yvi oljl
TRANSCRIPT
TEMPERATURE DEPENDENCE OF THE MAGNETIC SUSCEPTIBILITY
OF THE ORGANIC FREE RADICAL GALVINOXYL
APPROVED:
Major Professor
/YVI OLJL. Minor Professor
Director of the Departri nt of Physics
Dean of the Graduate School "
TEMPERATURE DEPENDENCE OF THE MAGNETIC SUSCEPTIBILITY
OF THE ORGANIC FREE RADICAL GALVINOXYL
THESIS
Presented to the Graduate Council of the
North Texas State University in Partial
Fulfillment of the Requirements
For the Degree of
MASTER OF SCIENCE
By
Sam W. Morphew, B. S.
Denton, Texas
August, 1965
TABLE OF CONTENTS
Page
LIST OF TABLES iv
LIST OF ILLUSTRATIONS v
Chapter
I. INTRODUCTION 1
Electron Spin Resonance Free Radicals
II. THEORETICAL BACKGROUND 12
Magnetic Behavior of Certain Substances Theory of ESR Measurement of Laboratory Production of Circularly-_
Polarized Radio-Frequency Magnetic Fields
Small-Modulation Detection Technique
III. APPARATUS 28
IV. PROCEDURE 37
V. RESULTS AND CONCLUSIONS 42
BIBLIOGRAPHY 53
ill
LIST OF TABLES
Table Page
I. Typical Meter Readings During a Run 38
II. Comparison of Galvinoxyl with Several Antiferromagnetic Substances . . . . . . 45
III. Comparison of Galvinoxyl with Several Stable Organic Free Radicals 48
xv
LIST OF ILLUSTRATIONS
Figure Page
1. Galvinoxyl (I) and its Parent Molecule (II) . . . g
2. Simple Oscillator Circuit ]_5
3. Inductance Coil Voltage Versus Steady Magnetic Field Strength . . . . . 21
4. Inductance Coil Voltage Variation Versus Magnetic Field Strength at H Less Than Hq . . 23
5. Inductance Coil Voltage Variation Versus Magnetic Field Strength at H Equal to HQ . . 23
6. Inductance Coil Voltage Variation Versus Magnetic Field Strength at H Greater Than HQ - 24
7. Lock-In Amplifier Output Versus Magnetic
Field. Strength 24
8. Block Diagram of Electrical Apparatus . . . . . . 29
9. Dewar Support Structure and. Sample Coil
Support Structure . . . . . . . . 31
10. Marginal Oscillator-Detector . . . . . . . . . . 33
11. Modulation Signal Amplifier 34
12. Magnetic Susceptibility of Galvinoxyl Versus Absolute Temperature-Run 1 . . . . . . . . . 43
13. Magnetic Susceptibility of Galvinoxyl Versus Absolute Temperature-Run 2 44
14. Inverse Magnetic Susceptibility of Galvinoxyl Versus Absolute Temperature-Run 1 46
15. Inverse Magnetic Susceptibility of Galvinoxyl Versus Absolute Temperature-Run 2 47
16. Absorption Line-Width Versus Absolute Temperature „ 50
CHAPTER I
INTRODUCTION
Electron Spin Resonance
Electronic magnetism arises from both the spin and
orbital angular momenta of electrons within a molecular or
atomic configuration. The magnetic moment of each electron
is proportional to the total of its spin and orbital angular
momentum. There is a large class of electronic configu-
rations in which the orbital contribution is quenched (16,
p. 288) and thus very small. The magnetic moment is then
due entirely to the spin angular momentum. The electrons
in atoms and compounds very often do not exhibit any ex-
ternal magnetic effect at all because of the pairing of
electron spins which occurs in most atoms and in normal
chemical bonding processes. One of the most important ex-
ceptions is found in the transition group of elements. The
members of this group have unfilled shells of electrons deep
within the atom. The process of chemical bonding involves
only the outermost electrons, and the deep-lying electrons
will thus remain unpaired. Another important exception
occurs in the case of molecules having an odd number of
electrons. Electron spin resonance absorption (ESR) pro-
vides a method for studying the magnetic behavior of such
2
electronic configurations having predominantly spin angular
momentum.
One can better understand the ESR phenomenon from a
consideration of the dynamics of an isolated electron in an
external magnetic field. Let the magnetic moment of the
electron be denoted by the vector quantity. The potential
energy of orientation of this magnetic moment in the external
magnetic field HQ is given by
E = -/Z ' H0 (1)
Since the magnetic moment is proportional to the spin angular
momentum, one can write
= -Ytif , (2)
where t is the gyromagnetic ratio for the electron
[= 17.6 x 10^ (sec • oe)~^]9 M is Planck's constant divided
by 2 TT , and S is the dimensionless angular momentum operator.
The minus sign indicates explicitly that the vectors and
5 are antiparallel (one takes > 0), and it arises because
of the negative charge on the electron. The Hamiltonian for
this free electron may thus be written
*Vfr- = -(-tffcS" )• Jt0 J (3)
and the energy levels are given by
E- y£ ms H0 J (*0
3
where ms is the spin magnetic quantum number of the electron
which may take any of the 2S + 1 values
+ o>*" S •
Since S = 1/2 for a free electron, there are two energy levels
separated by an energy difference
A£- E<ros= 1/2.) - i/as.1
AE- XKHo . ( 6 )
Transitions between these two energy levels thus require the
absorption or emission of a quantum of energy
That the emitted or absorbed radiation must be circularly
polarized may be seen from the following semi-classical argu-
ment. From classical electricity and magnetism (11, p. 132),
the torque a magnetic moment experiences in the external <mJSk
magnetic field HQ is given by
r * K . ( 7 )
But from Newton's second law, the torque is also equal to the
time rate of change of angular momentum. Thus,
• ( 8 )
k
A combination of equations (2), (7), and (8) yields the
equation of motion for a magnetic moment in the external -a
magnetic field HQ:
= ^H 0 • (9)
This equation of motion parallels that for the precessional
motion of a spinning symmetric top with angular momentum "L
precessing at the angular velocity <£" (15, p. 385). That is,
^ L l) — ut * L . (10)
By analogy,^ precesses in HQ at an angular velocity of
u? 88 V « 0 . (11)
This precessional motion of the magnetic moment in the mag-
netic field is called Larmor precession (8, p. 177; 16, p. 22).
