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Quadrupole transient effects and a super-regenerative spectrometer Sheikh, Aftab Ahmad 1963

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QUADRUPOLE TRANSIENT EFFECTS AND A SUPER-REGENERATIVE SPECTROMETER  by AFTAB AHMAD SHEIKH  A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of PHYSICS  We accept t h i s t h e s i s as conforming  t o the  required standard:  The UNIVERSITY OF BRITISH COLUMBIA SEPTEMBER 1963.  /  In  presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t  of ••  the requirements for an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree a v a i l a b l e for reference  that the L i b r a r y s h a l l , make i t  and study.  I f u r t h e r agree  mission for extensive copying of t h i s  t h e s i s for  freely  that p e r -  scholarly  purposes may be granted by the Head of my Department or by his representatives.  It  i s understood that copying, or p u b l i -  c a t i o n of t h i s t h e s i s for f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n p e r m i s s i o n .  Department of  PH /SlCS s  The U n i v e r s i t y of B r i t i s h Columbia,. Vancouver 8, Canada. Date  I 2- Sg^XjtVvv^eyV \ ^ k 3  ii  -  ABSTRACT  A f i e l d modulated constructed.  s u p e r - r e g e n e r a t i v e spectrometer  The theory of i t s o p e r a t i o n was  was  developed  put to t e s t by o b s e r v i n g the pure quadrupole resonance  and of  C h l o r i n e 3 5 i n Para —. d i - c h l o r o b e n z e n e powder a t room temperature.  The spectrometer's o p e r a t i o n i s c l o s e l y r e l a t e d t o  the quadrupole  transient effects.  So another experiment  was  done t o measure the amplitude and the decay time constant of Free I n d u c t i o n S i g n a l i n Para-di-chlorobenzene as a f u n c t i o n of  p u l s e width and magnetic  f i e l d , u s i n g a p u l s e d r.f.  m i t t e r , c o n s t r u c t e d f o r t h i s purpose,  . • •• experiment to  trans-  The r e s u l t s of t h i s  • i  '  <  were;then a p p l i e d t o the theory of the spectrometer  e x p l a i n i t s behaviour.  - vii-  ACKNOWLEDGMENT  I record my thanks to the Government of Canada f o r the award of the scholarship under the Colombo plan, which gave me a unique opportunity to carry out t h i s work at the Univ e r s i t y of B r i t i s h Columbia. I wish to express my sincere thanks to Professor M. Bloom for h i s many contributions to the understanding of the experiments described here and for his invaluable help i n i n t e r p r e t i n g the data.  His personal encouragement and  interest contributed much to the f i n a l success of the experiment. Mr. J.D. Noble helped me very much i n the construction of the pulsed, transmitter and i n carrying out the pulse experiment f o r which I am very much obliged.  I am also  grateful to Mr. C. White for h i s many useful  suggestions  in building up the Super-regenerative  Spectrometer.  F i n a l l y , I wish to thank the Government of Pakistan f o r selecting me as a r e c i p i e n t of the Colombo plan scholarship.  - iii  -  TABLE OF CONTENTS Page Abstract  < >  i i  L i s t of I l l u s t r a t i o n s  —-  Acknowledgement  •  — — «  Chapter I  Introduction  Chapter I I  Theory  V —  1  (The Pure  Quadrupole  Induction Signal) Chapter I I I  11  A  D e s c r i p t i o n o f the Apparatus  11  B  Measurement of T^  16  C  Measurement of T^  17  The R e s u l t s of the P u l s e Experiment  22  A  Amplitude and Time Constant of the Free I n d u c t i o n Decay  B  V  29  The Theory of S u p e r - r e g e n e r a t i v e Spectrometer  VI  22  D i s c u s s i o n of the Observed C h a r a c t e r i s t i c s o f Free I n d u c t i o n S i g n a l  Chapter  5  Apparatus and E x p e r i m e n t a l Procedure  Chapter IV  Chapter  VII  34  The D e s c r i p t i o n and Working of the S u p e r - r e g e n e r a t i v e Spectrometer  49  A  Oscillator  49  B  The Quenching  Circuit  53  C  The Frequency D i v i d e r  55  D  Audio A m p l i f i e r  57  E  Phase S h i f t e r  57  -iv-  Page F  Phase S e n s i t i v e D e t e c t o r  57  G  Power A m p l i f i e r  57  H  Helmholtz  59  I  Working of the Spectrometer  59  J  Measurements  62  coils  Chapter V I I  R e s u l t s o b t a i n e d w i t h the  Appendix  C i r c u i t Diagrams  Bibliography  Spectrometer  63 70 72  - V -  LIST OF ILLUSTRATIONS Page F i g . 2.1  9  F i g . 3.1  Block Diagram of the Pulse Apparatus  12  F i g . 3.2  Block Diagram of the Pulsed Transmitter  13  F i g . 3.3  C i r c u i t Diagram of the Transmitter  14  F i g . 3.4  Pulse Timing C i r c u i t  15  F i g . 3.5  Plot of In A  18  F i g . 3.6  Plot of  F i g . 4.1  Plot  F i g . 4.2  Plot of  1  F i g . 4;3  Plot of T  V  F i g . 4.4  Plot of Signal V  F i g . 4.5  Plot of Signal v.s. Magnetic F i e l d  F i g . 5.1  G f T  V .  t  In  t  8;  (Aoo  2*  V  - — . —  s.  -  A) V t  s#  t  s  H  24  2  Pulse-width c  Pulse-width  ——•--  t'. - 5.2 FF ii gg .. 6.1  28 36  50  Photograph of the Super-regenerative 51  C i r c u i t Diagram of the O s c i l l a t o r , .: Detector and Inegrator  F i g . 6.4  27  Block Diagram of the Super-^regenerative  Spectrometer F i g l 6.3  26  45  Spectrometer F i g . 6.2  21 23  H  V Q  2  C i r c u i t Diagram of the Quench Generator  52 54  - vi Page Fig.  6.5  C i r c u i t Diagram of the Frequency D i v i d e r  56  Fig.  6.6  C i r c u i t Diagram of Phase S e n s i t i v e D e t e c t o r  58  F i g . 7.1  P l o t of S i g n a l V  F i g . 7.2  P l o t of S i g n a l  Pulse-width s. V Quench Frequency  7.3  P l o t of S i g n a l  V  Fig.  Fig. A-l  S o  D  S o  Modulation F i e l d  64 66 68  C i r c u i t Diagram of P h a s e - S h i f t e r and Amplifier  F i g . A-2  ^  70  ' 4  C i r c u i t Diagram of Audio A m p l i f i e r  71  -  I.  1  -  INTRODUCTION  The purpose of t h i s work i s to study the o p e r a t i o n of a s u p e r - r e g e n e r a t i v e spectrometer  by o b s e r v i n g the pure quadrupole  resonance of C h l o r i n e 35 i n para-di-chlorobenzene  i n powder form,  '•6  A h i g h i n h e r e n t g a i n (of the order of 10  ) and the ease  w i t h which frequency can be swept over a wide range make the s u p e r r e g e n e r a t i v e spectrometer  v e r y u s e f u l i n s e a r c h i n g f o r un-?  known quadrupole resonance l i n e s . spectrometer  The o s c i l l a t o r used i n the  i s u s u a l l y of the C o l p i t i s  type,  However, i t  d i f f e r s from the standard form because i t i s turned o f f and  on  at a c e r t a i n r a t e by a p p l y i n g a s u i t a b l e "quenching" v o l t a g e a t one of the e l e c t r o d e s of the o s c i l l a t o r tube or the o s c i l l a t o r may  be made s e l f quenching by c o n n e c t i n g an RC network of  c i e n t l y l a r g e time constant to the g r i d of the tube.  suffi-  Thus the  output of the o s c i l l a t o r c o n s i s t s of a s e r i e s of p u l s e s , the frequency  of which i s the same as t h a t of the quench v o l t a g e .  The width of the p u l s e ,  i . e . the d u r a t i o n of the on-time of  the o s c i l l a t o r can be changed by s u i t a b l e c o n t r o l s . The o s c i l l a t o r , i n quadrupole resonance work, i s u s u a l l y operated  i n the l o g a r i t h m i c mode i . e . the r . f . o s c i l l a t i o n s  reach a steady v a l u e b e f o r e they are quenched.  In the absence  of any s i g n a l the r . f . o s c i l l a t i o n s are i n i t i a t e d by n o i s e . time d u r i n g which the r . f . o s c i l l a t i o n s a t t a i n v a l u e depends upon the amplitude the o s c i l l a t o r ' s frequency  their  steady  of the i n i t i a t i n g s i g n a l .  i s swept through  s i g n a l i s induced a c r o s s the c o i l .  Now  The  resonance,  When  a nuclear  the r . f . o s c i l l a t i o n s  s t a r t from the s i g n a l p l u s n o i s e , so they a t t a i n  their  steady  - 2 -  v a l u e sooner which i n c r e a s e s the p u l s e a r e a .  In the super-  r e g e n e r a t i v e spectrometer the o s c i l l a t o r i s f o l l o w e d by a det e c t o r and an i n t e g r a t o r .  Thus the i n t e g r a t e d output of the  d e t e c t o r i n c r e a s e s as the frequency of the o s c i l l a t o r through resonance,  thus g i v i n g an i n d i c a t i o n of  The frequency spectrum  passes  resonance.  of the o s c i l l a t o r , because of  quenching,  c o n s i s t s of a main c e n t r a l frequency w i t h s i d e bands on s i d e s s e p a r a t e d by the quench frequency. of s u f f i c i e n t  either  I f the s i d e bands are  i n t e n s i t y , they can a l s o e x c i t e the resonance  the o s c i l l a t o r ' s frequency i s scanned.  as  Thus the output o f the  spectrometer does not c o n s i s t of a s i n g l e l i n e but a number o f lines.  T h i s p r o p e r t y of the s u p e r - r e g e n e r a t i v e method i s e s -  p e c i a l l y c o n f u s i n g when i t i s necessary t o d e t e c t s m a l l s p l i t t i n g s of the quadrupole  resonance.  The g e n e r a t i o n of the n u c l e a r s i g n a l by the o s c i l l a t o r a t the resonance  frequency i s c l o s e l y a s s o c i a t e d w i t h the  pole t r a n s i e n t e f f e c t s  quadru-  (1) which can be q u a l i t a t i v e l y d e s c r i b e d  as f o l l o w s . The quadrupole the two  system has no net m a g n e t i z a t i o n because of  f o l d degeneracy  of the pure quadrupole  there e x i s t s a magnetization a x i s of | m>  VE  Ht  due t o the d i f f e r e n c e i n p o p u l a t i o n between the  and  | m-l)>  s t a t e s and s i m i l a r l y an e q u a l and oppo-| rn>  and  The d i s c u s s i o n here i s o n l y c o n f i n e d to  a quadrupole f u n c t i o n s of  However,  p a r a l l e l t o the symmetry  s i t e m a g n e t i s a t i o n e x i s t s because of states.  levels.  -  ,|m'-'l^>.  I = ^/2  system w i t h a x i a l symmetry, so t h a t the e i g e n I  z  g i v e n by  I |nnrv>-m|W^> 2  m  -  and  are a l s o the e i g e n f u n c t i o n s of the pure quadrupole The  l i n e a r l y p o l a r i z e d r . f . magnetic  Hamiltonian.  