the 200 K for Pyrex, due to the much lower EA for quartz. Since the iron
content of fused silica is ≈ 103 times smaller than for Pyrex, we estimate that %0
will be lower by a factor of about 30 and κ0 will be lower by a factor of about 103.
Using Eq. (7.1) we predict a transition temperature of ≈ 90 K, possibly too low for
us to see. If the broken-bond model is correct, then there may be no discernable
transition since both regimes would have small, negative activation energies. If there
are contributions to relaxation from both models, then a transition temperature
would be very difficult to predict, but would still be expected to be below that of
Pyrex due to the much lower EA.
101
7.3.3 Rb-coated Pyrex Glass
The effects of the presence of an alkali metal on 3He relaxation are not well
understood but are critical to wall relaxation times in spin-exchange cells. It has
been shown that the presence of an alkali greatly decreases the room temperature re-
laxation rate over bare cells of several types of glass [17, 19, 20, 45], and that a visible
coating of other pure metals can be very polarization friendly (i.e., nonrelaxive) [20].
Alkali metals are especially favorable because the loosely bound conduction electrons
prevent He, and other noble gases, from readily adsorbing [91]. Thus, alkali metals
have a very weak attractive potential for He adsorption [92]. More specifically, Heil
et al. show that the wall relaxation rate is proportional to the cube of the work
function of the metallic surface [6], thus alkali-metal surfaces, especially Rb and Cs
with relatively low work functions of 2.26 eV and 1.95 eV, respectively [75], result
in very long relaxation times. However, in spin-exchange cells it is not expected
that the alkali metal forms a perfect metallic surface in the entire cell. Therefore,
surface chemistry between the glass and alkali may also affect 3He relaxation by
altering the ability of the 3He to interact with iron ions. It is possible, for example,
that the alkali metal atoms block interstitial holes into which 3He could otherwise
diffuse [77], thereby inhibiting absorption relaxation. Unfortunately, relatively little
is known about the chemical effects of alkalis on Pyrex, other than that Corning,
the makers of Pyrex, warn consumers that hot alkalis will etch the surface [93].
7.4 Experimental
All of the cells tested were spherical, valved, and approximately 50 cm3. The
Pyrex spin-exchange cells and the quartz cells were fabricated by the University of
Utah glass blower, and the aluminosilicate cells were fabricated by the glass blower
at Princeton University. All cells were prepared and measured at Utah (see Chapter
102
4 for our cell fabrication and preparation techniques). No Rb was distilled into the
quartz and aluminosilicate cells, so they were prepared on a truncated manifold.
We note that the stem of the quartz cells consisted of a ≈ 2.5 cm length of quartz,
a graded seal, and a ≈ 2.5 cm length of Pyrex for the pull-off. The spin-exchange
cells contained ≈ 8 atm of 3He, and the bare cells contained ≈ 4 atm. Polarized gas
was introduced into the bare aluminosilicate and quartz cells using a gas-transfer
manifold (see Fig. 5.2) attached to our cell-filling system, which provided a nitrogen-
gas purge and vacuum. Gas was transferred by attaching an empty cell and a
spin-exchange cell, opening the cell valves, allowing the pressure to equilibrate, and
closing the valves. Several T1 measurements could be made on a single charge of gas.
All measurements were made at 30 G using the 100 kHz pulse NMR spectrometer
described in Chapter 2 and an RF coil on the cell stem (see Fig. 4.1). The initial
heights of the free-induction decays acquired at appropriate time intervals were fit
to a single exponential to extract T−11 . Very small flip angles were used to excite a
fraction of the gas in the stem for minimal global polarization destruction. Above-
room-temperature measurements were made in the oven normally used for heating
spin-exchange cells for SEOP, and the temperature was maintained to within a few
tenths of a degree by a resistive temperature detector and controller. Below-room-
temperature measurements were made in an insulated aluminum cylinder attached
to a liquid nitrogen dewar. The cell was cooled by boiling off the nitrogen with
heating tape submerged in the dewar controlled by a variable AC transformer. The
temperature was monitored using a thermocouple and maintained to within a few
degrees. During all measurements the cell valve was kept at room temperature to
prevent o-ring failure.
103
7.5 Results and Discussion
7.5.1 Aluminosilicate Glass
7.5.1.1 T > Room Remperature
Figure 7.1 shows a plot of T−11 vs. 1000/T for two bare aluminosilicate (GE-180)
cells for temperatures from room temperature up to about 460 K. The data do
not follow the form of Eq. (6.18), suggesting that diffusion through the glass may
not be a dominant mechanism of relaxation in this temperature range, consistent
with expectations. Perhaps these data represent the transitional regime between
adsorption- and absorption-based relaxation predicted in Sec. 7.3.1 to be around
300 K. In addition, the room temperature relaxation rate is comparable to bare
Pyrex, contrary to the prediction but consistent with the findings of other workers
0.10
0.15
0.20
0.25
2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4
Al1B
Al1A
T1-1
(h
ou
rs-1
)
1000/T (K-1)
Figure 7.1. Relaxation rate vs. 1000/T for two bare aluminosilicate (GE-180) cellsfor T ≤ 300 K. The cells were at ≈ 4 atm, and polarized gas was transferred in froma spin-exchange cell. The data show an apparent lack of dissolution-dominatedrelaxation, as expected for this very impermeable glass.
104
using various types of aluminosilicate glass [17, 19, 20, 44]. The cause of the much
lower than predicted relaxation rates in bare aluminosilicate is not understood.
7.5.1.2 T < Room Temperature
Figure 7.2 shows T−11 vs. 1000/T data for the same two cells shown in Fig.
7.1 for temperatures from about 100 K to room temperature. The solid line is a
best global fit of Eq. (6.24) to all the data and the dashed line represents the bare
Pyrex results from Chapter 6. The measured activation energy for adsorption on the
aluminsilicate is Ead = −0.69±0.05 kJ/mol. By comparison, the result for Pyrex was
Ead = −0.63 ± 0.03 kJ/mol. The excellent agreement between the aluminosilicate
10-2
10-1
100
3 4 5 6 7 8 9 10 11
Al1B
Al1A
Pyrex
T1-1
(h
ou
rs-1
)
1000/T (K-1)
Figure 7.2. Relaxation rate vs. 1000/T for two bare aluminosilicate (GE-180) cellsfor T ≥ 300 K. The cells were at ≈ 4 atm, and polarized gas was transferred fromspin-exchange cells. A global fit (solid line) of Eq. (6.24) gives Ead = −0.69± 0.05kJ/mol. For comparison, bare Pyrex data from Chapter 6 is plotted with a fit tothe same equation (dashed line). The similarity in the activation energy, reflectedby the slope of the lines, indicates that the relaxation mechanism in these cells issimilar to that in the bare Pyrex cells.
105
and Pyrex results strongly suggests that the same relaxation mechanisms dominate
in the different types of glass in this temperature regime. The difference in intercept
could be due to different concentrations of Fe3+ ions at the surface [although GE-180
has somewhat less iron than Pyrex (see Sec. 7.3.1)] or to differences in surface to
volume ratio. Little is known about microscopic surface smoothness of the different
types of reblown glass, although atomic force microscopy studies are currently being
done [78].
We note that the room-temperature T−11 measurements in Fig. 7.2 are about a
factor of two different from those in Fig. 7.1. The sets of data were taken with two
different charges of gas for each cell (polarized gas was transferred into the cells from
spin-exchange cells at room temperature), with the above-room-temperature data
taken first. The first charge of 3He was evacuated prior to the second introduction
of polarized gas. The dramatic drop in relaxation rate after the second charge
of gas is a mystery, but could be due to trace amounts of Rb atoms that were
transferred in with the polarized 3He (≈ 1018/cm3 at room temperature [13]). These
Rb atoms may have neutralized relaxive surface sites by reducing Fe3+ ions to Fe.
We showed in Chapter 3 that the 3He relaxation rates are certainly very sensitive
to the concentration of relaxation sites, and 3He may be sensitive enough to detect
such slight changes in Fe3+ surface concentrations.
