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UBC Theses and Dissertations

19 F broad line nuclear magnetic resonance study 1967

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The U n i v e r s i t y of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of MATTHEW RONALD BARR B„Sc„, The U n i v e r s i t y of B r i t i s h Columbia M„SCc, The U n i v e r s i t y of B r i t i s h Columbia THURSDAY, NOVEMBER 2, 1967, AT 10:00 A„M C IN ROOM 225, CHEMISTRY BUILDING COMMITTEE IN CHARGE Chairman: F-A. Kaempffer B.A. Dunell C o A o McDowell K„B„ Harvey D.E. McGreer R.C. Thompson D.L. W i l l i a m s E x t e r n a l Examinor: R.E. Richards P h y s i c a l Chemical Laboratory South Parks Road Oxford, England Research Supervisor: B.A- Dunell BROAD LINE NMR STUDIES ON WF > 5 S'F, .AsF c, 6 4 5 AND IF 7„AsF 5o ABSTRACT A general broad l i n e nuclear magnetic resonance 19 study was made of the F spectra of WF^ and the adducts IF • AsF,. and SF, - AsF,. to determine the temperature . - / 5 4 5 dependence - of the spectra, i n t e r p r e t the l i n e shapes with respect to i s o t r o p i c and anisotropic chemical s h i f t s and i d e n t i f y non-equivalent f l u o r i n e s i t e s i n the com- pounds . The temperature dependence of the second moment at 30 MHz indicated that r i g i d l a t t i c e condi- tions probably existed at 77°K for WF. and IF., « AsF r 6 7 5 but not for SF^ » AsF^„ The dependence indicated an o nmr t r a n s i t i o n i n the v i c i n i t y of 200 K for the f i r s t two compounds and one commencing below 77°K for the t h i r d . From the second moments in the v i c i n i t y of the t r a n s i t i o n s , a c t i v a t i o n energies were determined for the average motions involved„ The f i e l d dependence of the second moments of the compounds was examined, where possible, at 2, 16, 30, 40, 56,4, and 94,1 MHz at 77° and 295°Ko The coumpounds1 spectra were resolved, with varying degrees of success, into components., For WF, an approximate b r e s o l u t i o n could be made into two components corres- ponding to the four equatorial and two a x i a l f l u o r i n e s i n the d i s t o r t e d octahedron at 77°K. The two adducts could both be res o l v e d , e s p e c i a l l y at 295°K or above, i n t o components which supported the i o n i c formula- t i o n s I F * AsF. and SF* AsF. . Non-equivalent f l u o r i n e 6 6 3 6 s i t e s w i t h i n i n d i v i d u a l ions could not be detected. From the observed and estimated second moments of the resolved components above and below the t r a n s i t i o n s , the probable r e o r i e n t a t i o n s occuring above the t r a n s i t i o n s were suggested. The r i g i d l a t t i c e t h e o r e t i c a l second moment c a l c u l a t i o n s enabled suggestions to be made f o r the c r y s t a l s t r u c t u r e s of WF. and SFtAsF. and f o r the bond lengths i n IF>AsF^. 6 3 6 6 6 For the f i r s t there had been confusion, at l e a s t here, about the space group, while the second has not yet been the subject of reported X-ray s t u d i e s . A x i a l symmetry of the chemical s h i f t tensors was assumed. Then, t a k i n g account of the r e l a t i v e s h i f t s between the resolved components, average values of the chemical s h i f t a n i s o t r o p i e s f o r each of WF. + 6 and IF AsF,. were determined from expressions r e l a t i n g 6 6 the f i e l d squared dependence of the second moment to those q u a n t i t i e s . r The mean i s o t r o p i c s h i f t s of the t o t a l F spect r a f o r each compound were measured where p o s s i b l e at each f i e l d at 77° and 295°K w i t h respect to CF3COOH\ From those the s h i f t s of the r e s o l v e d components were c a l c u l a t e d r e l a t i v e to HF„ Then from the i s o t r o p i c s h i f t s and the a n i s o t r o p i e s , the p r i n c i p a l values of the a x i a l l y symmetric s h i f t tensors were determined. The p r i n c i p a l values enabled estimates to be made of I ( i o n i c ) and |2 (double bond) c h a r a c t e r s , n e g l e c t i n g h y b r i d i z a t i o n , i n the M-F bonds of the h e x a f l u o r i d e groups. From these values a p r e d i c t i o n was made f o r I and O i n the a x i a l and e q u a t o r i a l bonds i n PuF,. GRADUATE STUDIES F i e l d of Study: P h y s i c a l Chemistry Seminar i n Chemistry ( S p e c i a l L.G. H a r r i s o n Topic) Quantum Chemistry R.M. Hochstrasser Topics i n Chemical Physics C A . McDowell & B.A. Dune l l Spectroscopy & Molecular St r u c t u r e A.V. Bree L.W. Reeves R.B. Harvey C r y s t a l S t r u c t u r e s J. Trotter PUBLICATIONS M.R. Barr, B.A. Dunell & R.F. Grant - 'Premelting Phenomena i n Long-Chain Fatty Acids', Can. J . Chem., 41, 1188 (1963) . M.R. Barr, B.A. Dunell - 'Proton Magnetic Resonance Absorption i n High Temperature Phases of Anhydrous Sodium Stearate' Can J. Chem. 42, 1098 (1964). F BROAD LINE NUCLEAR MAGNETIC RESONANCE STUDY o f UiF 6 , I F ? • A s F 5 , S F 4 • A s F 5 by HIATTHEIU RONALD BARR B. S c . ( H o n s . ) , U.B.C., 1960 til . S c . , U.B.C., 19G3 A THESIS SU Bill ITTEO IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n t h e D e p a r t m e n t o f C h e m i s t r y We a c c e p t t h i s t h e s i s as 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 S e p t e m b e r , 1967 In p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r a n a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l m a k e i t f r e e l y a v a i l a b l e f o r r e f e r e n c e a n d S t u d y . I f u r t h e r a g r e e t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s m a y b e g r a n t e d b y t h e H e a d o f my D e p a r t m e n t o r b y h.i;s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t b e a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f T h e 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 V a n c o u v e r 8, C a n a d a Abstract A g e n e r a l broad l i n e n u c l e a r magnetic resonance study was made 19 of the F s p e c t r a of l!jF_ and the adducts I F_ • A s F c and o / b SF^ • AsFj. to determine the temperature dependence of the s p e c t r a , i n t e r p r e t the l i n e shapes w i t h r e s p e c t to i s o t r o p i c and a n i s o t r o p i c chemical s h i f t s and i d e n t i f y 'non-equivalent f l u o r i n e s i t e s i n the compounds. The temperature dependence of the second moment at 30 iYlHz i n d i - cated t h a t r i g i d l a t t i c e c o n d i t i o n s p r o b a b l y e x i s t e d a t 77°K f o r IL1 F and IF„ • AsF ' but not f o r SF. • A s F c „ The dependence i n d i c a t e d an / b 4 b nmr t r a n s i t i o n i n the v i c i n i t y of 200°K f o r the f i r s t two compounds o and one commencing below 77 K f o r the t h i r d . From the second moments i n the v i c i n i t y of the t r a n s i t i o n s , a c t i v a t i o n e n e r g i e s mere determined f o r the average motions i n v o l v e d . The f i e l d dependence of the second moments of the compounds was examined, where p o s s i b l e , a t 2, 16, 30, 40, 56.4, and 94.1 IYIHZ at 77°' o and 295 K. The compounds' s p e c t r a were r e s o l v e d , w i t h v a r y i n g degrees of success, i n t o components. For IMF an approximate r e s o l u t i o n c o u l d be made i n t o two components c o r r e s p o n d i n g to the f o u r e q u a t o r i a l and two a x i a l f l u o r i n e s i n the d i s t o r t e d octahedron a t 77°K. The two adducts could both be r e s o l v e d , e s p e c i a l l y at 295°K or above, i n t o components which supported the i o n i c f o r m u l a t i o n s IF* ^ s ^ g a n c^ SF* A s F c .. • Na n - e q u i v a l e n t F l u o r i n e s i t e s w i t h i n i n d i v i d u a l i ons c o u l d J D not be d e t e c t e d . r i i , - From the observed and es t i m a t e d second moments of the r e s o l v e d components above and below the t r a n s i t i o n s , the probable r e o r i e n t a t i o n s o c c u r i n g above the t r a n s i t i o n s were suggested. The r i g i d l a t t i c e t h e o r e t i c a l second moment c a l c u l a t i o n s enabled s u g g e s t i o n s to be mada f o r the c r y s t a l s t r u c t u r e s of U/pg and SF^AsFg and f o r the bond l e n g t h s i n IFg.AsF^ . For the f i r s t t h e r e had been c o n f u s i o n , a t l e a s t here, about the space group, w h i l e the second has not yet been the s u b j e c t of r e p o r t e d X-ray s t u d i e s . A x i a l symmetry of the chemical s h i f t t e n s o r s was assumed. Then, t a k i n g account of the r e l a t i v e s h i f t s between the r e s o l v a d components, averaqe v a l u e s of the c h e m i c a l s h i f t a n i s o t r o p i e s f o r each of 1!1F̂  and IF* AsF. were determined from e x p r e s s i o n s r e l a t i n d the f i e l d squared D b dependence of the second moment to those q u a n t i t i e s . 19 The mean i s o t r o p i c s h i f t s of the t o t a l F s p e c t r a f o r each com- o o pound were measured where p o s s i b l e a t each f i e l d a t 77 and 295 K w i t h r e s p e c t to CF. COOH. From those the s h i f t s of the r e s o l v e d components were c a l c u l a t e d r e l a t i v e to HF. Then from the i s o t r o p i c s h i f t s and the a n i s o t r o p i e s , the p r i n c i p a l values of the a x i a l l y symmetric s h i f t tensors were determined. The p r i n c i p a l v a l u e s enabled e s t i m a t e s to ba made of I ( i o n i c ) and (double bond) c h a r a c t e r s , n e g l e c t i n g h y b r i d - i z a t i o n , i n the ITi-F bonds of the h s x a f l u o r i d e groups. From these values a p r e d i c t i o n was made f o r I and ̂  i n the a x i a l and e q u a t o r i a l bonds i n PuF,. . o. TABLE OF CONTENTS CHAPTER PAGE I . INTRODUCTION 1 I I . NMR THEORY „ 5 I I I . EXPERIMENTAL PROCEDURE . 21 IV. RESULTS AND INTERPRETATION 27 G e n e r a l . . . . . . . . . . . . . . . . . 27 UIF-, 27 1. R e s u l t s 27 2. R e s o l u t i o n Attempts. I s o t r o p i c and A n i s o t r o p i c Chemical S h i f t s 33 3. Proposed C r y s t a l S t r u c t u r e . . . . . . . . . . . 43 4 . T h e o r e t i c a l R i g i d L a t t i c e Second foment . . . . . 47 5 . R e o r i e n t a t i o n i n the S o l i d . • 50 The AsFg Adducts 55 A. IF„ • AsF- 55 7 b 1. R e s u l t s . . . . . . . . . . . . . . . a 55 2. R e s o l u t i o n i n t o Components I s o t r o p i c and An i s o - t r o p i c Chemical S h i f t s 56 3. C r y s t a l S t r u c t u r e . . . . . . . . . • 60 4 . T h e o r e t i c a l R i g i d L a t t i c e Second Moment . . . . . 63 5 . R e o r i e n t a t i o n s i n the S o l i d . . . c . . . . . . • 64 B. SF. • A s F r „ . . . „ . 69 4 5 1. R e s u l t s 69 2. R e s o l u t i o n w i t h Components (see R e s u l t s a l s o ) . I s o t r o p i c and A n i s o t r o p i c Chemical S h i f t s . . . 70 - IV: - , i v CHAPTER PAGE 3. Proposed C r y s t a l S t r u c t u r e . . . . . . < > . 73 4 . T h e o r e t i c a l R i g i d L a t t i c e Second moment . . . 75 5. R e o r i e n t a t i o n s i n the S o l i d . . . . . . . 76 V. SUMMARY AND DISCUSSION „ 80 APPENDIX I . Computer Programs . . . . . 86 Program 1. C a l c u l a t i o n of E x p e r i m e n t a l Second Moments from D e r i v a t i v e Curves . . . . . . . . . . 87 Program 2, I n t e g r a t i o n of D e r i v a t i v e Curves to A b s o r p t i o n Curves . . . . . . . . . . . 90 Program 3. L i n e Shape Fu n c t i o n F(H) . . . . . . 93 Program 4. Doublet F i t 99 Program 5 0 T r a n s f o r m a t i o n of C o o r d i n a t e s . . . . 103 Program 6. T h e o r e t i c a l R i g i d L a t t i c e Second Moment C a l c u l a t i o n 105 Program 7. A c t i v a t i o n E n e r g i e s . . . . . . . 108 APPENDIX I l a . UIFg D e r i v a t i v e Curves f o r Temperature Dependence at 30 MHz . . . o 113 l i b . UJF, D e r i v a t i v e Curves f o r Temperature Dependence b a t 94.1 MHz 114 O TIC l i e . \iiF, D e r i v a t i v e Curves f o r F i e l d Dependence at 77 K l i b o APPENDIX I l i a . I F * A s F c D e r i v a t i v e Curves f o r Temperature Depen- b b dence a t 30 MHz . 116 I l l b . I F * A s F c D e r i v a t i v e Curves f o r F i e l d Dependence D O a t 295°K . . . 117 I I I c . I F * AsF" D e r i v a t i v e Curves f o r F i e l d Dependence D O a t 77°K • 118 - v - CHAPTER PAGE APPENDIX IVa. SF* flsfg D e r i v a t i v e Curves f o r Temperature Dependence at 30 PflHz . . . . . . . . . ng IVb. 5F* AsF D e r i v a t i v e Curves f o r F i e l d Dependence o o at 300°K . . . . . . . . . . . . o 120 IVc. SF* AsF^ D e r i v a t i v e Curves f o r F i e l d Dependence o at 77 K . . • *o o . . • . o o . • 121 REFERENCES 122 to 126 - v i LIST OF TABLES TABLE PAGE. 1. C e l l Parameters of IDF,. . . 44 fa 2. Atomic C o o r d i n a t e s , C e l l Dimensions, and Bond Lengths of UF g a t 298°K . . . . . . . . . 45 3. C a l c u l a t e d Atomic C o o r d i n a t e s and Bond Lengths f o r U1F6 at "253°K" . . . „ . 45 4. R i g i d D i p o l a r Second moments of U J a t 77°K . . . 49 5. X-Ray Powder S t r u c t u r e of I F * AsF~ ~ 295°K . . . 61 . 6 6 6. Atomic C o o r d i n a t e s f o r IF* AsFT ~ 295°X . . . . 62 fa b 7. R i g i d L a t t i c e Second Moment C o n t r i b u t i o n s to IF * AsF" 63 fa fa 8. X-Ray Powder Data f o r SF* SbF~ at 291°K 74 9. Estimated Atomic C o o r d i n a t e s f o r SF* AsF~ at "291°K" 75 o fa 10. " R i g i d L a t t i c e " Second Moment C o n t r i b u t i o n s to SF^ ^ s ^ g . . . . . . 76 11. Summary 82 - v i i - LIST OF FIGURES CURE TO FOLLO'JJ PAGE 1. U J . Temperature dependence of a b s o r p t i o n s p e c t r a at 30 MHz . . . . . . . . . . . . . . . 27 2. UJFg . Temperature dependence of second moment at 30 MHz 27 3. UJFg . Temperature dependence of l i n e u/idth at 30 and 94.1 MHz „ 27 4. UJFg . Chemical s h i f t of c e n t r o i d of spectrum r e l a - t i v e to CF 3 COOH 31 o 5. IiiFg . F i e l d dependence of a b s o r p t i o n s p e c t r a a t 77 K 32 o 6. IL'Fg . F i e l d dependence of l i n e width at 77 K . . . 32 o 7. IDF,, . F i e l d squared dependence of second moment at 77 K 33 fa 8. UJFg . Symmetrical component r e c o n s t r u c t i o n from . . 94.1 MHz s p e c t r a . . . . . . . . . . . . 35 9. UJFg . Symmetrical component r e c o n s t r u c t i o n from 2 MHz s p e c t r a . . . . o o . . . . . . . . . 35 10. 'uJFg . Asymmetrical r e c o n s t r u c t i o n f o r 6 - l i k e f l u o r i n e s . . . . . . . . . . . . . . 37 11. UJF,. . R e s o l u t i o n w i t h opposed asymmetries . . . . 38 fa 12. IDF_ . R e c o n s t r u c t i o n w i t h d o u b l e t and symmetric fa s i n g l e t . 0 0 . . . . . . . . . . . 0 39 13. llJFg . R e s o l u t i o n w i t h doublet and asymmetric s i n g l e t . . . . . . o . . . . . . * * 39 14. UJF . Proposed u n i t c a l l ( a l o n g c-axi.i) . . . . . 46 - V l l l - FIGURE TO FGLLOllJ PAGE 15. I F * AsF,. . Temperature dependence of a b s o r p t i o n o o s p e c t r a a t 30 MHz 55 16. IF* AsEg . Temperature dependence of second moment a t 30 MHz . . . . . . . . . . . . 55 17a. I F * AsFg . F i e l d dependence of a b s o r p t i o n s p e c t r a a t 295°K 56 17b. I F * AsF . F i e l d dependence of a b s o r p t i o n s p e c t r a a t 77°K 56 18. - IF* AsF . Chemical s h i f t of c e n t r o i d of spectrum r e l a - • b to CF 3C00H . 56 19. I F * ̂ sFg . F i e l d dependence of l i n e width at 77° and 295°K 57 20. I F * AsF, . F i e l d sauared dependence of second moment D O ' a t 77° and 295°K . . . . . . . . . . . . 57 21. SF* AsFg . Temperature dependence of a b s o r p t i o n s p e c t r a at 30 MHz ." . . . . 69 22. SF^ ^ s F ^ ° Temperature dependence of second moment at 30 MHz. . . o . . . . o o . . . . . . 69 23. SF* AsF^ . Chemical s h i f t of c e n t r o i d of soectrum r e l a - t i v e to CF^COOH 79 24a. SF* AsFg o F i e l d dependence of a b s o r p t i o n s p e c t r a a t 300°K 70 24b. SF* ftsFg . F i e l d dependence of a b s o r p t i o n s p e c t r a at 77 K . o o . o o . . o . . . • o • 0 70 25. SF* AsF^. • F i e l d squared dependence of second moment 0 0 at 77 and 300 K 72 26. SF* AsF- . Proposed u n i t c e l l (along a - a x i s ) . . . 75 27. I o n i c and double bond c h a r a c t e r i n h e x a f l u o r i d e groups as a f u n c t i o n of mean i s o t r o p i c chemical, s h i f t r e l a t i v e to HF 84 Acknowledgements Thanks are due to Dr. B.A. D u n e l l who d i r e c t e d t h i s r e - s e a r c h . His p a t i e n c e and a d v i c e have been much a p p r e c i a t e d . Acknowledgement i s a l s o made of frequ e n t a d v i c e and a s s i s t a n c e from Mr. l i J .R . Danzen i n c o e r c i n g and c a j o l i n g the spect r o m e t e r s i n t o o p e r a t i o n . H e l p f u l a d v i c e on programming was always cheer- f u l l y g i v e n by Mr. T. Cyr. Thanks are a l s o due to Dr. N e i l B a r t l e t t ' s p r o v i d i n g the f l u o r i n e compounds, which were made by Dr. Steve Beaton, and to Mr. Jack Passmore of the same group f o r making h i s vacuum system a v a i l a b l e to me when necessary. F i n a l l y warmest thanks are due to the unknown t h i e f who s t o l e Ted's t r a n s i s t o r r a d i o from our l a b 0 C H A P T E R 1 INTRODUCTION In the F a l l of 1964, a j o i n t p r o j e c t on the i n v e s t i g a t i o n of the n u c l e a r magnetic resonance s p e c t r a of the s o l i d a d d i t i o n com- pounds SF^ • BF^ , SF^ ° ^ s^5 a n c* ° u j a s undertaken i n c o l l - a b o r a t i o n w i t h Dr. N e i l B a r t l s t t and h i s co-workers. E x p l o r a t o r y s t u d i e s showed t h a t an exam i n a t i o n of the s i m p l e r molecule UJF_ o might be h e l p f u l . In the event, i t turned out th a t a complete i n t e r - p r e t a t i o n of the s p e c t r a of any of these compounds was made very d i f f i c u l t by combined i s o t r o p i c chemical s h i f t and che m i c a l s h i f t a n i s o t r o p y , both of which were s i g n i f i c a n t , but d i f f i c u l t to sepa- r a t e from one another and from d i r e c t 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 the s o l i d s . Because of the presence i n a l l samples of SF^ „ BF^ of a narrow, i m p u r i t y l i n e which grew as each sample aged, a t t e n t i o n was focused on the other two adducts. I t was obvious t h a t the AsF f l u o r i n e s would be i s o t r o p i c a l l y s h i f t e d from the f l u o r i n e s i n the SF^ or IV^ p o r t i o n s of the adducts. To study the e f f e c t of a n i s o t r o p i c s h i f t u n c o m p l i c a t e d by i s o t r o p i c s h i f t , a mo l e c u l e , s o l i d UJF , i n which tha f l u o r i n e s were expected to be e q u i v a l e n t , or very n e a r l y so, was s e l e c t e d . N on-equivalent f l u o r i n e s , however, were p r e s e n t i n UJF and a s e a r c h f o r a q u a n t i t a t i v e i n t e r p r e t a t i o n of the d e t a i l of the molecule's l i n e shape u l t i m a t e l y c c c u p i a d some t w o - t h i r d s of the time i n v o l v e d i n the r e s e a r c h . T h i s t h e s i s then became a g e n e r a l n u c l e a r magnetic resonance study of the f l u o r i n e 2 s p e c t r a o f SF̂ . ° AsF^ , I F ? • AsF^ , and s o l i d U/Fg , c o m p r i s i n g , inhere p o s s i b l e , temperature dependence, i n t e r p r e t a t i o n of the l i n e shapes w i t h r e s p e c t to i s o t r o p i c and a n i s o t r o p i c c h e m i c a l s h i f t s , and i d e n t i f i c a t i o n of e q u i v a l e n t f l u o r i n e atoms. The two AsF adducts are r e l a t i v e l y new compounds having been 5 r e p o r t e d o n l y d u r i n g the l a s t decade. In 1956, B a r t l e t t ( l ) r e - p o r t e d t h a t SF^, c o o r d i n a t e d w i t h A s F 5 i n the r a t i o of one mole of each to form a new compound, a white s o l i d . The f o l l o w i n g year he observed t h a t a displacement r e a c t i o n i n v o l v i n g t h i s adduct was a c o n v e n i e n t method f o r p u r i f y i n g SF̂ , ( 2 ) . In 1958 S e e l and Detmer (3) r e p o r t e d SF. • AsF,- and I F ^ . AsF,. . They noted t h a t the s t a b l e 4 b b 5 s o l i d s were a co n v e n i e n t form i n which to s t o r e gaseous f l u o r o com- pounds such as SF^ . They a l s o used IF.., . AsF_ as a source of pure f l u o r i n e ( 4 ) . In a lo n g e r paper i n another j o u r n a l (5) they d i s - cussed the compounds again and suggested an i o n i c f o r m u l a t i o n . In 1961, B a r t l e t t (6) r e p o r t e d i n g r e a t e r d e t a i l on SF . A s F c . 4 5 K o l d i t z ( 7 , 6, 9) has a l s o r e p o r t e d adducts of A s F 5 which are i o n i c . Beaton (10) from i n f r a r e d and X-ray s p e c t r a has shown t h a t the a c i d - base adduct IF • AsF i s indeed the i o n i c s a l t I F * AsF~ . Tebbe ' 5 6 6 and M u e t t a r t i e s ( l l ) and Young and May (12) a l s o have r e p o r t e d probable i o n i c a dducts of AsF^ . The symmetry of h e x a f l u o r i d e m o l e c u l e s has made them of i n t e r e s t to s p e c t r o s c o p i s t s and t h e o r e t i c i a n s f o r many years (13 to 3 0 ) o Thermodynamic v a l u e s are r e p o r t e d i n the p r e c e d i n g r e f e r e n c e s (14, 20, 21, 26, 28) and a l s o s e p a r a t e l y i n ether papers (31 to 35). In the 3 vapour phase octahedral symmetry appears well established For most hexafluorides (17, 18, 28, 30). Except for UF C (36) no d e t a i l e d D X-ray data e x i s t for the metal hexafluorides. Since the bond lengths (37a) and X-ray r e s u l t s (37b) a v a i l a b l e for U1FC do not per- D mit determination of the symmetry of the s o l i d , i t appeared that t h i s presented an e x c e l l e n t opportunity for broad l i n e nmr. For o UFg the X-ray data i n d i c a t e below +25 C a tetragonal d i s t o r t i o n with four short and two long bonds. B l i n c et a l (38) undertook a broadline nmr study of p o i y e r y s t a l l i n e UF i n which they i n t e r - D 19 o preted the F resonance spectrum below -30 C as a composite a r i s i n g from the i s o t r o p i c chemical s h i f t s of two d i f f e r e n t f l u o r i n e s i t e s present i n a 2:1 r a t i o . This i s i n agreement with the X-ray r e s u l t s . The work was at an external magnetic f i e l d of 9400 gauss, at which f i e l d a n i s t r o p i c chemical s h i f t of the components could not be detected. Working at higher magnetic f i e l d s , Rigny (39) concluded that anistropy was present. B l i n c and Rigny (40) l a t e r published a j o i n t l e t t e r on r e l a x a t i o n through ani s o t r o p i c chemical s h i f t i n UFg. P r i o r to the appearance of Rigny's t h e s i s , work was begun on p o i y e r y s t a l l i n e WF^ i n t h i s laboratory. While the experimental r e s u l t s were being i n t e r p r e t e d , B l i n c et a l (41) published a paper on the nmr and r e l a x a t i o n of hexafluoride, p o i y e r y s t a l l i n e s o l i d s which included WF^. The B l i n c spectra agreed w e l l with those ob- tained hare and the i n t e r p r e t a t i o n confirmed what was already known here - that i n t e r p r e t a t i o n was d i f f i c u l t . High r e s o l u t i o n nmr spectra of l i q u i d MoF and WF have been reported by Cady (26) and 4 - Rigny (42). In Cady's work the fluorides mere also examined belouj the s o l i d - s o l i d t r a n s i t i o n (about -8°C for both compounds) but the spectra were too broad for the l i n e s to be observed by high reso- l u t i o n . In the l i q u i d state both Cady and Rigny observed i n addi- 19 t i o n to the c e n t r a l peak, s i x small s a t e l l i t e peaks i n the F 95 97 19 spectrum of ffloF due to the ' Mo F coupling. For U f C a d y observed only a s i n g l e , c e n t r a l peak. However, Rigny observed two 183 19 s a t e l l i t e s corresponding to the UJ—— F coupling. CHAPTER II NMR THEORY Since the f i r s t s u c c e s s f u l nuclear magnetic resonance e x p e r i - ments mere reported i n 1946 by P u r c e l l , Torrey, and Pound (43) and Bloch, Hansen, and Packard (44) very many papers, reviews, and books on the phenomenon have appeared. For d e t a i l s of the theory one may r e f e r to Bloembergen, P u r c e l l , and Pound (45), reviews by Smith (46), Gutowsky (47, 48) and Pake (49), and books by Bloembergen (50), Andrew ( 5 l ) , Abragam (52), and S l i c h t e r (53) among others. Only i n f o r m a t i o n to supply a general o u t l i n e of the theory i s given i n t h i s s e c t i o n . Unless a s p e c i f i c reference i s given, i t i s to be understood that acknowledgment i s made to the above ( e s p e c i a l l y Andrew) for the m a t e r i a l i n t h i s chapter. Those n u c l e i which do not have even mass number and atomic number have a non-zero spin angular momentum I ti and a d i p o l a r mag- n o t i c moment |J = c o l i n e a r with i t . Prominent among these i s 19 the F nucleus. The magnetic moment i s also often expressed as p = <jjj0I where p e i s the nuclear magneton ( po= <^ ) and g i s the nuclear g - f a c t o r analogous to the Lande s p l i t t i n g f a c t o r . In the absence of an e x t e r n a l magnetic f i e l d the energy of a nuclear "magnet" i s independent of the o r i e n t a t i o n of the magnetic moment However, i n the presence of a f i e l d \\o , the moment i s s u b j e c t to a torque T"jJ*rfo which tends to a l i g n i t p a r a l l e l to the f i e l d . 