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UBC Theses and Dissertations

Deuteron magnetic resonance of TTF(d₀)-TCNQ(d₄) Kubik, Philip Roman 1977

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DEUTERON MAGNETIC RESONANCE OF T T F ( d Q ) - T C N Q ( d 4 ) by P H I L I P ROMAN KUBIK B . S c , U n i v e r s i t y o f B r i t i s h C o l u m b i a , 1974 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS We a c c e p t t h i s t h e s i s a s c o n f o r m i n g t o t h e r e q u i r e d s t a n d a r d THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1977 0 P h i l i p Roman K u b i k , 1977 In present ing th is thes is in p a r t i a l fu l f i lment of the requirements for an advanced degree at the Un ivers i ty of B r i t i s h Columbia, I agree that the L ibrary shal l make i t f ree ly ava i lab le for reference and study. I fur ther agree that permission for extensive copying o f th is thes is for scho la r ly purposes may be granted by the Head of my Department or by h is representa t ives . It is understood that copying or pub l ica t ion of th is thes is for f i n a n c i a l gain sha l l not be allowed without my wri t ten permission. Department of Physics  The Univers i ty of B r i t i s h Columbia 2075 Wesbrook Place Vancouver, Canada V6T 1W5 Date A p r i l . 1977 ABSTRACT The d e u t e r o n m a g n e t i c r e s o n a n c e o f powdered T T F ( d ^ ) T TCNQ(d 4) has been o b s e r v e d a t 4.2 K and 1.3 K. The l i n e s h a p e i s c h a r a c t e r i z e d by a q u a d r u p o l e s p l i t t i n g w i t h a c o u p l i n g 2 c o n s t a n t e q Q / h = 1 8 0 . 0 ± . 7 kHz and an asymmetry p a r a m e t e r n = . 0 8 0 ± . 0 0 2 . The c h a r g e d e n s i t y waves (CDW) t h a t a r e p r o p o s e d 2 t o e x i s t i n TTF-TCNQ b e l o w 54 K w i l l , m o d u l a t e e <qQ/ih i f t h e y o c c u r orir.the TCNQ c h a i n s . T h i s w i l l be m a n i f e s t e d by a c h a r -a c t e r i s t i c b r o a d e n i n g o f t h e s p e c t r u m . A l t h o u g h t h e b r o a d e n i n g i s a f a c t o r o f 2.4 g r e a t e r t h a n t h e e x p e c t e d d i p o l a r b r o a d e n -i n g , i t d o e s n o t seem t h a t t h e e x t r a b r o a d e n i n g c a n be a s c r i b e d t o t h e p r e s e n c e o f a CDW. We c a n o n l y e s t i m a t e an u p p e r l i m i t o f ^5% f o r t h e CDW a m p l i t u d e b a s e d o f t h e o b s e r v e d b r o a d e n i n g and t h e d i f f e r e n c e s i n t h e q u a d r u p o l e c o u p l i n g c o n s t a n t s o f T T F ( d n ) - T C N Q ( d .) and TCNQ(d ) . - i i i -TABLE OF CONTENTS Page ABSTRACT TABLE OF CONTENTS LIST OF TABLES LIST OF FIGURES ACKNOWLEDGEMENT CHAPTER I INTRODUCTION 1 I I DEUTERON MAGNETIC RESONANCE LINESHAPE 12 I I I EXPERIMENTAL DESIGN AND PROCEDURE 1) G e n e r a l D e s c r i p t i o n 19 2) S i g n a l : N o i s e O p t i m i z a t i o n 22 3) The Tuned C i r c u i t 25 4) F i e l d Sweep and M o d u l a t i o n 30 5) Homogeneity 36 IV RESULTS 38 V SOURCES OF BROADENING 4 8 VI CONCLUSIONS 59 BIBLIOGRAPHY 61 n i i i i v v v i - i v -LIST OF TABLES Tab l e Page I Quadrupole C o u p l i n g C o n s t a n t s and Asymmetry Parameters 4 6 I I Gross Atomic Charges 56 - v -L I S T OF FIGURES F i g u r e Page 1 One d i m e n s i o n a l , h a l f - f i l l e d e n e r g y band 3 2 A CDW i n a one d i m e n s i o n a l l a t t i c e 3 3 TTF and TCNQ m o l e c u l e s 5 4 U n i t c e l l o f TTF-TCNQ 6 5 E l a s t i c n e u t r o n s c a t t e r i n g 8 6 a ) L a b o r a t o r y and p r i n c i p a l a x i s c o o r d i n a t e 14 s y s t e m s b) S i n g l e c r y s t a l DMR l i n e s h a p e c) E f f e c t o f a v e r a g i n g o v e r a l l c r y s t a l o r i -e n t a t i o n s on t h e DMR l i n e s h a p e 7 G a u s s i a n b r o a d e n e d DMR l i n e s h a p e 16 8 E f f e c t o f a CDW on t h e DMR s p e c t r u m 18 9 B l o c k d i a g r a m o f t h e a p p a r a t u s 21 10 S c h e m a t i c cut-away d i a g r a m o f t h e b o t t o m 26 end o f t h e c r y o s t a t 11 Tuned c i r c u i t and m a t c h i n g n e t w o r k 2 8 12 P o s i t i o n o f t h e r o t a t i n g c o i l p r o b e 35 13 Main peak o f T T F ( d ^ ) - T C N Q ( d ^ ) d e r i v a t i v e 39 s i g n a l 14 O u t e r peak o f T T F ( d )-TCNQ(d 4) d e r i v a t i v e 40 s i g n a l 15 I n t e g r a l o f F i g . 13 41 16 Main peak o f TCNQ(d^) d e r i v a t i v e s i g n a l 44 17 P r o t o n a b s o r p t i o n s i g n a l o f T T F ( d . ) T C N Q ( d n ) 50 - v i -ACKNOWLEDGEMENT I g r a t e f u l l y acknowledge the s u p p o r t and encourage-ment o f Dr. W. N. Hardy. A l l o f the samples used i n t h i s p r o j e c t were c h e e r f u l l y p r o v i d e d by Dr. L. W e i l e r and h i s c o r w o r k e r s . F i n a l l y I w i s h t o thank the N a t i o n a l Research C o u n c i l o f Canada f o r a P o s t g r a d u a t e S c h o l a r s h i p . - L -C h a p t e r I  INTRODUCTION T e t r a t h i o f u l v a l e n e - t e t r a c y a n o q u i n o d i m e t h a n e (TTF-TCNQ) i s a c h a r g e t r a n s f e r c omplex t h a t e x h i b i t s many o f t h e p r o p e r t i e s o f a q u a s i one d i m e n s i o n a l (ID) s y s t e m . Thus TTF-TCNQ a p p e a r s t o o f f e r t h e o p p o r t u n i t y f o r e x p e r i m e n t a l v e r i f i c a t i o n o f ID t h e o r i e s . A v e r y e x t e n s i v e r e v i e w o f TTF-TCNQ and o t h e r h i g h l y a n i s o t r o p i c s y s t e m s i s g i v e n by A n d r e , B i e b e r , and G a u t i e r (1976) . S t r i c t l y ID s y s t e m s have some u n i q u e p r o p e r t i e s . P e i e r l s (1955) p o i n t e d o u t t h a t a p a r t i a l l y f i l l e d ID e l e c t r o n band i s u n s t a b l e w i t h r e s p e c t t o a s t a t i c l a t t i c e d i s t o r t i o n known as t h e P e i e r l s i n s t a b i l i t y . C o n s i d e r a n e l e c t r o n i c band f o r a ID l a t t i c e w i t h l a t t i c e c o n s t a n t b , w h i c h i s f i l l e d up t o t h e F e r m i momentum kp as shown i n F i g . l a . I f t h e r e a r e p e l e c t r o n s p e r l a t t i c e s i t e t h e n kp i s g i v e n b y : I - l The e l e c t r o n i c d e n s i t y o f s t a t e s N(E) f o r t h e band i s shown i n F i g . l b . F o r s u c h a band t h e e l e c t r o n i c e n e r g y c a n a l w a y s be l o w e r e d by a p e r i o d i c l a t t i c e d i s t o r t i o n . Maximum e n e r g y r e d u c t i o n o c c u r s i f t h e wave v e c t o r o f t h e d i s t o r t i o n i s 2 k F , r e s u l t i n g i n a s u p e r l a t t i c e w i t h a l a t t i c e c o n s t a n t ^ . T h i s opens a gap o f w i d t h A i n t h e band s t r u c t u r e a t i k F . The l a t t i c e d i s t o r t i o n p r o d u c e s a p o t e n t i a l w i t h t h e s u p e r l a t t i c e p e r i o d . The e l e c t r o n i c d e n s i t y i s m o d u l a t e d by t h e p o t e n t i a l c a u s i n g a c h a r g e d e n s i t y wave (CDW). - 2 -The lowering of the e l e c t r o n i c energy must compete with the i n c r e a s e i n e l a s t i c energy caused by the d i s t o r t i o n . For a simple t i g h t b i n d i n g model, which i s s u i t a b l e f o r a narrow band system such as TTF-TCNQ, the former always outweighs the l a t t e r a t low temperatures ( B e r l i n s k y , 1976) so t h a t one expects a p e r i o d i c l a t t i c e d i s t o r t i o n t o o c c u r . Two cases can be d i s t i n g u i s h e d which depend upon whether or not p i s a r a t i o n a l number. I f i t i s , the s u p e r l a t t i c e c o n t a i n s a r a t i o n a l number of l a t t i c e s i t e s : the CDW i s commensurate with the l a t t i c e . Two e q u i v a l e n t c o n f i g u r a t i o n s f o r the case p = h are d e p i c t e d i n F i g s . 2a and c. In F i g . 2c the CDW i s s h i f t e d by b with r e s p e c t t o the c o n f i g u r a t i o n i n F i g . 2a but the energy i s the same. However, the intermediate c o n f i g u r a t i o n i n which the CDW i s t r a n s l a t e d by b/2 has h i g h e r energy because the i o n cores don't know which way t o d i s t o r t . Therefore the CDW i s pinned to the l a t t i c e . F i g . 2b corresponds t o the case i n which p i s i r r a t i o n a l so the CDW i s incommensurate with the l a t t i c e . No matter how the CDW i s t r a n s l a t e d , the i o n cores can d i s t o r t s l i g h t l y t o produce a c o n f i g u r a t i o n o f the same energy. I f there were no d e f e c t s or i m p u r i t i e s t o p i n the CDW, a superconducting s t a t e would result because the CDW i s too massive t o be s c a t t e r e d by phonons. However, a CDW i n a ID system would be p a r t i c u l a r l y s u s c e p t i b l e t o such p i n n i n g . The f o r e g o i n g d i s c u s s i o n n e g l e c t s any mention of f l u c t u a t i o n e f f e c t s which are very important f o r ID systems. In f a c t there i s a theorem (Landau and L i f s h i t z , 1969) which s t a t e s t h a t ID systems with f o r c e s of f i n i t e range, as i n the t i g h t - 3 -F i g u r e 1) One d i m e n s i o n a l , h a l f - f i l l e d e n e r g y band w i t h a) l a t -t i c e c o n s t a n t b and b) w i t h a P e i e r l s d i s t o r t i o n w i t h wave v e c t o r 2k . The r e s p e c t i v e d e n s i t i e s r o f s t a t e s a r e shown i n c) and d ) . (c) F i g u r e 2) A CDW i n a ID l a t t i c e , a) Commensurate CDW w i t h p=^-. b) Incommensurate CDW c) A c o n f i g u r a t i o n e n e r g e t i c a l l y e q u i v a l e n t t o a) i n w h i c h t h e CDW i s d i s p l a c e d by b . - 4 -b i n d i n g model, cannot undergo a phase t r a n s i t i o n at a f i n i t e temperature because of f l u c t u a t i o n s . No r e a l system can be t r u l y ID. The c l o s e s t t h a t one can come i s a system of weakly coupled c h a i n s . Such a system can undergo a 3D phase t r a n s i t i o n at a f i n i t e temperature (Pincus, 1975) . TTF and TCNQ are both p l a n a r o r g a n i c molecules; they are shown i n F i g . 3. In the TTF-TCNQ c y s t a l , they s t a c k t o form separate TTF and TCNQ chains p a r a l l e l t o the c r y s t a l b a x i s (see F i g . 4b) . The u n i t c e l l o f TTF-TCNQ, c o n t a i n i n g 4 molecules, i s shown i n F i g . 4. The c r y s t a l s t r u c t u r e i s m o n o c l i n i c with space group P2i/c (Kistenmacher, P h i l l i p s , and Cowan, 1973). M o l e c u l a r o r b i t a l c a l c u l a t i o n s ( B e r l i n s k y , C a r o l a n and W e i l e r , 1974, and r e f e r e n c e s g i v e n there) show t h a t the h i g h e s t occupied molecular o r b i t a l s , the ones t h a t form the conduction band, are u o r b i t a l s . These are odd under r e f l e c t i o n through the plane of the molecule and o v e r l a p s t r o n g l y . T h i s leads t o a s t r o n g i n t e r a c t i o n down each c h a i n but the i n t e r c h a i n c o u p l i n g i s weak r e s u l t i n g i n a q u a s i ID system. The q u a s i ID nature of TTF-TCNQ i s evinced most n o t a b l y i n the DC c o n d u c t i v i t y . At room temperature TTF-TCNQ i s one of a s m a l l group of h i g h l y a n i s o t r o p i c o r g a n i c c o n d u c t o r s . The b a x i s c o n d u c t i v i t y at room temperature i s ^ 500 ( ft cm)"-'-. T y p i c a l o r g a n i c i n s u l a t o r s have c o n d u c t i v i t i e s % 1 0 - 1 0 t o 1 0 - 1 4 ( ft c m ) - 1 whereas copper has 1.7 x 1 0 6 ( ft c m ) - 1 . The t r a n s v e r s e c o n d u c t i v i t i e s of TTF-TCNQ are two orders of magnitude lower. (b) F i g u r e 4) U n i t c e l l of TTF-TCNQ. a) View down the b a x i s . The molecules at z=c/2 have t h e i r c e n t r o i d s a t y=b/2. b)View down the c* a x i s . The dimensions of the u n i t c e l l are (12.3,17.9,3.8) A. - 7 -The DC c o n d u c t i v i t y ( T i e d j e , 1975) has an approximately T~2 dependence (as opposed to T - 1 f o r normal pure metals) from 300 K down t o about 80 K. A m e t a l - i n s u l a t o r t r a n s i t i o n occurs at about 54 K and the c o n d u c t i v i t y plummets. At low temperatures TTF-TCNQ behaves l i k e a s m a l l gap semiconductor. Evidence of a phase t r a n s i t i o n i s a l s o g i v e n by s u s c e p t i b i l i t y (Scott et a l , 1974) , thermopower (Chaikin et a l , 1973) and s p e c i f i c heat (Craven et a l , 1974) measurements. The DC c o n d u c t i v i t y , thermopower and more rec e n t s p e c i f i c heat measurements (Djurek et a l , 1977) a l s o show the e x i s t e n c e o f another phase t r a n s i t i o n at 38 K. The s p e c i f i c data show i n a d d i t i o n t r a n s i t i o n s at 46 K and % 48-49 K. C o n s i d e r a b l e l i g h t was thrown on the nature of the t r a n s i t i o n s by d i f f r a c t i o n s t u d i e s u s i n g d i f f u s e X-ray s c a t t e r i n g at 2kp (Denoyer et a l , 1975 and Kagoshima et a l , 1975) and e l a s t i c neutron s c a t t e r i n g at 2k F (Comds et a l , 1976) . Below 38 K there i s a 3D s u p e r l a t t i c e w i t h long range order and a modulation p e r i o d of (4a x 3.4b x c ) . I t appears t o be incommensurate al o n g the c h a i n s . D i f f u s e X-ray s c a t t e r i n g i n d i c a t e s t h a t the d i s t o r t i o n i s s i n u s o i d a l and t h a t the p o l a r i z a t i o n of the d i s t o r t i o n i s i n the b d i r e c t i o n . The neutron r e s u l t s appear t o i n d i c a t e a s m a l l c component though t h i s i s r a t h e r i n c o n c l u s i v e . The modulation i n the b d i r e c t i o n i s unchanged up t o 54 K. The modulation p e r i o d i n the a d i r e c t i o n drops s h a r p l y at 38 K and then more g r a d u a l l y t o 2a at 54 K as shown i n F i g . 