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Electron resonance in the rotating reference frame Enga, Eric 1966

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(i)  ELECTRON RESONANCE IN THE ROTATING REFERENCE FRAME  by  ERIC  ENGA  B.A.Sc., U n i v e r s i t y o f B r i t i s h  1962  Columbia,  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE  REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department o f PHYSICS  accept t h i s  t h e s i s as conforming to the r e q u i r e d  standard  THE UNIVERSITY OF BRITISH COLUMBIA April  I966  In p r e s e n t i n g the  this  thesis  Columbia,  I agree that  the Library  a v a i l a b l e f o r r e f e r e n c e and s t u d y . mission  f o r extensive  p u r p o s e s may  of this  It. i s understood  thesis  for financial  w i t h o u t my w r i t t e n  permission.  Department o f  PHYSICS  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada February  thesis  by t h e Head o f my  2?th 1966  Columbia  per-  for scholarly  D e p a r t m e n t o r by  that  gain  of  s h a l l make i t f r e e l y  I f u r t h e r agree that  copying of t h i s  be g r a n t e d  representatives.,  cation  Date  fulfilment of  r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y  British  his  in partial  copying or  shall  publi-  n o t be a l l o w e d  (ii)  ABSTRACT  The magnetic  resonance s i g n a l o f a s p i n system quantized  i n the r o t a t i n g r e f e r e n c e frame was observed.  The experiment  c o n s i s t e d o f s u b j e c t i n g the e l e c t r o n s p i n s i n s o l i d  2,2  D i p h e n y l - l - P i c r y l h y d r a z y l (DPPH) to a s t r o n g r . f . f i e l d i n the 8 mm. microwave range and o b s e r v i n g the Larraor frequency corresponding to the e f f e c t i v e f i e l d  o f the r o t a t i n g  S i g n a l s from 7 to 52 Mc/s were observed.  frame.  The r e s u l t s a r e  compared with the theory developed by R e d f i e l d f o r t h i s case, utilizing  the concept of a s p i n  temperature.  Also observed were the Overhauser which a r e two p o s s i b l e ways i n which a  and S o l i d  effects,  net p o l a r i z a t i o n o f  one s p i n s p e c i e s ( i n t h i s case the protons i n DPPH) may be achieved from the s p i n - s p i n c o u p l i n g to another s p i n s p e c i e s (the  The enhancements obtained (60 and  e l e c t r o n s i n DPPH).  100)respectively) are h i g h e r than those so f a r r e p o r t e d , although experimental e r r o r s make d e t a i l e d comparisons  question-  able.  theory  of  The S o l i d e f f e c t i s compared with a s i m p l i f i e d  enhancement u t i l i z i n g  the s p i n temperature  put forward by I . Solomon.  concept, and  (iii)  TABLE OF CONTENTS Page ABSTRACT  i i  LIST OF FIGURES  iv, v  ACKNOWLEDGMENT  Vi  INTRODUCTION  1  THEORY AND EXPERIMENT, ROTATING FRAME SIGNALS .  k  THEORY AND EXPERIMENT, ENHANCEMENT EFFECTS . . .  28  APPARATUS  kl  BIBLIOGRAPHY  57  (iv)  LIST OF FIGURES  Figure  Page  1.  F i e l d s i n the R o t a t i n g Frame  2.  Components of the f i e l d  Ik  3.  L i n e Shape Symmetry i n the R o t a t i n g Frame  16  k.  Geometry to determine Hi  18  5.  D e r i v a t i v e t r a c e s , E l e c t r o n Resonance i n the R o t a t i n g Frame  experimentally  5  19, 20 and  6.  Geometrical r e l a t i o n s h i p of observed to a c t u a l l i n e width  25  7.  Derivative s i g n a l strength plotted against the angle of the e f f e c t i v e f i e l d with a ( Sin 0 ) ( c o s © ) curve f o r comparison  27  8.  L i n e width p l o t t e d a g a i n s t the angle of the e f f e c t i v e f i e l d with a (3cos*© -1) curve f o r comparison  27  9.  P l o t of Overhauser Enhancement  31  10.  Overhauser E f f e c t , sample l i n e shapes  32  11.  Overhauser E f f e c t , r e l a t i v e p o p u l a t i o n s obtained by s a t u r a t i n g t r a n s i t i o n  35  Spin temperature i n the R o t a t i n g Frame vs. the Distance from Resonance  37  13.  S o l i d E f f e c t Enhancement  39  Ik.  Block Diagram of Apparatus  kj>  15.  TE O i l Mode C a v i t y  Mt  16.  V a r i a b l e Coupling Device  kk  12.  21  (v)  LIST OF FIGURES  (continued)  Figure  Page  17.  TE Oik Mode C a v i t y  18.  Spectrometer  19.  Klystron Freq. S t a b i l i z e r  (Rectangular)  circuit  k5 k6 k7  (vi)  ACKNOWLEDGMENT  I wish to express my s i n c e r e s t a p p r e c i a t i o n to Dr. K.W. Gray f o r h i s constant  i n t e r e s t and a s s i s t a n c e  throughout  t h i s work.  I would a l s o l i k e t o thank Dr. M. Bloom f o r the d i s c u s s i o n s h e l d with him on the theory experiment and f o r p r o o f - r e a d i n g initial  and r e s u l t s o f the  the manuscript i n i t s  stages.  T h i s research was supported f i n a n c i a l l y by the award o f a N a t i o n a l Research C o u n c i l Bursary and by the award o f a B r i t i s h Columbia Hydro and Power A u t h o r i t y  Scholarship.  Some o f the equipment was bought through a N a t i o n a l Research C o u n c i l Grant to Dr. K.W. Gray.  -1-  INTRODUCTION  The main purpose of t h i s experiment was to observe d i r e c t l y the  resonance from a s p i n system quantized i n the r o t a t i n g  r e f e r e n c e frame.  An a u x i l i a r y o b j e c t i v e was to study enhancement  e f f e c t s due to c o u p l i n g s between two d i f f e r e n t s p i n s p e c i e s - i n t h i s case, e l e c t r o n s and p r o t o n s .  Both of these o b j e c t i v e s could  be accommodated u s i n g the same apparatus.  The t h e o r i e s f o r the  two e f f e c t s are c l o s e l y r e l a t e d as w e l l . The r o t a t i n g r e f e r e n c e frame (1*0 fields, a field  ( Ho-y  i s d e f i n e d by two magnetic  ) p a r a l l e l to Ho  , where Ho i s u s u a l l y  very s t r o n g and i s s t a t i c i n the l a b o r a t o r y frame, and a f i e l d Hi which i s p e r p e n d i c u l a r to Ho and i s r o t a t i n g about Ho with an angular v e l o c i t y to as seen from the l a b o r a t o r y frame.  The  r e s u l t a n t of ( Ho-^ ) and Hi i s c a l l e d the e f f e c t i v e f i e l d , H«« Normallythe field  Hi  i s very weak, and i f a s p i n system i s  s u b j e c t e d to such a f i e l d  c o n f i g u r a t i o n a resonance i s observed  when Ui = u> , where CJ, i s the Larmor angular v e l o c i t y of the s p i n s s  i n the f i e l d Ho simplified  .  The a n a l y s i s of t h i s resonance i s c o n s i d e r a b l y  when the equations of motion are transformed i n t o the  r o t a t i n g r e f e r e n c e frame, where i t i s found that the s p i n s precess about the e f f e c t i v e f i e l d , H«« . Much of the e a r l y work i n magnetic resonance can be e x p l a i n e d u s i n g a s e t of equations d e r i v e d by B l o c h .  The assumptions  i n h e r e n t i n these equations make them e s p e c i a l l y v a l i d  for liquids,  where the l a r g e d i p o l a r s p i n - s p i n c o u p l i n g s are averaged out by the  motion of the s p i n s . very s t r o n g , these  In s o l i d s , where the s p i n - s p i n c o u p l i n g s  equations  are l e s s s u c c e s s f u l , but s t i l l  provide a q u a l i t a t i v e understanding observed, i f Hi i s very weak.  Among other t h i n g s , these  H, it  saturate ( i . e . ,  becomes very s t r o n g , and was  equations  d i s p e r s i v e components of  the magnetization  will  i n l i q u i d s this i s true.  found that only the a b s o r p t i v e resonance was  there s t i l l  they  of the resonance phenomena  p r e d i c t that both the a b s o r p t i v e and resonance w i l l  are  disappear) i f But  i n solids  saturated;  remained the d i s p e r s i v e resonance which d i d not  saturate ( l ) . These two  types of resonance may  phase of the v o l t a g e  be thought of i n terms of  that the p r e c e s s i n g magnetization  "pick-up" c o i l surrounding  the sample.  induces  termed a b s o r p t i v e ; i f the v o l t a g e i s 90°  P h y s i c a l l y , these  two  of the magnetization  out of phase with  is  , even when Hi was  the p o s s i b i l i t y  very  of o b s e r v i n g  the  the degree of l a g  field.  T h i s r e s u l t meant that i n a s o l i d a magnetization a l o n g H«#  this i s  this i s called dispersive.  s i t u a t i o n s are c r e a t e d by to the a p p l i e d  in a  I f t h i s v o l t a g e i s i n phase  with the c u r r e n t i n the c o i l a power l o s s i s i n v o l v e d and  c u r r e n t no power l o s s i s i n v o l v e d and  the  still  existed  s t r o n g . T h i s being the case,  the resonance of the s p i n s  there  quantized  along H««  a t the Larmor frequency,Ui*. =H\\e$. To do  t h i s the s p i n s are  subjected  to a t h i r d f i e l d  to Heff which i s a  weak p e r t u r b i n g f i e l d T h i s was  oriented perpendicular  tuned to t h i s Larmor  accomplished, and  theory which was  frequency.  the r e s u l t s are compared with  developed f o r the l i m i t i n g case of a very  the  strong  -3-  f i e l d Hi .  The s p i n s used were the e l e c t r o n s  2 , 2 - D i p h e n y l - l - P i c r y l h y d r a z y l , known as DPPH.  o f the f r e e Typical  radical  line  shapes are i l l u s t r a t e d . The  r e s u l t s are i n q u a l i t a t i v e agreement with the theory, ex-  cept f o r a c e r t a i n s i g n a l which was not expected, and which remains unexplained. The the  enhancement e f f e c t s i n v o l v e d  electrons  i n DPPH, so that  e n t i a l l y to occupy s t a t e s equilibrium  states.  c o u p l i n g o f the protons to  the protons could be made  other than t h e i r s t a t i c  The two p o s s i b l e  prefer-  thermal  methods were used, the  Overhausser E f f e c t and the S o l i d E f f e c t , and r e s u l t s are given f o r both and compared with the theory.  These r e s u l t s are a l s o i n  q u a l i t a t i v e agreement with the theory.  