6 There i s an energy of i n t e r a c t i o n E 5 ~* U'Ho • I f Ho i s taken as the j j - d i r e c t i on, then inhere l a i s the component of the a n g u l a r momentum v e c t o r along Ho . The values of 1^ or m , the magnetic quantum number (the more u s u a l symbol f o r the component of angular momentum) are gi v e n by 19 the s e r i e s I , 1-1, . . . - ( i - l ) , - I . Hence f o r F where I = 2 > there are two p o s s i b l e o r i e n t a t i o n s f o r the component and two p o s s i b l e energy l e v e l s . The s e l e c t i o n r u l e for" t r a n s i t i o n s between the 19 energy l e v e l s i s /\m--l , t h e r e f o r e f o r F ^E = ~ V 1 \ H O • The frequency c o r r e s p o n d i n g to an allowed t r a n s i t i o n i s OJt-2XtV0 - The n u c l e a r moment jĵ  p r e c e s s e s about the e x t e r n a l f i e l d Ho at t h i s frequency, the Larmor p r e c e s s i o n frequency, <*>o • I R the n u c l e a r magnetic resonance experiment, a s m a l l , o s c i l l a t i n g r a d i o - frequency magnetic f i e l d H ( i s a p p l i e d at r i g h t angles to Ĥ c . When the frequency of o s c i l l a t i o n of Ĥ i equals , a resonance i n t e r a c t i o n occurs which may f l i p the nucleus from the upper to lower or lower to upper energy l e v e l . In the u s u a l e x p e r i m e n t a l arrangement the o s c i l l a t o r frequency i s kept f i x e d w h i l e the e x t e r n a l magnetic f i e l d i s s l o w l y v a r i e d to e f f e c t the resonance c o n d i t i o n . The above treatment f o r a s i n g l e nucleus may be extended to a system of weakly i n t e r a c t i n g n u c l e i . T h i s i s an e x c e l l e n t a p p r o x i m a t i o n to the c o n d i t i o n s i n matter i n bulk. At e q u i l i b r i u m ' i n an e x t e r n a l magnetic f i e l d there w i l l be, due to a Boltzman d i s t r i b u t i o n of e n e r g i e s , a s l i g h t excess of s p i n s i n the s t a t e 7 - *n~*h. c o r r e s p o n d i n g to the lower energy l e v e l f o r a F n u c l e u s . There can then be a net a b s o r p t i o n of energy by the n u c l e a r system i n an nmr experiment. This a b s o r p t i o n produces a measurable s i g n a l which i s c h a r a c t e r i s t i c of the system. The net a b s o r p t i o n would cease when the p o p u l a t i o n s of the two l e v e l s were e q u a l i z e d , but r e l a x a t i o n p r o c e s s e s e x i s t whereby the n u c l e i can d i s s i p a t e energy to the s u r r o u n d i n g l a t t i c e . So far', one expects an extremely narrow resonance l i n e . In l i q u i d s t h i s i s g e n e r a l l y r e a l i z e d . (There w i l l of course be un- c e r t a i n t y broadening, which i s fundamental to a l l s p e c t r a l measure- ments.) In r i g i d s o l i d s , however, l i n e widths are t y p i c a l l y of the order of s e v e r a l gauss. Apart from tha t r i v i a l cause of i n - homogeneity i n the e x t e r n a l magnetic f i e l d , which can be reduced to a n e g l i g i b l e v a l u e , there may e x i s t f o r a s p i n \ nucleus s p i n - s p i n , d i p o l a r , and chemical s h i f t broadening mechanisms. I f the n u c l e i i n v o l v e d are i d e n t i c a l , nucleus j produces at nu c l e u s k a magnetic f i e l d o s c i l l a t i n g at i t s Larmor frequency and a s p i n - s p i n t r a n s i t i o n i n v o l v i n g a mutual exchange of energy may o c c u r . This r e s u l t s i n a broadening of the order of_H^ where i s the f i e l d produced at nucleus j by nucleus k. In a d d i t i o n to s p i n - s p i n broadening, there w i l l always be a d i p o l a r broadening r e g a r d l e s s of whether l i k e or u n l i k e n u c l e i are p r e s e n t. Each nucleus e x p e r i e n c e s the r e s u l t a n t e f f e c t of t h e ' e x t e r n a l f i e l d H„ and the l o c a l f i e l d s Wx of a l l the other n u c l e i . The components of the l o c a l f i e l d s i n the d i r e c t i o n of Ho may i n c r e a s e or decrease Ho w i t h a r e s u l t a n t spread of resonance. **** In l i q u i d s the d i p o l a r broadening e f f e c t i s removed by the r a p i d m o t i o n a l a v e r a g i n g of the l o c a l f i e l d s to z e r o , but i n r i g i d , diamagnetic s o l i d s i t i s the p r i n c i p a l c o n t r i b u t i o n to l i n e w i d t h . S p i n - s p i n and d i p o l a r broadening were s t r i k i n g l y demon- s t r a t e d by Pake (54) i n a c l a s s i c experiment w i t h gypsum, -3 CaSO^ • ZH^O . Because of the r dependence of the d i p o l e i n t e r - a c t i o n , each proton i n the gypsum i s predominately i n f l u e n c e d by i t s p a r t n e r i n the water m o l e c u l e . Hence t h e r e are two resonance f r e q u e n c i e s g i v e n by H 0 ' H* t jjK S(3CO&* ,©-|) where H* * \\v/z. \l } i s the proton moment, r i s the p a i r s e p a r a t i o n , and & i s the angle between Ho and£ (the v e c t o r j o i n i n g the two n u c l e i ) . I f , as i n t h i s case, the n u c l e i are i d e n t i c a l , s p i n - s p i n exchange m o d i f i e s the c l a s s i c a l p i c t u r e to Ho' H*± ~ Ji K 3 ( 3 c o S a e - f ) m T h e u n i t c e l l c o n t a i n s two types of protons w i t h g e n e r a l l y d i f f e r e n t v a l u e s of & Depending on the o r i e n t a t i o n of a s i n g l e c r y s t a l one, two, three or four of the p o s s i b l e resonance l i n e s may be observed. C o n t r i - b u tions from d i s t a n t neighbours w i l l c o n t r i b u t e f u r t h e r broadening to the spectrum. I f the sample i s p o l y c r y s t a l l i n e w i t h the o r i e n t - a t i o n of. the d i p o l e p a i r s i s o t r o p i c a l l y d i s t r i b u t e d , a l i n e shape f u n c t i o n of the farm where \\~Ho"H* and the s i g n s are taken as p l u s f o r -3. 3 < 3 j j h - 9 and minus f o r -3^1* , can be d e r i v e d ( 5 4 ) . The p o i y e r y s t a l l i n e l i n e shape i s a do u b l e t which a g a i n i s f u r t h e r broadened by the l o c a l f i e l d s of a l l other n e i g h b o u r s . T h i s g e n e r a l l i n e shape f u n c t i o n w i l l be encountered a g a i n 0 The l i n e shapes f o r c e r t a i n t h r e e - s p i n and f o u r - s p i n systems have been c a l c u l a t e d , but f o r more g e n e r a l systems the task i s ex t r e m e l y d i f f i c u l t and i n any case the l a c k of d e t a i l i n the s p e c t r a makes the e f f o r t of l i t t l e use. F o r t u n a t e l y t h e r e e x i s t s a te c h n i q u e devised by Van Vleck whereby i n f o r m a t i o n can be e x t r a c t e d from the more c o m p l i c a t e d systems. T h i s method and i t s a p p l i c a t i o n s w i l l be d i s c u s s e d p r i o r to d e s c r i b i n g the e f f e c t o f c h e m i c a l s h i f t on l i n a broadening. Van Vleck (55) showed t h a t the moments of a resonance spectrum can be r e a d i l y c a l c u l a t e d . I f the normali z e d l i n e shape i s the f u n c t i o n where K i s the d i s t a n c e from the c e n t e r o f resonance, the h*h moment i s Sn~ f h^J^dh „ A l l the odd- numbered moments are zero s i n c e glK) i s an even f u n c t i o n f o r magnetic d i p o l a r broadening. Van Vleck c a l c u l a t e d second and f o u r t h moments f o r the g e n e r a l case. For a r i g i d p o i y e r y s t a l l i n e sample the second moment i s Sl= i K i ^ N " ^ • ̂ j N - ' X l . d . ^ ^ . . . . ( 2 ) . where I i s the s p i n number of the n u c l e i , | J e i s the n u c l e a r magneton, g i s the n u c l e a r g — f a c t o r , N i s the number of magnetic n u c l e i i n the system over which the sum j i s taken, and fjk. i s the magnitude - 10 of the v e c t o r j o i n i n g n u c l e i j and k. The f i r s t term accounts f o r d i p o l a r broadening by those n u c l e i whose resonance i s being ob- s e r v e d . The second term i s a c o n t r i b u t i o n to s p e c t r a l broadening by s p e c i e s of magnetic n u c l e i o t h e r than those a t resonance. ( i n 19 183 UiFg f o r example, F and UJ r e s p e c t i v e l y . ) During the course of a broad l i n e nmr i n v e s t i g a t i o n of a p o l y c r y s t a l l i n e s o l i d , one n o r m a l l y r e c o r d s the magnetic resonance spectrum over a range of temperatures v a r y i n g from low ( u s u a l l y l i q u i d n i t r o g e n temperature) up to room temperature or c o n s i d e r a b l y h i g h e r as d i c t a t e d by the na t u r e of the compound. I f the lowest temperature corresponds to a r i g i d l a t t i c e c o n d i t i o n , then a f t e r a c o r r e c t i o n f o r z e r o - p o i n t motion of the n u c l e i has been made ( 5 6 ) , the observed second moment, s h o u l d agree w i t h i n e x p e r i m e n t a l e r r o r w i t h the c a l c u l a t e d r i g i d l a t t i c e second moment. Any d i s c r e p a n c y w i l l be due to a d d i t i o n a l motion i n the c r y s t a l l a t t i c e . I f the c r y s t a l s t r u c t u r e has not been determined a resonable s t r u c t u r e may o f t e n be worked out by t r i a l from the nmr r i g i d l a t t i c e second moment. Even i f r i g i d l a t t i c e c o n d i t i o n s do not p r e v a i l , q u i t e r e s o n a b l e e s t i m a t e s of the probable s t r u c t u r e can be o b t a i n e d by con- s i d e r i n g the e f f e c t on second moment of p o s s i b l e motions i n the c r y s t a l l a t t i c e . The a p p l i c a t i o n of second moments i s a l s o u s e f u l i n d e t e r m i n i n g the p o s i t i o n s of p r o t o n s , which are d i f f i c u l t to l o c a t e a c c u r a t e l y by X-ray c r y s t a l l o g r a p h y . Since e q u a t i o n (2) -6 i n v o l v e s r , a h i g h l y a c c u r a t e i n t s r n u c l e a r d i s t a n c e r can - 11 f r e q u e n t l y be o b t a i n e d . In s i n g l e c r y s t a l s p e c t r a bond angles can be o b t a i n e d i n a d d i t i o n to bond l e n g t h s . Motion w i t h i n the l a t t i c e , whether of whole molecules or of s u b s t i t u e n t groups, c o n t r i b u t e s t o a time a v e r a g i n g of the l o c a l f i e l d s . The averaged f i e l d i s l e s s than the steady l o c a l f i e l d f o r a r i g i d system and as motion becomes more pronounced the resonance l i n e becomes narrower as l i q u i d - l i k e c o n d i t i o n s are approached. The narrowing of the l i n e may g i v e evidence of m o l e c u l a r motion aven though the frequency of r e o r i e n t a t i o n m3y be q u i t e s m a l l f o r each molecule. A p o t e n t i a l b a r r i e r o b v i o u s l y e x i s t s f o r t h i s motion and motion takes place when a molecule has s u f f i c i e n t energy to surmount the b a r r i e r . A very h i g h b a r r i e r produces an e s s e n t i a l l y r i g i d s t r u c t u r e although even then there may be r o t a t i o n a l o s c i l l a t i o n . In a r e o r i e n t a t i o n process which can be d e s c r i b e d by a s i n g l e frequency or c o r r e l a t i o n time, the temperature dependence of the c o r r e l a t i o n t i m e , t c , may be des- c r i b e d by ' r c = r 0 e.*p(^E/RT) ( 3 ) where AE i s the h e i g h t expressed i n energy per mole of the h i n d e r - i n g p o t e n t i a l . Then ths r e o r i e n t a t i o n r a t e , VC , d e f i n e d by Vc^V0 (-AE/R.T) o ( 4 ) The resonance l i n e narrows when the r e o r i e n t a t i o n r a t e becomes of the order of the frequency of the l i n e w i d t h . C a l c u l a t i o n of the l i n e shclpe f o r a c o m p l i c a t e d r e o r i e n t i n g system i s of course even 12 - more d i f f i c u l t than f o r a r i g i d system and again second moments are used. The change i n second moment m i l l depend on the nature of the r e o r i e n t a t i c n ( 5 7 ) . For a p o l y c r y s t a l l i n e m a t e r i a l c o n t a i n - i n g a system or group undergoing a f r e e r o t a t i o n over an n - f o l d p e r i o d i c p o t e n t i a l b a r r i e r whers tti 3 i e q u a t i o n (2) becomes, f o r the i n t r a m o l e c u l a r c o n t r i b u t i o n o n l y where YT^ i s the angle between the i n t e r n u c l e a r v e c t o r Jhj^ and the a x i s of r o t a t i o n . Each term has been reduced by the f a c t o r T h i s i s the r e d u c t i o n of only the i n t r a m o l e c u l a r second moment. That f o r the i n t e r r n o l e c u l a r moment i s much more c o m p l i c a t e d s i n c e t*«v: v a r i e s as w e l l 0 The only case i n which the i n t e r r n o l e c u l a r c o n t r i b u t i o n can be o b t a i n e d simply i s t h a t f o r i s o t r o p i c m o l e c u l a r r e o r i e n t a t i o n of a group about i t s m o l e c u l a r c e n t e r (58, 59, 60, 6 1 ) . The magnetic n u c l e i are c o n s i d e r e d to be c o n c e n t r a t e d at the m o l e c u l a r c e n t e r s and the d i s t a n c e s Y'^y. i n e q u a t i o n (2) are r e p l a c e d by , the c e n t e r - c e n t e r d i s t a n c e between a m o l e c u l e and i t s i ^ n e a r e s t neighbour. The e q u a t i o n becomes where No i s the number of resonant n u c l e i i n the molecule, i s t h the number of i n e a r e s t neighbours and the other q u a n t i t i e s are as b e f o r e . The i s o t r o p i c r e o r i e n t a t i o n averages the i n t r a m o l e c u l a r moment to zero and the c a l c u l a t e d sum i s the i n t e r r n o l e c u l a r c o n t r i - b u t i o n 0 I f the r e o r i e n t a t i o n i s not i s o t r o p i c , but about p r e f e r r e d 13 axes a t random the c a l c u l a t i o n i s more d i f f i c u l t (61, 62, 63, 64a) and the r e s u l t may d i f f e r from t h a t f o r i s o t r o p i c r e o r i e n t a t i o n by 5 to 15% (64b). A c t i v a t i o n e n e r g i e s f o r m o l e c u l a r r e o r i e n t a t i o n s may be de- r i v e d from a l o g Vc versus ^/T p l o t of e q u a t i o n ( 4 ) . The c o r r e l a - t i o n frequency i n terms of l i n e w i d t h i n gauss i s (based on Gutowsky and Pake (57) V l s fh ^ / U n 15 ( ^ " ^ ] . . . . . . . . ( 7 ) where i s the l i n e w i d t h i n the t r a n s i t i o n r e g i o n , i s the l i n e w i d t h above the t r a n s i t i o n , and i s tha t below the t r a n s i - t i o n , eC i s a co n s t a n t of the or d e r of u n i t y , and Jj i s the magnetic moment i n n u c l e a r magnetons. I f the l i n e shape changes d u r i n g the t r a n s i t i o n , l i n e w i d t h i s not a r e l i a b l e parameter ( 6 5 ) . S i n c e second moments are a more r e l i a b l e i n d i c a t i o n of temperature e f f e c t s the c o r r e l a t i o n time may be expressed a c c o r d i n g to Powles and 2 Gutowsky (66) i n terms of second moment i n gauss as where S A i s the second moment a t any p o i n t i n the t r a n s i t i o n r e g i o n , A B i s the second moment above the r e g i o n , S^ i s the second moment below the r e g i o n , and the o t h e r symbols are as befo r e . Unless only a s i n g l e motion i s o c c u r r i n g t h e s e are average values of and which are o b t a i n e d . A l s o an added u n c e r t a i n t y a r i s e s from the use of the l i n e w i d t h or second moment. The i n t e r m o l e c u l a r c o n t r i b u t i o n s to the resonance curve may vary w i t h motion and hence w i t h temperature i n a d i f f e r e n t f a s h i o n from the i n t r a m o l e c u l a r c o n t r i b u t i o n . Orders 14 of magnitude of VL or are probably the best that can be expected. A more r e l i a b l e approach i s to determine c o r r e l a t i o n times from spin- l a t t i c e r e l a x a t i o n measurements. This i s , however, not always experimentally convenient, while l i n e widths and second moments can always be obtained. Furthermore i f the motion taking place i s com- p l i c a t e d , and are, as noted above, average values. Compari- son of the observed second moment change with that c a l c u l a t e d on the basis af the possible motions occurring gives a more r e l i a b l e p icture of reorientations taking place i n complicated cases. The a c t i v a t i o n energy w i l l , however, provide supporting evidence for the occurrence of the suggested motion,, Chemical s h i f t also contributes to nuclear magnetic resonance line-broadening. In diamagnetic molecules, the most frequent subjects for nmr experiments, the ground state has, i n the absence of an external f i e l d , no r e s u l t a n t e l e c t r o n i c spin or e l e c t r o n i c o r b i t a l angular momentum (67). An external f i e l d induces an o r b i t a l motion i n the electrons of a molecule which i s superimposed on the electrons' motions about t h e i r n u c l e i . The motions constitute e f f e c t i v e currents within the molecule which produce at the nucleus a d d i t i o n a l magnetic f i e l d s which are p r o p o r t i o n a l to the external f i e l d !rU . The resultant f i e l d experienced by the nucleus i s expressed as (52, Chap. 6; 68, Chap. 1) H= tfft Cl-e) ( g ) where <5 i s a second rank tensor depondent on the e l e c t r o n i c cnviron- ment of the nucleus considered. The s h i f t i s a combination of 15 - diamagnetic and paramagnetic s h i e l d i n g e f f e c t s . The di a m a g n e t i c term i s e s s e n t i a l l y a Larmor p r e c e s s i o n , i n the f i e l d Ho > of the e l e c t r o n i c charges i n the molecule about the nucleus i n q u e s t i o n ; w h i l e the paramagnetic term a r i s e s from the p o l a r i z a t i o n of e l e c t r o n s h e l l s by H« (52, Chap. 6 ) . S l i c h t e r (53, p. 84) expressed the s h i e l d i n g a f t e r Ramsey (57) as J 4 r J . where e i s the e l e c t r o n i c charge, fn the e l e c t r o n i c mass, c the speed of l i g h t ; ^ , j * A and £ 0 , the wavefunctions and en e r g i e s of e l e c t r o n s th i n the ground and n e x c i t e d s t a t e s r e s p e c t i v e l y ; the t o t a l angu- l a r momentum o p e r a t o r J ^ * ? j (where £j i s the v e c t o r from the s h i e l d - ed nucleus to the e l e c t r o n whose c o o r d i n a t e s are * j , , S j and p̂ - i s the l i n e a r momentum),^*. i s the angular momentum op e r a t o r "ft - S ^—i i snd Y: i s the magnitude of fi . The sums j and k Ty ay J d* ) * are taken over the N e l e c t r o n s p r e s e n t and the sum n over the n s t a t e s . The two terms are of ap p r o x i m a t e l y equal magnitude and are r e s p e c t i v e l y the diamagnetic and the second-order paramagnetic con- t r i b u t i o n . As i n d i c a t e d by e q u a t i o n (10) the diamagnetic term i s a ground s t a t e c o n t r i b u t i o n . I t i s i n f a c t ( 5 7 ) , the same as Lamb's complete e x p r e s s i o n f o r the di a m a g n e t i c s h i e l d i n g of s i n g l e atoms (69)= 16 The paramagnetic term i s an e x c i t e d s t a t e c o n t r i b u t i o n from the magnetic f i e l d s s e t up by the o r b i t a l motions of the valence e l e c t r o n s (70-). In the absence of an e x t e r n a l s t a t i c f i e l d the o r b i t a l f i e l d s have a zer o average v a l u e but produce i n s t a n t a n e o u s f i e l d s of s e v e r a l thousand gauss a t the nucleu s . The a p p l i e d f i e l d produces a s l i g h t p o l a r i z a t i o n of these l a r g e f i e l d s and hence an a p p r e c i a b l e s h i e l d i n g . S i n c e the valence e l e c t r o n s are more r e a d i l y p o l a r i z e d , the p r i n c i p a l c o n t r i b u t i o n i s from thorn r a t h e r than from the c l o s e d s h e l l e l e c t r o n s . Ramsey (67) p o i n t e d out, however, t h a t the s e p a r a t i o n i n t o two d i s t i n c t terms i s a r t i f i c i a l and t h a t the terms are i n f a c t c l o s e l y r e l a t e d , , I n t h e i r d i s c u s s i o n of f l u o r i n e c h e m i c a l s h i f t s , S a i k a and S l i c h t e r (70) made a d i v i s i o n of the s h i f t i n t o three terms: (a) the diamagnetic c o r r e c t i o n f o r the r e l e v a n t atom. This i s a g a i n the Lamb term. I t accounts f o r only about 1% of the range o f f l u o r i n e s h i f t s observed. (b) the paramagnetic c o r r e c t i o n f o r the r e l e v a n t atom. This term i s p r i n c i p a l l y r e s p o n s i b l e f o r c h e m i c a l s h i f t s i n f l u o r i n e s . ( c ) the c o n t r i b u t i o n s from e l e c t r o n s i n other atoms. The e l e c t r o n s i n other atoms are e i t h e r i n c l o s e d s h e l l s and d i f f i c u l t to p o l a r i z e or i n valence s h e l l s i n which tha e l e c t r o n s although 1 i r e a d i l y p o l a r i z e d are s t i l l s u b j e c t to a / r f a l l i n g o f f of the i n t e r a c t i o n . The c o n t r i b u t i o n from t h i s term i s t h e r e f o r e s m a l l . 17 Although term (b) i s the p r i n c i p a l c o ntribution to the f l u o r i n e s h i f t , i n the case of electrons i n a purely s state (the electrons exert a zero instantaneous o r b i t a l magnetic f i e l d at the nucleus, while p and d electrons exert large f i e l d s ) the terms (a) and (c) would comprise the s h i f t . That i s , because of the s p h e r i c a l symmetry of an s s t a t e , the angular momentum operators make the second term of equation (10) equal to zero for a purely s state,. The paramagnetic term would be zero i n completely i o n i c F because of the f i l l e d L s h e l l , and have i t s maximum value i n covalent F^. Pople (68, Chap. 7) adds a fourth term to Saika and S l i c h t e r ' s : (d) the c o n t r i b u t i o n from interatomic currents. I f i t i s po s s i b l e for electrons to flow from one atom to another, as for example i n aromatic molecules, the interatomic currents can generate a d d i t i o n a l screening. Chemical s h i f t broadening of the resonance l i n e may have e i t h e r i s o t r o p i c or a n i s o t r o p i c o r i g i n s or both. I f a s o l i d contains non- equivalent n u c l e i there w i l l be a broadening of the resonance l i n e due to d i f f e r e n c e s i n i s o t r o p i c s h i f t . I f there are nuclei i n non- equivalent e l e c t r o n i c environments, Andrew (71) notes that the f o l l o w - i n g a d d i t i o n a l c o n t r i b u t i o n must be added to the second moment: where IB - i s the i s o t r o p i c mean s h i f t f o r nucleus v( where « u S 3 T v " ^ S i ( ° » x + ^ * ^ ............ (12a) where 6 ^ , , and are the p r i n c i p a l axes of the s h i f t t e n s o r . Even i f a s o l i d c o n t a i n s only n u c l e i i n i d e n t i c a l e l e c t r o n i c environments, there may be a chemical s h i f t c o n t r i b u t i o n to l i n e broadening. I f the ch e m i c a l s h i f t tensor,©", i s asymmetric, a probing e x t e r n a l f i e l d w i l l encounter d i f f e r e n t e l e c t r o n i c s c r e e n - i n g depending on the m o l e c u l a r o r i e n t a t i o n i n the f i e l d . The i n v e s t i g a t i o n of che m i c a l s h i f t a n i s o t r o p y i n p o i y - e r y s t a l l i n e s o l i d s i s based on the approach employed by Bloembergen and Rowland (72) w i t h t h a l l i c o x i d e . Andrew and T u n s t a l l (71) express the f i e l d e x p e r i e n c e d by a gi v e n nucleus i n a p o i y - e r y s t a l l i n e s o l i d as where ̂ -m, G~^^ are again the p r i n c i p a l axes of the s h i f t t e n s o r and %x> "X.JB » are the d i r e c t i o n c o s i n e s w i t h r e s p e c t to H© • The i f f " . ~ average f i e l d e x p e r i e n c e d by a l l the n u c l e i i f the c r y s t a l l i t e s i n the p o i y e r y s t a l l i n e sample are i s o t r o p i c a l l y d i s t r i b u t e d i s expressed by ...... (14) - 19 - For a x i a l symmetry about the z - a x i s = C O S © , G^-e^^-Gx » and 6̂" and H= H - K 0•••0• ( 1 5 ) where K - ± H0 C3 ~0 and where H and H are f i e l d s a t nuc l e u s 3 The n o r m a l i z e d l i n e shape i s then «o6» CiV5dT ,6+f)"% (") where - a ^ K — 2 3 The f u n c t i o n f ( h ) i s s i m i l a r i n form to equation ( l ) . The second moment of the l i n e shape given by equation (16) (17) and i f the d i p o l a r broadening i s d e s c r i b e d by a s y m m e t r i c a l , n o r m a l i z e d l i n e - shape f u n c t i o n g(h) then the t o t a l second moment i s (71, 73) V3»^4il(k)''3iW»^K,Ve1,-«iV ( 1 8 ) The c o r r e c t c e n t e r of moments i s not r e a d i l y apparent i n an asy- mmetric curve, but i f f i r s t and second moments are computed about a p o i n t c l o s e to the est i m a t e d c e n t e r ( t o minimize e r r o r ) the f i r s t moment gives the c e n t e r of moments d i r e c t l y and the second moment can be t r a n s f e r r e d to i t . I f the t r a n s f e r r e d second moment i s p l o t t e d a g a i n s t H6 , the a b s o l u t e v a l u e of the a n i s o t r o p y of - 20 chemical s h i f t can bs determined. The s i g n can be found from the d i r e c t i o n of asymmetry of the curve. The a n i s t r o p y may be used to p r o v i d e i n f o r m a t i o n about the type of bonding i n the s o l i d studied,, The i n t e r c e p t o f the p l o t w i l l g i v e the d i p o l a r second moment, and t h i s can be used as a broadening f u n c t i o n ( g a u s s i a n u s u a l l y ) on e q u a t i o n (16) to s y n t h e s i z e a curve f o r comparison w i t h the e x p e r i m e n t a l curve,, The e x t r a - p o l a t e d " d i p o l a r moment" w i l l of course i n c l u d e any f i e l d indepen- dent broadening which i s p r e s e n t . I f both i s o t r o p i c and a n i s o t r o p i c s h i f t s are p r e s e n t the second moment e q u a t i o n becomes Here the e x p r e s s i o n s (<S|~ S ^ e t c . are as i n equations ( l l ) and (12) and C6tt— £5j[) i s a n average a n i s o t r o p y f o r a l l the " i s o t r o p i c a l l y " s h i f t e d resonant n u c l e i . Unless the v a r i o u s n u c l e i are s u f f i c i e n t l y s h i f t e d from one another to permit a c o n f i d e n t r e s o l u t i o n of t h e . curve i n t o i t s components ( i n which case the i n d i v i d u a l may be determined a l s o ) the i n t e r p r e t a t i o n of the resonance spectrum may be very d i f f i c u l t . CHAPTER I I I EXPERIMENTAL PROCEDURE The SF. * AsF , IF_ • AsF_ , and UJF,. samples s u p p l i e d by 4 b / b b Dr. N e i l B a r t l e t t were prepared by Dr. S.P. Beaton. Only pure SF • AsF and IF • AsF samples mere used. For UJF both pure 4 5 / 5 b samples and samples doped w i t h I r F (up to one p a r t per thousand) b were run. In the l a t t e r case the paramagnetic i m p u r i t y was added to s h o r t e n the s p i n - l a t t i c e r e l a x a t i o n time, reduce s a t u r a t i o n , and improve the s i g n a l to n o i s e r a t i o i n the spectrum by p e r m i t t i n g the runs t o be made at h i g h e r r f f i e l d (H ( f i e l d ) . S p e c t r a were recorded over a two year p e r i o d u s i n g s e v e r a l d i f f e r e n t samples of each compound. At the end of the study comparisons were made bet- ween r e c e n t samples and samples s t o r e d f o r more than a year. Between runs samples were s t o r e d i n a d r y - i c e acetone bath or l i q u i d n i t r o g e n . The f l u o r i n e magnetic resonance s p e c t r a of the compounds were re c o r d e d on two V a r i a n 4250-type broad l i n e spectrometers, and on a U a r i a n HA100 h i g h r e s o l u t i o n s p e c t r o m e t e r . One of the broad l i n e s p e c t r o m e t e r s was a DP60 w i t h a U a r i a n 12 i n c h electromagnet and a 56.4 MHz V-4311 F i x e d Frequency RF U n i t . The other broad l i n a s p e c t r o m e t e r employed a Marian 6 i n c h electromagnet and a 30 MHz .V-431GA F i x e d Frequency RF U n i t and a 2-16 MHz V-4210A V a r i a b l e Frequency RF U n i t 0 The 2000 Hz sidebands of the V-3521A I n t e g r a t o r / 21 - 22 - Decoupler were used to p r o v i d e sweep modulation on the HA100. S i n c e the resonance l i n e s of the s o l i d s were very much wider than 2000 Hz, the r e s u l t i n g s p e c t r a were the f a m i l i a r d e r i v a t i v e s i g n a l s c u s t o m a r i l y observed i n broad l i n e work. Since the normal method of c a l i b r a t i n g the modulation a m p l i t u d e of a l o c k - i n d e t e c t o r by r e c o r d i n g the d e r i v a t i v e of a l i q u i d l i n e could not be used on the high r e s o l u t i o n s p e c t r o m e t e r , a minor problem was encountered i n d e t e r m i n i n g the a m p l i t u d e of the m o d u l a t i o n . However, when a l i q u i d s i g n a l i s scanned, the I n t e g r a t o r / D e c o u p l e r may be a d j u s t e d to g i v e zero amplitude f o r the c e n t e r band. Then a t t h a t p o i n t there i s a known mo d u l a t i o n i n d e x from which the modulation a m p l i - tude may be determined ( 7 4 ) . T h i s r e q u i r e d adjustment of the coarse a m p l i t u d e c o n t r o l i n the i n t e r i o r of the i n s t r u m e n t . I t was d i f f i c u l t to reproduce t h i s e x a c t v a l u e f o r each s e r i e s of runs w i t h - out r e c o r d i n g a t e d i o u s s e r i e s o f s i g n a l s on a s t r i p r e c o r d e r each time. However, i t was always s i m p l e to ensure t h a t the amplitude was below the p o i n t of known ampli t u d e which i n i t s e l f was s a f e (about 1.2 gauss peak to peak) and t h a t modulation broadening was absent. A more s e r i o u s problem was encountered i n o b t a i n i n g a pure a b s o r p t i o n d e r i v a t i v e of the resonance s i g n a l . B a l a n c i n g and phas- i n g were q u i t e c r i t i c a l and l a b o r i o u s . Operation on wide l i n e diode d e t e c t i o n w i t h the i n t r o d u c t i o n of a b s o r p t i o n leakage was q u i c k e r and s u r e r than phase d e t e c t i o n . I t a l s o produced a b a t t e r s i g n a l to n o i s e r a t i o . Standard o p e r a t i n g procedures were employed on the two broad, l i n e s p e c t r o m e t e r s . 23 The temperature dependence of the f l u o r i n e magnetic resonance o spectra mas studied at 30 MHz for a l l three compounds from 77 K to o o o above 300 K and for a few temperatures from 173 K to 283 K at 94.1 MHz for a sample of IrF.-doped U/F.. For low temperature runs at o o 30 MHz the temperature was c o n t r o l l e d by cooled nitrogen vapour' passed through a flow system which has been described by UJare (75). o Below about 220 K a l i q u i d nitrogen bath was used to cool the gas 0 Between 220°K and room temperature a dry-ice acetone bath was used. Above room temperature, heated, compressed a i r was used i n place of the tank nitrogen. The extremely e f f i c i e n t heater was of a double- pass heat exchanger type, i n c o r p o r a t i n g a 600V 1/cylindrical heating c o i l , designed by Ui.R. 3anzen for his work i n t h i s laboratory. Temperature c o n t r o l was approximately +5° around 100°K and +1° above 150°K. At 94.1 MHz the standard Varian V/-4341 Variable Temperature System was used. The temperature range of t h i s system i s stated to o o be -50 to +200 C, but i t was found that -100 C could be reachedo The maximum temperature v a r i a t i o n at the sample i s +1°C within the s p e c i f i e d range and ' c a l i b r a t i o n i s about +3°C. studied at the f o l l o w i n g temperatures and RF frequencies (He f i e l d ) . The Ho f i e l d dependence of the spectrum of each compound was Compound Temperature K RF Frequency MHz 94.1, 56.4, 40, 30 SF 4 o AsF 5 295-300 I F ? . AsF 5 77 295-300 94.1, 56.4, 40, 30 94.1, 56.4, 40, 30 94.1 94.1, 56.4, 40, 30, 16 77 173 77 94.1, 56.4, 40, 30, 16, 2 - 24 - F o r both IF„ • AsF,_ and UJF^ u s a b l e s p e c t r a c o u l d not be o b t a i n e d a t / 5 6 77°K and 94.1 UlHz due to the r e s t r i c t i o n on sample s i z e e x p l a i n e d o below. However, a 5 mm diameter sample of UJF^ run at 173 K and 94.1 MHz u s i n g the V-4341 temperature system d i d produce u s a b l e o s p e c t r a . For the f i x e d temperature work at 77 K, the samples were immersed i n dewars f i l l e d w i t h l i q u i d n i t r o g e n . The dewars have been d e s c r i b e d elsewhere (75, 7 6 ) . The dewar (5 mm O.D. ) used a t 94.1 MHz i n the HA100 s e v e r e l y r e s t r i c t e d sample s i z e to about 1,6 mm c a p i l l a r i e s and had the b a r e l y s u f f e r a b l e disadvantage t h a t i t would h o l d l i q u i d n i t r o g e n f o r only f o u r t o s i x minutes. A dewar w i t h a l a r g e r l i q u i d n i t r o g e n c a p a c i t y , though of course w i t h the same sample s i z e r e s t r i c t i o n , was made by the Department's g l a s s - blower, Mr. Rak. This dewar h e l d n i t r o g e n f o r more than two hours but c o u l d not be removed from the probe w i t h o u t f i r s t t a k i n g the l a t t e r out o f the magnet gap. The samples used were a l l p o i y e r y s t a l l i n e m a t e r i a l , the s p e c t r a o f which were independent of o r i e n t a t i o n i n the magnetic f i e l d M© • P r e l i m i n a r y s p e c t r a were scanned up to 500 gauss on e i t h e r s i d e o f resonance to e s t a b l i s h t h a t the resonance was con- f i n e d t o the r e g i o n s t u d i e d i n expanded s c a l e . A l s o , at each f r e - quency (He f i e l d ) p r e l i m i n a r y s p e c t r a were run to check the r f l e v e l f o r s a t u r a t i o n . The f i e l d Wt u-as v a r i e d over a wide range from about 0.05 mgauss t o 45 mgauss. Ulhan an r f r e g i o n was found where l i n e w i d t h s remained c o n s t a n t as the power was lowered, forward and r e - 25 verse scans mere run to check t h a t l i n e shape was the same f o r both d i r e c t i o n s . Ufhen an a p p a r e n t l y s a t i s f a c t o r y l e v e l had been found the r f l e v e l was f u r t h e r reduced to a s c e r t a i n t h a t no a d d i t i o n a l l i n e shape changes o c c u r r e d . In g e n e r a l , i t was found t h a t a l l three s t e p s were n e c e s s a r y . S i n c e a t l e a s t two c h e m i c a l l y s h i f t e d f l u o r i n e n u c l e i were p r e s e n t i n each molecule, s a t u r a t i o n e f f e c t s produced sometimes s u b t l e changes i n the s p e c t r a a f t e r an appar- e n t l y s a f e power l e v e l had e l i m i n a t e d the gross e f f e c t s . Around 0.5 to 1.0 mgauss was g e n e r a l l y a s a f e r e g i o n , but s p e c t r a were always checked over a range of r f power f o r s i g n s of s a t u r a t i o n , o At 77 K, the r e s t r i c t i o n p l a c e d on the sample s i z e by the dewars meant a poor p a c k i n g f a c t o r i n the r e c e i v e r c o i l . S ince the s a t u r a t i o n l e v e l was f a i r l y low (Hi under 1.5 mgauss) by the time the r f was reduced below s a t u r a t i o n , the s i g n a l to n o i s e r a t i o was poor i n some c a s e s . The a c t u a l r a t i o v a r i e d depending on sample and sample s i z e , and on the RF u n i t used and i t s o p e r a t i n g c o n d i t i o n . A high sweep mo d u l a t i o n c o u l d not be used to improve the s i g n a l to noise r a t i o s i n c e m o d u l a t i o n broadening would have caused a l o s s of s t r u c t u r e which would have t o t a l l y f r u s t r a t e d attempts to r e s o l v e the s p e c t r a i n t o t h e i r p o s s i b l e components. At the low m o d u l a t i o n amplitude used ( a p p r o x i m a t e l y 0.5 gauss peak to peak), modulation c o r r e c t i o n to the second moment was n e g l i g i b l e , but a r e l a t i v e l y low s i g n a l to n o i s e r a t i o had o f t e n to bs t o l e r a t e d . R a t i o s v a r i e d from about 4:1 i n some u n f a v o u r a b l e cases at 77°K to 45:1 under good - 26 - conditions at room temperature. No reference sample urns used i n the runs with v a r i a b l e temp- erature equipment or with the large dewar on the HA100, but a CF„C00H or C.F, reference was used i n the Ho f i e l d dependence runs 3 6 6 at 77°K and 300°K. Since the p u r i t y of the CF COOH standard was unknown, i t s chemical s h i f t r e l a t i v e , to Freon 11 was measured at the conclusion of the experiments. The s h i f t was + 76 021 ppm. Two sidebands were imposed on the reference's f l u o r i n e resonance with a Hewlett Packard model 200CD Audio O s c i l l a t o r . The f i e l d H»was scanned through one of the sidebands and, while scanning proceeded, the reference was replaced by the sample, the probe rebalanced i f necessary and the spectrum recorded. The sample was then replaced by the reference and the other sideband recorded. The p o s i t i o n of the reference resonance was taken as the midpoint between the two sidebands. A minimum of four spectra were recorded at each temperature i n the temperature dependence runs. In the H» f i e l d dependence runs, except at 94.1 IYIHZ where machine time was i n great demand, at l e a s t four referenced spectra were recorded at each frequency o o at 300 K and ten to twelve at 77 K, the temperature of greatest i n t e r e s t . In a d d i t i o n , at l e a s t a dozen non-referenced spectra o o were run for each sample at each frequency at 77 K and 300 K. CHAPTER IV RESULTS & INTERPRETATION Programs w r i t t e n f o r the U n i v e r s i t y of B r i t i s h Columbia's IBM 7040 computer p l a y e d an e x t e n s i v e p a r t i n d e t e r m i n i n g and e v a l u a t i n g the r e s u l t s o b t a i n e d here. The programs are l i s t e d t o - gether w i t h e x p l a n a t i o n s i n Appendix I . Samples of a l l t h r e e of wT , IF • AsF , and SF^ • AsF^ appeared q u i t e s t a b l e when s t o r e d i n d r y - i c e acetone or l i q u i d n i t r o g e n baths. There was no change e x h i b i t e d between s p e c t r a of the same samples taken a f t e r more than one year of s t o r a g e . S p e c t r a of a l l samples of the same compound were e x p e r i - m e n t a l l y c o n s i s t e n t whether o l d or f r e s h l y s u p p l i e d . 1. R e s u l t s Although samples which were doped w i t h paramagnetic I r F o c o u l d be run at a h i g h e r r f ( H ^ ) w i t h a r e s u l t a n t more f a v o u r a b l e s i g n a l to n o i s e r a t i o , both pure and doped samples of UJF behaved i d e n t i c a l l y w i t h i n e x p e r i m e n t a l e r r o r . Therefore no d i s t i n c t i o n i s made between pure or doped samples i n the r e s u l t s r e p o r t e d . F i g u r e 1 demonstrates the temperature dependence of the 19 F nmr s p e c t r a of 'wT̂  a t 30 IYIH . The a b s o r p t i o n s p e c t r a having a common x - s c a l e and being n o r m a l i z e d to c o n s t a n t a r e a , were 27 - To Follow Page 27 To F o l l o w Page 27 Figure 2, WF\/. Temperature dependence of second moment at 30 MHz T E M P E R A T U R E ° K To Follow Page 27 Figure 3. WF,. Temperature dependence of l i n e width at 30 and 94.1 MHz A A A A 8 0 1 2 0 I S O 2 0 0 2 4 0 2 8 0 T E M P E R A T U R E °K - 28 - o b t a i n e d by i n t e g r a t i o n from the d e r i v a t i v e curves u s i n g Program 2, Appendix I . Re p r o d u c t i o n s of d e r i v a t i v e curves f o r tempera- t u r e dependence a t 30 MHz and a l s o a t 94.1 rnHz are g i v e n i n Appendices I l a and l i b . F i g u r e s 2 and 3 show r e s p e c t i v e l y the second moment at 30 MHz ( c a l c u l a t e d w i t h Program 1, Appendix I u s i n g the method o u t l i n e d t h e r e ) and the l i n e width a t 30 MHz and 94.1 MHz (between extreme maxima and minima of the d e r i v a t i v e c u r v e ) as f u n c t i o n s of temperature. 2 The second moment remains c o n s t a n t at 9.0+0.4 gauss from o o 77 K t o a p p r o x i m a t e l y 180 K. As seen i n Figure 1, throughout t h i s r e g i o n t h e r e i s an asymmetry to high f i e l d which d i s a p p e a r s o 2 as the second moment drops between 180 and 220 K to 1.0+.05 gauss . Du r i n g the t r a n s i t i o n the l i n e changes from a s l i g h t l y asymmetric d e r i v a t i v e a t 180-185°K to a symmetric d e r i v a t i v e curve a t 205 to 210°K. The second moment remains constant a t 1.0 gauss from 220 to 262°K. Beyond t h i s r e g i o n t h ere i s a sudden drop between 262 o and 265 K to a v a l u e which c o u l d net be a c c u r a t e l y measured from the d e r i v a t i v e c u r v e . The b e h a v i o u r of the l i n e w i d t h at 30 MHz f o l l o w s the same p a t t e r n over the temperature range. I t i s c o n s t a n t a t 9.8+0.1 o o gauss from 77 to 180 K, dropping to 3.2+0.1 gauss by 2z0 K and dr o p p i n g a g a i n ( a f t e r r emaining c o n s t a n t a t 3.2 gauss) around 262 o o to 265 K t o a value of 0.1 gauss as measured at 269 K. Although the l i n e w i d t h measurement can be made between 265 and 287°K, i t - 29 - i s governed by the depth of m o d u l a t i o n which was 0.1 gauss peak to peak. The s p e c t r a i n t h i s r e g i o n were s i m i l a r whether taken above or below the m e l t i n g p o i n t of 276°K (orthorhombic to c u b i c c r y s t a l o o t r a n s i t i o n a t 265.0 K, m e l t i n g p o i n t at 276.4 K, and b o i l i n g p o i n t 290.3-290.7°K (20, 26)) and a l l had the appearance of l i q u i d - l i k e s p e c t r a . However, i n t e n s i t i e s were l e s s than and l i n e s were / o \ broader than t h a t of a l i q u i d s i g n a l (CF^COOH at 298 K) i n the same f i e l d . The appearance of the spectrum was r e a l l y more l i k e t h a t of a v i s c o u s l i q u i d w i t h i n t h i s range (265-2B7°K). V a r i a b l e temperature s p e c t r a a t 94.1 (111Hz (Appendix l i b ) show s i m i l a r behaviour to those a t 30 MHz. L i n e width i s of the order of 12.0+0.3 gauss between 173 and 183°K. By 193°K, asymmetry i s s t i l l p resent although i t i s b e g i n n i n g to d i s a p p e a r , and the l i n e has narrowed to 11.1 gauss. Between 223 and 270°K the d e r i v a t i v e curve i s s y m m e t r i c a l w i t h l i n e w i d t h 3.1+0.1 gauss. Although l i n e widths are p l o t t e d i n F i g u r e 3 there are not enough p o i n t s to f i x the t r a n s i t i o n s a c c u r a t e l y a t 94.1 MHz. The s i m i l a r behaviour and i d e n t i c a l l i n e w i d t h s of the s p e c t r a taken at 30 MHz and 94.1 MHz i n the r e g i o n above the nmr t r a n s i t i o n at ~ 185-205°K i n d i c a t e the absence of f i e l d dependent broadening t h e r e . Above the m a l t i n g p o i n t the 94.1 MHz s p e c t r a appear to i n d i - cate more l i q u i d - l i k e c h a r a c t e r than- the 30 MHz s p e c t r a . This d i f f e r e n c e may be due to d i f f e r e n t , temperature g r a d i e n t s along the samples i n the two c a s e s . In a d d i t i o n a l l 94.1 MHz s p e c t r a i n the narrow l i n e r e g i o n appear to e x h i b i t a s m a l l amount of d i s p e r - 30 s i o n which c o u l d not be balanced out. I n i t i a l l y i t was thought t h i s might be a low, broad peak i n d i c a t i n g a percentage of mole- c u l e s undergoing l e s s frequent r e o r i e n t a t i o n than those producing the narrow l i n e . However, the "two components" c o u l d not be brought i n t o phase and i t was d e c i d e d t h a t the e f f e c t was prob- a b l y due to the presence of a s m a l l amount of d i s p e r s i o n mode i n the s i g n a l . S i n c e the d i f f i c u l t y was not present a t 30 MHz, i t s o r i g i n a t 94.1 MHz may l i e i n an i n a b i l i t y i n t h i s w i d t h r e g i o n t o remove c o m p l e t e l y the d i s p e r s i o n mode when u s i n g the I n t e g r a t o r t o p r o v i d e m o d u l a t i o n . At temperatures below the nmr t r a n s i t i o n the 94.1 MHz s p e c t r a were q u i t e satisfactory„ The r e s u l t s agree w e l l , w i t h one e x c e p t i o n , with, those ob- t a i n e d i n d e p e n d e n t l y by B l i n c ( 4 1 ) . His second moment p l o t ( h i s F i g u r e 8) p l a c e s the low temperature nmr t r a n s i t i o n a t the same 2 p o i n t as found here. His r i g i d l a t t i c e second moment of 9 05 gauss i s of course somewhat higher due to the i n c r e a s e d a n i s o t r o p y at the h i g h e r f i e l d of h i s experiment (9500 gauss as a g a i n s t 7500 gauss a t 30 MHz). I t i s even s l i g h t l y h i g h e r than the v a l u e of 9„1 gauss o b t a i n e d by i n t e r p o l a t i n g our r e s u l t s at 9500 gauss, but i s c e r t a i n l y w i t h i n tha r e p r o d u c i b i l i t y of an nmr experiment. His l i n e w i d t h of about 10 gauss at 7250 gaus's f i e l d i s the same as our v a l u e i n t e r p o l a t e d at the same f i e l d and h i s 3 gauss l i n e width a t o . -41 C a t 9500 gauss i s again i n agreement. ( B l i n c ' s l i n e widths «< were e s t i m a t e d from h i s F i g u r e 5). However h i s value of about 31 1.8 gauss ( e s t i m a t e d from h i s F i g u r e 8) For the r e g i o n above the 200°K nmr t r a n s i t i o n i s s i g n i f i c a n t l y h i g h e r than our value of 2 1.0+0.05 gauss . S i n c e the a n i s o t r o p y has been averaged out i n t h i s r e g i o n , the d i f f e r e n c e cannot a r i s e from f i e l d dependent broadening. S i n c e l i n e widths appear the same i n both s t u d i e s , i t i s u n l i k e l y t h a t the d i f f e r e n c e a r i s e s from s a t u r a t i o n or mo d u l a t i o n broadening i n B l i n c ' s s p e c t r a . The a l t e r n a t i v e t h a t s a t u r a t i o n narrowing e x i s t s i n our s p e c t r a i s d i s c o u n t e d s i n c e g r e a t care was e x e r c i s e d i n c o n t r o l l i n g the r f ( H ) . l e v e l . The d i s c r e p a n c y may p o s s i b l y l i e i n a c c u r a t e l y d e t e r m i n i n g the t a i l s of the s p e c t r a . The s p e c t r a o b t a i n e d here are i n expanded s c a l e and have an e x c e l l e n t s i g n a l to n o i s e r a t i o . The second moments from them are t h e r e f o r e c o n s i d e r e d q u i t e a c c u r a t e . The lower second moment makes p o s s i b l e a s l i g h t l y d i f f e r e n t i n t e r p r e t a t i o n of the motions o c c u r r i n g i n t h i s temperature r e g i o n . This w i l l be d i s c u s s e d l a t e r . F i g u r e 4 shows the f i e l d dependence of the c e n t r o i d of the UJFg spectrum at 77°K. The c h e m i c a l s h i f t , measured w i t h r e s p e c t to an e x t e r n a l sample of CF^OOH at 295°K, i s -255+40 ppm. C a l - c u l a t e d r e l a t i v e to HF i t i s -380+40 ppm compared w i t h B l i n c ' s v a l u e of -440+20ppm o This i s not r e a l l y a s i g n i f i c a n t d i f f e r e n c e when the method used to o b t a i n the s h i f t (see Chapter I I I ) i s considered,, o o In F i g u r e 2 the c o n s t a n t second moment from 77 K to ~ 180 K S S f l V O ±d lHS OldOd-LOSI NV3IAI - 32 suggests t h a t , except f o r whatever zero p o i n t motion of the atoms o may be p r e s e n t , the wT̂ . l a t t i c e i s r i g i d a t 77 K. The constancy of the second moment i s i n i t s e l f no a b s o l u t e guarantee of r i g i d i t y , but as w i l l be seen below i t i s supported by comparison w i t h the c a l c u l a t e d t h e o r e t i c a l r i g i d l a t t i c e second moment. The a n i s o - o t r o p y o f the UiF^ spectrum can t h e r e f o r e be s a f e l y s t u d i e d at 77 K, some o 100 below the t r a n s i t i o n where motion averages out the e f f e c t . The f i e l d dependence of the average a b s o r p t i o n curves at 77°K i s shown i n F i g u r e 5 a t 2, 16, 30, 40, 56.4, and 94.1 MHz. Appendix l i e g i v e s d e r i v a t i v e s t y p i c a l of the s p e c t r a r e c o r d e d f o r F i g u r e 5. The ab- s o r p t i o n curves have a common x - s c a l e and are n o r m a l i z e d to con s t a n t a r e a . The 16 MHz s p e c t r a not q u i t e c o n s i s t e n t w i t h the o t h e r s . In c o n t r a s t to UF (38, 39, 41) there i s v i r t u a l l y no r e s o l u t i o n of the b s p e c t r a e x c e p t a t 94.1MHz. At t h i s frequency, the s p e c t r a were o a c t u a l l y taken a t 173-175 K. However, as i s apparent below, t h i s seems t o have been s u f f i c i e n t l y i n t o the r i g i d l a t t i c e r e g i o n to o b t a i n a v a l i d spectrum. The s p e c t r a at lower frequency appear i d e n t i c a l w i t h B l i n c s . The d e r i v a t i v e s at 30 MHz (7500 gauss) and 40 MHz (10,000 gauss) i n Appendix H e are very s i m i l a r to h i s 7250 and 9500 gauss s p e c t r a . As our s p e c t r a and the p l o t of the f i e l d dependence o f the l i n e width a t 77°K i n Figure 6 i n d i c a t e , t h e r e i s l i t t l e change i n l i n e width over the e n t i r e range of f i e l d s from 0.5;.Kgauss a t 2 MHz up to 23.5iKgauss at 94.1 MHz. The change as one goes to lower frequency i s r e a l l y only a s l i g h t narrowing which has the e f f e c t of f i l l i n g i n the s h o u l d e r on the h i g h f i e l d s i d e To F o l l o w Page 32 To Follow Page 3 2 Figure 6. WF^. F i e l d dependence of l i n e width a t 77°K O' 5 0 0 0 15,000 25,000 F I E L D ( H Q ) G A U S S 33 - of the s p e c t r a w i t h s c a r c e l y any change i n h e i g h t . At i n i t i a l stages of the i n v e s t i g a t i o n i t was thought t h a t s a t u r a t i o n e f f e c t s might be i n v o l v e d , but t h i s was l a t e r r u l e d out and the e f f e c t shown to be genuine by c a r e f u l checks of the r f (^) l e v e l . 2.- R e s o l u t i o n attempts - I s o t r o p i c and A n i s o t r o p i c Chemical S h i f t s I t was expected t h a t \11FC l i k e U C would probably have a d i s - b o t o r t e d s t r u c t u r e at low temperatures. There would l i k e l y be fo u r s h o r t e q u a t o r i a l bonds and two long a x i a i bonds w i t h the c h e m i c a l s h i f t t e n s o r s e x h i b i t i n g a x i a l symmetry along the bond d i r e c t i o n . f o r such a molecule 6, = fi„ = 6 „ = <S. = €> and 6 1 = = ^ . 