nmr instrumentation with solid state devices

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Master's Theses Graduate College

12-1978

NMR Instrumentation with Solid State Devices NMR Instrumentation with Solid State Devices

Syed M. Ahmed

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NMR INSTRUMENTATION WITH SOLID STATE DEVICES

by

Syed M. Ahmed

A Thesis Submitted to the

Faculty o f The Graduate College in p a r t ia l f u l f i l l m e n t

o f theDegree o f Master o f Arts

Western Michigan U n iv e rs ity Kalamazoo, Michigan

December 1978

Reproduced with permission of the copyright owner. Further reproduction prohibited without permission.

PREFACE

Since i t s development in the e a r ly f o r t i e s , NMR or Nuclear Mag

n e t ic Resonance has been a popular means o f probing in to the micro

scopic aspects o f m a tte r . The work described in th is th es is is an

e f f o r t towards construct in g two pieces o f apparatus which demonstrate

continuous wave (CW) and Pulsed NMR. The emphasis in th is p ro je c t

is on ins trum entation and in p a r t i c u la r , the problems encountered in

such a venture and how these various problems may be solved. How

e ve r , the re la te d theory has been included where necessary. The pre

sent work a lso shows how modern elements o f e le c t ro n ic s - fo r example,

in teg ra ted c i r c u i t s (o r ICs) can be u t i l i z e d to s im p l i fy the whole

p ro je c t tremendously.

Nuclei in a sample a t e q u i l ib r iu m possess both spin up and spin

down s ta te s . The corresponding magnetic quantum number m can assume

values ± i . In a steady magnetic f i e l d H0 the system's m agnetization

vec to r Mz w i l l po in t in the d i r e c t io n o f Hq and the to ta l magnetic

moment y w i l l precess around H0 w ith Larmor frequency cog- I f th is

system is e xc ite d e x t e r n a l ly by a ro ta t in g r f f i e l d Hj a t cog, the

spins o f the nuc le i w i l l f l i p to a h igher energy leve l m = - £ . As a

re s u l t y wi 11 t i p and energy w i l l be absorbed by the system. This is

c a l le d NMR absorp tion . George Pake (1 9 5 0 ) , Abragham (1961 ).

Two d is s ip a t io n mechanisms c a l le d the s p i n - l a t t i c e and sp in -sp in

in te ra c t io n s along w ith magnetic f i e l d inhomogeneity res to re the sys

tem to e q u i l ib r iu m over times ch ara c te r ize d by lo n g itu d in a l and

i i


transverse re la x a t io n times Tj and T2 . In l iq u id s the d i f fu s io n o f

nuclei due to temperature is responsible fo r re la x a t io n in both

transverse and lo n g itu d in a l d i r e c t io n s , hence T2 g ives the combined

e f f e c t o f both (above) processes. Contrary to t h is , so lid s have

d i f f e r e n t T j and T2 as nuclei are bound in a l a t t i c e s t ru c tu re . The

d is s ip a t io n mechanisms make continuous absorption p o ss ib le . The ab

sorption s ignal w idth (gaussian shape) is inverse ly proportiona l to

time T2 , which can be determined from the s ignal d i r e c t l y .

Another method o f study o f re la x a t io n times is by pulsed e x c i

ta t io n o f the above system. An intense r f burst a t Larmore frequency

is app lied and the dura tion o f the burst is adjusted to pu ll down

the m agnetization vector Mz in to the plane o f H i . In the plane o f

H i, Mz breaks up in to i t s components which s c a t te r a l l around Hq in

a c i r c l e . Over time T2 1 u n t i l th is s c a tte r in g is complete, the

system rad ia tes energy Cat wq) which is detected as an exponentia l

decay c a l le d Free Induction Decay CFID), The decay time T2 ’

includes the e f f e c t o f T j , T2 and magnetic f i e l d inhomogeneity.

The th i rd method o f determining re la x a t io n time is the sp in -

echo method in which two consecutive pulses o f 90° and 180° a t t d is

tance a p art are a p p l ie d . The 180° pulse f l i p s the sca ttered compo

nents o f Ji from the 90° pu lse , through l 80° . The components th a t

are s t i l l in the plane o f Hi then regroup a f t e r a time x from the

180° pu lse, as a re s u l t o f reversal o f the order o f the system. At

the po in t o f regrouping a signal c a l le d "spin-echo" ( re v iv a l o f

phase memory - Bloch, 19^*6) is e m it te d . The am plitude o f spin echo

i i i


is a decaying exponentia l function o f 2 t . The decay time o f the en

velope is the re la x a t io n time T2 ( in c lu s iv e o f T j ) independent o f

magnetic f i e l d inhomogeneity.

For th is p ro je c t CW NMR and pulsed NMR spectrometers were b u i l t

using s o l id s ta te devices. So lid s ta te devices have an advantage

over vacuum tubes in the areas o f response, working vo ltag es , de

coupling in the c i r c u i t r y , s iz e , and cost. However, s o l id s ta te

devices have only small s ignal handling c a p a b i l i t y and th e re fo re

s a tu ra te qu icker than vacuum tubes.

In th is p ro je c t FET's and IC *s were used fo r large impedance,

low n o is e , high gain and broad band a p p l ic a t io n s . The use o f wide

band v ideo a m p l i f ie r 1C (NE592K) in conjunction w ith FET's fo r the

f ro n t end in the re c e iv e r , s im p l i f ie s the design and takes care o f

the high impedance, low noise requirements w h ile the 1C provides

fa s t recovery from s a tu ra t io n .

Low e x c i ta t io n (10 to 12V pp) seemed to be the only problem in

the present apparatus. New products l i k e VMPA, VMOS FET tra n s is to rs

( S i l ic o n ix Incorporated) which have large power handling c a p a b i l i t ie s

a t high v o ltag e , o f f e r so lu tions to low amplitude e x c i ta t io n . Also

the re c e iv e r gain may prove to be low fo r some experiments (not per

formed here) in which case another id e n t ic a l a m p l i f ie r stage (minus

FET stage) can be added to the e x is t in g system.

Results fo r re la x a t io n time obtained from the CW NMR spectro

meter a re not r e l i a b le due to large sample s iz e : more magnetic f i e l d

inhomogeneity gets included. Also the method in i t s e l f is not very

iv


accura te . The apparatus works w ell and d isp lays the resonance e f f e c t

c le a r ly .

Results from pulsed NMR spectrometer are good e s p e c ia l ly fo r

g ly c e r in e and l ig h t machine o i l . The o th er two samples (CuSo^.S^O

and w ater) seem to l i e on the upper and lower l im i ts o f the apparatus

c a p a b i l i t y , which again depends s tro n g ly upon magnetic f i e l d homo

g en e ity .


ACKNOWLEDGEMENTS

I f in d i t d i f f i c u l t to exclude anyone who knows me personally

from being mentioned here. They have a l l contr ibuted d i r e c t l y or in

d i r e c t l y toward r e a l i z a t io n o f th is p ro je c t ; th e re fo re , I extend my

g ra t i tu d e to a l l my fr ie n d s and acquaintances.

My very special regards and thanks are due my adv isor,

Dr. K. Kameswara Rao; w ithout h is guidance and help th is work would

d e f i n i t e ly have not been possib le .