Classically, therefore, for the magnetic moment to experience
a constant tipping torque, the direction of the radiation must -a*
remain perpendicular to the vector /U. as j& precesses with an
angular velocity of *HQ. TO remain perpendicular at all times,
the radiation must be circularly polarized and must rotate at
an angular velocity of ^HQ.
The energy required for transitions between the magnetic
energy levels, Eq„ (6), may be combined with the usual Bohr
frequency condition
£- hJ - H o» (12)
to give
t UJ a Ho
or UJ - ¥ Ho (13)
Thus, the photon must have an angular velocity equal to that
of the angular precessional velocity of the magnetic moment
for absorption to be most probable. Such photons are radi-
ated in a circularly polarized magnetic field rotating with
a well-defined angular velocity (1, p. 3). The ESR phenome-
non may be induced when a configuration of electrons ex-
hibiting electronic magnetism is subjected to two perpen-e w X » « •
dicular magnetic fields:- one, Hq, constant M direction
and magnitude to produce the precession; the other, H]_,
circularly polarized with its angular velocity vector paral-ni.ifc ^
lei to Hq and rotating with an angular velocity of #Hq to
induce the transitions.
If a large number of electrons are considered to be non-
interacting to a first approximation, each of the electrons
will precess at the same rate in an external magnetic field
Ho; and each may either absorb or radiate energy, depending
on its initial state, upon interaction with a photon of
energy I^Hq. Boltzmann statistics may be used for these
non-interacting particles to determine the relative number of
spins in each of the two energy levels at equilibrium when
6
the HQ field is applied. The photons from the rotating
field are equally likely to induce transitions in either
direction. However, since at equilibrium there are more
spins in the lower energy level, there will be a net ab-
sorption of energy when the rotating field is also turned
on since more transitions will be induced upward than down-
ward. If the irradiation of the spin system is sufficiently
intense, the absorption process will tend to equalize the
populations of the two spin levels and thus reduce the possi-
bility for further absorption. This population equalization
by excessive irradiation is called saturation (2, p. 20).
With weak irradiation, however, the normal relaxation processes
which are responsible for the initial equilibrium distribution
will be sufficiently strong to maintain a condition of quasi-
equilibrium. If the relaxation process does predominate,
spins will be transferred back to the lower energy level by
giving up their excess energy to other degrees of freedom of
the system just as rapidly as they are transferred to the
higher energy level by the absorption process. The details
of the ESR process reveal much about the magnetic interactions
of the electronic configuration with its surroundings.
Using ESR, one can determine such quantities as electron
densities within paramagnetic molecules, nuclear spins, and
nuclear magnetic moments. ESR enables one to detect minute
quantities of paramagnetic material having no more than
7
approximately 10^ spins. Since both the bulk polarization
of a magnetic sample and. the strength of the ESR absorption
are dependent upon the population differences of various mag-
netic energy levels, the ESR process is also useful as an
indirect measure of the bulk magnetic susceptibility of the
absorbing material. Thus ESR is found to be a very important
and useful experimental technique.
The term "magnetic resonance" originated with Rabi and
his associates in molecular beam experiments (12). Zaviosky,
in 1945, was the first to observe experimentally ESR ab-
sorption in bulk material (13).
Free Radicals
A free radical is
a molecule, or part of a molecule, in which the normal chemical bonding has been modified so that an unpaired electron is left associated with the system . . . . The definition includes all the organic radicals which are formed by the abstraction of a hydrogen atom from a ring or hydrocarbon chain, and in fact any system in which the unpaired electron is moving in a molecular rather than in an atomic orbital (10, p. 2).
Such chemical systems have been studied extensively using ESR
techniques (10).
A recent addition to the growing list of known free radi-
cals has been compounded by Galvin M. Goppinger (4) and is
variously known as "galvinoxyl" or "Coppinger's radical".
It is a very dark blue crystalline compound which is isolated
from the oxidation of (II) by lead dioxide in ether or iso-
octane. Galvinoxyl is the compound (I). See Figure 1.
8
(I)
Q
(CH^ C C(CH3)j
( ^ C > V S C ( C H 3 ) i
Jf-Ctt
OH
Fig. 1—Galvinoxyl (I) and its parent molecule (II)
Coppinger himself has pointed out that the magnetic sus-
ceptibility of (I) indicates one unpaired electron per
molecule (4). He also noted that (I) was unreactive
toward oxygen, and thus very stable in air. Windle (17)
gives a ug" value for (I) of 2.006 t 0.0005, a very strong
indication that the magnetic moments are due to spin mo-
menta only (10, p. 17). Windle (17) and Smith (14) have
also observed that the ESR line-width of (I) increases
twenty to thirty per cent as its temperature is lowered
from 297°K to 77°K. Hyperfine coupling between the unpaired
electrons and nuclei in (I) has also been studied in some
detail (3, 9). However, no work on the bulk magnetic sus-
ceptibility appears yet to have been reported.
Many stable free radicals exhibit ferro- or antiferro-
magnetic behavior at low temperatures (3, 5, 6, 7), and these
9
substances have proven useful in studies of the magnetic
Structure of organic materials. An investigation of the
temperature dependence of the bulk magnetic susceptibility
of galvinoxyl was undertaken to determine whether or not
this substance also falls into this category of useful or-
ganic compounds.
CHAPTER BIBLIOGRAPHY
1. Abragam, A., The Principles of Nuclear Magnetism, Oxford, Clarendon Press, I96I.
2. Andrew, E, R., Nuclear Magnetic Resonance, Cambridge, University Press, 1956.
3. Becconsall, J. K.and others, "Electron Magnetic Resonance Study of Free Phenoxy Radicals," Proceedings of the Chemical Society (October, 1959), 308-309.