THEORY AND EXPERIMENT, ROTATING FRAME SIGNALS  One purpose of t h i s experiment was to observe d i r e c t l y the resonance s i g n a l from a s p i n system quantized i n the r o t a t i n g frame.  The p o s s i b i l i t y of doing t h i s arose when R e d f i e l d ( l )  showed that the a p p l i c a t i o n of a s t r o n g would s a t u r a t e signal.  the a b s o r p t i o n  This implied  r.f. field i n solids  s i g n a l but not the d i s p e r s i v e  that a magnetization e x i s t e d along the  e f f e c t i v e f i e l d i n the r o t a t i n g frame, which was comparable to the e q u i l i b r i u m magnetization i n the absence o f an r . f . f i e l d . To e x p l a i n t h i s behaviour, which completely v i o l a t e d the Bloch Equations, R e d f i e l d proposed, ad hoc, and l a t e r j u s t i f i e d on more general  grounds ( 3 ) , the e x i s t e n c e  of a s p i n  temperature i n the  r o t a t i n g frame, which could be used to o b t a i n a s t a t i s t i c a l d e s c r i p t i o n o f the s p i n system, thus g r e a t l y s i m p l i f y i n g the mathematical d e s c r i p t i o n o f the system. We f i r s t The  review b r i e f l y  the r o t a t i n g frame and i t s o r i g i n .  a p p l i c a t i o n of r o t a t i n g f i e l d H  (  static  field H  , perpendicular  to the  , w i l l cause s p i n f l i p s i n a p p r e c i a b l e  e  numbers  when the angular v e l o c i t y (*> o f H i s c l o s e to the Larmor frequency (  of the s p i n s , where :  (1)  = V Ho s  = gyromagnetic r a t i o n  The to Ho  r o t a t i n g frame i s d e f i n e d  so that one a x i s i s p a r a l l e l  while the other two axes r o t a t e about H  the f i e l d Hi  •  0  a t the frequency of  Thus Ho and Hi are s t a t i c i n t h i s frame.  -5-  The  a n a l y s i s of the motion of f r e e s p i n s i n t h i s frame  shows that the magnetic moment of the s p i n s a c t s as though i t experienced a s t a t i c  FIG.  The  1  f i e l d H«ff, shown i n F i g . l .  FIELDS IN THE  ROTATING FRAME  importance of the r o t a t i n g frame i s that i n i t the  f i e l d s are s t a t i c .  To be u s e f u l , however, we  must know the  behaviour of the macroscopic magnetization M of the s p i n s , Ho  or O) i s v a r i e d through the resonance A simply proven a d i a b a t i c  almost p a r a l l e l to H«ff  region.  theorem* shows that M  provided &  w i l l remain  i s varied s u f f i c i e n t l y  slowly.  However, a much more complicated a n a l y s i s i s necessary to the magnitude of M and  under v a r i o u s  as  conditions  of f i e l d  give  strength  spin interactions. We  w i l l sketch  considerations, can be  but  t h i s c a l c u l a t i o n g i v i n g only  the  basic  i g n o r i n g the d e t a i l e d c a l c u l a t i o n s , which  found i n the l i t e r a t u r e as  indicated.  *See, f o r example, A.Abragam, P r i n c i p l e s of Nuclear Magnetism.  -6-  In the presence o f an e x t e r n a l magnetic f i e l d ,  the s p i n  H a m i l t o n i a n °f( can be given as the sum o f the Zeeman i n t e r a c t i o n s , TE  , and the s p i n - s p i n i n t e r a c t i o n s °f(  We i n t r o d u c e  n  the expanded form of the s p i n Hamiltonian as  presented i n Abragam ( 2 ) .  The l a t t i c e i n t e r a c t i o n s are ignored.  In the l a b frame, f o r a s i n g l e s p i n s p e c i e s momentum I  represents  scalar.  of angular  ;  % -Z Ajk  .  +  - 3 '%\ ^° } (Ii  i n d i r e c t spin-spin coupling,  (I  s c a l a r and pseudo-  I f these are absent then :  When t h i s i s transformed i n t o the r o t a t i n g frame, represented by;  Tjf* = e it  wI?t  TT e  lwllt  W  i s found that the Zeeman p a r t i s time independent, but that  the s p i n - s p i n part c o n t a i n s  the time e x p l i c i t l y .  I t was f i r s t  M  shown by R e d f i e l d , ( l ) , (3), that i f the s t a t i c  field  l a r g e r than the l o c a l f i e l d H a t each s p i n s i t e  (which i s u s u a l l y  t  0  i s much  the c a s e ) , the time dependent terms have a n e g l i g i b l e i n f l u e n c e and  can be d i s c a r d e d .  Hamiltonian"  The r e s u l t i n g "truncated s p i n - s p i n  i s now denoted by "Tfc  .  We then have :  Bjk ~ ~ \ BjkC^cos ©)* - I) 1  F i n a l l y we note that f o r the s p i n s to come i n t o thermal e q u i l i b r i u m with each other and quantized necessary part  2*  a n <  along H,ff  , i t is  that there be an energy exchange between the Zeeman * the s p i n - s p i n p a r t  operators  do not commute.  *ff  fS  .  T h i s r e q u i r e s that  In order to e x h i b i t t h i s , J{  these  can be  rewritten. We i n t r o d u c e the components o f angular  momentum, I J J T X . I Y )  where the z - a x i s i s chosen to be along the e f f e c t i v e  field  We d e f i n e :  It-IX±IY The  (6)  r e s u l t i s then :  + E*.[(I,> + I y ) I « +  EW  EjKf  -Tr(3cos*e-0BjH  s  "k sin© c o s 0 B>k  ]  -8-  Note that i t i s the D and E terms which do not commute with Ig and are r e s p o n s i b l e f o r the thermal mixing.  F a r from  resonance,  when 0 i s s m a l l , so are the D and E terms. We now i n t r o d u c e the s p i n temperature  p o s t u l a t e and show how  t h i s , together with the Hamiltonian, p r e d i c t s the behaviour o f the magnetization M  .  We do t h i s by r e t u r n i n g to the l a b frame  where the s t a t e d e s c r i p t i o n of a s p i n system i n thermal  equilibrium  i s assumed to be g i v e n by a d e n s i t y matrix o f the form;  whereis  the s p i n  temperature.  The knowledge of*T$ and hence o f the d e n s i t y matrix, allows one  to c a l c u l a t e the e x p e c t a t i o n value of an operator Q, i . e .  <Q>= "trace (pQ) approximately  a t high  (q)  temperatures,  Then one f i n d s , f o r example :  (M) where N  a  number o f s p i n s  H.  i s the l o c a l  u« -  tn*t* C  t  field  Then the t b t a l magnetization ^  , given by  i s seen to be p a r a l l e l to R, , with the average  M= m  ift+QyVNii. 3KTs  value  -9-  which i s seen to be the C u r i e law f o r the m a g n e t i z a t i o n . Redfield valid  ( l ) , (3), has shown that the above c a l c u l a t i o n s are  i n the r o t a t i n g frame i f the correspondence:  ff'  n  is  used. However,  what Ts w i l l  we note that t h i s correspondence does not t e l l us be i n the r o t a t i n g frame.  As mentioned  b e f o r e , the  observed magnetization i n the r o t a t i n g frame i s o f the same order as the e q u i l i b r i u m magnetization Mo i n the f i e l d Ho y e t the e f f e c t i v e f i e l d H # i s much s m a l l e r than Wo e  the  .  T h i s r e q u i r e s that  temperature o f the s p i n s i n the r o t a t i n g frame be much c o l d e r  than the temperature of the s p i n s i n the absence o f the f i e l d When the f i e l d Hi i s absent, the s p i n s come i n t o  equilibrium  due to the s p i n - l a t t i c e i n t e r a c t i o n s , so t h a t the s p i n i s equal to the l a t t i c e  temperature.  s p i n i n t e r a c t i o n i s dominant lattice  Hi .  temperature  With the f i e l d Hi , the s p i n -  and Tt i s q u i t e d i f f e r e n t from the  temperature.  The c a l c u l a t i o n ( 2 ) of "Is can be done by a l l o w i n g f o r the s p i n - l a t t i c e i n t e r a c t i o n s which were n e g l e c t e d i n the H a m i l t o n i a n . The assumptions are that the c o r r e l a t i o n times f o r the s p i n - l a t t i c e i n t e r a c t i o n are very s h o r t (extreme narrowing) and that the s p i n lattice of  r e l a x a t i o n mechanism can be represented by the c o u p l i n g  the s p i n s with a l o c a l random f i e l d  at each s p i n  site.  10-  The exact c a l c u l a t i o n g i v e s the f o l l o w i n g r e s u l t : -  JL  Li'  H»4f Ho c o s  —  The C u r i e Law  (16)  e  07)  t<nee  then g i v e s f o r the magnetization i n the  r o t a t i n g frame:  M  *  Mo cos  Mo  8  0 8 )  Since the s p i n s are quantized along the e f f e c t i v e one  expects t h a t a resonance  field,  at the Larmor frequency 60 = 5fH f{ t  should be observable i n the r o t a t i n g frame.  The  difficulty  doing t h i s i s i n g e n e r a t i n g a l a r g e enough r o t a t i n g  field  so that the quanta are l a r g e enough to be observable. s p i n s are used, the theory was  of  I f nuclear  the quanta are g e n e r a l l y i n the audio range,  and  o r i g i n a l l y v e r i f i e d by i n d i r e c t l y o b s e r v i n g t h i s  signal, ( l ) . T h i s was  done by a p p l y i n g a f i e l d at the audio frequency, O)^  while o b s e r v i n g the d e r i v a t i v e of the " o r d i n a r y 'tiispersive resonance of  i n the l a b frame atO> = ija- (when H«H = H ).  t h i s resonance  (  The s t r e n g t h  was dependent on the audio frequency s i n c e the  magnetization would be p a r t i a l l y destroyed when Hcff = ~  , and  observed as a decrease i n the d i s p e r s i v e s i g n a l at H«# = Hi However, u s i n g an e l e c t r o n s p i n system enables one  was  .  to  i n c r e a s e the "audio" frequency i n t o the megacycle range with a microwave f i e l d Hi power k l y s t r o a .  , of about one We  gauss o b t a i n a b l e with a high  can estimate the s i g n a l s t r e n g t h by comparing  -11it  to a p r o t o n s i g n a l i n the same sample i n a s t a t i c  field  Ho  .  To do t h i s , we can compare the r e l a t i v e areas under the a b s o r p t i o n curves of the r e s p e c t i v e  signals.  The f r e e r a d i c a l DPPH was  chosen f o r our e l e c t r o n s p i n  system because i t has an e l e c t r o n l i n e - w i d t h of a few gauss, i s a s o l i d , and i s e a s i l y o b t a i n a b l e . it  The proton s p i n system  which  c o n t a i n s i s approximately t e n times as densely populated as  the e l e c t r o n s p i n system which we wish to observe. I f we assume a unique temperature  Tg  ( \^r)  i n the r o t a t i n g frame, then e q © ,  f o r the e l e c t r o n s p i n s  may  be used to o b t a i n the  r a t i o of the s u s c e p t i b i l i t i e s of the e l e c t r o n s p i n s i n the r o t a t i n g frame and the proton s p i n s iijrbhe l a b frame :  The p r o t o n s p i n temperature temperature Ti from eqn.