5b. The peak i n t e n s i t y , which i s p r o p o r t i o n a l t o the square o f the amplitude o f the d i s t o r t i o n , drops t o the background l e v e l at about 54 K as shown i n F i g . 5a. In a d d i t i o n , between 38 K and 54 K the peak broadens somewhat i n the a* d i r e c t i o n i n d i c a t i n g some l o s s o f long range o r d e r . I t s width - 8 -F i g u r e 5) E l a s t i c n e u t r o n s c a t t e r i n g , a) Peak i n t e n s i t y , b ) M o d u l a t i o n p e r i o d . - 9 -i s r e s o l u t i o n l i m i t e d i n the b* and c* d i r e c t i o n s throughout the range imp l y i n g c o r r e l a t i o n lengths > 100 A ° . E l a s t i c neutron s c a t t e r i n g i n p a r t i c u l a r i s i n p r i n c i p l e capable of g i v i n g much more i n f o r m a t i o n on the nature of s t r u c t u r e changes between the t r a n s i t i o n s . However, because the s a t e l l i t e peaks are very much weaker than the Bragg peaks very l i t t l e i n f o r m a t i o n has been obtained from the i n t e n s i t i e s . Apart from the r a t h e r i n c o n c l u s i v e i n f o r m a t i o n about the p o l a r i z a t i o n of the d i s t o r t i o n mentioned above, there are only two r e s u l t s of note. F i r s t , the TTF and TCNQ molecules appear t o be modulated as u n i t s : the d i s t o r t i o n i s i n t e r m o l e e u l a r r a t h e r than i n t r a -m o l e c u l a r . Secondly, the amplitude of the d i s t o r t i o n has been roughly estimated t o be 1%. The occurrence o f a P e i e r l s d i s t o r t i o n at 54 K i s w e l l e s t a b l i s h e d . I t i s n ' t c l e a r though whether the d i s t o r t i o n occurs on the TTF c h a i n s , the TCNQ chains, or both. N e i t h e r i s i t c l e a r why the modulation i n the a d i r e c t i o n and the peak i n t e n s i t y have the temperature dependences shown i n F i g . 5. Of p a r t i c u l a r i n t e r e s t i s the nature of the f i r s t order phase t r a n s i t i o n at 38 K. Since not much more s t r u c t u r a l i n f o r m a t i o n can be expected from d i f f r a c t i o n s t u d i e s u n t i l l a r g e r c r y s t a l s are a v a i l a b l e , one must look t o other t e c h n i q u e s . I t was mentioned above t h a t the l a t t i c e d i s t o r t i o n i s accompanied by a CDW with the same modulation p e r i o d . T h i s opens up a new avenue by a l l o w i n g one t o study the t r a n s i t i o n s by probing the e l e c t r i c f i e l d . One means of doing t h i s i s by examining the n u c l e a r magnetic resonance (NMR) s p e c t r a o f any n u c l e i i n TTF-TCNQ with - 10 -a quadrupole moment. The h a m i l t o n i a n f o r the i n t e r a c t i o n of such a nucleus with an e l e c t r o s t a t i c p o t e n t i a l can be w r i t t e n as a m u l t i p o l e expansion. The expansion w i l l c o n t a i n a term i n v o l v i n g the product of the e l e c t r i c f i e l d g r a d i e n t (EFG) and the n u c l e a r quadrupole moment. This term causes a s p l i t t i n g of the NMR l i n e s h a p e which i s p r o p o r t i o n a l t o the EFG at the nucleus being probed. The o n l y nucleus i n TTF-TGNQ with a non-zero quadrupole moment Q and a n a t u r a l abundance g r e a t e r than 1% i s N 1 4 . Since i t occurs o n l y i n TCNQ, o n l y those chains can be probed. No N 1 4 quadrupole resonance s t u d i e s have been made f o r TTF-TCNQ though some have been done on K-TCNQ (Murgich and P i s s a n e t z k y , 1973) . One can evade the problem of the p a u c i t y of quadrupolar n u c l e i by r e p l a c i n g some o f the n u c l e i t h a t have Q = O with i s o t o p e s t h a t have Q ^ O. The e l e c t r o n i c s t a t e s would be a f f e c t e d n e g l i g i b l y by such a change. For most n u c l e i t h i s would be very d i f f i c u l t and expensive but the H atoms can be r e p l a c e d by deuterons r e l a t i v e l y e a s i l y . One-can go so f a r as t o s e l e c t i v e l y d e u t e r a t e e i t h e r the TTF or the TCNQ mol e c u l e s . Each of them c o n t a i n s 4 protons i n p o s i t i o n s t h a t are e q u i v a l e n t i n the molecule ( F i g . 3 ) . Since the deuteron magnetic resonance (DMR) o f s e l e c t i v e l y d e u t e r a t e d samples o f TTF-TCNQ can p o t e n t i a l l y g i v e more i n f o r m a t i o n than N 1 4 quadrupole resonance, the former approach was taken i n t h i s study. The quadrupole moment of the deuteron i s too s m a l l to a l l o w the use of n u c l e a r quadrupole resonance i n zero magnetic f i e l d as c o u l d be done f o r N 1 4 . However, one can observe the quadrupole s p l i t t i n g o f the h i g h f i e l d NMR l i n e s h a p e . - 11 -I d e a l l y one would l i k e t o observe the DMR spectrum of a s i n g l e c r y s t a l o f deut e r a t e d TTF-TCNQ as the -temperature was v a r i e d i n the r e g i o n o f the t r a n s i t i o n s . Given the s m a l l s i z e o f s i n g l e c r y s t a l s o f TTF-TCNQ a v a i l a b l e when t h i s p r o j e c t was begun, s i n g l e c r y s t a l DMR d i d not seem f e a s i b l e . A l l o f the work d e s c r i b e d here employed powder samples which have a much more complicated spectrum than s i n g l e c r y s t a l s because the a b s o r p t i o n f r e q u e n c i e s depend on the c r y s t a l o r i e n t a t i o n . The DMR spectrum of TTF (dg) -TCNQ (d.4.) has been observed at 1.3 K and 4.2 K. An u n s u c c e s s f u l attempt was a l s o made at 77 K. Even at l i q u i d h e lium temperatures long s i g n a l a v e r a g i n g was r e q u i r e d . Therefore i t seems u n l i k e l y that the experiment i n i t s present form can be adapted t o study the termperature r e g i o n o f the phase t r a n s i t i o n s . The X-ray and neutron d i f f r a c t i o n s t u d i e s show t h a t below 38 K an incommensurate CDW should be e s t a b l i s h e d along the c h a i n s . The DMR l i n e s h a p e shows no obvious m a n i f e s t a t i o n o f a CDW on the TCNQ chains ; we can a t best p l a c e an upper l i m i t of 5. % on the CDW amplitude. F u r t h e r work on TTF (d4.) -TCNQ (dg) i s i n p r o g r e s s . C h a p t e r I I THE DEUTERON MAGNETIC RESONANCE LINESHAPE Good d i s c u s s i o n s o f t h e e f f e c t s o f e l e c t r i c q u a d r u p o l e i n t e r a c t i o n s on NMR l i n e s h a p e s a r e g i v e n by Abragam (1961) and S l i c h t e r ( 1 9 6 3 ) . A b r i e f r e c a p i t u l a t i o n w i l l be g i v e n h e r e . I n a m a g n e t i c f i e l d H, t h e h a m i l t o n i a n f o r a n u c l e u s w i t h s p i n I and q u a d r u p o l e moment Q i s : 2 % \ T YtlH-I + 4 l ^ 2 g 1 ) [31* - 1(1+1) + | n ( i 2 + i 2 } ] I I - l where t h e c o o r d i n a t e s y s t e m i s c h o s e n s o t h a t i f v i s t h e e l e c t r o s t a t i c p o t e n t i a l , t h e x, y , z a x e s a r e t h e p r i n c i p a l a x e s o f t h e EFG t e n s o r such t h a t I V z z ! > ^ v y y ' > ^ v x x ^ • eq = V z z h - ^xx v y y V Z z Y = n u c l e a r g y r o m a g n e t i c r a t i o J + = J x + i x Y l _ = l x - i i y The f i r s t t e r m i s t h e Zeeman i n t e r a c t i o n and t h e s e c o n d i s t h e q u a d r u p o l e i n t e r a c t i o n . e q i s t h e maximum component o f t h e EFG t e n s o r i n t h e p r i n c i p a l a x i s s y s t e m . n , t h e asymmetry p a r a m e t e r , measures t h e asymmetry o f t h e EFG a b o u t t h e z a x i s . e q and n c o m p l e t e l y s p e c i f y t h e EFG t e n s o r i n t h e p r i n c i p a l a x i s system b e c a u s e V must s a t i s f y P o i s s o n ' s e q u a t i o n . - 13 -We now d e f i n e a n o t h e r c o o r d i n a t e s y s t e m X,Y,Z s u c h t h a t H l i e s a l o n g t h e Z a x i s as shown i n F i g . 6 a . 9 i s t h e a n g l e between t h e z and Z a x e s w h i l e i s t h e a n g l e between t h e x and X a x e s . I n a s t r o n g m a g n e t i c f i e l d , t h e q u a d r u p o l e i n t e r a c t i o n c a n be t r e a t e d by f i r s t o r d e r p e r t u r b a t i o n t h e o r y . F o r a d e u t e r o n , t h e q u a d r u p o l e moment i s q u i t e s m a l l s o f i e l d s o f a few k i l o g a u s s a r e s u f f i c i e n t l y s t r o n g . The t r a n s i t i o n f r e q u e n c i e s f o r a s p i n 1 n u c l e u s s u c h as t h e d e u t e r o n a r e : f = f Q ± a (n , e., if. ) f Q n - 2 where f Q = y H z f Q = 3/2 e 2qQ/h = 3 c o s 2 6 . - l + n c o s ( 2 ^ ) ( c o s 2 0 - 1) f Q i s t h e Larmor f r e q u e n c y and f g i s 3/2 t i m e s t h e q u a d r u p o l e c o u p l i n g c o n s t a n t (QCC) . F o r a s i n g l e c r y s t a l i n w h i c h a l l d e u t e r o n s i t e s a r e e q u i v a l e n t , t h e NMR a b s o r p t i o n s p e c t r u m c o n s i s t s o f two peaks as shown i n F i g . 6b. The b r o a d e n i n g o f e a c h peak w i l l n o r m a l l y be d e t e r m i n e d by t h e d i p o l e - d i p o l e i n t e r a c t i o n s between t h e s p i n s . I f one h a s a powder s a m p l e , one must a v e r a g e o v e r a l l o r i e n t a t i o n s o f t h e c r y s t a l a x e s w i t h r e s p e c t t o t h e m a g n e t i c f i e l d . The r e s u l t i n g l i n e s h a p e s a r e g i v e n by e l l i p t i c i n t e g r a l s (Cohen and R e i f , 1 9 5 7 ) . The e f f e c t o f a v e r a g i n g on t h e u n b r o a d e n e d l o w e r peak i s shown i n F i g . 6c.-for s e v e r a l v a l u e s o f n ( B a r n e s and Bloom, 1 9 7 2 ) . The u p p e r peak g i v e s a l i n e s h a p e t h a t i s i d e n t i c a l e x c e p t t h a t i t i s r e f l e c t e d t h r o u g h f 0 . I f - 14 -F i g u r e 6 ) a ) L a b o r a t o r y c o o r d i n a t e s y s t e m ( s o l i d ) and EFG t e n s o r p r i n c i -p a l axes (dashed). (a) A A fcf a fQ (b) S i n g l e c r y s t a l DMR l i n e s h a p e w i t h a l l s p i n s equi-v a l e n t . (c) (f, - f 0 ) - / f o E f f e c t of ave r a g i n g over a l l c r y s t a l o r i e n t a t i o n s f o r the lower peak of b) (Barnes and Bloom, 1972) - 15 -n T^O, there are three main f e a t u r e s : a s i n g u l a r i t y at f Q - ^ f g (1 - n ) , a shoulder at. f Q - ^-f^ (1 ••+ n) and a step at f + i f n - I f n =0, the s i n g u l a r i t y and shoulder merge. In order t o see the e f f e c t of gaussian broadening, Barnes and Bloom (1972) have generated the lineshapes s y n t h e t i c a l l y using a computer. The complete unbroadened spectrum i s shown by the c i r c l e s i n F i g . 