4. Coppinger, Galvin M., "A Stable Phenoxy Radical Inert to Oxygen," Journal of the American Chemical Society, LXXIX (January, 1957), 501-502.
5. Duffy, William, "Magnetic Susceptibilities of Crystalline Stable Free Radicals in the 77°-293°K Temperature
• Range," Journal of Chemical Physics, XXXVI (January, 196 2), 490-493.
6. Edelstein, A. S., "Linear Ising Models and the Antiferro-magnetic Behavior of Certain Crystalline Organic Free Radicals," Journal of Chemical Physics, XL (January, 1964), 488-2+3T:
7. Edelstein, A. S. and M. Mandel, "Antiferromagnetic to Ferromagnetic Transitions in Organic Free Radicals," Journal of Chemical Physics, XXXV (September, 1961), 1130-1131.
8. Goldstein, Herbert, Classical Mechanics, Reading, Mass., Addison-Wesley Publishing Company, Inc., 1950.
9. Hakansson, Rolf, "Proton and Carbon-13 Splittings in the ESR Spectra of Two Phenoxy Radicals," Acta Chemica Scandinavica, XVII (No. 8, 1963), 2281-2284.
10. Ingram, D. J. E., Free Radicals as Studied by Electron Spin Resonance, London, Butterworths Scientific Publications, 1958.
11. Jackson, John David, Classical Electrodynamics, New York, John Wiley and Sons, Inc., 1963.
10
11
12. Kellogg, J.B.M. and S. Millman, "The Molecular Beam Magnetic Resonance Method. The Radiofrequency Spectra of Atoms and Molecules," Reviews of Modern Physics, XVIII (1946), 323-352.
13. Pake, George E., "Magnetic Resonance," Scientific American, CIC (August, 1958), 58-66.
14. Smith, William C., "Magnetic Susceptibility of a Crystal-line Free Radical," unpublished master's thesis, Department of Physics, North Texas State University, Denton, Texas, 1962.
15. Synge, John L. and Byron A. Griffith, Principles of Mechanics, New York, McGraw-Hill Book Company, Inc., 1959.
16. Van Vleck, J. H., The Theory of Electric and Magnetic Susceptibilities, London, Oxford Press, 1932.
17. Windle, J. J. and, ¥. H. Thurston, "Electron Spin Resonance in a Stable Phenoxy Radical," Journal of Chemical Physics, XXVII (December, 1957), 1429-1430.
CHAPTER II
THEORETICAL BACKGROUND
Magnetic Behavior of Certain Substances
A paramagnetic material consists of a collection of atoms
or molecules each of which possesses a small permanent mag-
netic moment. When such a material is subjected to a static,
unidirectional magnetic field, the field tends to align the
magnetic moments in its direction. Thermal agitation causes
the moments to be randomly orientated when there is no field,
and this same process prevents complete alignment when there
is one. The component of the total magnetic moment per unit
volume in the direction of an applied external magnetic field
is called the magnetization M. Since for weak fields M is - y
proportional to the polarizing field H, one may write
M « V ft , (14)
where the constant of proportionality X is called the magnetic
susceptibility. For most paramagnetic substances X is approxi-
mately 10"^ c.g.s. units at room temperature.
The magnetic susceptibility is far from being a constant
for paramagnetic materials. It is a function of temperature
due to the competition that exists between alignment with the
12
13
field and thermal disorder. At sufficiently high tempera-
tures all paramagnetic materials are observed to obey the
Curie-Weiss law (5, p. *+39) which relates % and the absolute
temperature T of the material in the following manner:
Q/cr-e) j (15)
where G is called the curie constant for the material and
0 is a characteristic temperature below which the Curie-
Weiss law is no longer valid. .
As the absolute temperature is lowered, thermal agitation
within a material subjected to a magnetic field becomes smaller
and thus tends less to prevent alignment of the magnetic mo-
ments with it. Two types of alignment processes are observed
to occur within materials as the temperature is lowered. For
some materials the reduction of thermal agitation permits the
complete alignment of all the magnetic moments with the field
as T approaches zero. For such materials, 0 is greater than
zero; and as the temperature of the material is reduced toward
9, X tends towards infinity fEq. 15}. For T less than 6, there
is a spontaneous magnetization of the material. Materials of
this type are called ferromagnetic. For many materials, how-
ever, the reduction of thermal agitation does not result in
the alignment of all the moments with the field. Rather, a
progressive pairing of the moments sets in, and below some
critical temperature Tc (called the Curie point) the
14
susceptibility decreases with decreasing temperature. Such
materials are called ant if erromagnetic. For such materials,
0 is less than zero. There exists no universal relationship
between 0 and the temperature at the Curie point.
A simple model (7, p. 10) which assumes the spin mag-
netic moments to be essentially non-interacting relates the
magnetic susceptibility to the absolute temperature as
follows:
X / UHT) j (16)
where N is the volume density of the magnetic moments,t
is Planck's constant divided by 2ff, V is the gyromagnetic
ratio, S is the spin value, and k is Boltzmann's constant.
This model gives a value of 0 equal to zero..
Other models which attempt to explain the departure
of X from the Curie-Weiss law at low temperatures (5, 3, 6)
assume some form of weak interaction among the moments.
Such models give rise to non-zero values for 0.
A measurement of C in equation (15) gives an indication
of the relative number of magnetic moments contributing to
the magnetic behavior of the material. A measurement of 0
gives an indication of the strength of the interaction of
the magnetic moments.
The determination of C requires an absolute measurement
of the value of X some temperature. However, to determine
15
9 one needs only relative measurement of at several
temperatures. A simple plot of vs. T permits 9 to be
read off directly as an intercept point. ESR techniques
are useful in such measurements of 9 because relative values
of X are easily obtained.
