UBC Theses and Dissertations

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UBC Theses and Dissertations

19 F broad line nuclear magnetic resonance study Barr, Matthew Ronald 1967

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The U n i v e r s i t y o f 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 o f 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 IN ROOM 225, CHEMISTRY BUILDING  COMMITTEE IN CHARGE Chairman: B.A. D u n e l l McDowell K„B„ Harvey C o A o  F-A. Kaempffer 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. R i c h a r d s P h y s i c a l Chemical Laboratory South P a r k s Road O x f o r d , England  Research S u p e r v i s o r :  B.A- D u n e l l  C  BROAD LINE NMR  STUDIES ON WF 6  >5  AND  S'F, .AsF , 4 5 c  IF „AsF o 7  5  ABSTRACT A g e n e r a l broad l i n e n u c l e a r magnetic resonance 19 study was made of the F s p e c t r a of WF^ and the adducts IF • AsF,. and SF, - AsF,. to determine the temperature .-/ 5 4 5 dependence - of the s p e c t r a , i n t e r p r e t with respect  to i s o t r o p i c  the l i n e  shapes  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 y n o n - e q u i v a l e n t 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  lattice  condi-  t i o n s p r o b a b l y e x i s t e d at 77°K f o r WF. and IF., « A s F 6 7 5 but not f o r SF^ » AsF^„ The dependence i n d i c a t e d an o r  nmr  transition  i n the v i c i n i t y  of 200 K f o r the  two compounds and one commencing below third.  first  77°K f o r the  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 were determined f o r the average motions The  field  involved„ dependence of the second moments  of the compounds was 16,  30,  40,  coumpounds  56,4, 1  and  examined, 94,1  MHz  where p o s s i b l e , at 2, at  77°  and  295°Ko  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  of s u c c e s s , i n t o components.,  F o r WF,  an  The  degrees  approximate  b  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 ponding to the f o u r e q u a t o r i a l and two a x i a l  fluorines  i n the d i s t o r t e d o c t a h e d r o n a t 77°K.  The two adducts  c o u l d b o t h be r e s o l v e d , e s p e c i a l l y a t 295°K or above, i n t o components w h i c h s u p p o r t e d the i o n i c f o r m u l a t i o n s I F * A s F . and SF* A s F . . N o n - e q u i v a l e n t 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 i o n s c o u l d n o t be d e t e c t e d . From t h e observed and e s t i m a t e d second moments o f 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 p r o b a b l e 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 e n a b l e d s u g g e s t i o n s t o be made f o r t h e c r y s t a l s t r u c t u r e s o f WF. and S F t A s F . and f o r the bond l e n g t h s i n IF>AsF^. 6 3 6 6 6 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 h e r e , about the space group, w h i l e the second has n o t y e t been t h e s u b j e c t o f r e p o r t e d X-ray  studies.  A x i a l symmetry o f the c h e m i c a l s h i f t t e n s o r s was assumed.  Then, t a k i n g account o f t h e r e l a t i v e  s h i f t s between the r e s o l v e d components, average 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 o f WF. + and I F AsF,. were determined from e x p r e s s i o n s r e l a t i n g 6 6 6  the f i e l d squared dependence o f t h e second moment t o 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 o f t h e t o t a l  F  s p e c t r a f o r each compound 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 t o CF COOH\ 3  From those t h e s h i f t s o f 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 t o HF„  Then from t h e 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 v a l u e s o f the a x i a l l y symmetric s h i f t t e n s o r s were d e t e r m i n e d .  The p r i n c i p a l v a l u e s e n a b l e d e s t i m a t e s t o be made o f 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 t h e M-F bonds o f t h e h e x a f l u o r i d e groups. and  From these v a l u e s a p r e d i c t i o n was made f o r I  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:  Physical  Seminar i n C h e m i s t r y  Chemistry  (Special  L.G. H a r r i s o n  Topic)  Quantum C h e m i s t r y  T o p i c s i n Chemical P h y s i c s  R.M. H o c h s t r a s s e r  C A . McDowell & B.A. D u n e l l  Spectroscopy & Molecular Structure  A.V. Bree L.W.  Reeves  R.B. Harvey  Crystal Structures  J. T r o t t e r  PUBLICATIONS  M.R. B a r r , B.A. D u n e l l & R.F. Grant - 'Premelting Phenomena i n Long-Chain F a t t y A c i d s ' , Can. J . Chem., 41, 1188 (1963) . M.R. B a r r , B.A. D u n e l l - 'Proton Magnetic Resonance A b s o r p t i o n i n High Temperature Phases o f Anhydrous Sodium S t e a r a t e ' Can J . Chem. 42, 1098 (1964).  F  BROAD L I N E  NUCLEAR M A G N E T I C RESONANCE  STUDY  of UiF  6  , I F  ?  • AsF  5  , SF  • AsF  4  5  by HIATTHEIU RONALD  BARR  B. S c . ( H o n s . ) ,  U.B.C., 1 9 6 0  til.  19G3  A THESIS  S c . , U.B.C.,  SU Bill I T T E O  IN P A R T I A L  THE R E Q U I R E M E N T S DOCTOR  in  FULFILMENT  FOR THE DEGREE  OF  OF  OF P H I L O S O P H Y  the Department of Chemistry  We  accept  required  this  thesis  as c o n f o r m i n g  to the  standard  THE U N I V E R S I T Y  OF B R I T I S H  September,  1967  COLUMBIA  In  presenting  for  an  that  advanced  the  Study.  thesis  degree  I further  for  agree  partial  the  make  that  it  freely  representatives.  h.i;s  of  this  thesis  may  for  permission.  of  The U n i v e r s i t y o f B r i t i s h V a n c o u v e r 8, Canada  Columbia  be  for  granted  It  is  financial  of  British  available  permission  or  by  fulfilment  U n i v e r s i t y of  purposes  my w r i t t e n  Department  at  in  scholarly  publication  without  thesis  Library shall  Department  or  this  the  Columbia,  I  reference  and  for  extensive  by  the  requirements  copying  Head o f  understood  gain  shall  this  my  that  not  of  agree  be  copying  allowed  Abstract  A g e n e r a l broad l i n e n u c l e a r magnetic  resonance  s t u d y was  made  19 of the  F s p e c t r a o f l!jF_ and o  S F ^ • AsFj. t o d e t e r m i n e i n t e r p r e t the l i n e chemical s h i f t s  t h e a d d u c t s I F_ • A s F / b c  and  the t e m p e r a t u r e dependence o f t h e s p e c t r a ,  shapes  w i t h r e s p e c t t o i s o t r o p i c and  anisotropic  and i d e n t i f y ' n o n - e q u i v a l e n t f l u o r i n e s i t e s  i n the  compounds. The  t e m p e r a t u r e dependence o f t h e s e c o n d moment a t 30 iYlHz i n d i -  c a t e d 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 IL F and IF„ • AsF ' but not f o r SF. • A s F „ The dependence i n d i c a t e d an / b 4 b 1  c  nmr  t r a n s i t i o n i n the v i c i n i t y  and one  o 77 K f o r the t h i r d .  commencing below  i n the v i c i n i t y  o f the t r a n s i t i o n s ,  f o r the a v e r a g e m o t i o n s The  field  examined,  o f 200°K f o r the f i r s t  two  compounds  From t h e s e c o n d  activation  moments  e n e r g i e s mere d e t e r m i n e d  involved.  