1 2 3 4 e 5 6 a Equation (19) than becomes v j ^ ^ ^ r ^ - ^ ^ f e - ^ * j f 4 - « - ) * J ••<2o) € and & correspond to the c e n t e r s o f zero f i r s t moment of the a e r r e s o l v e d a x i a l and e q u a t o r i a l components of the t o t a l curve. The f i n a l term i n s i d e the square b r a c k e t s i s the r e l a t i v e chemical s h i f t of the components. This e q u a t i o n i s given w i t h an i n c o r r e c t f a c t o r of 6 i n s t e a d of 2/3 before t h i s term by B l i n c ( 4 1 ) . I t i s probably a t y p o g r a p h i c a l e r r o r s i n c e equation (20) a p p l i e d to h i s data g i v e s a o p r o x i m a t e l y h i s r e p o r t e d r e s u l t s f o r IIF . 6 The averaged second moments of the s p e c t r a taken at 2, 16, 30, 40, 56.4, and 94.1 MHz were p l o t t e d a g a i n s t the square of. the f i e l d (H )„ F i g u r e 7 sho ws t h a t , as p r e d i c t e d by equation ( 2 0 ) , the p l o t g i v e s a s t r a i g h t l i n e . The e x p e r i m e n t a l value of g ( h ) , the zero f i e l d broadening," o b t a i n e d from the i n t e r c e p t i n F i g u r e 7 To Follow Page 33 F i g u r e 7. WF^* F i e l d squared dependence of second moment a t 77 A = B L I N C ( 4 1 ) O I O O 2 0 0 3 0 0 4 0 0 5 0 0 F I E L D S Q U A R E D ( H | ) K I L O G A U S S 2 34 i s 8.2+0.2 gauss . T h i s i s c o n s i d e r a b l y l a r g e r than the r i g i d l a t t i c e second moments p u b l i s h e d by B l i n c (41) f o r other hexa- 2 f l u o r i d e s (4 to 5 gauss , but no v a l u e mas g i v e n f o r WF -). o I n i t i a l attempts a t r e s o l u t i o n mere made p r i o r to running the 2 and 94.1 MHz s p e c t r a . I t was obvious from the l a c k of r e s o l u t i o n i n the 16 to 56.4 MHz s p e c t r a t h a t an exact d e t e r - m i n a t i o n of ths probable two components would be u n l i k e l y . S i n c e the a n i s o t r o p i e s of the components, i f p r e s e n t , would l i k e l y be q u i t e s i m i l a r i t was hoped, however, that at l e a s t a r e l a t i v e c h e m i c a l s h i f t and an average a n i s o t r o p y could be determined. Thus began a t i r e s o m e s e r i e s of r e s o l u t i o n attempts which showed t h a t a l a r g e v a r i e t y of r e s o l u t i o n s was p o s s i b l e , some pro m i s i n g and most p l a u s i b l e at one or more f i e l d s , but none of which was s a t i s f a c t o r y over the f u l l range. S p e c t r a were run a t 2 MHz to determine a good ap p r o x i m a t i o n to the zero f i e l d l i n e shape. The average second moment was 2 2 8.25 gauss , i n s p l e n d i d agreement w i t h the 8-. 2 gauss e x t r a p o l a t e d v a l u e . The l i n e shape was s y m m e t r i c a l but w i t h l i t t l e change i n h e i g h t or width from the shape a t h i g h e r f i e l d s . When the Warian HA100 and i t s 23.5 Kgauss f i e l d became a v a i l a b l e , s p e c t r a were run a t 94.1 fflHz. These s p e c t r a completed ths s t r a i g h t l i n e p l o t of second moment a g a i n s t f i e l d s q u a red. The improved r e s o l u t i o n i n the spectrum gave promise t h a t t h e r e were two components which c o u l d be s e p a r a t e d one from the o t h e r . There was some concern t h a t 35 s i n c e the s p e c t r a were run at 173 K, they might not be w i t h i n the r i g i d l a t t i c e r e g i o n , but the averaged second moment l i e s on the l i n e of F i g u r e 7 and the s p e c t r a seem v a l i d . U n f o r t u n a t e l y the 94.1 MHz s p e c t r a do not c l a r i f y matters a t a l l 0 They appear (see F i g u r e 8) to d e f i n e two w e l l r e s o l v e d peaks each of which i s v i r t u a l l y s ymmetrical about i t s midpoint and whose area r a t i o s are a q u i t e p r e c i s e 4 (low f i e l d ) to 2 ( h i g h f i e l d ) . The chem i c a l s h i f t between the peaks i s about 270+5 ppm. I f i n equ a t i o n (20) the a n i s o t r o p y i s put equal to z e r o , the s l o p e of the second moment l i n e i n f i g u r e 7 g i v e s a maximum value o f 220+10 ppm. The agreement between the s h i f t s i s perhaps hot too bad, but i f the UJFg spectrum i s composed of two, s y m m e t r i c a l , i s o t r o p i c a l l y s h i f t e d peaks, the e x p e r i m e n t a l curve s h o u l d narrow and i n c r e a s e i n h e i g h t ( i f c o n s t a n t area i s main- t a i n e d ) as the f i e l d i s lowered. F i g u r e 0 shows curves c o n s t r u c t e d by s h i f t i n g the two components r e s o l v e d at 94.1 MHz by 270 ppm at each f i e l d . As the f i g u r e i n d i c a t e s the c o n s t r u c t e d curves dc not agree w e l l w i t h the e x p e r i m e n t a l curves and even i n d i c a t e t a i l i n g to low r a t h e r than high f i e l d . I f one accepts the 220 ppm s h i f t and r e s o l v e s the 2 IVIHz curve i n t o two s i m i l a r components of 4:2 ar e a r a t i o s ( F i g u r e 9) a c o n s t r u c t e d curve can be f i t t e d to the e x p e r i m e n t a l curve at 15 and 30 MHz w i t h q u i t e good agreement but f a i l s a t h i g h e r f i e l d s . I f a 220 ppm r e s o l u t i o n i s attempted a t To Fo l l o w Page 35 Figure 8. WF^. Symmetrical component r e c o n s t r u c t i o n from 94.1 MHz spe c t r a HIGH FIELD —5*- 0 5G > i « t i i Solid Una experimental Broken line constructed To Follow Page 35 Figure 9. WF̂ . Symmetrical component reconstruction from 2 KHz spectra 36 94.1 MHz, the 4:2 area r a t i o cannot be m a i n t a i n e d P r i o r to ru n n i n g the s p e c t r a a t 94.1 MHz i t mas c o n s i d e r e d t h a t i n view of the f a i l u r e to r e s o l v e the components, the chemi- c a l s h i f t between the a x i a l and e q u a t o r i a l f l u o r i n e s might be so s m a l l t h a t there were s i x e s s e n t i a l l y e q u i v a l e n t f l u o r i n e s presentc In t h i s case e q u a t i o n (20) reduces to equation (18) and = 345+20 ppm. As i n d i c a t e d i n Bloembergen (72), Andrew (71) and Abragam (52, p„ 206, 220) a curve F(H) may be s y n t h e s i z e d f o r comparison w i t h the e x p e r i m e n t a l c u r v e . The form of the f u n c t i o n i s + 0 9 HH)-- J -f(Ho-H*)s(H-H0>JH< where f (Ho-H ) = - f ( h ) as d e f i n e d i n equ a t i o n ( 1 6 ) , H i s the a p p l i e d f i e l d a t the c e n t r o i d of the spectrum, H i s a g e n e r a l para- meter and Ho i s the a p p l i e d f i e l d . The asymmetries of the e x p e r i m e n t a l curves t a i l to high f i e l d . T h e refore the s i g n of |<5̂ j-6jJ i s p o s i t i v e . The d e t e r m i n a t i o n of (is^-6j) d e f i n e s f (Ho-H ) and f o r the broad- ening f u n c t i o n , S(H-Ho), the e x p e r i m e n t a l curve a t 2 MHz i s used. Use of the e x p e r i m e n t a l curve should p r o v i d e a much b e t t e r a p p r o x i - mation to the f i e l d independent broadening than the assumption of a gaussian l i n e shape having the e x t r a p o l a t e d zero f i e l d second moment as has been done p r e v i o u s l y . The f u n c t i o n was c a l c u l a t e d u s i n g Program 3, Appendix I where i t i s expressed i n a form s u i t a b l e f o r computing. The c o n s t r u c t e d curves are shown i n 37 - F i g u r e 10. Because of the r e l a t i v e l y s m a l l a n i s o t r o p y and the l a r g e (8.2 gauss ) e x p e r i m e n t a l broadening f u n c t i o n , the s y n t h e s i z e d curves are n e a r l y s y m m e t r i c a l w i t h o u t even a h i n t of a s h o u l d e r 0 T r i a l s showed t h a t a r e a s o n a b l e a p p r o x i m a t i o n to the e x p e r i m e n t a l l i n e shape (up to 56.4 MHz) c o u l d be obtained by u s i n g a much s m a l l e r broadening f u n c t i o n . T h i s however was i n c o m p a t i b l e w i t h the observed 2 MHz l i n e shape. F i n a l l y the 94.1 MHz s p e c t r a were completely at v a r i a n c e w i t h the concept of s i x l i k e f l u o r i n e s e x h i b i t i n g a x i a l symmetry of t h e i r s h i f t t e n s o r s . The 94 01 MHz s p e c t r a show a minimum, but e q u a t i o n (21) cannot have a minimum w i t h i n i t s range and n o n - e q u i v a l e n t f l u o r i n e s must be present to account f o r the l i n e shape. N a t u r a l l y as the f i e l d i s decreased the f i t of s y n t h e s i z e d to e x p e r i m e n t a l curve i n F i g u r e 10 becomes p r o g r e s s i v e l y b e t t e r from 30 MHz down u n t i l at 2 MHz i t f i t s e x a c t l y . This at l e a s t demonstrates t h a t the computer program works. The e f f e c t i v e n e s s of the program was f u r t h e r checked by i t s q u i t e good f i t of Rigny's (39) r e s o l v e d components of UF . D The most p r o b a b l e of a l l p o s s i b i l i t i e s was c o n s i d e r e d to be non-equivalent a x i a l and e q u i t o r i a l f l u o r i n e s which showed c h e m i c a l s h i f t a n i s o t r o p y . However, when r e s o l u t i o n was attempted at 94.1 MHz, the only frequency a t which i t was t r u l y f e a s i b l e to attempt r e s o l u - t i o n , the contours of ths composite curve produced two components of area r a t i o 4:2, which were only very f a i n t l y a s y m m e t r i c a l , and had a r e l a t i v e s h i f t of about 265 ppm. Tho s h i f t exceeds the maximum v a l u e To Follow Page 37 Figure 10. WF,. Asymmetrical reconstruction for 6-like fluorines 38 - of 220 ppm which i s o b t a i n e d i n the absence of a n i s o t r o p y . The r e s o l u t i o n i s s c a r c e l y d i f f e r e n t from the attempted r e s o l u t i o n i n t o s y m m e t r i c a l peaks. I f the r e l a t i v e s h i f t was kept below 220 ppm and the 4:2 area r a t i o s t i l l m a i n t a i n e d , some very i m p l a u s i b l y shaped components r e s u l t e d which were d i s r e g a r d e d . To a n t i c i p a t e s l i g h t l y , i f an average a n i s o t r o p y of about 300 ppm i s assumed, the r e l a t i v e s h i f t must be about 105 ppm. I f two s i m i l a r curves of 4:2 area r a t i o are again c o n s t r u c t e d from the e x p e r i m e n t a l 2 MHz curve then u s i n g the above a n i s o t r o p i e s and r e l a t i v e s h i f t , a f i t to the ex- p e r i m e n t a l curve can again be made which i s t o l e r a b l e to 30 MHz but i n c r e a s i n g l y bad above. The computed component curves are so n e a r l y s y m m e t r i c a l t h a t even opposing t h e i r d i r e c t i o n s of asymmetry makes l i t t l e change i n the shape of the t o t a l curve. Indeed, the con- s t r u c t e d curves are almost i d e n t i c a l w i t h those c o n s t r u c t e d i n F i g u r e 10 f o r the case of s i x l i k e f l u o r i n e s . The e x p e r i m e n t a l 2 MHz broadening f u n c t i o n i s dominant i n both cases. R e s o l u t i o n was a l s o attempted u s i n g opposed asymmetries as i n F i g u r e 11. The 94.1 MHz spectrum was r e s o l v e d i n t o two components - an area 4 curve a t low f i e l d and t a i l i n g to high f i e l d and an area 2 curve at high f i e l d and t a i l i n g to low f i e l d . T his seemed p r o m i s i n g a t 94.1, h o p e f u l at 56.4, but c l e a r l y f a i l i n g at 40 MHz, and hopeless at lower f r e q u e n c i e s , even i f the maximum 220 ppm s h i f t was used. In view of the above f a i l u r e s , n o n - a x i a l symmetry of the s h i f t t e n s o r must a l s o be c o n s i d e r e d p o s s i b l e . However s e p a r a t i o n i s To F o l l o w Page 38 39 c e r t a i n l y n o t s u f f i c i e n t a t 94.1 RlHz t o p e r m i t r e s o l u t i o n o f t h e s e more c o m p l i c a t e d l i n e s h a p e s . A t t e m p t s t o do so mere no b e t t e r t h a n i n t h e p r e c e d i n g c a s e s inhere a x i a l symmetry mas assumed. R e s o l u t i o n s mere a l s o a t t e m p t e d w i t h 5:1 and 3:3 a r e a r a t i o s o f t h e c o m p o n e n t s . They were c o n s p i c u o u s l y l e s s s u c c e s s f u l e v e n t h a n t h e p r e c e d i n g a t t e m p t s . T h e r e i s ' a l s o t h e p o s s i b i l i t y t h a t , t h e r e m i g h t e x i s t more t h a n two components. I f t h i s i s t h e c a s e r e s o l u t i o n i s u t t e r l y h o p e l e s s . T h e r e i s however one l a s t a t t e m p t t h a t c a n be made. I f t h e r e i s s u f f i c i e n t d i s t o r t i o n i n t h e m o l e c u l e t o p e r m i t a d o u b l e t i n t e r - a c t i o n , b o t h t h e m i n o r c h a n g e i n l i n e w i d t h as t h e f i e l d i s v a r i e d and t h e d i s t i n c t h i g h f i e l d peak a t 94.1 If]Hz m i g h t be e x p l a i n e d . The d o u b l e t component must be t o h i g h f i e l d t o p r o d u c e t h e h i g h f i e l d peak i n t h e 94.1 MHz s p e c t r u m . One c o u l d n o t have a v e r y b r o a d d o u b l e t w h i c h m i g h t have i t s c e n t e r o f moments t o low f i e l d o f t h e c e n t r o i d o f t h e s p e c t r u m . T h a t w o u l d make r , t h e s e p a r a t i o n between t h e n u c l e i i n v o l v e d i m p o s s i b l y s m a l l ( f r o m r e f e r e n c e 52, -3 p. 220, t h e d o u b l e t s p l i t t i n g i n g a u s s i s 3^r ). F i g u r e s 12 and 13 show two p o s s i b l e r e s o l u t i o n s a t 94.1 MHz i n v o l v i n g s e t s o f f o u r and two l i k e n u c l e i i n t h e c o m p o n e n t s . B o t h r e s o l u t i o n s , i n p a r t , p r o d u c e q u i t e p l a u s i b l e numbers. T h a t i n F i g u r e 12 has two components w h i c h do n o t have any a p p a r e n t a n i s o t r o p y o f c h e m i c a l s h i f t , , T h e i r i s o t r o p i c s h i f t i s 220 ppm, j u s t what i s p r e d i c t e d by e q u a t i o n ( 2 0 ) i n t h e a b s e n c e o f a n i s o t r o p y . The components ca n be u s e d as i n d i c a t e d To Follow Page 39 Figure 12. WF^. Reconstruction with doublet and symmetric $ single t To Follow Page 39 Figure 13. WF,. Resolution with doublet and asymmetric single t 4 0 - i n the f i g u r e to c o n s t r u c t curves whose s l o p e s have some q u a l i t a t i v e agreement w i t h the experiment curves and which agreement i s c e r t a i n l y no worse than i n o t h e r attempts. The other d o u b l e t r e s o l u t i o n , shown i n F i g u r e 13, i n v o l v e s a low f i e l d peak w i t h a very s t r a n g e asymmetry i n d e e d . The r e l a t i v e , i s o t r o p i c s h i f t i s about 115 ppm. I f the low f i e l d , a n i s o t r o p i c component's second moment i s p l o t t e d a g a i n s t the square of the f i e l d a v a l u e of (^~^j_) = + 3^3 PPm i s found. P u t t i n g t h i s v a l u e i n t o the a p p r o p r i a t e a n i s o t r o p i c term and remembering t h a t the ot h e r a n i s o t r o p i c term i s zer o s i n c e the d o u b l e t i s s y m m e t r i c a l , one o b t a i n s from equation (20) a r e l a t i v e s h i f t o f about 135 ppm. Th i s i s not bad agreement w i t h the 115 ppm found e x p e r i m e n t a l l y . O b v i o u s l y both of the r e s o l u t i o n s i n v o l v i n g d o u b l e t s cannot be c o r r e c t . In f a c t n e i t h e r of them i s . The doub- l e t s p l i t t i n g i s the same i n each case. Estimated from the.94,1 MHz r e s o l u t i o n s , i t i s 3 t o 5 gauss g i v i n g i n t e r n u c l e a r s e p a r a t i o n s of o about 2.4 and 2„0 A r e s p e c t i v e l y . In s h o r t , the i n t e r n u c l e a r d i s - tances i n the doublet w i l l be l i t t l e d i f f e r e n t from those i n the r e s t of the molecule and a d i s t i n c t doublet c o u l d not be seen. T h i s was v e r i f i e d u s i n g Program 4, Appendix I which i s based on Abragam's do u b l e t f i t t i n g procedure (52, p. 220). Using the parameters a v a i l - a b l e from t h i s work, the d o u b l e t c o u l d not be reproduced. There was o n l y a rounded curve w i t h no s i g n of do u b l e t s t r u c t u r e . F i n a l l y i t may be s t a t e d t h a t the d i f f i c u l t y e xperienced i n a t t e m p t i n g the r e s o l u t i o n of the UJF spectrum C3n not be a t t r i b u t e d 41 to e l e c t r o n c o u p l i n g of the ~^F and *^UJ i n the s o l i d . The c o n t r i - b u t i o n to the second moment from t h i s s p l i t t i n g a c c o r d i n g to Gutowsky (63) i s - ( 2 2 ) The c o u p l i n g c o n s t a n t X measured by Rigny (42) i s 43.8 Hz or 0.011 gauss. The a d d i t i o n t o the second moment from t h i s s o u rce m i l l t h e r e f o r e be n e g l i g i b l e . The r e s o l u t i o n t r i a l s are most u n s a t i s f a c t o r y . Mone of the attempts g i v e s a sure r e s u l t and none i s r e a l l y any more p l a u s i b l e than any of the o t h e r s . B l i n c (41) seemingly encountered s i m i l a r d i f f i c u l t y f o r , although he does show examples of r e s o l v e d , asy- mmetric curves w i t h approximate 4:2 area r a t i o f o r UJF , he g i v e s n e i t h e r v a l u e s f o r the a n i s t r o p i c s o b t a i n e d , nor a r e l a t i v e c h e m i c a l s h i f t f o r the components, nor a zero f i e l d second moment. From T ( measurements he does g i v e a v a l u e of J 6 „ " £ > J = 500+200 ppm and s t a t e s t h a t t h i s agrees w i t h i n e x p e r i m e n t a l e r r o r w i t h the a n i s t r o p y determined from l i n e width d a t a . The range 500 to 700 ppm i s c l e a r l y too high s i n c e i t would g i v e a n e g a t i v e value to the square of the r e l a t i v e c h e m i c a l s h i f t when a p p l i e d to our data u s i n g e q u a t i o n ( 2 0 ) . An upper l i m i t to the average a n i s o t r o p y i s s e t by the v a l u e of 345+20 ppm o b t a i n e d by assuming s i x l i k e f l u o r i n e s . This makes B l i n c ' s lower l i m i t of 300 ppm q u i t e f e a s i b l e . Uiith our data t h i s g i v e s a r e l a t i v e s h i f t between the components of about 105 ppm as noted e a r l i e r . I t i s not s u r p r i s i n g t h a t the curve i s d i f f i c u l t to r e s o l v e i f t h i s i s the case. Orders of magnitude are a l l t h a t can be expected. 42 Our data g i v e an upper l i m i t of 220+10 ppm to the r e l a t i v e s h i f t i f t h e r e i s zero a n i s o t r o p y . The val u e s of 300 ppm and 105 ppm f o r ) and ( 6 -€> ) are of a r e s o n a b l e order of magnitude t h e r e f o r e . They do not, u n f o r t u n a t e l y , permit a c c u r a t e r e c o n s t r u c t i o n of the e x p e r i m e n t a l c u r v e s . Moreover, i f the chemical s h i f t a n i s o t r o p y i s some t h r e e times greater' than the i s o t r o p i c s h i f t between the components, w i t h both phenomena being f i e l d dependent, i t i s s u r - p r i s i n g t h a t the 94.1 MHz s p e c t r a show an a c t u a l i n c r e a s e i n r e s o - l u t i o n r a t h e r than merely a change i n l i n e shape. The doublet s p e c t r a i n F i g u r e 12 r e a l l y do behave q u a l i t a t i v e l y i n a f a s h i o n very s i m i l a r to the e x p e r i m e n t a l s p e c t r a . T h e r e f o r e , although i t w i l l be assumed t h a t there are two asymmetric components of area r a t i o 4:2 c o r r e s p o n d i n g to fo u r e q u i t o r i a l and two a x i a l f l u o r i n e s a t low and h i g h f i e l d r e s p e c t i v e l y , i t would s t i l l be very i n t e r e s - t i n g to see the UJFg spectrum at 77°K and 200 MHz. Even i f an experiment were done at 200 MHz, i t might not s o l v e the r e s o l u t i o n problem i n UJFC, however. The attempts have D a l l been based on the premise t h a t i f a r e s o l u t i o n can be made at one f i e l d , the components w i l l r e t a i n t h e i r d i s t i n c t i d e n t i t i e s a t other f i e l d s and.using the observed chemical s h i f t can be summed to g i v e the" e x p e r i m e n t a l curves at those f i e l d s . In the case of extreme chemical s h i f t . a s f o r ona "component" a r i s i n g from f l u o r i n e n u c l e i and another from hydrogen n u c l e i , there would be a c l e a r r e s o l u t i o n a t high f i e l d s , the "components" would r e t a i n t h e i r i d e n t i t i e s a t lower f i e l d s , and a " t o t a l c u r ve" c o u l d be d e r i v e d from the 43 - "components" u s i n g the observed chemical s h i f t . In the other extreme of i d e n t i c a l n u c l e i , t h e re u / i l l be no change a r i s i n g from i s o t r o p i c s h i f t and the e x p e r i m e n t a l curves can again be reproduced throughout the range of f i e l d s a v a i l a b l e . However, f o r the i n t e r m e d i a t e case i n which s i m i l a r n u c l e i are i n components which are c h e m i c a l l y s h i f t e d by a s i g n i f i c a n t amount which i s non e t h e l e s s s m a l l e r than the d i p o l a r broadening, the component l i n e shapes cannot be d i s - e n t a n g l e d . For Uj'Fg a t low f i e l d s there appear to be s i x e s s e n t i a l l y e q u i v a l e n t f l u o r i n e s and at h i g h f i e l d s two more or l e s s d i s t i n c t components w i t h at i n t e r m e d i a t e f i e l d s a c o n f u s i n g mixture of the two extreme c a s e s . The r e s o l u t i o n attempts above have been p r e s e n t e d i n such d e t a i l m a i n l y to emphasize one p o i n t : i f r e s o l u t i o n i s not p r e s e n t i n the e x p e r i m e n t a l s p e c t r a i t cannot be found by making r e a s o n a b l e a t t e m p t s . The d i f f i c u l t y a r i s e s not from d e f i c i e n c i e s i n the experiment but from the na t u r e of the i n t e r a c t i o n s i n v o l v e d i n i n t e r m e d i a t e cases of mixed i s o t r o p i c and a n i s o t r o p i c c hemical s h i f t s . 3. Proposed C r y s t a l S t r u c t u r e A t h e o r e t i c a l , r i g i d l a t t i c e second moment can be computed f o r comparison w i t h the observed zero f i e l d or f i e l d independent second moment. No X-ray s i n g l e c r y s t a l study of UJF has been p u b l i s h e d . 6 The s t r u c t u r e suggested, here was based on the IJJ-F bond l e n g t h of o 1.833A from Uieinstock (37a) and c r y s t a l s t r u c t u r e i n f o r m a t i o n i n Table 1 s u p p l i e d by B a r t l e t t (37b) from a p r i v a t e communication from S i e g e i . 44 - Table 1 C e l l Parameters of UJF 6 2 7 3 ° K o 03 „ c e l l c u b i c a=6„28A , VX247.7A , ^ c a l c = 3.99 253°K o o3 >9 c e l l orthorhombic a=9.68A , V=434.1A , / ' c a l c = 4.56 b=8.Bl c=5.09 Z=4 - - space group Pmma? o Attempts to f i t the four UJFg molecules i n t o the u n i t c e l l a t 253 K produced what appeared to be unreasonable d i s t o r t i o n s and a s u s p i - c i o n arose t h a t Pmma might be a t r a n s c r i p t i o n e r r o r f o r Pnma. UJeinstock (77) may a c t u a l l y s t a t e t h a t UJF i s Pnma, but i t i s not q u i t e c l e a r whether he means t h a t a l l the hexafluorides he d i s c u s s e s are Pnma or on l y t h a t they are a l l orthorhombic. In any case i t was decided to base the UJFg second moment c a l c u l a t i o n s on a Pnma s t r u c t u r e f o r UF C. o Hoarde and 5troupe (36) g i v e the atomic c o o r d i n a t e s , c e l l dimensions and band l e n g t h s f o r UFg which are reproduced i n Table 2. - 45 - Table 2 Atomic C o o r d i n a t e s , C e l l Dimensions, and Bond Lengths of UF C at 293°l D U V X • 0.1295 0.014 y . 0.2500 0.093 z 0.081 0.250 O U-FtA 2.01 F2 0.014 0.407 0.250 F 3 0.246 0.407 - 0.083 2.01 V 0.246 0.093 - 0.083 2.01 F 5 0.003 0.250 — 0.250 2.13 F 6 • .250 0.250 0.417 average 2.12 2.05 Orthorhombic, Pnma, Z = 4 , s c a l e = 5.06 a=9.80 o , b=9.00, c=5.2GA S i n c e the r a t i o s of the c e l l dimensions f o r UIF^ and UF are a p p r o x i -6 o mately equal f o r each d i r e c t i o n f^r • • ~ 8.81 5.09 9.00 ~ 5.20 ~ 0.98-0.99^) and Z = 4 f o r both m o l e c u l e s , the same space group f o r both may be reason- a b l e . The r a t i o of UJF. t o UF. c e l l volume i s 0.95. The r a t i o of the 6 6 r e s p e c t i v e m o l e c u l a r volumes computed f o r crude, s p h e r i c a l molecules i n c l u d i n g f l u o r i n e van der UJaals r a d i i i s 0.82. In both cases the " s p h e r i c a l " volume exceeds the u n i t c e l l volume, but i n the UJF^ case the excess i s r e l a t i v e l y l e s s than i n the UF^ case. T h i s would give the UJFg molecule r e l a t i v e l y mora freedom to r e o r i e n t and i s c o n s i s t e n t o w i t h a c o m p a r a t i v e l y low temperature nmr t r a n s i t i o n at 200 K. In computing the 'JJF s t r u c t u r e , the c o o r d i n a t e s of a uranium o atom were chosen as a m o l e c u l a r o r i g i n . The atomic c o o r d i n a t e s f o r the f l u o r i n e atoms i n UF^ were a d j u s t e d r e l a t i v e to t h i s o r i g i n a c c o r d i n g to the f o l l o w i n g formulae to g i v e c o o r d i n a t e s f o r the - 46 - f l u o r i n e p o s i t i o n s i n UJF . b ( f l u o r i n e atomic coord, i n WFg- o r i g i n atomic coord.) ( c e l l dimension MF ) ( f l u o r i n e atomic coord, i n UF C- o r i g i n atomic coord.) ( c e l l dimension UF ) D average Ui-F bond l e n g t h average.U-F bond l e n g t h . 1 . 8 3 3 ~0.\M5)( ISO) Z05~ ~o-Z5'O0)(8.8j) . 