( lb  Ts  r  w i l l be equal to the l a t t i c e  , hence the s p i n temperature r a t i o may  be found  ).  Thus : 2k  I t may  =  Y; N*  HO  cose  / -\ 2 0  be e a s i l y shown u s i n g the Kramers-Kronig  that f o r a s u f f i c i e n t l y narrow resonance  line*  where 'X" i s the imaginary p a r t of the s u s c e p t i b i l i t y , resonance frequency and A  relations  CJJO  the  the a r e a under the resonance a b s o r p t i o n  *see f o r example S l i c h t e r , P r i n c i p l e s of Magnetic Resonance.  -12-  curve. S u b s t i t u t i n g eqn.(21 ) i n t o eqn.( 20 ) we o b t a i n :  Me Ho fir ~ utf V W  ft* _  U>« f e  r  P  (22)  cos O  +  F i n a l l y , one should i n c l u d e  the f a c t o r ( stn© )  a r i s e s from the method of d e t e c t i o n  which  i n the r o t a t i n g frame.  o r i g i n of t h i s f a c t o r i s shown i n the f o l l o w i n g  text.  The  Thus :  (23) In t h i s experiment these values are approximately the following,  f o r maximum e l e c t r o n s i g n a l :  £  ~ ffxfo  N'  (24)  3  JL  Thus one o b t a i n s :  %  *  (25)  1 0 0 0  The value f o r the l o c a l f i e l d Mt  i s based on the approximat-  i o n that i t should be of the same order as the l i n e width, which f o r the  electrons  assumed.  i n DPPH i s about *t gauss, hence  Note that the c a l c u l a t i o n of  /p\  p  rL'* 10 gauss i s 5  i s s e n s i t i v e to the  value of Hx which i s used. From t h i s c a l c u l a t i o n i t can be seen that the e l e c t r o n  spin  resonance s i g n a l i n the r o t a t i n g frame should be much l a r g e r than the proton s i g n a l i n the l a b frame, with both s p i n systems i n the same sample.  -13E x p e r i m e n t a l l y , the sample volume has to be as s m a l l as p o s s i b l e so as not to p e r t u r b g r e a t l y the microwave c a v i t y i n which i t i s i n s e r t e d , thus sample volumes approximately  1/6V*  s p h e r i c a l diameter were used.  In a d d i t i o n , one has to choose  between having the spectrometer  c o i l s h i e l d i n g the sample  the microwave f i e l d  or b e i n g l a r g e l y decoupled  by b e i n g o u t s i d e the c a v i t y . available  in  from  from the sample  These f a c t o r s a c t to reduce  the  signal.  The experimental r a t i o of the area of the e l e c t r o n resonance to the a r e a of the proton resonance for  was  the r e g i o n of maximum e l e c t r o n s i g n a l .  g r e a t e r than  100  T h i s value i s a  c o n s e r v a t i v e estimate which i s based on the s i g n a l to n o i s e r a t i o (S/N) S/N  of the r e s p e c t i v e s i g n a l s .  The  e l e c t r o n s i g n a l s had a  r a t i o of 75 f o r a sample volume i n which the proton s i g n a l  could not be seen.  The proton s i g n a l had a S/N  a sample volume about ten times l a r g e r . s i g n a l was  r a t i o of k f o r  Furthermore,  the e l e c t r o n  obtained u s i n g the r e c t a n g u l a r microwave c a v i t y f o r  which the spectrometer  c o i l i s l a r g e l y decoupled  from the sample,  but the proton s i g n a l was  obtained with the spectrometer  coil  surrounding the sample.  From these c o n s i d e r a t i o n s i t i s  p o s s i b l e t h a t the true r a t i o of the s i g n a l s t r e n g t h s i s near 1,000, i n reasonable agreement with the t h e o r e t i c a l  estimate.  By a p p l y i n g the p e r t u r b a t i o n f i e l d , H*. , near the frequency W  a  =  Heff  » p a r a l l e l to H  c  we  resonance  g a i n d i r e c t access to  the r o t a t i n g frame, s i n c e t h i s d i r e c t i o n i s s t a t i o n a r y i n both  the  -li+lab  and r o t a t i n g frames.  Ha  may  then be represented by i t s compon-  ents p a r a l l e l and p e r p e n d i c u l a r to Heff component w i l l  be the a c t u a l p e r t u r b i n g f i e l d .  i n F i g . 2 , t h i s component i s equal to  FIG.  , where the p e r p e n d i c u l a r  COMPONENTS  2.  OF  represented by two  seen  H* Sin©  THE  This l i n e a r l y o s c i l l a t i n g f i e l d  As can be  FIELD  H.  ( Ho.5in© ) may  now  be  c o u n t e r - r o t a t i n g components of equal amplitude i n  the standard method of resonance  analysis.  ents w i l l be r o t a t i n g i n the proper sense  One  of these compon-  to cause a  resonance.  The p r o b a b i l i t y of a s p i n f l i p i s p r o p o r t i o n a l to the square the amplitude  of the r o t a t i n g ( p e r t u r b i n g ) f i e l d , H  w i l l be p r o p o r t i o n a l to (  hence the s i g n a l  2 s , n  ©  ) .  The s i g n a l w i l l  p r o p o r t i o n a l to the magnetization given by eqn.(18 ). constant we  of  a l s o be For  , n e g l e c t i n g v a r i a t i o n s i n the l o c a l f i e l d WL  with  then have t h a t the 0 dependence of the s i g n a l should be pro-  p o r t i o n a l to the  product; S i g n a l oc  f o r constant  ffiffecos©  H«ff  A complete a n a l y s i s of the s i g n a l should i n c l u d e the e f f e c t s of  the component ( H cos0 ) and ft  the e f f e c t of the other r o t a t i n g  (26)  -15-  component of ( H o . sin ©  ).  i t was  felt  that H a was  sufficiently  s m a l l compared with H e f f ( H * < " j o H e { f ), to n e g l e c t the e f f e c t s of the ( H a cos © ( Ha sin ©  ) term.  ) cannot  However, the other r o t a t i n g component of  be n e g l e c t e d f o r the r e g i o n i n which H e t f i s  s m a l l , s i n c e i t i s off-resonance by the amount 2 H e f f .  Thus f o r  the r e g i o n i n which H « f f i s comparable with the resonance  line  width one would expect a s i g n i f i c a n t c o n t r i b u t i o n from t h i s term, g i v i n g r i s e to a l i n e o v e r l a p which w i l l cause a s h i f t i n the p o s i t i o n of the resonance F i n a l l y , one  a b s o r p t i o n peak.  can note t h a t eqn.  ( 1$) p r e d i c t s a magnetization  f o r G ^ O * w h i c h i s a n t i - p a r a l l e l to H e f f . a l s o be seen i n the lower quadrant resonance  Thus a s i g n a l should  of the r o t a t i n g frame.  r o t a t i n g component of the p e r t u r b i n g f i e l d  the lower quadrant  The  ( ^sme)  w i l l be opposite to t h a t i n the upper  n  quadrant  s i n c e the magnetization i s reversed with r e s p e c t to H e f f . lower quadrant  i  on-  A l s o , the  s i g n a l should be emissive r a t h e r than a b s o r p t i v e  s i n c e the magnetization i s i n i t s h i g h e s t p o t e n t i a l energy  state  with r e s p e c t to H e f f . So f a r we shape.  have i g n o r e d c o n s i d e r a t i o n s of the resonance  We may,  line-  f o r example, a t t r i b u t e the l i n e shape to a  v a r i a t i o n of the X -value of d i f f e r e n t s p i n s i n the sample, so t h a t each s p i n i s resonant i n a s l i g h t l y d i f f e r e n t f i e l d than that ao't its neighbours. ( Ho y -  In the r o t a t i n g frame, both the f i e l d  ) and i t s o r i g i n ( H o " ^ = O  d i f f e r depending on the  y -value.  component  ) with r e s p e c t to H o Thus each d i f f e r e n t  will Y -value  -16w i l l define  a d i f f e r e n t r o t a t i n g frame.  This i s i l l u s t r a t e d  i n Fig.(3) which shows how a s i g n a l i n the l a b frame  consisting  of two s p i k e s o f d i f f e r e n t Y"-values w i l l appear i n the r o t a t i n g frame as observed by sweeping Ho . signals exhibited  The e x p e r i m e n t a l l y observed  t h i s type o f symmetry.  I t should be noted that  the f o r e g o i n g i s an o v e r - s i m p l i f i e d  d e s c r i p t i o n which s u f f i c e s only to i l l u s t r a t e signals.  The l i n e shape o f the sample i s l a r g e l y determined by  the s p i n - s p i n  c o u p l i n g s which i n turn are i n f l u e n c e d  magnetic f i e l d s . that the  the symmetry o f the  Thus i t i s not c o r r e c t  by the a p p l i e d  t o say, f o r example,  the l i n e shape i n the r o t a t i n g frame w i l l be the same as i n l a b frame.  lab -frame signal  Ho  yppcr quadrant Signal y'  ObsorpW)  VZZZZZ"-, rotating frame si<jrwl observed by sweeping H o , U>s qnd W, fifeJ  loioef <^ warrant Signals  FIG. 3  LINE SHAPE  SYMMETRY  fN THE ROTATING- FRAME-  The  c a l c u l a t i o n of K  and © from the observed s i g n a l s i s AHo  e a s i l y done by measuring the s e p a r a t i o n the upper and illustrated of F i g . (3)1  lower quadrants of the r o t a t i n g frame.  i n Fig.(k).  then i t i s only necessary  There are three important The  first  sources  and  of t h i s  third  M«ff  effect  , since i n this region  the  i s very s m a l l , r e s u l t i n g i n a Hi  and  .  T h i s i s the  t h a t the e r r o r bars are l a r g e i n F i g s . (7) and The  calcul-  l i n e shape i s determined.  l a r g e u n c e r t a i n t y i n the value of ©  .  of e r r o r i n t h i s  An estimate  second e r r o r a r i s e s f o r s m a l l 0  d i f f e r e n c e between ^gr and He+f  ©  separation  i s the e f f e c t of l i n e o v e r l a p f o r s m a l l  can be made once the experimental  reason  to measure the  signal.  which has a l r e a d y been mentioned.  The  This i s  When the s i g n a l s e x h i b i t the symmetry  between the same p a r t s of the  ation.  of the s i g n a l s i n  (8) f o r s m a l l  e f f e c t i s a c o m p l i c a t i o n r a t h e r than an e r r o r  a r i s e s because the sample absorbs power from the microwave  c a v i t y at the " c a v i t y " resonance ( 0-= lowers the magnitude of the f i e l d H,  90°).  .  The  This i n turn very  short  r e l a x a t i o n times of the sampleCfor DPPH, TT = T»»iOsec. ) means that a l a r g e amount of power, of the order of watts, may absorbed.  