dependence o f the s e c o n d  where p o s s i b l e ,  moments o f the compounds  a t 2, 16, 30, 40,  56.4,  and 94.1  was  at  IYIHZ  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  o f s u c c e s s , i n t o components. be made i n t o two a x i a l  two  an a p p r o x i m a t e  resolution  could  components c o r r e s p o n d i n g to t h e f o u r e q u a t o r i a l  fluorines  adducts could  F o r IMF  degrees  i n the d i s t o r t e d  o c t a h e d r o n a t 77°K.  b o t h be r e s o l v e d , e s p e c i a l l y  The  two  a t 295°K o r above,  into  components w h i c h s u p p o r t e d the i o n i c  formulations IF* ^ ^g  SF* A s F  s i t e s w i t h i n i n d i v i d u a l ions  J  c  .. • N a n - e q u i v a l e n t F l u o r i n e  D  n o t be d e t e c t e d .  s  anc  and  ^ could  r ii, -  From t h e o b s e r v e d and e s t i m a t e d s e c o n d moments o f t h e r e s o l v e d components above and below t h e t r a n s i t i o n s ,  the probable  o c c u r i n g above t h e t r a n s i t i o n s were s u g g e s t e d . t h e o r e t i c a l s e c o n d moment c a l c u l a t i o n s for  The r i g i d  For the f i r s t  lattice  e n a b l e d s u g g e s t i o n s t o be mada  t h e c r y s t a l s t r u c t u r e s o f U/pg and SF^AsFg  l e n g t h s i n IFg.AsF^ .  reorientations  and f o r t h e bond  t h e r e had been c o n f u s i o n , a t  l e a s t h e r e , a b o u t t h e s p a c e g r o u p , w h i l e t h e second has n o t y e t been the s u b j e c t o f r e p o r t e d  X-ray  studies.  A x i a l symmetry o f t h e c h e m i c a l s h i f t t a k i n g account o f the r e l a t i v e s h i f t s averaqe  t e n s o r s was assumed.  Then,  between t h e r e s o l v a d components,  v a l u e s o f 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 o f 1!1F^ and  I F * A s F . were d e t e r m i n e d from e x p r e s s i o n s r e l a t i n d D b dependence o f t h e s e c o n d moment t o t h o s e  the f i e l d  squared  quantities.  19 The mean i s o t r o p i c  shifts  of the t o t a l  pound were measured where p o s s i b l e a t each r e s p e c t t o CF. COOH. were c a l c u l a t e d  From t h o s e the s h i f t s  relative  the a n i s o t r o p i e s ,  t o HF.  the p r i n c i p a l  F spectra o  field  a t 77  f o r each como and 295 K w i t h  of the resolved  components  Then from t h e i s o t r o p i c s h i f t s and values of the a x i a l l y  symmetric  t e n s o r s were d e t e r m i n e d .  The p r i n c i p a l  made o f I ( i o n i c ) and  ( d o u b l e bond) c h a r a c t e r s , n e g l e c t i n g  ization,  v a l u e s e n a b l e d e s t i m a t e s t o ba  i n t h e ITi-F bonds o f t h e h s x a f l u o r i d e g r o u p s .  v a l u e s a p r e d i c t i o n was made f o r I and ^ bonds i n PuF,. . o.  shift  hybrid-  From t h e s e  i n the a x i a l and e q u a t o r i a l  TABLE OF CONTENTS CHAPTER I. II. III. IV.  PAGE  INTRODUCTION NMR  1  THEORY  „  5  EXPERIMENTAL PROCEDURE  .  RESULTS AND INTERPRETATION General  21 27  . . . . . . . .  . . . . . . . . .  27  UIF-,  27  1. R e s u l t s  27  2. R e s o l u t i o n  Attempts.  Isotropic  and A n i s o t r o p i c  Chemical S h i f t s 3.  Proposed C r y s t a l  4.  Theoretical Rigid  5.  Reorientation  33 Structure  . . . . . . . . . . .  43  L a t t i c e Second foment . . . . .  47  i n the S o l i d  . •  50  The A s F g A d d u c t s  55  A. IF„ • A s F -  55  7  b  1. R e s u l t s  .  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  .  .  .  .  .  55  a  and A n i s o -  t r o p i c Chemical S h i f t s 3.  Crystal  4.  Theoretical Rigid  5.  Reorientations  Structure  B. SF. • A s F 4 5 1. R e s u l t s r  56  . . . . . . . . .  •  L a t t i c e Second Moment . . . . .  i n the S o l i d . . . „ . . . „  c  . . . . . .  60 63  • .  2. R e s o l u t i o n w i t h Components ( s e e 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 s . . .  64 69 69  70  - IV: - , iv CHAPTER  V.  PAGE 3.  Proposed C r y s t a l S t r u c t u r e  4.  Theoretical  5.  Reorientations  . . . . . . < > .  R i g i d L a t t i c e Second moment i n the S o l i d  .  .  .  73  . . .  .  .  .  .  76  SUMMARY AND DISCUSSION  APPENDIX I . Computer Program  .  .  .  .  .  2,  Curves .  Integration  Absorption  Curves  .  .  .  .  of D e r i v a t i v e  .  .  .  .  .  86  .  .  F(H) .  .  Line  Program  4.  Doublet F i t  Program  5  Transformation of Coordinates  Program  6.  Theoretical  .  .  .  87  .  .  90  .  .  93  Curves t o  3.  0  Shape F u n c t i o n  .  .  Program  .  .  .  .  99 .  .  .  .  103  R i g i d L a t t i c e Second Moment  Calculation Program APPENDIX I l a .  7.  105  A c t i v a t i o n Energies  UIFg D e r i v a t i v e a t 30 MHz .  lib.  b  .  Curves f o r Temperature  .  UJF, D e r i v a t i v e  .  .  .  .  .  .  .  108  Dependence 113  o  Curves f o r Temperature  Dependence  a t 94.1 MHz lie. APPENDIX I l i a .  114  \iiF, D e r i v a t i v e o IF* AsF b  c  O  C u r v e s f o r F i e l d Dependence a t 77 K  Derivative  Curves f o r Temperature  IF* AsF D  c  Depen. 116  Derivative  .  Curves f o r F i e l d  Dependence  .  I F * AsF" D e r i v a t i v e D  l i b  O  a t 295°K . IIIc.  TIC  b  dence a t 30 MHz Illb.  80  C a l c u l a t i o n o f 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 Program  „  Programs  1.  75  117 Curves f o r F i e l d  Dependence  O  a t 77°K  •  118  -  v  -  CHAPTER  APPENDIX  PAGE  I V a . SF*  fg  fls  Derivative  Dependence a t 30 IVb.  300°K  .  .  .  SF* AsF^ D e r i v a t i v e  o at 77 K REFERENCES  PflHz .  5 F * AsF D e r i v a t i v e o o at  IVc.  Curves f o r Temperature  .  .  •  .  .  .  .  .  Curves f o r F i e l d .  .  .  .  .  .  o  .  .  •  .  .  .  ng  Dependence .  Curves f o r F i e l d *o  .  .  .  o  120  Dependence o  o  .  •  121 122 to 126  -  v i  LIST  OF TABLES  TABLE  PAGE.  1.  Cell  P a r a m e t e r s o f IDF,. fa  2.  A t o m i c C o o r d i n a t e s , C e l l D i m e n s i o n s , and Bond Lengths of U F  3.  g  .  a t 298°K .  .  C a l c u l a t e d Atomic Coordinates U1F  6  a t "253°K" .  .  .  .  .  .  .  5.  X-Ray Powder S t r u c t u r e o f I F * A s F ~ ~ 295°K 6  7.  Rigid  77°K  6  f o r I F * AsFT ~ 295°X fa  L a t t i c e Second  45  .  D i p o l a r Second moments o f U J a t  Atomic Coordinates  .  „  Rigid  6.  .  44  and Bond L e n g t h s f o r  4.  .  .  .  45  . . .  49  . . .  61  . . . .  62  b  Moment C o n t r i b u t i o n s t o 63  8.  IF* AsF" fa fa X-Ray Powder D a t a f o r SF* SbF~ a t 291°K  9.  Estimated  75  10.  "Rigid  Atomic C o o r d i n a t e s  f o r SF* A s F ~ a t "291°K" o fa L a t t i c e " Second Moment C o n t r i b u t i o n s t o  SF^ ^ ^ g s  11.  Summary  74  .  .  .  .  .  .  76 82  -  v i i-  LIST OF FIGURES CURE 1.  TO FOLLO'JJ PAGE U J .  T e m p e r a t u r e dependence  a t 30 MHz 2.  UJFg .  .  ...  .  of absorption  .  .  T e m p e r a t u r e dependence  .  .  .  spectra  .  .  .  .  .  o f s e c o n d moment a t  30 MHz 3.  UJFg .  27  T e m p e r a t u r e dependence  o f l i n e u/idth a t 30 and  94.1 MHz 4.  UJFg . tive  „  to CF  31 o s p e c t r a a t 77 K o o f l i n e w i d t h a t 77 K . . .  Field  dependence  6.  IL'Fg .  Field  dependence  7.  IDF,, . fa UJFg .  Field  s q u a r e d dependence  'uJFg .  .  .  12.  UJF,. . fa IDF_ . fa  llJFg .  UJF  .  .  .  .  .  .  .  .  .  .  .  .  o  o  .  .  .  .  .  .  .  .  0  0  .  33  . 35  .  .  .  35  .  .  .  .  .  .  .  .  .  . .  . .  .  .  37  .  38  0  39  w i t h d o u b l e t and s y m m e t r i c  .  Resolution .  .  w i t h opposed a s y m m e t r i e s  Reconstruction  singlet 14.  .  Resolution  singlet 13.  .  .  32  Asymmetrical reconstruction f o r 6 - l i k e  fluorines 11.  o o f s e c o n d moment a t 77 K  32  S y m m e t r i c a l component r e c o n s t r u c t i o n from 2 MHz  spectra 10.  of absorption  S y m m e t r i c a l 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 . UJFg .  