1.833 Z oS 1 8 3 3 -o.o8/;($-.20) Z 0 5 " i value 0 1.833A given by UJeinstock was • a s ) the average of the p o s s i b l y non-equal bond l e n g t h s .in the low tempera- t u r e phase of \ilfr . The atomic c o o r d i n a t e s f o r UJF,. c a l c u l a t e d from o o equations (23) are given i n Table 3. Table 3 C a l c u l a t e d Atomic C o o r d i n a t e s and Bond Lengths f o r UiF^ at "253°K" F: F' X y z Ui-F A t .1295 .2500 .0810 _ .0250 . 1065 .2354 1.80 ,0250 „3935 .2 554 1„80 .2349 .3935 ~ .0688 1.80 .2349 . 1065 — . 0 6 8 8 1. 80 .0150 .2500 —„2213 1.90 . 2386 .2500 . 3879 1.90 average 1. 83 Orthorhornbi c, Pnma, Z-4 9 r , 9 0 68, b=8.81, c=5.09R The p o s i t i o n s are not of course a c c u r a t e to the number of s i g n i f i c a n t f i g u r e s r e t a i n e d i n t h i s t a b l e . To Follow Page J+6 Figure L+. WF^. Proposed unit c e l l (along c-axis) ' 1 a ATOMIC C O O R D I N A T E S O F T U N G S T E N I 0 . 1 3 , 0 . 2 5 , 0 . 0 8 2 - 0 . 1 3 , 0 . 7 5 , - 0 . 0 8 3 0 . 3 7 , 0 . 7 5 , 0 . 5 8 A- 0 . 6 3 , 0 . 2 5 , Q 4 2 P n m a a = 9 . 6 8 A Q 5 ° b = 8 . 8 I A 1 1 ' ' l — J C I R C L E S INDICATE c = 5 . 0 9 A F L U O R I N E Van der Waals radii - 4 7 The symmetry o p e r a t i o n s of the Pnma space group g i v e the other t h r e e p o s i t i o n s i n the u n i t c e l l . F i g u r e 14 shows the proposed s t r u c t u r e of iJJFg viewed along the c - a x i s . 4 . T h e o r e t i c a l R i g i d L a t t i c e Second Moment To p r o v i d e n u c l e a r p o s i t i o n s f o r the second moment c a l c u l a t i o n a s i m p l e l i n e a r t r a n s f o r m program (Program 5, Appendix I.) was w r i t t e n . I t t r a n s l a t e s the n u c l e a r p o s i t i o n s i n one u n i t c e l l i n t o p o s i t i o n s i n a block of u n i t c e l l s around the o r i g i n a l c e l l . In the computation o f . t h e r i g i d l a t t i c e t h e o r e t i c a l second moment t h e r e i s i n a d d i t i o n o to the assumption t h a t a reasonable UJFg s t r u c t u r e at 253 K can be o d e r i v e d from the UFg s t r u c t u r e at 298 K, the a d d i t i o n a l assumption t h a t the r e s u l t s w i l l be v a l i d a t 77°K. The two h o x a l u c r i d e s are s i m i l a r molecules and the temperatures at which the X-ray r e s u l t s are quoted are i n each case r a t h e r r o u g h l y the same d i s t a n c e below the m e l t i n g p o i n t s of the r e s p e c t i v e compounds. The f i r s t i s not an un- re a s o n a b l e a p p r o x i m a t i o n . The assumed UJF^ s t r u c t u r e , however, i s f o r a temperature above the nmr t r a n s i t i o n but i s used a t temperatures below the t r a n s i t i o n . This too i s .acceptable. X-ray s p e c t r o s c o p y and nmr sp e c t r o s c o p y . are s e n s i t i v e to d i f f e r e n t m o t i o n a l f r e q u e n c i e s . As f a r as X-ray i s concerned, the s t r u c t u r e i s e s s e n t i a l l y r i g i d and o the n u c l e a r p o s i t i o n s a t 253 K may g i v e a reasonable a p p r o x i m a t i o n to the p o s i t i o n s a t 77 K i f c o n t r a c t i o n of the l a t t i c e i s not too g r e a t i As w i l l be noted l a t e r , thermodynamic evidence r u l e s out the p o s s i - b i l i t y of a c r y s t a l s t r u c t u r e change between 77 and 253°K ( 2 8 ) . 48 Equation (2) gi v e s the t h e o r e t i c a l d i p o l a r second moment f o r a r i g i d , p o l y c r y s t a l l i n e s o l i d . The f i r s t term a p p l i e s to the F-F i n t e r a c t i o n s , the second to the UJ— F i n t e r a c t i o n s . The r e s p e c t i v e n u m e r i c a l c o e f f i c i e n t s are 316.8 and 0.27. When the 14^ n a t u r a l 183 abundance of UJ, the only i s o t o p e of tungsten w i t h a magnetic moment, i s c o n s i d e r e d , the UJ—F f a c t o r becomes ~ 0.04. The c o n t r i - b u t i o n from UJ-F i n t e r a c t i o n s i s n e g l i g i b l e and on l y F-F i n t e r - a c t i o n s need be summed i n e q u a t i o n ( 2 ) . The summation was c a r r i e d out on the IBM 7040 u s i n g Program 6, Appendix I u s i n g the n u c l e a r c o o r d i n a t e s generated by Program 5 and was extended to a r a d i u s of o 6A from molecule number one (any one of the f o u r ; i n the u n i t c e l l o -6 Because of the r dependence of the second moment, i t i s s u f f i c i e n t to assume the remainder of the n u c l e i are u n i f o r m l y d i s t r i b u t e d w i t h known d e n s i t y throughout the r e s t of the sample (51, p. 160). I f 2 the number of n u c l e i between r and r+dr i s 4 P r / ^ d r , i n h e r e ^ i s the ,o3 x number of n u c l e i per u n i t volume (A ), the a d d i t i o n a l c o n t r i b u t i o n i s g i v e n by . , C- i . ( 2 4 ) C O S n 4 ' Ciuimeritol { ^ c ^ y i t s fe / . .8 )4$* ' *• 3 r 3 The c o n t r i b u t i o n s to the t o t a l , t h e o r e t i c a l r i g i d l a t t i c e d i p o l a r 2 • - second moment of 8.14 gauss are given i n Table 4. - 49 Table 4 R i g i d D i p o l a r Second Moments of UiF g at 77°K 2 T o t a l I n t r a m o l e c u l a r .Second Moment „ 4.40 G o z T o t a l Second Moment w i t h i n 6K 7.80 G 6A3 " ^ 2 C o n t r i b u t i o n Outside  .34 G' T o t a l T h e o r e t i c a l Second Moment 8.14 G ^ Expe r i m e n t a l Second Moment 8.2+0.2 G Moderate d i s t o r t i o n makes l i t t l e d i f f e r e n c e to the second moment. Ths i n t r a m o l e c u l a r moment c a l c u l a t e d on the b a s i s of s i x equal ii'-F bonds of l e n g t h 1.833A3 each i s 4.31 gauss^. . The moment c a l c u l a t e d f o r four s h o r t e q u a t o r i a l (l.8oS) and two long a x i a l (l,9oS) bonds 2 i s 4.40 gauss only s l i g h t l y d i f f e r e n t . The c r y s t a l s t r u c t u r e assumed here r e c e i v e s some p a s s i v e support from the count of i n t e r n u c l e a r i n t e r a c t i o n s . The t h e o r e t i c a l second moment program i n d i c a t e s t h a t w i t h i n a range of 6.5 from the molecule chosen as o r i g i n , there are 152 F-F i n t e r a c t i o n s . Of these, 12 i n t e r a c t i o n s i n v o l v e n u c l e i w i t h s e p a r a t i o n s of l e s s than 2.70°, twice the f l u o r i n e van der UJaals r a d i u s . However, these i n t e r a c t i o n s are a l l i n t r a m o l e c u l a r . At l e a s t the s t r u c t u r e has the advantage of having no i n t o r m o l e c u l a r i n t e r a c t i o n s l e s s than the van o'er UJaals r a d i u s . T h i s of course does not say t h a t other s t r u c t u r e s e q u a l l y f a v o u r a b l e do not e x i s t . C o n s i d e r i n g t h a t the s t r u c t u r e i s based on o o X-ray r e s u l t s obtained a t 298 K, a d j u s t e d to 253 K, and a p p l i e d at o .77 K where thermal c o n t r a c t i o n might be s i g n i f i c a n t , the vary c l o s e agreement between t h e o r e t i c a l and e x p e r i m e n t a l second moments i s 50 - perhaps f o r t u i t o u s . Nonetheless i t i s en c o u r a g i n g . 5,, R e o r i e n t a t i o n i n the S o l i d Above the nmr t r a n s i t i o n around 180-210°K, the p u z z l i n g UIF^ l i n e shape becomes s y m m e t r i c a l . Between t h i s t r a n s i t i o n and the next around 265°K, the l i n e w i d t h has a c o n s t a n t value of about 3.2 gauss a t both 30 and 94.1 MHz. C l e a r l y whatever f i e l d depen- dent broadening e x i s t e d below 200°K, i t i s now averaged out. The second moment p l o t i n F i g u r e 2 shows a drop from a p p r o x i m a t e l y 2 2 9 gauss (8.2 gauss a t zero f i e l d ) below the lower t r a n s i t i o n to 2 1.05+0.05 gauss above the t r a n s i t i o n . S i n c e the w'Fg molecule i s appro x i m a t e l y s p e r i c a l , t h i s drop i n second moment to about 1 2 gauss may be due to the onset of i s o t r o p i c r o t a t i o n of the mole- c u l e about i t s c e n t e r of g r a v i t y . In t h i s case the i n t r a m o l e c u l a r second moment averages to z e r o and the only remaining c o n t r i b u t i o n i s from the i n t e r r n o l e c u l a r second moment (51, p. 173). For UJF., 5 the a p p r o p r i a t e form of e q u a t i o n (6) f o r i s o t r o p i c r e o r i e n t a t i o n i s 5, . « 3/4.AW0SN; R."fc (25) ° X tV3.t«er>- 0 fry * 1 * S i n c e t h i s c a l c u l a t i o n c o n c e n t r a t e s the f l u o r i n e n u c l e i at the molec- u l a r c e n t e r s , the sum i s computed u s i n g Program 6 w i t h the co- o r d i n a t e s of the tungsten n u c l e i as the c e n t e r s . The r e s u l t c o r r e c t e d f o r n u c l e i at d i s t a n c e s g r e a t e r than 6A5 i s 1.06 g a u s s 2 . This i s e x c e l l e n t agreement w i t h the e x p e r i m e n t a l value of 1.05+.05 2 gauss , but Smith (64b) p o i n t s out t h a t random ( n o n - i s o t r o p i c ) jumps 51 between e q u i v a l e n t p o s i t i o n s can give a second moment d i f f e r e n t from the i s o t r o p i c value by as l i t t l e as 5 to 15%. S i nee the expe r i m e n t a l value i t s e l f v a r i e s by 5%, i t i s i m p o s s i b l e to s t a t e p o s i t i v e l y t h a t an i s o t r o p i c r e o r i e n t a t i o n i s t a k i n g p l a c e . UJeinstock (37a, 77) c o n s i d e r s r o t a t i o n i n the s o l i d i s un- . 0 » l i k e l y at the s o l i d - s o l i d phase t r a n s i t i o n (255 K f o r '<HF ). He b e l i e v e s t h a t f o r a l l the h e x a f l u o r i d e s there i s l i t t l e d i f f e r e n c e , between the c u b i c s o l i d phase and the l i q u i d , a b e l i e f which our - r e s u l t s support, but t h a t f r e e r o t a t i o n occurs i n n e i t h e r phase. The nmr r e s u l t s , however, appear to i n d i c a t e a very c o n s i d e r a b l e r e o r i e n t a t i o n not only i n the c u b i c phase, but a l s o i n the o r t h o - rhombic phase, same 65° below the s o l i d - s o l i d t r a n s i t i o n to the cu b i c phase. A d m i t t e d l y t h e r e appears no s i g n of the t r a n s i t i o n o i n the v i c i n i t y of 200 K from thermodynamic d a t a . The heat c a p a c i t y curve for UJF_ i s smooth w i t h no break from 4°K to the p o i n t a t which fa the t r a n s i t i o n t o the c u b i c s t r u c t u r e takes p l a c e ( 2 8 ) . S i n c e there i s no change i n thermodynamic p r o p e r t i e s , the second moment drop can- o not be due to a change of c r y s t a l s t r u c t u r e at 200 K. I t must a r i s e from r e o r i e n t a t i o n s which, c o n s i d e r i n g the approach of the second moment to a value i n d i s t i n g u i s h a b l e from t h a t f o r i s o t r o p i c r e - o r i e n t a t i o n , average out not only the two d i f f e r e n t f l u o r i n e ' s i t e s , but a l s o to a c o n s i d e r a b l e degree the l o c a l f i e l d s as w e l l . As Fig u r e 14 and the count of i n t e r n u c l e a r d i s t a n c e s i n the t h e o r e t i c a l second moment c a l c u l a t i o n demonstrate, the molecules i n the UJF u n i t 52 c e l l i n t e r l o c k but do not o v e r l a p . There i s c l e a r l y room f o r con- s i d e r a b l e r e s t r i c t e d r e o r i e n t a t i o n . Approximating the molecules as spheres of r a d i u s 3.18A3 (UJ-F =.1.83 + van der UJaals F r a d i u s s 1.35) g i v e s a s e p a r a t i o n o f 6.36A5 between molecules f o r complete c l e a r a n c e . The s e p a r a t i o n s between the c e n t e r s of molecules 1, 2, 3, and 4 are 1-2, 5.68A3; 1-3, 5.60A3; 1-4, 5.14$; 2-3, 5.9o8; 2-4, 8.92A5; 3-4, 5.7oS. The o v e r l a p encountered d u r i n g i s o t r o p i c r e - o r i e n t a t i o n would not be i m p o s s i b l y l a r g e but i s r a t h e r s u b s t a n t i a l . Uieinstock's (77) evidence a g a i n s t a high degree of motion i n the s o l i d s t a t e s of the h e x a f l u o r i d e s i s based i n p a r t on thermo- dynamic grounds. He g i v e s the. e n t r o p i e s of f u s i o n f o r UF^, NpF^, and PuFg as 13.6, 12.8, and 13.7 eu r e s p e c t i v e l y . S i n c e these v a l u e s exceed Timmermans' (78) l i m i t o f 5 eu f o r p l a s t i c g l o b u l a r compounds, he concludes t h a t r o t a t i o n below the m e l t i n g p o i n t i s u n l i k e l y f o r these h e x a f l u o r i d e s . Cady (25) g i v e s the entropy of f u s i o n f o r UJF as 1.45 eu. T h i s v a l u e , which i s w e l l w i t h i n the Timmermans' l i m i t , would suggest t h a t f r e e r o t a t i o n i s p o s s i b l e . UJeinstock p o i n t s out t h a t P t F & has an entropy of f u s i o n of 3.2 eu and would on t h i s b a s i s q u a l i f y as a pJastic c r y s t a l and i t s s o l i d - s o l i d t r a n s i t i o n might be a consequence of the onset of r o t a t i o n . However, the t o t a l entropy change a s s o c i a t e d w i t h the two t r a n s i t i o n s , s o l i d - s o l i d and f u s i o n , i s o n l y 7.7+3.2=10.9 eu which i s c o n s i d e r a b l y l e s s than the r o t a t i o n - a l entropy of the molecule i n the vapour phase (22.1 eu at the f u s i o n p o i n t ) . S i n c e the 10.9 eu t o t a l w i l l i n c l u d e o t h e r as w e l l as 53 - r o t a t i o n a l entropy, the t o t a l r o t a t i o n a l entropy below the vapour phase w i l l be even smaller than 10.9 eu. He believes that there i s r e l a t i v e l y l i t t l e d i f f e r e n c e , with regard to r o t a t i o n , between the cubic s o l i d and the l i q u i d and that free r o t a t i o n does not occur i n e i t h e r case. Rotation at a lower t r a n s i t i o n would be even less l i k e l y then. Hence for UJF,- where the entropy of the b s o l i d - s o l i d t r a n s i t i o n i s 5.28 eu and the entropy of fusion i s 1.45 eu for a t o t a l of 6.73 eu against a vapour phase r o t a t i o n a l entropy of 21.8 eu, the same objections would apply. However, both the 5d t r a n s i t i o n s e r i e s hexafluorides, UJF̂ and PtFg, for which nmr r e s u l t s are a v a i l a b l e show "nmr t r a n s i - o o ti o n s " w e l l below t h e i r s o l i d - s o l i d t r a n s i t i o n s at 265 K and 276 K o r e s p e c t i v e l y . Blinc (41) places the UJF. t r a n s i t i o n at about 200 K, b o as do we, and the PtF c t r a n s i t i o n at about 250 K. From equation b (7) or (8) average frequencies V t of molecular r e o r i e n t a t i o n may be obtained. From an Arrhenius-type p l o t of In. ( ) against */T°K, an a c t i v a t i o n energy for the r e o r i e n t a t i o n may be determined. For o the t r a n s i t i o n at 200 K there i s an a c t i v a t i o n energy of 10.0+0.4 Kcal from second moment data and 15„0+0o9 Kcal from l i n e width data. In accord with Powles (65), the value derived from second moment data i s considered more r e l i a b l e . The c a l c u l a t i o n s were made using Program 7, Appendix I which was modified from Smith (79). The program gives a l e a s t squares f i t to the experimental l i n e width 54 data as used by Smith or to the second moment data as used here. The value 10.0 Kcal w i l l include a s l i g h t error due to the anis- otropy of the second moment, but i t seems a very reasonable a c t i - vation energy for molecular r e o r i e n t a t i o n . I t i s i n good agree- ment with the value of about 9 Kcal obtained by B l i n c with T( measurements. Because of the abrupt nature of the t r a n s i t i o n at 265 K n e i t h e r equation (7) nor (8) gives a meaningful a c t i v a t i o n energy for that change. The thermodynamic and nmr r e s u l t s are not contr a d i c t o r y . The phenomena are responsive to d i f f e r e n t frequencies of r e o r i e n t - a t i o n . For the nmr experiment, a high degree of r e o r i e n t a t i o n i m p l i e s a frequency of r e o r i e n t a t i o n of the order of th9 nmr l i n e 4 5 - 1 width, i . e . 10 - ID sec ; whereas the frequency of the re- o r i e n t a t i o n s must be of the order of 10"*- l O * 2 sec"* to a f f e c t the thermodynamic p r o p e r t i e s . I t i s consistent therefore for nmr to observe a t r a n s i t i o n which i n d i c a t e s a high degree of r e o r i e n t a t i o n w e l l below the s o l i d - s o l i d phase t r a n s i t i o n . B l i n c ' s value of 2 1.8 gauss above the nmr t r a n s i t i o n suggests that there may not be i s o t r o p i c r e o r i e n t a t i o n taking place above 200°K i n WF . The value 2 of 1.05+0.05 gauss obtained here suggests that as.far as an nmr experiment can detect, i s o t r o p i c r o t a t i o n can not be ruled out and, from the a c t i v a t i o n energy c a l c u l a t i o n , i s occurring through a hindering p o t e n t i a l b a r r i e r of 10 Kcal per mole. 55 The AsF 5 Adducts In the case of the two AsF adducts, there w i l l obviously b be non-equivalent f l u o r i n e n u c l e i present. As w i l l be seen below, the equivalent f l u o r i n e s are grouped as IF* and AsF i n the 6 b IF • AsF adduct and as SF* and AsF. i n the SF ; • AsF_ adduct. t o J> b 4 b There may w e l l be non-equivalent f l u o r i n e s w i t h i n these groups, but there i s no p o s s i b i l i t y of i d e n t i f y i n g them i n a broad l i n e nmr experiment when even the major non-equivalences are so small compared to d i p o l a r broadening. A. I F ? • AsF 5 1. Results Figure 15 shows the temperature dependence of the IF^.» AsF^ f l u o r i n e absorption spectrum at 30 MHz. As for the previous com- pound, the curves have a common x-scale and are integrated to a constant, a r b i t r a r y area from the d e r i v a t i v e s . Reproductions of t y p i c a l d e r i v a t i v e s are given i n Appendix I l i a . Figure 16 i s a pl o t of the averaged second moments of the d e r i v a t i v e curves. The 2 o second moment i s constant at ll o6+0.6 gauss from 77 K up to about 205°K at which point the moment begins dropping u n t i l 2.1+0.2 gauss^ o o i s reached at 235 K. I t then remains constant up to 295 K, the highest temperature recorded.A preliminary l i n e width study i n d i - cated no other t r a n s i t i o n from 77° to above 370°K (79a). At 77°K o the spectrum t a i l s to high f i e l d . By 174 K the spectrum appears to be approximately symmetrical and at 217°K, within the t r a n s i t i o n To Follow Page 55 Figure 15. IF^AsF^ . Temperature dependence of absorption spectra at 30 MHz T o F o l l o w Page 55 T E M P E R A T U R E °K 56 region, i t narrows and begins to t a i l to low F i e l d . At 295 K the spectrum i s much narrower and has a s l i g h t yet d i s t i n c t asymmetry towards low f i e l d . As may be seen by examining the highe.r f i e l d o spectra at 77 and 295 K , t h i s e f f e c t i s indeed r e a l . I t does, however, present a d i s t i n c t d i f f i c u l t y i n deciding what i s the l i n e width between maximum and minimum on the d e r i v a t i v e curve and f a r t h i s reason no v a r i a b l e temperature l i n e width p l o t i s given. 2,^ Resolution i n t o Components. I s o t r o p i c and A n i s o t r o p i c Chemical S h i f t s ; . Figures 17a and 17b show the f i e l d dependence of the o o IF^ <» "sFg absorption spectra at 300 and 77 K. T y p i c a l d e r i - vatives of the spectra are given i n Appendices I H b and I I I c . As o Figure 17a demonstrates the spectrum at 94.1 MHz and 300 K can be resolved i n t o two quite symmetrical components. There is. : a comparatively broad component to low f i e l d and a narrow component at high F i e l d . The r e l a t i v e areas of the components are 1.1:1 and the i s o t r o p i c chemical s h i f t between them i s 153+10 ppm. The compo- nents are equidistant on e i t h e r side of the centroid of the t o t a l curve, which, from Figure 18, has a chemical s h i f t of -54+8 ppm with respect to our CF^OOH standard at 295-300°K. The f i g u r e i n d i c a t e s that the s h i f t of the centroid with respect to the reference at o o 300 K i s the same whether the adduct i s at 77 or 300 K. The 1.1:1 r a t i o of the areas of the components implies that the twelve fluorines known to be present i n the IF • AsF adduct are To F o l l o w Page 56 Figure 17a. I F 0 A s F 6 • F i e l d dependence of absorption s p e c t r a at 295°K To Follow Page 56 Figure 17b. IFTAsF, . F i e l d dependence of absorption b b spectra at 77°K ' To Follow Page 56 Figure 18. IF*AsF£ . Chemical shift of centroid of spectrum relative to CF̂ COOH CO if) D < h L L I CO 1 . 5 - I O o Q_ O cc -0.5 h o CO z < LU o o O = 2 9 5 ° K A = 7 7 ° K 5 0 0 0 <?"=-54t 8 ppm 1 5 , 0 0 0 2 5 , 0 0 0 F I E L D ( H o ) G A U S S 57 o arranged i n two d i s t i n c t groups of s i x f l u o r i n e s each at 300 K. (For IF^ and AsF^ the r a t i o would have been 1.4:1). This supports the i o n i c formulation IF! A S F . suggested by Seel and 6 o Detmer (5) and confirmed by Beaton (10). Figure 19 gives the f i e l d dependence of the l i n e width at 77 and 295°K. For the 295°K spectra the slope of the p l o t i s 140+25 ppm i n agreement with the chemical s h i f t determined from the resolved curves at 94.1 MHz. • This confirms that the resol u t i o n does involve components which are not completely overlapped and which have no: asymmetry. For IF* AsF we may D O take e x = a 2 = e z = a 4 = a5 = s 6 = * A s and 57 .= eQ = § g = e 1 0 €T, , = C, = C» where 6„ and 6TT denote the mean i s o t r o p i c 11 Li. 1 As I s h i f t s for f l u o r i n e atoms bonded to arsenic and iodine respec- t i v e l y . I f , as the r e s o l u t i o n at 94.1 MHz and Figure 19 suggest, the asymmetry i n the components i s averaged out, equation (19) becomes * Jf(<sAs-S,)1 . . . . . . . . . . . . (26 ) The r e l a t i v e p o s i t i o n s of <T and 6" with respect to high or M S 1 ' low f i e l d cannot be determined from t h i s equation, but may be deduced from other considerations. I t w i l l be indicated l a t e r that the As-group i s to high f i e l d of the I-group. From equation (25) and the slope of the 295°K l i n e i n Figure 20, which shows the f i e l d squared dependence of the second moment, the r e l a t i v e chemical s h i f t between the components i s (**"pjS - €1 ) = 135 + 8 ppm. This i s quite reasonable agreement with To Fol l o w Page 57 F I E L D ( H Q ) G A U S S To Follow Page 57 F I E L D S Q U A R E D . ( H f ) K I L O G A U S S 2 58 the value of 153+10 ppm from the r e s o l u t i o n and confirms both the o absence of anisotropy at 295 K and the accuracy of the r e s o l u t i o n . In Figure 17a, the broken curve has been constructed by s h i f t i n g the two components resolved at 94.1 RlHz r e l a t i v e to each other with a s h i f t of 153 ppm. Although at low f i e l d s the con- structed curve i s t a l l e r than the experimental curve, l i n e width i s about the same and the constructed and experimental curves have o very s i m i l a r shapes. E v i d e n t l y , i n the region 235-295 K, the spec- trum i s composed of two d i s t i n c t curves whose area r a t i o s are a quite d e f i n i t e 1.1:1. From comparison of the l i n e shapes of the components with those of the SF̂ , • AsF^ adduct, i t i s concluded 2 that the t a l l component (second moment 0.7 gauss ) to high f i e l d i s the AsF grouping and the short component (second moment 2.0 6 2 ^ gauss ) to low f i e l d i s the IF^ grouping.Confirmation comes from Christe et a l (80), from whom a chemical s h i f t of -126.6 ppm with respect to HF can be obtained for AsF^ i n HF s o l u t i o n . In our work the s h i f t of the c e n t r o i d of the t o t a l IF* AsF curve i s 0 D -54+8 ppm with respect to CF„C00H. The AsF peak i s to high f i e l d and the mean s h i f t between the components i s 143+10 ppm. (The estimatesof the s h i f t range from 135+8 through 140+25, to 153+10 ppm). This places the AsF,. peak i n s o l i d IF* AsF. at — 0 D O -100+20 ppm r e l a t i v e to HF i n f a i r agreement with Christe's value. The IF* group w i l l be at —243+20 ppm r e l a t i v e to HF„ For the 77°K spectra to t a i l i n the opposite d i r e c t i o n to the high temperature spectra, anisotropy of chemical s h i f t almost - 59 c e r t a i n l y must be pre s e n t a t the lower temperature. As w i l l be seen below when the IF* AsF c r y s t a l s t r u c t u r e i s mentioned, the o b I-F and As-F bond l e n g t h s are q u i t e s i m i l a r . The groups are n e a r l y i d e n t i c a l i n s i z e and shape ( t h e r e i s a s l i g h t d i s t o r t i o n i n the As-group). When they are at 77°K where^ because of the o o co n s t a n c y of second moment between 77 and 205 K, they are both presumably r i g i d , they w i l l have p r o b a b l y c l o s e l y s i m i l a r second 2 moments of about 10.7 gauss each, the same value as the e x t r a - p o l a t e d zero f i e l d , d i p o l a r second moment. This i s v e r i f i e d below f o l l o w i n g Table 7 w i t h the t h e o r e t i c a l r i g i d l a t t i c e c a l c u l a t i o n s of the second moment. ( i f a l l other f a c t o r s are i d e n t i c a l , the 1-group s h o u l d have a s l i g h t l y g r e a t e r second moment because of the g r e a t e r magnitude of the F-I than the F-As i n t e r a c t i o n . ) The o l i n e shapes too w i l l be q u i t e s i m i l a r at 77 K and, i n the absence of a n i s o t r o p i c s h i f t , the t o t a l curve would be s y m m e t r i c a l . The d i r e c t i o n of the asymmetry - to high f i e l d - give s a p o s i t i v e v a l u e t o the . a n i s o t r o p i e s or at l e a s t to t h e i r net e f f e c t . They w i l l a lmost c e r t a i n l y both be p o s i t i v e . F i g u r e 18 showed t h a t the r e l a t i v e s h i f t of the c e n t r o i d o of the t o t a l curve w i t h r e s p e c t to CF^COOH was the same at 77 o and 300 K. I f we make the reaso n a b l e assumption t h a t the r e l a t i v e s h i f t between the components remains the same at both temperatures o an e s t i m a t e can be made of the chemical s h i f t a n i s o t r o p y a t 77 K by a p p l y i n g the equation .... (27) 60 - to t hs 77 l i n e i n F i g u r e 20. From the upper l i m i t of the r e l a t i v e s h i f t of 153+10 ppm, the average s h i f t of 143+10 ppm, and the lower l i m i t of 135-8 ppm, average a n i s o t r o p i c s of about 310, 333, and 355 ppm r e s p e c t i v e l y are o b t a i n e d . How c l o s e l y the a n i s o t r o p i c s o f the i n d i v i d u a l groups approach the average value i s d i f f i c u l t t o say. The average i t s e l f appears to be of a reasonable magnitude s i n c e i t i s q u i t e s i m i l a r to the approximate 300 ppm f o r U J . The broken curve i n F i g u r e 17b shows curves r e c o n s t r u c t e d from two 2 e q u a l components of 10.7 gauss second moment, having 333 ppm a n i s - o t r o p i e s , and w i t h r e l a t i v e s h i f t of 143 ppm. Si n c e a gaussian broadening f u n c t i o n has been a p p l i e d to eq u a t i o n ( 1 6 ) , the con- s t r u c t e d curve i s perhaps too narrow. Compared to the gaussian c u r v e of the same second moment, the e x p e r i m e n t a l z e r o f i e l d curve found f o r UJF^ was r a t h e r wider towards the top, but w i t h o u t such e x t e n s i v e wings. T h i s would make the c o n s t r u c t e d curves i n F i g u r e 17b i n somewhat b e t t e r agreement w i t h the observed shapes. How- e v e r , the q u a l i t a t i v e agreement w i t h the e x p e r i m e n t a l l i n e shape i s not bad c o n s i d e r i n g the assumptions i n v o l v e d , 3. C r y s t a l S t r u c t u r e Beaton (10) has determined the s t r u c t u r e of IF*'AsF. from C D powder X-ray d a t a , presumably a t room temperature. His i n f o r m a t i o n i s summarized i n Table 5. 