7.5.2 Quartz
Figure 7.3 shows T−11 vs. 1000/T for two bare quartz cells for temperatures
ranging from about 100 K to 460 K. Neither cell shows relaxation characteristic
of the iron-free model. The data appear to support the iron relaxation model, as
the activation energy of relaxation is positive in most of the temperature range. For
these cells, the average activation energy is EA = 2.5±0.2 kJ/mol. This is somewhat
106
10-1
100
2 4 6 8 10 12
Q4A
Q4B
T1-1
(h
ou
rs-1
)
1000/T (K-1)
Figure 7.3. Relaxation rate vs. 1000/T for two bare quartz (GE fused silica) cells at≈ 4 atm. Polarized gas was transferred into these cells from spin-exchange cells. Thesolid lines represent fits of Eq. (6.18) to the data for which absorption dominates,above about 130 K. The data were taken in two segments: above and below roomtemperature. For reasons that are not clear, the behavior of Cell Q4B above roomtemperature is inconsistent, and these data were not included in the curve fit. Theaverage activation energy EA for both cells is 2.5 ± 0.2 kJ/mol. A minimum inT−1
1 is apparent at ≈ 120 K, where there is a transition between absorption andadsorption relaxation, close to the predicted value of ≈ 90 K.
lower than the predicted value of 7.2 kJ/mol in the iron-dominating limit. Perhaps
the low iron concentration is allowing the two regimes to compete. Figure 7.3 shows
a minimum in T−11 occurring at about 120 K, where there is a transition between
absorption and adsorption relaxation. This temperature is lower than we saw in
Pyrex, as anticipated, and is very close to the transition temperature of about 90 K
predicted in Sec. 7.3.2. It may be interesting to repeat this experiment with a very
high purity quartz, such as Suprasil, to see if the broken-bond model can be verified.
As an aside, we note that the room temperature relaxation rates for bare quartz
are rather short. We have seen relaxation times as long as about 30 hours in Rb-
107
coated quartz, and Heil et al. have seen similar times in a quartz cell containing Cs.
These relaxation times are not as long as those for most alkali-coated Pyrex cells,
indicating that the glass still plays an important relaxation role in alkali-coated cells.
Section 7.5.3 discusses relaxation in Rb-coated cells in greater detail.
7.5.3 Pyrex Glass
We measured the relaxation rates for several Rb-coated Pyrex cells in the temper-
ature range 393 K to 295 K (see Fig. 7.4). It is difficult to measure accurately T−11
at higher temperatures, because spin-exchange interactions with the alkali metal
will dominate 3He relaxation. Spin-exchange rates are difficult to calculate since
10-3
10-2
2.4 2.6 2.8 3.0 3.2 3.4
K1B
9B
15B
18A deg'd
1000/T (K-1)
T1-1
(ho
urs
-1)
Figure 7.4. Wall T−11 measurements of several spin-exchange cells for T > 295 K.
All of the cells contain Rb except for cell K1B, which contains potassium. He–Hedipole relaxation and spin-exchange relaxation rates have been subtracted from thedata. The cells with the smallest wall rates show some temperature dependence, butthis dependence becomes less apparent in shorter T1 cells. The cells do not displaybehavior modelled by Eq. (6.18), which was derived for bare Pyrex.
108
Rb number densities are not always understood and we currently have no method
of direct measurement. We approximated the Rb number density using the vapor
pressure curve presented by Killian [13]. As shown in Fig. 7.4, no single, consistent
relaxation mechanism seems to dominate spin-exchange cells. Cell K1B, which
contains potassium (all other cells contain Rb), has a strong increase in T−11 with de-
creasing temperature, an effect directly opposite to that predicted by the bare-Pyrex
dissolution model. Cell 9B has a weaker temperature dependence, but also opposite
to that of the bare-Pyrex model. Cell 18A has a slight temperature dependence
which is absent when the cell is magnetized (with a room temperature relaxation
rate of about 0.35 h−1). Cell 15B behaves differently from all the other cells with an
apparent local minimum in T−11 somewhere between about 350 K and 300 K, similar
to what is predicted for aluminosilicate glass (see Sec. 7.3.1). Cells 6A and 18A when
magnetized (not shown in Fig. 7.4) were also measured in the same temperature
range, and they showed no temperature dependence whatsoever; each had a room
temperature relaxation rate of about 0.35 h−1. These two cells and the bare cells
discussed in Chapter 6 had similar relaxation rates at ≈ 380 K but very different
behaviors with changing temperature: the bare cells’ T−11 ’s followed Eq. (6.18) while
6A and 18A (magnetized) had T−11 s independent of temperature. It appears from
Fig. 7.4 and cells 6A and 18A (magnetized) that the shortest-lifetime cells show
the least temperature dependence, suggesting that temperature dependence can be
masked by faster wall relaxation mechanisms.
The data in Fig. 7.4, when compared to Fig. 6.1, suggest that the alkali metal
strongly inhibits dissolution of 3He into the glass. It appears that adsorption-like
relaxation is especially significant in cell K1B whose T−11 increases dramatically as
the temperature decreases. To be consistent with the adsorption model in Eq. (6.24),
the activation energy of adsorption for cell K1B would have to be much lower than
109
that of bare Pyrex. A fit of the K1B data to Eq. (6.24) gives Ead ≈ −6.7 kJ/mol,
which is significantly more attractive than the −0.63 kJ/mol we measured for bare
Pyrex. Data for cell 9B gives Ead ≈ −1.3 kJ/mol. This is much weaker than Ead for
K1B, but still significantly stronger than for the bare Pyrex. Because He is so weakly
adsorptive to alkali metals, we hesitate to attribute wall relaxation in alkali-coated
cells to a mechanism that appears so strongly adsorptive and easily masked by faster
mechanisms. We have presented models for two potential relaxation mechanisms
that can be temperature-dependent through the gas diffusion coefficient D. It can
be shown that D ∝ T 3/2 for a dilute ideal gas [94]. The two models are T1 hysteresis
[see Eq. (3.1)] and magnetic field gradient relaxation [see Eq. (1.6)]. Magnetic field
gradients cause T1 ∝ 1/D, which results in behavior opposite to what is observed
in Rb-coated cells. However, the T1 hysteresis model predicts relaxation due to
magnetic sites with T1 ∝ D, which gives a temperature dependence qualitatively
consistent to what is observed. Magnetic sites that are not thoroughly degaussed or
are slightly aligned by the 30 G SEOP field could, therefore, be the major cause of
3He relaxation in the longest-lifetime cells. Whatever the cause of relaxation, our
results strongly indicate that increases in wall relaxation rates at high temperatures
are not responsible for the low (≤ 50%) 3He polarizations that we achieve.
We, along with other researchers [14, 73, 78], desire to know how the Rb interacts
with the glass in order to gain a better understanding of relaxation mechanisms in
spin-exchange cells. It was shown in Chapter 3 that Rb has the effect of reducing
the relaxation rate by a factor of 10 or more vs. the T−11 measured in the same cell
before Rb was introduced. Other workers have demonstrated a similar phenomenon
[19, 20]. By comparing the temperature-dependence data from Chapter 6 and Secs.
7.5.1 and 7.5.2 to alkali-coated cells in Fig. 7.4, it appears that the presence of
the Rb inhibits dissolution relaxation significantly, if not completely. We suggest
110
five possible explanations for this: (1) The Rb acts to block sites into which the
3He might dissolve by fitting into the “holes” of the irregular glass lattice; (2) The
Rb reduces the Fe3+ ions at or near the surface to less-relaxive Fe; (3) The Rb,
which is known to etch Pyrex, creates a new, amorphous layer on top of the glass
substrate; (4) Rb oxides could form at the surface from residual oxygen in the glass;
(5) The Rb forms a thin, metallic coating over most of the glass, which would be
very nonrelaxive to polarized 3He.