f i e l d a p p l i e d d u r i n g the  p u l s e i s e q u i v a l e n t t o two c i r c u l a r l y p o l a r i z e d f i e l d s , the one i n phase w i t h the p r e c e s s i n g m a g n e t i z a t i o n v e c t o r r o t a t e s i t by angle a.  The remaining component of the l i n e a r l y  r . f . magnetic  polarized  f i e l d r o t a t e s the other m a g n e t i z a t i o n v e c t o r by  the same angle a.  Thus both r o t a t i n g components o f r . f . f i e l d  are u t i l i z e d i n quadrupole  resonance.  A f t e r the p u l s e , each o f  the m a g n e t i z a t i o n v e c t o r s begins t o p r e c e s s about  the symmetry  a x i s a t an angle a, i n o p p o s i t e d i r e c t i o n s and thereby they g i v e r i s e t o an o s c i l l a t i n g m a g n e t i z a t i o n p a r a l l e l to the a x i s o f the r . f . c o i l . of  The v o l t a g e induced a c r o s s the r . f . c o i l because  t h i s o s c i l l a t i n g m a g n e t i z a t i o n forms the i n d u c t i o n s i g n a l .  Thus i n quadrupole  p u l s e experiments  the t r a n s m i t t i n g and r e -  c e i v i n g c o i l s a r e e s s e n t i a l l y the same. begins t o decay w i t h a time c o n s t a n t  T  The i n d u c t i o n s i g n a l 2  because o f spread i n  p r e c e s s i o n a l frequency o f the n u c l e i . In  order t o observe the quadrupole  s u p e r - r e g e n e r a t i v e spectrometer  resonance  s i g n a l s , the  i s u s u a l l y operated such  that  the time between two s u c c e s s i v e p u l s e s i s much s h o r t e r than T 1 (about — ± —  10  2  o f T ) , so the i n d u c t i o n s i g n a l f o l l o w i n g a p u l s e 0  i s o n l y p a r t i a l l y decayed  d u r i n g the o f f - t i m e .  The v o l t a g e  a c r o s s the c o i l a t the end o f the o f f p e r i o d i s r e s p o n s i b l e f o r the i n i t i a t i o n o f the next b u r s t o f r . f , o s c i l l a t i o n and i t i s t h i s v o l t a g e t h a t determines  the spectrometers a c t i o n .  The  a c t u a l s i g n a l o b t a i n e d by the spectrometer i s observed by subj e c t i n g the r . f . c o i l c o n t a i n i n g the specimen t o a s i n u s o i d a l magnetic  field.  The magnetic  f i e l d d r a s t i c a l l y changes T  2  and  thereby causes smearing o f the resonance Thus the s i g n a l i s modulated magnetic  modulation.  l i n e twice a c y c l e .  a t twice the frequency o f the  Thus the modulation a l l o w s the use o f a  narrow band-width a m p l i f i e r which improves considerably.  the s i g n a l t o n o i s e  The n o i s e i s f u r t h e r reduced by the use of a  phase s e n s i t i v e d e t e c t o r .  Thus we can study the theory o f the  spectrometer's o p e r a t i o n o n l y when the v a l u e of T of the v a r i o u s parameter  2  as a f u n c t i o n  o f the spectrometer i s known.  The f i r s t p a r t o f the t h e s i s d e s c r i b e s the p u l s e experiment which was done t o measure the amplitude and the decay time  con-  s t a n t o f the i n d u c t i o n s i g n a l as a f u n c t i o n o f the magnetic f i e l d and p u l s e width w i t h a d i s c u s s i o n o f the r e s u l t s o b t a i n e d . The theory o f the spectrometer i s developed i n p a r t I I the r e s u l t s o f p a r t I are used t o i n t e r p r e t the t h e o r y .  and then  II.  THEORY  The Pure Quadrupole I n d u c t i o n S i g n a l . As d i s c u s s e d i n the a r t i c l e by Cohen and R e i f (2) the Hamiltonian  f o r the i n t e r a c t i o n o f the quadrupole moment o f a  nucleus with an a x i a l l y symmetric e l e c t r i c f i e l d g r a d i e n t a t the n u c l e a r s i t e due t o surrounding  VE  changes i s g i v e n by: (2.1)  where  V E i s symmetric about an a x i s i n space , say  Z - axis.  e q  i s the s c a l e r e l e c t r i c f i e l d  e Q  i s the s c a l e r n u c l e a r e l e c t r i c quadrupole moment.  A S  [<HGL IZ]  3 8  >  interaction  ( ^  °* *  n  e  e  is  e  n  *  ). a r e simultaneous  u  n  c  gradient.  *l°  n  °*  s  quadrupole  eigenfunctions of  I • • z  Therefore  ' ^ = ^ 0 ^ and  I z  N' «. = 1  m  m  l  ^ T  t  t  ^ = ^ .  (2.2)  • m  An r . f . f i e l d 2H^coswt which couples t o the n u c l e a r magn e t i c moment induces t r a n s i t i o n s between the v a r i o u s energy l e v e l s g i v e n by (2.2) c o r r e s p o n d i n g  to  A  m  ~ ± !•  Because o f  the degeneracy o f the + m s t a t e s , there a r e I t r a n s i t i o n quencies  f o r i n t e g r a l s p i n s and I - ^  fre-  f o r half integral spins.  Being concerned w i t h C h l o r i n e , we w i l l c o n s i d e r a s i n g l e t r a n s i 3  tion for I =  /2 t o i l l u s t r a t e the g e n e r a l p r o p e r t i e s o f i n -  - 6 -  duction s i g n a l s . In nuclear magnetic resonance experiments i n i t i a l l y a net magnetization s t a t i c magnetic f i e l d  H  M  ( 3 ) , there exists  i n the d i r e c t i o n of the  Q  ( Z d i r e c t i o n ) because the nuclear  Q  spins when i n thermal equilibrium with their surrounding are populated among the (21 + 1) l e v e l s according to the Boltzmann d i s t r i b u t i o n law. This magnetization i s rotated by an r . f . magnetic f i e l d ~y  \ H |  applied at r i g h t to H by an angle  2H cosu t 1  ty  Q  q  1 . y H _ *^>S A H where t (j *  provided  i s the width of the applied r . f . pulse, of the nucleus,  w  Q  y  denotes the l i n e width. ponents of  M  H  Q  t u  y the gyromagnetic  the resonance frequency and  ratio  AK  After the pulse non-vanishing x - y com-  exist and a voltage proportional to  M Sin(^H tw) 0  1  i s developed across the sample c o i l placed at r i g h t angles to H . The s i g n a l decays i n a time O  T , the time taken f o r the *i 0  nuclear spins to "dephase". In case of quadrupole systems, i t can be shown that the expectation value of nuclear magnetization i s zero, at thermal equilibrium. Expanding i n terms of the eigenfunctions of the quadrupole interaction  M/ - T f M/  At thermal equilibrium, the population of the states i s governed by the Boltzmann equation.  - 7 -  - Em KT  XT N  m  B  u  a  t  .'.  E  e  m N  m so t h a t Thus no macroscopic equilibrium;  -m  =  E  = N. —m I =0. z  n u c l e a r magnetization i s present a t thermal  I t i s t h e r e f o r e not obvious t h a t f r e e i n d u c t i o n  e f f e c t s s i m i l a r l y t o those p r e v i o u s l y mentioned can be p r o duced t h e r e .  However, a quantum mechanical  c a l c u l a t i o n (4)  shows t h a t the e f f e c t of i n d u c i n g magnetic t r a n s i t i o n s by p u l s e s of the r . f . magnetic f i e l d  i s t o produce a macroscropic  t i n g nuclear magnetization. f i e l d gradient  For the case of a symmetric  V E , t h i s magnetizan i s produced  p e r p e n d i c u l a r t o the a x i s of symmetry of n a l motion can be g i v e n a s e m i c l a s s i c a l A quadrupole  Q  i n p o p u l a t i o n between  description. magnetization  However, t h e r e e x i s t s  a l o n g the symmetry a x i s due t o d i f f e r e n c e  \ m)>  and  | m - i/>  e q u a l and o p p o s i t e m a g n e t i z a t i o n due t o states.  i n the plane  system has no net macroscopic  H  electric  V E , and i t p r o c e s s i o -  due t o two f o l d degeneracy of +_ ro s t a t e s . a magnetization  oscilla-  s t a t e s and an  - |m>  ,  -Jro-l^  We w i l l c o n s i d e r these two magnetization v e c t o r s  separately. The  p o p u l a t i o n d i f f e r e n c e between  | lii^  and  s t a t e s , a t thermal e q u i l i b r i u m and f o r E ^ - E i s g i v e n by Boltzmann s t a t i s t i c s as where zation  N  N(E  i s the no. o f resonant n u c l e i . M  Q  m  m -  ^ / KT  - E -i) m  | ro-J^ <<f  / KT(2I+-1)  T h e r e f o r e the magneti-  due t o t h i s d i f f e r e n c e o f p o p u l a t i o n i s  M = N^(r7^-E^-,)/KT(2.T+l) 0  1,  (2.3)  The at  l i n e a r l y p o l a r i z e d r . f . magnetic f i e l d  2H^cosut a p p l i e d  r i g h t angles t o symmetry a x i s (Z a x i s ) i s e q u i v a l e n t t o two  f i e l d s r o t a t i n g i n x y plane, one i n c l o c k w i s e sense and the other i n c o u n t e r - c l o c k - w i s e sense.  The c o u n t e r - c l o c k w i s e  r o t a t i n g magnetic f i e l d r o t a t e s the magnetization ^fdyH^tu  angle  by an along  During the p u l s e the components of mag-  n e t i z a t i o n MJJ, My and M (5).  Q  and then there e x i s t s a m a g n e t i z a t i o n  each o f the three axes.  equation  M  obey equations s i m i l a r t o Bloch's  z  A t r a n s f o r m a t i o n i s made t o a frame o f r e f e r e n c e  i n which the (x, y) plane r o t a t e s a t the frequency o f the applied r . f . f i e l d H .  T h e r e f o r e the v e c t o r (M , M , M ) i n x  the l a b o r a t o r y frame transforms  t o the v e c t o r M (u,  z  v, M ) i n Z  the r o t a t i n g frame, where ponent.  i s f i x e d p a r a l l e l t o the u  The t r a n s f o r m a t i o n i s given by ( f o r p o s i t i v e e M  =  M„ M z  = =  u coscjt  -  q QJ  2  v s i n wt  -.(u s i n u t + v c o s u t ) M z  S i m i l a r l y the m a g n e t i z a t i o n  com-  due t o  (2.4)  -m.. - (m - 1) ?  s t a t e s i s r o t a t e d by the c l o c k w i s e r o t a t i n g magnetic  field.  Thus both the r o t a t i n g components o f the r . f . f i e l d a r e u t i l i z e d i n quadrupole  resonance. M M  The  Y  y  observed  pair of  m M y  M, z  x  =  u coswt  -  =  + (u \ sin ut  v sin ut +  v coswt) y  =  M (m) + M (-m) = 2(u cosut - v s i n u t )  =  My(m) + My(-m) = 0  =  M (m) - M (-m) = 0. z z  X  (2.5)  i n d u c t i o n due t o equal c o n t r i b u t i o n from  s t a t e s i s o b t a i n e d by (2.4) and (2.5).  X  M  M , My f o r t h i s case a r e g i v e n by  X  both  -  9  FIG. 2.1  -  - 10  -  Thus no s i g n a l of i n d u c t i o n would be detected  in a coil  at  both t o d e t e c t  r i g h t angles to the r . f . c o i l which serves  as w e l l as t r a n s m i t Fig.  (2.1)  shows a v e c t o r model of macroscopic s p i n  and y.  eVQ  moment M ( j m  during a  M  2H^.  c e s s i o n i n an a x i a l e l e c t r i c f i e l d g r a d i e n t of  oriented  The  and M(~m)  pre-  f o r p o s i t i v e signs  s p e c i a l case i s shown where the macroscopic are r o t a t e d by 90° about the r . f . f i e l d  pulse.  