Theory of ESR Measurement of X©
If a parallel R-L-G circuit is connected to a constant
current generator [Fig. 2],
Co/iato-nt
Curreivt
Genera^ ©p
.if Pr
A
fL
' Fig. 2—Simple oscillator circuit
the voltage measured across the terminals A-B of the tuned
circuit is
V = I I
where Z is the parallel impedance of the R-L-G circuit. The
introduction of a magnetic material into the coil Lo will
produce a change AL in the inductance which is proportional
16
to the magnetic susceptibility of the material (1, p. 39).
This change may be used as a measure of susceptibility.
In the long solenoid approximation, the inductance
is given by
L-yU.Nx <A/i) t
wher e. ju. = J + V1T X (c.g.s. units) is the magnetic permea-
bility of the material filling the coil, N is the number of
turns, A is the cross-sectional area, and A is the length.
Thus, the introduction of a medium of susceptibility X
shifts the inductance by an amount
L-L0* HfrX*l(A/J)-HirXLo . (17)
The fact that the medium may not completely fill the coil
may be taken into account by introducing a fractional
"filling factor"^ , and allowance for a lossy material may
be included by writing
. (is)
Thus
*iirLQ f t K'-iX") . ' (19)
Andrew has shown (1, p. 39) that if the circuit of Fig. 2
is tuned to resonance with the generator, the small change
AL in inductance leads to a change in the magnitude of the
parallel impedance given by
17
A2/2 0« L LL/La) } (20)
where Q is the quality factor of the coil, and I m stands
for "imaginary part". Thus
-HIT ^ q 2o , (21)
and this change in impedance is reflected in a decrease of
V a b given by
A v = hit q ve . (22)
The imaginary part of the susceptibility X'1 is appreciably
different from zero only in the neighborhood of a resonance
absorption, so that the voltage-shift procedure for de-
termining the susceptibility implied in Eq. (22) is very
insensitive except under conditions of resonance absorption.
The imaginary part "^"of the susceptibility [Eq. (18)]
which is descriptive of the dynamic radio-frequency polari-
zation occurring in ESR is related to the static magnetic
susceptibility K by
"k ft (1, p. So) j (23)
where o- 7T is the Larmor precessional frequency of the
electronic moments in the applied field HQ and g(^) is a
line-shape factor, a bell-shaped function having its maximum
value at and so normalized that
18
A combination of Eqs. (22) and (23) yields
4V= - <24) ,
The usual practice is not to make ESR measurements at
a single fixed value of frequency and magnetic field but
rather to vary either ^ or H and thus to sweep through the
magnetic resonance condition. If the frequency is swept
linearly with time so that one may write
J — i Const6.ni) -tr j
then it follows that
ZfrzVa q J o X o 1 '/«•«*.} (25)
or
& -Iconst. /<zfrl\/0 f~AVtt) dt . (26)
Thus, the area under the AV-vs.-time curve is directly
proportional to the static susceptibility of the absorbing
material, and relative measurements of may be made simply
by comparing these experimental areas, provided the pro-
portionality factors indicated in Eq. (26),, as well as the
appropriate properties of any experimental apparatus used
to amplify or display AV, are held constant: in any series of
measurements.
19
Laboratory Production of Circularly Polarized Radio-Frequency Magnetic Fields
True circularly polarized radio-frequency fields are
very difficult to produce experimentally. In practice,
however, one may sometimes take advantage of the fact that
if two such fields are present in the same plane but rotating
in opposite directions with the same angular velocity, the
result is a linearly polarized field, the direction of which
depends upon the phase relationship of the two constituents.
Thus, one can easily reverse the situation by creating a
linearly polarized radio-frequency field within a solenoid
impressed with a radio-frequency voltage. From this field
a mathematical decomposition yields two counterrotating,
circularly polarized radio-frequency magnetic fields. If
the equation for the linear field is
Hj s L 2.^ cos uit
the two circularly polarized constituents are
4. 6(0 = C0* ? Hi
= l hl&o& wt +3 .
In the ESR process, however, one of these two fields will be
rotating in the same direction as the precessing magnetic
moments and one in the opposite direction. It has been shown
20
that the field rotating in the direction opposite to the
precession has negligible effect upon the magnetic moments
and their orientation (2).
Small-Modulation Detection Technique
If the voltage drop across the inductance coil [Fig. 2]
is plotted as a function of the magnetic field H with
held constant, the result will appear somewhat like the
inverted bell-shaped curve of Figure 3. HQ is the value of
the field when g(^) attains its maximum value [Eq. ( 2 3 ) ] .
The change in voltage which occurs at magnetic resonance may
or may not be detected experimentally as H sweeps through HQ,
depending upon how large- the fractional change &V/VQ is rela-
tive to the circuit noise and stray pickup. The sensitivity
of detection may be significantly increased if the linearly
varying magnetic field has superimposed upon it a sinusiodally
varying magnetic field of constant amplitude, phase, and
frequency. With such modulation the change in voltage will
manifest itself as an amplitude and phase modulation of the
radio-frequency signal impressed upon the tuned circuit by
the constant-current generator. This modulation may be
detected and amplified with narrow-band apparatus, thus
enhancing considerably the signal-to-noise ratio in the
measurements.
Consider what happens when the average value of the
modulated field at some instant of time is slightly less than
21
f V
Hr.
Fig. 3--InduGtan.ee ooil voltage versus steady magnetic field stength.
22
the resonance value HQ, as can be seen in Figure k. The
period of the modulation field is small compared with the
time required to sweep the steady field through the reso-
nance condition, and the amplitude of the modulation field
is much less than the line-width of the absorption curve.
As the modulation field swings back and forth about the
steady-field value, the voltage-drop variation across the
coil will vary in amplitude as the slope of the curve repre-
senting the line-shape function. The frequency of this
variation will be the same as that of the modulation field.