First, if the Rb blocks diffusion of 3He into the glass, disrupting the otherwise
dominant relaxation mechanism of interactions with Fe3+ ions in the bulk of the
glass, then a significant decrease in T−11 would be expected. The one cell containing
K in Fig. 7.4 had a much stronger absorption-like temperature dependence then
the cells with Rb, suggesting even less dissolution is occurring in this cell than the
others. Perhaps the smaller K atoms are more effective than the Rb at entering
the glass matrix and, therefore, are more effective at blocking dissolution of 3He.
Altemose [85] demonstrated that addition of any alkali oxide to a simple borosilicate
glass increased the activation energy of permeation and diffusion to He significantly,
while the activation energy of solubility was only weakly affected. Not all alkalis had
equivalent effects: he showed that as the diameter of the alkali ion was increased, the
activation energy of permeation at room temperature decreased until the alkali was
as large as Rb+. The addition of Rb or Cs had the effect of increasing the activation
energy when compared to K (or Na, but not Li). He proposed that K+ fits very well
into the holes of the irregular glass network, while Rb+ and Cs+ are large enough
to actually spread the glass network slightly. Although we added the alkali after
the glass was fabricated (Altemose added an alkali oxide prior to fabrication), it is
still reasonable to assume that the alkali was able to enter the glass network to the
depth of perhaps a few nm. The result would not be a totally impermeable surface,
111
so this possibility could only be a contributing factor.
Second, if the Rb reduces the relaxive Fe3+ ions to Fe at the surface and some
depth into the glass, then a significant relaxation mechanism will be diminished.
This possibility is effectively equivalent to the first since they both inhibit the ability
of the 3He to interact with relaxive Fe3+ ions. In Chapter 6 we showed that the
magnetization penetration depth in Pyrex is about 30 nm. It is unlikely that the Rb
is able to reduce Fe3+ ions to such a depth. The radius of a Rb+ ion is about 1.7 A
and the average hole diameter in the glass lattice is about 3 A [18], thus making
it difficult for the large Rb atoms to diffuse deeply into the glass. Therefore, this
possibility could also only be a contributing factor.
Third, it is possible that the result of the alkali reacting with (etching) the glass
is the formation of a thin, relatively impermeable, amorphous layer coating the cell.
As stated above, the insertion of an alkali during glass formation may fill random
holes in an irregular glass structure, reducing the He permeation rate significantly. If
a Rb-rich amorphous layer is formed during the initial interaction of the Rb with the
glass, then the layer would be significantly less permeable than the Pyrex substrate,
resulting in a longer-lifetime cell. This thin layer would also form a protective layer
to inhibit further etching by the Rb. In a separate experiment, we measured the
relaxation rate in each of several cells three times: first bare, then with Rb, finally
with the Rb rinsed out (see Sec. 8.5.2). We found that the rinsed cells had a marginal
improvement in T−11 vs. the original bare cells (typically a factor of ≈ 2 improvement
compared to the the factor of ≈ 10 when the Rb was still present). This suggests
that, if such a layer is formed, it is not solely responsible for the observed decrease
in relaxation rates in Rb-coated cells. We note that the cells showed T1 hysteresis
both after the Rb was introduced and after the Rb was rinsed out, whereas before
the introduction of Rb they did not. In addition, two of these cells were rinsed
112
with HCl after the Rb was rinsed out, then additional Rb was distilled in. The cell
relaxation rates exhibited only slight changes before and after the HCl rinse, possibly
suggesting that the acid was not effective in affecting the Rb-exposed glass. Further
experiments to reveal chemical changes to the glass surface would be necessary to
form any conclusions.
Fourth, we have already shown that Rb oxides are very nonrelaxive (see Sec.
4.12). The presence of such oxides in regular spin-exchange cells has been observed,
since the dark, nonmetallic oxides are often seen in cells that have been sitting on the
shelf for several weeks or months. Such oxides at the surface would act as a physical
barrier which might inhibit the permeation or adsorption of 3He thus reducing the
measured relaxation rate somewhat.
Fifth, a metallic coating of Rb on the glass surface would inhibit permeation and
adsorption. A metallic layer should be very nonrelaxive because they are weakly
adsorptive to 3He; an alkali metal surface is the most inert to noble gas adsorption
[91]. Heil et al. showed that a coating of Cs, the alkali metal with the largest atomic
radius, is very effective at inhibiting 3He relaxation [20]. A metallic layer can be as
thin as <1 monolayer, as long as the electron wave functions overlap. The formation
of a thin, continuous metallic layer would require a smooth glass surface and for the
adsorbed alkali be in equilibrium with the vapor. As the vapor pressure increases,
surface wetting occurs and may enhance the metallic layer thereby improving the
measured T−11 . A spin-exchange cell with a perfectly smooth surface would have very
favorable relaxation characteristics, but slight surface imperfections or impurities
would cause breaks in the metallic layer allowing for interactions of the 3He with
the glass [95]. Also, large magnetic sites may protrude through the layer and cause
relaxation.
It is certainly possible that all five phenomena occur in a cell to varying degrees.
As the first four phenomena are independent of cell geometry and probably occur
113
relatively equally in all cells, the best spin-exchange cells are probably those with
the smoothest, cleanest surface and therefore the best metallic coating. The number
of magnetic sites also plays a key role, and we believe that a very few sites can make
the difference between a long- and short-lifetime cell. In Chapter 3 we predicted
that ≈ 4× 104 sites occupy a typical cell, and cell-to-cell variation of a factor of two
is easy to imagine. Since that number is beyond our control during cell fabrication
and cell smoothness may or may not be a function of how the cells are blown, the
overall wall relaxation properties may be beyond control. One can only maximize
the chances of making a quality call through good preparation practices, which we
have detailed in Chapter 4.
7.6 Conclusion
We have shown that the presence of Rb in spin-exchange cells significantly inhibits
relaxive interactions of 3He with the glass surface and bulk glass by preventing 3He
from dissolving into the glass or adsorbing to the glass, contributing significantly to
long relaxation times observed in Rb-coated cells. Importantly, temperature depen-
dent changes to wall relaxation rates do not contribute to low polarizations achieved
during SEOP. We have also shown that interactions of dissolved 3He with Fe3+
ions in fused silica is a significant relaxation mechanism and that dissolution-based
relaxation is not significant in GE-180 cells at room temperature. The low observed
relaxation time in GE-180 cells indicates that mechanisms other than absorption
dominate the relaxation at the temperatures studied. The results of these studies
will help in the search for a quantitative understanding of relaxation in spin-exchange
cells, hopefully resulting in a better understanding of effective cell fabrication and
preparation protocols.
CHAPTER 8
CELL RINSING
8.1 Abstract
We show that rinsing cells with acids is not effective in eliminating T1 hysteresis
or in improving cell relaxation times. In fact, cells rinsed with acid tend to have
lower than average relaxation times and exhibit T1 hysteresis more strongly than
unrinsed cells. Also, we provide evidence in separate experiments that the magnetic
sites responsible for T1 hysteresis originate in the glass and are not brought in by
the Rb. In one experiment we rinsed cells with a chemical reducing agent, and in
another experiment we removed the Rb from cells. In both cases, T1 hysteresis was
observed.
8.2 Introduction
In Chapter 3 we showed that ferromagnetic sites at or near the surface of the
cells can be a major source of relaxation in spin-exchange cells. A key goal in our
work and the work of others [78] has been the elimination of such sites, which would
be a significant step towards consistent production of very long lifetime cells that
never require degaussing. However, since degaussing has proven to be reliable and
effective, a reasonable alternative is producing very long lifetime cells that may need
periodic degaussing. This chapter addresses several of our efforts to either eliminate
the sites or improve our cell preparation protocol.
115
The production of long-lifetime cells requires an understanding of physical phe-
nomena of 3He interactions at the cell surface. We have repeatedly shown in this
thesis that the basic model of relaxation, Eq. (1.9), does not accurately describe
3He relaxation. While other chapters of this thesis have addressed the dependence
of T1 on external parameters, such as temperature or magnetic field, this chapter
addresses effects of altering the interior surface of cells with three specific goals:
first, to investigate the origin of the magnetic sites, which should make it easier to
eliminate them; second, to eliminate T1 hysteresis by eliminating the magnetic sites;
third, to develop a method of producing consistently long-lifetime cells in spite of
T1 hysteresis effects.