7a f o r ri = .18. The e f f e c t of gaussian broadening i s shown by the s o l i d l i n e . In t h i s experiment the d e r i v a t i v e of the a b s o r p t i o n was detected: t h i s i s shown i n F i g . 7b. To a very good approximation, the small outer peaks occur at f 0 - h f Q / the main peaks at f Q + \ f g (1-n ) , and the ba s e l i n e c r o s s i n g s at f Q + \ f g (1 + n ). n and the QCC can be found a f t e r i d e n t i f i c a t i o n of any two of these f e a t u r e s . Now consider the e f f e c t of a CDW on the s i n g l e c r y s t a l lineshape shown i n F i g . 6b. The simplest case i s that of a ID s i n u s o i d a l , commensurate CDW w i t h a s u p e r l a t t i c e period nb where n i s an i n t e g e r . In general the EFG w i l l have n d i f f e r e n t values at the n u c l e i so each of the two l i n e s of F i g . 6b w i l l be s p l i t i n t o a group of n s a t e l l i t e l i n e s . The s p l i t t i n g between the new s a t e l l i t e s i n each group w i l l not be constant and some l i n e s may c o i n c i d e r e s u l t i n g i n a s i n g l e peak w i t h increased i n t e n s i t y . C l e a r l y i f n i s made l a r g e , the s e p a r a t i o n of the s a t e l l i t e s i n each group w i l l be correspondingly reduced. E v e n t u a l l y that s e p a r a t i o n w i l l become l e s s than the gaussian broadening and each group of s a t e l l i t e s w i l l form a s i n g l e broadened l i n e . - 16 -T 1 S A T E L L I T E LINE SHAPE 1} » 018 «oo UNBROADENEO DISTRIBUTION — BROADENED LINE S H A P E z 0 .40 0 . 6 0 < f -V / f Q 1 1 1 • 1 1 DERIVATIVE OF S A T E L L I T E LINE SHAPE 7) * 0.18 i i i 1 1 1 1 - 0 . 6 0 - 0 . 4 0 - 0 2 0 0 0 0 0 2 0 0 . 4 0 0 6 0 UJ ' o u i u i o (b) ( F " V / F Q F i g u r e 7)a)Complete DMR a b s o r p t i o n l i n e s h a p e f o r a powder generated by computer.b) D e r i v a t i v e o f a) (Barnes and Bloom, 1972). - 17 -A p i n n e d , i n commensurate CDW i s o b t a i n e d i n t h e l i m i t as n a p p r o a c h e s i n f i n i t y . F o l l s t a e d t and S l i c h t e r (1975) have c a l c u l a t e d t h e NMR s p e c t r u m f o r t h i s c a s e . C o n s i d e r a c u b i c c r y s t a l l a t t i c e w i t h a p l a n e s i n u s o i d a l CDW o f a m p l i t u d e p and wave v e c t o r $. The e l e c t r o n d e n s i t y n ( r ) a t t h e p o i n t r i s : -»- -> n ( r ) = n Q f l + p c o s (Q *r) > I I - 3 P o i s s o n ' s e q u a t i o n g i v e s t h e EFG t o b e : eq = -4 n. p n D c o s (Q* .r) 11-4 The NMR l i n e s h a p e S ( f - f D ) r e s u l t i n g f r o m t h e CDW w i l l b e : -h } I I - 5 S ( f - f Q ) = IT 1 {1 - f f - f o l2 M where f = 3/2 e 2 q Q /h M H M and e q M = maximum v a l u e o f eq 4 «i p n Q T h i s l i n e s h a p e i s shown i n F i g . 8. Q u a l i t a t i v e l y one w o u l d e x p e c t a s i m i l a r shape s i n c e more n u c l e i w i l l e x p e r i e n c e EFG's i n t h e n e i g h b o u r h o o d s o f t h e maxima and minima t h a n n e a r z e r o . F o r a powder sample w i t h g a u s s i a n b r o a d e n i n g , i t w o u l d be n e c e s s a r y t o c o n v o l u t e F i g . 8 w i t h F i g . 7a. - 18 -F i g u r e 8) D i s t r i b u t i o n f u n c t i o n S ( f - f ) f o r a p l a n e , s i n -o u s o i d a l CDW i n an i s o t r o p i c l a t t i c e . - 19 -C h a p t e r I I I EXPERIMENTAL DESIGN AND PROCEDURE 1) G e n e r a l D e s c r i p t i o n A c o n t i n u o u s wave, f i x e d f r e q u e n c y ( 8 . 5 MHz) NMR a b s o r p t i o n s p e c t r o m e t e r w i t h Q-meter d e t e c t i o n was employed f o r t h e s e e x p e r i m e n t s . RF power was s u p p l i e d t o a h i g h Q p a r a l l e l r e s o n a n t c i r c u i t by a h i g h o u t p u t impedance c u r r e n t g e n e r a t o r . A t t h e t u n e d c i r c u i t r e s o n a n c e and w i t h no s a m p l e , t h e impedance a c r o s s t h e c o i l i s : R - QOJL I I I - l where .'co = 2 H ( r e s o n a n c e f r e q u e n c y ) L = c o i l i n d u c t a n c e I f t h e NMR sample i s p l a c e d i n t h e c o i l and i f Q>> 1 , t h e impedance Z becomes (Abragam, 1 9 6 1 ) : Z = R { l - i 4 H n Q x (co,) } I I I - 2 where n = r a t i o o f t h e sample volume t o t h e c o i l volume = f i l l i n g f a c t o r X ('co') = complex s u s c e p t i b i l i t y o f t h e sample = x ' U) - i x " (o») I f t h e impedance o f t h e c u r r e n t g e n e r a t o r i s much g r e a t e r t h a n t h e t u n e d c i r c u i t i m p edance, t h e n t h e r e l a t i v e change i n t h e v o l t a g e a c r o s s t h e c o i l i s : - 20 -A V / V = | A Z / Z | ' = - 4 i Q n x " (u) I H - 3 A v/v i s p r o p o r t i o n a l t o the NMR a b s o r p t i o n s i g n a l X " ( W ) . The tuned c i r c u i t v o l t a g e V was a m p l i f i e d d i r e c t l y . A bridge was not r e q u i r e d t o prevent s a t u r a t i o n of the p r e a m p l i f i e r because of. the low RF l e v e l s needed to a v o i d s a t u r a t i o n of the resonance. A block diagram of the apparatus i s shown i n F i g . 9. A s t a t i c magnetic f i e l d H was a p p l i e d u s i n g a Magnion 9 inch pole p i e c e electromagnet c o n t r o l l e d by an FFC-4 F i e l d Regulator with a r o t a t i n g c o i l probe. The f i e l d was swept s l o w l y , t y p i c a l l y through 100 G over 50 s, u s i n g disc-shaped "pancake" c o i l s mounted on the pole f a c e s . Small s i n u s o i d a l modulation o f about 1 G at an audio frequency f m was a p p l i e d p a r a l l e l t o "H u s i n g s m a l l c o i l s mounted i n s i d e the l i q u i d h e l i u m c r y o s t a t . The fundamental component of the modulated s i g n a l was d e t e c t e d by a PAR 122 l o c k - i n d e t e c t o r so as t o o b t a i n the d e r i v a t i v e of x " • In order t o maximize the s i g n a l t o n o i s e (S:N) r a t i o a l l experiments on TTF-TCNQ were performed i n the range 1.3 K t o 4.2 K. T h i s made i t p o s s i b l e t o use a l i q u i d h e lium cooled p r e a m p l i f i e r which had a n o i s e temperature of 8 K when operated at 4.2 K. A f t e r the RF s i g n a l was a m p l i f i e d by the preamp, i t was a m p l i f i e d a g a i n at room temperature be f o r e going i n t o a diode d e t e c t o r . The s i g n a l a t the frequency f m was then de t e c t e d by the l o c k - i n d e t e c t o r . The output of the l o c k - i n d e t e c t o r was added t o two sweep c a l i b r a t i o n markers i n the Sweep Marker Generator and then went i n t o a F a b r i t e k 1062 S i g n a l Averager. HP 461A AMP HP 8640A SIGNAL GENERATOR - HP 5327A TIMER-COUNTER TUNED CIRCUIT LIQUID HELIUM COOLED PREAMP LIQUID HELIUM HP 7100B CHART RECORDER FABRITEK 1062 SIGNAL out AVERAGER In sweep out r J KEPCO • BIPOLAR J OP-AMP J 36-5M SWEEP MARKER GENERATOR — v V W .5 fi MANGANIN RESISTOR mjsa PANCAKE COILS F i g u r e 9) B l o c k diagram o f t h e a p p a r a t u s . PAR 122 LOCK-IN AMP out signal in reference IEC F54A FUNCTION GENERATOR PAR 112 PREAMP HP 400D VOLTMETER v W -10 fl MODULATION COILS - 2 2 -2 ) S i g n a l : N o i s e O p t i m i z a t i o n The DMR s i g n a l o f d e u t e r a t e d TTF-TCNQ i s v e r y weak s o i t i s e s s e n t i a l t o make e v e r y e f f o r t t o m a x i m i z e t h e S:N r a t i o . The weak s i g n a l i s t h e r e s u l t o f a number o f u n f a v o u r a b l e c o n d i t i o n s : t h e d e n s i t y o f s p i n s i s low (14% o f t h a t i n H 2 O ) , t h e p a c k i n g f r a c t i o n o f t h e powdered sample i s low ( = 1 0 % ) , t h e g y r o m a g n e t i c r a t i o o f d e u t e r o n s i s s m a l l a n d , f i n a l l y , one i s w o r k i n g w i t h a v e r y b r o a d powder s p e c t r u m . Abragam (1961) has g i v e n a n a p p r o x i m a t e e q u a t i o n f o r t h e S :N r a t i o o f an NMR s p e c t r o m e t e r u n d e r t h e f o l l o w i n g c o n d i t i o n s : 1) no q u a d r u p o l e s p l i t t i n g ; 2 ) t h e s p i n l a t t i c e r e l a x a t i o n t i m e T|_ and t r a n s v e r s e r e l a x a t i o n t i m e T 2 a r e e q u a l ; 3) n e g l i g i b l e inhomogeneous b r o a d e n i n g by t h e magnet; 4) t h e RF f i e l d i s c h o s e n t o g i v e t h e maximum s i g n a l . T h i s means t h a t i f 2 H n i s t h e a m p l i t u d e o f t h e RF m a g n e t i c f i e l d , i t must s a t i s f y y 2H^2T^T2 = 1. I f Abragam's e q u a t i o n i s m o d i f i e d t o a l l o w Ti ^ T 2 , w h i c h i s t h e c a s e f o r TTF-TCNQ, one g e t s : S:N - yft 1(1+1) N n 12 F 2 ' . Q Vc 3 T 2 I 2 (kT) 3 A f T]_ J I I I - 4 where I = n u c l e a r s p i n F = n o i s e f i g u r e o f t h e d e t e c t i o n s y s t e m N = number o f s p i n s / u n i t volume o f t h e sample V c = volume o f t h e RF c o i l A f = b a n d w i d t h o f t h e d e t e c t i o n s y s t e m T = t e m p e r a t u r e k = B o l t z m a n n ' s c o n s t a n t - 23 -E q u a t i o n I I I - l i n c l u d e s a r e d u c t i o n by /8- b e c a u s e t h e d e r i v a t i v e o f t h e a b s o r p t i o n i s o b s e r v e d (Andrew, 1955) . The p a r a m e t e r s w h i c h a r e u n d e r t h e e x p e r i m e n t e r ' s c o n t r o l a r e Q, F, n , V c , T and A f . The maximum v a l u e o f to t h a t one c a n u s e i s l i m i t e d by t h e a v a i l a b l e m a g n e t i c f i e l d (13 k G i n t h e s e e x p e r i m e n t s ) s i n c e to' = y H a t r e s o n a n c e . The e q u a t i o n s u g g e s t s t h a t i t i s d e s i r a b l e t o make T a s l o w a s p o s s i b l e . T h e r e a r e two r e a s o n s f o r t h i s . The s t a t i c s u s c e p t i b i l i t y X 0 a T - 1 a n d t h e J o h n s o n n o i s e f r o m t h e t u n e d c i r c u i t i s p r o p o r t i o n a l t o T^. H o w e v e r , t h e s i t u a t i o n i s more c o m p l i c a t e d b e c a u s e b o t h Q a n d T]_ a r e t e m p e r a t u r e d e p e n d e n t . I f t h e Q w e r e l i m i t e d o n l y by l o s s e s i n t h e c o i l , i t w o u l d i n c r e a s e a s T d e c r e a s e d b e c a u s e i n t h e n o r m a l s k i n d e p t h r e g i o n —V Q a p 2 w h e r e p xs t h e r e s i s t i v i t y o f t h e c o i l m a t e r i a l . I n p r a c t i c e t h e r e w i l l be o t h e r l o s s e s a s w e l l s u c h a s d i s s i p a t i o n i n t h e c a p a c i t o r , c o i l h o l d e r , a n d t h e o u t e r s h i e l d w h i c h may o r may n o t d e c r e a s e a s q u i c k l y . The Q o f t h e s a m p l e r e s o n a n t c i r c u i t d e s c r i b e d h e r e i n c r e a s e d f r o m 95 a t room t e m p e r a t u r e t o a b o u t 850 a t 4.2 K. S i n c e t h e r e s i s t i v i t y o f c o m m e r c i a l c o p p e r d e c r e a s e s by a b o u t a f a c t o r o f 100 o v e r t h e same t e m p e r a t u r e r a n g e , t h e l o s s e s must be p r i m a r i l y i n t h e c o p p e r . Tj_ n o r m a l l y i n c r e a s e s a s T d e c r e a s e s . F o r some s u b s t a n c e s TJL may i n c r e a s e s u f f i c i e n t l y t h a t one i s b e t t e r o f f w o r k i n g a t h i g h e r t e m p e r a t u r e s . , H o w e v e r , t h i s i s n o t t h e c a s e f o r t h e DMR s i g n a l o f TTF-TCNQ. B e t w e e n 4.2 K a n d 1.3 K t h e d e u t e r o n r e l a x a t i o n t i m e c h a n g e d by o n l y a f a c t o r o f 3/2. T h i s g i v e s a n e x p e c t e d i m p r o v e m e n t i n S:N b e t w e e n 4.2 K and 1.3 K o f a b o u t 5 w h i c h was r e a l i z e d i n p r a c t i c e . A n a t t e m p t was made t o o b s e r v e t h e s i g n a l a t 77 K t o no a v a i l . - 24 -E q u a t i o n I I I - . 