When H equals HQ, the voltage-drop variation will appear as
in Figure 5. Here the variation has a frequency twice that
in Figure 4. In Figure 6 the voltage variation is shown
when H is slightly greater than HQ. Note that the voltage
variation is opposite in phase to that in Figure 4 but of
the same frequency. As H sweeps through resonance, the
voltage variation across the tuned circuit will simulate that
of the first derivative of the curve representing the line-
shape function g(^) if one considers only changes in ampli-
tude and phase at the frequency equal to that of the modu-
lation field. This can be seen in Figure 7. A narrow-band,
phase-sensitive (lock-in) amplifier may be used to detect
that component of the modulated oscillator voltage which is
proportional to the derivative of the absorption line-shape.
23
Fig. ^--Inductance coil voltage vari-ation versus magnetic field strength at H less than HQ.
t V V-g-VSTT
W—> H,
Fig. 5—Inductance coil voltage vari-ation versus magnetic field strength at H equal to HQ.
vd
v
24
<44 -*
H - >
Fig. 6--Inductance coil voltage vari-ation versus magnetic field strength at H greater than Hq.
o
c-i
o o
J
height" b - width
H ~ >
Fig. 7--Lock-in amplifier output versus magnetic field strength.
25
Since it has been shown that )(0 is proportional to the
area under the AV-vs.-time curve, it is necessary to inte-
grate once the data produced by the small modulation technique
in order to determine relative susceptibilities. A description
of how the area under the line-shape curve is related to the .
width and height of its derivative [Fig. 7j is now given.
Most spin-only absorption curves are of the classical
damped-oscillator (Lorentzian) form (4, p. 121). In the X-Y
plane this line-shape is of the form
y= / (i+-KaX»0 J (27)
where and are constants. Taking the first and second
derivatives of such a function, one gets
f- (i + K txz) z
Evaluating these derivatives at the points of inflection,
one finds that
Kx- <a<tbV3 K"a= .
where a and b are as defined in Fig. 7. Thus
Y ~ (fa a b* ) /[(3 £>*/</) +x*J . (29
2.6
Integrating, one gets
? Z Y J * * dx = ( t f / f o H a . b * ) . (30)
Thus, the area under the Lorentzian line is proportional to
the height times width-squared as measured on the derivative.
For other line-shapes, the results differ only by the value 0 * •
of the numerical factor preceding ab . Since it has been
shown that }t0 is proportional to the area under the experi-
mental curve [Eq. ( 26 )J , relative susceptibilities may be
compared by taking the ratios of ab from the derivative
data, provided the line-shape is the same for all the data.
CHAPTER BIBLIOGRAPHY
1. Andrew, E. R., Nuclear Magnetic Resonance, Cambridge, University Press, 1956.
2. BLoch, F. and A. Siegert, "Magnetic Resonance for Non-rotating Fields," Physical Review, LVII (March, 1940), 522-527.
3. Griffiths, R. B., "Thermodynamic Properties of Finite Chains of Exchange-Coupled Atoms," U. S. Air Force Technical Report 131-17, AFOSR 1934, 1961.
4. Ingram, D.J.E., Free Radicals as Studied by Electron Spin Resonance, London, Butterworths Scientific Publications, 1958.
5. Kittel, Charles, Introduction to Solid State Physics, • New York, John Wiley and Sons, Inc., 1953.
6. Nagaraiya, T. and others, "Antiferromagnetism," Advances in Physics, IV (January, 1965), 1-109.
7. Pake, G. E., Paramagnetic Resonance, New York, W. A. Benjamin, 1962.
27
CHAPTER III
APPARATUS
Figure 8 is a block diagram of the electrical apparatus
used in the investigation. Situated within the inner square
of dashed lines is the solenoid of copper wire used to gener-
ate the linearly polarized field. H- . This solenoid, the
sample coil, was approximately 1.5 inches long and had an
inner diameter designed to accommodate snugly a l/4-dram
glass shell vial. A teflon vial of the same size and ca-
pacity was used to contain the galvinoxyl sample during this
investigation, however, in order to eliminate the possibility
of the spurious resonance absorptions sometimes observed in
glass. Passing through the cork stopper of the sample vial
were the two leads to a copper-constantan thermocouple whose
junction was located at the center of the sample.
Within the outer square of dashed lines are shown the
two sets of Helmholtz coils used to create the steady magnetic
field HQ and the field which modulated HQ. The HQ coils were
commercially built and had a mean diameter of 6.5 inches. A
direct current of one ampere passing through the set produced
a 220-gauss magnetic field in the central region between the
coils. The modulation coils were constructed locally, each
coil containing fifty-one turns of wire. The two sections
28
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Fig, 8--Block diagram of electrical apparatus
30
were wound on a plastic tube six inches in diameter and Were
separated approximately the same distance apart as the sections
of the commercial coils. The diameter of the modulation coils
was chosen such that they could be positioned concentrically
within the "HQ coils.
The sample coil was suspended within the inner of two
concentric glass Dewars, as shown in Fig. 9. The inner Dewar
was sealed to and supported by a brass plate which rested on
top of the wooden structure surrounding the Dewars. This
plate had a hole at its center slightly smaller than the
inside diameter of the inner Dewar. The inner Dewar had pro-
visions for connection to a vacuum pump so that when the hole
in the plate was sealed, the inner Dewar could be evacuated.
The outer Dewar was open to the atmosphere and rested on the
bottom of the wooden structure. The two sets of Helmholtz
coils were held off the bottom of this structure by a wooden
stilt, and the inner set of coils encircled the outer Dewar.
Shown also in Fig. 9 is the apparatus by which the sample
and the sample coil in which it rested were suspended within
the inner Dewar so that both were in the homogeneous region of
the magnetic fields of the two sets of coils outside the Dewars.
A concentric copper wire within the stainless steel tube was
held away from the inner walls by triangular pieces of teflon
sheet pierced with a hole at their centers so that this tube
and wire doubled as a coaxial cable providing electrical
31
Fig. 9--Dewar support structure and sample coil support structure.
32
connection to the sample coil as well as rigid support. The
length of the lower section of the tube determined the height
of the stilt supporting the coils.
A marginal oscillator-detector was connected by a flexi-
ble, shielded cable to the top of the rigid coaxial cable.