It has often been suggested that we rinse cells with acid to accomplish the second
goal. We have generally had poor results using cells rinsed with acids. Specifically,
cells we rinsed with HF were particularly poor and had magnetized T−11 ’s higher
than their unmagnetized or degaussed T−11 ’s by factors of 20 to 100, far greater
than the typical factor of ≈ 2 for unrinsed cells. Other acids, such as nitric acid,
have been tried by B. Saam and T. Gentile [73], with mixed results. We have found
that acids do not remove T1 hysteresis-causing iron sites, but often enhance the
effect, possibly by exposing additional sites by etching the glass.
8.3 Theory
Iron and its oxides are known impurities in Pyrex at a concentration of ≈ 0.04%
by weight [18]. Our hypothesis for the origination of T1 hysteresis is that small
clusters of iron oxides (Fe2O3) may be distributed homogeneously throughout the
glass. Clusters that end up at the surface of a cell and are exposed to Rb may be
reduced to bulk iron, forming multidomain magnetic sites. This is plausible because
the energy required to reduce Fe3+ to Fe2+ is 0.77 eV and to reduce Fe2+ to Fe is
116
−0.45 eV, while the Rb oxidation potential is 2.93 eV [96]. That is, Fe3+ accepts an
electron if 0.77 eV is donated with it, whereas Fe2+ accepts two electrons and returns
0.45 eV. These sites, when magnetized, have a dramatic effect on wall relaxation of
polarized 3He. To achieve the goal of consistently producing robust, long-lifetime
spin-exchange cells for magnetic resonance imaging, it is desirable to remove the
iron clusters without any adverse effects on the wall relaxation rates. In theory,
the use of a gentle acid rinse to dissolve a significant number of sites would result
in long-lifetime cells that do not exhibit T1 hysteresis. If the surface of the glass is
etched, however, the resulting increase in surface area and/or exposure of additional
sites may result in very short lifetime cells.
Other rinsing techniques employed in this chapter were done to study the cell
surface by observing 3He relaxation rates. As stated above, we believe that the Rb
acts as a reducing agent on Fe3+ ions already in the glass. The use of a chemical
reducing agent can provide evidence both that the iron originates in the glass and
that the Rb reduces Fe3+ to Fe. A bare cell can be rinsed with a reducing agent such
as decamethylcobaltocene (DMC) [97] and tested for T1 hysteresis using polarized
gas that is transferred into the cell. The oxidation potential of DMC is 1.47 eV
[98], more than sufficient to reduce Fe3+. A second technique is to rinse Rb out of a
cell and measure the relaxation characteristics of HP 3He in the resulting bare cell.
Thus, effects that the Rb has on the glass surface may be detected. For example,
if the magnetic sites are brought in with the Rb, then it is reasonable to assume
that they should be rinsed out with the Rb, and the T1 hysteresis would vanish. Or,
if Rb etches the glass in a manner that exposes additional surface area, then the
relaxation rates in a rinsed cell should be faster than in the same cell before Rb is
introduced.
Another approach is to ignore the magnetic sites, since cells can be degaussed
117
if needed, and concentrate on techniques for making the longest lifetime cells.
Compared to many other types of glass, Pyrex is quite permeable to He [77], so
limiting diffusion of 3He into the bulk of the glass will limit relaxation due to
interactions with paramagnetic impurities such as Fe3+. It has been shown that
alkali-rich borosilicate glasses are less permeable to He than Pyrex by an order
of magnitude or more [83]. Further, it was demonstrated that potassium, among
all alkalis, fit best into the interstitial gaps of the amorphous glass structure, thus
inhibiting He diffusion most effectively [85]. Two of the best spin-exchange cells that
we ever produced contained K instead of Rb. Therefore, it is possible that treating
the cells with K prior to introducing Rb will result in very long-lifetime cells.
8.4 Experimental
We tested Pyrex cells, both Rb-coated and bare (not containing Rb). Cells that
contained Rb were prepared according to our usual methods outlined in Chapter
4. Bare cells were prepared as usual, but the Rb distillation steps were skipped.
Polarized gas was transferred into the bare cells using the gas transfer manifold
discussed in Chapter 5 (see Fig. 5.2). All T−11 measurements were made using
100 kHz pulse NMR detection (described in Chapter 2) at ≈ 30 G. Very small
flip angles, delivered through a coil on the cell stem (see Fig. 4.1), were used
to minimize magnetization destruction. Relaxation rates were typically measured
in three situations: unmagnetized, magnetized, and degaussed. As in Chapter 3,
unmagnetized refers to a newly fabricated cell that has not previously been exposed
to a high magnetic field. A magnetized cell has been exposed to a high magnetic
field (typically ≈ 104 G) of an electromagnet, and a cell is degaussed by exposing
it to an oscillating, decreasing magnetic field. The set of three measurements was
usually done with no intervening heating of the cell or exposure to laser light. The
118
cells were transported to and from the electromagnet in a battery-powered solenoid
to prevent polarization loss.
Acid and DMC rinses were done after cell fabrication but prior to attaching
the cell to a manifold. With the valve removed, the rinse could be easily added
and drained through the stem, after which the cells were thoroughly rinsed with
deionized water. The three acid solutions used were 10% HF, 37% HCl, and Aqua
Regia (3 parts HCl, 1 part HNO3).
Some cells were tested bare, but after containing Rb. To rinse Rb out of a cell,
the pressure was relieved, the valve was removed, and the tip of the cell stem cut
off. The Rb was allowed to react with the room air until it was no longer volatile.
Ethanol was then added through the stem and the cell thoroughly rinsed several
times. The cells were reattached to a manifold for evacuation and baking prior to
the introduction of HP 3He. We assumed that the reactions of the Rb with air or
the ethanol did not affect the glass surface.
8.5 Results/Discussion
8.5.1 Reducing-agent Rinse
To test the hypothesis that Rb acts as a reducing agent in the cells by reducing
existing iron oxide clusters to bulk iron, we rinsed two cells, labelled 13A and 13B,
with DMC. The unmagnetized, magnetized, and degaussed relaxation rates are
shown in Fig. 8.1. Both cells show T1 hysteresis to a slight degree, but more so
than any of the several other bare, unrinsed cells that we have tested. For example,
when cell 11A was tested bare with no rinses and prior to introduction of Rb, it
showed no T1 hysteresis even though its relaxation rates were similar to those of cells
13A and 13B (see Fig. 3.3). Cell 13B had an especially fast relaxation rate, much
faster than predicted for bare Pyrex in Chapter 6 and faster than other bare cells
119
0.10
0.15
0.20
0.25
0.30
0.35
0.40
un
mag
mag
deg
13A
13B
T1-1
(h
ou
rs-1
)
Figure 8.1. Cells rinsed with a chemical reducing agent. Cells 13A and 13B wererinsed with DMC for several minutes after fabrication but prior to baking. Bothcells show T1 hysteresis, representing the only T1 hysteresis that we have observedin six bare Pyrex cells tested. Error bars are too small to see. These data supportthe hypotheses that magnetic sites are intrinsic to the glass and are not introducedby the Rb, and that the Rb acts as a reducing agent.
we have observed. If T1 hysteresis effects were masked in other bare cells by faster
wall relaxation mechanisms, then we expect that no hysteresis would be detected
in such a short-lifetime cell. These data support our hypothesis that the magnetic
sites originate in the glass, and that existing iron oxide sites are being reduced to
give rise to T1 hysteresis.