If a s m a l l magnetic f i e l d H Z a x i s f o r example, such that  0  y  i s a p p l i e d to the s p i n s H  Q  <CX  e q  Q the e n t i r e  2  v e c t o r diagram can be thought of as p r e c e s s i n g  about H  d i r e c t i o n determined by the s i g n of y.  Therefor  of alignment about the  and M(_ )  X  a x i s of M ^ j  along  m  the  Q  in a  symmetry  i s removed,  which i n essence means that the degeneracy of the + m s t a t e s i s removed.  A low  appear along  frequency modulated i n d u c t i o n s i g n a l w i l l  the y a x i s as w e l l as the x a x i s due  t i o n a l precession  imposed by H .  to the  then addi-  - 11 -  III. A.  APPARATUS AND EXPERIMENTAL  PROCEDURE  D e s c r i p t i o n o f the Apparatus. A b l o c k diagram of the apparatus used f o r the p u l s e e x p e r i -  ment i s shown i n F i g u r e (3.1). The b l o c k and c i r c u i t diagram of the p u l s e d t r a n s m i t t e r are g i v e n i n F i g u r e s (3.2) and (3.3) r e s p e c t i v e l y . p a r t of tube  c o n v e r t s the p o s i t i v e p u l s e s from T e k t r o n i x Type  163 PUlse generator i n t o n e g a t i v e p u l s e s . and cathode  The f i r s t  of tube V  The s c r e e n g r i d ,  grid  together with the tuned c i r c u i t a r e con-  nected as a H a r t l e y o s c i l l a t o r which i s allowed t o o s c i l l a t e o n l y when the tube V its grid.  Thus  i s switched o f f by the n e g a t i v e p u l s e a t  a c t s as a gate.  The s p e c i a l f e a t u r e of the  t r a n s m i t t e r i s t h a t the o s c i l l a t o r i s e l e c t r o n coupled t o the plate of  and thus t o the l o a d which makes i t q u i t e immune  to the changes of the l o a d .  a c t s as a tuned b u f f e r a m p l i f i e r  whose output i s f e d t o a tuned p u s h - p u l l power a m p l i f i e r  (V ) 6 operates  through the gate formed by V „ . The power a m p l i f i e r V 5 6 o n l y when the n e g a t i v e p u l s e from V switches the gate tube V 1 5 o f f , which a l l o w s the use of the 829B tube a t much h i g h e r tages than i t s normal r a t i n g s .  The cathode  of V  vol-  i s a t -300 5  v o l t s so t h a t i t s heater must a l s o be a t -300 v o l t s d.c. 4 |if condenser connected p u l s e energy.  The  a t the output stage i s t o s t o r e the  The c o i l s of the H a r t l e y o s c i l l a t o r ,  tuned  b u f f e r a m p l i f i e r and t h a t of the power a m p l i f i e r a r e mounted mutually a t r i g h t angles t o a v o i d any d i r e c t  pick-up.  PRF- AMPLIFIER  T E KTRONIX T Y P E IG3  ARENBERG WIDE-BAND  IPULSE GENERATOR  AMPLIFIER  SAMPLE  HELMHOLTS COtL.% v  PULSE TIMER  SWEEP TI6GER  FlG3rl  a R.0 •  <•  R.C FILTER -<-  BLOCK DIAGRAM OF THE PULSE APPARATUS  DETECTOR  Hartley Oscill elecb-iron Coupled to its load  Amplifier  •> OUT  FIG. 3-2 BLOCK DIAGRAM  OF  PUT  Pulsed Transmitter  6SN7 -300 «-  \ZAU7  >o  C0\LS 1 OSCILLATOR ^ T O R N S / , g SPACE  170  2. BUTTER 63 V-AC T U R K S \5 4  - 3 0 0 V  -.01  r  + 1200  FIG 33  TRANSMITTER  +750  6SN7  6SN7  6SN7  C.R-0 TRiQQCR  FIG3.4  PULSE TIMING- CIRCUIT  6SN7  - 16 -  The c i r c u i t of the p u l s e - t i m e r i s g i v e n i n F i g . (3.4). It consists of four m u l t i - v i b r a t o r s .  The f i r s t one i s f r e e -  running and i t s R-C time c o n s t a n t determines the r e p e t i t i o n r a t e . I t t r i g g e r s the second m u l t i - v i b r a t o r .  The R-C time constant  of t h i s m u l t i r v i b r a t o r determines the d e l a y time.  The p u l s e s  from the second m u l t i - v i b r a t o r t r i g g e r the t h i r d and f o u r t h multivibrators.  The two 6SL7 tubes mix the p u l s e s producing  a t r i g g e r f o r the t r a n s m i t t e r . B.  Measurement of T . g  The t r a n s m i t t e r was mounted j u s t a t the top of Helmholtz c o i l s used t o p r o v i d e a d.c  magnetic f i e l d .  The c o i l  con-  t a i n i n g the sample i . e . para-di-chlorobenzene was suspended a t the c e n t r e of the Helmholtz c o i l s by s t a i n l e s s s t e e l about l o " l o n g . line.  tubing  T h i s was done t o a v o i d the use of a h a l f wave-  The C h l o r i n e 35 pure quadrupole resonance i n p - d i c h l o r o -  benzene was found t o be a t 34.2 MC/sec a t room temperature and 34.7 MC/sec a t l i q u i d n i t r o g e n temperature as measured by a s u p e r - r e g e n e r a t i v e spectrometer.  These r e s u l t s were i n agreement  w i t h the p r e v i o u s measurements as g i v e n i n (6) and ( 7 ) . The p r e a m p l i f i e r was tuned t o 34.2  MC/sec by o b s e r v i n g proton  induction signals i n glycerine.  The v a r i o u s s t a g e s of the  t r a n s m i t t e r were tuned t o 34.2 MC/sec by a H a l l c r a f t e r * s r e c e i v e r model SX-42.  The pure quadrupole i n d u c t i o n s i g n a l was seen w i t h -  out much d i f f i c u l t y .  The s i g n a l s under the v a r i o u s c o n d i t i o n s  of magnetic f i e l d and p u l s e - w i d t h were r e c o r d e d on f i l m w i t h a Dumont scope camera type 2620.  - 17 -  The  l i n e shape of the i n d u c t i o n s i g n a l s can be approximated  by a Gaussian f u n c t i o n .  Thus the amplitude o f the i n d u c t i o n  t a i l a t i n s t a n t " t " a f t e r the pulse  i s g i v e n by  A =Ae b  Fig.(3.5)gives 2 t  (3.1)  0  two t y p i c a l decay curves ( p l o t o f l o g A ( t ) versus  ). The curve A corresponds t o z e r o f i e l d and B corresponds t o  a magnetic f i e l d due t o 75 m i l l i a m p e r e s T  current.  measurements were made as a f u n c t i o n o f magnetic  Q  and  p u l s e width both a t room and l i q u i d n i t r o g e n  The  r e s u l t s are given  C.  Measurement o f The  i n the next  temperatures.  chapter.  presence o f f r e e i n d u c t i o n s i g n a l s i n n u c l e a r  resonance r e q u i r e s t h a t , before  field  quadrupole  a p p l i c a t i o n o f the f i r s t  of r . f . , there be a d i f f e r e n c e i n the p o p u l a t i o n s l e v e l s between which t r a n s i t i o n s a r e induced.  pulse  o f the energy  The i n i t i a l  amplitude o f the i n d u c t i o n s i g n a l i s p r o p o r t i o n a l t o t h i s  differ-  ence i n p o p u l a t i o n , n. For a s p i n /2 system, 3  = 3/  n  where  n  3/2  "  n  **+3/2 n  +  n  2  -3/2  =  n  t l i e  V2 P°P l u  °*  a t i o n  m = and  n  l/2  =  n  +l/2  +  n  -l/2 ~  t n  ® population m  t n  ®  |^ | o  f  =  We assume t h a t t h i s d i f f e r e n c e o f p o p u l a t i o n  states  the states. has been e s t a b l i s h e d  by the n u c l e i coming i n t o thermal e q u i l i b r i u m w i t h t h e i r  sur-  - 19 -  roundings before the f i r s t pulse has been applied. Now  the e f f e c t of inducing transitions i s to change the  surplus population from i t s equilibrium value.  For a two  energy l e v e l system the surplus population, when the system i s not at thermal equilibrium, w i l l recover toward i t s equilibrium value exponentially with a time constant T^, the spin l a t t i c e relaxation time -  d  dt where n  Q  n  »  -- (t) n  T ] L  i s the surplus population when the spin i s at thermal  equilibrium and n ^ . Therefore  n  ( t )  i s the surplus population at a time " t " . r -| (t - U ) = n - [ n - n J e ^ . Q  Q  ( t i )  Suppose we apply pulses of r - f at t=0 and at t= T length of the pulses being tw.  V(tw) and V( T  + tw) are the  amplitude of the signal following the two pulses. an angle  Q,  with the symmetry axis of  , the  If,  makes  VE, the following  can be shown (8) V(tu) - V(  a  T + t ) w  f ( S, ) e  ~ 1 T  where f (SO = Si/rv 0. ( &  H.USi/rv Q.) [l- Coo (»/5 * H,G SA/fv6,)] w  Thus even i n case of c r y s t a l l i n e powder where an integration 9|  must be performed over log  , ~~  [ V ( t ) - V( T + t ) ~J w  u  i s given by the slope of  vs T  curve.  At room temper-  ature, T^ was measured by e x c i t i n g the sample by two pulses of i d e n t i c a l widths such that the s i g n a l following the f i r s t pulse i s maximum.  For t h i s pulse width the s i g n a l following the  second pulse was found to be close to i t s minimum value, though  - 20  -  not q u i t e z e r o .  The  second pulse was  measured as a f u n c t i o n of the time i n t e r v a l  between the two 26.6  amplitude of the s i g n a l f o l l o w i n g the  pulses.  The  v a l u e of T^ thus o b t a i n e d i s  + 2.5 m i l l i s e c o n d s . At l i q u i d n i t r o g e n temperature T^ was  l o n g so the sample was  expected to be q u i t e  s a t u r a t e d at time t=0 by a t r a i n of  c l o s e l y spaced r . f . p u l s e s which produce the i n i t i a l  non-  e q u i l i b r i u m c o n d i t i o n of z e r o p o p u l a t i o n d i f f e r e n c e .  Then  a t a d e f i n i t e time " t " l a t t e r a s i n g l e pulse was measure the s u r p l u s of the p o p u l a t i o n recovered The v a l u e of T^ thus o b t a i n e d  a p p l i e d to i n time " t %  i s 570 + 25 m i l l i - s e c o n d s .  v a l u e s are c l o s e to those g i v e n i n r e f e r e n c e s  (9) and  (10),  p l o t of the s i g n a l (at l i q u i d n i t r o g e n temperature) versus i s shown i n F i g . (3.6).  These A time  - 22  IV.  THE  RESULTS OF THE  -  PULSE EXPERIMENT  In a s u p e r - r e g e n e r a t i v e spectrometer, i s e x c i t e d by a s e r i e s of r . f . p u l s e s and  the quadrupole system the s i g n a l i s observed  by a p p l y i n g a s i n u s o i d a l magnetic f i e l d modulation. of  the spectrometer,  a knowledge of T  2  The  theory  as d i s c u s s e d i n the next c h a p t e r , r e q u i r e s  and the amplitude  of the i n d u c t i o n s i g n a l as  a f u n c t i o n of magnetic f i e l d and p u l s e width and a l s o the v a l u e of  T^,  f o r para-di-chlorobenzene,  the substance  the s u p e r - r e g e n e r a t i v e spectrometer. experiment r e p o r t e d here  may  Amplitude and Time Constant Fig.  (4.1) shows T  The o b j e c t of the p u l s e  i s to p r o v i d e t h i s i n f o r m a t i o n so t h a t  the theory of the spectrometer A,  be worked out.  of the Free I n d u c t i o n Decay  , the decay time constant of the f r e e  2  i n d u c t i o n s i g n a l as d e f i n e d by equation the c u r r e n t through  the  (3.1), as a f u n c t i o n of  Helmholtz c o i l s producing  f i e l d f o r a p u l s e width of 60 usee. field  the magnetic  The v a l u e of the magnetic  i n gauss can be o b t a i n e d by m u l t i p l y i n g the c u r r e n t i n  m i l l i - a m p e r e s by  ,068,  as c a l c u l a t e d by the dimensions of the  Helmholtz c o i l s g i v e n i n Chapter  VI.  By the F i g u r e (4.2) which shows a p l o t of square well  used to t e s t  of the magnetic f i e l d ,  1 T*2"  a g a i n s t the  i t i s seen t h a t T 2 * i s f i t t e d  quite  by  4** where T  2  A + KTfY  -(4.1)  i s the v a l u e of the decay time constant of the f r e e  FIG 41 T*4H  25 -  i n d u c t i o n s i g n a l i n z e r o f i e l d and T * i s the value 2  to  f i e l d "H".  K and A a r e c o n s t a n t s .  s t a n t s and the equation Fig.  (4.1) i s g i v e n  (4,3) shows T  corresponding  A d i s c u s s i o n , o f the conlatter.  as a f u n c t i o n o f pulse width i n the 2  absence o f magnetic f i e l d .  The g e n e r a l t r e n d i s t h a t T i n 2  c r e a s e s with i n c r e a s i n g p u l s e width. that T  2  I t should be emphasized  i s here t h e decay time parameter f o r a Gaussian  the i n d u c t i o n s i g n a l versus time as given by equation From f i g u r e it  p l o t of  (3,1).  (3.5A) which shows a r e p r e s e n t a t i v e i n d u c t i o n decay  i s seen t h a t the decay i s o n l y Gaussian  large f r a c t i o n  f o r l o n g times.  A  (of the order o f i ) o f the s i g n a l decays i n a  much s h o r t e r time than T  2 >  I t was d i f f i c u l t  q u a n t i t a t i v e measurements o f the behaviour  t o make a c c u r a t e  o f the s h o r t time  component as a f u n c t i o n o f p u l s e width because o f s i g n a l t o n o i s e problems a t s h o r t pulse l e n g t h s and r e c e i v e r s a t u r a t i o n e f f e c t s . In l a r g e magnetic f i e l d s f i t t e d a Gaussian  (H \>> 10 gauss) the i n d u c t i o n decay  curve over the e n t i r e range w i t h i n the e x p e r i -  mental e r r o r . Fig.  (4.4) shows the amplitude  immediately for  o f the i n d u c t i o n s i g n a l  f o l l o w i n g the pulse as a f u n c t i o n o f the pulse-width  the v a r i o u s v a l u e s o f the c u r r e n t producing  field.  the magnetic  The s i g n a l seems t o reach a broad maxima f o r p u l s e widths  near 50 usee, f o r low a p p l i e d f i e l d s and a t lower pulse widths as the e x t e r n a l f i e l d Fig. current  i s increased.  (4.5) shows the i n d u c t i o n s i g n a l as a f u n c t i o n o f the (producing the e x t e r n a l magnetic f i e l d ) f o r the v a r i o u s  v a l u e s o f p u l s e widths.  The curves corresponding  u seconds a r e approximately  t o 50 and 60  the same as t h a t o f 40 u seconds  FIG 4.3  Tz Vs. PULSE-WIDTH  - 27 -  - 28  I  o  i 50  i  loo FIG 4 5  i  i  V5o  2oo  SIGNAL Vs. MAGNETIC  \  .2-50  FIELD  MILL! AMP 3oo  - 29 p u l s e width.  The curves may  be summarized q u a l i t a t i v e l y by n o t i n g  t h a t the s i g n a l tends t o decrease as the a p p l i e d f i e l d  is in-  c r e a s e d , the r a t e of decrease b e i n g g r e a t e r f o r l o n g e r p u l s e widths. B.  D i s c u s s i o n o f the Observed C h a r a c t e r i s t i c s of Free Induction Signal As shown i n Chapter I I , the e i g e n f u n c t i o n s of pure  quadru-  p o l e H a m i l t o n i a n , i n case of a x i a l symmetry are the e i g e n f u n c t i o n s o f I£ (the Z component of the s p i n ) . I ^  Z  l  and the s t a t e s  »  m  | n£>  |+ /2^> 3  where ,  j+  « + /2,  m  1  */2y>  When we a p p l y a c o n s t a n t magnetic  + /2  f o r I » /2,  3  3  are two f o l d  field  H  degenerate.  a t p o l a r angles  i n a c o o r d i n a t e system having the symmetry a x i s of  VE  as Z a x i s ,  u s i n g f i r s t o r d e r p e r t u r b a t i o n theory i t can be shown that e f f e c t o f magnetic f i e l d  for  e  2  q Q  ^>^>  degeneracy o f + p s t a t e s and a l s o t o mix + l e a v e a l l o t h e r m s t a t e s pure ( 5 ) ,  O  the  y\l i s to remove the /2 s t a t e s and yet  The c o e f f i c i e n t d e t e r m i n i n g  the  p r o p o r t i o n o f +_ ,1/2 s t a t e s i n the mixed s t a t e are f u n c t i o n s 2 1/2  of  f ( 8 ) = (1 + tan©  )  .  Now  the time dependent  density  matrix "/'"can be c a l c u l a t e d u s i n g the e q u a t i o n o f motion  where  j{  i s the t o t a l H a m i l t o n i a n c o n s i s t i n g of the pure qua-  drupole and the Zeeman p a r t s . d e r r i v a t l v e of used was  M (t)  «  The i n d u c t i o n s i g n a l i s the time  y "h Trace (I  f).  As the sample  i n powder form, the s i g n a l o b t a i n e d by t a k i n g the time  d e r r i v a t i v e of M ($) w i l l  have t o be averaged over a l l the  Q , <ft.  v a l u e s of  The matrix elements of the d e n s i t y matrix  c o n t a i n c o m p l i c a t e d f u n c t i o n s of f ( 9 ) , a v e r a g i n g becomes" very d i f f i c u l t .  due  t o which t h i s  As t h i s p u l s e experiment  was  performed o n l y t o know the v a l u e s of the v a r i o u s parameters o c c u r i n g i n the theory of the s u p e r - r e g e n e r a t i v e i t was  spectrometer,  not c o n s i d e r e d worthwhile t o c a r r y out the a v e r a g i n g  to i t s v e r y c o m p l i c a t e d  due  nature.  Instead the r e s u l t s o b t a i n e d from the p u l s e experiment have been i n t e r p r e t e d s e m i - e m p i r i c a l l y based on a p h y s i c a l  inter-  p r e t a t i o n of the exact programme d e s c r i b e d above. The  decrease  i n the v a l u e of T  w i t h the magnetic  g  can be e x p l a i n e d i n terms of l i n e broadening Zeeman s p l i t t i n g of the pure quadrupole e q  2  Q  ^>  yE  t  because of the  levels  (11).  the frequency c o r r e s p o n d i n g t o  For  \+ ' / 3/  2  between  H  and symmetry a x i s of  H  VE).  * • J  >  t r a n s i t i o n s p l i t s i n t o f o u r f r e q u e n c i e s ; the amount of b e i n g dependent upon the a p p l i e d f i e l d  field  1  ' ^  splitting  and 6 (the angle Both Q and H,  being  not the same f o r a l l n u c l e i , w i l l g i v e r i s e t o a d i s t r i b u t i o n of the resonance frequency  thus broadening  the l i n e width  so T* being i n v e r s e l y p r o p o r t i o n a l t o l i n e width w i l l In the absence of the e x t e r n a l magnetic f i e l d , the i n d u c t i o n s i g n a l b e i n g Gaussian,  the amplitude  a t i n s t a n t " t " a f t e r the p u l s e i s A ( t ) a e x t e r n a l magnetic f i e l d nuated  i n the presence  1  0  gauss).  2  the decay of of the s i g n a l .  When the atte-  which i s of the order of  As the decay of the s i g n a l , '  of the a p p l i e d f i e l d ,  t a l l y t o be Gaussian,  ^ T|  decrease.  i s a p p l i e d , the s i g n a l i s f u r t h e r  because of the l i n e broadening  yYL f o r l a r g e H ( ^  e  and  i t i s reasonable  i s a l s o found to write  experimen-  31 -  e  At 1  fWZ  ^ -  - e  B + K Y '  H  2  where  2  B  «  1 f 2  (4.2)  This r e l a t i o n Is the same as equation (4.1) which gives the observed dependance of T  it2  upon  H  with the exception of  constant B. For large H, the major attenuation of the induction signal w i l l be due to l i n e broadening caused by H. S the order of  1 . and then  The experimental value of  K K  2  w i l l be of  as obtained by the slope of the  test of the v a l i d i t y of (4.1).  (4.2).  T  should be of the order of one.  curve shown i n F i g . (4.2) i s 1.7.  should be of the order of  c  1  This provides a f a i r l y good  The intercept of t h i s curve as predicted by the equation  However t h i s intercept i s found to be negative.  This  i s because the values of T * as shown i n F i g . (4.1) are only + 5% which gives quite a wide range f o r the values of e s p e c i a l l y at high f i e l d .  1  Thus a l i n e can be drawn from the high  f i e l d points, omitting the low f i e l d points, with a p o s i t i v e intercept.  But we are concerned with low values of f i e l d i n  the spectrometer, so the curve i n F i g . (4.2) has been drawn to include the low f i e l d points, even though i t has a negative intercept.  This means that the constant B i n equation (4.2) has  been changed with another constant A i n the empirical equation (4.1)  which takes care of the consequences a r i s i n g due to the  departure from the high f i e l d  approximation.  - 32 The field  decrease o f the i n d u c t i o n s i g n a l w i t h the magnetic  can a l s o be e x p l a i n e d i n terms of the l i n e broadening.  the l i m i t i n g case when  H  ^>  the r . f . magnetic f i e l d ) , range  Z^w  <^  y H  —  (H^ i s h a l f the amplitude o f  o n l y those n u c l e i w i t h i n a frequency  o f the frequency  w  o f the r . f . f i e l d ,  will  1  be e x c i t e d so as t o c o n t r i b u t e a p p r e c i a b l y t o M e f f e c t i v e value of M to  In  decrease when  H  and M .  x  y  The  i n e q u a t i o n (2.3) should, t h e r e f o r e , begin  Q  becomes of order o f H^.  s i g n a l , being p r o p o r t i o n a l t o M , a l s o o  T h e r e f o r e the  decreases.  Another f a c t o r which a l s o c o n t r i b u t e s t o the a t t e n u a t i o n of the s i g n a l i s the r e l a x a t i o n d u r i n g the p u l s e which occurs when T  2  drops t o such a v a l u e , due t o i n c r e a s e o f H, t h a t i t becomes  comparable and f i n a l l y  even much l e s s than t , the p u l s e width. u  For s m a l l pulse-widths o f the order o f 10 - 20 usee, the angle through which.M  i s r o t a t e d d u r i n g the p u l s e i s v e r y s m a l l , so  the e f f e c t o f decrease  i n the e f f e c t i v e v a l u e o f M  pronounced and a l s o T * r e q u i r e s a l a r g e f i e l d become comparable w i t h t . w  H  20 gauss) t o o f the  o f the f i e l d a t s h o r t p u l s e  get as l a r g e as 25 gauss when the r e l a x a t i o n  d u r i n g the p u l s e becomes s i g n i f i c a n t . s t r a t e d by the curves o f F i g . ( 4 . 