rela-  COOH  3  IiiFg .  9.  27  Chemical s h i f t of c e n t r o i d of spectrum  5.  8.  27  .  .  .  .  .  .  .  .  .  .  w i t h d o u b l e t and a s y m m e t r i c .  .  .  Proposed u n i t c a l l  .  o  (along  .  .  .  .  c-axi.i) .  .  .  .  .  *  .  *  .  39 46  -  V l l l -  FIGURE 15.  TO FGLLOllJ PAGE I F * AsF,. . o o  T e m p e r a t u r e dependence  of absorption  s p e c t r a a t 30 MHz 16.  I F * AsEg  .  MHz . 17a.  55  T e m p e r a t u r e dependence  .  I F * AsFg .  .  .  .  Field  .  .  .  .  dependence  o f s e c o n d moment a t 30  .  .  .  55  of a b s o r p t i o n  spectra at  295°K 17b.  56  I F * AsF  .  Field  dependence  of absorption spectra a t  77°K 18. -  56  I F * AsF •  .  C h e m i c a l s h i f t o f c e n t r o i d of spectrum r e l a -  b  to CF C00H . I F * ^ s F g . F i e l d dependence  56  3  19.  o f l i n e w i d t h a t 77° and  295°K 20.  57  IF* AsF, . D  Field  s a u a r e d dependence  a t 77° and 295°K 21.  o f s e c o n d moment  '  O  SF* AsFg .  .  .  .  .  .  T e m p e r a t u r e dependence  .  .  .  SF^ ^ s F ^ °  T e m p e r a t u r e dependence  SF* A s F ^ . tive  24a.  . .  o  .  .  .  .  .  .  57  spectra  ." .  30 M H z . 23.  .  of absorption  a t 30 MHz 22.  .  .  .  .  o f s e c o n d moment a t o  .  o  .  .  .  Chemical s h i f t of c e n t r o i d of soectrum  . .  79  Field  dependence  of absorption  spectra at  300°K 24b.  70  SF* ftsFg . 77 K  25.  69  rela-  t o CF^COOH  SF* AsFg o  69  Field  .  o  SF* AsF^. • 0  a t 77  o  Field  dependence o  .  o  of a b s o r p t i o n  .  .  o  s q u a r e d dependence  .  .  spectra at .  •  o  0  •  70  o f s e c o n d moment  0  and 300 K Proposed u n i t c e l l  72  26.  SF* A s F - .  (along a - a x i s )  . . .  27.  I o n i c and d o u b l e 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 o f mean i s o t r o p i c c h e m i c a l , s h i f t r e l a t i v e  75  t o HF 84  Acknowledgements  Thanks a r e due t o D r . B.A. D u n e l l who d i r e c t e d t h i s r e search. H i s 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 o f f r e q u 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 t h e s p e c t r o m e t e r s into operation. H e l p f u l a d v i c e on programming was a l w a y s c h e e r f u l l y g i v e n by Mr. T. C y r . Thanks a r e a l s o due t o Dr. N e i l B a r t l e t t ' s p r o v i d i n g t h e f l u o r i n e compounds, w h i c h were made by Dr. S t e v e B e a t o n , and t o Mr. Jack Passmore o f t h e same g r o u p f o r m a k i n g h i s vacuum s y s t e m a v a i l a b l e t o me when n e c e s s a r y . Finally warmest t h a n k s a r e due t o t h e 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 o u r l a b 0  CHAPTER  1  INTRODUCTION  In the F a l l  o f 1964, a j o i n t p r o j e c t on t h e i n v e s t i g a t i o n o f  the n u c l e a r magnetic  resonance  pounds SF^ • BF^ , SF^ ° ^ ^ 5 s  a b o r a t i o n w i t h Dr. N e i l  s p e c t r a o f the s o l i d a n c  *  °  a d d i t i o n com-  undertaken  u j a s  B a r t l s t t and h i s c o - w o r k e r s .  in coll-  Exploratory  s t u d i e s showed t h a t an e x a m i n a t i o n o f t h e s i m p l e r m o l e c u l e UJF_ o  might  be h e l p f u l .  In t h e e v e n t , i t t u r n e d o u t t h a t a c o m p l e t e  inter-  pretation  o f t h e s p e c t r a o f any o f t h e s e compounds was made v e r y  difficult  by combined i s o t r o p i c  anisotropy, rate  from  b o t h o f w h i c h were s i g n i f i c a n t ,  Because o f t h e p r e s e n c e  i m p u r i t y l i n e which  f l u o r i n e s would  grew as each sample aged,  be i s o t r o p i c a l l y  shifted  o f the d e t a i l  shift,  t h a f l u o r i n e s were e x p e c t e d  o r v e r y n e a r l y s o , was s e l e c t e d . were p r e s e n t i n UJF  from t h e f l u o r i n e s i n  To s t u d y t h e e f f e c t o f  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 , i n which  Non-equivalent  t w o - t h i r d s o f the time i n v o l v e d  a molecule,  t o be e q u i v a l e n t , fluorines,  and a s e a r c h f o r a q u a n t i t a t i v e  of the m o l e c u l e ' s  i n the r e s e a r c h . resonance  however,  interpretation  l i n e shape u l t i m a t e l y  became a g e n e r a l n u c l e a r m a g n e t i c  attention  I t was o b v i o u s t h a t t h e  t h e SF^ o r IV^ p o r t i o n s o f t h e a d d u c t s .  s o l i d UJF  t o sepa-  i n a l l samples o f SF^ „ BF^ o f  was f o c u s e d on t h e o t h e r two a d d u c t s . AsF  but d i f f i c u l t  shift  one a n o t h e r 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 . a narrow,  c h e m i c a l s h i f t and c h e m i c a l  c c c u p i a d some  This thesis  then  study o f the f l u o r i n e  2  s p e c t r a o f SF^. ° A s F ^ , I F  • A s F ^ , and s o l i d U/F  ?  ,  g  comprising,  inhere p o s s i b l e , t e m p e r a t u r e d e p e n d e n c e , i n t e r p r e t a t i o n o f the l i n e shapes w i t h r e s p e c t and  identification The two AsF  reported ported  to i s o t r o p i c of equivalent  the l a s t decade.  t h a t SF^, c o o r d i n a t e d  e a c h t o form a new  with AsF  compound,  observed that a displacement method  fluorine  adducts are r e l a t i v e l y  5  only during  convenient  and a n i s o t r o p i c c h e m i c a l  a white  solid.  fluorine  (4).  1961,  Bartlett  ( l ) re-  o f one mole o f  The  f o l l o w i n g year  again  and s u g g e s t e d an i o n i c  . AsF  ' and  Muettarties  adducts of A s F  5  c  6  ( l l ) and Young and May  .  which a r e i o n i c . that the a c i d -  t h e i o n i c s a l t I F * AsF~ .  5  In  5  and X - r a y s p e c t r a has shown  i s indeed  dis-  formulation.  i n g r e a t e r d e t a i l on SF  ( 7 , 6, 9) has a l s o r e p o r t e d  • AsF  o f pure  p a p e r i n a n o t h e r j o u r n a l ( 5 ) they  (6) reported  base a d d u c t I F  (3)  They n o t e d t h a t t h e s t a b l e  They a l s o used IF.., . AsF_ as a s o u r c e  B e a t o n ( 1 0 ) from i n f r a r e d  he  In 1958 S e e l and Detmer  4 Kolditz  been  form i n w h i c h to s t o r e g a s e o u s f l u o r o com-  In a longer  c u s s e d t h e compounds  having  r e a c t i o n i n v o l v i n g t h i s a d d u c t was a  r e p o r t e d SF. • AsF,- and I F ^ . AsF,. . 4 b b 5  pounds s u c h as SF^ .  new compounds  i n the r a t i o  f o r p u r i f y i n g SF^, ( 2 ) .  s o l i d s were a c o n v e n i e n t  atoms.  In 1956, B a r t l e t t  5  shifts,  Tebbe  6  ( 1 2 ) a l s o have r e p o r t e d  probable  i o n i c adducts of AsF^ . The symmetry o f h e x a f l u o r i d e m o l e c u l e s has made them o f i n t e r e s t t o 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 y e a r s Thermodynamic v a l u e s 21,  are reported  i n the p r e c e d i n g  (13 t o 3 0 ) references  26, 2 8 ) and a l s o s e p a r a t e l y i n e t h e r p a p e r s (31 t o 3 5 ) .  o  ( 1 4 , 20, I n the  3  vapour phase o c t a h e d r a l symmetry appears w e l l e s t a b l i s h e d For most h e x a f l u o r i d e s (17, 18, 28, 30).  Except f o r UF  C  (36) no d e t a i l e d  D  X-ray data e x i s t f o r the metal h e x a f l u o r i d e s .  S i n c e the bond  l e n g t h s (37a) and X-ray r e s u l t s (37b) a v a i l a b l e f o r U1F do not perC  D  mit  d e t e r m i n a t i o n of the symmetry of the s o l i d , i t appeared t h a t  t h i s presented an e x c e l l e n t o p p o r t u n i t y 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 t e t r a g o n a l d i s t o r t i o n w i t h four s h o r t and two long bonds.  