4 i m p l i e s t h a t one s h o u l d make t h e band w i d t h o f t h e d e t e c t i o n s y s t e m as n a r r o w as p o s s i b l e . T h i s c a n be done e i t h e r by m a k i n g t h e l o c k - i n d e t e c t o r t i m e c o n s t a n t l o n g , w h i c h r e q u i r e s a s l o w sweep r a t e , o r by k e e p i n g t h e t i m e c o n s t a n t s h o r t and a v e r a g i n g many f a s t sweeps i n a s i g n a l a v e r a g e r . The r e l a t i v e m e r i t s o f t h e two t e c h n i q u e s a r e d i s c u s s e d i n s e c t i o n I I I - 4 . I t h as a l r e a d y been m e n t i o n e d t h a t f o r TTF-TCNQ t h e S :N c a n be i m p r o v e d by c o o l i n g , t h e a p p a r a t u s t o l i q u i d h e l i u m t e m p e r a t u r e s b e c a u s e o f t h e f a c t o r Q 2 T ^ xn e q u a t i o n III-4 . A f a c t o r o f T - 1 improvement r e s u l t s f r o m s i m p l y c o o l i n g t h e s a m p l e . The a d d i t i o n a l Q 2 T 2 improvement o n l y a r i s e s i f t h e e n t i r e t u n e d c i r c u i t i s c o o l e d . C o n s i d e r t h e c a s e o f a p a r a l l e l r e s o n a n t c i r c u i t where t h e sample c o i l i s c o o l e d b u t t h e t u n i n g c a p a c i t o r and t h e p r e a m p l i f i e r a r e n o t . The p r e a m p l i f i e r i s assumed t o have i n f i n i t e i n p u t r e s i s t a n c e b u t f i n i t e i n p u t c a p a c i t a n c e . I t wo u l d be n e c e s s a r y t o have a c o a x i a l c a b l e b etween t h e c o i l and t u n i n g c a p a c i t o r . S i n c e t h e c a b l e goes f r o m 4.2 K t o 295 K i t w o u l d r e q u i r e low t h e r m a l c o n d u c t i v i t y w h i c h g e n e r a l l y i m p l i e s a r e l a t i v e l y h i g h e l e c t r i c a l r e s i s t a n c e . T h i s w o u l d l o w e r t h e Q and i t w o u l d i n c r e a s e t h e e f f e c t i v e n o i s e t e m p e r a t u r e o f t h e t u n e d c i r c u i t b e c a u s e much o f t h e c i r c u i t w o u l d be above 4.2 K. The c i r c u i t c a n be im p r o v e d by c o o l i n g t h e c a p a c i t o r but t h e f u l l b e n e f i t i s s t i l l n o t a c h i e v e d b e c a u s e t h e d i s t r i b u t e d c a p a c i t a n c e o f t h e c o a x i a l c a b l e and t h e i n p u t c a p a c i t a n c e o f t h e preamp f o r m p a r t o f t h e t u n e d c i r c u i t . The f u l l e f f e c t o f t h e f a c t o r Q^ T - ^ c a n o n l y be a t t a i n e d by c o o l i n g t h e p r e a m p l i f i e r s i n c e i t forms p a r t o f t h e t u n e d c i r c u i t . I n t h e p r e s e n t s y s t e m we have u s e d a Ge J F E T p r e a m p l i f i e r w h i c h c a n be c o o l e d t o 4.2 K (Hardy and G r a y , 1 9 6 9 ) . U s i n g a n NMR s i g n a l , t h e n o i s e f i g u r e o f t h e preamp was measured t o be ~ 2 f o r a matched s o u r c e r e s i s t a n c e - 25 -at 4.2 K. This agrees q u i t e w e l l with the r e s u l t s of Hardy and Gray (1969). The cooled preamp does have the disadvantage of i n c r e a s i n g the l i q u i d h e lium b o i l - o f f r a t e . At 4.2 K, about h a l f o f the b o i l - o f f was due t o power d i s s i p a t i o n i n the preamp. 3) The Tuned C i r c u i t A diagram of the bottom end of the c r y o s t a t i s shown i n F i g . 10. I t s d e s i g n was governed by t h r e e g u i d i n g p r i n c i p l e s : t o maximize the Q, t o keep H atoms away from the c o i l so that the proton resonance of TTF-TCNQ c o u l d be s t u d i e d , and t o minimize m i c r o p h o n i c s . The f i r s t two o b j e c t i v e s were q u i t e s u c c e s s f u l but, except a t the lowest RF and modulation l e v e l s used , t h e r e remained some microphonic pickup caused by the modulation f i e l d . The c o a x i a l c a b l e s a t the bottom end of the c r y o s t a t were copper and the s o l d e r j o i n t s i n the tuned c i r c u i t were made with pure indium s o l d e r . Although indium doesn't become superconduct-in g because of the 13 kG magnetic f i e l d , i t has a very low normal s t a t e r e s i s t i v i t y a t 4.2 K because of i t s high p u r i t y . The inner s u r f a c e s of the outer brass s h i e l d were e l e c t r o p l a t e d with copper t o reduce eddy c u r r e n t l o s s e s . The c o i l h o l d e r was c o n s t r u c t e d from T e f l o n because i t i s a v e r y low l o s s d i e l e c t r i c and i t c o n t a i n s no p r o t o n s . The modulation c o i l s were c o n s t r u c t e d from Formvar coated copper wire and cemented i n p l a c e u s i n g a low l o s s c o i l c o a t i n g o f d i s s o l v e d p o l y s t y r e n e . F i n a l l y , they were wrapped i n T e f l o n t a p e . The s m a l l r e s i d u a l proton s i g n a l t h at was observed with the sample removed came from the modulation c o i l s and the B a k e l i t e rods screwed i n t o the c o i l h o l d e r . COPPER COAXIAL — CABLE FROM THE SIGNAL GENERATOR TEFLON COIL FORMER-i i i -COPPER COAXIAL CABLE TO THE . PREAMP • BAKELITE ROD •COPPER-PLATED BRASS SHIELD • TUNING CAPACITOR •MODULATION COILS RF COILf' F i g u r e 10) Schematic cut-away diagram o f t h e bottom end o f the c r y o s t a t . - 2 7 -The 400 pF t u n i n g c a p a c i t a n c e c o n s i s t e d o f a 100 pF and a 300 pF r e c t a n g u l a r s i l v e r e d - m i c a c a p a c i t o r s ( S p r a g u e ) . The Q's were measured a t room t e m p e r a t u r e t o be a b o u t 1400 u s i n g a n HP 4342A Q m e t e r . The RF c o i l c o n s i s t e d o f 11 t u r n s o f b a r e 26 AWG c o p p e r w i r e wrapped on a t h i n , g r o o v e d T e f l o n c y l i n d e r . The c o i l was wrapped i n T e f l o n t a p e and f i t s n u g l y i n s i d e t h e m o d u l a t i o n c o i l f o r m . A 200 mg TTF-TCNQ powder sample was p l a c e d i n a p y r e x t u b e w h i c h had b e e n drawn o v e r a c a r b o n m a n d r i l t o r e d u c e t h e w a l l t h i c k n e s s t o .4 mm. The t u b e s were e v a c u a t e d , f i l l e d w i t h He gas and s e a l e d . They f i t s n u g l y i n t h e c o i l f o r m when i t was c o o l e d t o 77 K o r b e l o w . I n o r d e r t o m i n i m i z e t h e n o i s e f i g u r e o f t h e preamp t h e impedance a c r o s s i t s i n p u t must be r e a l and i t must be matched t o t h e T1XM12 J F E T ' s a t t h e preamp i n p u t . The optimum s o u r c e r e s i s t a n c e i s t h e v a l u e t h a t makes t h e c u r r e n t n o i s e e q u a l t o t h e v o l t a g e n o i s e . A t 4.2 K, f o r t h e p a r t i c u l a r d e v i c e s u s e d , i t i s 2.9 k f i (Hardy and G r a y , 1 9 6 9 ) . A t 4.2 K, t h e t u n e d c i r c u i t h as a Q o f 850 g i v i n g i t an e q u i v a l e n t p a r a l l e l r e s i s t a n c e o f 41 k f i S i n c e t h i s g r e a t l y e x c e e d s t h e optimum v a l u e , a m a t c h i n g n e t w o r k i s r e q u i r e d . The n e t w o r k u s e d i s shown i n F i g . 1 1 a . I n t h e d i a g r a m : R = e q u i v a l e n t p a r a l l e l r e s i s t a n c e o f t h e t u n e d c i r c u i t Z-JL - impedance a c r o s s t h e c o i l Z Q = o u t p u t impedance o f t h e m a t c h i n g c i r c u i t C]^ i n c l u d e s t h e c a p a c i t a n c e o f t h e c o a x i a l c a b l e f r o m t h e m a t c h i n g c i r c u i t t o t h e t u n e d c i r c u i t C 3 i n c l u d e s t h e i n p u t c a p a c i t a n c e o f t h e preamp (~ 7pF) 295 K 4.2 K HP 8640A SIGNAL GENERATOR 6=n 1' pF J 50ft 0 T - i - i r\r\ —*— 20 pF PREAMP R 1 100 'pF 300 pF 47 PF I (b) F i g u r e 11) The tuned c i r c u i t and matching network. - 29 -I t i s easy t o show that : Z i = 0,-L + i£(coL - 4.) 1 1 1 - 5 where C = Ci .+ 2 3 C2+C3 The resonance c o n d i t i o n f o r Vj_ i s co ^ LC = 1. Note t h a t because the matching impedances are both c a p a c i t i v e , V Q i s i n phase with Vj_ and i s a l s o maximum when co2LC = 1 . By s t r a i g h t -forward but t e d i o u s c a l c u l a t i o n , one can o b t a i n the f o l l o w i n g e x p r e s s i o n f o r Z 0 : Z = 1 + i Q (co^L C a -1) T T T _ ^ O •„,. r,. r i j . •,' / , - . V2T r. T V i 111-6 ICO ) C b [ 1 + iQ OA^LC -1) ] where C a = C^ + C2 C b = C 2 + C 3 Note t h a t although Zj_ i s r e a l a t resonance , Z Q i s i n g e n e r a l complex. However, i t can be made approximately r e a l by choosing C2 and C3 so t h a t they s a t i s f y : c 2 + c 3 R >> c 2 2 C2 and C3 were chosen to be 20 pF and 54 pF r e s p e c t i v e l y which made Zo = 2.9 k fi at 4 . 2 K as r e q u i r e d . The r e s u l t s of the a n a l y s i s above were confirmed at room temperature w i t h an HP 4815 A RF V e c t o r Impedance Meter s i n c e the v alue o f the input c a p a c i t a n c e of the preamp wasn't w e l l known. The tuned c i r c u i t i s shown i n F i g . l i b . The 1 pF, 20 pF and 47 pF c a p a c i t o r s were C o r n e l l - D u b l i e r epoxy-dipped s i l v e r e d mica. The 100 pF and 300 pF c a p a c i t o r s were r e c t a n g u l a r Sprague s i l v e r e d -- 30 -mica. The capacitance of the cable from the tuned c i r c u i t to the matching network was about 10 pF. Some e f f o r t was expended in measuring the Q's of various capacitors at room temperature with an HP 4342 A Q-meter. Sprague rectangular silvered-mica capacitors had the highest Q's (about 1400). Cornell-Dublier rectangular silvered-mica capacitors had Q's almost as high. One might expect a capacitor with a Teflon d i e l e c t r i c to have a higher Q because the d i s s i p a t i o n i n Teflon i s lower than in mica. However, we didn't have any Teflon capacitors. The Cornell-Dublier epoxy dipped silvered-mica capacitors had lower Q's than the rectangular ones - about 800 for the 20 pF and 47 pF capacitors and about 500 for the miniature 1 pF capacitor. The 1 pF, 100 pF and 300 pF capacitors were non-magnetic. The 20 pF arid 47 pF capacitors were magnetic but they were situated about 30 cm away from the RF c o i l . 4) F i e l d Sweep and Modulation It has already been mentioned that there are two basic approaches to making the bandwidth A f of the detection system narrow. One can use a few slow sweeps with a long lock-in detector time constant or many fast sweeps with a short time constant . If the noise spectrum at the output of the lock-in i s white and there is no saturation of the resonance s i g n a l , then the two techniques are equally e f f i c i e n t . In each case A f~~^- i s proportional to the t o t a l observation time.. However, fast scans ac t u a l l y have several advantages over slow scans. In practice noise i s n ' t white: there i s always excess noise at low frequencies. This type of noise amounts to a d r i f t i n the - 31 -b a s e l i n e d u r i n g a l o n g s c a n b u t i t i s a p p r o x i m a t e l y c o n s t a n t d u r i n g a s h o r t s c a n so i t o n l y r e s u l t s i n a DC o f f s e t f r o m one s c a n t o t h e n e x t . A s i n g l e s c a n w i t h a l o n g t i m e c o n s t a n t i s more s e n s i t i v e t o s t r o n g but b r i e f d i s t u r b a n c e s s u c h as e l e c t r i c a l e q u i p ment b e i n g t u r n e d on i n a n o t h e r p a r t o f t h e room. I f one u s e s t h e a v e r a g e o f many s c a n s , t h e e f f e c t o f t h e d i s t u r b a n c e w i l l be s l i g h t b e c a u s e i t a p p e a r s on o n l y one s c a n . A f u r t h e r c o n s i d e r a t i o n i s t h a t i n o r d e r t o g e t maximum S:N one must s a t u r a t e t h e r e s o n a n c e s i g n a l somewhat. The amount o f s a t u r a t i o n depends upon t h e amount o f power a p p l i e d and t h e l e n g t h o f t i m e f o r w h i c h i t i s a p p l i e d . By u s i n g many f a s t s c a n s t h e s p i n s a r e s a t u r a t e d e v e n l y ( i f t h e y a l l h a v e t h e same s a t u r a t i o n t i m e ) s o t h a t t h e m a g n i t u d e o f t h e s i g n a l d e c r e a s e s u n i f o r m l y . On t h e o t h e r h a n d , i n a s l o w s c a n some s p i n s a r e s a t u r a t e d b e f o r e t h e o t h e r s s o t h a t t h e l i n e s h a p e w i l l be d i s t o r t e d . F i n a l l y , w i t h f a s t s c a n s one c a n w a t c h t h e s i g n a l b u i l d up and s t o p t h e s c a n s when s a t u r a t i o n becomes t o o s e v e r e . I f a s i n g l e s l o w s c a n i s u s e d , t h e e n t i r e s c a n i s w a s t e d i f s a t u r a t i o n i s t o o s e v e r e . F o r t h e r e a s o n s c i t e d a b o v e t h e f a s t s c a n t e c h n i q u e a p p e a r s t o be c o n s i d e r a b l y more a t t r a c t i v e t h a n t h e s l o w o n e . O r i g i n a l l y we h a d i n t e n d e d t o t a k e t h e f o r m e r method t o i t s e x t r e m e l i m i t by u s i n g sweep r a t e s o f 20-100 Hz and e l i m i n a t i n g t h e l o c k - i n d e t e c t o r and s m a l l m o d u l a t i o n . 