5 ) . spectrometer,  (  T h i s makes the amplitude  s i g n a l more o r l e s s independent widths, t i l l  becomes l e s s  Q  T h i s e f f e c t i s demonAs i n the s u p e r - r e g e n e r a t i v e  pulse-widths a r e o f the order o f 15 ixsec and the  peak v a l u e of modulation  field  i s about 3 gauss, we may omit the  e f f e c t o f the modulation  f i e l d on the amplitude  o f the s i g n a l  just following a pulse. The  i n c r e a s e o f the s i g n a l ' s amplitude  width f o r constant  w i t h i n c r e a s i n g pulse  can be e x p l a i n e d by the f a c t  (12) t h a t the  - 33 -  s i g n a l i s p r o p o r t i o n a l t o S i n ( ,^3 yE^iu i s the angle between As  S i n 6^)  and the symmetry a x i s o f  has got a random o r i e n t a t i o n , so  where 0  7E, i s quite i n -  homogeneous which e x p l a i n s the f a c t t h a t the maxima observed i n the curves o f F i g . (4.4) a r e ' v e r y broad:.  - 34 -  V.  THE THEORY OF SUPER-REGENERATIVE SPECTROMETER  A super-regenerative receiver i s characterized by the r e peated build-up and decay of s e l f - o s c i l l a t i o n s i n a valve o s c i l l a t o r , known as the super-regenerative o s c i l l a t o r , operating on, or near, the signal frequency.  The c i r c u i t i s made a l t e r n a t e l y  o s c i l l a t o r y and non-oscillatory by the a p p l i c a t i o n of a periodic voltage to one of the electrodes of the o s c i l l a t o r valve.  The  source of t h i s periodic voltage i s u s a l l y a separate quench osc i l l a t o r , although self-quenching may be arranged by a suitable choice of the g r i d leak and g r i d condenser of the superregenerative o s c i l l a t o r .  In either case the quench frequency i s  necessarily much lower than the natural frequency of the superregenerative o s c i l l a t o r but must be higher than that of the signal modulation. The sample i s subjected to bursts of high r . f . power by placing i t into the o s c i l l a t o r ' s c o i l .  At resonance the o s c i l -  l a t i o n s b u i l d up from the nuclear s i g n a l voltage developed  across  the c o i l , otherwise they s t a r t from noise e x i s t i n g i n the c i r c u i t . During the period of build-up the o s c i l l a t i o n s may become as much as a m i l l i o n times greater the s i g n a l . There are two c l e a r l y defined modes of the operation of the o s c i l l a t o r with separate quench, according to whether or not the o s c i l l a t i o n s are allowed to b u i l d up to an equilibrium value, as i n a normal o s c i l l a t o r , before they are quenched. If the o s c i l l a t i o n s which b u i l d up during a single quench cycle are  - 35 -  quenched before they reach the l i m i t i n g e q u i l i b r i u m amplitude determined  by the tube c h a r a c t e r i s t i c ,  p r o p o r t i o n a l t o the s i g n a l o s c i l l a t i o n s grew. the l i n e a r mode.  t h e i r peak amplitude i s  (or n o i s e J v o l t a g e from which the  The o s c i l l a t o r i s then s a i d  t o operate i n  I f , however, the b u i l d - u p p e r i o d i s made l o n g  enough; the o s c i l l a t i o n s reach a steady v a l u e b e f o r e they a r e quenched and the o s c i l l a t o r i s s a i d  t o operate i n l o g a r i t h m i c  mode, as the o u t p u t , i n t h i s mode o f o p e r a t i o n , i n c r e a s e s as l o g ^ ( V / v i ) as s i g n a l v o l t a g e i n c r e a s e s from  to V .  2  2  The o s c i l l a t o r was operated i n l o g a r i t h m i c mode by a n e a r l y r e c t a n g u l a r quench v o l t a g e .  The o s c i l l a t o r ' s a c t i o n under these  c o n d i t i o n s has been shown i n F i g . ( 5 . 1 ) . p a r t o f the quench c y c l e , total effective G = G  q  During the q u i e s c e n t  when the v a l v e i s not conducting, the  conductance i s determined  by c i r c u i t l o s e s , i . e .  and the v o l t a g e a c r o s s the c i r c u i t i s t h a t due t o n o i s e  or n u c l e a r s i g n a l .  As soon as the quench v o l t a g e gets higher  than the v o l t a g e a t which the o s c i l l a t i o n s s t a r t , the conductance G becomes n e g a t i v e , s e l f o s c i l l a t i o n begin t o b u i l d up a t the resonant frequency o f the c i r c u i t formed by thus the s u p e r - r e g e n e r a t i v e p e r i o d s t a r t s . the o s c i l l a t i o n s b u i l d up l i n e a r l y t i l l amplitude  L  and  C  and  In the b e g i n n i n g ,  the time T  L  when the  o f the o s c i l l a t i o n i s l a r g e enough f o r l i m i t a t i o n t o  begin due t o c u r v a t u r e o f the tubes c h a r a c t e r i s t i c . mode o f the o s c i l l a t o r ' s o p e r a t i o n t i l l  T_ i s e s s e n t i a l l y  l i n e a r a f t e r which i t changes t o l o g a r i t h m i c . t i o n amplitude  Thus the  As the o s c i l l a -  f u r t h e r i n c r e a s e s , t h e conductance  steadily  decreases t o z e r o ( 1 3 ) . On r e a c h i n g zero i t remains t h e r e u n t i l the end o f the s u p e r - r e g e n e r a t i v e p e r i o d , d u r i n g which  - 36  ftUENCH  W A V E - F O R M  0SCIIATIONSTART?H|  CUT-OFF  M E AM  (-^r)  TIME  fi-R\D  VOLT M E  4  CONDUCTANCE TIME  j Sl)PER-RE.GENE|RATWeV"  DAMPING PERIOD  PERIOD  SENSITIVITY  -TIME  T  SAflPLINQ PERIOD  Q$ClLftT|QN  | AMPLITUDE  TIME  | BUILD-UP STARTS  FIG 5-1  <>  - 37 time the  o s c i l l a t i o n s are maintained a t t h e i r e q u i l i b r i u m  plitude.  At the end of the s u p e r - r e g e n e r a t i v e p e r i o d , the  am-  conductance becomes p o s i t i v e and the o s c i l l a t i o n s are damped out t i l l  the next quench c y c l e .  The damping d u r i n g the quench  c y c l e s h o u l d be s u f f i c i e n t t o reduce the s e l f o s c i l l a t i o n s below n o i s e l e v e l b e f o r e the b u i l d up s t a r t s a g a i n otherwise the o s c i l l a t o r s e t t l e s down i n the coherent s t a t e . The maximum s e n s i t i v i t y o c c u r s e x a c t l y a t the time when the t o t a l conductance G goes from p o s i t i v e t o n e g a t i v e t = 0.  The s i g n a l v o l t a g e a c r o s s the c r i c u i t at t h i s  at instant  p l a y s the g r e a t e s t r o l e i n the d e t e r m i n a t i o n of the time a t which the amplitude o f the s e l f - o s c i l l a t i o n s a t t a i n s i t s e q u i librium value.  An element of s i g n a l o c c u r r i n g b e f o r e time t = 0  has time t o decay b e f o r e b u i l d up s t a r t s and, consequently, has l e s s e f f e c t than a s i m i l a r s i g n a l o c c u r r i n g a t t = 0.  An  element of s i g n a l , a r r i v i n g l a t e r than t h i s i n s t a n t , a g a i n has l e s s e f f e c t because p a r t of the b u i l d - u p has e x p i r e d b e f o r e i t s arrival.  The s i g n a l i s , t h e r e f o r e , sampled  each quench c y c l e .  f o r a short p e r i o d i n  Over the g r e a t e r p a r t o f the c y c l e , the  s i g n a l has a n e g l i g i b l e e f f e c t .  The way  i n which the s e n s i t i -  v i t y v a r i e s w i t h time depends upon the nature o f quench and upon the tube's and c i r c u i t parameter's.  In the l o g a r i t h m i c  mode the amplitude of the o s c i l l a t i o n envelope i s always same.  The s i g n a l advances  the  the apparant s t a r t i n g time o f the  o s c i l l a t i o n s thus i n c r e a s i n g the area under the envelope as shown i n F i g . (5,1 d ) .  Thus the a r e a o f the envelope changes  w i t h the amplitude o f the s i g n a l .  A suitable detector c i r c u i t  c o n v e r t s t h i s once more i n t o a change of amplitude.  - 38 -  Now we calculate the nuclear s i g n a l induced i n the c o i l . The nuclear spin i s subjected to bursts of high r . f . power which brings about,, several e f f e c t s . I.  The nuclear absorption during the presence of r . f .  power reduces the Q of the c o i l and thus reduces the integrated pulse energy. I I . Any coherent nuclear precession, which may occur when T  2  i s comparable to or greater than the quench period, w i l l  cause the r . f . bursts to be i n i t i a t e d e a r l i e r by nuclear signals rather than by noise.  This l a t t e r e f f e c t gives r i s e to an  increased integrated s i g n a l response. Dean (14) suggests that the second mechanism i s the dominant one for quadrupole resonance detection by the super-regenerative method.  A c a l c u l a t i o n of the s i g n a l , based upon the second  mechanism, has been made. During one quench period time  "tw"  T  ,*the o s c i l l a t o r i s on for  and i s o f f for the rest; of the quench period.  the output of the super-regenerative  Thus  o s c i l l a t o r can be supposed to  consist of a s e r i e s of equally spaced pulses of equal widths. The quadrupole system i s excited by the pulses and i t relaxes both l o n g i t u d i n a l l y as well as transversely between the time i n t e r v a l during successive pulses t i l l a steady state i s reached. The quadrupole system has a magnetization i f along the symmetry axis (Z axis) due to difference i n population between  - 39 - a . Usually  respectively, then  i s much longer than the  time i n t e r v a l between two consecutive pulses and T longer or comparable with the l a t t e r . component of M equilibrium value  2  Therefore the longitudinal  w i l l be i n process of relaxing towards i t s —=7  —">  M o  and the transverse component of M  w i l l be decaying during the time between the pulses. angle between ~ll and a  i s also  Let the  Z axis just before the second pulse be  . Further rotation of magnetization w i l l depend upon the  phase of the r . f . o s c i l l a t i o n s during the pulse r e l a t i v e to the phase of ~M?  This phase difference depends upon the conductance  of the c i r c u i t during the on and o f f periods, the departure of the frequencies of the pulse from the resonance frequency and the past history as w e l l .  As the various parameters specifying  the phase may vary from pulse to pulse, t h i s phase difference may be assumed to be random.  