I would a lso thank Professor A. Spence o f the Department o f

Physics a t Michigan S ta te U n iv e rs i ty , Lansing, Michigan, fo r va luab le

discussions and a llow ing me the o pportu n ity to spend some time in his

NMR lab o ra to ry .

A lso , I would l ik e to acknowledge the h e lp , both f in a n c ia l and

academic, extended by the Physics Department a t Western Michigan

U n iv e rs ity and Vid-e-Com Engineering, Kalamazoo, Michigan fo r sparing

various components used in th is p ro je c t .

F in a l ly , I would l i k e to thank the members o f the Graduate Com

m itte e fo r t h e i r time reviewing th is work. A lso , A ,J . and G.G. fo r

typing the rough and f in a l d r a f ts .

Syed M. Ahmed


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UniversityMicrofilms

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1312613

AHMED* SYED M.NMR INSTRUMENTATION KITH SOLID STATE DEVICES.

WESTERN MICHIGAN U N IV E R S IT Y , M . A . , 1978

UniversityMicrofilms

International 300 n ze e b r o a d , a n n a r b o r , mi «8 io6


DEDICATION

To my fa th e r

vi i


TABLE OF CONTENTS

CHAPTER PAGE

I INTRODUCTION .......................................................................................... 1

I I CONTINUOUS WAVE TECHNIQUES OF OBSERVING NMR . . . . 4

D escrip tion o f the Techniques ........................................ 4

D escrip tion o f the Apparatus ............................................. 5

Marginal O s c i l la to r ............................................................. 5

A m p l i f ie r .................................................................................... 7

Results and Discussion ............................................................. 9

I I I PULSED TECHNIQUES OF OBSERVING N M R ............................................ 14

D escrip tion o f the T e c h n iq u e ...................................................14

D escrip tion o f the A p p a r a tu s ...................................................18

O s c i l l a t o r .......................................................................................... 18

Gate and the Gate D r i v e r ......................................................... 21

B uffer A m p l i f ie r ...................................................................... 23

Tank Coil and Probe A s s em b ly ................................................25

R e c e i v e r .............................................................................................. 27

The Spin-Echo Attachment fo r Pulse Generator . . 28

Generator T r ig g e r Source ................................................... 31

Results and Discussion 33

Results fo r FID . . . . . ................... . . . . . . 33

Results fo r Spin-Echo . . . . . . . ........................ 35

vi i i


TABLES

TABLE PAGE

2.1 F ie ld Modulation AH vs. Linewidth fo rG l y c e r i n e ...........................................................................................11

2 .2 Relaxation Times & Linewidths fo r a l l Samples . . . . 13

3.1 FID Envelope fo r G l y c e r i n e ............................................................. 36

3 .2 FID Envelope fo r W a t e r ...................................................................... 38

3 .3 FID Envelope fo r CuSOi* 5H2O (IN) ....................................................39

3 . A FID Envelope fo r L ight Machine O il (LMO) ............................AO

3 .5 Spin-Echo Amplitude fo r G lycerine ........................................... A3

3 .6 Spin-Echo Engelope fo r L igh t Machine Oil (LMO) . . . A5

3 .7 Relaxation Times fo r A l l Samples Using PulsedT e c h n i q u e s ......................................................................................A 7

ix


FIGURES

FIGURE PAGE

2.1 Marginal O s c i l la to r ....................................................................... 6

2 .2 Frequency Monitor ........................................................................... 8

2 .3 NMR Absorption Signal fo r G l y c e r i n e ....................................... 10

3.1 Various Phases o f FID S Spin-Echo Formation . . . . 16

3 .2 Block D ia g ra m ...........................................................................................19

3 .3 O s c i l la to r S B u f f e r ............................................................................ 20

3 . A Diode Gate & Gate D r i v e r .............................................................. 22

3 .5 B uffer A m p l i f i e r ........................................................................... 2A

3 .6 Sketch o f NMR Probe w ith Tank Coil S Diodes . . . . 26

3 .7 Receiver A m p li f ie r ....................................................................... 29

3 .8 Gen. Attachment fo r 180° P u l s e s ................................................ 30

3 .9 T r ig g e r Source fo r Pulse Generator .............................. 32

3 .1 0 FID Signal fo r G l y c e r i n e .......................... ....... .......................3A

3.11 FID P lo t fo r G l y c e r i n e ................................................................... 37

3 .12 Spin-Echo fo r G lycerine a t D i f f e r e n t t ................................A2

3 .13 Spin-Echo Amplitude P lo t fo r G lycerine ........................ kk

x


I . INTRODUCTION

The roots o f NMR can be traced as f a r back as 1924, to P a u l i 's

explanation o f hyperf in e s p l i t t i n g o f o p t ic a l spectra using nuclear

magnetic moments. The f i r s t successful NMR experiments were per

formed independently by P u r c e l l , Torrey and Pound (1946 ), and by

Bloch, Hansen and Packard (1946 ). These were extended by Bloembergen

(1948 ). Hahn (1950) used pulse techniques in determining the re la x a

t io n time in l iq u id s and developed spin-echo techniques which over

come the problem o f magnetic f i e l d inhomogeneity. Pulse techniques

are c o n t in u a lly undergoing changes as newer s o l id s ta te devices are

becoming a v a i la b le .

The nucleus studied in th is in v e s t ig a t io n is proton, and has

nuclear spin quantum number I = 2 . The magnitude o f the nuclear1

angular momentum vector is [ l ( I + 1) ] J fi and the magnetic quantum

number m can take the values + i and - £ . When such a substance is

placed in a steady magnetic f i e l d H0 , the m = +£ s ta te , in which the

spin vector is along the d ire c t io n o f H0 , w i l l have a lower energy

than the m = -2 s ta te , in which the spin vector is in the opposite

d ir e c t io n . Each in d iv id u a l magnetic moment vector ( in the same

d ire c t io n as spin vec tor) precesses around H0 w ith a c h a r a c te r is t ic

frequency c a l le d the Larmor frequency, ojq. The Larmor frequency and

H0 are re la te d by the fo l lo w in g expression

uj q = y H q ( 1 . 1 )

where y is the gyromagnetic r a t io o f proton. The d i f fe re n c e o f

1


2energy in the two s ta te s is hojg. This frequency f o r protons is 21 .3

MHz in a f i e l d o f 5KGauss.

I f a t th is p o in t another magnetic f i e l d vector Hj ro ta t in g a t

Larmor frequency is brought a t 9 0 ° to Hg i t s c i r c u l a r ly p o la r ize d

component ro ta t in g in the same sense as the nuclear spins induces

t r a n s it io n s from the low energy s ta te (spin up) to the high energy

s ta te (spin down). For th is to happen the f i e l d Hg and the f r e

quency o f H1 have to s a t is f y eq. 1 .1 . This phenomenon is c a l le d

Nuclear Magnetic Resonance.