B l i n c et a l (38) undertook a  b r o a d l i n e 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 preted the  o 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 p r e s e n t i n a 2:1 r a t i o .  This i s i n agreement w i t h the X-ray r e s u l t s .  The work was a t an e x t e r n a l 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  t h a t a n i s t r o p y was p r e s e n t .  B l i n c and Rigny (40) l a t e r p u b l i s h e d a  j o i n t l e t t e r on r e l a x a t i o n through a n i 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 this laboratory.  While the e x p e r i m e n t a l  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) p u b l i s h e d a paper on the nmr and r e l a x a t i o n of h e x a f l u o r i d e , p o i y e r y s t a l l i n e s o l i d s which i n c l u d e d WF^.  The B l i n c s p e c t r a agreed w e l l w i t h those ob-  t a i n e d 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 . s p e c t r a of l i q u i d MoF  and WF  High r e s o l u t i o n  nmr  have been reported by Cady (26) and  4  -  Rigny ( 4 2 ) . In Cady's work the f l u o r i d e s mere a l s o 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 f o r both compounds) but the s p e c t r a were too broad f o r the l i n e s to be observed by high lution.  reso-  In the l i q u i d s t a t e both Cady and Rigny observed i n a d d i -  19 t i o n to the c e n t r a l peak, s i x s m a l l 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 c o u p l i n g . For U f C a d y observed only a s i n g l e , c e n t r a l peak. 183 s a t e l l i t e s corresponding to the  However, Rigny observed two  19 UJ—— F coupling.  CHAPTER II  NMR  Since  the  first  ments mere r e p o r t e d Bloch, books one  Hansen,  successful  i n 1946 Packard  n u c l e a r magnetic  by P u r c e l l ,  refer  t o Bloembergen,  others.  (43)  For d e t a i l s  and  Pake  ( 4 9 ) , and  books  ( 5 0 ) , Andrew ( 5 l ) , Abragam  ( 5 2 ) , and  Slichter  given i n t h i s  is  t o be u n d e r s t o o d  (47, 48)  to s u p p l y a g e n e r a l  section. that  Unless a s p e c i f i c acknowledgment  Andrew) f o r the m a t e r i a l nuclei  which  number have a n o n - z e r o n o t i c moment |J =  and  o f the t h e o r y  (45), reviews  is  Those  Pound  and Pound  Only i n f o r m a t i o n  (especially  T o r r e y , and  experi-  Purcell,  ( 4 6 ) , Gutowsky  Bloembergen  resonance  (44) v e r y many p a p e r s , r e v i e w s , and  on the phenomenon have a p p e a r e d .  may  Smith  and  THEORY  outline  by (53) among  o f the t h e o r y  reference i s given, i t  i s made t o the above  i n this chapter.  do n o t have even mass number and  spin  by  a n g u l a r momentum  colinear  with i t .  magnetic  moment i s a l s o  I ti  and  Prominent  atomic  a dipolar  mag-  among t h e s e i s  19 the  F nucleus.  p = <jjj I  where  nuclear  g-factor  absence  o f an e x t e r n a l m a g n e t i c  0  p  The e  i s the n u c l e a r  analogous  magneton  field  However, i n t h e p r e s e n c e o f a f i e l d torque  T"jJ*rfo  which  o  the energy  tends  \\o  to a l i g n  e x p r e s s e d as  ( p = <^ ) and g i s t h e  t o the Lande s p l i t t i n g  "magnet" i s i n d e p e n d e n t o f the o r i e n t a t i o n  a  often  factor.  In the  of a nuclear  o f the m a g n e t i c  moment  , the moment i s s u b j e c t i t parallel  to the  field.  to  6  T h e r e i s an e n e r g y t a k e n as t h e la  of i n t e r a c t i o n  j j - d i r e c t i on,  E  5  ~* U'Ho  •  I f Ho  then  is inhere  i s t h e component o f t h e a n g u l a r momentum v e c t o r a l o n g  The  or m  values o f 1^  , the magnetic  Ho .  quantum number ( t h e more  u s u a l symbol f o r t h e component o f a n g u l a r momentum) a r e g i v e n by 19 the s e r i e s  I , 1-1, . . . - ( i - l ) ,  -I.  Hence f o r  F where  there  I=2>  a r e two p o s s i b l e o r i e n t a t i o n s  f o r t h e component and two p o s s i b l e  energy  levels.  rule  energy  l e v e l s i s /\m--l  The s e l e c t i o n  for" t r a n s i t i o n s between t h e 19 F ^E ~V1\HO  , therefore for  •  =  The  f r e q u e n c y c o r r e s p o n d i n g t o an a l l o w e d t r a n s i t i o n i s OJ -2XtV t  n u c l e a r moment jj^ p r e c e s s e s about t h e e x t e r n a l  The this  0  field  f r e q u e n c y , t h e Larmor p r e c e s s i o n f r e q u e n c y , <*>o •  nuclear magnetic  resonance  experiment,  H  field  When t h e f r e q u e n c y  o f o s c i l l a t i o n o f H^i e q u a l s  interaction  occurs which  (  i s applied  may f l i p  lower or lower to upper energy  I the R  , a  resonance  from t h e u p p e r t o  In the usual experimental  arrangement t h e 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  i s slowly varied  field  radio-  t o H^c .  at r i g h t angles  the nucleus  level.  Ho a t  a small, o s c i l l a t i n g  frequency magnetic  -  to effect  the resonance  condition. The a system  above t r e a t m e n t o f weakly  f o r a s i n g l e n u c l e u s may be e x t e n d e d t o  interacting nuclei.  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 t o the c o n d i t i o n s i n m a t t e r in  an e x t e r n a l m a g n e t i c  distribution  field  there w i l l  of e n e r g i e s , a s l i g h t excess  i n bulk.  At e q u i l i b r i u m '  be, due t o a  Boltzman  of spins i n the s t a t e  7  -  *n~*h. c o r r e s p o n d i n g t o t h e l o w e r e n e r g y l e v e l f o r a  F nucleus.  T h e r e can t h e n be a n e t a b s o r p t i o n o f e n e r g y by the n u c l e a r in  an nmr  experiment.  system  T h i s 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 o f the system.  The n e t  absorption  w o u l d c e a s e when t h e p o p u l a t i o n s o f t h e 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  dissipate  e n e r g y t o the s u r r o u n d i n g l a t t i c e . So far', one e x p e c t s an e x t r e m e l y narrow r e s o n a n c e l i n e . liquids  this i s generally  certainty ments.) the  realized.  In r i g i d  gauss.  A p a r t from t h a t r i v i a l magnetic  t o a n e g l i g i b l e v a l u e , t h e r e may d i p o l a r , and  chemical s h i f t  I f the n u c l e i  involved  nucleus k a magnetic f i e l d a spin-spin  is  w h i c h can be r e d u c e d  e x i s t for a spin \ nucleus spin  -  b r o a d e n i n g mechanisms.  are i d e n t i c a l , nucleus j produces at  oscillating  a t i t s Larmor f r e q u e n c y and may  T h i s r e s u l t s i n a b r o a d e n i n g o f the o r d e r o f _ H ^ where  the f i e l d  dipolar  p r o d u c e d a t n u c l e u s j by n u c l e u s k. to s p i n - s p i n  broadening, there w i l l  b r o a d e n i n g r e g a r d l e s s o f whether l i k e  present.  external The  field,  cause of i n -  t r a n s i t i o n i n v o l v i n g a m u t u a l exchange o f e n e r g y  In a d d i t i o n  are  measure-  s o l i d s , however, l i n e w i d t h s a r e t y p i c a l l y o f  homogeneity i n the e x t e r n a l  occur.  o f c o u r s e be un-  broadening, which i s fundamental to a l l s p e c t r a l  order of s e v e r a l  spin,  (There w i l l  In  field  or u n l i k e  E a c h n u c l e u s e x p e r i e n c e s the r e s u l t a n t H„ and the l o c a l f i e l d s  a l w a y s be a nuclei  e f f e c t of the'  Wx o f a l l t h e o t h e r n u c l e i .  