61 - Table 5 X-Ray Powder S t r u c t u r e of IF* AsF~ ~ 295°K o o Space Group Pa3 c u b i c ZQ = 9.4935+0.0005A atomic parameters As i n 4 (a) (0, 0, 0) I i n 4(b) ( i , A, i ) F i n 24(d) (x, y, z) x=0.0980; y=0.1377; z=-0.0489 F i n 24(d) ( x , y, z) x=0.6001; y=0.6431; z=0 e4411 bond d i s t a n c e s and angles As-F 1 .678* F-As-F = 86.5° 1 -F 1.75^* F- 1-F = 90 C i n t e r m o l e c u l a r d i s t a n c e s .0 (3) F...F at 2.81.8 (3) F...F at 2.95.8 (3) F...F a t 2 .978 (3) F...F a t 3 „ 0 4 8 These d i s t a n c e s may be too s m a l l . See t e x t below c Beaton p o i n t s out t h a t the bond l e n g t h s d e r i v e d from h i s X-ray data may be r a t h e r s h o r t , the As-F l e n g t h i n p a r t i c u l a r . He a s c r i b e s t h i s to h i s n e g l e c t of thermal motion when d e t e r m i n i n g the bond l e n g t h s and suggests t h a t such a c o r r e c t i o n might be 0.l8 or more. As evidence he c i t e s Copeland e t a l ( 8 l ) who found i n a s a l t of AsF~ t h a t the As-F bond l e n g t h c o r r e c t e d f o r thermal 6 motion was 1.77^8 and un c o r r e c t e d was 1.65A. T r o t t e r (82) con- s i d e r s t h a t t h i s appears a r a t h e r l a r g e c o r r e c t i o n f o r thermal 62 motion. However, i f one a r b i t r a r i l y a p p l i e s a c o r r e c t i o n of O.lR to each of Beaton's bond l e n g t h s , both of them are s t i l l w i t h i n the ranges g i v e n i n the I n t e r a t o m i c D i s t a n c e s Supplement ( 8 3 ) . There, v a l u e s of 1.71, 1.85, 1,80, and 1.83 are given f o r I-F bond l e n g t h s i n I F ? and 1.80+Q.05A5 f o r the As-F bond lengths i n - 0 0 AsF o In t h i s l a s t , the F-As-F angle i s given as 88.3 +2.1 . • — In Table 6 the f i r s t column of atomic c o o r d i n a t e s c o n t a i n s Beaton's v a l u e s , the second c o n t a i n s h i s c o o r d i n a t e s a d j u s t e d f o r the 0.1A5 i n c r e a s e i n bond l e n g t h . Only the f i r s t " m o l e c u l e " i n the u n i t c e l l i s g i v e n , the symmetry o p e r a t i o n s w i l l of course give the o t h e r t h r e e . Table 6 Atomic C o o r d i n a t e s f o r IF* AsF" ~ 0 b 295°K x Thermally y Thermally 2 Thermally Adjus ted Adjusted Adjusted Beaton Beaton Beaton Beaton Beaton Beaton 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000 0.0980 0.1039 0.1377 0.1460 -0.0489 -0.0518 • 0.0489 -0.0518 0.0980 0.1039 0.1377 0.1460 0.1377 0.1460 -0.0489. -0.0518 0.098.0 0.1039 0.0980 -0.1039 -0.1377 -0.1460 0.0489 0.0518 0.0489 0.0518 -0.0980 -0.1039 -0.1377 -0.1460 0.1377 -0.1460 0.0481 0.0518 -0.0980 -0.1039 0.5000 0.5000 0.5000 0.5000 0.5000 0.5000 0.6001 0.6058 0.6431 0.6513 0.4411 0.4377 0.4411 0.4377 0.6001 0.6058 0.6431 0.6513 0.6431 0.6513 0.4411 0.4377 0.6001 0.6058 0.3999 0.3942 0.3569 0.3487 0.5589 0.5623 0.5589 0.5623 0,3999 0.3942 0.3569 0.3487 0.3569 0.3487 0.5589 0.5623 0.3999 0.3942 As I F 1 0 F 1 1 12 (1) (2) "Thermally a d j u s t e d Beaton" means th a t the c o o r d i n a t e l i s t e d under "Beaton"has been i n c r e a s e d to a l l o w f o r an e s t i m a t e d +0.lS thermal c o r r e c t i o n to the bond l e n g t h . I t i s not meant to imply a c c u r a c y to four s i g n i f i c a n t f i g u r e s i n t h i s t a b l e . 63 - 4. T h e o r e t i c a l R i g i d L a t t i c e 5econd Moment For I F * AsF,. , e q u a t i o n (2) f o r the t h e o r e t i c a l r i g i d 6 o . l a t t i c e second moment w i l l have a t h i r d term s i m i l a r to the second. The n u m e r i c a l f a c t o r s w i l l be 316.8, 23.4, and 74.3 f o r the F-F, F-As, and F-I sums r e s p e c t i v e l y . Table 7 gi v e s the second moment c o n t r i b u t i o n s from c a l c u l a t i o n s based both on Beaton's atomic c o o r d i n a t e s a d j u s t e d f o r thermal motion and on h i s unad j u s t e d c o o r d i n a t e s . For Beaton's u n c o r r e c t e d values only the t o t a l second moment i s shown. In c a l c u l a t i n g the second moments i t has been assumed t h a t the c o o r d i n a t e s o o at 295 K w i l l ba i n re a s o n a b l e a p p r o x i m a t i o n to those a t 77 K. Table 7 R i g i d L a t t i c e Second Moment C o n t r i b u t i o n s to I F + AsF 6 o From Beaton's a d j u s t e d c o o r d i n a t e s Second Moment Gauss F-F F-As F-I T o t a l I F6 A s F 6 T o t a l ( i n c l u d i n g i n t e g r a l 8.78 0.39 0.98 10.40 c o n t r i b u t i o n s over 6A5 of 0.35, O.fJO, and 0.01 gauss ) IF+6 A s F 6 INTRA 4.75 0.38- 0.93 6.06 AsF* o TOTAL ( t c 6A 5) 4.71 0.38 0.04 5.13 AsF" o INTRA 2.71 0.38 0.00 3.09 K TOTAL ( t o 68) 4.07 0.01 0.93 5.01 INTRA 2.04 0.00 0.93 2.97 From Beaton's c o o r d i n a t e s ( l O ) I F6 A s F 6 TOTAL ( i n c l u d i n g above 10 o68 0.54 1.34 12 0 56 i n t e g r a l c o n t r i b u t i o n s ) E x t r a p o l a t e d Zero F i e l d Second Moment 10.7 Note: A l l c o n t r i b u t i o n s i n t h i s t a b l e are based on a 1 2 - f l u o r i n e I F + AsF" u n i t . N i n e q u a t i o n (2) has been taken as 12 f o r 6 6 . a l l groups. Zero point v i b r a t i o n a l motion would decrease the t h e o r e t i c a l second moment somewhat, but contraction of the c r y s t a l l a t t i c e between o o 295 K, where the structure was determined and 77 K where i t was applied to the c a l c u l a t i o n of the t h e o r e t i c a l moments would increase the values somewhat more. The good agreement between the t h e o r e t i c a l second moment based on the adjusted coordinates and the zero f i e l d second moment i n d i c a t e s that the "thermal c o r r e c t i o n " was probably of the r i g h t order. The probable bond lengths therefore are of the same order as those l i s t e d i n the Interatomic Distances Supplement as Beaton suggested, and are longer than those he reported,. The contributions of the IF* and AsF groups to the t o t a l o o second moment (up to 6A5 radius from the center of the relevant group) 2 are 5„01 and 5.13 gauss r e s p e c t i v e l y . Since these are based on a 12 12 f l u o r i n e u n i t , the values must be m u l t i p l i e d by /5 to obtain the second moments the i n d i v i d u a l components would have i f they could be o 2 resolved 'out at 77 K. This gives 10.20 and 10.44 gauss r e s p e c t i v e l y when the c o n t r i b u t i o n for d i s t a n t n u c l e i i s included. Both values are 2 i n good agreement with the 10.7 gauss assumed above for the attempted reconstruction of the experimental curves i n Figure 17b 0 5. Reorientations i n the S o l i d Above t h e i r respective nmr t r a n s i t i o n s a l l three of the IF* , AsF^. , and UJF̂  groups e x h i b i t symmetrical spectra. Below the t r a n s i t i o n the UJFg spectra e x h i b i t asymmetry presumably both because of anisotropy of the s h i f t tensors and because of the non-equivalent s i t e s of the a x i a l and equatorial f l u o r i n e s i n the molecule. In UJF 65 - above the t r a n s i t i o n , motions average out both the chemical s h i f t anisotropy and the mean i s o t r o p i c s h i f t between the non-equivalent f l u o r i n e s , to give a s i n g l e , symmetrical l i n e . S i m i l a r motions are l i k e l y i n v o l v e d above the t r a n s i t i o n i n IF* AsF which i s also b fa o around 200 K. In the case of tha s a l t , there are two symmetrical, but d i s t i n c t components above the t r a n s i t i o n . Whatever motions occur can average out only the ani s o t r o p i c s h i f t and non-equiva- lences ( i f present) w i t h i n each d i f f e r e n t i o n . The dif f e r e n c e s between the f l u o r i n e s attached to the cation and those attached to the anion are a consequence of t h e i r bonding to the respective I and As atoms and are not averaged out. The r e l a t i v e s h i f t between the ions therefore remains regardless of the degree of r e o r i e n t a t i o n . UJith regard to the ac t u a l r e o r i e n t a t i o n s which are occurring above the t r a n s i t i o n , i t appears that that AsF^ i s undergoing mora + o extensive motion than the IF i o n . I t s second moment at 295 K i s D 2 about 0.7 gauss , a value quite consistent with i s o t r o p i c re- o r i e n t a t i o n about i t s center of mass. The IF* component, however, 2 has a broader l i n e and a greater second moment, 2.0 gauss . In ex- p l a i n i n g or at l e a s t r a t i o n a l i z i n g the r i g i d l a t t i c e l i n e shape, we stated that both the IF* and AsF^ component l i n e shapes would probably b b be s i m i l a r since the two ions were s i m i l a r i n si z e and geometry. This i s s a t i s f a c t o r y i n the r i g i d l a t t i c e , but would appear true also at higher temperatures since the two groups presumably w i l l experience and be influenced equally by the same barrier to r e o r i e n t a t i o n . The more frequent r e o r i e n t a t i o n e x h i b i t e d at 295°K by the AsF than the 66 IFg group may be a consequence of the shorter As-F bond le n g t h a About any axis of r o t a t i o n , the moment of i n e r t i a of the AsF ion 6 i s some 10% l e s s than that for the IF* ion. This estimate mas o made using regular octahedra. In fact the AsF. octabedra are b d i s t o r t e d ( 1 0 ) . The compression, however, i s along a 3 a x i s . The e f f e c t merely squeezes the faces of the octahedra together and the centers of mass s t i l l coincide with those of the As atoms so that the As atoms s t i l l make no c o n t r i b u t i o n to the moments of i n e r t i a . Although the moment of i n e r t i a i s increased for r o t a t i o n about the 3 a x i s , i t i s reduced for r o t a t i o n about an axis at r i g h t angles to the 3 axis along which compression occurs. Since q u a l i t a t i v e l y one expects a r e o r i e n t a t i o n to occur p r e f e r e n t i a l l y about the axis with the l e a s t moment of i n e r t i a , then i t w i l l take place about t h i s l a s t axis where the moment i s even less than i n the undistortad case. Hence the AsF ion undergoes more frequent r e o r i e n t a t i o n at b 2 9 5 ° K than the IF* i o n . b The above view i s confirmed by Das (84) who points out that the p r o b a b i l i t y of t r a n s i t i o n from one p o t e n t i a l w e l l to the next .over an n-fold b a r r i e r i s W r W t + W T ' (28) where and \Â . are the p r o b a b i l i t i e s for c l a s s i c a l r o t a t i o n over the b a r r i e r and quantum mechanical tunneling through the b a r r i e r res- p e c t i v e l y . Since for a l l r o t a t i n g groups other than those i n v o l v i n g only protons i s n e g l i g i b l e , the p r o b a b i l i t y reduces to w w c - sL[y±\ e / M ( 2 9 ) 67 - where I i s the e f f e c t i v e moment of i n e r t i a and where Vo, the a c t i -e r r ' v a t i o n energy or h e i g h t o f the h i n d e r i n g p o t e n t i a l b a r r i e r , may be determined from e q u a t i o n ( 8 ) . From e q u a t i o n (29), i t i s obvious t h a t the s m a l l e r I e f f » the g r e a t e r i s the p r o b a b i l i t y of r e o r i e n t a t i o n . Hence the AsF group can l o g i c a l l y be expected to undergo more f r e -o quent r e o r i e n t a t i o n than the I F * group at a gi v e n temperature, pro-fa v i d e d t h a t the temperature i s h i g h enough f o r the motion to occur,. A l though the above q u a l i t a t i v e l y p r e d i c t s a h i g h e r p r o b a b i l i t y f o r AsFg r e o r i e n t a t i o n , the a c t u a l p r o b a b i l i t i e s d i f f e r by l e s s than 10%„ I t may be t h a t , c o n t r a r y to the assumption above, the groups do en- counter d i f f e r e n t b a r r i e r s w i t h the AsF.. b a r r i e r to r e o r i e n t a t i o n o being the l e s s e r . 2 The narrow AsF l i n e w i t h i t s 0„7 gauss second moment can be o o accounted f o r a t 295 K by assuming i s o t r o p i c r e o r i e n t a t i o n of the group as noted e a r l i e r . The broader l i n e of the IF* component has o 2 a second moment of 2„0 gauss , however, which i s c l e a r l y much hi g h e r 2 than the 1 gauss v a l u e p r e d i c t e d f o r i s o t r o p i c r e o r i e n t a t i o n . I t i s too h i g h a l s o f o r r e o r i e n t a t i o n a t random 'about the symmetry axes of the o c t a h e d r a l group. This would have the e f f e c t t h a t each f l u o - r i n e spent l / 6 of i t s time at each p o s i t i o n and would reduce the second moment to a v a l u e o n l y s l i g h t l y l a r g e r than t h a t f o r i s o t r o p i c r e o r i e n t a t i o n ( 6 3 ) . As noted i n e q u a t i o n ( 5 ) , r e o r i e n t a t i o n s about a s i n g l e symmetry a x i s reduce each c o n t r i b u t i o n to the i n t r a g r o u p d i p o l a r broadening by a f a c t o r t (3 C o s ^ ^ - t ) 2 where V j ^ i s the angle between the i n t e r n u c l e a r v e c t o r and the a x i s of r o t a t i o n . 68 - Th i s f a c t o r holds f o r st e p w i s e r e o r i e n t a t i o n about an n - f o l d a x i s w i t h H-3 and f o r c l a s s i c a l r o t a t i o n about any a x i s ( 5 7 ). For the IF* i o n there are two - , t h r e e - , and f o u r f o l d symmetry axes about which r e o r i e n t a t i o n might o c c u r . The i n t r a g r o u p second moments f o r I F ^ are 2.04, 2 017, and 1 093 gauss r e s p e c t i v e l y f o r r e o r i e n t a t i o n s about the » and axes. In a d d i t i o n to t h i s i n t r a g r o u p c o n t r i b u t i o n t h e r e w i l l be an i n t e r g r o u p c o n t r i b u t i o n . The AsFg group appears to be undergoing an i s o t r o p i c r e o r i e n t a t i o n i n which i t s i n t r a g r o u p second moment would be averaged to zero,, 2 Therefore i t s 0.7 gauss second moment i s due e n t i r e l y to i n t e r - group i n t e r a c t i o n s and can be used to estimate an i n t e r g r o u p second moment f o r the s i m i l a r I F * group. T h i s makes the t o t a l second • 2 moments of the c a t i o n 2.74, 2.87, and 2.63 gauss f o r , , a n <^ r e o r i e n t a t i o n s . A l l these exceed the e x p e r i m e n t a l value of 2.0 2 + gauss by more than 30%. The a c t u a l motion which IF i s undergoing b must t h e r e f o r e be l e s s than r e o r i e n t a t i o n about o c t a h e d r a l axes a t random but g r e a t e r than r e o r i e n t a t i o n about a s i n g l e a x i s . Perhaps the motion i s a combination of r e o r i e n t a t i o n about one a x i s and simultaneous o s c i l l a t i o n about another. This i m p l i e s t h a t d i f f e r e n t r e o r i e n t a t i o n a l b a r r i e r s may e x i s t f o r the IF* and AsF. i o n s 0 6 6 The average a c t i v a t i o n energy f o r the combined motions was determined from an A r r h e n i u s p l o t of equation (8) to be 19+4 K c a l per mole. This energy i s v e r y . h i g h . Because of the s c a t t e r i n F i g u r e 16 of the p o i n t s j u s t below the t r a n s i t i o n ; i t i s p o s s i b l e t h a t the change i n second moment as drawn i s s h a r p e r than i t r e a l l y i s . A l e s s - 69 - abrupt t r a n s i t i o n would have a lower a c t i v a t i o n energy. I f the t r a n s i t i o n i s indeed t h i s a b r u p t , the a c t i v a t i o n energy found may not be v a l i d o I n s tead of a change i n motion w i t h i n a s o l i d phase of f i x e d c r y s t a l s t r u c t u r e , the t r a n s i t i o n may mark an a c t u a l c r y s t a l t r a n s i t i o n , , B. SF^ • AsF<- 1» R e s u l t s F i g u r e 21 shows the temperature dependence of the SF^ • AsF^ a b s o r p t i o n spectrum at 30 ffiHz. The a b s o r p t i o n curves have the same x - s c a l e and are i n t e g r a t e d to a c o n s t a n t , a r b i t r a r y area from the d e r i v a t i v e c u r v e s . Appendix IVa c o n t a i n s r e p r o d u c t i o n s of the a c t u a l d e r i v a t i v e s i n c l u d i n g some f o r temperatures higher than the h i g h e s t value shown i n Figure 2 1 c F i g u r e 22 i s a p l o t of the tem- p e r a t u r e dependence of the averaged second moments at 30 fslHz. The second moment does not appear to achieve a r i g i d l a t t i c e value by o o 77 K, the lowest temperature reached i n the s t u d y . At 77 K the 2 second moment i s 5 09+0 03 gauss . From t h a t temperature i t drops 2 o g r a d u a l l y i n a smooth curve to 1.85+0.1 gauss around 200 K. The b second moment remains constant at t h i s value u n t i l 336 K. Through- o out the r e g i o n from 77 to 336 K, the 30 IT!Hz a b s o r p t i o n s p e c t r a are o almost s y m m e t r i c a l , w i t h a s l i g h t t a i l i n g to low f i e l d . Above 336 K the a b s o r p t i o n s were so narrow t h a t the i n t e g r a t e d s p e c t r a were not p l o t t e d . The d e r i v a t i v e curves i n Appendix IVa show a marked i n c r e a s e o o i n motion b e g i n n i n g at 336 K. The d e r i v a t i v e a t 320 i s s i m i l a r to o t h a t at 295 K9 which shows a s h o u l d e r on the low f i e l d h a l f of the To Follow Page 69 T O T A L S E C O N D M O M E N T G A U S S 2 69 sS^d M O T T O i oj, 70 d e r i v a t i v e . The s p e c t r a a t 336 have a very g e n e r a l s i m i l a r i t y i n o shape and a s i m i l a r second moment to those a t 320 , but the s h o u l d e r o has now become a narrow component. Second moment drops at 336 to a 2 o o o v a l u e o f about 0.1 gauss by 342 K. Between 342 and 373 K, the h i g h e s t temperature r e c o r d e d , the second moment remains c o n s t a n t , o By 342 K t h e r e i s an almost complete r e s o l u t i o n of the spectrum i n t o two components w i t h an i s o t r o p i c chemical s h i f t of 97 Q5+5 ppm. The r e s o l u t i o n i s s l i g h t l y b e t t e r a t 373°K, but the chemical s h i f t i s e x a c t l y the same. Appendix IVa as noted above shows the temperature dependence o f the d e r i v a t i v e l i n e a t 30 MHz. The g r a d u a l s h i f t of the low f i e l d s h o u l d e r towards hig h f i e l d changes the l i n e shape i n a manner which makes i t d i f f i c u l t , as w i t h I F * AsF^ , to d e f i n e a c o n s i s t e n t peak to peak l i n e w i d t h from the d e r i v a t i v e . For t h i s reason no p l o t of v a r i a b l e ' temperature l i n e w i d t h i s g i v e n . The c h e m i c a l s h i f t f o r the t o t a l curve w i t h r e s p e c t to CF C00H i s g i v e n i n F i g u r e 23. Al t h o u g h i t appears t h a t there might be a o temperature dependence of the s h i f t r e l a t i v e to CF^COOH at 300 K , the s c a t t e r i s so g r e a t t h a t i t cannot be e s t a b l i s h e d . The s h i f t d etermined from F i g u r e 23 i s -40+15 ppm. 2 0 R e s o l u t i o n w i t h Components (see R e s u l t s a l s o ) . I s o t r o p i c and A n i s o t r o p i c C h e m i c a l S h i f t . F i g u r e s 24a and b show the f i e l d dependence of the a b s o r p t i o n o o s p e c t r a a t 300 K and 77 K. Appendices IVb and IVc g i v e the d e r i v a t i v e curves f o r these s p e c t r a F i g u r e 24a demonstrates t h a t one can make a To Follow Page 70 Figure 23. SFoAsF, . Chemical shift of centroid of spectrum J 6 relative to CF C00H O 5 0 0 0 15,000 25 ,000 F I E L D ( H Q ) G A U S S To Follow Page 70 To Follow Page 7 0 Solid line experimental Broken line constructed 71 r e s o l u t i o n of the curve a t 300 K and 94.1 IYIHZ. The r a t i o of the area under the t a l l , h i g h f i e l d peak to that under the s h o r t , low f i e l d peak i s 2.2:1, from which i t i s concluded t h a t t h e r e are t w i c e as many f l u o r i n e s i n v o l v e d i n the high f i e l d peak as i n the low f i e l d . Hence at 300°K the SF^ • AsF^ adduct i s p r o b a b l y the i o n i c s a l t SF* ^sFg f o r the e x p e r i m e n t a l r a t i o of areas under the components i s g r e a t e r than 6:3, not between 6:3 and 5:4. The high 2 f i e l d component has a second moment of about 0.9 gauss and the low 2 f i e l d component one of 1.1 gauss . The r e l a t i v e chemical s h i f t between the two components as r e s o l v e d at 94.1 MHz and 300°K i s 105+10 ppm i n agreement w i t h the value determined i n the 30 !Y1 Hz o o s p e c t r a a t 342 K and above. The components at 300 K o b t a i n e d from the r e s o l u t i o n of the 94.1 MHz spectrum, are each s y m m e t r i c a l about t h e i r c e n t e r s w i t h no s u g g e s t i o n of asymmetry. As shown by the broken l i n e s i n F i g u r e 24a the components, w i t h a s h i f t of about 100 ppm, g i v e a reasonable r e p r o d u c t i o n of the e x p e r i m e n t a l spectrum a t each lower frequency i n v e s t i g a t e d . From the approximate 100 ppm s h i f t . b e t w e e n the components and the -40+15 ppm s h i f t of the t o t a l o curve w i t h r e s p e c t to CF^COOH at 300 K, the s h i f t s of the components w i t h r e s p e c t t o any standard can be determined. R e l a t i v e to HF the hi g h f i e l d component i s a t -107+20 ppm and the low f i e l d component at -207+20 ppm. Since the AsF~ i o n i s common to both the A s F 5 adducts, i t i s undoubtedly the peak found at about -100+20 ppm i n each. The c a t i o n i n each adduct i s then the low f i e l d component i n each case. 72 - I t i s a l s o possible to make a r e s o l u t i o n i n t o components at 94.1 fflHz and 77°K. The r e s o l u t i o n was based on the contours of the curve and the assumption that the l i n s shapes of the components o would be roughly s i m i l a r at 77 and 300 K. Two f a i r l y symmetrical components are obtained with a r e l a t i v e shi'ft of 185+20 ppm which might be "squeezed" to 160+20 ppm but no more. As indi c a t e d l a t e r even t h i s value may be too great 0 The area of the t a l l e r , high f i e l d curve (AsF ) to that of the shorter, low f i e l d curve (SF*) i s b -J 1 09:1, again p r o v i d i n g support for the 2:1 area r a t i o required by the i o n i c formulation of the adduct. The AsF component has a second b 2 + 2 moment of 2.8 gauss , the SF^ component one of 4 07 gauss . S h i f t i n g the two curves appropriately gives a reasonable reproduction of the l i n e shapes at lower frequencies as indicated by the broken curves i n Figure 24b. Figure 25 shows the f i e l d squared dependence of the second o o moment at 300 and 77 K. Since there was no asymmetry evident i n the resolved components at e i t h e r temperature, the f i e l d squared depen- dence of the second moment must be due e n t i r e l y to the mean, i s o t r o p i c chemical s h i f t . Since C. = 6 n = G = § and 6. = = 6 C = 6 „ = 5_ = 1 £ O 5 4 3 0 ( 0 6„ = <>„ where the S and As re f e r to the flu o r i n e s h i f t i n SF* and 9 As 3 AsF~ r e s p e c t i v e l y , and there i s no detectable anisotropy present, equation (19) becomes = jx (k ) + ̂ -\U(G>U-6S . (30) From equation (30) the 300°K l i n e gives a value of the r e l a t i v e s h i f t of 87+10 ppm i n good agreement with the two other values for 295°K and To Follow Page 72 Figure 25. SF„AsF7 . Field squared dependence of second moment • at 77° and 300°K 73 above. Indeed, because of the small slope of the second moment l i n e , 2 a change of only +0.2 gauss i n the average second moment at 94.1 MHz would bring t h i s s h i f t up to about 100 ppm i n even c l o s e r agreement o with the values found by r e s o l u t i o n of the spectra. From the 77 K l i n e on i s o t r o p i c s h i f t of 110+10 ppm i s obtained. This agreement o o with the value at 300 K confirms that there i s no anisotropy at 77 K. o I t a l s o suggests that the r e s o l u t i o n at 77 may be i n e r r o r . Although the shape of the experimental curve appears to d i c t a t e components with a s h i f t of at l e a s t 160+20 ppm, i n the absence of r e s o l u t i o n i n the experimental curve i t s e l f , there i s c e r t a i n l y room for e r r o r . Probably the 110+10 ppm value from Figure 25 i s more r e l i a b l e . 