8.5.2 Rb Rinses
One method of investigating the effects of the presence of Rb on 3He relaxation
is to measure T−11 before and after Rb is rinsed from a cell. This may indicate
whether effects of the Rb (i.e., long wall lifetimes and T1 hysteresis) depend on the
presence of Rb. Figure 8.2 shows relaxation rates of three cells before and after
120
0.01
0.1
1
10
5B 11A StL
deg with Rbmag with Rbdeg rinsedmag rinsed
T1-1
(h
ou
rs-1
)
Figure 8.2. Relaxation rates for three different cells before and after Rb is rinsedout. Error bars are to small to see. The cell labelled StL was made by collaboratorsat Washington University. The three cells were measured both magnetized anddegaussed when they contained Rb and again after the Rb was rinsed out. Polarizedgas was transferred into the rinsed cells to make the measurements. The cellsgenerally have longer relaxation times when the Rb is present, but they still showT1 hysteresis when rinsed.
the Rb was rinsed out. Two important features are shown in the figure. First, the
degaussed relaxation times of the cells, represented by circles, are generally better
when the cells contained Rb (cell StL showed little change). Second, the rinsed cells
still magnetize, verifying that the Rb itself is not responsible for T1 hysteresis, and
suggesting that the magnetic sites that are responsible are permanently attached to
the cell. This is evidence against the sites having been introduced by the Rb during
distillation, and supports the idea that reduced iron oxide causes T1 hysteresis.
Figure 8.3 shows data from cell 11A only. The cell was measured prior to any
Rb distillation (bare), after Rb was distilled in, and after the Rb was rinsed out.
This figure emphasizes both the lack of T1 hysteresis before the addition of Rb and
121
10-2
10-1
100
un
mag
mag
deg
11A bare11A11A rinsed
T1-1
(h
ou
rs-1
)
Figure 8.3. Relaxation rates for cell 11A when bare (new, no Rb), with Rb, and withthe Rb rinsed out. Error bars are too small to see. Polarized gas was transferredinto the cell for measurements without Rb. When rinsed, the relaxation rate isbetter than the bare cell, but not as good when it contained Rb. This indicates thatchanges to the glass by the Rb are both friendly to polarized gas and permanent.
the dramatic reduction in T−11 after Rb was introduced. The significant difference
in T−11 between the bare and rinsed measurements indicates that rinsing a cell with
Rb alters the surface in such a way to make the cell less relaxive. This may include
filling the holes of the amorphous glass into which 3He would otherwise diffuse and
relax. As noted in Sec. 8.5.1, T1 hysteresis was measured in bare cell 13B in spite
of the very fast relaxation rate. The fact that cell 11A, when bare (open circles in
Fig. 8.3), did not show any measurable hysteresis indicates that magnetic sites were
not present or were not significant contributors to 3He relaxation. This is further
evidence that Rb acts as a reducing agent in creating magnetic sites.
122
8.5.3 Acid Rinses
8.5.3.1 HF Rinse
The first cells rinsed with acid, labelled 5A and 5B, were cylindrical with rounded
ends with a volume of≈ 35 cm3. These cells were rinsed with a 10% hydrofluoric acid
(HF) solution for several minutes after initial fabrication and prior to attaching them
to the manifold for preparation. As shown in Fig. 8.4, these cells had unmagnetized
relaxation rates of about 0.025 h−1 for 5A and 0.091 h−1 for 5B. We note that the
unmaganetized rate of 5B is uncharacteristically high compared to that of most other
cells we have made (see Fig. 4.6). We have no explanation for the large difference in
unmagnetized relaxation rates between the two cells, since the cells were fabricated
and prepared in exactly the same way and at the same time, but we have observed
similar discrepancies in other cell pairs. These cells were not particularly “good”
10-2
10-1
100
101
un
mag
mag
deg
5A
5B
T1-1
(h
ou
rs-1
)
Figure 8.4. T1 hysteresis of HF-rinsed cells. Error bars are too small to see. Cells5A and 5B were rinsed with a 10% solution of HF for a few minutes prior toRb distillation. Both cells have magnetized T−1
1 s significantly higher than whendegaussed, indicating that a higher than average number of magnetic sites werepresent. It is apparent that rinsing with HF is not beneficial.
123
(we loosely define a good cell as one with T−11 ≤ 0.025 h−1), and they magnetized
abnormally strongly, by factors of 20 to 100 compared to a more typical factor of
≈ 2. The magnetized T−11 of 5B, 10 h−1, is by far the highest relaxation rate we
have measured for any spin-exchange cell.
To further understand the relaxation of 3He in Pyrex exposed to HF, we prepared
several samples of flat, ≈ 1 mm thick Pyrex glass for atomic force microscopy (AFM)
studies. The samples differed from glass used to make our cells because they were
not “reblown” (see Sec. 4.5). Some samples were untreated and others were rinsed
with HF. The HF-rinsed samples were rinsed in a 10% solution for several minutes,
then rinsed thoroughly with deionized water. The unrinsed samples were gently
cleansed with ethanol and a lint-free wipe. The AFM images indicate that HF
makes the surface very rough leaving many small pits and crevices, increasing the
surface area significantly (compare Figs. 8.5 and 8.6). In addition, it is possible
that HF simply exposed more potential magnetic sites than it removed. Although
0µm
12µm
24µm0µm
12µm
24µm
65nm
32nm
0nm
Figure 8.5. An AFM image of an untreated Pyrex sample. The ≈ 1 cm3 sample offlat Pyrex was rinsed with ethanol and a lint-free wipe prior to imaging. The imageshows a random section of the sample 24 µm on a side with a vertical scale of 65nm.
124
0µm
12µm
24µm0µm
12µm
24µm
90nm
0nm
45nm
Figure 8.6. An AFM image of a Pyrex sample rinsed with a 10% HF solution forseveral minutes. The image shows a random section of the sample 24 µm on a sidewith a vertical scale of 90 nm. This sample is much more rough than the sampleshown in Fig. 8.5, which likely explains why cells rinsed with HF had relatively highrelaxation rates and magnetized very strongly (see Fig. 8.4).
several researchers have observed that the presence of Rb dramatically improves
wall relaxation times over bare glass [17, 19, 20, 45], the damage done by the HF
rinse may be beyond repair.
8.5.3.2 Aqua Regia Rinse
Next we rinsed cells 16A and 16B with aqua regia (AR), a solution of 3 parts
HCl and 1 part HNO3. We used this acid in an effort to dissolve surface iron sites
because the acid does not aggressively attack glass. These cells were spherical with
a volume of ≈ 50 cm3. The bodies of the cells were submerged in a beaker of the
AR solution overnight with the capillaries sticking out; the cells were found floating
partially submerged in the morning. After flushing thoroughly with deionized water,
the cells were attached to a manifold for baking and Rb distillation. These cells had
unmagnetized T−11 ’s of about 0.028 h−1 for 16A and 0.083 h−1 for 16B (see Fig.
125
8.7). Again, we have no explanation for the large discrepancy in the rates between
the two cells, since they were prepared identically. We note that these cells did not
fully degauss to the original T−11 , nor were they considered good. However, these
cells magnetized by a factor of ≈ 3 to 10, which is less than the factor of ≈ 20 to
100 for cells 5A and 5B rinsed with HF but more than the typical factor of ≈ 2.
Sufficient etching of the glass by the AR may have taken place to expose at least as
many potential sites as may have been dissolved while increasing the surface area
somewhat.
8.5.3.3 HF and HCl Rinse
The next experiment involved cells 18A and 18B, both spherical 50 cm3 Pyrex
cells. We chose to initially rinse with an aggressive acid to expose as many sites
10-2
10-1
100
un
mag
mag
deg
16A
16B
T1-1
(h
ou
rs-1
)
Figure 8.7. T1 hysteresis of cells rinsed with aqua regia. Both cells magnetizesignificantly, but not to the extent of the cells rinsed with HF (see Fig. 8.4). It isapparent that rinsing with AR is not beneficial to cell quality, nor does it eliminateT1 hysteresis.
126
near the surface as possible, then to rinse with an acid that does not etch glass
aggressively. The idea of the second rinse was to dissolve the sites that were exposed
by the first rinse while avoiding exposure of additional sites. We rinsed the cells first
with a 10% HF solution for several minutes and then with a 37% HCl solution for
several minutes. The cells were then attached to a manifold and prepared as normal.