components o f the l o c a l f i e l d s i n the d i r e c t i o n o f Ho  may  increase  o r d e c r e a s e Ho w i t h ****  In l i q u i d s t h e d i p o l a r  a resultant  spread of resonance.  b r o a d e n i n g e f f e c t i s removed by t h e r a p i d  motional averaging of the l o c a l f i e l d s  t o 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  width. Spin-spin strated  and d i p o l a r  b r o a d e n i n g were s t r i k i n g l y demon-  by Pake ( 5 4 ) i n a c l a s s i c e x p e r i m e n t w i t h -3  CaSO^ • ZH^O  .  Because o f t h e r  gypsum,  dependence o f t h e d i p o l e  inter-  a c t i o n , each p r o t o n i n t h e gypsum i s p r e d o m i n a t e l y i n f l u e n c e d its  partner i n the water molecule.  is  Hence t h e r e a r e two r e s o n a n c e  H ' H* t jjK (3CO&* ©-|)  f r e q u e n c i e s g i v e n by  S  t h e p r o t o n moment, r i s t h e p a i r s e p a r a t i o n ,  v e c t o r j o i n i n g t h e two n u c l e i ) .  c l a s s i c a l picture  to  c o n t a i n s two t y p e s o f p r o t o n s w i t h Depending on t h e o r i e n t a t i o n or  four  of the p o s s i b l e  ation  m  T  h  e  u  n  t  cell  o f a s i n g l e c r y s t a l one, two, t h r e e  r e s o n a n c e l i n e s may be o b s e r v e d .  pairs  i  d i f f e r e n t values of &  contribute  further  I f t h e sample i s p o l y c r y s t a l l i n e w i t h  of. t h e d i p o l e  function  a  generally  b u t i o n s from d i s t a n t n e i g h b o u r s w i l l to t h e s p e c t r u m .  I f , as i n  exchange m o d i f i e s  Ho' H*± ~ Ji K ( 3 c o S e - f ) 3  }  and & i s t h e a n g l e  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 the  H* * \\v/z. \l  where  ,  0  between Ho and£ ( t h e  by  Contribroadening the o r i e n t -  isotropically distributed, a line  shape  o f t h e farm  where \\~Ho"H* and the s i g n s  a r e t a k e n as p l u s  f o r -3.  3  < 3 j j h  -  and  9  minus f o r -3^1*  poiyerystalline  , can be d e r i v e d ( 5 4 ) .  line  shape i s a d o u b l e t w h i c h a g a i n i s f u r t h e r  b r o a d e n e d by t h e l o c a l  fields  of a l l other neighbours.  g e n e r a l l i n e shape f u n c t i o n w i l l The  line  s y s t e m s have been c a l c u l a t e d ,  in  difficult  e x i s t s a technique e x t r a c t e d from  its  devised  and i n any case  Vleck  by Van V l e c k whereby i n f o r m a t i o n c a n  for  systems.  T h i s method and  broadening.  calculated.  t h e h*  h  moment i s  S~ n  numbered moments a r e z e r o s i n c e glK) dipolar  Fortunately there  I f the normalized  line  shape  where K i s the d i s t a n c e from t h e c e n t e r o f  the f u n c t i o n  resonance,  use.  ( 5 5 ) showed t h a t t h e moments o f a r e s o n a n c e  s p e c t r u m can be r e a d i l y is  of l i t t l e  the l a c k of d e t a i l  be d i s c u s s e d p r i o r t o d e s c r i b i n g t h e 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 Van  0  t h r e e - s p i n and f o u r - s p i n  t h e more c o m p l i c a t e d  applications will  again  This  b u t f o r more g e n e r a l s y s t e m s t h e  t h e s p e c t r a makes t h e e f f o r t  be  be e n c o u n t e r e d  shapes f o r c e r t a i n  task i s extremely  The  broadening.  the general case.  f h^J^dh  „  A l l t h e odd-  i s an even f u n c t i o n f o r m a g n e t i c  Van V l e c k c a l c u l a t e d  second and f o u r t h moments  F o r a r i g i d p o i y e r y s t a l l i n e sample t h e  s e c o n d moment i s  = i K i ^ N " ^  Sl  • ^jN-'Xl.d.^^  where I i s t h e s p i n number o f t h e n u c l e i , | J g  e  ....(2).  i s t h e n u c l e a r magneton,  i s t h e n u c l e a r g — f a c t o r , N i s t h e number o f m a g n e t i c n u c l e i i n  t h e s y s t e m over w h i c h t h e sum j i s t a k e n , and fjk.  i s the magnitude  -  of  10  the vector j o i n i n g n u c l e i  j and k.  d i p o l a r b r o a d e n i n g by t h o s e n u c l e i served.  The s e c o n d  term a c c o u n t s f o r  whose r e s o n a n c e i s b e i n g ob-  term i s a c o n t r i b u t i o n t o s p e c t r a l  by s p e c i e s o f m a g n e t i c n u c l e i 19 UiFg f o r example,  The f i r s t  broadening  o t h e r than t h o s e a t r e s o n a n c e . ( i n  183 F and  UJ r e s p e c t i v e l y . )  D u r i n g t h e c o u r s e o f a b r o a d l i n e nmr i n v e s t i g a t i o n polycrystalline solid,  one n o r m a l l y r e c o r d s t h e m a g n e t i c  s p e c t r u m o v e r a range o f t e m p e r a t u r e s v a r y i n g liquid  nitrogen  from low ( u s u a l l y  by t h e n a t u r e o f t h e compound.  temperature corresponds to a r i g i d  the  resonance  t e m p e r a t u r e ) up t o room t e m p e r a t u r e o r 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  a correction  of a  lattice  I f the lowest  condition,  f o r z e r o - p o i n t motion o f the n u c l e i  then  after  has been made ( 5 6 ) ,  o b s e r v e d s e c o n d moment, s h o u l d a g r e e w i t h i n e x p e r i m e n t a l e r r o r  with  the c a l c u l a t e d  will  be due t o a d d i t i o n a l m o t i o n i n t h e c r y s t a l l a t t i c e .  crystal often  rigid  lattice  Any d i s c r e p a n c y I f the  s t r u c t u r e has n o t been d e t e r m i n e d a r e s o n a b l e s t r u c t u r e may  be worked o u t by t r i a l  moment.  s e c o n d moment.  Even i f r i g i d  from t h e nmr r i g i d  lattice  lattice  second  c o n d i t i o n s do n o t p r e v a i l ,  quite  r e s o n a b l e e s t i m a t e s o f t h e p r o b a b l e s t r u c t u r e can be o b t a i n e d by c o n sidering crystal  t h e e f f e c t on s e c o n d moment o f p o s s i b l e m o t i o n s lattice.  i n the  The a p p l i c a t i o n o f s e c o n d moments i s a l s o  useful  i n d e t e r m i n i n g the p o s i t i o n s o f p r o t o n s , which a r e d i f f i c u l t to locate accurately  by X - r a y c r y s t a l l o g r a p h y .  Since equation (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  -  frequently  be o b t a i n e d .  I n s i n g l e c r y s t a l s p e c t r a bond a n g l e s  can be o b t a i n e d i n a d d i t i o n Motion w i t h i n of  fields.  field  f o r a r i g i d system  are  averaged  line  approached.  m o l e c u l a r motion  field  and as m o t i o n  aven though  f o r t h i s motion  sufficient produces may  energy  cribed  give evidence  of m3y  A very high  has  barrier  r i g i d s t r u c t u r e a l t h o u g h even t h e n t h e r e  oscillation.  In a r e o r i e n t a t i o n process  f r e q u e n c y or c o r r e l a t i o n time,t  c  which  t i m e , the  , may  be  des-  by  where AE  c  = r  potential.  The  0  e.*p(^E/RT)  ( 3 )  i s t h e h e i g h t e x p r e s s e d i n energy  p e r mole o f the h i n d e r -  Then t h s r e o r i e n t a t i o n r a t e , V  C  Vc^V  of  conditions  t a k e s p l a c e when a m o l e c u l e  dependence o f the c o r r e l a t i o n  ' r  ing  pronounced  A potential barrier obviously  t o surmount the b a r r i e r .  c a n be d e s c r i b e d by a s i n g l e temperature  as l i q u i d - l i k e  local  the frequency of r e o r i e n t a t i o n  and m o t i o n  an e s s e n t i a l l y  be r o t a t i o n a l  becomes more  n a r r o w i n g o f t h e l i n e may  be q u i t e s m a l l f o r each m o l e c u l e . exists  i s l e s s than the s t e a d y  becomes n a r r o w e r  The  or  c o n t r i b u t e s t o a time a v e r a g i n g o f the  local  the resonance  t o bond l e n g t h s .  