3. Proposed C r y s t a l Structure No X-ray study i s a v a i l a b l e for SF*. AsF^. . Some information i s a v a i l a b l e for SF^ • SbF^ f enough to make a guess at the structure of SF* AsFg._ In the absence of a r i g i d l a t t i c e second moment for comparison with the t h e o r e t i c a l moment for the model, the guess must be rather tenta- t i v e . B a r t l e t t (6) has determined a c r y s t a l structure from powder data for SF^ ° SbFj. . The determination was not f u l l y completed but the symmetry suggested an i o n i c formulation SF* SbF. . Muetterties (85) j b a l s o suggested the i o n i c formulation for the adduct as the most l i k e l y of two p o s s i b l e s t r u c t u r e s . B a r t l e t t ' s information i s summarized i n Table 8. 7 4 - T a b l e 8 X-Ray Data f o r SF* SbF~ at 291°K Simple c u b i c a = 5,625 + 0.0028 = 1 7 8 8 3 • Abs.= 3 ' 1 * ° a • / c a l c . = 3 ' ° 3 ' Z = 1 The I n t e r a t o m i c D i s t a n c e s Supplement (83) g i v e s an Sb-F ( s i n g l e c r y s t a l ) bond l e n g t h of 1.788, and i n the bond l e n g t h range noted e a r l i e r an As-F (powder) l e n g t h of I.808. The SbF c and AsF,. groups w i l l have b b n e a r l y the same symmetry and volume then and the SF* SbF^ s t r u c t u r e may be a r e a s o n a b l e a p p r o x i m a t i o n t o the SF* AsF,, s t r u c t u r e . However the J> b atomic c o o r d i n a t e s are not known f o r SF* SbF- and a f u r t h e r approxima- •J b t i o n must be made 0 The AsFg groups may be p l a c e d at the c o r n e r s of the s i m p l e c u b i c c e l l . They c o u l d be approximated f o r the purposes of a second moment c a l c u l a t i o n as spheres (86) s i n c e the o r i e n t a t i o n s of the octahedra i n the c e l l are unknown. However, Program 6 i s designed to use n u c l e a r c o o r d i n a t e s and the (0, 0, 0) AsF^ group from T'F^+AsFg was chosen a f t e r c o n s i d e r a b l e t r i a l and e r r o r w i t h a model. Octahedra having t h i s o r i e n t a t i o n were p l a c e d a t the four c o r n e r s of the c e l l 0 The SF* group w i l l be i n the c e n t e r of the c e l l a t (•??, - j , 5 ) , but i t i s u n l i k e l y (82) t h a t the s u l f u r atom w i l l be at the exact c e n t e r . The group was p l a c e d so t h a t the three f l u o r i n e s were i n an e q u i l a t e r a l t r i a n g l e c e n t e r e d on (̂ -, \ y \) and p a r a l l e l to the a-b plane of the c e l l . Then the s u l f u r atom and i t s lone p a i r can f i t along tha v e r t i c a l a x i s p a s s i n g through (£, \ y \ ) . In the model i t appeared t hat - 75 - the SF* group c o u l d r o t a t e q u i t e f r e e l y about the a x i s through the 5 atom and ( 5 , - j , . Table 9 g i v e s the atomic c o o r d i n a t e s c a l c u l a t e d f o r the assumed SF* A s F c u n i t c e l l a t "291°K" and a p p l i e d a t 77°K 0 In d e t e r m i n i n g the c o o r d i n a t e s f o r the AsF^ groups, As-F bond l e n g t h s of 1 0778, as f o r the p r e v i o u s adduct, were used. Figure 26 shows a view Table 9 Estimated Atomic C o o r d i n a t e s f o r SF* AsF~ a t "291°K" 0 0 As F, 0.0000 0.0000 0.0000 0.1754 0.2464 -0.0874 -0.0S74 0.1754 0.2464 0.2464 -0.0874 0.1754 -0.1754 -0.2464 0.0874 0.0874 -0.1754 -0.2464 -0.2464 0.0874 -0.1754 0.5000 0.5000 0.4074 0.3693 0.2736 0.5000 0.7614 0.5000 0.5000 0.3693 0.7264 0.5000 I t i s not meant to i m o l y accuracy to fo u r s i g n i f i c a n t f i g u r e s . down the a - a x i s f o r the proposed s t r u c t u r e . 4. T h e o r e t i c a l R i g i d L a t t i c e Second moment and R e o r i e n t a t i o n s i n the S o l i d . The t h e o r e t i c a l r i g i d l a t t i c e second moment f o r SF* AsF~ c a l c u l a t e d 3 6 2 by Program 6 from the above c o o r d i n a t e s i n 9.4 gauss . Only c o n t r i b u t i o n s from F-F and F-As i n t e r a c t i o n s need be summed s i n c e the n a t u r a l abundance 33 of S, the only s t a b l e , magnetic i s o t o p e of s u l f u r i s so low (0.74/b) t h a t F-S i n t e r a c t i o n s a r e . n e g l i g i b l e . There are a g r e a t many assumptions i n - v o l v e d i n the c a l c u l a t i o n and no e x p e r i m e n t a l v a l u e i s a v a i l a b l e as a To Follow Page 75 F i g u r e 26. SF*AsF£ . Proposed u n i t c e l l (along a-axis) c A P R O P O S E D POS IT ION O F A s A T C O R N E R S P R O P O S E D POS IT ION O F "S AT ( 1/ 1/ , 1 / ) 2 2 2 P 2 3 Qo = 5.6 A O 5 A C I R C L E S IND ICATE F L U O R I N E Von d e r Wools radii check. Indeed the count of i n t e r n u c l e a r d i s t a n c e s which Program 6 can p r o v i d e shows t h a t the SF* i o n i s somewhat crowded i n i t s assumed p o s i t i o n . There are fou r SF* i n t e r g r o u p c o n t a c t s w i t h s u rrounding AsF^ i o n s . Two are not too severe being 2.5 and 2.68 , but the o t h e r two are 2.2A w e l l under tw i c e the 1.358 f l u o r i n e van der UJaals r a d i u s . I n s p i t e of t h i s the c a l c u l a t e d second moment seems of a reaso n a b l e magnitude. The v a r i o u s c o n t r i b u t i o n s to the t o t a l second moment are l i s t e d i n Table 10. Table 10 " R i g i d L a t t i c e " Second Moment C o n t r i b u t i o n s to SF* AsFg 2 Second Moment Gauss F-F F-As TOTAL- S F 3 A S F 6 TOTAL ( i n c l u d i n g i n t e g r a l c o n t r i b u t i o n over s8 of 0.31 gauss^ to F-F) 8.80 0.52 9.42 S F 3 flsF6 INTRA 4.72 0.51 5.23 AsF~ 0 TOTAL ( t o e8) 5.96 0.51 6.47 AsF" 0 INTRA • 3.62 0.50 4.12 TOTAL ( t o 68) •2.63 0.01 2.64 INTRA 0.77 0.00 0.77 Note: A l l c o n t r i b u t i o n s i n t h i s t a b l e are based on a 9 - f l u o r i n e u n i t SF+ AsF" . N i n equation (2) J D has been taken as 9 f o r a l l oroups. 56 R e o r i e n t a t i o n s i n the S o l i d One t h i n g to n o t i c e i n Table 10 i s t h a t t o t a l second moment f o r the component SF* cu r v e , i f i t c o u l d be r e s o l v e d out, i s - 77 - 9 2 2.64 x = gauss w h i l e i t s i n t r a g r o u p second moment i s only 9 2 + 0.77 x = 2.3 gauss . In d e t e r m i n i n g p o s i t i o n s i n the SF^ i o n , i t was assumed i n agreement w i t h B a r t l e t t (6) t h a t because of the e l e c t r o n l o n g p a i r on the s u l f u r , the i o n would have an o p p r o x i - mately t e t r a h e d r a l c o n f i g u r a t i o n . Therefore S-F bond l e n g t h s of 1.56$ (83) and F-S-F angles o f 109° 28' were used. The presence of a lone p a i r w i l l r e p e l the three bond p a i r s somewhat more than a bond p a i r ( 7 ) . The bond angle w i l l t h e r e f o r e be somewhat l e s s than the t e t r a h e d r a l a n g l e . This would reduce the i n t r a - g r c u p F-F d i s t a n c e s o f 2 5 S and would hence reduce the r a t h e r heavy 2 p r o p o r t i o n of i n t e r (7.9 - 2.3 = 5.6 gauss ) to intra-group' second 2 + moment (2.3 gauss ) i n the SF^ i o n . A p o s i t i o n i n the u n i t c e l l which t i l t e d the i o n away from i t s assumed p o s i t i o n would a l s o change the second moment. However, r e d u c i n g the t e t r a h e d r a l angle would reduce the e f f e c t i v e volume of the i o n and g i v e . i t mors freedom i n the AsF^. "cage" c o n s i s t e n t w i t h i t s c o n s i d e r a b l e motion as low as o 0 77 K. The most probable motion a t 77 i s r e o r i e n t a t i o n about the a x i s . The sh r i n k a g e of the i o n due to the s m a l l e r bond angle would a l s o reduce the moment of i n e r t i a about t h i s a x i s and f u r t h e r enhance the i o n ' s - a b i l i t y to r e o r i e n t . The c a l c u l a t e d zero f i e l d r i g i d l a t t i c e second moment i s about 2 0 9.4 gauss yet the e x p e r i m e n t a l moment a t 30 fflHz and 77 K, which i n - c l u d e s a c o n t r i b u t i o n from i s o t r o p i c c h e m i c a l s h i f t , i s only 5 09 gaus The t h e o r e t i c a l zero f i e l d anion and c a t i o n r e s o l v e d curves would 9 , 2 2 have second moments of about 6.47 x /6 = 9 07 gauss and 7.9 gauss r e s p e c t i v e l y i f they c o u l d be measured a t t h e i r r i g i d l a t t i c e 78 t e m p e r a t u r e . T h e i r a c t u a l r e s o l v e d components at 77°K and 30 MHz 2 2 have moments o f 2.8 gauss and 4.7 gauss . Obviously by 77°, the motion i n the groups i s s u f f i c i e n t not only to average out tha a n i s o t r o p y ( s i n c e the components are s y m m e t r i c a l ) , but a l s o to o p a r t i a l l y average out the d i p o l a r i n t e r a c t i o n s . By 220 K the t o t a l second moment of the e x p e r i m e n t a l 30 MHz curve has f a l l e n 2 to about 1.9 gauss . Si n c e t h e r e i s no a n i s o t r o p y i n t h i s r e g i o n above the t r a n s i t i o n ; the r e s o l u t i o n i n t o components made at 94.1 IYIHz and 300°K w i l l be v a l i d here too ( t h e r e i s v i r t u a l l y no change i n l i n e shape from 200 to 295°K at 30 MHz). The second 2 2 + — moments are 1.1 gauss and 0.9 gauss f o r the SF„ and AsF~ i o n s r e s p e c t i v e l y . The anion s u r e l y and the c a t i o n very l i k e l y a re undergoing i s o t r o p i c or near i s o t r o p i c r e o r i e n t a t i o n above the t r a n s i t i o n . In the absence of a r i g i d l a t t i c e second moment, i t i s im- p o s s i b l e to o b t a i n a r e l i a b l e a c t i v a t i o n energy f o r the t r a n s i t i o n . One can of c o u r s e e s t i m a t e a reaso n a b l e value f o r the e x p e r i m e n t a l r i g i d l a t t i c e second moment a t 30 MHz ( a t which frequency the temperature dependence s t u d i e s were made) and e v e n t u a l l y a r r i v e a t an a c t i v a t i o n energy. T h i s was done and an energy of about 1 K c a l per mole o b t a i n e d . I t i s of course an even c r u d e r e s t i m a t e than one n o r m a l l y o b t a i n s from second moment studies,, The t r a n s i t i o n between 336 and 342°K i s too abrupt to g i v e a me a n i n g f u l a c t i v a t i o n energy. The value of the t o t a l second moment i s about 0.1 gauss which includes the co n t r i b u t i o n from r e l a t i v e s h i f t between the i o n s . D i f f u s i o n of the ions i s probably taking place through the s o l i d . Although the sample i s rather" p l a s t i c • looking at 373 K, i t remains s o l i d and does not melt even when hel d at that temperature for several hours. CHAPTER \l SUMMARY AMD DISCUSSION I t i s d i f f i c u l t to o b t a i n p r e c i s e r e s u l t s f o r the t h r e e compounds s t u d i e d . T h i s i s p a r t i c u l a r l y so w i t h 'wTg . The most pr o b a b l e r e s o l u - t i o n of t h a t compound i s i n t o two components separated by a mean i s o - t r o p i c s h i f t o f 105 ppm and each w i t h an average a n i s o t r o p i c s h i f t of 300 ppm. S i n c e no a c c u r a t e r e s o l u t i o n c o u l d be made, no v a l u e s were quoted f o r the zero f i e l d , d i p o l a r broadening of each. From the theo- r e t i c a l r i g i d l a t t i c e second moment, the c o n t r i b u t i o n s of the a x i a l and e q u a t o r i a l f l u o r i n e s to the t o t a l second moment f o r the molecule are 2 2 2.71 gauss and 5.44 gauss r e s p e c t i v e l y . Weighted a c c o r d i n g to the r e l a t i v e numbers of f l u o r i n e s i n v o l v e d i n each, they would g i v e 2 8.14 gauss f o r each component i f they c o u l d be r e s o l v e d out. These second moments are v i r t u a l l y i d e n t i c a l to the second moment of the observed z e r o f i e l d curve ( a c t u a l l y a t 2 MHz) which was used as a broadening f u n c t i o n (components weighted 4:2 by area) i n the attempted r e c o n s t r u c t i o n based on the s h i f t s mentioned, immediately above. I t was assumed t h a t the i n d i v i d u a l l i n e shapes would be s i m i l a r to t h a t of the t o t a l curve at zero f i e l d . The second moment, however, says n o t h i n g about l i n e shape. L i n e shapes are much more d i f f i c u l t to p r e d i c t than are second moments, which, of c o u r s e , i s the d i f f i c u l t y here. For the two AsF,. adducts r e s o l u t i o n i n t o components can be made and r e l a t i v e s h i f t s d etermined. However, even f o r IF* AsF. only D o average a n i s o t r o p i c s c o u l d be estimated f o r the two components. No r e l i a b l e v a l u e at a l l c o u l d be obtained f o r SF* AsF~ s i n c e a r i g i d - 80 - 81 l a t t i c e mas not found within the temperature range of the i n v e s t i g a t i o n . A l l three of the compounds showed a t r a n s i t i o n i n the second moment curve around 200°K from which a c t i v a t i o n energies of varying r e l i a b i l i t y were determined for the probable r e o r i e n t a t i o n s occurring. The type of r e o r i e n t a t i o n was deduced from the magnitude of the change i n the second moment of the t o t a l curve or resolved component,, "Table 11 summarizes what are considered to be the best values obtained here f o r the i s o t r o p i c and ani s o t r o p i c s h i f t s , second moments, t r a n s i t i o n temperatures, and possible r e o r i e n t a t i o n s i n the s o l i d s . A l l these have been discussed i n d e t a i l e a r l i e r . F i n a l l y , i t i s possible from the an i s o t r o p i c and mean i s o t r o p i c chemical s h i f t s to draw some conclusions about bond character i n the hexafluoride groups. For f l u o r i n e , the p r i n c i p a l c o n t r i b u t i o n to chemical s h i f t i s from the paramagnetic term i n equation (10) according to Saika and S l i c h t e r (70) and Karplus and Das (88). Following t h e i r treatment, Andrew ( 7 l ) has expressed the chemical s h i f t i n terms of l o c a l i z e d bond parameters I * / ^ 7 , and s which are re s p e c t i v e l y the i o n i c character, double bond character, and degree of sp h y b r i d i z a t i o n i n the bond o r b i t a l . Then for a f l u o r i n e atom bonded i n the z - d i r e c t i o n , the p r i n c i p a l values of the paramagnetic c o n t r i b u t i o n to the chemical s h i f t tensor are Table 11 Summary Compound or A B Group ppm ppm ^ 6 -300+40 e q u a t o r i a l F -435+40 ~300 a x i a l F -325+40 ~300 IF* AsF" o o -170+8 "I -245+20 ~333 AsF~ 6 -100+20 ~333 -155+15 -205+20 AsF~ o -105+20 SF* AsF" o o GAUSS D . GAUSS' Kcal/mole 8.25+0.2 1.0+0.05 180-210 10.0+0.4 I s o t r o p i c or near i s o t r o p i c » . . 1 8.14 1 10.7+0.2 2.1+0.2 205-235 19+4' 10.20 1 2-.0 10.44 1 0.7 1.9+0.1 <77-200 ~1 5.9+0.3 9.4l 4.7 2 7.9 1 2. 8 2 9.7l 1.1 0.9 342-373°K 336-342 Q.l Reorientation about one axis and simultaneous o s c i l l a t i o n about another. Is o t r o p i c or near i s o t r o p i c I s o t r o p i c or near i s o t r o p i c I s o t r o p i c D i f f u s i o n B. C. 0. £. F. G. lYlean i s o t r o p i c chemical s h i f t to nearest 5 ppm r e l a t i v e to HF. Anisotropy of Chemical s h i f t [S 11 Zero f i e l d second moment 77°K. Second moment at 295°K. T r a n s i t i o n temperature range. A c t i v a t i o n energy. Possible r e o r i e n t a t i o n above t r a n s i t i o n temperature. 1. Calculated for theo- r e t i c a l , r i g i d l a t t i c e . 2. Not a r i g i d l a t t i c e . - 83 The e x p r e s s i o n s a n d r e l a t e to ff -bonding i n the xz and yz planeso Such fT-bonds may be formed by the o v e r l a p of the f l u o r i n e p and p o r b i t a l s w i t h the d and d c e n t r a l atom o r b i t a l s 0 The K x K y xz yz chemical s h i f t i s expected to v a r y , a c c o r d i n g to the i o n i c c h a r a c t e r of the bond, from HF the most i o n i c down to F^ the most covalento Although h y b r i d i z a t i o n c o u l d have the same e f f e c t as i o n i c c h a r a c t e r , S a i k a and S l i c h t e r n e g l e c t e d i t because of the d i f f i c u l t y of making a n u m e r i c a l e s t i m a t e . Although Andrew has taken account of h y b r i d i - z a t i o n , we s h a l l f o l l o w S a i k a and S l i c h t e r and a l s o Rigny (39) i n i g n o r i n g it„ When h y b r i d i z a t i o n i s n e g l e c t e d , then, i n the case of a x i a l symmetry of the c h e m i c a l s h i f t : t e n s o r where 6 = . and & = ZZ IJ XX = ̂ ± » e q u a t i o n s (31) reduce t o e„-isc(y-/>z) <32) , 6 j . = f 6 o ( l - I ^ D where = / ^ y = a n d / ^ a n d 1 a r e as'above. From K a r p l u s and Das the c o e f f i c i e n t ^ q = -863 ppm. They p o i n t out, however, t h a t the exact value o f ^ q i s not i m p o r t a n t s i n c e i t does not a f f e c t the tre n d s c a l c u l a t e d and i t i s the t r e n d s , not the a c t u a l v a l u e s , which are of primary s i g n i f i c a n c e . The mean i s o t r o p i c c h e m i c a l s h i f t may be w r i t t e n S~-~Tr6 --^(S^ + Sy^ ̂ ^iz) . . . . . c o . . . (33) o r f o r a x i a l symmetry o f t h e s h i f t t e n s o r S:i(Z6J.+<5„) ( 3 4 ) I f § i s m e asured r e l a t i v e t o HF, t h e n t h e k n o w l e d g e o f (€5,, ~ Gx.) e n a b l e s i n d i v i d u a l v a l u e s o f 6 „ and ^ j , to 0 8 o b t a i n e d f o r s u b - s t i t u t i o n i n t o e q u a t i o n s ( 3 2 ) . O n l y a v e r a g e v a l u e s o f ( <3,, ( o L ) a r e a v a i l a b l e h e r e , but B l i n c ( 4 1 ) r e p o r t s v a l u e s o f 640+50 and 670+50 f o r U F & and 1300+100 and 1380+100 ppm f o r P t F f i f o r t h e a x i a l and e q u a t o r i a l c o mponents r e s p e c t i v e l y . I n o u r c a s e , t h e r e f o r e , t h e a v e r a g e a n i s o t r o p i e s a r e p r o b a b l y good a p p r o x i m a t i o n s t o t h e v a l u e s f o r t h e i n d i v i d u a l c o m p o n e n t s 0 V a l u e s o f ^ and I f o r t h e h e x a - f l u o r i d e g r o u p s s t u d i e d h e r e and a l s o f o r UF a r e p l o t t e d i n F i g u r e 27 as a f u n c t i o n o f mean i s o t r o p i c s h i f t w i t h r e s p e c t t o HF. From F i g u r e 2 7 , v a l u e s of ^ = ^ 0.01 and I = ~ 0.8 can be e s t i m a t e d f o r t h e 5-F bond i n SF* . However, K a r p l u s and Das c a u t i o n t h a t s u c h p l o t s be c o n s i d e r e d o n l y as a p p l y i n g t o g r o u p s o f s i m i l a r compounds. F i g u r e 27 w i l l be t a k e n o n l y as h o l d i n g f o r h e x a f l u o r i d e g r o u p s . I n d e e d e v e n t h e v a l u e o f f o r t h e UF^ a x i a l component de- v i a t e s w i d e l y from t h e p l o t a l t h o u g h t h s v a l u e f o r I i s i n good a g r e e ment. A l s o n e i t h e r a x i a l n o r e q u a t o r i a l component o f P t F ^ can be f i t t e d t o t h e p l o t . B o t h c o mponents l i e f a r o u t s i d e t h e r a n g e o f s h i f t s f ound h e r e and g i v e m e a n i n g l e s s v a l u e s o f and I . However, a l t h o u g h B l i n c ( 4 1 ) was u n a b l e t o d e t e r m i n e t h e a n i s t r o p i e s o f t h e components i n PuF^ , he was a b l e t o e s t i m a t e mean i s o t r o p i c c h e m i c a l To F o l l o w Page 84 O - 2 0 0 - 4 0 0 - 6 0 0 - 8 0 0 -IOOO - 1 2 0 0 M E A N I S O T R O P I C S H I F T P P M 8 5 s h i f t s of -440 and -1070 ppm r e l a t i v e to HF f o r the a x i a l and equa- t o r i a l components r e s p e c t i v e l y . These s h i f t s do l i e w i t h i n the range of s h i f t s i n F i g u r e 27. From the f i g u r e we can p r e d i c t 0.1, I = 0.6 f o r the a x i a l f l u o r i n e bonds a n d ^ ^ = 0.38, I = 0.03 f o r the e q u a t o r i a l bonds. APPENDIX I COMPUTER PROGRAMS A H the programs i n t h i s appendix have been w r i t t e n i n or adapted t o F o r t r a n IV as compatible w i t h the U n i v e r s i t y of B r i t i s h Columbia's IBM 7040 (now t e m p o r a r i l y 7044) computer. Some of the programs have been t i d i e d up s l i g h t l y from the form i n which they were used. However t h i s merely i n v o l v e d changing n o t a t i o n t h a t might have been c o n f u s i n g . Some q u a n t i t i e s which r e a l l y could be i n p u t as data s t i l l appear i n s t e a d i n the programs themselves. These are o b v i o u s , however, and can e a s i l y be changed by any one w i s h i n g to adapt the programs f o r h i s own use. 86 - 87 Program 1. C a l c u l a t i o n of E x p e r i m e n t a l Second moments from D e r i v a t i v e Curves. T h i s program i s f o r the g e n e r a l case of an asymmetric d e r i - v a t i v e c u r v e . For an asymmetric curve the second moment i s 2 Sffl = S - (Fiil) . SM i s the second moment about the c e n t r o i d of the c u r v e , S i s the second moment computed about any p o i n t (taken a t the e s t i m a t e d c e n t r o i d to minimize e r r o r ) , and F!K1 i s the f i r s t moment computed about the same p o i n t . For the d e r i v a t i v e curve the second moment i s 3 sxy U £ » y > ——- where s c a l e = gauss per d i v i s i o n . The l a s t term i n the equ a t i o n f o r Sf(l i s Andrew's (89) c o r r e c t i o n f o r modulation broadening, i s o n e - h a l f the peak to peak m o d u l a t i o n . In the measurement of the e x p e r i m e n t a l c u r v e s , the x - a x i s of the spectrum i s d i v i d e d i n t o c o n v e n i e n t , e q u a l d i v i s i o n s , f o r which a c a l i b r a t i o n has been d e t e r - mined, and the c o r r e s p o n d i n g y v a l u e s measured i n a r b i t r a r y u n i t s 0 The y v a l u e s a r e w r i t t e n d i r e c t l y on computer data sheets and the remainder o f the d e t e r m i n a t i o n of the second moment i s c a r r i e d out by the computer. N : the i d e n t i f i c a t i o n number of the d e r i v a t i v e curve or TRACE N l = t o t a l number of data p o i n t s on t r a c e N N2 = t o t a l number of data p o i n t s on the f i r s t h a l f of i n c l u d i n g the c r o s s - e v e r p o i n t i n the middle. the curve SCALE : = gauss per d i v i s i o n PfflOD : : A Km = \ peak to peak "modulation TEMP : : temperature i n degrees I Y r y a m p l i t u d e i n a r b i t r a r y u n i t s f o r each of the Ml d i v i s i ons equal sm, s, and Ffil are as d e s c r i b e d above. 88 I t i s i m m a t e r i a l a t which end of the spectrum measurement i s com- menced. However to a v o i d c o n f u s i o n as to f i e l d d i r e c t i o n i n Program 2 , i f i n t e g r a t i n g d e r i v a t i v e s which are o n l y s l i g h t l y asy- mmetric, i t i s recommended t h a t a c o n s i s t e n t p o l i c y be f o l l o w e d . S t a r t always a t the low f i e l d end and choose the s i g n of IY p o s i - t i v e i n t h a t h a l f of the spectrum. s • I; i " S F O R T R A N " " • ./.i C E X P E R I M E N T A L S E C O N D M O M E N T j. .. D . I M E N S J . 0 N I.Yi..2 0 J D . J . . » C..L9,.,) . _ _ __ '. 1 F O R M A T ( J. 9 I 4 , X 5 2 F O R M A T ( 3 I 4 , F 7 . 4 > F 6 . 2 > F 5 . 0 » 3 A 6 ) 3 _ F CRM AT J IX » 5 H J R _ A C E , 4 X » 1 H T > 5 X »J_HS »_1 OA? 2 H£M »1 OX»?HSM) ""'" W R I T E ' " ' ( " 6 7 3 7 """ "" "" 4 F O R M A T ( I X , I 5 » F 6 . 1 » F 9 . 2 > . 1 X , F 8 . 2 » 5 X , F 6 . 2 » 5X , 8 A 6 ) 5 ,. R E A D . ( 5 » 2 . ) N.» HI »N2 > SCAL E » PMOD » TEMP »(C( I ) » I = 1» 8 ) „ _ " 6 R E A D ( 5 » 1 ) ( I Y {' I ) , I = l 7 N l ) K F M = 0 ! . _ . _ _ ^ D O 1 0 J = 1 » N 1 I = J - N 2 _ . < = I * I I Y ( J } ~ K F M = K + K F M I S = K * I + I S _ _ _ T o ~ I A = ~ I A + " f * I YTJ ) S U M = I S _ A . = I A .;_ _ _.. ; _ ' F M =",< F M ' " F M = . 