In the absence o f an r f f i e l d the nu c lea r spins are in e q u i l i

brium a t the temperature o f the substance and the population o f the

lower energy leve l exceeds th a t o f the upper level by the Boltzmann

f a c to r . Hence the net magnetic moment o f the substance w i l l have a

non-zero component along the d i re c t io n s o f H g . At resonance the r f

f i e l d Hj reduces the excess o f population in the lower energy s ta te

by f l ip p in g spin-up s ta te s to spin-down. One can observe a steady

NMR absorption s ignal in a macroscopic sample s ince the in te ra c t io n s

amongst the spins and the spin s y s te m - la t t ic e in te ra c t io n s tend to

re s to re the o r ig in a l p o p u la t ion .

Since the spin system is in thermal e q u i l ib r iu m w ith the l a t t i c e

some o f the excess energy in the spin system w i l l be d is s ip a te d to

the l a t t i c e . This process is exponentia l in n a tu re and has a charac

t e r i s t i c time T j c a l le d s p i n - l a t t i c e or thermal re la x a t io n tim e.

This is a lso the c h a r a c te r is t ic time in which the magnetic moment

component along the d i r e c t io n o f Hg is restored to i t s steady s ta te

value ( o f f resonance). Hence i t is c a l le d lo n g itu d in a l re la x a t io n


3

re la x a t io n t im e.

Each nuclear spin f in d s i t s e l f not only in an ap p lied magnetic

f i e l d H0 , but a lso in a small local magnetic f i e l d produced by the

neighboring sp ins. This sp in -sp in in te ra c t io n makes the resonance

not p e r fe c t ly sharp as suggested in eq. 1 .1 . The resonance l in e w i l l

have a w idth comparable to the average local f i e l d . The l inew id th

o f the resonance is re la te d to a c h a r a c te r is t ic time T2 (sp in -sp in

re la x a t io n time) by the fo l lo w in g equation (Andrew, 1958).

AH, = - f - (1 .2 )2 yT2

The sp in -sp in in te ra c t io n time T2 is the time during which the

in d iv id u a l nuc lear spins precess around H0 in phase, inducing a non

zero magnetic f i e l d component along the d ire c t io n perpend icu lar to

H0 . Hence T2 is c a l le d transverse re la x a t io n tim e.

In d i l u t e l iq u id s the thermal a g i ta t io n causes both lo n g itu d i

nal and transverse components to reach e q u i l ib r iu m in comparable

tim es, hence T j = T2 .

There are b a s ic a l ly two techniques fo r studying NMR, the con

tinuous e x c i ta t io n method and the pulse e x c i ta t io n method. In the

f i r s t method the nuclei in the sample are e xc ited by a continuous

wave (CW) e le c t r o n ic o s c i l l a t o r (source o f Hj f i e l d ) a t Larmor f r e

quency. In the second method the e x c i ta t io n is in the form of

bursts o f r f f i e l d a t Larmor frequency.

The method, apparatus, and re s u lts fo r the CW technique are

covered in Chapter I I , and the pulsed technique is covered in

Chapter I I I .


I I . CONTINUOUS WAVE TECHNIQUES OF OBSERVING NMR

A. Descrip tion o f the Technique

In the absorption mode d e tec t io n o f NMR, w ith continuous radio

frequency wave e x c i ta t io n , the energy supplied by the r f f i e l d to the

nucle i is monitored. The sample is put in a te s t tube and the te s t

tube is placed in the tank c i r c u i t o f an r f o s c i l l a t o r . This allows

a good coupling between the o s c i l l a t o r and sample fo r energy tra n s fe r

(Bloch, 1946). The tank c i r c u i t is b u i l t p h y s ic a lly separate from

the res t o f the o s c i l l a t o r c i r c u i t to keep the e le c t ro n ic c i r c u i t

away from the magnetic f i e l d H0 . The tank c i r c u i t conta in ing the

sample te s t tube is now placed in the magnetic f i e l d Hg such th a t the

tank c o i l ax is is a t 90° to the f i e l d H0 . At resonance the energy

supplied to the nuclei is more than a t o f f resonance. The r f o s c i l

l a t o r used in the method o s c i l l a t e s m arg ina lly or weakly. This is

accomplished w ith an a d ju s tab le feedback so th a t i t can be operated

a t a po in t where i t b a re ly o s c i l l a t e s . The current supplied to the

o s c i l l a t o r is monitored and the e x tra current drawn by the o s c i l l a

t o r a t resonance is a m p lif ie d and displayed on the o sc il lo sco p e .

The signal is Gaussian in shape and the lin ew id th is defined

as the w idth o f the signal a t h a l f maximum am plitude. Eq. 1 .2 which

gives the re la t io n between re la x a t io n time and the l in e width is

v a l id only fo r a p e r fe c t ly homogeneous Hq. In p ra c t ic e Hq is never

p e r fe c t ly homogeneous fo r a l l the nuclei throughout the volume o f

the sample. This is l i k e the l o c a l - f i e l d e f f e c t broadening the

resonance; hence the l in ew id th observed in the experiment is given

4


5

by the fo l lo w in g equation:

AH = (2 .1 )

y m

T2* is the c o n tr ib u t io n from the magnetic f i e l d inhomogeneities

The resonance l in ew id th in an inhomogeneous magnetic f i e l d is

more than in a p e r fe c t ly homogeneous f i e l d by a fa c to r determined by

T2* .

The s ize o f the sample determines the s ig n a l - to -n o is e r a t io and

the w idth o f the s ig n a l . The la rg e r sample gives a b e t te r s ig n a l -

to -n o is e r a t i o , but the signal becomes broader owing to the magnetic

f i e l d inhomogeneities.

B. D escrip tion o f the Apparatus

1. Marginal O s c i l la to r

The c i r c u i t diagram o f the o s c i l l a t o r is shown in F ig . 2 .1 .

The o s c i l l a t o r is o f the C o lp i t ts type using 2N5^59 FET fo r low

d r i f t and noise on a copper s t r i p m atr ix -b o ard . I t operates margin

a l l y around 130 yA. The tank c i r c u i t c o i l consists o f 12 turns o f

18 swg enamel w ire , wound d i r e c t l y over the te s t tube conta in ing the

sample. The diameter o f the te s t tube is 1 cm. Since the c o i l is

r i g i d , i t a lso functions as a te s t tube h o ld er. The c o i l is mounted

a t the end o f 12", 3 /8 " diameter copper tub ing . One end o f the c o i l

is grounded to the tube w h ile the o th e r runs v ia a piece o f RG59U

cable through the tub ing . The o th er end o f the tubing is f ix e d w ith

an Amphenol connector ( to make the tank c i r c u i t detachable) to a


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7“ x 5" x 3“ aluminum box. The box then contains both the o s c i l l a

to r and a m p l i f ie r c i r c u i t boards.

A good ground is es tab lish ed w ith in the box by running a piece

o f copper w ire b ra id along the length o f the box. A l l ground con

nections are t ie d to the b ra id which in turn is t ie d to the box.

This arrangement reduces the noise tremendously.

The o s c i l l a t o r regeneration contro l (p o s i t iv e feedback) is pro

vided a t the broadside o f the box along w ith frequency contro l and

a m p l i f ie r n u ll c o n tro l . The frequency contro l is achieved by vary ing

the capacitance across the tank c o i l w ith a v a r ia b le cap ac ito r and

geared d r iv e . The frequency range thus obtained is k MHz, s ta r t in g

a t 12.8 MHz.