This detector was supplied by Scientifica Instruments as part
of their "V.H.F. Electron Spin Resonance Apparatus'1, Figure
10 shows the schematic of the assembled unit. The dashed
lines, indicating the two connections X and Y, show modifi-
cations added to allow the monitoring (not measuring) of the
solenoid voltage and measurement of the operating frequency
of the oscillator. A Hewlett-Packard model A-ll AR voltmeter
was used to monitor the voltage, and a Northeastern model
14-20 C frequency counter was used to measure the frequency.
The 200-volt *,,B+M for the oscillator was taken from a Heath-1
kit model PS-4 regulated power supply; the filament voltage
was taken from a 6-volt storage battery.
The power supply for the commercial coils was a voltage-
regulated device. The output voltage of the supply was vari-
able and controlled by a Helipot-type resistor in the feed-
back loop. This Helipot was connected to a reversible electric
motor. Such an arrangement allowed one to increase or decrease
linearly the value of the steady magnetic field at will.
The signal source for the modulation coils is schematicly
represented in Fig. 11. At the outset of the investigation
33
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! this signal amplifier was connected in series with the ! W* M
commercial HQ coils and power supply. That is, there were
no separate modulation coils. However, the steady current
was sufficient to saturate the core of the amplifier output
transformer and thus cause the modulation level to vary with
the D.C. field. The separate modulation coils were con-
structed to circumvent this difficulty. The power supplies
for the signal amplifier were identical to, but not the same
ones as, those used with the oscillator-detector. A Ballantine
model 643 voltmeter was used to measure the voltage across the
modulation coils.
The 155-cps signal,. amplified and impedance-matched by
the modulation-signal amplifier, was taken from a Hewlett-
Packard model 202 D variable-frequency oscillator.
An Electronics, Missiles, and Communications, Inc. model
RJB phase-sensitive detector, or lock-in amplifier, was con-
nected to the output of the oscillator-detector in order to
improve the signal-to-noise ratio of the detection system.
The output of the lock-in amplifier was displayed on a Heathkit
model EUW-20 strip-chart recorder.
The temperature of the experimental sample was monitored
with a copper-constantan thermocouple. The leads for this
thermocouple were brought out of the inner Dewar through a
small hole in the brass plate of the sample-coil support.
This hole was filled with epoxy cement after the wires were
36
installed in order to seal off the hole. The reference
junction for this thermocouple was immersed in an ice-water
bath. , The resulting thermocouple voltage was measured with
a Leeds and Northrup model 7553 K-3 potentiometer. The
working voltage was taken from a 2-volt storage battery and
the reference voltage from a standard cell. The galvanometer
used to indicate balance of the potentiometer was a Leeds and
Northrup model 2*+30-C having a sensitivity of 0.0029 microamps
per millimeter. With this arrangement thermal emf differences
of one microvolt were detectable, corresponding to temperature
differences of 0.06°K in the liquid-nitrogen temperature range.
CHAPTER IV
PROCEDURE
The various pieces of electrical apparatus were inter-
connected as previously described £Ch. 3J . The electrical
apparatus was turned on several hours in advance of the
beginning of each run in order to allow sufficient time for
the equipment to reach stable operating conditions. The
thermocouple reference-temperature bath of ice and water was
prepared three to four hours prior to each run.
At the beginning of each run, liquid nitrogen, was trans-
ferred into the inner-Dewar cavity until the level of the
liquid was approximately ten cm. above the sample. The cavity
was then sealed off with the sample support plate, and the
vacuum pump used to evacuate the cavity was turned on. A
valve was placed between the pump and the cavity to control
the pumping rate. At high pumping rates, the upper surface
of the liquid nitrogen was found to freeze rapidly. The
continued boiling of the liquid below the frozen surface
jarred the sample and sample coil, thereby introducing strong
spurious signals into the oscillator-detector output. When
the lowest possible temperature was attained, about 65°K as
determined by the thermocouple junction within the sample,
the readings of the several monitoring meters were recorded.
37
38
Throughout the subsequent run, these values were maintained
in order to insure the proportionality between and the
area under the measured absorption curves [Eq. (26)J . Table I
lists typical values for one run.
TABLE I
TYPICAL METER READINGS DURING A RUN
X-Y voltage 0.002 volts Oscillator operating frequency 48 megacycles per second Modulation-signal-amplifier voltage 0.90 volts Modulation-signal-amplifier fre-
quency 155 cycles per second Reference-signal-to-lock-in-
amplifier current 0.40- mamp
The 0.90-volt 155-cycle-per-second signal applied to
the modulation coils produced a modulation field of 15.35
gauss. Andrew (1) indicates that the modulation amplitude
should be only one eighth of the absorption line-width for
the recorded line not to be broadened due to over-modulation.
As typical line-widths for galvinoxyl were later found to be
30 gauss, it must be assumed that some broadening did occur.
But, if it can be assumed that only relative measurements
of line-width were needed and that the broadening effect
was constant, the over-modulation is insignificant.
When the temperature of the sample began to rise due to
the lowering of the nitrogen level below the sample coil, the
measurement of the variation of the voltage drop across the
39
R-L-C circuit as a function of temperature was begun. To
keep the rate of temperature rise small, the wooden structure
supporting the Dewars was surrounded with a layer of paper.
This layer reduced the radiant energy incident upon the sample
and the convection currents carrying heat to the Dewars from
the room. With this arrangement the rate of temperature rise
in the 77°K region was 0.6°K per minute. As the temperature
of the galvinoxyl sample slowly rose, the steady magnetic
field was swept linearly back and forth through the resonance
value. The steady field was increased and decreased only over
a sufficient region to determine the width of the absorption
curve between maximum and minimum slopes [Fig. 7~j . The value
of the field at resonance was fixed by holding the frequency
of the oscillator-detector constant. Continuous measurements
were made near 70°K after it was established that the critical
temperature for galvinoxyl was in this region. At tempera-
tures above 100°K, only periodic measurements were made.
The temperature of the sample was measured at the center
of each sweep through resonance with the potentiometer and
its related equipment. The resonance curves were matched with
the appropriate temperature by code numbers assigned at the
time of measurement.