An approximate c a l c u l a t i o n f o r the s i z e of  samples shows t h a t H, may  be reduced by 25$  due  to t h i s  be the effect.  -18-  FIG, 4  GEOMETRY  TO DETERM/NE  H, EXPERIMENTALLY  Examples o f the s i g n a l s obtained a r e shown i n F i g . ( 5 ) . that s i n c e a l o c k - i n d e t e c t o r  was used, the t r a c e s as i.shown are  the d e r i v a t i v e s o f the a c t u a l s i g n a l s . sweeping  Ho  e l e c t r o n system were  The  These were obtained by  through both resonances, while modulating i t a t Wm  to operate the l o c k - i n d e t e c t o r .  electrons  Note  could  ~ [0  9  The r e l a x a t i o n times of the  sees, and as tdm was  -~(OOcps  t  the  be considered to be always i n e q u i l i b r i u m .  two s i d e s i g n a l s i n the t r a c e s seem to agree very  with the p r e d i c t e d  behaviour.  well  The value of H,as determined by the  s p a c i n g AHo f a l l s i n t o the range o f values expected from the c a l c u l a t i o n s based on the c a v i t y dimensions and the k l y s t r o n power (see c a v i t y d e s c r i p t i o n i n apparatus s e c t i o n ) .  Unfort-  u n a t e l y , no means was a v a i l a b l e to measure independently Hi « or changes i n Hi , ( i . e . .by measuring the power d e l i v e r e d  to the  c a v i t y ) so that no data can be given i n which the c o n t r o l l e d parameter was Hi  .  It i s desirable  to have Hi as l a r g e as p o s s i b l e  (both  -19-  Rectanjulqr-  Ccwity  Same as  above , except  ©- 1*' H i - [ gauss  FIG. 5(a)  DERIVATIVE TRACESi ELECTRON ROTATING FRAME  RESONANCE IN THE  -20C^lindncal  Canity  f* 51.315 Mc/j Modulation Time  23cp5 , 1.5 gauss  Constant  ./ sec.  Total duration of sweep  70 sec  Spectrometer coil out s i parcillel te Ho perpendicular to Ho  Note:  Center  line  *^  remain*  unchanged  Cylindrical  CauiTy  f * 23.337 Mc/s. Modulation  80 cps , /.S"jjauss  TTme Constant Total &t>eep  FIG.  5(b)  DERIVATIVE TRACES, ELECTRON RESONANCE ROTATING- FRAMG  /N  THE  I sec (00 sec  FIG. 5 d  SAMPLE SIGNAL  FIGS. 5" C * d  FROM MELTED OR AMORPHOUS  DPPH  -22because the theory assumes t h i s , thereby  increased).  l a r g e Hi  and because the s i g n a l s i z e i s  However, h e a t i n g e f f e c t s occur along with a  , which make the i n t e r p r e t a t i o n of the r e s u l t s  The h e a t i n g , and  eventual m e l t i n g , of the samples was  difficult.  caused by  both d i e l e c t r i c l o s s e s of the sample i n the microwave e l e c t r i c f i e l d and by the a b s o r p t i o n of energy a t the. s p i n resonance. I t was  found  t h a t , i f very s m a l l samples were used, m e l t i n g  occurred at about Hi  Hi  = 2 gauss i n the c i r c u l a r c a v i t y and  = 2.8gauss i n the r e c t a n g u l a r c a v i t y . For both a s i n g l e c r y s t a l and a powdered c r y s t a l l i n e sample  i n a low  f i e l d Hi  As the s i z e of Hi  , s i g n a l s such as those i n Fig.5(c) were was  i n c r e a s e d the l i n e shape changed to that  shown i n F i g . 5 ( d ) . T h i s change i n l i n e shape would occur and  i s most l i k e l y  the r e s u l t of the sample m e l t i n g .  samples when they were taken out had the sample was repeated  allowed  observed.  to c o o l and  suddenly  A l l such  a g l a s s y appearance.  the low  Hi  If  s i g n a l s were  the l i n e shape remained as shown i n F i g . 5 ( d ) .  An unexpected r e s u l t was  the appearance of a center s i g n a l  which can be seen i n the t r a c e s shown i n F i g . 5 ( b ) .  Its origin  i s unknown but the f o l l o w i n g t h i n g s were noted about i t :(a)  I t was  i n others.  present i n some of the observed  s i g n a l s but  not  " T h i s appears to be r e l a t e d to the degree of  r . f . h e a t i n g of the sample. (b)  I t was  observed  with d i f f e r e n t shapes and  s i z e s which  -23Hi  appear to be r e l a t e d to the s t r e n g t h of the f i e l d the frequency u)ns at which the f i e l d (c)  Ho was  , and  modulated.  I t i s independent of the d i r e c t i o n of the p e r t u r b i n g  field  Ha • (d)  I t always occurs  at the c a v i t y resonance ( Ho=  (e)  I t appears to occur  "^r ).  only i n samples which are or have been  melted by the r . f . h e a t i n g .  A p o s s i b l e e x p l a n a t i o n of t h i s l i n e i s that i t i s a z e r o frequency resonance i n the l a b frame. t h i s view.  The  Notes (c) and  l a r g e s i z e of the s i g n a l may  assuming that near Q = 90°,  (d)  support  be e x p l a i n a b l e  by  the Zeeman s p i n system a s s o c i a t e d  Heff g i v e s i t s energy to the l o c a l f i e l d s p i n system as  with  Heff  becomes comparable i n s i z e to Hu , thus c o o l i n g the s p i n s i n the local field  system.  T h i s i n t u r n would i n c r e a s e the s i z e of  zero frequency resonance by the same f a c t o r as the r e l a t i v e populations  the  spin  are changed by the c o o l i n g e f f e c t .  By changing the c o u p l i n g to the microwave c a v i t y i t was p o s s i b l e to vary c a l i b r a t i o n was by o b s e r v i n g  the s t r e n g t h of the f i e l d a v a i l a b l e to i n d i c a t e how  the s i g n a l .  The  expected ( 5in0 ) ( c o s 0 )  determined  angle Q of H«ff was f  z  much Hi v a r i e d , except  the s i z e of Hi  and a p l o t of s i g n a l s t r e n g t h .vs @ was The  no  A s s e r i e s of s i g n a l s were observed f o r  v a r i o u s c o u p l i n g p o s i t i o n s and i l l u s t r a t e d i n F i g . (if).  Hi , although  as  also calculated  made as shown i n F i g .  v a r i a t i o n i s a l s o shown.  (7).  As can be •a. seen, the observed' s i g n a l tends to f o l l o w the ( s i n 0 ) ( c o s © )  curve.  F o r a l l these p o i n t s the spectrometer frequency was  held constant was  changed to vary 0 The  0 are  (thus (Heff| at maximum s i g n a l was constant) and Hi  (Sin©)(  c o s  as i s explained  .  ©)  curve n e g l e c t s  e a r l i e r i n the t e x t .  on  The experimental p o i n t s  the amplitudes o f the d e r i v a t i v e s i g n a l s and are not c o r r e c t e d  f o r the v a r i a t i o n i n l i n e - w i d t h . and  the dependence o f  This l a s t c o r r e c t i o n i s small  i t would tend to reduce the amplitude o f the l a r g e Q p o i n t s  r e l a t i v e to the low 0 The  points.  samples were i n the melted or amorphous s t a t e f o r a l l o f  the p l o t t e d p o i n t s .  The a c t u a l temperature o f the sample  probably v a r i e d g r e a t l y between the v a r i o u s p o i n t s s i n c e the power d e l i v e r e d to the c a v i t y was changed to vary  Hi , thus the  degree of sample h e a t i n g a l s o v a r i e d . The  experimental p o i n t s are not c o r r e c t e d  l i n e overlap.  f o r the e f f e c t o f  I f t h i s c o r r e c t i o n was made the p o i n t s would be  s h i f t e d about 5° to a l a r g e r ©  value.  The f a c t that the  s c a t t e r of the p o i n t s i s l a r g e r than the a s s o c i a t e d measurement i e r r o r s i n d i c a t e s that an e f f e c t such as the temperature v a r i a t i o n i s predominant, and s m a l l c o r r e c t i o n s are not of much value. An i n t e r e s t i n g f e a t u r e o f the theory  which i t was hoped to  v e r i f y i s the ( 3 c o s © - ! ) dependence o f the d i p o l e s p i n - s p i n 1  c o u p l i n g given i n e q n . ( 7 ) .  Note that f o r the angle a t which  t h i s f a c t o r i s zero a pronounced l i n e narrowing should be observable.  -25-  In f a c t , s i n c e narrowed,  the resonance e l e c t r o n l i n e i n DPPH i s exchange  we observe an averaged d i p o l a r c o u p l i n g  forra ( 3 c o s * 0 - | )  .  An i n d i c a t i o n o f t h i s narrowing e f f e c t was  obtained i n the f o l l o w i n g  manner:-  The l i n e widths of the s i g n a l s p r e v i o u s l y (7)  which has the  are p l o t t e d i n F i g . (8).  described  for Fig.  The expected v a r i a t i o n of l i n e  width i s based on the geometry of the way the s i g n a l s were o b t a i n e d . This i s i l l u s t r a t e d i n F i g . ( 6 ) .  FIG.  6.  GEOMETRICAL LINE  RELATIONSHIP  OF  OBSERVE-D  TO  ACTUAL  M D T H  The resonance l i n e c e n t e r (maximum s i g n a l ) i s assumed to occur f o r the e f f e c t i v e f i e l d marked H maximum slope  c  .  The p o i n t s o f  o f the resonance l i n e are assumed to occur when the  e f f e c t i v e f i e l d has the value marked  .  Since the s p e c t r o -  meter frequency does not change as Hi i s v a r i e d the v a l u e s o f and He w i l l be the same f o r v a r i o u s angles i f no l i n e occurs. as ©  narrowing  But the l i n e width as observed w i l l appear to narrow  i s reduced s i n c e the l i n e i s observed as a f u n c t i o n o f the  change o f Ho . The l i n e width which i s p l o t t e d i s the average o f the l i n e s i n each quadrant o f the r o t a t i n g frame.  The s i g n a l s  exhibited  the symmetry shown i n Fig.(3) t o the extent that the lower quadrant s i g n a l % l i n e width ( i l l u s t r a t e d i n Fig.(8)) was cons i s t e n t l y about 15$ l a r g e r than that o f the upper quadrant ,  The experimental l i n e width narrowed  signal/  as © was i n c r e a s e d ,  e x a c t l y o p p o s i t e to the expected r e s u l t , i f no l i n e  narrowing i  o c c u r r e d , and t h i s may be an i n d i c a t i o n o f the ( 3 c o £ © ~ |  )  f a c t o r , which reduces the d i p o l a r c o u p l i n g o f the s p i n s f o r a predominantly exchange narrowed 2( Hfc - H c ), l i n e width.  (see Fig.(6)  sample.  The true l i n e width i s  ) and i s e a s i l y found from the observed  T h i s i s a l s o p l o t t e d i n Fig.(8), with a ( 3 c o s * e - | ) X  curve f o r comparison.  I t i s p o s s i b l e that the minimum o f the  l i n e width would a c t u a l l y occur a t 5 ^ . 