A separate wide-band a m p l i f ie r (F ig . 2 .2 ) a llows frequency

m onitoring . In th is experiment the frequency was only determined

a f t e r the measurements on s ignal were made, because o f a noisy f r e

quency counter. Some d e v ia t io n in frequency occurs when cables are

attached to the a m p l i f ie r but th is was measured to be less than

0.5%.

2 . A m p li f ie r

The a m p l i f ie r is b u i l t using a p7^1 op era t io n a l a m p l i f ie r . The

c i r c u i t diagram is shown in F ig . 2 .1 . The gain o f the a m p l i f ie r is

around 2000. An e x te rn a l contro l over o f f s e t n u ll is provided, be

cause w ith d i f f e r e n t samples d i f f e r e n t conditions o f m a rg in a l i ty are

e s ta b l is h e d . So a small change in input vo ltag e occurs which has to

be balanced o f f fo r optimum a m p l i f ie r o p e ra t io n . The a m p l i f ie r is


8

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9

d .c . connected to the point in the o s c i l l a t o r c i r c u i t which l ie s on

the branch carry ing the o s c i l l a t o r c u rre n t . Once the nu ll is es ta

b lished (zero d .c . leve l a t the output) the a m p l i f ie r picks up any

dev ia t io n s from the n u l l condition and a m p li f ie s them. The output

is connected to a scope or X-Y recorder d i r e c t l y .

C. Results and Discussion

The steady magnetic f i e l d H0 is modulated w ith 60 Hz by passing

60 Hz c u rren t through a p a ir o f yoke c o i ls wound around the Hg mag

net poles. The p r in c ip a l f i e l d Hg in the above case is passed twice

in one c yc le .

(H 0 - AH) Hg = = (H 0 + AH)

The e x te n t o f scan 2aH is important. This has to be determined

e x p e r im e n ta l ly . For a s u i ta b le value o f modulating current the s ig

nal is obta ined . L a ter the modulating current is adjusted to get a

region o f constant w idth o f the signal fo r v a r ia t io n s in the modula

t in g c u rre n t . Large modulating current d is to r ts the Hg f i e l d and

hence shortens the re la x a t io n time T2 ; correspondingly the signal

width increases.

The s ignal fo r g ly ce r in e is shown in F ig . 2 .3 - The s iz e o f the

sample used in the experiment was approximately 2 c .c . The l in e

w idth is measured fo r a number o f modulation se tt in g s and the data

is given in Table 2 .1 . A value o f the l in ew id th was chosen in an

area where the l in ew id th v a r ia t io n was f a i r l y constant. The value

o f T2 is c a lc u la te d from th is l inew id th to be 0 .38 msec. The un

c e r t a in ty in the value can be as high as 10% due to the inaccuracy


10

Fig 2.3 NMR Absorption Signal

for Glycerine.(a) off resonance(b) at resonance


I I

Modulation AH Gauss

LinewidthGauss

1.4 0.202.2 0.242.5 0.282.9 0.293.3 0.293.8 0.284.2 0.274.5 0.295.3 0.325.9 0.30

Table 2.1 Field Modulation AH vs Linewidth for Glycerine


12

o f the method.

The experiment is repeated fo r w ater and CuSO^.S^O ( IN )

samples. The value o f T2 1 fo r w ater was found to be 0 .3 ^ msec and

th a t fo r CuSOij.SI^O was 0 .39 msec. The value o f l inew id ths and the

re la x a t io n times fo r a l l the th ree compounds a re given in Table 2 .2 .

The value obtained fo r a l l the th ree compounds is approxim ately the

same and i t was found from pulsed measurements th a t the c o n tr ib u t io n

from the magnetic f i e l d inhomogeneity dominated the c o n tr ib u t io n

from s p in -s p in in te r a c t io n .


.13

SampleLine-widthGauss

Relaxation Time

T' mSec

Water 0.325 0. 34

Glycerine 0.286 0.38

CuS0^5Hp 0.285 0.39

Table 2.2 Relaxation Times & Linewidths

for all Samples


I I I . PULSED TECHNIQUES OF DETERMINING NMR

A. D escrip tion o f the Technique

I f a s in g le r f pulse is applied to a sample a t resonance, the

f i e l d s trength Hj w i l l t i p the lon g itu d in a l m agnetization Mz away

from the H0 d ire c t io n because the r f f i e l d induces t ra n s it io n s from

the spin-up to spin-down s ta te . The angle through which Mz ro tates

depends upon the energy contained in the burst envelope.

I f the applied e x c i ta t io n (H ^ energy is s u f f ic ie n t the Mz can

be made to t ip through 90° w ith respect to the d ire c t io n o f magnetic

f i e l d which brings i t in to the plane w ith Hj (F ig . 3 -1 A ). Rotation

o f Mz through such precise angles is r e la t i v e ly easy to achieve w ith

pulsed e x c i ta t io n , using bursts a t Larmor frequency o f s u ita b le amp

l i tu d e and width x given by the r e la t io n (Carr and P u rc e l l , 1954)CO

YHlTCJ = 6

I f 0 in the above expression is made 9 0 ° , then the corresponding

burst duration x is c a l le d 90° pulse. The pulse width x must beCO (0

very much less than T2 , hence large Hj amplitude and narrow x^ must

be used, x o f 50p sec or less would enable studying l iq u id samples(0

whose T2 l i e in the range o f several msec.

The transverse magnetization a f t e r a s in g le 90° pulse w i l l

g rad u a lly decay a t time constant T2 ‘ determined (eq. 2 . 2) by the

sp in -sp in re la x a t io n time (T2) and the c h a r a c te r is t ic time o f con

t r ib u t io n from magnetic f i e l d innomogeneities (T2* ) . This time is

the same as the time which determines the lin ew id th in CW experiment.

14


15

The e x p o n e n t ia l ly decaying transverse m agnetization a f t e r a 90° pulse

is c a l le d Free Induction Decay (F ID ) . Immediately a f t e r the 90°

pulse, the net m agnetization is in X-Y plane w ith in d iv id u a l magnetic

moment vectors precessing in phase around H0 . Because o f sp in -sp in

in te ra c t io n and magnetic f i e l d inhomogeneities the in d iv id u a l mag

n e t ic moment vectors g rad u a lly get out o f phase. A f t e r time T2 '

the in d iv id u a l magnetic moment vectors spread out in a c i r c l e in the

X-Y plane po in tin g in a l l possib le d i r e c t io n s . Due to th is random

d is t r ib u t io n mutual c a n c e l la t io n o f the magnetic moments takes place

and the net re s u l t is zero .

I f another pulse o f 180° w idth is app lied a f t e r the 90° pulse,

the precession o f in d iv id u a l magnetic moments can be reversed and

manifested in what is c a l le d spin-echo (Hahn 1950a, 1950b, 1952).