t h e l a t t i c e , w h e t h e r o f whole m o l e c u l e s  s u b s t i t u e n t groups, The  11  resonance  (-AE/R.T)  0  line  narrows  , d e f i n e d by  o  when the r e o r i e n t a t i o n  the o r d e r o f t h e f r e q u e n c y o f the l i n e w i d t h .  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 s y s t e m  (4)  rate  Calculation  becomes of the  i s o f c o u r s e even  12  more d i f f i c u l t are of  used.  than f o r a r i g i d  -  s y s t e m and a g a i n s e c o n d  The change i n s e c o n d moment m i l l  moments  depend on t h e n a t u r e  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  contain-  i n g a s y s t e m o r g r o u p u n d e r g o i n g a f r e e r o t a t i o n o v e r an n - f o l d periodic the  intramolecular  where and  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  YT^  contribution  only  i s t h e a n g l e between t h e i n t e r n u c l e a r  the a x i s of r o t a t i o n .  Each term has been r e d u c e d  T h i s i s the r e d u c t i o n s e c o n d moment.  vector  of only  the  Jhj^  by t h e f a c t o r intramolecular  T h a t f o r t h e 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 interrnolecular contribution  as w e l l  0  The o n l y  case i n which the  c a n be o b t a i n e d s i m p l y 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 o f a group about i t s m o l e c u l a r center  ( 5 8 , 59, 60, 6 1 ) .  The m a g n e t i c n u c l e i a r e c o n s i d e r e d t o be  c o n c e n t r a t e d a t t h e m o l e c u l a r c e n t e r s and t h e d i s t a n c e s equation  (2) are replaced  a m o l e c u l e and i t s i  by  , the center-center  ^ nearest neighbour.  Y'^y.  distance  in between  The e q u a t i o n becomes  where No i s t h e number o f r e s o n a n t n u c l e i i n t h e m o l e c u l e ,  is  th the as  number o f i before.  n e a r e s t n e i g h b o u r s and t h e o t h e r q u a n t i t i e s a 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 a v e r a g e s t h e  moment t o z e r o and t h e c a l c u l a t e d bution  0  intramolecular  sum i s t h e i n t e r r n o l e c u l a r  I f t h e r e o r i e n t a t i o n i s n o t i s o t r o p i c , but about  contri-  preferred  13  axes and  a t random t h e c a l c u l a t i o n i s more d i f f i c u l t t h e r e s u l t may d i f f e r  ( 6 1 , 62, 63, 64a)  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 t o 15% ( 6 4 b ) . 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 derived tion  from a l o g V  c  v e r s u s ^/T  f r e q u e n c y i n terms  plot of equation (4).  The c o r r e l a -  o f l i n e w i d t h i n gauss i s ( b a s e d on  Gutowsky and Pake ( 5 7 ) V  l  ^ /  fh  s  where  U  n  15  (  ^  "  ^  ]  ........(7)  i s the l i n e width 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 t h e t r a n s i t i o n , and  i s t h a t below  the t r a n s i -  t i o n , eC i s a c o n s t a n t o f t h e o r d e r o f u n i t y , and Jj i s t h e m a g n e t i c moment i n n u c l e a r magnetons. transition,  I f t h e l i n e shape  line width i snot a r e l i a b l e  changes  parameter  d u r i n g the  (65).  Since  s e c o n d moments a r e a more r e l i a b l e i n d i c a t i o n o f t e m p e r a t u r e  effects  the c o r r e l a t i o n  t i m e may be e x p r e s s e d a c c o r d i n g t o P o w l e s and 2 Gutowsky ( 6 6 ) i n terms o f s e c o n d moment i n gauss as  where S A is below  A  i s t h e s e c o n d moment a t any p o i n t i n t h e t r a n s i t i o n  region,  B t h e s e c o n d moment above t h e r e g i o n , S^ i s t h e second moment t h e r e g i o n , and t h e o t h e r s y m b o l s  a s i n g l e motion i s o c c u r r i n g which are o b t a i n e d .  a r e as b e f o r e .  Unless  t h e s e a r e average values o f  A l s o an added u n c e r t a i n t y a r i s e s  o f t h e l i n e w i d t h o r s e c o n d moment.  and  from t h e u s e  The i n t e r m o l e c u l a r  contributions  t o t h e r e s o n a n c e c u r v e may v a r y w i t h m o t i o n and hence w i t h in a different  only  temperature  f a s h i o n from t h e 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 V  or  L  are probably the best t h a t 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 s p i n l a t t i c e r e l a x a t i o n measurements.  This i s , however, not always  e x p e r i m e n t a l l y c o n v e n i e n t , w h i l e l i n e widths and second moments can always be o b t a i n e d . plicated,  Furthermore i f the motion t a k i n g p l a c e i s com-  and  a r e , as noted above, average v a l u e s .  Compari-  son of the observed second moment change w i t h that c a l c u l a t e d on the b a s i s af the p o s s i b l e motions o c c u r r i n g gives a more r e l i a b l e p i c t u r e of r e o r i e n t a t i o n s t a k i n g p l a c e i n c o m p l i c a t e d cases.  The  activation  energy w i l l , however, p r o v i d e s u p p o r t i n g evidence f o r the occurrence of the suggested motion,, Chemical s h i f t a l s o c o n t r i b u t e s to n u c l e a r magnetic resonance line-broadening.  In diamagnetic molecules, the most f r e q u e n t s u b j e c t s  for nmr experiments, the ground s t a t e has, i n the absence of an e x t e r n a l 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 s p i n or e l e c t r o n i c angular momentum ( 6 7 ) .  orbital  An e x t e r n a l f i e l d induces an o r b i t a l motion  i n the e l e c t r o n s of a molecule which i s superimposed on the e l e c t r o n s ' motions about t h e i r n u c l e i .  The motions c o n s t i t u t e e f f e c t i v e c u r r e n t s  w i t h i n 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 e x t e r n a l f i e l d  !rU  .  The  r e s u l t a n t f i e l d e x p e r i e n c e d by the nucleus i s expressed as (52, Chap. 6; 68, Chap. 1) H= tf  ft  Cl-e)  ( g )  where <5 i s a second rank t e n s o r depondent on the e l e c t r o n i c c n v i r o n ment of the nucleus c o n s i d e r e d . The s h i f t i s a combination of  15  d i a m a g n e t i c and p a r a m a g n e t i c  -  shielding  effects.  The d i a m a g n e t i c  term i s e s s e n t i a l l y a L a r m o r p r e c e s s i o n , i n t h e f i e l d e l e c t r o n i c charges i n t h e m o l e c u l e about while the paramagnetic shells  term  arises  from  Ho > o f t h e  the n u c l e u s i n q u e s t i o n ; the p o l a r i z a t i o n of e l e c t r o n  by H« ( 5 2 , Chap. 6 ) . Slichter  ( 5 3 , p. 84) e x p r e s s e d t h e s h i e l d i n g a f t e r Ramsey ( 5 7 )  as  4  J  where e i s t h e e l e c t r o n i c c h a r g e , of l i g h t ; ^ , j *  A  and £  ,  0  r  J.  fn t h e e l e c t r o n i c mass, c t h e speed  the wavefunctions  and e n e r g i e s o f  electrons  th in  t h e ground  and n  excited  states  l a r momentum o p e r a t o r J ^ * ? j ed n u c l e u s t o t h e e l e c t r o n is  t h e l i n e a r momentum),^*.  "ft  - S ^—i  i snd Y:  d* )  *  whose c o o r d i n a t e s a r e * j ,  i s t h e m a g n i t u d e o f fi .  are  taken over the N e l e c t r o n s  states.  the s h i e l d -  , Sj  and p^-  The sums j and k  p r e s e n t and t h e sum n o v e r t h e n  The two terms a r e o f a p p r o x i m a t e l y e q u a l m a g n i t u d e and a r e  respectively tribution. ground  angu-  i s t h e a n g u l a r momentum o p e r a t o r  ay  J  the t o t a l  (where £j i s t h e v e c t o r from  T  y  respectively;  state  complete  t h e d i a m a g n e t i c and t h e s e c o n d - o r d e r As i n d i c a t e d  paramagnetic  con-  by e q u a t i o n ( 1 0 ) t h e d i a m a g n e t i c term i s a  contribution.  