3y t h i s method one o b t a i n s t h e a b s o r p t i o n s i g n a l d i r e c t l y , r a t h e r t h a n i t s d e r i v a t i v e , s o t h a t t h e r e i s a n a d d i t i o n a l f a c t o r o f / 8 improvement i n S :N. A c r y o s t a t was b u i l t w h i c h was t h e same as t h e one d e s c r i b e d above a p a r t f r o m some m o d i f i c a t i o n s t o t h e b o t t o m e n d . The m o d u l a t i o n c o i l s w e r e n ' t r e q u i r e d s o t h e d i a m e t e r o f t h e RF - 32 -c o i l c o u l d be l a r g e r . T h i s i n c r e a s e d i t s Q and more i m p o r t a n t l y the f i l l i n g f a c t o r . A l s o the s u p p o r t i n g rods f o r the T e f l o n c o i l form were copper r a t h e r t h a n B a k e l i t e . There were no H atoms near the RF c o i l . The sweep f i e l d was produced by pancake c o i l s mounted on t h e p o l e f a c e s o f the magnet. The c r y o s t a t j u s t d e s c r i b e d was an u n q u a l i f i e d d i s a s t e r because o f v e r y s e v e r e m i c r o p h o n i c s t h a t r e s u l t e d from the i n t e r a c t i o n o f eddy c u r r e n t s induced by t h e sweep f i e l d w i t h t h e s t a t i c magnetic f i e l d . . . The sweep c o i l s produce eddy c u r r e n t s i n any c o n d u c t o r between them so t h a t the c o n d u c t o r w i l l have an o s c i l l a t i n g magnetic moment. U n l e s s the shape o f t h e c o n d u c t o r has a c e r t a i n symmetry and t h e sweep f i e l d i s e x a c t l y p a r a l l e l t o the s t a t i c f i e l d H, t h e magnetic moment w i l l have a component p e r p e n d i c u l a r t o ft*. T h i s i n d u c e s a t o r q u e on the c o n d u c t o r c a u s i n g i t t o move. Any m o t i o n o f c o n d u c t o r s near t h e RF c o i l c auses a s h i f t i n t h e tuned c i r c u i t resonance f r e q u e n c y which r e s u l t s i n a m p l i t u d e m o d u l a t i o n o f the RF v o l t a g e a c r o s s t h e c o i l . S i n c e t h e induced magnetic moments have the same t i m e dependence as the sweep f i e l d , c o h e r e n t i n t e r f e r e n c e r e s u l t s . T h i s form o f i n t e r f e r e n c e was p a r t i c u l a r l y s e v e r e f o r t h e system d e s c r i b e d above. The Q was v e r y h i g h so t h a t s m a l l s h i f t s i n t h e resonance f r e q u e n c y caused l a r g e a m p l i t u d e m o d u l a t i o n . I n a d d i t i o n , t h e resonance s i g n a l was q u i t e broad so l a r g e sweep f i e l d s , up t o 100 G, were r e q u i r e d . The pancake c o i l s were q u i t e l a r g e , i n o r d e r t o produce a homogeneous f i e Id , so t h a t eddy c u r r e n t s were induced over the e n t i r e bottom end o f the c r y o s t a t . S i n c e t h e c o n d u c t i v i t y o f the m e t a l p a r t s was h i g h , p a r t i c u l a r l y when the c r y o s t a t was c o o l e d , the eddy c u r r e n t s were v e r y l a r g e . - 33 -A l t h o u g h t h e c o h e r e n t i n t e r f e r e n c e was w o r s t a t low t e m p e r a t u r e s , i t was s i g n i f i c a n t a t room t e m p e r a t u r e as w e l l . I n f a c t i f one s i m p l y h e l d a b r a s s r o d i n t h e magnet gap w i t h t h e sweep c o i l s and magnet on, t h e r e was n o t i c e a b l e v i b r a t i o n . I n o r d e r t o r e d u c e t h e c o h e r e n t i n t e r f e r e n c e , t h e c r y o s t a t d e s i g n was m o d i f i e d s o t h a t s l o w sweeps and s m a l l s i n u s o i d a l m o d u l a t i o n w i t h l o c k - i n d e t e c t i o n c o u l d be u s e d . M e t a l p a r t s n e a r t h e RF c o i l were e l i m i n a t e d a s much as p o s s i b l e . S m a l l m o d u l a t i o n c o i l s mounted i n t h e c r y o s t a t were u s e d s o t h a t t h e m o d u l a t i o n f i e l d e x t e n d e d o v e r a much s m a l l e r r e g i o n o f t h e c r y o s t a t t h a n t h e sweep f i e l d . The m o d u l a t i o n f i e l d was o n l y r e q u i r e d t o be a b o u t 1 G w h i c h i s much l e s s t h a n t h e 100 G sweep f i e l d . The c r y o s t a t was r o t a t e d t o m i n i m i z e t h e m o d u l a t i o n p i c k u p by a l i g n i n g t h e a x i s o f t h e m o d u l a t i o n c o i l s p a r a l l e l t o t h e s t a t i c f i e l d . The p i c k u p was f u r t h e r r e d u c e d by c a r e f u l t u n i n g o f t h e s i g n a l g e n e r a t o r f r e q u e n c y . When i t i s e x a c t l y e q u a l t o t h e t u n e d c i r c u i t r e s o n a n c e f r e q u e n c y , t h e a m p l i t u d e m o d u l a t i o n r e s u l t i n g f r o m s m a l l s h i f t s i n t h e t u n e d c i r c u i t r e s o n a n c e f r e q u e n c y i s z e r o t o f i r s t o r d e r . The f r e q u e n c y was t u n e d by f r e q u e n c y m o d u l a t i n g t h e s i g n a l g e n e r a t o r a t t h e l o c k - i n d e t e c t o r r e f e r e n c e f r e q u e n c y . F o r s m a l l m o d u l a t i o n , t h e s i g n a l a t t h e o u t p u t o f t h e l o c k - i n d e t e c t o r was t h e d e r i v a t i v e o f t h e t u n e d c i r c u i t r e s o n a n c e c u r v e and was a n u l l a t r e s o n a n c e . E v e n w i t h t h e s e p r e c a u t i o n s , t h e m o d u l a t i o n p i c k u p w a s n ' t c o m p l e t e l y e l i m i n a t e d . However, i t amounted t o o n l y a c o n s t a n t o f f s e t a t t h e low RF and m o d u l a t i o n a m p l i t u d e s r e q u i r e d f o r t h e TTF-TCNQ r e s o n a n c e s i g n a l s a t 4 K. - 34 -The f i e l d sweep c i r c u i t i s shown i n F i g . 9. The sweep c o i l s , which were mounted on t h e p o l e f a c e s o f t h e magnet, were d r i v e n by a Kepco B i p o l a r Op-Amp 36-5M o p e r a t e d as a v o l t a g e c o n t r o l l e d c u r r e n t s o u r c e . The c o n t r o l v o l t a g e was t h e "sweep o u t " s i g n a l from the F a b r i t e k 1062 S i g n a l A v e r a g e r . The "sweep o u t " v o l t a g e was p r o p o r t i o n a l t o t h e s i g n a l a v e r a g e r c h a n n e l number. A .5 ohm Manganin w i r e r e s i s t o r was used as the c u r r e n t sense r e s i s t o r f o r t h e Kepco BOP s i n c e t h e r e was s i g n i f i c a n t h e a t i n g and hence change i n r e s i s t a n c e o f t h e copper pancake c o i l s . The manganin w i r e was h eated t o o but i t has a much lower t e mperature c o e f f i c i e n t of r e s i s t i v i t y t h a n c o p p e r . The Magnion FFC-4 F i e l d R e g u l a t o r c o n t r o l l e d t h e magnetic f i e l d by comparing t h e s i g n a l from a r o t a t i n g c o i l probe w i t h a r e f e r e n c e v o l t a g e . I f t h e probe senses the sweep f i e l d , t h e magnet w i l l r e g u l a t e a g a i n s t i t . One can p r e v e n t t h i s by making the o u t e r d i a m e t e r o f t h e sweep c o i l s l e s s t h a n the d i a m e t e r o f the p o l e f a c e s and p o s i t i o n i n g the probe so t h a t i t i s i n a r e g i o n where the sweep f i e l d p e r p e n d i c u l a r t o t h e probe i s n e a r l y z e r o . T h i s i s shown i n F i g . 12. The probe c o u l d be p o s i t i o n e d so t h a t i t d e t e c t e d l e s s t h a n one t h o u s a n d t h o f t h e sweep f i e l d a t t h e sample. A t t h a t p o s i t i o n , t h e s t a t i c f i e l d sensed by t h e probe was about 500 G l e s s t h a n t h e f i e l d a t the sample when a 13 kG f i e l d was a p p l i e d . The v o l t a g e a c r o s s the manganin sense r e s i s t o r , which i s p r o p o r t i o n a l t o t h e c u r r e n t i n t h e sweep c o i l s , was used t o t r i g g e r two marker p u l s e s i n the Sweep Marker G e n e r a t o r . These were added t o t h e l o c k - i n d e t e c t o r o u t p u t b e f o r e i t went i n t o t h e s i g n a l a v e r a g e r . The p u l s e s a l l o w e d one t o c a l i b r a t e the sweep - 35 -ROTATING COIL PROBE PANCAKE COILS F i g u r e 12) P o s i t i o n o f the r o t a t i n g c o i l probe so t h a t t h e component o f the f i e l d o f the pancake c o i l s p e r -p e n d i c u l a r t o t h e r o t a t i n g c o i l probe i s n u l l e d . - 36 -and t o c h e c k f o r d r i f t i n t h e sweep. No d r i f t was e v e r o b s e r v e d s o i t must have been l e s s t h a n one c h a n n e l w i d t h o f t h e s i g n a l a v e r a g e r o v e r s e v e r a l h o u r s . The sweep was c a l i b r a t e d as a f u n c t i o n o f t h e s e n s e v o l t a g e and t h e l i n e a r i t y was c h e c k e d u s i n g t h e DMR o f D 2 0 a t room t e m p e r a t u r e . The m a g n e t i c f i e l d was. k e p t f i x e d and t h e f r e q u e n c y was c h a n g e d . S i n c e t h e t u n e d c i r c u i t h a d a f i x e d r e s o n a n c e f r e q u e n c y , a s m a l l amount o f d i s p e r s i o n was mixed i n t o t h e r e s o n a n c e s i g n a l when i t was n e a r t h e ends o f t h e sweep. The s t a t i c m a g n e t i c f i e l d was c a l i b r a t e d d u r i n g each r u n b e c a u s e t h e m a g n e t i c f i e l d d i f f e r e d by a few g a u s s each t i m e i t was t u r n e d on t o 13 kG. The r e s o n a n c e s i g n a l o f s o l i d d e u t e r i u m (33% para-D2) a t 4 K was u s e d f o r t h i s p u r p o s e . 5) H o m o g e n e i t y The l i n e w i d t h o f t h e DMR s i g n a l o f TTF (d Q)-TCNQ ( d 4 ) was n a r r o w enough (2.8 G FWHM) t h a t some c a r e was r e q u i r e d i n p o s i t i o n i n g t h e sample i n t h e magnet g a p . I t s h o u l d be i n t h e r e g i o n o f maximum h o m o g e n e i t y i n o r d e r t o m i n i m i z e inhomogeneous b r o a d e n i n g b y t h e magnet.. T h i s was done a t 4.2 K by v a r y i n g t h e c r y o s t a t p o s i t i o n u n t i l t h e b e s t D 2 s i g n a l was o b t a i n e d . S i n c e t h e c r y o s t a t c o n t r a c t s by a b o u t 3 mm f r o m room t e m p e r a t u r e t o 4.2 K, t h e p o s i t i o n i n g had t o be done a t low t e m p e r a t u r e . F i r s t t h e b e s t s i g n a l was o b t a i n e d w i t h no c u r r e n t i n t h e sweep c o i l s . A s m a l l sweep c u r r e n t was r u n t h r o u g h t h e m o d u l a t i o n c o i l s s o t h a t t h e r e s o n a n c e c o u l d be o b s e r v e d on a n o s c i l l o s c o p e . Some f a i r l y inhomogeneous s h i m c o i l s were mounted on t h e p o l e f a c e s o f t h e magnet and t h e DC c u r r e n t t h r o u g h them was v a r i e d u n t i l t h e - 37 -b e s t s i g n a l was o b t a i n e d . The l i n e s h a p e was n o t v e r y s e n s i t i v e t o t h e s h i m c o i l c u r r e n t i n t h e r e g i o n o f t h e maximum h o m o g e n e i t y . Then l a r g e p o s i t i v e and n e g a t i v e DC c u r r e n t s were r u n t h r o u g h t h e sweep c o i l s and t h e r e s o n a n c e s i g n a l was o b s e r v e d i n e a c h c a s e . The maximum c u r r e n t s t h a t c o u l d be s u p p l i e d by t h e Kepco op-amp were u s e d , c o r r e s p o n d i n g t o f i e l d s o f t 80 G. The s h i m c o i l c u r r e n t was t h e n v a r i e d . As one w o u l d e x p e c t , i t wasn't p o s s i b l e t o m a x i m i z e t h e h o m o g e n e i t y a t b o t h ends o f t h e sweep s i m u l t a n e o u s l y s o t h e b e s t compromise was o b t a i n e d . The l i n e s h a p e s o b t a i n e d w i t h l a r g e DC c u r r e n t s i n t h e sweep c o i l s were much more s e n s i t i v e t o t h e s h i m c o i l c u r r e n t t h a n t h e l i n e s h a p e o b t a i n e d w i t h z e r o c u r r e n t i n t h e sweep c o i l s . Once t h e s h i m c o i l c u r r e n t was a d j u s t e d f o r t h e b e s t h o m o g e n e i t y a t t h e ends o f t h e sweep, t h e i n c r e a s e i n l i n e w i d t h a t t h e c e n t r e o f t h e sweep was n e g l i g i b l e . The s i g n a l s a t t h e ends o f a t 80 G sweep were % 5% b r o a d e r t h a n t h e s i g n a l a t t h e c e n t r e . The peak t o peak l i n e w i d t h o f t h e d e r i v a t i v e o f t h e D 2 a b s o r p t i o n s i g n a l was measured t o be 1.69 .05 G. The measurement was made w i t h H]_. = .50 mG and a m o d u l a t i o n w i d t h o f .12 G. A t t h a t RF l e v e l t h e r e was n e g l i g i b l e s a t u r a t i o n . The s i g n a l was s l i g h t l y a s y m m e t r i c , one peak b e i n g a b o u t 3% h i g h e r t h a n t h e o t h e r . T h i s seems t o be an. i n h o m o g e n e i t y e f f e c t . W. N. H a r d y ( p r i v a t e c o m m u n i c a t i o n ) has g i v e n t h e l i n e w i d t h a s 1.7 G s o t h e b r o a d e n i n g due t o t h e magnet i n h o m o g e n e i t y i s i n s i g n i f i c a n t . T h i s c o n c l u s i o n i s s u p p o r t e d by t h e o b s e r v a t i o n o f t h e DMR s i g n a l o f D2O a t room t e m p e r a t u r e . The l i n e w i d t h was measured t o be .19 G w h i c h i s due e n t i r e l y t o t h e magnet i n h o m o g e n e i t y . S i n c e t h e d e u t e r o n l i n e w i d t h (FWHM) o f TTF (d Q)-TCNQ ( d 4 ) was 2.8 G t h e b r o a d e n i n g due t o t h e magnet i n h o m o g e n e i t y c a n be n e g l e c t e d . - 38 -C h a p t e r IV  RESULTS The low f i e l d h a l f o f t h e d e r i v a t i v e o f t h e d e u t e r o n a b s o r p t i o n s i g n a l o f TTF ( d Q ) -TCNQ ( d 4 ) i s shown i n F i g . 