The spin-echo is expla ined as fo llo w s:

The 180° pulse app lied a t a time x a f t e r the cessation o f the

f i r s t pulse (F ig . 3 -1 E, F) reverses the transverse components of the

in d iv id u a l magnetic moment vec to rs . Hence a t a time x beyond the

second pu lse, a l l the magnetic moments w i l l be back in phase

(F ig . 3 .1H , I ) . The spin-echo is a combination o f two f re e induction

decays back to back a t a time 2x from the 90° pulse. The amplitude

o f spin-echo is not the same as the o r ig in a l FID, s ince some spins

lose t h e i r phase coherence due to sp in -sp in in te ra c t io n s and some

spins have returned to the spin-up s ta te due to s p i n - l a t t i c e in t e r

a c t io n s . The envelope o f the spin-echo amplitudes is an exponen

t i a l l y decaying curve w ith a c h a r a c te r is t ic time T2 , which a lso in

cludes some e f f e c t due to T j .


16


17

For observing NMR there are two d i f f e r e n t sample c o i l configu

ra t io n s , the d o u b le -c o il method and the s in g le -c o i l method. In the

d o u b le -c o il method, separate c o i ls a re used fo r t ra n s m it te r and

re ce ive r and the re c e iv e r c o i l is a ligned a t 90° w ith the t ra n s m it te r

c o i l . Both c o i ls are perpend icu lar to H0 and the re c e iv e r c o i l is

c lo s e ly wound around the sample fo r maximum coupling . Since the re

c e iv e r c o i l is a t 90° to the t ra n s m it te r c o i l , i t detects only the

signal from the sample.

The disadvantages in th is technique are th a t e x tra power is re

quired fo r the t ra n s m it te r to overcome ra d ia t io n losses as the

t ra n s m it te r c o i l is p h y s ic a lly away from the sample. Also i t is

d i f f i c u l t to m aintain o r th o g o n a l i ty between the t ra n s m it te r and re

c e iv e r c o i I s .

In the s in g le -c o i l method a s in g le c o i l serves both as tra n s

m i t te r and re c e iv e r c o i l . The s in g le c o i l technique provides a

d is t in c t advantage o f low coupling losses between the system and

sample fo r both t ra n s m it te r and re c e iv e r . The major problem, how

e v e r , is the d i r e c t p ick-up o f e x c i ta t io n from the t ra n s m it te r by the

re c e iv e r . The d i r e c t p ick -u p , being large in am plitude, saturates

the re c e iv e r , i . e . , the output o f the re ce ive r goes high and does

not re tu rn to zero immediately a f t e r the e x c i ta t io n subsides.

In th is experiment the s in g le -c o i l method was employed a f t e r

so lv ing the problem o f re c e iv e r s a tu ra t io n by using a fa s t recovery

re c e iv e r .

An e le c t r o n ic o s c i l l a t o r operating a t Larmor frequency is the

source o f the o s c i l l a t in g f i e l d , as in CW NMR. This o s c i l l a t o r


18

should be s ta b le and does not have to operate m a rg in a l ly . The o u t

put o f the o s c i l l a t o r is fed in to a gate which is switched on and o f f

e le c t r o n ic a l ly by a p u lse -g en era to r . The output o f the gate is the

burst o f r f o f desired dura tion (d u ra tio n may be varied by vary ing

the on-t im e o f the g a te -p u ls e ) . This burst o f r f a t Larmor f r e

quency impinges upon a tank c i r c u i t tuned to th a t frequency. The

sample te s t tube is inserted in to the tank c o i ls and the c o i l is

placed in the magnetic f i e l d H0 .

A high-impedance r f a m p l i f ie r is hooked up to the sample c o i l

p a r a l le l to the e x c i ta t io n . This a m p l i f ie r acts as a re ce ive r and

picks up the e x c i ta t io n (burs t) along w ith the FID signal fo l lo w in g

the b u rs t .

B. D escrip tion o f the Apparatus

The block diagram o f the apparatus isstrawn in F ig . 3 .2 . A l l

the components o f the system except fo r the pulse generator (DATA-

PULSE genera tor model #110 B) were designed and constructed. The

d e s c r ip t io n o f each o f the components o f the system fo llo w s . The

spin-echo attachment fo r the pulse generator generates 90° and 180°

pulses fo r observing spin echos. This is bypassed w h ile observing

the f re e induction decay.

1. O sc i1la t o r

The c i r c u i t o f the o s c i l l a t o r is shown in F ig . 3 *3 . The o s c i l

l a t o r is a C o lp i t t - t y p e w ith c ry s ta l con tro l fo r frequency s t a b i l i t y .

The main o s c i l l a t o r is b u i l t around a s in g le : 2N3904 t ra n s is to r (Q j) .

A v a r ia b le contro l on feedback is provided to se t the amplitude a t

some s u i ta b le leve l along w ith waveform symmetry. The frequency of


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taken from the c o l le c to r o f the t r a n s is to r (which c a r r ie s the tank

c i r c u i t ) and is fed in to an e m it te r fo l lo w e r (Q2 ) which provides

is o la t io n from the d i r e c t load and a m p li f ie s power. The output from

the e m it te r fo l lo w e r is s u f f ic ie n t to d r iv e a 75ft load. The output

o f the o s c i l l a t o r is set a t about IV pp.

2 . Gate and the Gate D r iv er

The c i r c u i t diagram fo r the gate and the gate d r iv e r is shown

in F ig . 3 -^ . The diode gate c i r c u i t was taken from Hawk, Sharp and

Tolan (197*0 . The c i r c u i t was modified fo r operation a t lower f r e

quencies. The diodes are o f high-speed switching type 1N485. The

gate was b u i l t in a copper box w ith separate compartments fo r each

component.

The switching operation o f the gate is as fo l lo w s . When +2V

are app lied a t the switching in p u t, diodes Dj and D2 a re turned on

w h ile D3 is turned o f f . This allows the r f ( o s c i l l a t o r outpu t) to

go through from to L2 and o u t . I f -2V are app lied a t the

switching in put, Dj and D2 are turned o f f w h ile D3 is turned on.

Therefore the r f gets a ttenuated through a r a t io (^ rev/ ^ f o r ^

diodes Dj and D2 . This a t te n tu a t io n is fu r th e r enhanced by

(R /Z . ) o f the inductor L? and the load, rev L z

The r is e and f a l l times o f the gate a re less than 50 nsec, which

is h a l f the period o f the r f wave. I t has good a tte n u a t io n and the

base l in e in the o f f s ta te is much less than 1 mV. The in s e r t io n

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22

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The gate d r iv e r c i r c u i t s h i f t s the leve l o f the pulse genera

to r output to ±2V. Also i t provides power to d r iv e the gate. The

d r iv e r (Q2 Stage) is designed so th a t in the longer ( o f f period)

duty cyc le the load is t ra n s fe rre d to the negative power supply

d i r e c t l y . The o n -cycle (dura tion o f pulse) is only a small f ra c t io n

o f the o f f - c y c le , in the on-tim e the t r a n s is to r (Q.2 ) is turned hard

on and connects the load to the +5V supply. This a llows minimum

d is s ip a t io n o f power ins ide Q.2 . Q2 needs a 3V d r iv e from +VCC to

cut o f f to approxim ately +2V fo r tu rn -o n . This is provided by the

d r iv e r Q^. Qj is d riven by the pulse generator between 0 to +2V or

more.