7 ° ,  f o r which ( 3 c o s * © - |  )  = 0. The e r r o r bars i n F i g s . (7) errors involved i n c a l c u l a t i n g © amplitudes o f the s i g n a l s .  and (8)  i l l u s t r a t e the r e l a t i v e  and i n measuring  the r e s p e c t i v e  They do not r e p r e s e n t the e r r o r s  due t o such t h i n g s as the temperature v a r i a t i o n o f the sample (which i s unknown) o r l i n e o v e r l a p . An announcement o f another group's o b s e r v a t i o n o f the r o t a t i n g frame s i g n a l s i s g i v e n i n r e f e r e n c e (k).  -27-  FIG. 5 4- -  LINE WIDTH IN THE RorAT»N«FRAME V* ANOLE OF THE BFFecTive FIELD, WITH A  f3co4*0-r)  Z  C U R V E  Expected uana'tion  measured  on t4» a * i « , no narrouMn.^ —  FOR  COMPARISON  - — — O b s e r v e d On  g  Ho  l i n e u/idHi vnensi/pfd a«is  (-fift««0  —-7  x  \ ^  Corrected (measured  V ^  V  \  l i n e <*»i4fk 4 Ion)  H*ff —  1  \  Base line Sianal  ^tline cuid-tK 10  20  6  ( DECREE S)  do  £0  HO  FIG. T DERIVATIVE SICfVAL STKEWfrTH V 5 A N C L E O F THE EFFECTIVE F I E L D , WITH A s m e cos© CURV& F O R .  KM  l  C O M P A R I S O N  X  Sin*0 cose  IO  20  6  FIGS.  7 * 8  H e f f ="3.6  o Hew" 3.1  (DEG-REES)  30  HO  fauss^ J W J .  SO  -28-  THEORY AND EXPERIMENT, - ENHANCEMENT EFFECTS  The next f e a t u r e o f the experiment was to observe proton enhancement e f f e c t s due t o c o u p l i n g  mechanisms between the  e l e c t r o n s and protons i n the sample (DPPH).  The two p o s s i b l e  methods o f doing t h i s can be q u i c k l y sketched with the f o l l o w i n g s i m p l i f i e d p i c t u r e :Suppose we have two s p e c i e s I  and S  AI'S  , both o f s p i n 1/2.  o f s p i n s o f angular momentum, Suppose a l s o a s c a l a r i n t e r a c t i o n ,  , i s present and that the I  s p i n s can r e l a x only by under-  going mutual s p i n f l i p s with the 5 s p i n s , o f p r o b a b i l i t y In a l a r g e f i e l d  Ho ,  I?  and St  W(+-)^ C-+) .  a r e approximately good  quantum numbers, and we w i l l have the four s t a t e s o f the t o t a l system, (+•+), ( + - ) ,  (-+ ), ( —  ) where + / - r e p r e s e n t s a s p i n  p a r a l l e l t o / a n t i - p a r a l l e l to Ho , and the f i r s t / second s i g n represents populations  the i / s s p e c i e s .  L e t H+, *\- and NI+, N- be the  o f the two p o s s i b l e s t a t e s f o r the I and S s p e c i e s ,  respectively. Then i n the steady s t a t e c o n d i t i o n we have :  n+N- Wc+-)^(-+) * n-N+W(-4-)--c -} +  The l a t t i c e a t temperature Ti. s e t s up the Boltzman r a t i o ;  And f o r the s p i n s i n e q u i l i b r i u m with the l a t t i c e :  (27)  -29-  (30)  -i  Suppose we  s a t u r a t e the p o p u l a t i o n s of the S s p e c i e s by ^sHo  a p p l y i n g energy at the frequency (a)  , so that  N4=  N-  ,  then :  -H± =  w  c-+w+-)  _  € X P  /_  M l b M i k \  (31)  T h i s i s known as the Overhauser e f f e c t Suppose we  supply energy a t the frequency  equalize  W(-+)-±(+-) - VV(+-)-(-+)  (b) then  :  (Vs-fi)!"!© , to  k  />» \ ?  nts  n-  M±. =  N-  exp  (h2LHo) PV  W  KTL /  T h i s i s known as the S o l i d e f f e c t .  (Note that the (b) e x p r e s s i o n  i s obtained but o p p o s i t e i n s i g n i f the t r a n s i t i o n (•+•* ) ^ at frequency  ()/z+Ki) Ho  )  i s considered i n s t e a d of (-f- ) ^  (  )  ( — +)  ).  P r o v i d e d j ^ l >| Yl| an enhancement of the X s p e c i e s i s obtained i n both cases.  A thorough d i s c u s s i o n of the a p p l i c a t i o n s of these  two methods i s given i n Abragam ( 2 ) .  The  r e s u l t s can be summar-  i z e d as given below : (a)  I f the i n t e r a c t i o n between the I and  S s p i n s i s modulated by  r a p i d movement of the s p i n s (as i n l i q u i d s ) , of i f exchange narrowi n g occurs because of r a p i d e l e c t r o n s p i n f l i p s 4- s t a t e s are pure and W(+-)-*(-+) .  (as i n DPPH), the  i t i s i m p o s s i b l e to induce the  T h i s i s a completely  transition  forbidden t r a n s i t i o n .  can n e v e r t h e l e s s occur as an i n t e r n a l r e l a x a t i o n e f f e c t ) .  (It Thus  -30only the Overhauser e f f e c t (b)  applies.  For cases i n which the c o u p l i n g between the s p i n s i s s t a t i c ,  the k s t a t e s are not pure and i t i s p o s s i b l e to observe effect.  the S o l i d  In the s t a t i c case, the d i p o l a r c o u p l i n g i s u s u a l l y the  dominant e f f e c t because of the term I t S g ,  corresponding to a  s p i n f l i p o f the X s p e c i e s but not the S s p e c i e s , which r e q u i r e s much l e s s energy  than the mutual s p i n f l i p s r e q u i r e d f o r the  Overhauser e f f e c t .  F o r t h i s reason only one o f the e f f e c t s  dominate a g i v e n substance  will  i n the above l i m i t i n g case .  The Overhauser e f f e c t i s easy  to demonstrate with  this  experimental set-up s i n c e the sample (DPPH) i s exchange narrowed ( n o n - s t a t i c ) and the s t r o n g  r f . f i e l d Hi necessary  f o r the  r o t a t i n g frame a l s o p a r t i a l l y s a t u r a t e s the e l e c t r o n resonance a t Us Ho  •  A l l that i s necessary i s to o r i e n t the p e r t u r b i n g  f i e l d Ho. p e r p e n d i c u l a r to Ho , a t a frequency Ula= KT Ho to observe  the protons.  e l e c t r o n s p i n resonances  , i n order  By a r r a n g i n g t h a t both the n u c l e a r and occur f o r the "same value o f Ho the en-  hanced proton s i g n a l i s e a s i l y  observed.  A p l o t o f the enhancement obtained i s given i n F i g . ( R ) . T g i s was obtained by sweeping the f i e l d H , modulated a t td,n f o r 0  the l o c k i n  d e t e c t o r , through the proton and e l e c t r o n  while h o l d i n g the spectrometer sweep.  resonances,  frequency UJo. constant f o r each  The maximum d e r i v a t i v e signal h e i g h t was then p l o t t e d  vs U/o. f o r each sweep. A s e t of the enhanced d e r i v a t i v e l i n e shapes are shomn i n Fig. (|0).  The spectrometer  frequency i s g i v e n under each l i n e .  31-  MAXIMUM  INCREASE  IN SKHVAL •= 4-30  H,  LESS  T H A N .7 G A U S S  o I  o  O /  \  SIGNAL  FIG.  °l  PLOT  -L  51.800  J  S1.T00  FREQUENCY  OF OVERHAUSER  si.loo  (Mc/s)  ENHANCEMENT  737  762  783  785" 79 <f  T h e -frequency over 5 1 M c  wnder eacl< line is the number o f kilocycles  ad whic^  each line uias ofeserve</.  S«e t e x t  •for explainaii on  83? 807  Ceoo)  FIG. 10  OVERHAUSER  EFFECT,  SAMPLE  LINE  SHAPES  -33A c t u a l l y , the  spectrometer frequency was  through the e l e c t r o n resonance, 6 Kc/s.  The  " p u l l e d " as Ho passed  being lowered  i n each case by  f r e q u e n c i e s given i n the diagrams are the lowest  v a l u e s , and correspond c l o s e l y to the l i n e c e n t e r s .  The  frequency p u l l i n g i s presumably because the c o i l was  heated  the sample which at resonance  i s absorbing  by  c a v i t y power.  Since a few minutes elapsed between each sweep the k l y s t r o n frequency would sometimes d r i f t  a few megacycles.  p a r t i a l l y allowed f o r by matching d i f f e r e n c e i n frequency was The  This  was  l i n e shapes and assuming the  caused by the k l y s t r o n  drifting.  frequency i n each of the brackets i s an a r b i t r a r y c h o i c e to  allow f o r t h i s . The odd l i n e shapes are p a r t i a l l y e x p l a i n e d by the v a r i a b l e s involved.  The sample h e a t i n g causes the proton l i n e to narrow as  the f i e l d Ho sweeps through the e l e c t r o n resonance,  and s i n c e t h i s  i s a l s o the enhancement r e g i o n , the proton l i n e i s a l s o enhanced. A l s o , s i n c e the enhancement r e g i o n i s comparable i n width to the proton l i n e width  (22 Kc, unenhanced), the enhanced proton l i n e  i s d i s t o r t e d , being enhanced more on the s i d e c l o s e r to the enhancement c e n t e r .  F i n a l l y , the frequency p u l l i n g e f f e c t means  that each recorded l i n e shape i s a composite d i f f e r i n g i n s i z e and shape due of  at  to the causes already g i v e n , each  which i s sampled as the spectrometer A frequency swept run was  one, made up of l i n e s  frequency i s p u l l e d .  done i n which Hb was  v a r i o u s values near the e l e c t r o n resonance  the frequency p u l l i n g , e f f e c t and  h e l d constant  i n order to e l i m i n a t e  s i m i l a r l i n e shapes were obtained  -3^w i t h enhancements o f the same o r d e r . The observed s i g n a l i n c r e a s e d i f f e r s from the t r u e ment f o r two reasons :  enhance-  the l i n e n a r r o w i n g due t o h e a t i n g , and  the s p e c t r o m e t e r response.  The amount o f l i n e n a r r o w i n g i s  d i f f i c u l t t o e s t i m a t e because o f the odd l i n e shapes, but i f the w i d t h o f the c e n t e r peak o f the l i n e shapes i s t a k e n as r e p r e s e n t i n g the narrowest l i n e sampled, then the l i n e n a r r o w i n g i s approximately a f a c t o r of f i v e .  The s i g n a l i n c r e a s e from t h i s  e f f e c t i s then about a f a c t o r o f f i v e .  The o t h e r p o s s i b l e e r r o r  i s from t h e s p e c t r o m e t e r , s i n c e one cannot expect i t t o respond l i n e a r l y t o such l a r g e v a r i a t i o n s i n s i g n a l s t r e n g t h , b u t no c a l i b r a t i o n was done t o c o r r e c t f o r t h i s . The e l e c t r o n resonance was n e a r l y s a t u r a t e d i n t h i s  experi-  ment, hence the enhancement s h o u l d be v e r y near the maximum possible.  Assuming an e r r o r by a f a c t o r o f f i v e from the causes  mentioned, the enhancement was about 60. an enhancement o f 6 a t 300°  T h i s can be compared wi  w i t h the e l e c t r o n resonance 1/3  s a t u r a t e d g i v e n i n r e f e r e n c e ( 6 ) and an enhancement o f 30 a t h.2.