5 * F M * S C A L E / A _ S = S C A L E * S C A L E * S U M _ / ( A * 3 . ) _ '_ _ _ ~ S M = S - F M * " ' F N r - 7 ' 2 _ 5 * P M W R I T E ( 6 » 4 ) N » T E M P » S » F M » S M » ( C ( I ) » 1 = 1 > 8 ) G O T O 5 _ _____ • _ _ ' ___' . _ E N D - " ~ ~ - - — - —-- • S E N T R Y 90 Program 2. I n t e g r a t i o n of D e r i v a t i v e Curves to A b s o r p t i o n Curves. This program i n t e g r a t e s the d e r i v a t i v e curves to a b s o r p t i o n s p e c t r a u s i n g the data punched f o r the second moment c a l c u l a t i o n s . The i n t e g r a t i o n i s performed u s i n g r e c t a n g u l a r s t r i p s which,when s m a l l enough^are s u f f i c i e n t l y a c c u r a t e f o r broad l i n e nmr. NWBR = i d e n t i f i c a t i o n number of d e r i v a t i v e curve N = t o t a l number of data p o i n t s SCALE = gauss per d i v i s i o n (on the d e r i v a t i v e c u r v e ) IY = y amplitudes of the N p o i n t s on the d e r i v a t i v e curve In the body of the program the G ( l ) ' s are the amplitudes of the a b s o r p t i o n curve a t p o i n t s separated one from another by the d i s - tance SCALE. BL i s a c o r r e c t i o n parameter a p p l i e d to G ( l ) to en- sure t h a t G ( l ) approaches zero a t both l i m i t s of the i n t e g r a t i o n . Z, the DEVIATION, g i v e s an es t i m a t e of the accuracy of the i n t e g r a - t i o n . I t i s expressed as a percentage i n terms of G(N) and X the maximum amplitude of the a b s o r p t i o n c u r v e . FNORfil n o r m a l i z e s the s p e c t r a to c o n s t a n t a r b i t r a r y area f o r comparison w i t h each o t h e r . The punch i n s t r u c t i o n produces data f o r use i n Program 2 . This l a s t program outputs the data from Program 2 on an X-Y p l o t t e r . The program was w r i t t e n to g i v e a c o n s t a n t x - s c a l e to a l l the absor- p t i o n curves so t h a t comparison c o u l d be made d i r e c t l y between the a r e a - n o r m a l i z e d c u r v e s . S i n c e the program c a l l s s p e c i a l r o u t i n e s which were w r i t t e n e x p r e s s l y f o r the computer here by the computing • c e n t e r s t a f f , i t cannot be used elsewhere. 2 0 1 $ FORT RAN C INTEGRATION OF DERIVATIVE CURVE DIME N S J O N G ( 1 0 0 ) » T I T L E ( 9 ) > I Y ( 1 0 0 ) " READ( 5 > 1 ) NMBR J N « SCALE > (~TITLE( I ) » I = 1 »9 F0RMAT(A4»I<+»4X»F7o4*6X»9A6) READ ( 5 * 2 ) ( I Y ( I ) »_ I = 1 »N ) FORMAT!19 14> 4 X ) H = 0. Dp 10.: = .:..». N H = H +FLOAT( I Y( I ) ) G ( I ) = H * S C A L E . ._Z = G..(. NJ : WR I 10 2 9 3 0 100 1 1 0 40 ' E ( 6 » 1 2 ) N M B R » ( T I T L E ( I ) , I BL = G ( N ) / F L O A T ( N ) DO„.2_9. _ _ I _ 1 »N_ G ( I ) X = 0 Y = 0 DO'" ' 1.9) = G ( I ) - F L O A T ( I ) # B L o I -vO- 3 0 I = 1 , N I F ( G ( I ! .GT.X)X = I F ( Y . G T . G f I ) ) Y = "CONTINUE I F ( X. LT . ( -Y ) ) X = Z=Z*100./x "AREA = O'C DO 1 0 0 1=1,M AREA = A R E A + G ( I ) G ( I ) G { I.!. Y •SCALE 1 1 ~ i 2 S E N T R Y F N O R M = 1 0 0 0 . / A R E A DO 1 1 0 1=1,N G ( I ) =G (_I Hi-FNORM ^ " W R I T E ; 6 » 4 0 ) A R ' E A V Z F O R M A T ( 7 0 X > 5 H A R E A = , F 1 0 . 1 » 5 X * 1 0 H D E V I A T I O N = » F 1 0 . 4 ) W R I T E ( 6 . 1 1 ) ( G ( I ) » I_= 1_» N J '"PUNCH1 > NMBR >N > S C A L E * PUNCH 11 * ( G ( I ) » I = 1 » N ) FORMAT ( 1 0 F 8 . 2 ) _ ~FbRiMATr'3X\T4TrOX 79 K&) ~ " ~ " GO TO 20 END L a $ IB F T C '• C REMEMBER L A S T S P E C , N , S C A L E CARD MUST BE BLANK. TO C A L L P L O T N D D I M E N S I O N X ( 1 0 0 ) » Y ( 1 0 0 ) 1 2 C A L L P L O T S R E A D ( 5 , 2 ) S P E C , N , S C A L E FORMAT ( F 4 . 0 , I 4 , 4 X , F 7 . 4 ) • • 3 4 I F ( N . L E . O ) GO TO 100 R E A D ( 5 , 4 ) < Y ( I ) , I = 1 , N ) FORMAT ( 1 0 F 8 . 2 ) •- — 10 D E E X = S C A L E / 2 . 5 4 D E E Y = 0 . 0 3 S = F L O A T ( N - l > * D E E X DO 10 I = 1 , N X( I ) = F L O A T ( I ) * D E E X DO 11 I = 1 • N o CP5 vO 11 Y ( I ) =Y ( I ) *DEEY . IF ( Y ( I ) . L T . (-0 .25. ) ) Y ( I ) = ( - 0 . 2 5 ) C A L L NUMBER' ( 5 . , 8 . , 0 . 14 , S P E C , 0 . , - 1 ) 4 ro 1 ^ ' 12 DO 12 I = 1 , N C A L L SYMBOL (X ( I ) , Y ( I ) , 0 . 1 4 , 3 , 0 . , - I ) C A L L P L O T ( ( S + 2 . ) , 0 . , - 3 ) 1 0 0 GO TO 1 C A L L P L O T N D S T O P S E N T R Y END - 93 Program 3. L i n e Shape F u n c t i o n F(H). Thi s program s y n t h e s i z e s a curve F(H) u s i n g e x p e r i m e n t a l l y determined values of - ^ ) a r | d the zero f i e l d d i p o l a r second moment. I t i s w r i t t e n f o r the case of e q u i v a l e n t n u c l e i e x h i b i t i n g a x i a l symmetry of t h e i r s h i f t t e n s o r s . I f n o n - e q u i v a l e n t n u c l e i are p r e s e n t , two or more s y n t h e s i z e d curves a p p r o p r i a t e l y s h i f t e d r e l a t i v e to each o t h e r may be u s e d 0 F(H) i s given by equ a t i o n (21), S i n c e the c e n t r o i d of the s y n t h e s i z e d curve w i l l be superimposed on t h a t of the e x p e r i m e n t a l curve, H w i l l be i d e n t i c a l i n each case and may be chosen equal to zero f o r the program. T h e r e f o r e F(H) = f(H0)S(H-H0)DH0 (A) where f (HO) * ( I HO V I ALPHA J (Q) and the c o n s t a n t i n equation (B) i s omitted s i n c e the f u n c t i o n F(H) w i l l i t s e l f be n o r m a l i z e d i n the program. Two programs, 3a and 3b, are given below. For 3a the e x p e r i - mental l i n e shape at 2 MHz has been used as the broadening f u n c t i o n S(H-HO) and f o r 3b the broadening f u n c t i o n i s a gaussian f u n c t i o n having the same second moment as the e x t r a p o l a t e d zero " f i e l d second moment. The former mas used w i t h UiF_ and the l a t t e r w i t h IF* AsF 6 6 D Program 3a. ALPHA = the "a" d e f i n e d under e q u a t i o n (16) SCALE = s e p a r a t i o n i n . g a u s s between the data p o i n t s on the e x p e r i m e n t a l broadening f u n c t i o n ( e b f . ) . 94 Program 3a Contd. NY = the number of data p o i n t s ^ i n c l u d i n g the centroid_, on the l e f t h a l f of ebf. Nffl = t o t a l number of data p o i n t s on e b f . Y ( l ) = an am p l i t u d e on ebf. H and DHO = (where DHO = dHo) are as d e f i n e d under e q u a t i o n ( 2 1 ) . AlflP = the maximum a m p l i t u d e of the e x p e r i m e n t a l c u r v e . I f the curve c o n s i s t s o f two or more components, the s y n t h e s i z e d curve must be n o r m a l i z e d to the a r e a , not the h e i g h t of the e x p e r i m e n t a l curve. Program 3b. ALPHA i s as f o r 3a. BETA i s the square r o o t of the e x t r a p o l a t e d z e r o f i e l d d i p o l a r r i g i d l a t t i c e second moment. H, DHO, and Amp are as f o r 3a. Both programs output values of F(H) - l a b e l l e d F(K) here - f o r val u e s of H - l a b e l l e d C(K) here. Note that i n the a c t u a l programs SH(H-HO) i s w r i t t e n as SH(HO). SIBFTC C 3 4 10 11 20 21 22 ANISOTROPIC FUNCTION WITH EXPERIMENTAL ..D.I M..ENSJ..ON.JF_(...00.)_*_G_(_1 0_0_L?. .Y...L]._00.)._.. COMMON A LPHA» SCA LE .NY ,NM »Y,H,DHO READ (5».l) NM FORMAT...! 4X ,.I_3 ) "RE A D < 5 . 2 ) " (Y il") . T = 1 »~NM ) FORMAT (10F8.1) _WR I T E j_6L>_2_..) ! Y_(_I_)__»_I = 1 ._NMJ. READ (5.4) ALPHA .SCALE .NY.AMP FORMAT (4X .2F12.4 .4X . I3 .4X .F12 .4 ) .WRITE. (.6... 4 ) + L.PH A...S.C AJ=.E iNY_ t AM.E H=-20. DH=0.5 DHO=0.1 __ DC 11 K=T»80 F(K ) =0. H = H + D H ' GTK )' = H ~ ' " ~ ™ " " ~ HO=-ALPHA+0.01 IF(H.GT.2 0.) GO TO_3_ "bo1 o" L = 1 .?000* HO=HO+DHO IF(HO.GT.(2.ALPHA)) GO TO 'F ( K )"=F (;< ) +F'HVH'OT^SHI H'O'T FMAX=0. DO 2 0 N= 1.8 0 _ IF(FMAX.LT CONTINUE FMAX=AMP/FMAX D C 2 1 N = T , ' 8 0 F ( N ) = F ( N ) *FM + X WR I TE. ( 6 , 22 ) ( G ( K) "FORMAT"" ( 1X Y 2 F 12". 4 ) GO TO 3 END BROADENING FUNCTION 1 1 ( N ) ) F M A X = F ( N ) Ti F ( K ) » K=l» 80 ) o n . . . ^ .. _ v O . S I B F T C F H F U N C T I O N F H ( H O ) C ,OMMQN.._. A L P H A... S C A. L £ A . N . X ...N. K.» Y.vrd..»±LO__ D I M E N S I O N Y ( 0 0 ) F H = 1 . + H O . / A L P H A • FH_= 1 . Z.SQ..R IIFH..) R E T U R N E N D S 1 3 F 7 C S H . . _ F U N C T I O N S H ( H O ) ' C O M M O N A L P H A » S C A L E » N Y , N M » Y , H , D H O _ D I M E N S I O N Y ( I 'OO ) _ F E J = F L O A T ( N Y ) + ( H - H O ) / S C A L E J = F E J I ' F ( U . L E . O ) G O T O 1 1 0 I F ( J . G E . N M ) G O T O 1 1 0 B E L O W = Y ( J ) A 3 0 V E = Y ( J + l ) _ FT N K = ( A B O V E - B ' E L O W ) * ( F E J - F L O A T ( J ) G O T O 1 1 1 i io_ SH = O. ; . G O T 0 1 1 2 1 1 1 SH=BELOW+FINK 112 _ „ C 0 N T I NU .E R E T U R N E N D , ; 0 - SFORTRAN C ANISOTROPIC FUNCTION WITH GAUSSIAN BROADENING FUNCTION PJ.MF.NS„lp̂ N_..XL.lO..Q.i.»Gixĝ .L Oi 1! 1 2 COMMON ALPHA,BETA,H READ (5,2) ALPHA, BET A,AMP FORMAT ( 1 X , 3 F 1 2 . 4 ) "WRYTY'T6\'2)TCPHATBITA - - - - - -- - - SETA=1./(2.*BETA*BETA) H = -20.. _ DH = 0.5 DHO=0.1 ...DO ..1.1 <=..: ,3 0. ___ .._ ' F(K) = 6. H=H+DH ^ ._G.(.K..)..=.H _ _ _ _ . cq HO=-ALPHA+0.oi 3 I F (H .GT.20.) GO TO 1 • '2 ...DO 10 :J-1 ,2 000 ... . _ _ HO=HO+D'HO ' " ° " I F (HO .GT . (2 . *ALPHA ) ) GO TO 11 10 F ( K ) = F ' ( K ) + F H (_HO ) * S H i H O ) _ I I ~ F M A X " = 6 " . " " " " """"""" D O 2 0 N= 1,8 0 I F ( F M A X . L T . F ( N ) ) F M A X = F ( N ) 2 0 C O N ' f l N U E , F M A X = A M P / F M A X _ . . D O 2.1... NL=1 .'.8 0 2 1 22 F ( N ) =F ( N ) -»FMAX WRITE (6, 2 2 ) (G(K)»F(K)»K=1»80) FORMAT ( 1 X , 2 F 1 2 . 4 ) G O T O 1 END $ FORT RAN FUNCTION FH(HO) COMMON A L P H A , B E T A , H F H =1 , + H O / A L P H A F H=1„ / S O R T ( F H ) ..REIURN.._ END SFORTRAN . F U N C I J 0_N._.SH.(.HOJ...._.._ COMMON A L P H A , B E T A , H 5 H = E X P ( - ( H - H O ) * ( H - H O .RETURN END SENTRY 3 99 Program A. Doublet F i t . This program i s from Dr. P. Raghunathan of t h i s Department and i s based on Abragam (52, p. 220). ALPHA and BETA are r e l a t e d by SiTl = ~ oL2 +/S * where Sffl i s the second moment of the e x p e r i m e n t a l curve and oC = ^ y t v t - " 3 where r i s the es t i m a t e d d o u b l e t s p l i t t i n g . H i s a g a i n a g e n e r a l f i e l d parameter. X i s the HO of Program 3 and Abragam (52, p.220). The program puts out a m p l i t u d e s , 5Urn", f o r v a l u e s , H. These i n the e x i s t i n g program (which was w r i t t e n f o r a s i n g l e use and never put i n t o " p o l i s h e d " form) are s c a l e d by hand to the amplitude o f the e x p e r i m e n t a l curve f o r comparison of l i n e shapes. D i f f e r e n t v alues of r are t r i e d u n t i l a f i t i s o b t a i n e d . $ I Br r TC 2 1 22 10 90 91 DOUBLET FIT DIMENSION C< 14) COMMON ALPHA,BETA,X READ( 5,22>.<C( I ) » 1 = 1 FORMAT(IX , 1 3A 6 , A l ) 14 ) 01 Tl v, A W'RITE(6»22)(C(I)»I = 1»14) PRINT 10 _F0RM AT (J X . 34HD0UBL ET_L IjN ESHAP E READ(5,1) ALPHA,BETA DX= 0o0125 .X = 2_,.JtALPHA H = 0. DO 100 1=1,1000 H= H+(40.*DX) FIT ABRAGAM P219) IF (H.EQ.ALPHA) H=(40.*DX SUM = 0. D. /- .-.3... * .ALPHA . DO 90 J= 1 ,4000 H " o " D = D + IF(D.GT f = H-D I F ( D . L T I F(D.GT DX . ( 3 *A LP HA) ) GO TO 91 (-ALPHA))P = FH(D) .ALPHA)P=FO(D) _ I F( ABS ( D ) . LT . ALPHA )_P = FL ( D) SUM = P*SH(T)*DX+SUM CONTINUE. ___ . WRITE(6,2) H, SUM 1 FORMAT(2F12.8) 2 FORMAT ( 1X»2HH=»F12_.8»10X,5HF I F ( h.GT . (3 . * 3 E Y A ) ) "GOT5To'l" 100 CONTINUE 101 CONTINUE _ _ GC T O 2 1 " " ' " " END »F13.4 ) S I B F T C FHD FUNC ' COMM I F ( D IF ( D RELY. END SIB F T C SHT FUNC COMM SH = RETU END SIBFTC FLD FUNC COMM A= D F L = RETU END SIBFTC FQD FUNC COMM I F ( D I F ( D RETU EN_D_ SENTRY" TION FH(D) QN ALPHA,3ETA,X . LT.X )'FH = 0. . GT .X ) FH= ( -D/ALPHA+i . ) *>• RN -0.5) TI.ON_.SHJ_T )._ ON ALPHA,BETA,X EX P ( - T * T * 0 . 5 / ( B E T A * B E T A ) ) / (BETA*2.505) RN T I ON F L ( D ) ON ALPHA,BETA,X /ALPHA (-A+l. ) * * ( - 0 . 5 RN -(-? + ( A+l . ) ------ ( -0 , TION FQ(D) ON ALPHA,BETA,X .GT.X)FQ=0. .LT.X)FQ •= (6+1. RN **'( -0 . 5 - 102 - 103 Program .5 0 T r a n s f o r m a t i o n of Coordinates,, T h i s program g e n e r a t e s bl o c k s of u n i t c e l l s around a c e l l [ l a b e l l e d (0, 0, 0 ) ] from which i t i s d e s i r e d to compute i n t e r - a c t i o n s . I t g i v e s the c o o r d i n a t e s of a l l n u c l e i w i t h i n the c e l l s . A I , BI, d l i s the d e s i g n a t i o n of the c e l l from which the program s t a r t s (not 0, 0, 0. S t a r t i n g from 0, 0, 0 would give the c e l l s i n o n l y one h a l f o f the b l o c k ) . Am, Bm, CfH i s the d e s i g n a t i o n of the c e l l at which the program f i n i s h e s . XA, YB, zc are the u n i t c e l l dimensions i n angstroms. XI, YI, ZI are the atomic c o o r d i n a t e s of the n u c l e i i n the u n i t c e l l . NUC l a b e l s the u n i t c e l l n u c l e i i f d e s i r e d . The punched o u t p u t X, Y, Z ( t h e A, B, C,and NUC are merely l a b e l l - i n g ) i s used i n Program 6 f o r the t h e o r e t i c a l second moment c a l c u - l a t i o n . SFORTRAN C RECTANGULAR COORDINATES _ 1. EPR.MAI.J.6.F5....0..) 3 FORMAT(3F8.4) • 4 FORMAT(3F10.4,A6) 7 FOR.MAXi.lH0J _ 50 .FORMAT(5X»3F8.4,5X,3F5.0»A6) R E AD ( 5 »1) A I ,BI ,CI ,AM,BM,CM : W R I T E ( 6 , 1 ) A I , 3 I , C I ,A M , B M , Cft READ(5,3) XA,Y3 , Z C WRITE(6,3) XA , Y B , Z C __8 _ R E AD ( 5 _X l_» Y I , Z I >_NUC WRITE(6»4> XI ,YI , Z I ,NUC A = AI B = BI _. C = C I GO TO 100 10_ CONTINUE. C=C+1. IF(C.GT.CM) GO TO 11 GO....TO ICC , 11 CONTINUE C = CI 3=3+1. IF(B.GT.BM) GO TO 12 •. GO TO 100 12 CONTINUE C = CI B = BI A = A+1. •v I F ( A. GT . AM ) GO . TO 101 . 100 CONTINUE X=(XI+A)*XA " "Y =TY" I"+BY*"Y'B" Z=(ZI+C)*ZC WRITE (6,50) X»Y_,Z_,A»_B»_Cj_NUC ""'PUNCH'""50 ,X", Y ,Z , A , 3 , C V N U C GO TO 10 101 • CONTINUE WR I"T"E""("6','7'T GO TO 8 END 105 - Program 6. T h e o r e t i c a l R i g i d L a t t i c e 5econd Moment C a l c u l a t i o n T h i s program computes the t h e o r e t i c a l r i g i d l a t t i c e second moment u s i n g the n u c l e a r c o o r d i n a t e s ( i n angstroms) generated by Program 5. I t was adapted from UJ.R. Danzen's o r i g i n a l program w r i t t e n f o r the IBM 1620. LS RMAX FACT NN=DEN NVAN NMB N I , NM 3 1 , 3M K I , KM X ( I ) , SM = 1, 2. 1 i n s t r u c t s the computer to read i n a new s e t of data cards and do c a l c u l a t i o n s . 2 i n s t r u c t s i t to do f u r t h e r c a l c u l a t i o n s w i t h the d a t a . up to which the sum i s c a r r i e d . angs troms between n u c l e i UJaals r a d i u s . s e p a r a t e d by = d i s t a n c e i n = the f a c t o r i n e q uation (2) as i s a p p l i c a b l e . = N as i n e q u a t i o n ( 2 ) . = count of i n t e r a c t i o n s l e s s than the van der = the count of i n t e r a c t i o n s w i t h i n the d i s t a n c e RMAX. i s l i s t of data cards read i n . i s the l i s t of parameters j i n r j k i n e q u a t i o n ( 2 ) . i s the l i s t of parameters k i n r j k i n e q u a t i o n ( 2 ) . Y ( l ) , Z ( l ) are the n u c l e a r c o o r d i n a t e s i n angstroms generated by Program 5. = t h e o r e t i c a l r i g i d l a t t i c e second moment. _ _ _ _• _ _ _ __ b S I B F T C 9 C THEORETICAL SECOND. MOMENT <• ...C _ _ _ _ : 8 DIMENS I ONX(2 00 0) »Y(2000 ) ,Z ( ? 0 0 0) »A(?0 00) ,8(2 0 00) ,C(20 00) ,NUC(2 000) 5 55. FORMAT(1H1,7X»26HTHEORETICAL SECOND MOMEMTS»22X»14HPR06 4 WRJ MRB) 0! .7 4_ F..ORMAT.U_2....FJ_..0̂ ^̂  J . _ i'l" 7 5 FORMAT { I 5 , I 5 , r 1 1. 8 ) Z\ 88 FORMAT (5X , 3F8.4»5X , 3F5.0 • A6 ) r 9 9 FORMAT ( 10H0THEO SM = • F 6 . 2 » 8 X • I 5 »_i 4 H R_ LESS _T H FJ41_,_2 H. ... AJ ._. ... j. 1 0 0 F O R M A T ( 1H0") 101 FORMAT(24X,I5»21H R LESS THAN 2.70 A///) _104 F0'RMAT__(_5X »Jj_l._0i.4ji W R I T E ! 6 » 5 5 ! WRITE(6>100) 8 0 RE A D. ( 5..» 7±) LS , RMAX > FAC T , NN » N I »NM»JI ,JM»KI »KM ; „ RMS = RMAX*RMAX . i DEN = NN A = o ; : o~~ NVAN=0 O NMB = 0 SUMR = 0 . 0 » WRITE (6, 7 4 ) LS,RMAX»FACT»NN»NI » N M» J I »JM»KI»KM GO TO i 1 ,2 ) ,L'S 1 DO 10 I = Nl,NM 10 READ(5,88) X ( I ) , Y ( I ) , 2 ( I ) , A ( I ) , 8 ( I ) , C ( I ) , N U C ( I ) 2 DO 30 J = J I , J M D 0.._ 3 0....K ..=_..K.I.»!<M I F ( K . E Q . J ) GO TO 30 15 DZ = ABS( Z ( K ) - Z ( J ) ) IF(DZ.GE.RMAX) GO TO 3 0 16 DY = ABS( Y(K.) - Y ( J ) ) IF(DY.GE.RMAX) GO TO 30 17 DX = ABS ( X ( K. > - X ( J ) ) ii. IF(DX.GE.RMAX) GO TO 30 10 18 RS = DX*DX + DY-^DY + DZ*DZ 9 _ _ I F ( RS.GE.RMS )_G0 TO_ 30 ____ a TFTRSVGEY772 9 ) """GO TO 4 0 / NVAN=NVAN+1 5 40 CONTINUE s 20 SUMR = SUMR + . 1./{RS*RS*RS) NMB = NM3 + 1 3 30 CONTINUE X < CC cr co 5 : s: z 3 Z < 1 0 •> > * s: z — CO z ~ UJ —• r-H Q. 0> O \ o> •—i 1— * U vO <a; — — U_ L U U J — H- I— 11 I-H >-> cr. ex. o CO o \— o o z 108 Program 7. A c t i v a t i o n E n e r g i e s . T h i s program i s Smith's (79) program f o r the c a l c u l a t i o n of a c t i v a t i o n e n e r g i e s from l i n e widths i n nmr t r a n s i t i o n r e g i o n s . I t i s l i s t e d here as adapted f o r the IBM 7040 by Dr. Raghunathan. I t i s , as noted, w r i t t e n f o r l i n e widths as i n e q u a t i o n (7.). How- ever i t can be used w i t h o u t m o d i f i c a t i o n f o r second moments as i n l 2 e q u a t i o n (8) p r o v i d e d (Sffl) 2 and SM are used i n s t e a d of /\H and /̂ H S I B F T C M O D B P P C I F ' Y O U D O A L L T H E S E C A L C U L A T I O N S B Y H A N D A N D P L O T T H E M I T 1 5 E A S I E R T O C _ S E E _ W H A T I S G O I N G O N . _ _ _ _ C M O D I F I E D B P P L I N E N A R R O W I N G A N A L Y S I S C D I F F E R S F R O M O R I G I N A L C A S E B Y I N C L U S I O N O F T E R M A G I N N U M E R A T O R O F C B P P _ E Q N _ P H Y _ S _ R E V _ 1 9 4 S _ _ V O L _ 7 3 P 6 _ 7 _ ? . F O R P R O T O N S A G = 7 6 7 . 5 _ 7 T H I S P R O G R A M U S E S T H E M O D I F I E D B P P E O N T O D E R I V E T H E C O R R E L A T I O N C - F R E Q U E N C Y , M A K E S A L E A S T S Q U A R E S F I T O F L N ( C O R . F R . Q ) T O A S T . L I N E C W H E N P L O T T E D V S . l / R T , D E R I V E S T H E _ A C T I V A I . I O N . E N E R G Y A N D _ _ I _ N F « T E M P . _ _ " C C O R R E L . F R E Q . F T O M T H E F I T . P R O G R A M T H E N R E V E R S E S T H E P R O C E S S T O G I V E C T H E O R E T I C A L F I T T O T H E L I N E W I D T H V S . T E M P . D A T A P L O T . ' -C _ _' _ . _ . D E . F I N IT I O N S - I N P U T _ _ - C • C A L P H A = D A T A C O M M E N T S E . G . NAME OF C O M P O U N D » D A T E . C ' T E M P . I N D E G . K E L V I N . , D E L T A H = L I N E W I D T H ( G A U S S ) I N N A R R O W I N G R E G I 0 5 C ( L E S S T H A N C > G R E A T E R T H A N B ) . C = A V G . L I N E W I D T H B E L O W T R A N S I T I O N . _____ 7"~~"'B"= AVGTL iTEwYbY77"_7v7TRAN'STTTONVAG="PARA'METER'""DE PEN DENT ON 'NUCLR " " ~ "• C S P E C I E S > = 7 6 7 . 6 F O R H . D E L M I N = M I N L I N E W I D T H I N R E G I O N O F T H E O R E T I C C F I T , G R E A T E R JHAN B . D E L M A X ~ M A X L I N E W I D T H __ I N _ R E G I O N O F _ _ T H E O R E T I C F I T , C L E S S T H A N 7 7 " " D 7 7 T 7 C = " T 7 N E W I D T H I N C R E M E N T F O R " T H E O R Y F I T . N = N O . O F vD C D A T A P O I N T S . . . . C C A L C U L A T E D . . Q U M L T J J J A f c . . . . P l ^ _.. . _ _ C C 0 R F R Q = D E R I V E D C O R R E L . F R E 0 . R E C I P T = 1 / T E M P . X L N F R G = L N O F C O R F R Q . C R C P R T = 1 / ( R - T E M P ) , W H E R E R= 1 . 9 8 6 9 C A L / D E G - M O L E . C _ E A C T = A C T I V A T I O N _ E N E R G Y ( C _ A L / M O L E ) , E R E A C T = E R R O R I N S A M E • F R Q M A X = ' c " T N F ;" T Y r ;jp;" "cb R'RTL . F R E ' Q T f isr'TH FOR F T 7 7 E R" F R O =Tf S E R R OR 7f H b E L = L IN E - " " " " " " ~ " C W I D T H I N T H E O R . F I T . T H T E M P = T E M P . I N T H E O R . F I T . T H F R Q = C O R R E L . F R E O C I N T H E O R . F I T . _ . D I M E N S ' I O ' N T E M P ( 5 0 0 ) , D E L f A H ( 5 0 0 ) , C O R F R Q ( 5 0 0 ) , R E C I P T ( 5 0 0 ) , 1 X L N F R Q ( 5 0 0 > , X S I N ( 5 0 0 ) , X C O S ( 5 0 0 ) » X T A N ( 5 0 0 ) , R C P R T ( 5 0 0 ) , A L P H A ( 1 2 ) , 2 T H F R Q ( 5 0 0 ) » T H T E M PJ_ 5 0 0 J , T H D E L [ 500) , THS_iNjj500_) , T H C O J 5 0 0 J , T ' H T A N ( 5 0 0 ) ^ '" '"PRINTlb 1 0 F O R M A T ( I X , A - 9 H N M R L I N E W I D T H . D A T A T R E A T E D A C C O R D I N G T O G . W . S M I T H ) 1 5 R E A D . ( 5 * 2 0 ) ( A . L P H A ( I ) , 1 = 1 , 1 2 ) T ' O " ' " " F O R M A T " ( " l " 2 A 6 " ) " " " " " " " " " " ~ " W R I T E •( 6 , 3 0 ) ( A L P H A ( I ) , I = 1 , 1 2 ) 3 0 F O R M A T ( 1 X , 1 . 2 A 6 ) _ _ • ' " 3 5 " R E A D " ' ' ( 5 , 4 0 ) N * C * B » A G ~ ~ ' " " " " " ' " " " 4 0 F O R M A T ( I 5 , 3 F 1 5 . 5 ) R E A D ( 5 , 5 0 ) ( TEMPj I ) >DE_ L _ T A H ( I ) , I = 1 _ , N ) ""'5 0 " F O R M A T ( 6 - 1 2 . 5 ) ~ " ~ " " " ' " ' ' " " " " " " " " " DO 6 0 I = 1 * N X S I N ( I ) = S I N ( 1 . 5 7 0 7 - - - ( DELTA .H ( I ) « • * 2 - B * * 2 ) / ( C * # 2 - S * * 2 ) ) _ _ _ _ _ _ _ — - - - XCOS( I ) =COS( 1. 5707*( DELTAH ( I ) **2-B**2 ) / ( C**2-B**2 ) ) 9 XTAN( I )=XSIN( I ) /XCOSt I ) .: CORFRQXXif.AG*DELlAHJ.J.,i../i<I.AMI..L.._ - __ 8 XLNFRQ ( I ) =AI_OG ( GORFRQ ( I ) ) G RECI PT ( I ) = 1. /TEMP ! I ) ' (.: _P_C P.R.I. n.J.=J_<^ : 11 6 0 CONTINUE Z\ 65 WRITE(6,70.).N,C,B,AG 7.0 F.O.RMAX(.,.1H..O...,̂  LATTICE _LjNE Wj..PJ.H._... =....,.£. 1 0. .5,, 5 ,X.,_2.QH ; I INARROWED- LINEWIDTH =,F10.5,5X , A HAG =,F15.5) PRINT 8 0 __8.0 _ FORMAT.„.Ll.HJ).A.lAAa.6_HJEMRJ.DPG 114HCOR.FREQ.(CPS),10X,6H1/TEMP»10X,13HLN(COR.FREQ.),11X,4H1/RT) WR I T E ( 6 > 90 ) ( TEMP ( I )'» DEL T AH ( I ) » CORFRQ ( I ) , R EC IP T( I ) » XLN F RQ ( I ) » l.RCP.RT ( i ) vL=.i.'._iJ_.: _ : _._ "" 9 0 • FORMAT ( 1H »2X,F12.5»8X»Fl2«5»7X?El4.6»9X»Fl6.7»9"x . , SUMX =0.0 SUMY = 0.0 H DO 200 J=l ,N SUMX = SUMX+ RCPRT(J) .....SUMY . = 5 UM Y +, XLN F R OJ..J.) I... 2 00 "' CONfINUE CALL LSQFIT(N,RCPRT,XLNFRQ,SUMX,SUMY,0,P,STDERO»STDERP,XAV, _1YAV»N0G0) _ _ FROMAX = EXP(Q) ERFRO = EXPC0)*STDERG _. EACT = ( - l . ) * P _ _ _ _ _ " ' "" E R E A C T = (~-l. ) *STDERP WRITE (6,210)FRQMAX,ERFRO,EACT , EREACT 210 FORMAT ( 1 HO ,_2 5 HCOR . FRO AT INF. TEMP .__= » EJL 2 . 5 ,_2_X , 7H E_R ROR =»E12.5_* ^15X','l2HACfTV. " EN". ' = T E T _ T 5 , T ' H C A L/MOL ,""""2X", 7H"E"RR"6"R~""= , E12 . 5 "»7HCA L/MCL ) READ (5,220) DELMAX,DELMIN.DEL INC i?. _ _ _ 2 2 . 0 . . F O R M A T ( 3 F 1 0 . 5 )_ .. _ 1 1 . N 0 i' N C = ( D E L M A X " - ~ D ETM I N ) / 5 EIT'N C" + 0 . " ~0 6 Y 10 N S W = N O I N C + 1 * _DO_ 2 3 0 _ K _ = 1 _ » N S W ' a " " ~ " A X = :< """" " 7 T H D E L ( K ! = D E L M I N + ( A K - 1 . ) - - - D E L I N G 5 C B = C * * 2 - B * * 2 " " " " " " T H S N V ' K ) = SYN ( 'Y ."5YoT*7fHDTLT^ 4 T H C O ( K ) =COS ( 1 . 5 7 0 7 - - - ( T H D E L ( K ) * * 2 - B * * 2 ) /CB ) 3 T H T A N ( K ) = T H S N ( K ) / T H C O ( K ) t • ' • • f s 5 THF RQ ( K ) = ( AG*THDEL MoT/THTANfflo • : e * ' THTEMP ( K ) =EACT/( 1 .9869*AL0G ( FRQMAX/THFRO ( K ) ) ) i 23.0 C.ON.II..N.UE .. „ ! . 3 * PRINT 2 40 6 240 FORMAT(l ,H0»34X»47HTHEORETICAL MODIFIED BPP LEAST SQUARES DATA FIT) fit I __. PRINT 2 50 _ _ _ _ _ _ . : _ __ _ _ _ T " ' " " 2 5 C ? F R > 7 A T ( T H T 7 "kTLVil^r»T7xViTHXYNE ' ' W T D T ' H T G A z i ' > 1USS) ,17X,27HCORRELATION FREQUENCY (CPS)) • ' ' WR I T E ( 6 • 2 60 ) ( TH TEMP' ( K ) » _TH DJEL (_KJ » THFRQ ( K ) , K=l _̂SW_)__ _ " " 2 6 6 " " F ' 0 R " M A T " ( T ' H 7 1 4 X 7 ? 1 1 . 5 t 30X 7F 167 5 7 2 8 X ,E14. 6 ) " "" " GO TO 15 END _ _ _______ SI 3FTC ' " ' ~ ~ '" " SUBROUT INE L S Q F I T ( N , X , Y » SUMX , SUMY ,3»C , S T DER3 , STDERC ,X A V ,Y A V ,NOGO) _ DIMENSION X( 500) , YJ 500_) _ ' . " I F ( ' N - 2 ) i o 5 " d / f d 5 o ' , f o o b ' " ' " " " " i " 1000 AN = N XAV = SUMX/AN : K YAV=SUMY'/AN'" ~ ~ ~ ~ ~ " " ~ '" ~ " " ~ " " H DIFXY=0. _ _ DI.FXSO = p. __ _ _ » DO 10 10 J = 1 » N ~ - - - -.— DIFXY = DIFXY + (X( J ) - XAV)*Y ( J ) DIFXSQ= D I FX SQ__+ J_X_U )- _XA_V_)j-»-2 1010 'CONTINUE C=DIFXY/DIFXSQ B=YAV-C*XA'V D S Q = 0 "" ™ ~ " ' " ' " ' " " " " " ' " " " " " " " " " . XSQ = 0. .. DO 1020 J= 1,N . _ _ _ _ ' • DSQ = DSQ"+ ( B+C*X ( jT-Yi~j)T**2 " ~ " ~~~ "" " XSQ = XSQ+ X ( U ) * * 2 _ 1020 CONTINUE __ • _ _ . . Q = SQRT iDSQ/'"('AN-2 .77 " " ~ ~ ~ " ~ " " " 0 DEE = AN*XSQ - ( AN*XAV ) * • _ < _ _ _ I F ( D E E ) 1 0 5O,1050» 103 0 _ _ _ . 1 10 30 Q0VRTD= Q / SQR T ( DEE ) - - - - - - - - ---. - - STDE RC = QOVRTD*SQRT(AN) ; _ STDERB_= QOVRTD*SQRJ(XSQ) \ ' " " " " " N ' O " G O ' " ~ " = " I " " ' " " " " " : PRINT 1.040 3 . 1040 FORMAT(1H »52HNOGO = 1, THEREFORE LSQFIT HAS MADE A SUCCESSFUL FIT 1) GO TO 1100 .1C!5 0..  NO.GO.. = ...2 .. PRINT 1060 1060 FORMAT(1H» 84HN0GO = 2, LSQFIT UNSUCCESSFUL DUE TO DEE LESS THAN 0 1R = 0 » OR TO N LESS THAN OR = 2.) 1100 RETURN END SENTRY - 113 - Appendix I l a , WFv Derivative Curves for Temperature Dependence at 30 MHz• - 114 - - 115 - Appendix l i e . WF̂  Derivative Curves for Field Dependence at 77 K 2 MHz modulation amplitude R = reference - 116 - 7 7 "K t I ' ' ' 4 0 5G Appendix I l i a . IF^AsF^ Derivative Curves for Temperature Dependence at 3 0 MHz 2 1 7 ° K 174 ° K 2 6 8 "K = modulation amplitude 0 53 R r reference - l i s - Appendix I I I c . I F / A S F A . Derivative Curves f o r F i e l d Dependence 56.4 MHz at 77 K 40 MHz 30 MHz : modulation amplitude R = reference  94.1 MHz Appendix IVb. SF*AsF^ Derivative Curves f o r F i e l d Dependence at 300"K 56.4 MHz J__.«iV,H_ I 30 MHz = modulation amplitude R s reference v  - 122 - References W. B a r t l e t t & P.L, Robinson, Chemistry _ I n d u s t r y , 1351 (1956). W. B a r t l e t t _ P.L. Robinson, Proc. Chem. Soc. (London), 230 (1957) F. S e e l & 0. Detmer, Angeuj. Chemie, 70, 163 (1958). F. S e e l & 0. Detmer, Angeiu. Chemie, 70_, 4 7 0 (1958). F. S e e l & 0. Detmer, Z. Anorg. A l l g s m . Chem., 301, 113 (1959). M. B a r t l e t t _ P.L. Robinson, 3. Chem. Soc., 3417 (1961). L. K o l d i t z , D. Uleisz, & U. Calov, Z. Anorg. Allgem. Chem., 316, 261 (1962). L. K o l d i t z , & E. R o e s e l , Z. 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