3. B u ffe r A m p li f ie r

The c i r c u i t diagram o f the b u f fe r a m p l i f ie r is shown in

F ig . 3 .5 . The use o f an a m p l i f ie r a f t e r the gate makes things more

manageable. The a m p l i f ie r should have enough gain to provide an

output meeting the burst amplitude requirement. A lso i t should be

low noise and l in e a r to avoid d is t o r t io n . The output impedance o f

the a m p l i f ie r should be high to o f f e r minimum load on the tank c o il

during o f f - t im e . A p a i r o f cross-coupled diodes in between the am

p l i f i e r and tank c o i l helps to improve not only a t te n tu a t io n but

a lso b u ffe rs the a m p l i f ie r from the tank c o i l during o f f - t im e .

This a m p l i f ie r is a broad-band r f a m p l i f ie r . I t operates in

the d i f f e r e n t i a l mode which is p a r t i c u la r l y s u i ta b le fo r r f because

o f low input capac itan ce . Also d i f fe re n c e a m p l i f ie r s possess large

s ig n a l-h a n d lin g c a p a c ity . T ra n s is to rs Q} and Q2 form the d if fe re n c e

a m p l i f ie r w ith Q.3 serv ing as a constant c u rren t source ( fo r


24

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temperature s t a b i l i t y o f Qj and Q.2) . The s in g le ended (one input

t ie d to ground) gain o f th is a m p l i f ie r is around 12 (a t 8 .3 MHz).

The output o f the a m p l i f ie r is taken a t the c o l le c to r o f Q2 anc* 9oes

through the is o la t io n diodes to the tank c i r c u i t . This is set a t

10V pp.

k . Tank Coil and Probe Assembly

A sketch o f the tank c o i l and probe assembly is shown in F ig .

3 .6 . In the s in g le -c o i l method, the tank c o i l acts as e x c i to r during

burst-on and as re ce ive r during b u r s t -o f f cyc le . This c o i l th e re fo re

should have a high Q.. But too large a Q prolongs the inherent

" r in g in g " o f the tank c i r c u i t a f t e r the b u rs t . I f the r ing ing is o f

s u f f ic ie n t am plitude, i t acts as a continuation o f burst (e x c i ta

t i o n ) . The ring ing u n fo rtu n a te ly is in e v i ta b le in a s in g le c o i l

system. Therefore a t r a d e - o f f between high Q. and ring ing has to be

made. The cross-coupled diodes o f f e r a load through the a m p l i f ie r

output impedance fo r s ignals la rg e r than 1 .2 to 1.4V pp ( fo r Si

diodes) present across the tank c o i l . This cuts down the ring ing

leve l to 1 .2 to 1 .4V pp. I f the r ing ing is kept to i t s minimum i t

usua lly las ts a couple o f ysec.

The tank c o i l is wound w ith 20 swg enamel w ir e , 28 tu rn s , using

the sample te s t tube (k mm. d ia . ) as a form. L a te r the te s t tube is

pu lled out and the c o i l s tre tched to the approximate length o f 14"

(h a lf -s p a ce ) fo r high Q.. The c o i l is mounted in a frame o f 3" x 6"

made from 14" wide 16# copper s t r i p . The c o i l s i t s approximately 1"

from the f a r end, ins ide a 2" x 3" compartment formed by adding a

r ib to the main frame. A 3 /8 " hole was bored in the frame d i r e c t ly


Reproduced

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without

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Tank trimmer C, Receiver coupling

trimmer CaReceiver

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Ficr 3.6Sketch of NMR Probe with Tank Coil & Diodes

MON

27

above the c o i l . The sample te s t tube is f ix e d to a s to p -c o rk . The

stop-cork is inserted in to the hole in the frame, such th a t the t e s t -

tube is lowered in to the c o i l below. The main frame is f ix e d w ith

the v a r ia b le c a p a c ito r Cj along w ith the f ix e d 500 pf c ap ac ito r and

the cross-coupled diodes. The second v a r ia b le re ce ive r coupling

cap a c ito r C2 is f ix e d a t the o th e r end o f the frame, c lose to the

output fo r the re c e iv e r . Two BNC outputs are provided fo r connecting

the e x c i ta t io n and re ce ive r system. The tank c o i l is connected to

the re c e iv e r and e x c i ta t io n BNC connectors by a 20-gauge w ire running

through feedthrough te rm in a ls f ix e d in the r ib s .

The main frame is f ix e d to a hollow square aluminum pipe (1" x

1 " ) , about 2 f t . long. The rod is held in an aluminum v ic e - ja w g r ip

f ix e d on the magnet frame. This a llows the probe end (frame) to be

l i f t e d above and out o f the magnetic f i e l d fo r changing samples and

set-up procedure. When the probe is lowered in to the magnetic f i e l d ,

the copper frame is about 1" out o f the magnetic f i e l d . This allows

the re c e iv e r box to be mounted r ig h t over the frame w ithout the use

o f cab les . A la rg e aluminum box was used fo r holding the sm aller

o s c i l l a t o r , gate and a m p li fe r boxes, a l l a t once. These boxes were

held together by a ground (copper w ire ) b ra id soldered to each box

and to the power supply ground. The power supply connections were

provided on the b igger box and adequately decoupled. From th is point

power was d is t r ib u te d to the res t o f the system. The switching sys

tem was, however, kept outs ide and was connected by a cab le .

5 . Receiver

A h igh -ga in (45 d b ) , low-noise and fa s t -re c o v e ry re c e iv e r system


28

was designed and b u i l t to de tec t the NMR s ig n a l . The c i r c u i t diagram

o f the re c e ive r is shown in F ig . 3 .7 . The s ig n a l - to -n o is e r a t io can

be improved tremendously by employing good r f construction techniques,

e . g . , good ground, s h ie ld in g and short connecting wires or cab les .

Special care has to be taken in b u ild in g the f ro n t end o f the

re ce ive r ( f i r s t section o f a m p l i f ie r fo l lo w in g the rece iv in g c o i l ) .

Any noise generated in the f i r s t stage is m u lt ip l ie d in the subsequent

stages. Hence the re c e iv e r f ro n t end is chosen to be a high input

impedance FET b u f fe r (Q.^, Q2 ) .

The output o f the b u f fe r is fed in to the input o f a h igh-ga in

video a m p li fe r . The main element o f the video a m p l i f ie r is the

1C NE592K. The 1C is w ired fo r maximum gain which is around db.

The bandwidth o f the 1C a t maximum gain is around 50 MHz. The o u t

put o f the video a m p l i f ie r is then fed in to the b u ffe r (Q3) . The

f i n a l output is taken a f t e r the b u f fe r . A small (5 ^H) a d ju s tab le

inductor is placed in s e r ie s w ith the output to balance the scope

probe capacitance. This inductor is adjusted fo r maximum s ig n a l .

The re c e iv e r c i r c u i t was b u i l t in a small copper-sheet box w ith

BNC connector fo r input and ou tp u t. Good power supply decoupling has

been employed wherever necessary. The re ce iv e r box was d i r e c t l y

hooked to the main frame (no cable used) by the BNC male to BNC f e

male coupling . The re c e iv e r s i t s "piggy-back" on the o u te r end o f

the main frame ju s t o u ts ide the magnetic f i e l d .