° g i v e n i n r e f e r e n c e ( T ) \ ^ a l t h o u g h i n t h i s experiment the s t a t e o f the sample i s i n doubt,  i t i i s most l i k e l y i n a l i q u i d o r a  hot amorphous s t a t e . I t s h o u l d be noted t h a t the enhancement s h o u l d be temperature independent, as d i s t i n c t from the p o l a r i z a t i o n which i s s t r o n g l y temperature  dependent.  From the t h e o r y g i v e n , i t can be seen t h a t the t h e o r e t i c a l maximum enhancement i s a p p r o x i m a t e l y the r a t i o o f the If- v a l u e s  -35of the electron and proton, which i s 660.  The theory given does  not include leakage effects, and a more complete picture can be given as follows :In F i g . (II), with  the four energy levels of the system are shown  the possible relaxation modes given as fractions of the main  electronic t r a n s i t i o n , labeled OJ .  The relative populations of  these levels are l i s t e d next to the diagram;  column (a) represents  the thermal equilibrium populations, columns (b) and (c) represent the populations when the ui transition i s saturated, and the i n d i c ated relaxations occur.  The relative nuclear populations are  given at the bottom of each column.  (a) -thermal eauil.  1  C-  o  =b-0  I i\  N  I \  t  i y I / \ I / \ 1/  l  «* *'  w I  x  b  w  relative population  ! I  1  \  af?  -A e  z  FIG. I I  f  CO  ^ appro*, relative nuclear population  OVERHAUSER EFFECT, RELATIVE POPULATIONS OBTAINED BY SATURATING TRANSITION u)  -36-  The cut r e l a x a t i o n w i l l be caused by thermal motion " c o l l i s i o n s " between the e l e c t r o n s and p r o t o n s , s i m u l t a n e o u s l y f l i p p i n g both s p i n s , w i t h the excess energy b e i n g taken up by the e l e c t r o n t r a n s l a t i o n a l energy, which q u i c k l y t h e r m a l i z e s w i t h the lattice.  The fu» r e l a x a t i o n can be caused by a f l u c t u a t i n g  d i p o l a r o r o r b i t a l hfs  interaction.  F i n a l l y , paramagnetic  i m p u r i t i e s and quadupolar e f f e c t s may give ;'.the bw c  which r e p r e s e n t d i r e c t n u c l e a r - l a t t i c e  relaxations,  relaxation.  The p r i n c i p l e r e l a x a t i o n mode can be i n f e r r e d from the s i g n of  the enhancement.  From t h e d a t a , the enhanced s i g n a l i s o f the  same s i g n t o t h e unenhanced s i g n a l , i n d i c a t i n g t h a t fu> i s the main r e l a x a t i o n mode. The S o l i d e f f e c t i s more i n t e r e s t i n g s i n c e i t has a ready i n t e r p r e t a t i o n i n terms o f t h e r o t a t i n g frame s p i n temperature. The correspondence between t h i s e x p l a n a t i o n and the former one i s g i v e n by Solomon ( 8 ) . As noted p r e v i o u s l y , i n the r o t a t i n g frame, the e l e c t r o n s are  quantized along  Hctf  •  By a d j u s t i n g the s i z e  o f H « f f so  t h a t the e l e c t r o n quanta a r e j u s t e q u a l t o t h e p r o t o n quanta i n the f i e l d  H o , i . e . :-  one e x p e c t s a t h e r m a l c o n t a c t between the two s p i n systems, s i n c e mutual s p i n f l i p s among the two s p e c i e s w i l l conserve energy. As a l r e a d y g i v e n , the temperature r a t i o n b e t w e e n the l a t t i c e temperature Ti- and the e l e c t r o n s p i n temperature T4 i s :-  -37-  I f we d e f i n e  the distance  *  * Ho  uii = t h e n we c a n r e w r i t e £  This  from r e s o n a n c e i n t h e r o t a t i n g frame a s :  (35)  angular velocity e q n . (34-) =  -  H  »  o f Hi  , l a b frame  as : (36)  A  may be p l o t t e d a s shown i n F i g . ( (2. ) .  + He  T5  -He  F I G . 12.  SPIN THE  Hu  TEMPERATURE DISTANCE  i s the l o c a l  /N T H E FROM  ROTATING  FRAME  VS  RESONANCE  f i e l d a t each e l e c t r o n s p i n s i t e .  of t h e order o f t h e width o f the e l e c t r o n resonance l i n e . region  of thermal contact  i s the region  of overlap  It i s The  of the electron  -38-  and  nuclear l i n e s , and  i f the e l e c t r o n l i n e i s wide, that i s to  say:  which i s the g e n e r a l case,  then the thermal contact i s r e a l i z e d  the d i p o l a r i n t e r a c t i o n , i n a l l of the domain where 3jL g r e a t e r than By be  via  is  1.  the mechanisms of a thermal contact the n u c l e a r s p i n s  will  cooled to the same temperature as the e l e c t r o n s p i n s , and  s i n c e the enhancement i s p r o p o r t i o n a l to the r e l a t i v e i n c r e a s e i n magnetization, a t u r e , we ratio  Ts  which i s i n v e r s e l y p r o p o r t i o n a l to the s p i n temper-  then have the n u c l e a r enhancement given simply  the  plotted i n Fig. ( 1 2 ) .  Such an enhancement i s e a s i l y obtained  with t h i s  u s i n g a sample of DPPH d i s s o l v e d i n p o l y s t y r e n e styrene separates  (9).  apparatus, The  poly-  the DPPH molecules so t h a t the exchange narrow-  i n g e f f e c t disappears The  by  and  the s p i n - s p i n i n t e r a c t i o n i s d i p o l a r .  p e r t u r b i n g f i e l d H * was  i n order to observe the proton  oriented perpendicular  resonance which was  Ho  to  chosen to be a  c e r t a i n d i s t a n c e ( A ) from the c a v i t y resonance by f i x i n g ^ a . . The  field  HP was  modulated at the frequency  l o c k - i n d e t e c t o r , and  was  enhancement so obtained a f u n c t i o n of A ( 1 3 ) . the f i e l d  t*)m to operate  used to sweep out the l i n e .  f o r each frequency  , the d i s t a n c e from  U)*. was  the  The  then p l o t t e d as  resonance, as shown i n F i g .  T h i s method of o b t a i n i n g the enhancement, by sweeping H© , means that A  sweep, and a t f i r s t  i s c o n s t a n t l y changed d u r i n g  the  thought i t would seem t h a t t h i s i s not what  -39o  o. o.  ^.  factor  (.T3l)  (5 a r b i t r a r y  to f i t CMryta.  • \  \  PLOT O F OBSERVED  \  P W T O N LIME FREQUENCY •  h  ENHANCEMENT  WITH  THEOBENCAL  VS  COMPARED  CURVE  VS  A  z in  2 til u < X Z  O  -  o. I  Hi  Experimental Theoretic* I  points  \  cwri/e  \. \ • \ .  s-  \  o o-  51.too  51.700  T  T  51.800'  PROTON  —i—  LINE  i  FREQUENCY  -10  -20  -30  PI5TA.MCE  ,  a nee  F R O M  f=  Constant S1.95S-  "Total  SOLID  EFFECT  — I — 30 30  RESONANCE  fO  CcAUSS)  fcla.tiu'e "Ttcne  sec.  Gam  Siana/ 2.0  Constant 3 sec  Me  EAKancewienT "  SAMPLE :  FIG. 13  -I  — I — 2 00 2  , Mot F n h a n c e d  -iqnol  Relative G a m I Time  52.000  (rAC/s)  -I— IO IO  O  r  SI«\0O  DPPH  ^0  Diluted  ENHANCEMENT  m  Polystyrene  $0  -HOi s suggested by eqn. ( 36), each value o f the  i n which A  i s assumed constant f o r A  enhancement curve, whereby changing  success-  i v e l y and sweeping out the proton l i n e one would o b t a i n the t o t a l curve.  T h i s i s a c t u a l l y e q u i v a l e n t to the method used, s i n c e by  h o l d i n g the proton frequency of the spectrometer constant while Ho i s swept through i t , only the value o f A o c c u r r i n g a t the same i n s t a n t as the proton l i n e w i l l c o n t r i b u t e to the enhancement o f the proton l i n e , and even though A  will  subsequently  pass through r e g i o n s i n which the e l e c t r o n s are f u r t h e r c o o l e d , t h i s w i l l not a f f e c t assumption  the proton l i n e a l r e a d y swept out.  i s , o f course, that the e l e c t r o n s p i n  w i l l f o l l o w the changing  A  The  temperature  , and that the proton enhancement  i s maximized as i t i s swept o u t .  The t o t a l d u r a t i o n o f the  sweep -for A to t r a v e r s e 50 gauss on both s i d e s of the resonance was 1 0 0 seconds, and o f t h i s about 5 seconds out the proton l i n e to i t s i n f l e c t i o n p o i n t s . felt  was spent sweeping These times were  to be l o n g enough f o r e q u i l i b r i u m to be e s t a b l i s h e d  value o f A  .  The requirement curve i s that HL  f o r each  that F i g . ( 12. ) r e p r e s e n t the enhancement  X$Ht ^  18 gauss.  Since  , which i n t h i s case r e q u i r e s t h a t Hu  i s o f the same order as the  e l e c t r o n l i n e width, which f o r the d i l u t e d about 2 0 gauss, t h i s requirement  DPPH sample used was  i s approximately met.  The maxima o f the experimental curve occur very near the value A = i  l 8 . ^ gauss which by c o i n c i d e n c e f o r t h i s sample i s  the same f o r both the p r e d i c t e d value  H***"^ 4  and  A = "1^ H^ + Z HL*) (where 2  = 13 gaugs.f)j and the r e g i o n o f maximum o v e r l a p of  -klthe e l e c t r o n and proton With t h i s value by  eqn.36 should  lines.  of A  , the maximum enhancement p r e d i c t e d  be 3 3 1 , whereas the observed maximum was only 1 0 0 /  For comparison, eqn. ( 3 6 ) i s p l o t t e d i n F i g . ( it  i s m u l t i p l i e d by an a r b i t r a r y constant  curve obtained.  This constant  ), except that  to match i t b e t t e r to the  could perhaps represent  losses  i n the heat t r a n s f e r or l o s s e s which would prevent the e l e c t r o n s being cooled of A  to the p r e d i c t e d temperature.  For large  values  , the shape of the curve does not match the experimental  curve a t a l l ,  which may i n d i c a t e that t h e p r o t o n - e l e c t r o n  o v e r l a p was not great  enough to couple e f f i c i e n t l y  line  the two  systems ( i . e . , the requirement o f eqn. (37) was not f u l l y met), or i t may i n d i c a t e t h a t the e l e c t r o n s p i n temperature departs from the p r e d i c t i o n s o f eqn. ( 3 4 )  f o r t h i s sample.  -k2-  APPARATUS  The  apparatus c o n s i s t e d o f a tunable, high power k l y s t r o n ,  a high f i e l d  magnet, a high frequency  spectrometer,  two s p e c i a l l y designed  a b s o r p t i o n resonance microwave c a v i t i e s , a  phase l o c k - i n d e t e c t o r , an o s c i l l o s c o p e , an audio a m p l i f i e r , a c h a r t r e c o r d e r and a l o n g d u r a t i o n sawtooth generator, with  along  the a s s o c i a t e d power s u p p l i e s and s t a b i l i z i n g networks. The  k l y s t r o n provided  frequency  o f 3^ K Mc/s.  the s t r o n g r o t a t i n g f i e l d Hi The corresponding  field  , at a  Ho f o r a  Larmoirr p r e c e s s i o n r a t e of 3H K Mc/s f o r e l e c t r o n s i s about 12 K i l o g a u s s which was provided  by the high f i e l d  magnet.  