The unmagnetized T−11 s of these cells were about 0.022 h−1 for 18A and 0.037 h−1
for 18B (see Fig. 8.8). (We note that in this chapter the “B” cells are consistently of
shorter T1. We feel this is just a coincidence, since this behavior is reversed or totally
absent in other cell pairs. Cell placement on the manifold is random, and labels are
assigned only after the cells are attached.) Similar to other acid-rinsed cells, the
original T−11 ’s were not fully recovered by degaussing. These cells magnetized by
a factor of ≈ 10 to 30, stronger than typical cells that have not been rinsed, and
stronger than the cells rinsed with AR. To better understand the effects of rinsing
10-2
10-1
100
un
mag
mag
deg
18A
18B
T1-1
(h
ou
rs-1
)
Figure 8.8. T1 hysteresis of cells rinsed with HF and HCl. Error bars are too smallto see. Cells 18A and 18B were rinsed with a 10% HF sloution then a 37% HClsolution prior to Rb distillation.
127
with HCl, we prepared samples of flat Pyrex rinsed with a 37% HCl solution for
AFM; see Fig. 8.9. It is difficult to discern surface characteristics from Fig. 8.9, but
the results of T−11 measurements indicate that HCl has similar qualitative effects as
the other acids we used. Specifically, it may increase the surface area and expose
additional relaxation sites.
8.5.3.4 Intervening HCl Rinse
Finally, two other cells, 5B′ and 11A′, were rinsed with acids. The prime denotes
that the original Rb was rinsed out and Rb distilled in a second time. 5B′, originally
labelled 5B, was previously rinsed with HF prior to initial Rb distilation (see Sec.
8.5.3.1); its relaxation properties are described above (see Fig. 8.4). 11A′ was
initially prepared as a normal, unrinsed cell labelled 11A (see Fig. 8.3), which
reflected a more typical factor of two change in rate when magnetized. The Rb was
rinsed from both cells with ethanol, then the cells were rinsed with an HCl solution
for several minutes. The idea was to eliminate magnetic sites whose existence
0µm
12µm
24µm0µm
12µm
24µm0nm
10nm
20nm
Figure 8.9. Atomic force microscopy of a bare Pyrex sample rinsed with HCl.Compare to Figs. 8.5 and 8.6, noting the difference in vertical scale.
128
had been verified; this is the key difference between this experiment and previous
acid-rinse experiments. After the HCl rinse, the cells were reattached to a manifold,
baked, and Rb distilled in. Figure 8.10 shows T1 hysteresis results before and after
the intervening HCl rinse. Surprisingly, the unmagnetized and degaussed relaxation
rates for each cell before and after the rinse are similar, implying that wall relaxation
properties were not affected much by the intervening acid rinse. This suggests that
the cell wall relaxation properties are largely set during the fabrication process or
the initial introduction of Rb.
10-2
10-1
100
101unm
ag
mag
deg
5B5B'11A11A'
T1-1
(ho
urs
-1)
Figure 8.10. T1 hysteresis of Rb and HCl rinsed cells. Error bars are too small tosee. Cell 5B′ (originally cell 5B, see Figure 8.4) was rinsed with HF prior to initialRb distillation. The Rb was rinsed out, the cell was rinsed with HCl, then the cellwas attached to a new manifold Rb distilled in again. Cell 11A′ (originally 11A) wasinitially prepared as a standard spin-exchange cell. The Rb was rinsed out and thecell prepared again with 5B′. The data show that the unmagnetized and degaussedrates were similar before and after the acid rinse, possibly indicating that the aciddoes not have a dramatic effect on cells that have contained Rb.
129
8.5.4 Potassium Rinse
It has been shown that K is the most effective of the alkali metals in filling
interstitial gaps in a borosilicate glass matrix [85]. In fact, two of the longest-lifetime
spin-exchange cells we have made contained K instead of Rb (cells 12A and 12B in
Fig. 4.6). We prepared two standard spin-exchange cells normally except that the
manifold had a second retort for a K ampoule [33] positioned between the liquid
nitrogen trap and the “B” cell (see Sec. 4.5 for a detailed description of a standard
manifold). After baking but prior to Rb distillation, a small amount of K (≈ 30
mg) was distilled into each cell. The cells were then heated to ≈ 200 C for several
hours to imitate the heating during optical pumping that the previous K-coated
cells experienced. This period of heating effectively drove all visible quantities of
K from the cells. However, we think that K was present long enough to chemically
interact with the entire cell surface. Finally, Rb was distilled into the cells. It is
certain that some K was distilled in also, since the two metals became mixed in the
manifold. The relaxation rates of these cells, labeled 20A and 20B, were measured.
The unmagnetized rates of the cells were 0.035 h−1 and 0.029 h−1, respectively. (The
magnetized rates of these cells were not measured since they were being used for
low-field hysteresis measurements; see Sec. 5.5.2.) It seems that pretreating with K
is not any better at inhibiting relaxation than simply introducing Rb.
8.6 Conclusion
We have demonstrated that rinsing cells with acid prior to Rb distillation is an
ineffective treatment. The acid-rinsed cells had higher than average relaxation rates
when unmagnetized or degaussed, and they tended to magnetize more strongly than
unrinsed cells (that is, for the acid rinsed cells, the ratio of the magnetized rate to
the unmagnetized rate was larger than average). This behavior suggests that the
130
acids etched the cell surface to expose additional surface area and potential relaxive
magnetic sites. However, cells that were rinsed with Rb prior to an acid rinse did
not show a significant change in relaxation rate before and after the acid rinse.
This indicates that the cell properties may be largely established upon initial Rb
distillation.
We have also demonstrated that bare Pyrex cells can demonstrate T1 hysteresis
when rinsed with a chemical reducing agent. This is evidence in favor of the
hypothesis that the magnetic sites originate in the glass, and that Rb behaves as a
reducing agent in the cells. Further evidence is seen in cells that have had their Rb
rinsed out. These cells have somewhat higher rates than when the Rb was present,
but they continued to show T1 hysteresis even in the absence of Rb.
We acknowledge J. Miller of the University of Utah Chemistry Department for
his assistance with the DMC rinsing. We also acknowledge J. Kyle and M. Delong
for assistance with the acid rinses. Our thanks to B. Anger and C. Inglefield of
Weber State University for the AFM images.
CHAPTER 9
MRI OF FLOWING POLARIZED 3He
9.1 Abstract
To demonstrate the feasibility of gas flow imaging in physiologically relevant
phantoms, we imaged flowing HP 3He using both a spin tagging, time-of-flight
technique and velocity-sensitive phase encoding. The images were made using
straight and curved tube phantoms with an inner diameter approximately the same
as an adult rat trachea. We imaged flow and diffusion with a resolution of 625 µm,
high enough to see a clear velocity and diffusion distribution in the tube. The spin
tagging images were made with a resolution of 315 µm, and rapid signal wash-out
due to diffusion is clearly visible. This chapter is a discussion of the results of the
first velocity and diffusion maps made on flowing HP 3He. These experiments were
feasible because of our success at making long-lifetime spin-exchange cells.
9.2 Introduction
Magnetic resonance imaging (MRI) is typically a spin-density imaging technique
that takes advantage of the unequal energy-level populations of an ensemble of
nuclei in an external magnetic field. The thermal equilibrium population difference
is simply a Boltzman distribution. The energy difference is ∆E = hγB0, where γ
is the nuclear gyromagnetic ratio and B0 is the external magnetic field strength,
conventionally along the z-axis. Each nuclear spin precesses about the external field
132
with a frequency ω0 = γB0, called the Larmor frequency, and tends to align itself
with the field, resulting in a net magnetization of the sample. The application of
a radio frequency (RF) magnetic field at ω0 and orthogonal to B0 causes energy
absorption by the nuclei and tips the net magnetization away from B0. When the
RF field is turned off, the precession of the nuclear spins about B0 induces a voltage
in a pick-up coil, which is often the same coil that delivers the RF field. Magnetic
field gradients can be used to spatially encode the spins. For example, a gradient
G = ∂Bz/∂xi applied in an arbitrary direction xi gives a field B(xi) = B0 + Gxi.