6. The Spin-Echo Attachment fo r the Pulse Generator

The schematic diagram is shown in F ig . 3 .8 . The pulse generator

attachment is used to produce l 80°pu lses from the double-pulse


29

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generator output fo r the spin-echo experim ent. Double p o s it iv e p u l

ses (o f the same w idth) from the generator en te r the NAND (7^00) gate

Al and get in v e r te d . The JK f l i p - f l o p (7^73) is a d iv id e -b y -tw o

counter which changes s ta te a t the negative -go ing edge o f the second

pulse. This t r ig g e rs the monostable m u l t iv ib r a to r (7^121) which

generates a pulse o f w idth determined by RC.

The output o f the monostable m u l t iv ib r a to r is inverted in A

and app lied to A3 . The second input o f A3 is t ie d to output o f Aj

which gives a t the output o f A3 two pulses , w ith leading-edge r e la

t io n s h ip w ith the in p u t. The tim ing o f the c i r c u i t is a lso shown

in F ig . 3 .7 . The w idth o f the f i r s t pulse and the d is tance between

the two pulses are var ied a t the pulse g enera to r . The w idth o f the

second pulse is var ied by changing the 1 potentiom eter in the c i r

c u i t . The JK f l i p - f l o p is reset p r io r to the a r r i v a l o f the f i r s t

pulse from the genera to r .

7- Generator T r ig g e r Source

A schematic diagram o f the t r ig g e r source is given in F ig . 3 -9 .

The Data Pulse Model 110 B pulse generator has a in te rn a l t r ig g e r

which is l im ite d to 50 Hz. In the FID and spin-echo experiments a

low re p e t i t io n ra te fo r the pulses is req u ired . The t r ig g e r source

o f F ig . 3 -9 can be attached to the pulse generator ex terna l t r ig g e r

inpu t. An NE 555 1C is connected as a m u l t iv ib r a to r o f f ix e d on-

time (T = R2C) and v a r ia b le o f f - t im e = RiC) . The maximum

o f f - t im e is approxim ately 1 sec. In the output a negative -go ing

pulse is generated w ith a r e p e t i t io n ra te determined by R C.


32

G\n

-HEn


Trigger

Source

for

Pulse

Gene

rato

r.

C. Results and Discussion

The apparatus is connected as shown in the block diagram F ig .

3 .2 . Except fo r the magnet which requires a few hours to s t a b i l i z e ,

the res t o f the c i r c u i t can be turned on and used almost immediately

Sample s-tee in th is experiment is im portant, s ince a la rg e r sampl

would involve a la rg e r c ro ss -sec t io n o f magnetic f i e l d H0 . This

would make the e f f e c t o f inhomogeneity more pronounced, g iv ing r is e

to u n c a l le d - fo r t ra n s ie n t phenomena. In th is experiment th in -w a lle d

te s t tubes (4 mm. in diam eter) c on ta in ing a sample l iq u id column o f

about 1 inch, were used.

1. Results fo r FID

For the FID experiment the pulse generator attachment c i r c u i t

is not used. The pulse generator output is set fo r s in g le pulse

and run d i r e c t l y in to the g a te -d r iv e r . The o s c i l l a t o r frequency is

kept constant a t ^0 and f i e l d Ho v ar ie d w ithout modulation. A f te r

the s ignal is observed i t is maximized by changing the pulse width

to 9 0 ° . The re c e iv e r coupling c ap a c ito r (C2 in F ig . 3 -7 ) is trimmed

f o r maximum am plitude o f the s ig n a l . Also i t s re la x a t io n time is

optim ized by moving the sample p o s it io n to a more homogeneous spot

in the magnetic f i e l d .

The s ignal is an exponentia l decay envelope, in the case o f

s t r a ig h t r f a m p l i f ic a t io n (as in th is experiment) and the signal fo r

g ly c e r in e is shown in F ig . 3 .1 0 . At s l i g h t ly o ff-resonance posi

t io n s the s ignal s p l i t s up in to beats which reduce in number but

increase in am plitude c lo s e r to Hq as can be seen from F ig . 3 .1 0 .


34

Fig 3.10 FID Signal for Glycerine.(a) at slightly off resonance(b) at resonance


35

The data fo r various points along the decay vs. the time are

read o f f on the scope in conjunction w ith the sweep tim e . When

noting the decay tim e , i t is advisab le to s t a r t a t some p o in t (couple

o f hundred ysec - or even 1 msec i f necessary) a f t e r the peak. The

f i r s t po rt io n is u su a lly not a continuous exponentia l fu nc tion owing

to recovery time o f rece ive r and r in g in g .

The n a tu ra l logarithm o f amplitude o f the decay signal a t various

points is p lo t te d versus tim e. The slope o f th is graph is the com

bined e f f e c t o f Jz and inhomogeneity (Eq. 2 . 2 ) .

The FID amplitudes (A) fo r g ly c e r in e a re given in Table 3 .1 .

The p lo t o f the 1n(A) vs. time is given in F ig . 3 -11 . The best pos

s ib le s t r a ig h t l in e is drawn connecting the points and the slope o f

the s t r a ig h t l in e gives l z fo r g ly c e r in e to be 0 .884 msec.

The experiment is repeated fo r w a te r , IN w ater s o lu t io n o f

CuSO ‘ 5H20, and l ig h t machine o i l . The FID amplitudes are given in

Tables 3 .2 , 3 .3 , and 3-4 re s p e c t iv e ly . The value o f T2 1 fo r water

is 0 .875 msec, th a t fo r l ig h t machine o i l , 0 .816 msec, and th a t fo r

CuSO *5H20 s o lu t io n , 0 .37 msec.

2 . Results fo r Spin-Echo

The basic setup and operation is the same as in the case o f FID,

except fo r the pulse generator attachm ent. The pulse generator a t

tachment is connected to the generator and the generator output is

set fo r double pulses. The attachment output is fed in to the gate

d r iv e r d i r e c t l y . The attachment output is monitored. When the pulse

w idth contro l in the attachment c i r c u i t is v a r ie d the second pulse is

widened. I f i t is the f i r s t pulse th a t widens, pressing the reset


36

T, mSec. FID Amp. X50 mV.

In (Amp)

0 4 1.39

1 3.3 1.19

2 2.5 0.92

3 2 0.69

4 1.6 0.47

5 1.3 0.26

6 1 0

Table 3.1 FID Envelope for Glycerine

T*r = 108 p-Sec.


37

aa

UUU]2

u2

<Uc-rHu0Vi-H

iH 1—1• ocou

tJ 0-H falfa -p

0rHfaoHfa

n s a n i n d w v a u j d n ili


T mSecFID Amp. 50 mV In (Amp)

0 1.4 0.34

0.2 0.8 -0.22

0.4 0.6 i—iin•01

0.6 0.5 -0.69

00.o 0.4 -0.92

1 0.2 -1.61

Table 3.2 FID Envelope for Water

*C„ = 48 jJL Sec


39

T mSecFID Amp.