sample was mounted i n the microwave c a v i t y with the very pick-up  The small  c o i l o f the spectrometer which could d e t e c t the n u c l e a r  or e l e c t r o n i c s i g n a l .  E x t e r n a l to the c a v i t y were two s m a l l  Helmholtz c o i l s to provide a modulation o f Ho o f up to 8 0 gauss for  p r e s e n t a t i o n o f the s i g n a l on the o s c i l l o s c o p e , or only  f r a c t i o n s o f a gauss f o r the o p e r a t i o n of the l o c k - i n d e t e c t o r and  p r e s e n t a t i o n of the s i g n a l on the c h a r t r e c o r d e r .  field  sweep o f Ho was obtained  A variable  by f e e d i n g a v a r i a b l e d u r a t i o n saw-  tooth wave form v i a an a t t e n u a t o r i n t o the magnet power supply. In t h i s manner Ho could be a d j u s t e d to  many hundred gauss, with a  to sweep from s e v e r a l gauss  d u r a t i o n o f sweep o f up to 2 0 0  seconds. A block diagram i s given i n F i g . l ' f .  -k3-  High G-air.  Electron 10 Counter  Filament Supply 100 Volt Stabilised HV 5«ppf«j  Balanced  Audio P r e Amp  O  Balanced Line Hiah Freonencv, .Spectromeler  Audio  Pauper Amplifier  Audio Signal Generator  Line. Microvvave  Sample and Spectrometer Coil  (  Cavity  V * Helrnnoltj Coil  Lock- ir. Detector  Chart Recorder  Variable Coupiincj Device* Attenuator^ Directional (lOdt)  Coupler  j-  -1  LW  1  Xtal  Detector 20 Watt kflystron  20 Watt Load 3 Port Circulator  Magnet Power Supply  %  Variable Dura+ior*  Cauify and Kiqsfron Water looted  Attenuator  FIG.  I If  BLOCK  DIAGRAM  OF A P P A R A T U S  T~r : i  -2ifO  1 1 1 1  T  .060 .060  . 0M-7 Oia. hole -fer Sqmple  013 D i « .  TEFLON  FILLER  FIG. 15  SAMPLE BOBBIN (TEFLON)  TEOII MODE CAVITY  Slot far mot/in.^ T<f|on insert CUTAWAY  FIG. 16  VIEW  SHOWING  VARIABLE  BRASS  /NSERTS  COUPLING  M WR-22 W/o  DEVICE  -45Teflon  Sample Holder  Spectrometer Silver* Plating  Couplmq Hole.071  Dio..  W/G  Flanq e.  Coil  Soldered onto  Sample  Cauitu Water Cooling  SIDE  VIEW  CUTAWAY Slot for introducing Sample Surrounding to  TOP  .00+  imetal roachmed thickness  VIEW  1-2-  .071 Dio,.  jn .100 Oia.  AUtO  T  .88R-  OIO  H  h-  .oso  Oia  #60  LUCITE CAVITY  FIG.  17  P L A S T I C FORM rVAS  ON W H I C H  SAMPLE  ELECTRQPLATEQ  TE  0/4-  MODE  CAVITY  (KECTANCTULAR.)  BOBBIN  Drill  (TEFLON)  -46-  Battery I-IOO Volts Regulated  Supply  -6 Vo/ts  UTC A- 18  1 **L * Sample  Coil  Twin Line t© Coil  Sample coil #U-6 wire  Length « L  Spectrometer  Circuit  Freq. CMc/s) L i t inch, L* 4 0 inch s  IL t v m s  5"5"  30  6 inches  30  20  |S  10  12. inches  FIG. 18  Appro*. Center  HQA-7  2 T 0 K  •v^^A^Wr|i^--LW  125 k m  T'.? * |u  •—llli  300 V  (too cps)  •iiho"  _  SK  J  «.3  VOC  6 VDC (FLOATING)  .04 15K R= G E 120 V 3W LAMP  FIG. IS  0* »  (B)  Klystron Free. Stabiliser  )  IN SERIES WITH BEAM Sum*/ TO KLYSTRON  -48-  The  r e c t a n g u l a r c a v i t y , shown i n F i g . 1 7 , was designed to a t 34 K Mc/s.  resonate plastic  form the exact  I t was made by f i r s t c o n s t r u c t i n g a shape of the i n s i d e of the c a v i t y , with  p r o t r u s i o n s f o r the s l o t and c o u p l i n g h o l e .  T h i s was f l a s h e d  with s i l v e r and then e l e c t r o p l a t e d with copper to a t h i c k n e s s of about 1 / 1 6 i n c h by the E l e c t r i c a l E n g i n e e r i n g  Department.  The  o u t s i d e was then machined and the p l a s t i c d i s s o l v e d o u t . The  advantage of t h i s c a v i t y i s that the r e g i o n o f s t r o n g  magnetic f i e l d  occurs a t the w a l l o f the c a v i t y so that i t i s  p o s s i b l e to have the spectrometer c o i l j u s t o u t s i d e the c a v i t y and  the sample i n s i d e .  perturb to  With t h i s arrangement the c o i l ,  does not  the c a v i t y mode and there are no s h i e l d i n g e f f e c t s due  the c o i l being around the sample. Since up to 2 0 watts of power could be d i s s i p a t e d i n the  c a v i t y , water c o o l i n g was p r o v i d e d . The was  r e c t a n g u l a r c a v i t y Q f a c t o r , without  a sample i n i t ,  measured on a microwave t e s t bench to be 1 6 0 0 loaded,  4000  unloaded. A simple  means o f e s t i m a t i n g the f i e l d s t r e n g t h i n the  c a v i t y i s provided  by the formula :  where P i s i n ergs/ power d i s s i p a t e d i n the c a v i t y sec, H i s i n gauss, c a v i t y magnetic V  c  i s i n cm' , volume o f c a v i t y  field  -49-  T h i s formula i s a r r i v e d a t from the d e f i n i t i o n o f the Quality  factor Q = energy s t o r e d energy l o s t per c y l e  where the energy s t o r e d i s assumed to be e n t i r e l y i n the magnetic field,  d i s t r i b u t e d u n i f o r m l y over the c a v i t y volume.  The energy  l o s t per c y c l e i s j u s t the energy s u p p l i e d to the c a v i t y per cycle. Assuming P = 10 watts  L0 = (2 IT ) x 34 x 10  9  o  Vc =  .567  Q, =  1000  we get H = 2.3 gauss. T h i s formula does not account f o r the f i e l d the  within  c a v i t y which, f o r the mode o f t h i s c a v i t y , i s approximately . t  sinusoidal i n character. the  distribution  maximum f i e l d  Thus the average f i e l d  i s about .7 o f  w i t h i n one h a l f - w a v e l e n g t h s e c t i o n .  The  c a v i t y was designed so that the sample i s p l a c e d i n the r e g i o n where the magnetic f i e l d s of two such s e c t i o n s r e i n f o r c e , so that the  t o t a l maximum l i n e a r l y o s c i l l a t i n g f i e l d  should experience i s about 6.5 gauss. ponent needed  which the sample  Hence the r o t a t i n g com-  f o r the r o t a t i n g frame ( Hi ) should be h a l f o f  t h i s v a l u e , or about 3.2 gauss. The maximum observed value o f H  t  , measured by the method  d e s c r i b e d i n the theory of t h i s experiment, was 2.9 gauss, i n reasonable agreement  with t h i s expected v a l u e .  -50-  Th e c y l i n d r i c a l c a v i t y shown i n F i g . 15 was a l s o c o n s t r u c t e d . A dielectric  f i l l i n g o f t e f l o n was used to reduce the volume and  hence i n c r e a s e the magnetic f i e l d .  The dimensions were obtained  from a c y l i n d r i c a l c a v i t y mode c h a r t QO)with s u i t a b l e allowance for  the t e f l o n f i l l i n g ,  f o r resonance a t 3^ K Mc/s.  mode used the maximum magnetic f i e l d  In the  i s a x i a l , hence the sample,  with the spectrometer c o i l wrapped around i t , was placed i n the c e n t e r o f the c a v i t y on a mount which could be r o t a t e d to change the  o r i e n t a t i o n of the c o i l .  T h i s f e a t u r e was very u s e f u l f o r  s t u d y i n g the enhancement e f f e c t s s i n c e i t was necessary to r o t a t e the c o i l 90° between the proton and e l e c t r o n "pick-up" positions. Using eqn.38, and assuming P = 10 watts CO.= 2TT(34 x 1 0 ) 9  V= .356 cm Q= 1000  3  c  t  we get H = 2.88 gauss. T h i s i n d i c a t e s that the maximum magnetic f i e l d  i n the  r o t a t i n g frame ( H i ) should be approximately 3 gauss.  This  could not be checked by experiment s i n c e i t was found that the samples melted as H i approached 2 gauss.  Below t h i s value  good s i g n a l s could be obtained with the spectrometer c o i l i n s i d e the c a v i t y , but i t was necessary to have the c o i l the  and  lead-out wires symetric about the c a v i t y a x i s or a l a r g e  noise pick-up o c c u r r e d .  -51-  The  v a r i a b l e c o u p l i n g device shown i n F i g . l 6 i s d e s c r i b e d i n  the r e f e r e n c e f l l } .  I t simply  c o n s i s t s o f a s h o r t l e n g t h of  waveguide which i s dimensioned beyond c u t - o f f , with a t e f l o n s l i d e r which can be i n s e r t e d so that the a d d i t i o n of the d i e l e c t r i c b r i n g s i t above c u t - o f f .  Changing the p o s i t i o n o f  the s l i d e r changes the c o u p l i n g between the input and the output so that the c a v i t y impedance can be w e l l matched to the waveguide. The  c o u p l i n g hole i n each c a v i t y was made l a r g e enough so  that the c a v i t y by i t s e l f , coupled. optimize  loaded  with the sample, was over-  The v a r i a b l e c o u p l e r could then be adjusted to the c o u p l i n g .  No a t t e n u a t o r was provided  i n the microwave set-up to  a d j u s t the power d e l i v e r e d to the c a v i t y .  T h i s was a major  shortcoming o f the equipment s i n c e e x p e r i m e n t a l l y  one would l i k e  an e x t e r n a l measure of the s t r e n g t h of the r o t a t i n g f i e l d of the r o t a t i n g frame which could be provided attenuator.  Reducing the power without  problems o f s t a b i l i t y . at  t h i s frequency  operated  by a c a l i b r a t e d  an a t t e n u a t o r  The k l y s t r o n operated  presented  satisfactorily  i n only one mode, hence i t could only be  a t one power l e v e l .  T h i s meant that the c o u p l i n g to  the c a v i t y had to be reduced, or that the k l y s t r o n frequency had to  be off-t«ned from exact resonance, i n order to change the  power d e l i v e r e d to the c a v i t y .  Both o f these methods were  used, but they were not s a t i s f a c t o r y because the h i g h power l e v e l tends to p u l l the k l y s t r o n frequency  reflected  making i t  -52unstable.  A l s o , such s e t t i n g s were not r e p r o d u c i b l e s i n c e the  c o u p l i n g d e v i c e was not c a l i b r a t e d and no frequency meter was available. The k l y s t r o n was made by the E l l i o t from 52 to 34.5 at  3^ K Mc/s,  temperature  K Mc/s,  Valve Co.,  tunable  with a power output o f over 20  watts  and water c o o l e d , making i t very s t a b l e f o r  changes.  