So the angle between 1? and Z axis  after the second pulse w i l l be  a* ^ «  take place when other pulses a r r i v e .  + 2  a  *  T  h  e  s  a  m  e  e v e n  ts  Thus the problem of finding  out the angle between ~M and Z axis after the quadrupole system has been excited by a t r a i n of pulses i s s i m i l a r to that of a random walk i n which there i s a c e r t a i n amount of relaxation during the period of two successive steps.  In actual practice  we get the Integrated e f f e c t of the pulses i n a c e r t a i n time determined  by the time constant of the phase sensitive detector.  The detected output of the super-regenerative o s c i l l a t o r - d e t e c t o r V ( ) w i l l consist of a steady value V and a f l u c t u a t i n g compot  nent  A V^ j t  •'•  V  (t) =  *  +  AV  ( t )  - 40 We assume that  AV( j  i s a Gaussian variable i . e . at any time  t  i t has an a p r i o r i probability of being between <JLvwhere P  given by P  -  ( v )  A&  (  V  ~  V  )  /  j  2  V  and V-fdV  6  + cx>  and  P jdlV = I  and  W  J^\)^  - &  -co  The signal that we measure when the time constant of the phasesensitive-detector i s  T* '  r  c  i s ayprox. given b-y r  Vo)^ = V + J L JAV< d t b  t)  o 0 The square mean variance of the signal i s given by re /  We now  flit' J d l b ' AMtf) A V ( t " ;  assume that the fluctuations are governed by a correT  l a t i o n time which i n our case i s the same as quench period z  -r^/r  -W  r  and t = t ' - t" , It i s e a s i l y shown that  Therefore the R.M.S. f r a c t i o n a l noise =  A t y p i c a l value of T T = 20 usee  and  and T  c  Tc  Tc  V used i n the spectrometer  = 2.5 sec which even for  a s i g n a l to noise as high as 62500 .  are  8 = V gives  Thus we see that the  randomness i n the phase-difference between  M  and the r . f .  o s c i l l a t i o n s during the pulse has got p r a c t i c a l l y no e f f e c t upon the s i g n a l under the p r a c t i c a l operating conditions.  Hence  we can assume that i n the steady state the angle between the  - 41 Z axis and magnetization, after a pulse, i s always relaxes to a  a_  which  s  s  because of T, t i l l the advent of next pulse which 1  rotates i t to a  Q  again.  I f M~  i s the magnitude of the mag-  netization before a pulse, then the amplitude of the s i g n a l just after the pulse w i l l be proportional to M~ Sin o . Now to s s calculate M~ we make the following assumptions and approxis mations. +  I.  I t i s assumed that a l l pulses are of i d e n t i c a l widths. The r i s e time of a pulse depends upon the amplitude of  the signal which i n i t i a t e s the pulse. n  The signal s t a r t i n g the  pulse i s proportional to magnetization before the (n - 1)  pulse.  As the magnetizations before the I, I I , I I I , ... pulses  are d i f f e r e n t , so the r i s e time of the corresponding pulses w i l l also be d i f f e r e n t .  In practice, the r i s e time of the pulse i s  only a very small f r a c t i o n of even the shortest pulse.  So we  can, to a good approximation, neglect the difference i n r i s e times as compared to the width of the pulses and assume that a l l pulses are of equal width. II.  I t i s assumed that pulses are very short as compared to T . 2  This corresponds to the e f f e c t i v e f i e l d i n the rotating r e f e r ence frame being governed only by H^,so that the precession during the time r . f . pulse i s applied may be referred to as pure nutation. In the spectrometer, the value of pulse-width i s abbut one tenth of T  2  even i n the presence of the modulation f i e l d , so  t h i s approximation  i s well j u s t i f i e d .  42 III.  The relaxation during the pulse i s neglected.  The results  of the pulse experiment show that the signal i s independent of  * the external magnetic f i e l d i . e . T (  0  f o r short pulse width  ex. 10 usee) and f o r low values of f i e l d ( — 5 gauss) thus  showing that the relaxation during the pulse, under these conditions can be neglected.  The spectrometer was operated to  s a t i s f y these conditions. IV.  The e f f e c t of transverse components of magnetization i n  establishing the value of steady state magnetization i s neglected. • —± If the magnetization  i s rotated by the f i r s t pulse by  a , the x, y components of magnetization a f t e r the  an angle  pulse w i l l be proportional to M  1  Sin a.  As a ^ .05 radian,  X  these components w i l l be n e g l i g i b l e as compared to Z component cos a .  =  Thus the main contribution to the steady state  magnetization w i l l come from the r o t a t i o n and relaxation of the Z component of magnetization. V. i s supposed to be uniform. Note that H i s never uniform f o r a powder since Hj  e  f  f  = H  1  Sin 8^  symmetry axis of VI.  where 0^ i s the angle between  and the  "VE.  Special e f f e c t s due to tendency of spin systems to  e s t a b l i s h a "spin temperature" i n the rotating reference frame are neglected (15), Now we calculate the value of the magnetization i n the steady state within the frame-work of these approximations.  - 43 Suppose a pulse of width t  w  Is applied at the time  Let the Z component of magnetization represented by M~ ^ j z  M before the pulse be z  and after the pulse by M * ( ) .  n  nr  n  If M  z  obeys the equation dM dt  .  z  M  - M T  Q  2  x  then i t can be shown that = Mo- { M - M (<YO] e 0  and  M ,„, = z^ * +  n  a  where the n  t n  C - ) 5  2  M , . cos a z\«i  1  (5.2)  i s the angle through which  M ( ) z n  i s rotated by  pulse.  Now we consider the value of IT" (n) where n = 0, 1, 2, 3 ... z to form a suitable expression for M~(n). Z  st I  pulse:-  M (1) = M_ z M+(l) = Mo cos a. z u  nd II  pulse: By putting n = 1 i n (5.1)  M = M© (i - e. j + Mocooo<e * ... T,  T  2  By (5.2) III  r d  M  o  D  O  o  C (  ,_ ^  _  pulse:-  - V  M (3)=M0o-fi 2  +  and  +  ) + M Coo^C»-e 0  M CoOo( -e. 0  -TV.  +  +  Je  M0 ODU e  -TZ. \  T  1  44 IV  t h  pulse:-  _ . " + . /\T M C^ - Mo - CW tW ) r  e  2  0  - r/ T/ ,  -T/T 7;  ~ VT lr  ^ M (\-e ) + M Cci c(i-€. )e T  0  0  0  Thus the expression for M (n) forms a geometric progression with f i r s t term as M .". M  Due .*.  (1 - e  ) and common r a t i o as cos a e  1  '  ,  (steady state) = sum of geometric series as n-» «»  to assumption IV, M = M . z s the amplitude of the induction s i g n a l j u s t following the  pulse i s  "V-  This s i g n a l decays with a time constant T * during the time 2  T - t  w  and i n i t i a t e s the r . f . o s c i l l a t i o n s of the next pulse  at the end of the quench period  T  . However the e f f e c t of  the assumption VI i s to introduce an uncertainty i n the e f f e c t i v e zero of time f o r the Gaussian decay of the induction s i g n a l (16). Thus the time i n t e r v a l l i e s i n between  T - t  T* - t  w  and T  w  i s replaced by T .  where  T  So the nuclear s i g n a l that  i n i t i a t e s the r . f . o s c i l l a t i o n s i s  V(W,T) = ° ° ' M  S  f c  l*?-**  e.  2  (5.3)  Now, knowing the nuclear s i g n a l that i n i t i a t e s the r . f . o s c i l l a tions, we can calculate the voltage of the s i g n a l given by the spectrometer.  Figure (5.2) shows the b u i l d up envelope, a f t e r  time T^ ( F i g . 5.1), i n greater d e t a i l .  The two curves represent  - 45 -  - 46 the b u i l d up from two voltages reached at time T  L  and Vg.  i s the voltage  by the o s c i l l a t i o n s b u i l d i n g up from a  sample of noise i n the s e n s i t i v e period, e a r l i e r i n the cycle. V  i s due to s i g n a l plus noise.  For the time being, we are  considering the events i n a single quench cycle. noise voltage  Although  the  i s indeterminate for a single cycle, i t s  r.m.s. value i s given by  .  -  2 where  V*  input, and u  i s the mean square noise at input^V^ i s the signal i s the voltage gain during the i n t e r v a l of linear  L  build-up i . e . from the instant build-up s t a r t s to T^.  For  s i m p l i c i t y , l e t us take the b u i l d up curves to be truely exponential i n form u n t i l they are suddenly limited at the equilibrium value V .  As we are s t a r t i n g with the values of  m  voltages at t = T , we s h a l l hence-forth measure L  time from  t h i s point and not from the beginning of the true build-up period. As V i s even less than one-hundreth of V . the z, m n  difference i n area to the l e f t of v e r t i c a l axis i s n e g l i g i b l e . Thus the incremental area to the r i g h t of axis (shaded i n F i g . 4.2) represents the increase i n output due to signal during a single cycle of quench. Referring to F i g . (5.2)  Vm = v » e -  -Me  - 47 where  a  i s the time constant of build-up « 2 c Gl  i s the capacitance of the tuned c i r c u i t and  , where i s the con-  ductance of the c i r c u i t during the on period (13). .*..  ti = a 1 n  V m and t« = a 1 n Vi Hence the incremental area i s given by  V m V  .  2  (5.4)  For signals greater than noise, the f i r s t term i n the bracket i s of the order of V  whilst the second i s much smaller. m  Thus we can write  As the 1 . 5 cycle narrow-band width amplifier and the phasesensitive detector used i n the output stage of the  spectrometer,  allow only a very narrow spectrum of noise to e f f e c t the f i n a l s i g n a l , so We can assume that V  V" .  2  n  Thus  The f i n a l signal voltage as recorded by the spectrometer w i l l be  V = where T  a,V^  2^ V s / ( ^ ~ ^  i s the quench period and  spectrometer determined presence of fact that  T  K  i s a constant of the  by the detector, amplifiers, etc.  The  i n the denominator of 5 . 5 i s because of the  A A i s the increase i n area of a single pulse and  the voltage V i s the integrated e f f e c t of 7c  ( 5 < 5 )  pulses where  i s the time constant of the phase-sensitive-detector.  -  As  f  48  i s a variable quantity,  constant  -  i t has been separated from the  K.  Substituting the value of V from (5.3) into s  V - A t ^ r ) - -LJ£ _  where  Mo(t-€.  (5.5),  (  )Si/Yvc£s  5.6)  and B i s  the constant of the spectrometer. In Chapter IV the following emperical formula was obeyed 1 T^22  Here H  m  H  A  +  K  2 r  2 H  i s the modulation magnetic f i e l d given by  cos U n f t , substituting the value of T  V = 1 U ( T ) - 1 ( T ' \ KJL^WT-)-!. 