50 mV In(Amp)

0 2.8 1.03

0.1 2.4 0.88

O • to 1.8 0.59

0.3 1.4 0.34

0.4 1.2 0.18

0.5 0.9 -0.11

0.6 0.6 -0.51

Table 3.3 FID Envelope for CuSQj, 5Hp (IN)


ko

T mSecFID Amp

50 mV In(Amp)

0 4 1.39

o • to 3.6 1.28

0.4 3 1.10

0.6 2.4 0.88

0.8 1.8 0.59

1 1.3 0.26

1.2 1 0

Table 3.4 FID Envelope for

Light Machine Oil (LMO) Xu, = 108 jitSec


switch on the attachment board t ra n s fe rs the contro l to the second

pulse.

The f i r s t pulse is set fo r 9 0 ° . The second pulse is set a t

tw ice the w idth o f the f i r s t w ith small separation between the pu l

ses. The re s t o f the procedure is s im i la r to FID.

When the echo appears, i t is a t a d is tan ce equal to 2t , where

is the d is tance between 90° and 180° pulses. The echo am plitude is

maximum when the two pulses are c lose toge ther and decreases as the

pulses are set f a r th e r a p a r t . The spin echos fo r g ly c e r in e are

shown in F ig . 3 .12 fo r two d i f f e r e n t d istances between the pu lses.

The FID is a lso seen in the same f ig u re a f t e r the 90° pulse.

The amplitude o f the echo signal fo r various s e t t in g s o f the

distance between pulses is measured. The natura l logarithm o f the

echo amplitude is p lo t te d vs. 2 t . The slope o f th is graph y ie ld s

the re la x a t io n time T2 . The echo amplitudes fo r g ly c e r in e are

given in Table 3 .5 . The p lo t o f In B vs. 2x is shown in F ig . 3 .1 3 .

The slope o f the s t r a ig h t l in e gives T2 fo r g ly ce r in e to be 22.5^

msec.

The experiment was repeated fo r l ig h t machine o i l and the spin

echo amplitudes are given in Table 3 -6 . The value o f T2 fo r l ig h t

machine o i l was found to be 5^.1 msec.

Using the values o f T2 determined by spin-echo experiment and

T2 ‘ determined by FID, the magnetic f i e l d inhomogeneity fa c to r T2*

is c a lc u la te d from the data on g ly c e r in e and l ig h t machine o i l ,

using the Eq. 2 .2 . The re s u lts a re 0 .92 msec and 0 .8 3 msec respec

t i v e l y . An average value o f 0 .87 msec fo r T2* is used fo r the


42

Fig- 3.12 Spin echo for Glycerine

at different *T


43

2 mSec. Spin Echo Amp. 5 OmV

In (Amp)

0 3 1.09

2 2.6 0.96

4 2.4 0.88

6 2.2 0.79

8 2 0.69

10 1.8 0.59

12 1.6 0.47

Table 3.5~Spin Echo Amplitude for Glycerine

*£» = 108 jJ-Sec


kh

a

Uyui2Z•i

y2•-tt-

ni—t

•

roC•H

(DC-HU<DO>i

rHouom•porH04<u•o•P•H

o.coa)£3•HaCO

samrndwv bi-o s jb n~iae♦


45

2T mSecSpinecho Amp 5 OmV In(Amp)

0 2.7 0.99

2 2.6 0.96

4 2.5 0.92

6 2.4 0.88

8 2.1 0.74

10 2 0.69

Table 3.6 Spin Echo Envelope for Light Machine Oil (LMO)

Tio = 108 i*.Sec


46

subsequent c a lc u la t io n s .

Spin echo could not be observed fo r CuSO *5H20 ( IN ) s o lu t io n ,

owing to com paratively longer response time o f the system and broader

pulse w id ths . However, using the FID decay time T2 ‘ and inhomogen

e i t y fa c to r T2* the value o f T2 was c a lc u la ted to be approxim ately

1.6 msec.

For w a te r , spin echo was observed. The signal was weak and no

n o ticeab le change in amplitude was detected over most o f the range

o f 2 t a v a i la b le . This made accurate measurements d i f f i c u l t . Again

the above procedure was app lied and the c a lc u la te d value was found

to be 152 msec.

Results o f spin-echo re la x a t io n times are included in Table

3 .7 along w ith FID re s u lts and magnetic f i e l d inhomogeneity fa c to rs

c a lc u la ted from Eq. 2 .2 .

3 . Summary and Conclusions

The re s u lts from pulsed spectrometer are given in Table 3 -7 .

The constancy o f the magnetic f i e l d inhomogeneity fa c to ry c a lc u la te d

from the FID and spin-echo data fo r g ly ce r in e and l ig h t machine o i l

v e r i f i e s the accuracy o f the d a ta . Furthermore, the value o f T2 fo r

g ly c e r in e reported in l i t e r a t u r e is 23 msec and compares favo rab ly

w ith the r e s u l t determined in the experim ent. The reported

value fo r l i g h t machine o i l is 4 8 ,2m s e c and compares favo rab ly w ith

the r e s u l t determined in the experiment.

The re s u lts from spin-echo measurements could not be obtained

fo r the o ther two samples and the values o f T2 fo r these samples are

c a lc u la te d by using the FID data and the magnetic f i e l d inhomogeneity.


Reproduced

with perm

ission of the

copyright ow

ner. Further


without

permission.

Relaxation Times fo r A l l Samples Using Pulsed Techniques

SampleFID-

decay T mSec

Spinecho decay T mSec

Mag.Field inhomog. T mSec

From Eq. T mSec

Reported value T mSec

Glycerine 0.88 22.5 0.92 - 23

LMO 0.82 54.1 0.83 - 48.2

Water 0.87 - - 152 2300

C11SO4, 0.37 - - 1.6 1.1

Table 3.7

48

fa c to r c a lc u la te d from g ly c e r in e and l ig h t machine o i l da ta . The

agreement between the experimental values and the reported values

fo r these samples is not good due to the fa c t th a t these l i e on the

upper and lower l im i t s o f the apparatus c a p a b i l i t y , which again

depends s tro n g ly upon magnetic f i e l d homogeneity.


REFERENCES

1. Abragham, A . , P r in c ip le s o f Nuclear Magnetism, Oxford U n iv e rs ity Press, 1961.

2 . Andrews, E. R . , Nuclear Magnetic Resonance, Cambridge, 1963-

3 . Bloch, F . , Physics Review 7 0 , 460 (1946 ).

4 . Block, F . ; Hansen, W.; Packard, M . ; Physics Review 7 0 , 460 (1946 ).

5 . Bloembergen, N . , Nuclear Magnetic R e la x a t io n , Benjamin, 1961.

6 . Hahn, E. L . , Physics Review 76 , 145 (19^*9) -

7 . Hahn, E. L . , Physics Today, Nov. 1953.

8 . Hahn, E. L . , Physics Today, Nov. 1953-

9. Hawk, Robert M . ; Sharp, Robert R . , To lan , John W .; Physics Review 45, 1 (1974 ).

10. Pake, George E . , American Journal o f Physics 18 , 438 (1950 ).

11. P u rc e l l , E. M . ; T o rrey , H. C .; and Pound, R. V . ; Physics Review 69, 37 (1946 ).

49


nmr instrumentation with solid state devices

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