This encodes the nuclear spins along the xi axis with a unique position-dependent
Larmor frequency ω(xi) = γB(xi). Thus, the intensity of the response at a given
frequency is proportional to the spin density at the corresponding position. By
appropriate use of gradients, an image can be produced by sampling a sufficient
number of positions in the sample.
The last several years has witnessed rapid development of the use of hyperpo-
larized (HP) gas as the signal source for MRI, especially of pulmonary air spaces.
Advances in MRI strategies have allowed researchers to visualize 6th generation
airway branches in live rats [99]. Other studies of 3He diffusion coefficients in
lung tissues have revealed significant physiological differences between healthy and
diseased tissue [100]. Clinical use of HP gas would provide spatial and temporal
resolution not possible with any other pulmonary imaging modalities.
The work described in this chapter uses HP gas to map flow velocities, a technique
that has drawn little attention, since most images are maps of spin density. HP
gas allows for very rapid imaging because the enormous nonequilibrium nuclear
polarization eliminates the need to wait for the magnetization to relax back to
thermal equilibrium between pulses. Thus, images of gas flowing, for example into
lung air spaces, can be made in virtual “real time,” that is, images can be made in
133
sufficiently rapid succession to visualize flow dynamics. This is especially important
when imaging 3He because the diffusion coefficient is very high. Diffusion through
field gradients causes signal attenuation due to dephasing of the magnetization.
The data we collected was preliminary for the purpose of demonstrating the
feasibility of flow measurements using HP gas in physiologically relevant phantoms.
The Virtual Lung project at Pacific Northwest National Laboratory (PNNL) uses
computational fluid dynamics (CFD) models to predict long-term disease progres-
sion in pulmonary tissue. Model validation requires flow data of gas in the bronchial
tree and diffusion data in alveolar air spaces. In March of 2002 I transported the
polarizing equipment and several spin-exchange cells to Richland, WA to perform
the preliminary imaging experiments in collaboration with Dr. Kevin Minard. This
work was largely possible due to our success at making long-lifetime cells, since we
usually required cells to sit for many hours after polarizing and prior to imaging
while relying on minimal polarization loss. This was because we could polarize a
sample of gas every 12 hours, but we could only image during regular working hours.
9.3 Theory
The effects of diffusion on bulk flow and vice versa in a rapidly diffusing gas
like He are not well understood, particularly at physiologically relevant flow rates.
In flow measurements, rapid diffusion may cause significant signal attenuation, due
to the magnetization dephasing that occurs in the presence of a magnetic field
gradient, thereby setting a lower limit on the measurable flow rate. If laminar flow
is established, then random sampling of gas atoms between streamlines will affect
the measured diffusion coefficient by making it appear even higher, an effect called
Taylor dispersion [101].
134
A bipolar gradient sequence, or an equivalent sequence with unipolar gradients
separated by a π pulse (a π pulse is an RF pulse that inverts the magnetization by
rotating it 180) is sensitive to both velocity and diffusion by changing the phase
and attenuation of the signal, respectively. Such a pulse sequence is shown in Fig.
9.1. If flow is at a constant velocity V , then the phase change Φ for a moving spin
is [102]:
Φ = γV∫
tG(t) dt , (9.1)
where γ is the gyromagnetic ratio and G(t) is the applied gradient parallel to the
velocity component being measured. The sequence shown in Fig. 9.1 has (idealized)
rectangular gradients of duration T separated by a time Td. From Eq. (9.1) the
resulting phase change experienced by constantly moving spins is:
Φ = γV GTTd. (9.2)
RF
Td
Signalπ pulseπ/2 pulse
G
Figure 9.1. The velocity and diffusion sensitive gradient sequence used to make im-ages in Fig. 9.3. The sequence is run twice, once with the gradients off (indicated bythe dashed lines) and once with the gradients on. The phase change is proportionalto the velocity, and the signal attenuation determines the diffusion coefficient. Thegradients are applied in a direction parallel to the measured velocity and diffusion.
135
Using the same pulse sequence, the signal attenuation due to diffusion is [102]:
exp[−γ2G2DT 2 (Td − T/3)
], (9.3)
where D is the diffusion coefficient. Thus, two measurements of phase and attenua-
tion, one with the bipolar gradients off and the other with the gradients on, can be
used to extract velocity and diffusion coefficients.
An effective method of visualizing flow in a phantom is called multistripe tagging
[103]. A stripe is a region of the sample in which all of the magnetization has been
destroyed. Stripes can be “tagged” using an RF pulse generated by modulating
a series of evenly spaced, uniform, rectangular pulses with a sinc function, where
sinc(t) ≡ sin(πt)/πt. The effective region of striping is determined by the pulse
width, the profile and width of each stripe are determined by the sinc envelope, and
the stripe spacing is determined by the applied gradient and pulse spacing. The
striping pulse puts the magnetization of the stripe regions into the transverse plane,
after which a “crusher” gradient destroys all transverse magnetization so that no net
magnetization remains in the stripes. By incrementally increasing the delay time
between stripe tagging and imaging, a temporal progression of the stripes can be
seen as the fluid moves.
9.4 Experimental
These experiments were conducted at PNNL using the polarization apparatus and
spin-exchange cells transported from Utah. Polarized gas was delivered to various
phantoms using a home-built, small-animal ventilator similar to others [104]. The
ventilator controlled delivery and mixing of the gases. The experimental set-up is
136
schematically shown in Fig. 9.2. HP 3He was dispensed from a high-pressure cell into
an evacuated Tedlar (DuPont) bag, which is contained in a sealed box. The gas was
then pneumatically forced out of the bag with dry N2 gas and through a tube to a
pneumatic valve at a controlled rate by pressurizing the box. The pneumatic valve,
placed in the magnet core, allows mixing of the 3He with up to three other gases.
We used a mixture of approximately 10% 3He and 90% N2 gas with a total flow rate,
monitored with separate flow meters, of approximately 200 cm3/min, physiologically
relevant for a rat. The phantoms used were elastic tubes with an inner diameter of
≈ 2.3 mm, comparable to an adult rat trachea. Each experiment used ≈ 350 cm3
of 3He at an initial polarization of ≈ 30%. The measured polarization of the gas at
the phantom was 7 ± 2 %. The images were made in a 30 cm diameter, horizontal
bore, 1.5 T superconducting magnet with a tuned RF coil. No slice selection was
used in the images.
X
X
ventilator
Tedlar
bag
magnet
pneumatic valve
N
N2
He
N2
source
regulator valves
flow meters
3He
to imaging phantom
Figure 9.2. Experimental set-up for MRI flow imaging.
137
9.5 Results and Discussion
Figure 9.3 shows an image of measured velocity vs. position, or velocity map
(green background), and an apparent diffusion coefficient (ADC) map (black back-
ground). The direction of gas flow is indicated by the dashed arrow. No slice
selection was used, so the measured velocity and diffusion at any position in the
image is a projection through an axis perpendicular to the direction of flow. For
the velocity map, the color scale represents velocities between +84 cm/s in violet
through 0 cm/s in green to −84 cm/s in red. For the ADC map, violet represents
2.3 cm2/s, green is 1.1 cm2/s, and red is 0 cm2/s. For both images the field of view
is about 6 cm × 6 cm, and the spatial resolution is 625 µm.
The velocity map shows flow velocities parallel to the motion probing gradient
in the range of ± 84 cm/s in the vertical sections, parallel (or antiparallel) with
the direction of the applied motion-probing gradients (indicated by the bold arrow),
Figure 9.3. Velocity map (left) and ADC map (right) for flowing HP 3He througha tube. The bold arrow shows the direction of applied motion probing gradientsand the dashed arrow indicates direction of gas flow. The color scale on the far leftapplies differently to both maps. For the velocity map, the scale represents velocitiesfrom +84 cm/s (violet) to −84 cm/s (red). For the ADC map, the scale representsADC values from 2.3 cm2/s (violet) to 1.1 cm2/s (green) to the limiting case of 0cm2/s (red). The field of view is 6 cm × 6 cm, and the spatial resolution is 625 µm.