7  2  i n (5.6)  tfJ^^c^ic^C  (5.7)  A strong signal was observed when the phase-sensitive detector was tuned to 2u/ . According to equation (5.7) i t i s given by m  The r e s u l t s obtained with the spectrometer have been discussed in Chapter VII on the basis of equation ( 5 . 8 ) and the data of Chapter IV.  - 49 -  VI.  THE DESCRIPTION AND WORKING OF THE "SUPER-REGENERATIVE SPECTROMETER"  A block diagram of the super-regenerative spectrometer i s given i n F i g . (6.1) and i t s photograph has been shown i n F i g . (6.2).  A.  The O s c i l l a t o r The c i r c u i t diagram of the o s c i l l a t o r , detector and i n t e -  grator together with the c i r c u i t that allows the quench voltage applied to the o s c i l l a t o r has been shown i n F i g .  (6.3).  The basic c i r c u i t was designed by Dean (14) f o r use i n the region of 30 MC/sec.  The present c i r c u i t has been taken from  McCall's thesis (17) a f t e r suitable modification. The o s c i l l a t o r i s the grounded-plate version of the C o l p i t t ' s oscillator.  The quenching action i s as follows:  The two halves  of the 6J6(V ), i n p a r a l l e l , have their cathodes t i e d to the 1  cathode of the o s c i l l a t o r tube V 2 . The plates of V^ are bypassed for r . f .  When a positive pulse from the external  quenching c i r c u i t i s applied to the g r i d of Vji, the additional cathode bias shuts o f f V . 2  Thus the o s c i l l a t o r i s operating  only during that part of the quench during which V^ i s no conducting. At the time V^ i s cut o f f , the cathode impedance i s shunted across part of the tuned c i r c u i t .  This large positive conductance  shortens the decay time-constant of the tank c i r c u i t and aids i n quickly damping out the free o s c i l l a t i o n s . _  C. R.O  AUDIO AMPLIFIER  INTEGRATOR  RECORDER  £  AUDIO GENERATOR  NARROW  BAND-WIDTH AMPLIFIER  DETECTOR  PHASE SENSITIVE DETECTOR  x  cn  QUENCH GENERATOR  FREQUENCY  OSCILLATOR  DIVIDER  PHASE SHIFTER  A MOTOR DRIVE  6-1 THE  SAMPLE HELMHOLTS COIl  -0" AWMETER  SUPER-REGENER/  POWER AMPLIFIER  AUDIO G E N E R A T O R  SPECTROMETER  O  - 51 -  FIG 6-3  OSCILLATOR , DETECTOR  AND  INTEGRATOR  -  53  -  It i s important that t h i s impedance should not have any damping e f f e c t during the on-period of the o s c i l l a t o r and to ensure t h i s , the g r i d of Vj must be very negative order of - 120 volts).  (of the  A fixed bias that can be set from 0>- 90  v o l t s i s provided by a battery and potentiometer (shown i n the quench c i r c u i t ) .  The o v e r - a l l positive to negative swing of the  quench voltage i s about 120 v o l t s . The frequency of the o s c i l l a t o r i s changed by driving the ) tuning condenser slowly by a motor.  The motor drive can be  replaced by connecting a variable-capactiy diode i n p a r a l l e l with the tuning condenser as shown by dotted l i n e i n the c i r c u i t diagram.  The sawtooth has a period  of about 5 - 1 0  minutes.  A variable capacity-divider, following the tank c i r c u i t , allows some control of the f r a c t i o n of the tank voltage applied to the g r i d of the i n f i n i t e impedance detector V .  The output  from the cathode of V_ i s fed into a four section, RC f i l t e r network which integrates the pulse area. output i s fed to a cathode follower played on an oscilloscope.  Part of the detector's  whose output i s d i s -  The on - o f f time of the o s c i l l a t o r  i s measured from t h i s wave-form. B.  The Quenching C i r c u i t The c i r c u i t diagram of the quenching c i r c u i t i s given i n  Fig. ( 6 . 4 ) .  The input to the c i r c u i t i s provided by a  Hewlett-Packard audio o s c i l l a t o r (Model 200 DR). of the input varried from 10 K.C. / s e c The tubes  The frequency  to 70 K.C./sec.  and V"2 square the sine-wave input.  followed by a d i f f e r e n t i a t i n g network.  They are  The r e s u l t i n g positive  FIG 6-M  QUENCH  GENERATOR  - 55 and negative pips appear at the g r i d of Vg which has a fixed negative bias, well below the cut-off.  Therefore only the  positive pip a f f e c t s the tube current. The output pip from V^ triggers the "one-shot" multivibrator formed by V  4  and Vg.  With no input, V  4  i s cut o f f  and V i s conducting V and V have a common plate load. 5 4 3  Thus  the positive p i p at the grid of Vg appears as a negative pip at the plate of V  4  and the g r i d of Vgj i n i t i a t i n g the change  to metastable state.  The duration of t h i s state i s determined  by the R and c values i n the grid of V and the setting of the 4 potentiometer i n the grid of V4.  The output, taken from either  plate, i s a square wave i n which the duration of the positive and negative portions may be varied.  The multi-vibrator's out-  put, after having been amplified by Vg i s biased by a 90 v o l t battery and then applied to the g r i d of the quenching tube. The potentiometer i n the bias battery c i r c u i t i s found to have a fine control over the on - o f f time of the o s c i l l a t o r , C, The Frequency-Divider The c i r c u i t diagram of the frequency-divider i s shown i n Fig,  (6.5)-  The tubes V j and V  2  convert the input sine wave  to a square wave which triggers a bistable multi-vibrator formed by tubes V3 and V4,  The output of the multi-vibrator i s a  square wave of half the frequency of the input.  The tubes V5  and V7 together with the L,C, f i l t e r s allow only the fundamental sine wave to pass to the output stage which i s a cathode follower formed by tube Vg,  Thus the output of the cathode-follower i s a  sine wave of half the frequency of the input sine wave. The  FIG 6.5 FREQUENCY  DIVIDER  57  tube V  -  i s o l a t e s the m u l t i - v i b r a t o r from the f i l t e r  stages.  5  D.  The Audio A m p l i f i e r The audio a m p l i f i e r i s a modified v e r s i o n of Metropolitan  V i c k e r ' s Main A m p l i f i e r .  I t s c i r c u i t diagram has been given i n 3  the Appendix,  I t has an over a l l gain = 3 . 7 x 10 .  bandwidth from 10 c y c l e s / s e c to 300 c y c l e s / s e c .  I t has a  This band-  width i s because of the c a p a c i t o r s c,, and c . 2  E,  The Phase S h i f t e r The c i r c u i t diagram of the phase s h i f t e r i s given i n the  Appendix.  I t changes the phase from 0 to 3 2 0 ° .  output s i g n a l changes with the s e t t i n g of phase.  However, the Thus with  each s e t t i n g of phase, the input to the phase s h i f t e r has to be adjusted for constant output. F.  The Phase-Sensitive Detector The c i r c u i t diagram of the p h a s e - s e n s i t i v e detector as  shown i n F i g . (6.6) i s due to Schuster (18).  The c i r c u i t con-  s i s t s of a pentode tube V j the p l a t e load of which i s switched a l t e r n a t e l y to  and R by the reference s i g n a l . 2  The input  s i g n a l at the g r i d of the pentode e s t a b l i s h e s a p l a t e current i — gm eg and the s w i t c h i n g tube (V<j ) determines which of the two r e s i s t o r s Rj or R w i l l be traversed by the c u r r e n t .  This  i s accomplished by a reference voltage about 30 v o l t s i n the secondary of T^ a p p l i e d to g r i d s of V^., a l t e r n a t e l y c u t t i n g o f f one-half of the tube and causing the other h a l f to conduct. The switch tubes ( V  9  , V K ) have a r e s i s t a n c e of about 7000 ohms 2  FIG 6.6  PHASE SENSITIVE DETECTOR  - 59 where as the pentode  has a r e s i s t a n c e of 1.5 Meg ohms.  This  feature assures the balance s t a b i l i t y of the c i r c u i t r e l a t i v e to v a r i a t i o n s i n s w i t c h i n g tube c h a r a c t e r i s t i c s or reference voltage. Long time constants f o l l o w i n g the detector are obtained by feeding the d . c . output t o a p a i r o f cathode f o l l o w e r s ( V 3 , V 4 ) through the appropriate R - C elements, G.  The power a m p l i f i e r used i s Bogon's Model M 3 0  amplifier.  0  boaster  The narrow bandwidth a m p l i f i e r i s White's Operational  S e l e c t i v e A m p l i f i e r Model 236A together with White's twin T of type 546. H.  ,  The Helmholtz C o i l s Each c o i l has 1350 turns and a r e s i s t a n c e of 30 ohms.  Their  mean radius as w e l l as the distance between t h e i r centres i s 7 inches.  A c a l c u l a t i o n shows that the peak value of the magnetic  f i e l d at the centre of the c o i l s i s given by where  i  .096 x i gauss  i s the r . m . s . value of the a l t e r n a t i n g current  fol-  lowing through the c o i l i n m i l l i - a m p e r e s , I.  Working.of the Spectrometer To achieve a good f i l l i n g f a c t o r , the c o i l of the o s c i l l a t o r  i s placed d i r e c t l y i n t o the sample (para-di-chloro-benzene) kept at the centre of the Helmholtz c o i l s .  The o s c i l l a t o r s frequency  i s s l o w l y changed by d e r i v i n g the tuning condenser by a motor. The passage of the d e r i v i n g frequency through the resonance should be "slow a d i a b a t i c " .  This requires  ~  ^<  - 60 where  i s the l i n e width i n frequency u n i t s . During the experiment, o s c i l l a t o r ' s frequency was d r i v e n at  the r a t e 3.290 K C / s e c . 2  Thus the aforesaid c o n d i t i o n i s w e l l  s a t i s f i e d as the l i n e width i s about 50 KC. A l s o the t o t a l time taken b y the d e r i v i n g frequency to cross the l i n e should be at l e a s t s e v e r a l times the time constant of the detector.  phase-sensitive  At the same time a good s i g n a l - t o - n o i s e r a t i o  requires the time constant to be as large as p o s s i b l e .  A time  constant of 5 sec was found to be a good compromise between these requirements.  As the frequency passes through the resonance,  nuclear s i g n a l i s induced across the c o i l .  the  To record the r e -  sonance the s i g n a l i s modulated by a s i n u s o i d a l magnetic of 82.5 c p . s . and having a peak value about  5 gauss.  