I t i s i n f a c t ( 5 7 ) , t h e same as Lamb's  e x p r e s s i o n f o r the d i a m a g n e t i c s h i e l d i n g  o f s i n g l e atoms (69)=  16  The  p a r a m a g n e t i c 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 electrons orbital fields field  s e t up by t h e o r b i t a l m o t i o n s o f t h e v a l e n c e  (70-).  fields  I n t h e absence o f an e x t e r n a l s t a t i c have a z e r o  of several  average value  t h o u s a n d gauss a t t h e n u c l e u s .  shielding.  Since  more r e a d i l y p o l a r i z e d , t h e p r i n c i p a l rather  than  from t h e c l o s e d  artificial  is  i n t o two d i s t i n c t t e r m s i s  of the s h i f t i n t o three  S a i k a and terms:  t h e d i a m a g n e t i c c o r r e c t i o n f o r t h e r e l e v a n t atom.  again  t h e Lamb t e r m .  range o f f l u o r i n e s h i f t s (b)  I t accounts  term i s p r i n c i p a l l y  observed.  responsible  the contributions  electrons  i n other  f o r chemical s h i f t s  from e l e c t r o n s i n o t h e r  atom.  atoms.  The  atoms a r e 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  1 p o l a r i z e d are s t i l l  interaction.  This  i n fluorines.  to p o l a r i z e o r i n valence s h e l l s i n which tha e l e c t r o n s  readily  This  f o r o n l y a b o u t 1% o f t h e  t h e paramagnetic c o r r e c t i o n f o r the r e l e v a n t  (c)  thorn  Ramsey ( 6 7 ) p o i n t e d  of f l u o r i n e chemical s h i f t s ,  ( 7 0 ) made a d i v i s i o n  (a)  c o n t r i b u t i o n i s from  and t h a t t h e terms a r e i n f a c t c l o s e l y r e l a t e d , ,  In t h e i r d i s c u s s i o n Slichter  f i e l d s and  the valence e l e c t r o n s are  shell electrons.  however, t h a t the s e p a r a t i o n  instantaneous  The a p p l i e 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  h e n c e an a p p r e c i a b l e  out,  but p r o d u c e  f i e l d the  subject  to a  The c o n t r i b u t i o n from t h i s  although  i  /r  falling  o f f of the  term i s t h e r e f o r e  small.  17  Although term (b) i s the p r i n c i p a l c o n t r i b u t i o n t o the f l u o r i n e s h i f t , i n the case o f e l e c t r o n s i n a p u r e l y s s t a t e (the e l e c t r o n s e x e r t a z e r o i n s t a n t a n e o u s o r b i t a l magnetic f i e l d a t the n u c l e u s , w h i l e p and d e l e c t r o n s e x e r t l a r g e 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  o f an s s t a t e , the a n g u l a r momentum o p e r a t o r s make the second term o f e q u a t i o n (10) equal t o zero f o r a p u r e l y s state,. term would be zero i n completely i o n i c F  The paramagnetic  because of the f i l l e d L  s h e l l , and have i t s maximum value i n c o v a l e n t F^. Pople (68, Chap. 7) adds a f o u r t h term to S a i k a 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 i n t e r a t o m i c c u r r e n t s .  Ifi t is  p o s s i b l e f o r e l e c t r o n s to flow from one atom to another, as f o r example i n aromatic m o l e c u l e s , the i n t e r a t o m i c c u r r e n t s 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-  e q u i v a l e n t n u c l e i t h e r e w i l l be a broadening of the resonance l i n e due t o 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  n u c l e i i n non-  e q u i v a l e n t 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  is  t h e i s o t r o p i c mean s h i f t  -  v(  f o r nucleus  where  «u 3 S  T v  where 6 ^ ,  "^  S  i ( ° » x + ^ * ^  , and  ............ ( 1 2 a )  a r e t h e p r i n c i p a l axes o f the s h i f t  tensor. Even i f a s o l i d c o n t a i n s o n l y n u c l e i e n v i r o n m e n t s , t h e r e may be a c h e m i c a l broadening. probing  I f the chemical  external field  will  shift  investigation  shift  contribution  electronic to l i n e  tensor,©", i s a s y m m e t r i c , a  encounter d i f f e r e n t e l e c t r o n i c  i n g d e p e n d i n g on t h e m o l e c u l a r The  i n identical  orientation  of chemical  shift  screen-  i n the f i e l d . anisotropy i n poiy-  erystalline  s o l i d s i s based on t h e a p p r o a c h employed by Bloembergen  and  (72) with t h a l l i c  Rowland  express  the f i e l d  erystalline  oxide.  experienced  Andrew and T u n s t a l l ( 7 1 )  by a g i v e n n u c l e u s  i n a poiy-  s o l i d as  where ^-m,  G~^^ a r e a g a i n  and %x> "X.JB »  i f f "  average f i e l d  t h e p r i n c i p a l axes o f the s h i f t  are the d i r e c t i o n  experienced  the p o i y e r y s t a l l i n e  c o s i n e s w i t h r e s p e c t t o H© •  by a l l t h e n u c l e i  .  ~  tensor The  i f the c r y s t a l l i t e s i n  sample a r e 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 e x p r e s s e d  by  ...... (14)  -  19  -  For a x i a l symmetry a b o u t t h e z - a x i s  G^-e^^-Gx  » and 6^"  COS©,  =  and  H= H - K where K - ± H 3 The n o r m a l i z e d  ••• •  0  3  line  ( 1 5 )  and where H and H a r e f i e l d s a t n u c l e u s  shape i s t h e n  «o6» CiV5dT 6+f)" ,  (")  %  2 3  where - a ^ K —  The  ~0  C  0  0  f u n c t i o n f ( h ) i s s i m i l a r i n form t o e q u a t i o n ( l ) . The  s e c o n d moment o f t h e l i n e  shape g i v e n by e q u a t i o n ( 1 6 )  (17) and  i f the d i p o l a r  normalized is  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 ,  l i n e - shape f u n c t i o n g ( h ) t h e n t h e t o t a l  l  1  (18)  i  c o r r e c t c e n t e r o f moments i s n o t r e a d i l y a p p a r e n t  mmetric curve,  but i f f i r s t  center  ( t o minimize  moment g i v e s t h e c e n t e r o f moments d i r e c t l y be t r a n s f e r r e d t o i t .  plotted against H  6  i n an a s y -  and s e c o n d moments a r e computed  a p o i n t c l o s e t o the e s t i m a t e d  can  moment  ( 7 1 , 73)  V3»^4i (k)''3iW»^K,Ve ,-« V The  second  about  e r r o r ) the f i r s t  and t h e second  moment  I f t h e t r a n s f e r r e d s e c o n d moment i s  , the a b s o l u t e v a l u e o f t h e a n i s o t r o p y o f  -  chemical s h i f t  20  c a n bs d e t e r m i n e d .  from t h e d i r e c t i o n  The s i g n can be found  o f asymmetry o f t h e c u r v e .  The a n i s t r o p y  may be used t o p r o v i d e i n f o r m a t i o n a b o u t t h e t y p e o f b o n d i n g i n the  s o l i d studied,,  the  d i p o l a r second  The i n t e r c e p t o f t h e p l o t w i l l moment, and t h i s  give  c a n be used as a b r o a d e n i n g  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 ( 1 6 ) t o s y n t h e s i z e a curve f o r comparison  w i t h t h e e x p e r i m e n t a l curve,,  p o l a t e d " d i p o l a r moment" w i l l  The e x t r a -  o f c o u r s e i n c l u d e any f i e l d  indepen-  dent broadening w h i c h i s p r e s e n t . If  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 a r e p r e s e n t t h e  second moment e q u a t i o n becomes  Here t h e e x p r e s s i o n s (<S|~ S ^ e t c . a r e as i n e q u a t i o n s ( l l ) and ( 1 2 ) and  C6 — £5j[) i s tt  a  n  average  s h i f t e d resonant n u c l e i . shifted  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 " Unless the various n u c l e i are s u f f i c i e n t l y  from one a n o t h e r t o p e r m i t a c o n f i d e n t r e s o l u t i o n o f t h e .  