c i r c u l a t o r was a 3 p o r t , high power type made by  The  F e r r o t e c Inc., with a band pass from 33.85 to.34.15 K Mc/s, and i s o l a t i o n g r e a t e r than 25 db  , with a VSWR b e t t e r than  1.08.  The dummy l o a d was rated a t 20 watts, with a VSWR o f 1.10. frequency s t a b i l i z e r d e t e c t s the l 8 0 ° phase change o f  The  the microwaves as the frequency goes through the c a v i t y resonance drift  ( f o r an overcoupled c a v i t y ) and then c o r r e c t s the  by a l t e r i n g the beam v o l t a g e .  The microwaves are s l i g h t l y  modulated a t 10 Kc/s, and the r e f l e c t e d component from the c a v i t y i s detected v i a a d i r e c t i o n a l c o u p l e r and h i g h frequency The 10 Kc/s s i g n a l i s a m p l i f i e d and compared with  crystal.  the o r i g i n a l 10 Kc/s s i g n a l i n a phase d e t e c t o r . of  The output  the phase d e t e c t o r i s a p o s i t i v e o r negative D.C. v o l t a g e ,  depending  on which s i d e o f the c a v i t y resonance  frequency l i e s . connected  the microwave  T h i s e r r o r v o l t a g e i s a p p l i e d to four s e r i e s  t r a n s i s t o r s i n the beam c u r r e n t supply.  The t r a n s -  i s t o r s provide a maximum o f 120 v o l t s change i n the beam v o l t a g e which corresponds to a frequency change o f about yfi Mc/s.  A f t e r the warm-up p e r i o d t h i s i s ample s t a b i l i z a t i o n .  -53The k l y s t r o n power supply ( S l e e ) was found to be p o o r l y f i l t e r e d , and d e l i v e r e d an o b j e c t i o n a b l e 60 cps component to the k l y s t r o n which was both frequency and amplitude on to the microwaves.  To overcome t h i s ,  modulated  two a d d i t i o n a l L-C  f i l t e r s e c t i o n s were added to the beam v o l t a g e supply. reduced  These  the 60 cps component t o l e s s than one v o l t i n 3000  volts. The spectrometer i s a s l i g h t l y modified form o f the one d e s c r i b e d by Benedek and Kushida (12) The 6J6  and V o l k o f f e t a l l  (13).  tube operates as a p u s h - p u l l o s c i l l a t o r with the  frequency determined by the sample c o i l and the b u t t e r f l y tuning capacitor.  F o r maximum s i g n a l the g r i d - p l a t e  c a p a c i t o r s are tuned f o r marginal o s c i l l a t i o n .  feedback  The s i g n a l  i s observed when the Q f a c t o r o f the sample c o i l i s changed by the changing susceptance o f the sample so that energy i s removed from the o s c i l l a t o r c i r c u i t . c o n d i t i o n s i n the c i r c u i t cause a s l i g h t  additional The changed  change i n the c u r r e n t  d e l i v e r e d to the c i r c u i t v i a the p l a t e supply, and s i n c e the s i g n a l i s modulated magnetic  a t a frequency cJ because o f the modulated a  f i e l d , i t can be detected v i a the transformer i n the  p l a t e supply as an audio s i g n a l at<^«. .  This s i g n a l i s fed  v i a a balanced l i n e to a h i g h g a i n p r e a m p l i f i e r ( T e k t r o n i x , Type E) and can be d i s p l a y e d on the o s c i l l o s c o p e o r f e d to the l o c k - i n d e t e c t o r and d i s p l a y e d on a c h a r t r e c o r d e r . balanced l i n e i s necessary because  The  o f the h i g h output impedence  -54-  of  the  transformer.  The  frequency  i s monitored  t r a n s i s t o r a m p l i f i e r connected  by means of the wide-band to the p l a t e c i r c u i t .  a m p l i f i e r d e l i v e r s a v o l t a g e output of .1 over 1 v o l t at 10  i n t o a 50  Mc/s  The a d d i t i o n of a s m a l l D.C. adapted the instrument in  the noise  ohm  v o l t s at 60  Mc/s  and  load.  motor and  to frequency  This  r e d u c t i o n gears  sweeping with no i n c r e a s e  level.  The instrument  i s assembled i n a 1/4  tube, 4 inches i n diameter  and  12  inch thick  brass  inches l o n g , d i v i d e d i n t o  3 compartments f o r s h i e l d i n g purposes.  The  f i r s t compartment  c o n t a i n s the o s c i l l a t o r c i r c u i t which i s assembled on a b a k e l i t e board connected  to avoid ground l o o p s .  to the c e n t e r dummy p i n of the tube socket, and a l l  components are arranged a v o i d unbalanced oscillation.  as symmetrically as p o s s i b l e to  feed-back which would cause s p u r i o u s  RG-22/U twin l i n e s h i e l d e d cable was  t r a n s m i s s i o n l i n e to connect The  to the sample  used as a  coil.  second compartment c o n t a i n s the r . f . d e c o u p l i n g  f i l t e r s and  the t h i r d  the meter and The  A l l r . f . grounds are  compartment c o n t a i n s the audio  the t r a n s i s t o r r . f . a m p l i f i e r .  instrument  has been operated  between 4 and  100  Above 60  i t i s necessary  Mc/s  components,  Mc/s  with only changing  m i s s i o n l i n e s i n c e otherwise a few i n c h e s l o n g .  very  to use a 1/2  satisfactorily the sample  coil.  wavelength t r a n s -  the t r a n s m i s s i o n l i n e would be only  For example, the maximum frequency  a t which  -55a Ih  i n c h t r a n s m i s s i o n l i n e can be used i s about 60 Mc/s.  a c o i l of 1/2  turn.  The  m i s s i o n l i n e transforms  reason  noted  that the t r a n s -  the impedance of the c o i l as seen at  the g r i d c i r c u i t at the h i g h e r I t was  f o r t h i s i s simply  with  frequencies.  that the c a p a c i t y to ground of the t r a n s -  m i s s i o n l i n e could g r e a t l y reduce the s i g n a l s i z e but that i t had  little  or no e f f e c t on the s i g n a l to noise r a t i o .  the o s c i l l a t i o n l e v e l , and  hence s i g n a l s i z e , can be  by means of the feedback c a p a c i t o r s no e f f o r t was  Since adjusted  made to use  a t r a n s m i s s i o n l i n e with l e s s c a p a c i t y to ground. The  meter i n the c i r c u i t measures the D.C.  c u r r e n t produced  by the c l i p p i n g a c t i o n of the tube g r i d s on the p o s i t i v e h a l f of the r . f . wave-form. amplitude  The meter r e a d i n g t h e r e f o r e i n d i c a t e s the  of the r . f . o s c i l l a t i o n s .  The  amount of c l i p p i n g  o c c u r r i n g f o r a given o s c i l l a t i o n l e v e l can be a d j u s t e d  by  changing the g r i d b i a s r e s i s t o r i n the cathode c i r c u i t . t h i s c i r c u i t a 50 producing  about  ohm  7S«0L  r e s i s t o r was  found  In  to be a good v a l u e ,  of r e c t i f i e d c u r r e n t i n the most s e n s i t i v e  r e g i o n of o p e r a t i o n . At 52 Mc/s,  a s i g n a l to noise r a t i o of 50  to 1 was  obtained  f o r the proton s i g n a l i n doped water, u s i n g a sample c o i l a 1/16  i n c h i n s i d e diameter and  i n the water, and  k turns of #32  with  wire, a l l immersed  d i s p l a y e d on the o s c i l l o s c o p e .  Most l i n e shapes as d i s p l a y e d on the o s c i l l o s c o p e appeared to be a mixture  of a b s o r p t i v e and  d i s p e r s i v e modes, but the same  s i g n a l when swept through slowly and  presented  on the c h a r t  -56-  r e c o r d e r v i a the l o c k - i n d e t e c t o r was always a pure a b s o r p t i v e mode.  The o s c i l l o s c o p e  p r e s e n t a t i o n d i d not change apprec-  i a b l y with modulation frequency down to 15 c p s . Since i t i s almost c e r t a i n that the spectrometer i s not sensitive  to the d i s p e r s i v e  must be d i s t o r t e d , the  mode, the o s c i l l o s c o p e  presentation  caused perhaps by a bandwidth l i m i t a t i o n i n  spectrometer. The modulation audio a m p l i f i e r i s t r a n s i s t o r i z e d and  d e l i v e r s up to 1$ amperes of audio s i g n a l a t 12 v o l t s pk. to pk. to the modulation Helmoltz c o i l s . p a r a l l e l , consist diameter.  The c o i l s a r e connected i n  o f kO turns o f #26 wire each and a r e 5 cm. i n  A one ohm s e r i e s r e s i s t o r and a 10 ohm p a r a l l e l  r e s i s t o r a r e used i n the output to damp out s p u r i o u s o s c i l l a t i o n s due to the l a r g e inductance o f the c o i l s .  T h i s combination  produces up to 80 gauss modulation a t 2k c p s . The audio s i g n a l generator was b u i l t i n t o the l o c k - i n D e t e c t o r , which was a commercial u n i t b u i l t by P r i n c e t o n A p p l i e d Research Inc.  This u n i t can be c o n t i n u o u s l y v a r i e d  a t i o n with a modulation frequency from 1.5  f o r oper-  cps to 150 Kc/s, with  time c o n s t a n t s up to 10 seconds, and i s equipped to d i r e c t l y operate the c h a r t r e c o r d e r , which was a V a r i a n u n i t .  -57-  BIBLIOGRAPHY  1.  R e d f i e l d , Phys. Rev.  98, 1787 (1955).  2.  A. Abragam, P r i n c i p l e s o f Nuclear Magnetism (Oxford Univ. P r e s s , London, 196l).  3.  R e d f i e l d , Phys. Rev.  4.  O'Brien, Jacobsmerger, H i l l and Askeku, B u l l e t i n o f American P h y s i c a l S o c i e t y , 467, No. 8, 1963.  5.  A. Overhauser, Phys. Rev. 89, 689 (1953);  6.  H.G. B e l g e r s , L . Van Der K i n t and J.S. Van Wieringen,  128, 2251 (1962).  (1953).  92, 4 l l  Phys. Rev. 95, 1683 (1954).  7.  M.A.H. McCausland, T h e s i s (Oxford, O r i e l C o l l e g e ,  1959).  8.  I . Solomon, P o l a r i s a t i o n dynamique e t d e t e c t i o n des signaux de resonance par double i r r a d i a t i o n (Magnetic and E l e c t r i c Resonance and R e l a x a t i o n , I963, John Wiley and Sons).  9.  M. B o r g h i n i and A. Abragam, Compt. rend 248, 1803 (1959).  10.  Ginzton, Microwave Measurements. (McGraw-Hill, New York,  1957). 11.  J.P. Gordon, R.S.I., 32, 658 (1961).  12.  G.B. Benedek and T. Kushida, Phys. Rev.  13. 14.  118, 46 (i960).  G. V o l k o f f , H. Petch and D. S m e l l i e , Can. J . Phys. 30,  270 (1952).  Rabi, Ramsey and Schwinger,  167  (1954).  Revs. Modern Phys. 26,  

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