field As the  Zeeman s p l i t t i n g of the pure quadrupole l e v e l s depends upon the o r i e n t a t i o n of the e l e c t r i c f i e l d gradient a x i s with respect  to  the magnetic f i e l d and t h i s o r i e n t a t i o n being random i n case of powder sample,  the resonance i s smeared twice a c y c l e by the  modulating magnetic f i e l d .  Thus the s i g n a l appears at the second  harmonic of the modulation frequency i . e . at 165 c . p . s . as the output of the i n t e g r a t o r .  This s i g n a l after being a m p l i f i e d by  the a u d i o - a m p l i f i e r and the narrow-band-width a m p l i f i e r appears at the input of phase-sensitive d e t e c t o r .  The band-width of the  a m p l i f i e r i s only 2 c . p . s . , so i t cuts down the noise c o n s i d e r ably.  The noise i s further cut down by the  detector.  phase-sensitive  The reference s i g n a l for the phase-sensitive  detector  i s provided by a Hewlett Packard Audio o s c i l l a t o r Model 200 AB through a phase s h i f t e r .  To keep the phase difference between  the two s i g n a l s feeding the phase-sensitive detector  constant,  - 61 -  the same audio  o s c i l l a t o r provides the modulation s i g n a l .  As  the frequency of the modulation signal i s half of the reference s i g n a l , so the audio o s c i l l a t o r feeds a frequency divider which halves the frequency and then drives a power amplifier. power amplifier supplies current to the modulation coils.  The  Helmholtz  The maximum current obtained was 400 milli-amperes, The  value of the current usually used for modulation was 3 0 - 5 0 milliamperes.  The output of the phase-sensitive detector i s  recorded by E sterline-Angles D.C. mlllia meter Model AW. A  The  signal as recorded by the ameter i s maximum when the nuclear signal i s i n phase with the reference s i g n a l . s e t t i n g the phase s h i f t e r .  T h i s i s done by  The f i e l d modulation has been used  to avoid the response of the spectrometer to spurious signals which were previously observed i n a s e l f quenched frequency modulated o s c i l l a t o r . i s very complicated.  The frequency spectrum of the o s c i l l a t o r Because of quenching, i t consists of a  central frequency with side bands on either sides separated by the quench frequency.  The best way to locate the central f r e -  quency i s to switch o f f the audio o s c i l l a t o r feeding the quench generator so that the o s c i l l a t o r i s pperating continuously. Then i t s frequency can be e a s i l y measured by a receiver.  The  central frequency of the quenched o s c i l l a t o r , which i s very close to t h i s frequency i s f i n a l l y determined by switching on the audioo s c i l l a t o r and changing the quench frequency.  I t i s only the  central frequency that does not s h i f t by changing the quench frequency.  This fact locates the central frequency.  - 62 J.  :  Measurements The amplitude of the signal was measured as a function of  the quench frequency and the modulation current.  Then, f o r a  p a r t i c u l a r quench frequency and.modulation current, the signal was measured as a function of the on-off time of the o s c i l l a t o r . The results have been given i n the next section. ments were taken at room temperature.  These measure-  VII.  RESULTS OBTAINED WITH THE SPECTROMETER  The spectrometer was operated with low modulation f i e l d (  ~ 3 gauss) so as to s a t i s f y most of the conditions under  which the theory f o r the spectrometer was developed i n Chapter V, Figure (7.1) shows the amplitude of the signal as a function of the pulse width (on-time of the o s c i l l a t o r ) f o r the various values of the quench frequency. I.  Three e f f e c t s are quite prominent.  The amplitude of the s i g n a l goes through a broad maxima as the pulse width i s increased.  II.  The maxima becomes broader as the quench frequency i s decreased.  ' I I I . In the regions of maxima, the amplitude of the signal increases with the quench frequency. The following explanation f o r the r e s u l t can be given. The theory of the spectrometer was based on the assumption that the mode of the o s c i l l a t o r ' s operation i s always l o g a r i t h mic and the pulses are rectangular i . e . the r i s e and f a l l time of the pulse i s n e g l i g i b l e as compared to i t s f l a t portion. For short pulse widths (  —  5 usee), neither of these approximations  hold and i n the l i m i t of very short pulses the spectrometer should be operating i n the l i n e a r mode.  In the l i n e a r mode the spectro-  meter output w i l l be proportional to V  g  instead of l n V  s  as i n  logarithmic mode and increasing pulse width should give i n creasing s i g n a l .  As the pulse width i s further increased we  64 -  FIG-7.1  SIGNAL Vs. PULSE-WIDTH  —.PULSE-WIDTH  13!  L.  1  _4  -I  5—  1  \  1  1  -AO  1  \h 1  1  J  L5  SEC 1  - 65 come across such values of pulse width for which the spectrometer operates between the l i n e a r and logarithmic modes and the signal goes through a broad maxima over a c e r t a i n range of pulse width.  In t h i s plateau, the signal as predicted by the  equation (5.8) should vary as  ~  independent  Note that the dependence of signal upon logarithmic mode. ^  of  T  f ' holds only i n the  Figure (7.2) shows a plot of the signal versus  f o r the various values of pulse width, conforming  prediction.  A plot of the s i g n a l against  values of. ( T  or tw.  this  for different  - to) also, gives the same r e s u l t .  On the r i g h t side of the plateau, the spectrometer  operates  i n the logarithmic mode because now the pulse width i s quite large as compared with the r i s e time and the pulses can be assumed to be rectangular.  In t h i s region the theory predicts  that the s i g n a l i s proportional to T*  '  . The exact value of  i s not known but i t should lie between  T  and  T -tw.  i  As the value of  T  decreases by increasing the pulse-width,  therefore the s i g n a l drops for longer values of pulse-width. However, the decrease i n signal amplitude i s faster than predicted by the theory-.  This i s most probably because of the  changes i n the tube parameters with the increase of the on-time of the o s c i l l a t o r .  This factor may also contribute to the  existance of a d e f i n i t e plateau f o r long curve with a simple maximum.  T  , rather than a  In addition to t h i s , the condition  that the time decay constant of the r . f . o s c i l l a t i o n s should be quite large as compared with the off-time of the o s c i l l a t o r , i s also not s a t i s f i e d f o r long pulses.  - 66 -  FIG  1.2  SIGNAL VS. OiUENCH FREQUENCY  - 67 Figure (7.3) shows the s i g n a l against the r.m.s. value of the modulation current.  The peak value of the modulation  field  i n gauss can be obtained by multiplying the r.m.s. value of the current i n milli-amperes by .097. At low f i e l d s ( ^ 2 . 5 gauss) the signal i s proportional to the square of the f i e l d as predicted by the equation (5.8).  As the f i e l d i s further increased,  the s i g n a l increases less r a p i d l y than that given by H m and i t f i n a l l y begins to drop after passing through a broad maxima at about 10 gauss.  The decrease of the signal at the high values  of f i e l d can be explained by considering the e f f e c t s which attenuate the amplitude of the free induction s i g n a l as d i s cussed i n Chapter IV. The best operating conditions of the spectrometer can be summarized as follows. I.  I t was found experimentally that the spectrometer i s  most s e n s i t i v e when the noise i n the detector's output, at the instant when the o s c i l l a t i o n s are building up, can be seen on the oscilloscope.  This can be achieved by adjusting the  controls of the quench generator to a proper on-time of the oscillator.  This adjustment i s quite easy to make because a  part of the detector's output i s always displayed on the o s c i l l o s cope. II.  The frequency of the quench generator should be high  (50 - 100 KC/sec),  At the high quench frequency, the region i n  which the spectrometer can be operated f o r maximum signal i s very narrow.  So care should be taken i n selecting a proper on-  time of the o s c i l l a t o r . i s obtained by step I.  A good indication of the proper  time  - 68 -  FIG 7-3  SIGNAL Vs. MODULATION FIELD.  •  III,  -  69  -  The peak value of the modulation magnetic  should be about 5 - 7  gaus3  field  for c h l o r i n e 35 n u c l e i i n P a r a - d i -  chlorobenzene.  For other systems, the optimum modulating f i e l d  w i l l depend on  Tg  and on the nuclear gyromagnetic r a t i o  y.  The other operating c o n d i t i o n s of the spectrometer have been described i n Chapter VI while d i s c u s s i n g the working of the  spectrometer.  - 70 -  APPENDIX  HG.A2 AUD\0 AMPLIFIER  - 72 -  BIBLIOGRAPHY  1.  T.P. Das and E.L. Hahn, Nuclear Quadrupole Resonance Spectroscopy, S o l i d State Physics; Supplement I (1958), p. 70 - 80.  2.  M,H,  Cohen and F. Reif, Nuclear Quadrupole e f f e c t s i n  nuclear magnetic resonance;  S o l i d State Physics 5, 321 (1957).  3.  E.L. Hahn, Phys,Rev. 80, 980 (1950).  4.  M. Bloom, E.L. Hahn, and B. Herzog, Phys,Rev. 97, 1700  (1955).  5.  M. Bloom, E.L. Hahn, and B. Herzog, Phys.Rev. 97, 1702  (1955).  6.  Wang, Towens, Schawlow, Holden, Phys.Rev. 86, 809 (1952).  7.  Meal, J.Am.Chemical Soc. 74, 6121  8.  M. Bloom, Ph.D.  9.  B. Herzog and E.L. Hahn, Phys.Rev. 103, 148 (1956).  10.  (1952).  Thesis, University of I l l i n o i s (1954).  P.A. Bender, D.A,  Jennings and W.H.  T a n t i l l o , J,Chem.Physics  32, 499 (1960). 11.  T.P. Das and E.L. Hahn, Nuclear Quadrupole Resonance Spectroscopy!s(1958), p, 7 - 12.  12.  M. Bloom, E.L. Hahn and B. Herzog, Phys,Rev. 97, 1704 (1955)  - 73 -  13,  J.R, Whitehead, Super-regenerative Receivers, Cambridge University Press.  14.  C. Dean, Ph.D. Thesis, Harvard University  15,  Abraghamj  16.  W.I, Goldberg, Private communications with M. Bloom,  17,  D. McCall, Ph.D. Thesis, Department of Chemistry, University of I l l i n o i s  18.  (1952).  The P r i n c i p l e s of Nuclear Magnetism, p. 545.  (1954).  N.A. Schuster; Rev. of S c i e n t i f i c Ins. 22, 254 (1951).  

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