138
which agrees well with the known flow rate of approximately ± 80 cm/s. In the turn
at the top, where the bulk flow is perpendicular to the motion-probing direction,
the measured velocity transitions through zero from negative to positive values, as
expected.
The ADC map shows diffusion coefficient values in a range of 2.3 cm2/s to 0
cm2/s. The value of 1.1 cm2/s measured in the turn is close to ADC values of dilute
3He in nitrogen with no bulk flow [100]. The somewhat higher values measured in
the straight segments suggest the presence of Taylor dispersion [101]: as 3He atoms
diffuse between different flow stream lines, the mean square displacement in the
direction of the flow increases and is reflected as a higher ADC.
Figure 9.4 shows a sequence of images taken after stripes, with separation of
≈ 1 cm, were burned into the flowing gas, and corresponding 1-d projections on
the right. These images were made by creating ≈ 3.5 mm wide stripes, then
imaging the remaining magnetization after increasing time delays. The 15 images
are temporally spaced by 1 ms with an initial 1 ms delay between the RF pulse
and the first image, thus showing flow progression over 16 ms. Spatial resolution is
315 µm. The stripes are clearly visible, with more intense signal in blue and less
intense in red. Motion of the gas can be seen as the stripes progress to the left
(the vertical dashed lines were added to guide the eye). The stripes blurred almost
immediately as diffusion caused mixing between the stripes and the regions with
magnetization, with nearly thorough mixing having taken place after only 16 ms.
This is reasonable if we assume D ≈ 1.1 cm2/s for dilute 3He in nitrogen, which was
measured in Fig. 9.3. This corresponds to a mean linear distance traveled for each
atom of about 1.3 mm after 16 ms. Since magnetization was diffusing into stripes
from both ends, the 3.5 mm stripes should be nearly filled after 16 ms, as observed.
139
TIME
≈1 cm
Figure 9.4. Visualization of real-time MRI of 3He flowing through a tube. The 3Hewas diluted to a ≈ 10% concentration then flowed through a 2.3 mm i.d. tube at ≈200 ml/min. Stripes were burned in (less intense signal is red, more intense signal isblue), and images were taken at 1 ms intervals. The rapid diffusion of the 3He (≈ 1cm2/s) caused immediate mixing of the polarized gas with the stripes until the signalwas almost evenly distributed after only 16 ms. Corresponding 1-d projections ofthe signal are on the right. The dashed lines are added to guide the eye.
140
9.6 Conclusion
We have demonstrated the feasibility of MRI velocity and diffusion maps of
flowing HP 3He. The very high diffusion coefficient of 3He, which may be enhanced
by Taylor dispersion, places a lower limit on the velocity that can be measured. The
high diffusion coefficient also complicated efforts to visualize flow of 3He through
a tube by rapidly washing-out the striping pattern created by the rf pulse. The
results of these imaging experiments are difficult to interpret without a knowledge
of the actual flow dynamics. In order to make this imaging technique useful, MRI
results will have to be compared to computational models of flow in the simple
tube phantoms. One can then proceed with model validation in more complicated
phantoms.
We acknowledge K. Minard at PNNL for his MRI expertise used in setting up and
running the pulse sequences. Thanks to G. Samuelson for designing and building
the ventilator.
APPENDIX
INTERMEDIATE-FIELD
SPECTROMETER
The NMR spectrometer used in Chapter 5 was built especially to handle NMR
frequencies from about 300 kHz to about 3 MHz. It does a very adequate job, but
suffers in signal-to-noise at the lower frequencies because we use a single, ≈ 0.8 µH
probe in series with a 50 Ω resistor for all frequencies. This spectrometer is very
similar in principle to the spectrometer described in Chapter 2 but consists of
RF components designed to handle the higher frequencies. It was built in three
13”×17”×3” chassis boxes. Each of the boxes is described below.
Box 1 (Fig. A.1) contains the power supply and RF-pulse power amplifier. The
RF from the synthesizer is split by a ZSC-2-1 power splitter [105], which is mounted
outside the box for additional shielding for the internal components. The two ZAD-1
frequency mixers [105] act as gates to prevent RF leakage to the coil. The ZAD-1
has three ports labeled “L,” “I,” and “R.” “L” is the local oscillator input, and “I”
and “R” are the intermediate frequency (IF) and RF ports, respecitvely, both of
which can act as an input or an output. The variable attenuator [106] can be used
to switch in as much as 65 dB in the RF pulse line. The ZHL-32A broadband power
amplifier [105] amplifies the RF pulse which is then sent to the duplexer in Box 2.
Box 2 (Fig. A.2) contains the receiver and duplexer. A ZSC-2-1 power splitter
acts as the duplexer. The ZSC-2-1 has three ports labeled “S,” “1,” and “2.” Ports
142
ZAD-1 ZAD-1
L I R L I R1
S
20-65 dB
ATTENUATOR
ZSC-2-1
POWER
AMP
GATE
INPUTS
SYNTH IN
PSD
BOX 3
+15V DC
BOX 2
POWER
AMP
BOX 2
POWER SUPPLY
+24 V DC
ZHL-
32A
Figure A.1. Box 1 of the intermediate-field spectrometer. This box contains thepower supply, RF-pulse gates, and the RF-pulse power amplifier.
“1” and “2” are isolated from each other, so the splitter acts as a switch in this ap-
plication. Although not ideal, it does an adequate job at these frequencies. Initially,
a switchable, tuned LC circuit, similar to that used in the 100 kHz spectrometer,
was used. However, we found that such a duplexer added too much noise to the
NMR signal. The preamp [107] is powered by an isolated +15 VDC input from Box
1 for additional noise reduction, and it has been modified by the manufacturer to
143
PREAMP
+15 V IN FROM BOX 1
PREAMP OUT TO
BOX 3
ZSC-2-1
2 S 1
TO NMR PROBE
POWER AMP IN FROM BOX 1
DUPLEXER
DIODE GATES
MITEQ
Figure A.2. Box 2 of the intermediate-field spectrometer. This box contains theNMR signal receiver and the duplexer.
144
have a < 50 µs recovery time. Diode gates are contained in Bud boxes (indicated
by the dashed squares) for additional shielding.
Box 3 (Fig. A.3) contains both the pulse generation circuitry and phase detector
(separated from each other by the dashed line in the figure). Figure A.4 shows the
details of the pulse generator and low-pass filter section. The pulse length can be
continuously varied from 10 µs to 10 ms. The variable attenuator can be used to
switch in as much as 65 dB in the receiver line to avoid saturating the ZFL-500
amplifier [105]. The pulse generator circuit requires +5 VDC and the ZFL-500
requires +15 VDC, both provided by the power supply in Box 1.
This spectrometer was designed and built with heavy reliance on the expertise
and advise of M. Conradi. B. Anger and S. Morgan did most of the actual assembly.
145
ZAD-1
LOW-PASS
SECTION
0-65 dB
ATTEN-
UA
SYNTH IN
FROM BOX 1
PREAMP
IN FROM
BOX 2
L I R
PULSE
GENERA
CIRCUIT
SIGNAL
OU
SCOPE
SCOPE
TRIGGER
Z500
AMP
PHASE
SENSITIVE
DETECTOR
GATE
OUTPUTS BOX 1
Figure A.3. Box 3 of the intermediate-field spectrometer. This box contains thepulse generator circuitry, NMR signal amplifier, and the phase detector. See Fig.A.4 for pulse generator and low-pass filter details.
146
74121Q
+5
+5
+5
+5
SCOPE
TRIGGER
GATES
330
330 330
3306.8k
6.8k
PULSE GENERA CIRCUIT
+5 143
4
7
11 10
74121 DETAILS
2.0k
+5
25k 0.0068
0.068
0.68
SWITCH
center: 10-100 µs
left: 100-1000 µs
right: 1-10 ms
OU
SCOPE
3.3k1.0k
270 .001
IN
FROM
PSD ROTARY SWITCH
.001.0033 .01 .022 .05 .1 .18 .47
LOW-PASS FILTER DETAILS
Figure A.4. Intermediate field spectrometer pulse generator and low-pass filtersection details. See Fig. A.3.
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