During the run, the radio-frequency voltage across the
X-Y connection in the oscillator-detector was found to de-
crease with increasing temperature. To maintain the voltage
40
measured at the outset of the run, the "B+" impressed upon
the oscillator-detector was increased when necessary. Un-
fortunately, this increase also changed the gain of the
amplifier within the oscillator-detector. A series of subse-
quent measurements on the sensitivity of the amplifier gain
to plate voltage changes, however, showed that the gain of
the amplifier varied by no more than one per cent due to the
actual experimental adjustments of the T,B+" supply.
CHAPTER BIBLIOGRAPHY
1. Andrew, E. R., "Nuclear Magnetic Resonance Modulation Correction," Physical Review, XCX (July, 1953), 425,
41
CHAPTER V
RESULTS AND CONCLUSIONS
The data collected in two independent runs are shown
in Figures 12 and 13. The magnetic susceptibility, indi-
cated in arbitrary units, is actually a plot of height times
width-squared for the absorption spectra of the raw data, a
quantity which is proportional to the susceptibility [Eq. (30)]|
The horizontal scale shows the voltage output of the thermo-
couple system after its conversion to absolute temperature
equivalents. The thermocouple system was calibrated after
the data were obtained. This calibration was done by im-
mersing the "galvinoxyl junction" in liquid nitrogen, in
liquid oxygen, and in an ice-water mixture. The thermal emf
differences obtained in each case were compared with values
taken from published data for a copper-constantan thermo-
couple (8). The thermal emf differences observed for the
three calibration temperatures were such that the system used
to measure the temperature of the galvinoxyl was believed to
have indicated within *0.5°K of the true temperature in the
temperature region of 77°K. Therefore, in the plotting of
Figures 12 and 13, and in all others related to temperature,
the microvolt readings of the thermocouple €tmf differences
were converted directly to absolute temperature equivalents
using the reference previously cited.
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45
In both Figures 12 and 13 the most significant feature
is the region of maximum susceptibility. On both figures
the temperature Tc at which this maximum occurs is 70otl"K.
The subsequent decrease in susceptibility indicates that some
form of antiferromagnetic transition of the sample with pro-
gressive spin-pairing occurs below this temperature.
A plot of inverse susceptibility, ^ , versus absolute
temperature is shown in Figures 14 and 15. The slope of the
data above the X point was determined by the method of m m
least squares in order to get a best estimate for the Curie-
Weiss constant Q for galvinoxyl. From both sets of data the
average 0 was -6 2°t2°K.
A comparison of TQ and 9 for galvinoxyl with like temper-
atures for several well-known antiferromagnetic substances
is shown in Table II (6, p. 438).
TABLE II
COMPARISON OF GALVINOXYL WITH SEVERAL ANTIFERROMAGNETIC SUBSTANCES*
Substance Tc (in °K) 0 (in -°K) e/Tc
MnO 122 610 5.0
MnS 165 528 3.2 MnF£ 72 113 1.57 FeF2 79 117 1.48
NiCl2 49.6 68.2 1.37 Galvinoxyl 70+1 62t2 0.891.04
"^Source: (6)
12-280
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s
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| « / i i ? w c p d IT) rH,
3M P3
48
Table III shows a similar comparison of galvinoxyl with,
several other stable organic free radicals (9, 2, k, 1).
TABLE III
COMPARISON OF GALVINOXYL WITH SEVERAL STABLE ORGANIC FREE RADICALS
Substance Tc (in °K) 0 (in -°K) CD
Hi
D
P icry1-Amino-Carbazyl
Wurster's Blue Perchlorate
1,3-Bisdipheny-lene-2-Phenyl Allyl
Galvinoxyl
80a
186a
6d
70+1
51.7b
36.0°
2.2d
62t2
0.6
0.2
0.4 0.891.04
aSource: (9). ^Source: (2).
cSource: ^Source:
(4). (1).
The ratio 0/T_ for galvinoxyl is thus seen to lie between
those of common inorganic antiferromagnetic materials and those
of previously observed organic free radicals having antiferro-
magnetic low-temperature behavior. Values of this ratio in
the range 1 , Q/Tc4? 5 are predicted on the basis of simple
cubic two-sublattice models for the interaction between spins
(7), whereas values in the range 0.4^0/Tc4 1 are predicted
on the basis of one-dimensional chain-interaction models (5).
The relative smallness of the ratio 9/Tc for most radicals
has been taken as evidence for essentially one-dimensional
spin-spin interactions in these materials (3). Such an
49
assumption also appears reasonable on the basis of crystal-
structure data available for one radical (10) and the likeli-
hood that most of these molecules are planar, thus stacking
closely in one direction. The value of Q/Tr obtained for
galvinoxyl seems to indicate a fairly simple one-dimensional
magnetic structure for this radical also. Thus, galvinoxyl
appears to be a useful carrier for the experimental study
of electron spins which are magnetically coupled in one
direction.
The increase in line-width with decreasing temperature
[Fig. 16J which sets in the neighborhood of Tc is consistent
with previous observations (11, 12). This phenomenon is
generally understood to arise because of the larger local
fields produced by the ordered spin arrangement which sets
in below Tc.
An extended, study of the temperature dependence of
below Tc would be useful in the determination of the details
of the antiferromagnetic coupling in galvinoxyl.
W A V
CHAPTER BIBLIOGRAPHY
1. Anderson, M. E. and others, "Proton Resonance Shifts and Electron Susceptibilities in 1,3-Bisdiphenylene-2-Phenyl Allyl," Journal of Chemical Physics, XXXV (October, 1961), 1527-1528.
2. Duffy, William, "Magnetic Susceptibilities of Crystalline Stable Free Radicals in the 77°-293°K Temperature Range," Journal of Chemical Physics, XXXVI (January, 1962), 490-493.
3. Edelstein, A. S., "Linear Ising Model and the Antiferro-magnetic Behavior of Certain Crystalline Organic Free Radicals," Journal of Chemical Physics, XL (January, 1964), 488-495.