13 and 14. F i g . 13 shows t h e mai n g r o u p o f s a t e l l i t e peaks - t h e d e r i v a t i v e o f t h e s h o u l d e r and t h e s i n g u l a r i t y . F i g . 14 shows one o f t h e s m a l l o u t e r peaks - t h e d e r i v a t i v e o f t h e s t e p . F i g . 15 was o b t a i n e d by i n t e g r a t i n g t h e c u r v e i n F i g . 13 on t h e s i g n a l a v e r a g e r . The s p e c t r a were o b t a i n e d i n a 13 kG m a g n e t i c f i e l d a t a t e m p e r a t u r e o f 1.3 K. A t 1.3 K t h e d e u t e r o n s p i n - l a t t i c e r e l a x a t i o n t i m e T i was o f t h e o r d e r o f 1600 s s o v e r y low RF l e v e l s were r e q u i r e d t o a v o i d s a t u r a t i o n . S i n c e T i i s much g r e a t e r t h a n t h e t i m e f o r a s i n g l e s c a n (50 s ) , i t i s p o s s i b l e t h a t a l t h o u g h t h e r e i s no n o t i c e a b l e s a t u r a t i o n a f t e r a s i n g l e s c a n , s a t u r a t i o n may become s u b s t a n t i a l a f t e r s e v e r a l s c a n s have a c c u m u l a t e d i n t h e s i g n a l a v e r a g e r . F i g . 13 was o b t a i n e d f r o m t h e a c c u m u l a t i o n o f 42 s c a n s o f 50 s e a c h a t an RF l e v e l o f Hi = .41 mG. A f t e r t h e s c a n s were c o m p l e t e d , a s i n g l e s c a n was made at h i g h e r RF and m o d u l a t i o n l e v e l s . The s i g n a l was f o u n d t o be b a d l y d i s t o r t e d . However, w h i l e m a k i n g t h e 42 s c a n s t h e s i g n a l was r e c o r d e d a f t e r 8, 16, and 32 s c a n s . T h e r e was no n o t i c e a b l e i n c r e a s e i n d i s t o r t i o n between them s o i t seems t h a t F i g . 13 i s r e l a t i v e l y u n d i s t o r t e d . O t h e r r u n s w i t h l o w e r S:N r a t i o s h a v e been made a t RF l e v e l s down t o Hi = .084 mG. A f t e r t h e s e r u n s , a s i n g l e s c a n a t h i g h e r RF and m o d u l a t i o n l e v e l s was u n d i s t o r t e d s o no s i g n i f i c a n t d i s t o r t i o n by s a t u r a t i o n had o c c u r r e d . 10 G WIDTH gure 13) Low f i e l d main s a t e l l i t e peaks of T T F ( d Q ) - T C N Q ( d ^ ) d e r i v a t i v e DMR s i g n a l , 42 scans o f 50 s each w i t h H. ,41 mG. - 40 -MODULATION 10 G WIDTH h: F i g u r e 14) Low f i e l d o u t e r peak o f the TTF(d )-TCNQ(d 4) d e r i -v a t i v e DMR s i g n a l . 32 scans o f 50 s each w i t h H 1 = .39 mG. F i g u r e 15) I n t e g r a l o f F i g . 13. - 42 -C o m p a r i s o n o f t h e s e s c a n s w i t h F i g . 13 i n d i c a t e d t h a t no s i g n i f i c a n t d i s t o r t i o n had o c c u r r e d i n F i g . 13. The o u t e r peak shown i n F i g . 14 i s t h e a c c u m u l a t i o n o f 32 s c a n s w i t h H]_ = .39 mG. B e c a u s e t h e o u t e r peaks a r e much weaker t h a n t h e m a i n peaks i t was n e c e s s a r y t o i n c r e a s e t h e m o d u l a t i o n a m p l i t u d e o v e r t h a t u s e d i n F i g . 13 by a f a c t o r o f two. T h i s i n c r e a s e d t h e l i n e w i d t h by a b o u t 10%. C o m p a r i s o n o f F i g . 13-1.5 w i t h F i g . 7 shows t h a t t h e DMR s p e c t r u m o f TTF-TCNQ ( d 4 ) i s q u i t e s i m i l a r t o t h e computer g e n e r a t e d s p e c t r a o f B a r n e s and Bloom e x c e p t t h a t t h e homogeneous b r o a d e n i n g o f t h e TTF-TCNQ ( d 4 ) s i g n a l i s much l e s s . T h e r e i s no o b v i o u s m a n i f e s t a t i o n o f a CDW. I t was p o i n t e d o u t i n C h a p t e r I t h a t a t 54 K TTF-TCNQ u n d e r g o e s a s i n u s o i d a l l a t t i c e d i s t o r t i o n w h i c h i s p o l a r i z e d p r i m a r i l y (or p e r h a p s t o t a l l y ) a l o n g t h e b a x i s . The m o d u l a t i o n p e r i o d i n t h e a d i r e c t i o n depends upon t h e d i f f e r e n c e i n phase o f t h e d i s t o r t i o n on a d j a c e n t TTF and TCNQ c h a i n s . G i v e n t h a t t h e m o d u l a t i o n p e r i o d i n t h e b d i r e c t i o n i s 3^4 b, t h e s e r e s u l t s a r e c o n s i s t e n t w i t h t h e model o f a ID c o n d u c t i o n band w i t h a c h a r g e t r a n s f e r p e r m o l e c u l e p s u c h t h a t : P - - f " (2 kp) - V - f - L - -59 IV-1 One c a n g e t a n e s t i m a t e , o f t h e maximum p o s s i b l e e f f e c t o f a CDW by c o m p a r i n g t h e QCC's o f TCNQ ( d 4 ) and TTF-TCNQ ( d 4 ) . The c h a r g e on t h e T C N Q - i o n makes a c o n t r i b u t i o n t o t h e EFG n o t p r e s e n t i n n e u t r a l TCNQ. L e t us assume t h a t below 38 K t h e r e i s a p i n n e d , i n c o m m e n s u r a t e CDW a l o n g t h e TCNQ c h a i n s t h a t c o n s i s t s - 43 -o f a s i n u s o i d a l m o d u l a t i o n o f t h e c h a r g e d e n s i t y a l o n g t h o s e c h a i n s . S i n c e t h e c h a r g e t r a n s f e r r e d f r o m t h e TCNQ t o t h e TTF goes i n t o t h e ID . c o n d u c t i o n band d e s c r i b e d a b o v e , t h e maximum p o s s i b l e a m p l i t u d e o f t h e CDW i s e q u a l t o t h e d i f f e r e n c e i n t h e a v e r a g e c h a r g e d e n s i t y i n T C N Q - * 6 and n e u t r a l TCNQ. C o n s e q u e n t l y we l o o k e d f o r t h e d e u t e r o n r e s o n a n c e s i g n a l o f TCNQ ( d 4 ) . F i g . 16 shows t h e a c c u m u l a t i o n o f 18 s c a n s o f 50 s ea c h u s i n g a n RF l e v e l o f Hi = .53 mG. The r e l a x a t i o n t i m e wasn't measured b e c a u s e o f t h e p o o r S:N r a t i o but j u d g i n g f r o m t h e s a t u r a t i o n e f f e c t s i t a p p e a r s t o be o f t h e o r d e r o f a n h o u r o r more. T h e r e a p p e a r s t o be some d i s t o r t i o n o f t h e l i n e s h a p e shown i n F i g . 16 but i t i s o n l y o f t h e same m a g n i t u d e as t h e n o i s e . One o f t h e m a j o r r e a s o n s f o r t h e d i f f i c u l t i e s i n o b s e r v i n g t h e DMR o f TTF-TCNQ ( d 4 ) and TCNQ ( d 4 ) i s t h a t T i i s v e r y l o n g s o low RF l e v e l s must be u s e d . One c a n o f t e n s h o r t e n T i by i n t r o d u c i n g p a r a m a g n e t i c i m p u r i t i e s w h i c h c o u p l e s t r o n g l y t o t h e —8 l a t t i c e , h a v i n g Tj_ 's o f t h e o r d e r o f 10 s . T h e i r l a r g e l o c a l f i e l d s r e l a x n e a r b y n u c l e i w h i c h i n t u r n r e l a x t h e i r n e i g h b o u r s by s p i n d i f f u s i o n . P a r a m a g n e t i c i m p u r i t i e s c a n be i n t r o d u c e d by i r r a d i a t i o n w i t h X- o r y - r a y s o r by d i s s o l v i n g t h e sample w i t h a p a r a -m a g n e t i c s a l t and r e c r y s t a l l i z i n g t h e s o l u t e . The mai n s t u m b l i n g b l o c k s a r e t h a t i n t h e f o r m e r c a s e r e c o m b i n a t i o n may o c c u r and i n t h e l a t t e r c a s e t h e two components may r e c r y s t a l l i z e s e p a r a t e l y . I f l a r g e c o n c e n t r a t i o n s o f i m p u r i t i e s a r e i n t r o d u c e d , t h e DMR s i g n a l w i l l be b r o a d e n e d . F i g u r e 16) High f i e l d main s a t e l l i t e peaks of TCNQ(d^) d e r i v a t i v e DMR s i g n a l . 18 scans of 50 s each w i t h H, = .53 mG. - 45 -S e v e r a l u n s u c c e s s f u l a t t e m p t s were made t o o b s e r v e t h e TCNQ(d 4) s i g n a l u s i n g a d i f f e r e n t c r y o s t a t f r o m t h e one d e s c r i b e d a b o v e . The sample was i r r a d i a t e d f o r up t o 9 h o u r s w i t h 120 keV X - r a y s w i t h no a p p a r e n t e f f e c t . I n o r d e r t o s l o w down p o s s i b l e r e c o m b i n a t i o n , t h e sample was i r r a d i a t e d w h i l e c o o l e d by l i q u i d n i t r o g e n and i m m e d i a t e l y a f t e r w a r d p l a c e d i n a c r y o s t a t c o o l e d t o 77 K. The sample was o n l y e x p o s e d t o t e m p e r a t u r e s above 77 K f o r a few s e c o n d s when i t was t r a n s f e r r e d f r o m t h e l i q u i d n i t r o g e n b a t h t o t h e c r y o s t a t . T h i s was a l s o i n e f f e c t u a l . More r e c e n t l y , a f t e r t h e TCNQ ( d 4 ) s i g n a l had been o b s e r v e d , a n a t t e m p t was made t o dope t h e sample w i t h Mn t o improve t h e S:N. Mn [TCNQ (d 4)] 2 was made, d i s s o l v e d w i t h TCNQ ( d 4 ) and t h e s o l u t e r e c r y s t a l l i z e d . Enough Mn was us e d t o g i v e c o n c e n t r a t i o n s o f .01% Mn (by w e i g h t ) and .05% Mn on two d i f f e r e n t o c c a s i o n s . I t i s n ' t known how many o f t h e i m p u r i t i e s a c t u a l l y went i n t o t h e new c r y s t a l s t h o u g h . The c o l o u r o f t h e c r y s t a l s (orange-brown) was u n c h a n g e d . T h e r e was no d i s t i n c t improvement i n t h e s i g n a l . We have o b t a i n e d v a l u e s o f t h e QCC and n f r o m t h e peak p o s i t i o n s o f t h e DMR s i g n a l s a s d e s c r i b e d i n C h a p t e r I I . Th e s e a r e shown i n T a b l e I . - 46 -T a b l e I Q u a d r u p o l e C o u p l i n g C o n s t a n t s  and Asymmetry P a r a m e t e r s Sample e2qQ/h (kHz) T (K) TTF ( d 0 ) -TCNQ ( d 4 ) 180.0 ± .7 .080 t .002 1.3 TCNQ(d 4) 167.0 t .9 .061 - .005 4.2 - 47 -The d i f f e r e n c e i n the QCC's f o r the n e u t r a l and charged TCNQ i s 13 kHz. T h e r e f o r e a c c o r d i n g t o our p r e v i o u s d i s c u s s i o n , the maximum range o f QCC's t h a t c o u l d be produced by a CDW i s 26 kHz. E x p e r i m e n t a l l y , t h e r e s o l u t i o n i s l i m i t e d by t h e b r o a d e n i n g . As a. f i r s t e s t i m a t e t h i s i s g i v e n by the FWHM of t h e main peak of F i g . 13 which i s 1.8±.2 kHz. T h i s v a l u e has been c o r r e c t e d f o r t h e w i d t h o f the m o d u l a t i o n (Andrew, 1953). S i n c e t h e b r o a d e n i n g i s r e l a t i v e l y s m a l l , the main peak i s w e l l s e p a r a t e d from t h e o t h e r f e a t u r e s so i t s w i d t h s h o u l d n o t be a f f e c t e d by n v e r y much. The e f f e c t o f a p l a n e , s i n u s o i d a l , incommensurate CDW on a q u a d r u p o l a r l i n e s h a p e was shown i n F i g . 8. I f one assumes a two peaked d i s t r i b u t i o n o f t h i s form i n TTF-TCNQ and g a u s s i a n b r o a d e n i n g , t h e n i t s h o u l d be p o s s i b l e t o r e s o l v e the peaks i f t h e i r s p l i t t i n g i s g r e a t e r than about t w i c e t h e s t a n d a r d d e v i a t i o n , a, o f the b r o a d e n i n g f u n c t i o n . The sum o f two g a u s s i a n peaks, each w i t h a s t a n d a r d d e v i a t i o n a, can be r e s o l v e d under t h e s e c o n d i t i o n s . I f t h e i r s e p a r a t i o n i s e q u a l t o 2a, the n a s i n g l e peaked f u n c t i o n w i t h a FWHM = 4a r e s u l t s . T h e r e f o r e i n TTF-TCNQ, w i t h t h e s e a s s u m p t i o n s , i t s h o u l d be p o s s i b l e t o r e s o l v e a d i s t r i b u t i o n e q u a l t o one h a l f of t h e FWHM. The l i m i t o f r e s o l u t i o n f o r a d i s t r i b u t i o n o f QCC1 s would then be ( 1 / 2 ) ( 8 / 3 ) ( 1 . 8 ) = 2.4 kHz from t h e w i d t h o f t h e main peaks. A c t u a l l y a CDW would n o t be a p l a n e wave i n TTF-TCNQ. However, o n l y t h e EFG a t the d e u t e r o n s i t e s i s i m p o r t a n t . Neutron s c a t t e r i n g i n d i c a t e s t h a t i t h e CDW s h o u l d be s i n u s o i d a l a l o n g t h e c h a i n s . I f th e de u t e r o n s a r e e q u i v a l e n t , then a t t h e i r s i t e s a l o n g a c h a i n t h e EFG s h o u l d be th e same as i f the CDW were a p l a n e wave. I t i s shown i n Chapter V t h a t the d i p o l a r b r o a d e n i n g i s n o t e x p e c t e d t o be g a u s s i a n . The e s t i m a t e o f the l i m i t o f r e s o l u t i o n g i v e n above may n o t be v a l i d t h e n . I n any event the d i s t r i b u t i o n o f QCC's c o u l d be a t most t w i c e as much i f i t were r e s p o n s i b l e f o r a l l o f th e b r o a d e n i n g . - 48 -Chapter V SOURCES OF BROADENING A l t h o u g h t h e r e i s no o b v i o u s d i s t r i b u t i o n o f QCC's i n the e x p e r i m e n t a l DMR spectrum o f TTF-TCNQ(d 4), i t remains t o c o n s i d e r whether the b r o a d e n i n g can be acc o u n t e d f o r by the d i p o l e - d i p o l e i n t e r a c t i o n s between t h e s p i n s or whether i t may be due t o an u n r e s o l v e d s p l i t t i n g . I f one assumes a r i g i d l a t t i c e model c o n t a i n i n g o n l y one t y p e o f s p i n , t h e n t h e second moment f o r t h e d i p o l a r b r o a d e n i n g i s (Abragam, 1961) : <AH 2> I : [ = Y j * I 2 K I + 1) (1 - 3 c o s 2 0 . k ) 2 v - 1 k ^ j 6 -> . . . i k . . where r j ^ l s t h e p o s i t i o n v e c t o r between s p i n s j and k and e.j^. i s the a n g l e between r and H . A l l s p i n s a r e assumed t o be e q u i v a l e n t . 3 K For a powder w i t h randomly o r i e n t e d c r y s t a l l i t e s t h i s becomes: <AH 2> 1 ] ; =(3/5) Y j ' n 2 K I + 1) £ ' r T £ ,V-2 B e f o r e a p p l y i n g t h i s t e c h n i q u e t o t h e d e u t e r o n l i n e w i d t h , i t s v a l i d i t y was checked u s i n g t h e p r o t o n resonance o f T T F ( d 4 ) -TCNQ (d 0) • < A H 2 > I I was c a l c u l a t e d c o n s i d e r i n g o n l y t h e d i p o l e -d i p o l e i n t e r a c t i o n s between p r o t o n s . The c o n t r i b u t i o n t o <A , H >, from p r o t o n s on t h e same m o l e c u l e i s 3.08 G 2; 97% i s from t h e - 49 -n e a r e s t p r o t o n a l o n e . The c o n t r i b u t i o n f r o m t h e p r o t o n s on t h e two n e a r e s t n e i g h b o u r m o l e c u l e s on t h e same c h a i n i s .64 . A l l o t h e r d i p o l e - d i p o l e i n t e r a c t i o n s ( i n c l u d i n g H-D and H-N) a r e i n s i g n i f i c a n t s o t h e c a l c u l a t e d s q u a r e r o o t o f t h e p r o t o n s e c o n d moment i s 1.93 G. The e x p e r i m e n t a l p r o t o n a b s o r p t i o n s i g n a l f r o m TTF ( d 4 ) -TCNQ ( d 0 ) i s shown i n F i g . 17. The l i n e s h a p e i s c h a r a c t e r i s t i c o f a s y s t e m i n w h i c h t h e s h o r t e s t H-H d i s t a n c e i s much l e s s t h a n a l l o t h e r H-H d i s t a n c e s . The d i p o l e - d i p o l e i n t e r a c t i o n o f a p r o t o n w i t h i t s n e a r e s t n e i g h b o u r t h e n makes t h e domi n a n t c o n t r i b u t i o n t o t h e s e c o n d moment. T h i s was s e e n t o be t h e c a s e i n t h e c a l c u l a t i o n a b o v e . The s q u a r e r o o t o f t h e s e c o n d moment was measured t o be 1.60 G u s i n g a 36 p o i n t n u m e r i c a l i n t e g r a t i o n o f t h e l i n e s h a p e o v e r a 12 G r a n g e . A c o r r e c t i o n was made f o r t h e r e s i d u a l p r o t o n s i g n a l w i t h t h e sample r e m o v e d . The agre e m e n t between t h e measured and c a l c u l a t e d v a l u e s i s m o d e r a t e l y g o o d . The d i s c r e p a n c y p r e s u m a b l y a r i s e s b e c a u s e t h e c o n t r i b u t i o n t o t h e e x p e r i m e n t a l v a l u e f r o m t h e w i n g s was b u r i e d i n n o i s e . The peak t o peak s e p a r a t i o n o f t h e d e r i v a t i v e s i g n a l was 3.77 - .07 G w h i c h compares f a i r l y w e l l w i t h t h e v a l u e o f 4.0 G g i v e n by R y b a c z e w s k i ( 1 9 7 4 ) . p r o t o n s a r e r e p l a c e d by d e u t e r o n s . E q u a t i o n V-2 i m p l i e s t h a t i f t h e l i n e s h a p e s a r e g a u s s i a n , t h e n t h e r a t i o o f t h e d e u t e r o n d i p o l a r l i n e w i d t h t o t h a t o f t h e p r o t o n s i s : U s i n g e q u a t i o n V-2 one c a n e s t i m a t e t h e b r o a d e n i n g i f t h e ,1/2 V-3 •-= .25 I — — f 2.0 G F i g u r e 17) P r o t o n a b s o r p t i o n s i g n a l o f TTF(d^)-TGNQ(d Q). = .21 mG. The r e s i d u a l p r o t o n s i g n a l w i t h no sample i s shown by the dashed l i n e . - 51 -The e x p e r i m e n t a l d e u t e r o n l i n e w i d t h c a n be o b t a i n e d f r o m t h e w i d t h o f t h e main peak i n F i g . 13 w h i c h i s 2.8 - .3 G FWHM. U s i n g t h e e x p e r i m e n t a l v a l u e o f t h e p r o t o n FWHM w h i c h i s 4.60 G, e q u a t i o n V-3 g i v e s a n e x p e c t e d v a l u e o f 1.15 G f o r t h e d e u t e r o n FWHM; t h e r e i s a f a c t o r o f 2.4 d i s c r e p a n c y . The p r o t o n s i g n a l i s n o t g a u s s i a n so t h e d e u t e r o n l i n e s h a p e s h o u l d n ' t be e i t h e r . However, c o n s i d e r i n g t h e S:N r a t i o o f t h e d e u t e r o n s i g n a l t h i s a p p r o x i m a t i o n i s r e a s o n a b l e . D e s p i t e t h e i n a d e q u a c i e s o f t h e c a l c u l a t i o n a b o v e . , t h e d i s c r e p a n c y seems r a t h e r l a r g e . A p a r t f r o m CDW e f f e c t s , t h e r e a r e two o t h e r p o s s i b l e s o u r c e s o f a d d i t i o n a l b r o a d e n i n g t h a t w i l l be d i s c u s s e d b e l o w . F i r s t , t h e r a t i o o f t h e p r o t o n m a g n e t i c moment t o t h a t o f t h e d e u t e r o n i s 6.51. C o n s e q u e n t l y o t h e r s p e c i e s o f s p i n s w i l l h a v e a much g r e a t e r e f f e c t o n . t h e d e u t e r o n d i p o l a r b r o a d e n i n g t h a n on t h a t o f t h e p r o t o n s . S e c o n d l y , some o f t h e d e u t e r o n s i t e s may be i n e q u i v a l e n t . In t h e f o l l o w i n g d i s c u s s i o n m o l e c u l e s w i l l be l a b e l l e d by t h e p o s i t i o n s o f t h e i r c e n t r o i d s u s i n g t h e c r y s t a l axes as c o o r d i n a t e a x e s . T h i s c o o r d i n a t e s y s t e m i s shown i n F i g . 4. The atoms on each m o l e c u l e a r e l a b e l l e d as i n F i g . 3. F o r example H(8) on TCNQ a t (a/2 , 0, 0) means t h e H atom a t p o s i t i o n 8 (see F i g . 3) o f t h e TCNQ m o l e c u l e whose c e n t r o i d i s l o c a t e d a t (a/2 , 0, 0) (see F i g . 4) . A l l i n t e r a t o m i c d i s t a n c e s a r e o b t a i n e d f r o m t h e X - r a y d i f f r a c t i o n d a t a o f K i s t e n m a c h e r , P h i l l i p s and Cowan (1974) . C o n s i d e r a c r y s t a l o f TTF ( d 0 ) -TCNQ {64) . U s i n g t h e same d i p o l e - d i p o l e i n t e r a c t i o n s a s i n t h e c a l c u l a t i o n o f <AH 2> HH a b o v e , one f i n d s t h a t < A H 2 > n n = .233 G 2 . The p r o t o n s on t h e - 52 -TTF m o l e c u l e s w i l l make a n a d d i t i o n a l c o n t r i b u t i o n . The e f f e c t o f p r o t o n s on t h e d e u t e r o n s e c o n d moment i s g i v e n by (Abragam, 1961) . C o n s i d e r D(8) on TCNQ a t ( a / 2 , 0, 0 ) . The n e a r e s t p r o t o n i s H(2) on TTF a t (0.-, b , 0) (4.39 A s e p a r a t i o n ) and t h e s e c o n d n e a r e s t i s H(2) on TTF a t (0, 0, 0) (4.58 A s e p a r a t i o n ) . The p r o t o n s H ( l ' ) on t h e same m o l e c u l e s a r e a l i t t l e f a r t h e r away. A l l o t h e r s a r e f a r enough away t h a t t h e i r c o n t r i b u t i o n i s n ' t v e r y s i g n i f i c a n t . T h e r e f o r e a r e a s o n a b l e e s t i m a t e o f t h e p r o t o n c o n t r i b u t i o n w o u l d be t o t a k e t w i c e t h e e f f e c t o f t h e two n e a r e s t p r o t o n s . I f one does t h i s t h e r e s u l t i s <AH 2> p D = .086 G 2. T h i s o n l y i n c r e a s e s <AH^> 2 by 17%. I t c a n n o t a c c o u n t f o r more t h a n a s m a l l p a r t o f t h e e x t r a b r o a d e n i n g o f t h e d e u t e r o n l i n e s h a p e . 14 The N n u c l e i a l s o make a c o n t r i b u t i o n t o t h e d e u t e r o n s e c o n d moment. The e f f e c t o f t h e n e a r e s t N"^ n u c l e u s ( s e p a r a t i o n i s 2.91 A) i s . <AH2>.Tn = .0037 G 2. S i n c e a l l o t h e r N 1 4 n u c l e i ND a r e c o n s i d e r a b l y f a r t h e r away, t h i s c o n t r i b u t i o n i s i n s i g n i f i c a n t . I t i s now n e c e s s a r y t o c o n s i d e r w h e t h e r a l l o f t h e d e u t e r o n s i t e s a r e e q u i v a l e n t . F i g . 6c shows t h a t f o r a powder sample t h e s p e c t r u m depends o n l y upon e q and n : i t i s a v e r a g e d o v e r a l l o r i e n t a t i o n s o f t h e p r i n c i p a l a x e s w i t h r e s p e c t t o S. Thus i n a powder two s i t e s a r e i n e q u i v a l e n t o n l y i f t h e y have d i f f e r e n t v a l u e s o f e q o r n . The maximum component o f t h e EFG t e n s o r i n t h e p r i n c i p a l a x i s s y s t e m , e q , c a n be w r i t t e n as t h e sum o f n u c l e a r and e l e c t r o n i c c o n t r i b u t i o n s . eq = eE Z k ( 3 c o s 2 e k ~ D r ~ 3 - eE < ^ | ( 3 c o s 2 0 . - l ) r . 3 | ^ > = ec*n " e % V-5 where k d e n o t e s n u c l e i , j d e n o t e s e l e c t r o n s , Z^ i s t h e c h a r g e o f t h e k ^ n u c l e u s , r k i s i t s p o s i t i o n , 8-^  i s t h e a n g l e between r k and t h e p r i n c i p a l z a x i s , and i s t h e e l e c t r o n i c wave f u n c t i o n . I n TTF-TCNQ a l l H atoms a r e bonded t o C atoms s o t h e d o m i n a n t n u c l e a r c o n t r i b u t i o n t o eq a t t h e H atom i s f r o m t h e C atom. T y p i c a l l y f o r C-D bonds t h e c a r b o n n u c l e u s g i v e s 90% o f t h e n u c l e a r c o n t r i b u t i o n t o eq (Rinne and D e p i r e u x , 1972) . The c o n t r i b u t i o n o f t h e I s o r b i t a l o f t h e d e u t e r o n t o e q e i s z e r o b e c a u s e t h a t o r b i t a l i s s p h e r i c a l l y s y m m e t r i c . The d e u t e r o n 2p o r b i t a l s a r e t o o h i g h i n e n e r g y t o be o c c u p i e d t o any a p p r e c i a b l e e x t e n t s o t h e d e u t e r o n o r b i t a l s make no c o n t r i b u t i o n t o e q e . The d o m i n a n t c o n t r i b u t i o n t o e q e i s f r o m t h e C o r b i t a l s . T y p i c a l l y o v e r 70% o f e q e a r i s e s f r o m t h e C-D b o n d i n g o r b i t a l a l o n e (Rinne and D e p i r e u x , 19 72) . I n many c a s e s e q n c a n be c a l c u l a t e d q u i t e a c c u r a t e l y , i t i s a l w a y s p o s i t i v e . | eq | i s a l w a y s f o u n d t o be s m a l l e r t h a n e q n s o e q e must a l s o be p o s i t i v e . I n a l l c a s e s where t h e s i g n o f t h e d e u t e r o n QCC h a s b e e n d e t e r m i n e d e x p e r i m e n t a l l y i t h a s been p o s i t i v e . S i n c e t h e q u a d r u p o l e moment Q o f t h e d e u t e r o n i s a l s o p o s i t i v e , e q n must a l w a y s be g r e a t e r t h a n e q e . T y p i c a l l y t h e e l e c t r o n s s h i e l d 8 0% o f t h e E F G p r o d u c e d by t h e C n u c l e u s i n a - 54 -C-D bond ( B e r s o h n , 1 9 6 0 ) . S i n c e e q a r i s e s f r o m t h e n e a r c a n c e l l a t i o n o f two terms i t i s v e r y s e n s i t i v e t o s m a l l c h a n g es i n t h e e l e c t r o n i c c h a r g e d e n s i t y . One m i g h t h ave e x p e c t e d t h e QCC o f t h e T C N Q - " 6 i o n t o be s m a l l e r t h a n t h a t o f n e u t r a l TCNQ. S i n c e T C N Q - " 6 has a d d i t i o n a l e l e c t r o n i c c h a r g e as compared w i t h n e u t r a l TCNQ, i t seems r e a s o n a b l e t o e x p e c t t h a t t h e e l e c t r o n i c c o n t r i b u t i o n t o eq w o u l d be l a r g e r i n t h e f o r m e r . T h i s w o u l d make e q s m a l l e r a c c o r d i n g t o e q u a t i o n V-5 whereas T a b l e I shows t h a t i t i s l a r g e r . However, t h e r e seems t o be no r e l a t i o n between t h e QCC and t h e f o r m a l c h a r g e on a n i o n ( O l y m p i a , W e i , and F u n g , 1969) . F o r example ND4 + h a s a l o w e r d e u t e r o n QCC t h a n ND 3. I n an i s o l a t e d m o l e c u l e o f TCNQ a l l o f t h e d e u t e r o n s a r e e q u i v a l e n t ; i . e . , t h e y have t h e same eq and n . F i g . 