4. Edelstein, A. S. and M. Mandel, ''Antiferromagnet ic to • Ferromagnetic Transitions in Organic Free Radicals," Journal of Chemical Physics, XXXV (September, 1961), 1130-1131.
5. Griffiths, R. B., "Thermodynamic Properties of Finite Chains of Exchange-Coupled Atoms," U.S. Air Force Technical Report 131-17, AFOSR 1934, 1961.
6. Kittel, Charles, Introduction to Solid State Physics, New York, John Wiley and Sons, Inc., 1953.
7. Nagamiya, T. and others, 'TAntiferromagnetism," Advances in Physics, IV (January, 1965), 1-109.
8. National Bureau of Standards, Circular 561, Washington, Government Printing Office, 1955.
9. Porter, Wilbur, "Antiferromagnetic Ordering in Picryl-Amino-Carbazyl," unpublished master's thesis, Department of Physics, North Texas State University,
, Denton, Texas, 1964.
10. Turner, J. D. and A. C. Albrecht, unpublished report cited in Thomas, D. D. and Others, "Exciton Magnetic Resonance in Wurster's Blue Perchlorate," Journal of • Chemical Physics, XXXIX (November, 1963), 2321-23297
51
52
11. Smith., William C., "Magnetic Susceptibility of a Crystal-line Free Radical," unpublished master's thesis, Department of Physics, North Texas State University, Denton, Texas, 1962.
12. Windle, J. J. and W. H. Thurston, "Electron Spin Resonance in a Stable Phenoxy Radical," Journal of Chemical Physics, XXVII (December, 1957), 1429-P+30.
BIBLIOGRAPHY
Books
Abragam, A., The Principles of Nuclear Magnetism, Oxford, Clarendon Press, 1961.
Andrew, E. R., Nuclear Magnetic Resonance, Cambridge, Uni-versity Press, 1956.
Goldstein, Herbert, Classical Mechanics, Reading, Mass., Addison-Wesley Publishing Company, Inc., 1950.
Ingram, D.J.E., Free Radicals as Studied by Electron Spin Resonance, London, Butterworths Scientific Publications, 1958.
Jackson, John David, Classical Electrodynamics, New York, John Wiley and Sons, Inc., 1963.
Kittel, Charles, Introduction to Solid State Physics, New York, John Wiley and Sons, Inc., 1953.
Pake, G. E., Paramagnetic Resonance, New York, W. A. Benjamin, 1962.
Synge, John L. and. Byron A. Griffith, Principles of Mechanics, New York, McGraw-Hill Book Company, Inc., 1959.
Van Vleck, J. H., The Theory of Electric and Magnetic Sus-ceptibilities , London, Oxford Press, 1932.
Articles
Anderson, M. E. and others, "Proton Resonance Shifts and Electron Susceptibilities in l,3-Bisdiph.enylene-2-Phenyl Allyl," Journal of Chemical Physics, XXXV (October, 1961), 1527-1528.
Andrew, E. R., "Nuclear Magnetic Resonance Modulation Cor-rection," Physical Review, XCI (July, 1953), 425.
53
54
Becconsall, J.K. and others, "Electron Magnetic Resonance Study of Free Phenoxy Radicals," Proceedings of the Chemical Society (October, 1959), 308-309.
Bloch, F. and A. Siegert, "Magnetic Resonance for Nonrotating Fields," Physical Review, LVII (March, 1940), 522-527.
Coppinger, Galvin M., "A Stable Phenoxy Radical Inert to Oxygen," Journal of the American Chemical. Society, LXXIX (January, 1957), 501-502.
Duffy, -William, "Magnetic Susceptibilities of Crystalline Stable Free Radicals in the 77°~293°K Temperature Range," Journal of Chemical Physics, XXXVI (January, 1962), 490-493.
Edelstein, A.S., "Linear Ising Models and the Antiferromagnetic Behavior of Certain Crystalline Organic Free Radicals," Journal of Chemical Physics, XL (January, 1964), 488-495.
Edelstein, A.S. and M. Mandel, "Antiferromagnetic to Ferro-magnetic Transitions in Organic Free Radicals," Journal of Chemical Physics, XXXV (September, 1961), 1130-1131.
Hakansson, Rolf, "Proton and Carbon-13 Splittings in the ESR Spectra of Two Phenoxy Radicals," Acta Chemica Scandinavica, XVII (No. 8, 1963), 2281-2284.
Kellogg, J.B.M. and S. Millman, "The Molecular Beam Magnetic Resonance Method. The Radiofrequency Spectra of Atoms and Molecules," Reviews of Modern Physics, XVIII (1946), 323-352.
Nagamiya, T. and others, "Antiferromagnetism," Advances in Physics, IV (January, 1965), 1-109.
Pake, George E., "Magnetic Resonance," Scientific American, CIC (August, 1958), 58-66.
Windle, J.J. and W.H. Thurston, "Electron Spin Resonance in a Stable Phenoxy Radical," Journal of Chemical Physics, XXVII (December, 1957), 1429-1430.
Reports
Griffiths, R.B., "Thermodynamic Properties of Finite Chains of Exchange-Coupled Atoms," U.S. Air Force Technical Report 131-17, AFOSR 1934, 1961.
55
National Bureau of Standards, Circular 561, Washington, Government Printing Office, 1955.
Unpublished Materials
Porter, Wilbur, "Antiferromagnetic Ordering in Picryl-Amino-Carbazyl," unpublished master's thesis, Department of Physics, North Texas State University, Denton, Texas, 1964.
Smith, William C., "Magnetic Susceptibility of a Crystalline Free Radical," unpublished master's thesis, Department of Physics, North Texas State University, Denton, Texas, 1962,
Turner, J.D. and A.C. Albrecht, unpublished, report cited in Thomas, D.D. and Others, "Exciton Magnetic Resonance in Wurster's Blue Perchlorate," Journal of Chemical Physics, XXXIX (November, 1963), 2321-2329.