4 shows t h a t f o r a g i v e n TCNQ m o l e c u l e i n a T T F ( d o ) - T C N Q ( d 4 ) c r y s t a l , D(8) and D(8') a r e e q u i v a l e n t and D(9) and D(9') a r e e q u i v a l e n t but D(8) and D(9) a r e i n e q u i v a l e n t . F o r a d j a c e n t m o l e c u l e s a l o n g t h e C a x i s (one o f w h i c h i s d e n o t e d by a n a s t e r i s k ) , H(8) and H.(8')* a r e e q u i v a l e n t as a r e H(9) and H ( 9 ' ) * . T h e r e f o r e i n t h e c r y s t a l as a w h o l e t h e r e a r e two i n e q u i v a l e n t s i t e s . The i n e q u i v a l e n c e a r i s e s b e c a u s e t h e a and c a x e s a r e n o t o r t h o g o n a l . S i n c e one n o r m a l l y e x p e c t s e q t o be d e t e r m i n e d by t h e C n u c l e u s and C o r b i t a l s , t h e i n e q u i v a l e n c e s h o u l d be s m a l l . The i n e q u i v a l e n c e o f t h e d e u t e r o n s on t h e TCNQ m o l e c u l e s a r i s e s p r i m a r i l y f r o m i n t e r a c t i o n s w i t h t h e two a d j a c e n t rows a l o n g t h e a a x i s . One c a n e s t i m a t e t h e amount o f t h e i n e q u i v a l e n c e c a u s e d by m o l e c u l e s i n t h e s e rows by c a l c u l a t i n g t h e EFG's u s i n g a p o i n t c h a r g e m o d e l . U s i n g a M u l l i k e n p o p u l a t i o n a n a l y s i s ( M u l l i k e n , 1 9 5 5 ) , one c a n o b t a i n a model i n - 55 -w h i c h t h e e l e c t r o n s a r e d i s t r i b u t e d among t h e a t o m i c o r b i t a l s o f t h e m o l e c u l e s . From t h i s d i s t r i b u t i o n , one c a n o b t a i n t h e " g r o s s a t o m i c c h a r g e " , c , f o r e a c h atom. The EFG a t a p o i n t i n a n e i g h b o u r i n g m o l e c u l e c a n t h e n be e s t i m a t e d by t r e a t i n g t h e g r o s s a t o m i c c h a r g e s a s p o i n t c h a r g e s l o c a t e d a t t h e c e n t r e s o f t h e i r r e s p e c t i v e a t o m s . The g r o s s a t o m i c c h a r g e s f o r T T F ° , T T F - 1 , T C N Q ° , T C N Q - 1 and TCNQ ^ h a v e been d e t e r m i n e d f r o m s e l f c o n s i s t e n t f i e l d m o l e c u l a r o r b i t a l c a l c u l a t i o n s ( R a t n e r , 1974 and J o h a n s e n , 1 9 7 5 ) . The r e s u l t s a r e summarized i n T a b l e I I . - 56 -T a b l e I I G r o s s Atomic' C h a r g e s c / e A) TCNQ Atom T C N Q ° TCNQ 1 TCNQ C(9) -.04 -.06 -.08 C(7) .10 .07 .03 C(6) .07 -.06 -.17 C(5) -.16 -.15 -.14 N(2) -.03 -.15 -.26 H(9) .14 .10 .05 B) TTF Atom T T F ° TTF 4" S ( l ) .018 .185 C ( l ) -.024 -.006 C(3) -.005 .116 - 57 -The TCNQ d a t a shows t h a t t h e g r o s s a t o m i c c h a r g e s s c a l e w i t h t h e c h a r g e on t h e m o l e c u l e s . T h i s w i l l be assumed t o be a l s o t r u e f o r T T F . I t s h o u l d be p o i n t e d o u t t h a t t h e a b s o l u t e v a l u e s o f t h e g r o s s c h a r g e s g e n e r a l l y depend s t r o n g l y on t h e s e t o f b a s i s f u n c t i o n s u s e d . The r e l a t i v e v a l u e s f o r t h e same m o l e c u l e w i t h d i f f e r e n t c h a r g e s a r e u s u a l l y f a i r l y c o n s i s t e n t t h o u g h . The o n l y e x p e r i m e n t a l c o n f i r m a t i o n o f t h e s e c a l c u l a t i o n s i s t h e N 1 4 NMR d a t a . M u r g i c h and P i s s a n e t z k y (1973) f o u n d t h a t t h e i n c r e a s e i n c h a r g e on K-TCNQ as compared w i t h n e u t r a l TCNQ i s .13 e . T h i s a g r e e s q u i t e w e l l w i t h J o h a n s e n ' s c a l c u l a t e d v a l u e o f .12 e . I f one s c a l e s t h e v a l u e s o f c g i v e n i n T a b l e I I t o a m o l e c u l a r c h a r g e o f .6, one f i n d s t h a t i n TCNQ "^ t h e n e g a t i v e c h a r g e i s p r e d o m i n a n t l y on t h e CN g r o u p s w h i l e i n TTF." 6 t h e p o s i t i v e c h a r g e i s p r e d o m i n a n t l y on t h e s u l f u r and t h e c e n t r a l c a r b o n s . O n l y t h e s e c h a r g e s were u s e d i n t h e EFG c a l c u l a t i o n b e l o w . The o u t e r C atoms o f TTF a r e a l m o s t n e u t r a l . C o n s i d e r t h e i n e q u i v a l e n t d e u t e r o n s D(8') and D(9') on TCNQ a t (a/2 , b/2, c/2) . The p o i n t c h a r g e s p r i m a r i l y r e s p o n s i b l e f o r t h e i n e q u i v a l e n c e a r e l o c a t e d on t h e TCNQ m o l e c u l e a t (a/ 2 , 0, 0) and t h e TTF m o l e c u l e a t (0, b, 0) . C h a r g e s on o t h e r m o l e c u l e s w i l l make f a i r l y s m a l l c o n t r i b u t i o n s b e c a u s e t h e EFG has a n r - 3 d e p e n d e n c e . C o n s i d e r i n g t h e a c c u r a c y o f t h e a b s o l u t e v a l u e s o f c , i t i s p o i n t l e s s t o i n c l u d e t h e s e o t h e r c h a r g e s . S i n c e t h e C n u c l e u s and C-D b o n d i n g o r b i t a l p r o v i d e t h e do m i n a n t c o n t r i b u t i o n s t o t h e d e u t e r o n EFG, t h e z a x i s o f t h e p r i n c i p a l a x i s s y s t e m c a n be a p p r o x i m a t e d v e r y w e l l by t h e C-D bond a x i s . F u r t h e r m o r e s i n c e t h e EFG p r o d u c e d by t h e p o i n t - 58 -charges on n e i g h b o u r i n g m o l e c u l e s i s a s m a l l p e r t u r b a t i o n , one o n l y needs t o c o n s i d e r i t s V z z component. Other components have o n l y a second o r d e r e f f e c t . The c o n t r i b u t i o n s t o eq a t each o f D(8') and D(9') on TCNQ a t ( a / 2 , b/2 , c/2) from t h e p o i n t charges l o c a t e d a t N ( l ) , N(2) , C (4) , and C (5) on (a /2 , 0 , 0) and a t S (1) , S (2) , and C (3) on TTF a t (0, b, 0) have been c a l c u l a t e d . The r e s u l t s a r e : q [D(8') ] = -2.1 x 1 0 2 1 c m - 3 q [ D (9 ') ] = .8 x 1 0 2 1 cm" 3 2 T h i s d i f f e r e n c e would produce a d i s t r i b u t i o n i n e qQ/h e q u a l t o .29 kHz,, and hence a b r o a d e n i n g o f (3/8) ( 2 H / Y ) ( • 29) = .17 G i n the main.peak w h i c h - i s much l e s s t h a n the o b s e r v e d w i d t h o f 2.8 G. One c o n c l u d e s t h a t t h e e x t r a b r o a d e n i n g cannot be caused by t h e e x i s t e n c e o f two i n e q u i v a l e n t s i t e s . - 59 -CHAPTER VI CONCLUSIONS The c a l c u l a t i o n s o f Ch a p t e r V i n d i c a t e t h a t t h e w i d t h o f the DMR s i g n a l o f TTF(d^)-TCNQ(d^) cannot be accounted f o r by e i t h e r the d i p o l a r b r o a d e n i n g o r the i n e q u i v a l e n c e o f the de u t e r o n s i t e s . One i s tempted t o a s c r i b e t h e b r o a d e n i n g t o a d i s t r i b u t i o n o f QCC 1s caused by a CDW. However, t h e r e i s a fundamental d i f f i c u l t y w i t h d o i n g t h i s . F i g . 7b shows t h a t the s p l i t t i n g between the two o u t e r peaks o f the DMR 2 spectrum i s fQ=(3/2)e qQ/h whereas between t h e two main peaks i t i s ( 1 / 2 ) f Q ( l + n ) - ( 1 / 2 ) f f o r TTF-TCNQ s i n c e n<<l. T h e r e f o r e a d i s t r i b u t i o n o f EFG 1s would cause t w i c e as much b r o a d e n i n g i n t h e o u t e r peaks as i n the main ones. The measured FWHM's are 2.8±.3 G f o r the main peaks and -3.1 G f o r t h e o u t e r peaks a f t e r c o r r e c t i n g f o r the w i d t h o f the m o d u l a t i o n (Andrew, 1953). The d i f f e r e n c e i s o n l y o f the o r d e r o f the e x p e r i r m e ntal e r r o r . I t i s by no means l a r g e enough t o a l l o w one t o a t t r i b u t e the w i d t h o f the main peaks t o a d i s t r i b u t i o n o f QCC's. The d i f f e r e n c e i n the w i d t h s , i f i t i s s i g n i f i c a n t , can p r o b a b l y be a c c o u n t e d f o r by the s m a l l i n e q u i v a l e n c e o f the d e u t e r o n s i t e s d i s c u s s e d i n Chapter V. The r e s u l t o f t h e c a l c u l a t i o n t h e r e i m p l i e d a d i s t r i b u t i o n o f QCC's o f the o r d e r o f .29 kHz wide. T h i s would i m p l y a b r o a d e n i n g o f t h e main peaks by (3 / 8 ) ( 2 u / y ) ( . 2 9 ) = . 1 7 G and o f t h e o u t e r peaks by t w i c e as much—.34 G. T h i s mechanism would cause the o u t e r peaks t o be .17 G w i d e r than the main ones. I t seems t h a t the d i f f e r e n c e i n the w i d t h s o f the peaks can be acc o u n t e d f o r w i t h o u t i n v o k i n g the e x i s t e n c e o f a CDW. - 60 -A l t h o u g h t h e r e i s no e v i d e n c e o f the e x i s t e n c e o f a CDW, one can put an upper l i m i t on the a m p l i t u d e o f a CDW i f one d i d e x i s t u s i n g the FWHM o f th e o u t e r peak w h i c h i s 2.0 kHz. I n accor d a n c e w i t h t h e argument a t the end o f Chapter IV, i f one assumes t h a t a d i s t r i b u t i o n o f QCC 1s e q u a l t o one h a l f o f the FWHM c o u l d be r e s o l v e d , then t h e l i m i t o f r e s o -l u t i o n f o r a d i s t r i b u t i o n o f QCC 1s i s (1/2)(4/3)(2.0)=1.3 kHz. From a comparison o f t h e QCC 1s o f TCNQ(d^) and TTF(d^)-TCNQ(d^), the d i s c u s s i o n o f Chapter IV sug g e s t e d t h a t the maximum range of QCC 1s a CDW c o u l d produce i s 26 kHz. T h e r e f o r e an e s t i m a t e o f the maximum p o s s i b l e a m p l i t u d e o f a CDW on the TCNQ c h a i n s i s ^5%. - 61 -BIBLIOGRAPHY Abragam, A, THE PRINCIPLES OF NUCLEAR MAGNETISM, O x f o r d U n i -v e r s i t y P r e s s , London (1961) A n d r e , J J , B i e b e r , A, and G a u t i e r , F, Ann. P h y s . , 1, 145 (1976) Andrew, ER, P h y s . Rev., 9_1, 425 (1953) Andrew, ER, NUCLEAR MAGNETIC RESONANCE, Cambridge U n i v e r s i t y P r e s s , Cambridge (19 55) B a r n e s , RG, Adv. i n NQR, 1, 335 (1972) B a r n e s , RG, and Bloom, JW, J . Chem. P h y s . , 5J7, 3082 (1972) B e r l i n s k y , A J , Contemp. P h y s . , 1/7 , 331 (1976) B e r l i n s k y , A J , C a r o l a n , J F , and W e i l e r , L, S o l . S t . Comm., 15, 795 (1974) B e r s o h n , R, J . 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Phys.,5_l, 1610 (1969) P e i e r l s , RE, QUANTUM THEORY OF SOLIDS, O x f o r d U n i v e r s i t y P r e s s , London, (1955) P i n c u s , P, LOW DIMENSIONAL COOPERATIVE PHENOMENA, e d . HJ K e l l e r , Plenum P r e s s , New Y o r k (1975) R a t n e r , MA, S a b i n , JR, B a l l , E E , Chem. P h y s . L e t t . , 28_, 393 (1974) R i n n e , M and D e p i r e u x , J , Adv. i n NQR,1, 357 (1972) R y b a c z e w s k i , E F , PhD T h e s i s , U. o f P e n n s y l v a n i a , u n p u b l i s h e d (1974) S c o t t , J C , G a r i t o , AF, and H e e g e r , A J , P h y s . Rev. B 1_0, 3131 (1974) S l i c h t e r , CP, PRINCIPLES OF MAGNETIC RESONANCE, H a r p e r and Row, New Y o r k ,(1963) T i e d j e , T, M a s t e r ' s T h e s i s , U. o f B r i t i s h C o l u m b i a , u n p u b l i s h e d (1975) 

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