c u r v e i n t o i t s components ( i n w h i c h  case the i n d i v i d u a l  may be d e t e r m i n e d a l s o ) t h e i n t e r p r e t a t i o n o f t h e r e s o n a n c e may be v e r y  difficult.  spectrum  CHAPTER I I I  EXPERIMENTAL  PROCEDURE  The SF. * AsF , I F _ • AsF_ , and UJF,. s a m p l e s s u p p l i e d by 4 b / b b Dr. N e i l SF  4  B a r t l e t t were p r e p a r e d by D r . S.P. B e a t o n .  • AsF  5  and I F /  • AsF 5  s a m p l e s mere u s e d .  s a m p l e s and s a m p l e s doped w i t h were r u n .  In the l a t t e r  the s i g n a l  pure  F o r UJF both p u r e b  I r F (up t o one p a r t p e r t h o u s a n d ) b  c a s e t h e p a r a m a g n e t i c i m p u r i t y was added  to shorten the s p i n - l a t t i c e and i m p r o v e  Only  relaxation  time, reduce  saturation,  t o n o i s e r a t i o i n t h e s p e c t r u m by p e r m i t t i n g  t h e r u n s t o be made a t h i g h e r r f f i e l d  (H  field).  (  S p e c t r a were  r e c o r d e d o v e r a two y e a r 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 s a m p l e s o f e a c h compound.  A t t h e end o f t h e s t u d y c o m p a r i s o n s were made b e t -  ween r e c e n t s a m p l e s and s a m p l e s s t o r e d  f o r more t h a n a y e a r .  Between r u n s s a m p l e s were s t o r e d i n a d r y - i c e a c e t o n e b a t h or liquid  nitrogen. The f l u o r i n e m a g n e t i c r e s o n a n c e s p e c t r a o f t h e compounds were  r e c o r d e d on two V a r i a n 4 2 5 0 - t y p e  b r o a d l i n e s p e c t r o m e t e r s , 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 o f t h e broad  line  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 e l e c t r o m a g n e t and a 56.4 MHz V-4311 F i x e d  F r e q u e n c y RF U n i t .  The o t h e r broad  lina  s p e c t r o m e t e r e m p l o y e d a M a r i a n 6 i n c h e l e c t r o m a g n e t and a 30 MHz .V-431GA  Fixed  F r e q u e n c y RF U n i t and a 2-16 MHz V-4210A  F r e q u e n c y RF U n i t  0  Variable  The 2000 Hz s i d e b a n d s o f t h e V-3521A  21  Integrator/  -  Decoupler  were u s e d  S i n c e the r e s o n a n c e 2000 Hz,  -  to p r o v i d e sweep m o d u l a t i o n on t h e HA100. l i n e s o f t h e s o l i d s were v e r y much w i d e r  the r e s u l t i n g s p e c t r a were t h e f a m i l i a r d e r i v a t i v e  c u s t o m a r i l y observed of  22  calibrating  recording  i n broad  l i n e work.  S i n c e the n o r m a l  the m o d u l a t i o n a m p l i t u d e of a l o c k - i n  the d e r i v a t i v e  of a l i q u i d  in  d e t e r m i n i n g the a m p l i t u d e o f t h e m o d u l a t i o n .  liquid to  problem  s i g n a l i s scanned,  t h e r e i s a known m o d u l a t i o n i n d e x from w h i c h tude may  be d e t e r m i n e d  (74).  This required  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 difficult  to reproduce  was  However, when a be a d j u s t e d  Then a t t h a t p o i n t the m o d u l a t i o n a m p l i adjustment  o f the  o f runs  always s i m p l e t o ensure t h a t the  gauss peak t o p e a k ) and  A more s e r i o u s p r o b l e m  was  and  encountered  laborious.  was  safe  signal.  signal  to n o i s e r a t i o .  on t h e two  broad, l i n e  was  in obtaining a B a l a n c i n g and  O p e r a t i o n on wide  I t a l s o produced  pure phas-  line  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 q u i c k e r and s u r e r than phase d e t e c t i o n .  with-  amplitude  that modulation broadening  a b s o r p t i o n d e r i v a t i v e of the resonance were q u i t e c r i t i c a l  I t was  on a s t r i p r e c o r d e r each  below t h e p o i n t o f known a m p l i t u d e w h i c h i n i t s e l f  absent.  encountered  t h i s e x a c t v a l u e f o r each s e r i e s  However, i t was  ( a b o u t 1.2  ing  was  on  o f the i n s t r u m e n t .  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 time.  d e t e c t o r by  t h e I n t e g r a t o r / D e c o u p l e r may  g i v e z e r o a m p l i t u d e f o r t h e c e n t e r band.  signals method  l i n e c o u l d n o t be used  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  than  was  a batter  S t a n d a r d o p e r a t i n g p r o c e d u r e s were employed spectrometers.  23  The temperature dependence of the f l u o r i n e magnetic resonance o f o r a l l three compounds from 77 K to o o o above 300 K and f o r a few temperatures from 173 K to 283 K a t 94.1  s p e c t r a mas s t u d i e d at 30 MHz  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 n i t r o g e n vapour' passed through a flow system which has been d e s c r i b e d by UJare  (75).  o  Below about 220 K a l i q u i d n i t r o g e n bath was used to c o o l the g a s  0  Between 2 2 0 ° K and room temperature a d r y - i c e acetone bath was used. Above room temperature, heated, compressed the  tank n i t r o g e n .  a i r was used i n place of  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 6 0 0 V / c y l i n d r i c a l heating 1  c o i l , designed by Ui.R. 3anzen f o r h i s work i n t h i s  laboratory.  Temperature c o n t r o l was a p p r o x i m a t e l y +5° around 100°K and +1° above 150°K.  At 94.1 MHz  the standard V a r i a n V/-4341 V a r i a b l e  Temperature  System was used. The temperature range of t h i s system i s s t a t e d to o o be -50 to +200 C, but i t was found t h a t -100 C could be reachedo The maximum temperature v a r i a t i o n a t the sample i s +1°C w i t h i n 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. The Ho f i e l d dependence of the spectrum of each compound was s t u d i e d at the f o l l o w i n g temperatures and RF frequencies (He Compound SF o AsF  5  IF  5  4  ?  . AsF  Temperature 295-300 77 295-300 77 173 77  K  field).  RF Frequency MHz 94.1, 56.4, 40, 30 94.1, 56.4, 94.1, 56.4, 94.1, 56.4, 94.1 94.1, 56.4, 16, 2  40, 30, 16 40, 30 40, 30 40, 30,  -  For  24  -  b o t h IF„ • AsF,_ and UJF^ u s a b l e s p e c t r a c o u l d n o t be o b t a i n e d / 5 6  77°K and 94.1 UlHz due  to the r e s t r i c t i o n  on sample  size  at  explained o  below.  However, a 5 mm  94.1 MHz  using  d i a m e t e r sample  o f UJF^ r u n a t 173 K  and  the V-4341 t e m p e r a t u r e s y s t e m d i d p r o d u c e u s a b l e o  spectra.  For the f i x e d  t e m p e r a t u r e work a t 77 K, t h e s a m p l e s  immersed i n d e w a r s f i l l e d w i t h been d e s c r i b e d 94.1 MHz mm  would  elsewhere (75, 76).  i n t h e HA100 s e v e r e l y  capillaries hold  liquid nitrogen. The  The dewars have  dewar (5 mm  restricted  were  sample  O.D. ) used  at  s i z e to about  1,6  and had the b a r e l y s u f f e r a b l e d i s a d v a n t a g e t h a t i t  l i q u i d nitrogen  f o r only  four to s i x minutes.  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 same sample  size restriction,  b l o w e r , Mr.  Rak.  A dewar  of course w i t h  was made by t h e D e p a r t m e n t ' s  T h i s dewar h e l d n i t r o g e n  the  glass-  f o r more than two  hours  b u t c o u l d n o t be removed from t h e probe w i t h o u t f i r s t t a k i n g t h e latter  o u t o f t h e magnet The  samples  gap.  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 , t h e  s p e c t r a o f w h i c h were i n d e p e n d e n t o f o r i e n t a t i o n i n the m a g n e t i c M© •  field  P r e l i m i n a r y s p e c t r a were s c a n n e d up t o 500 gauss  e i t h e r s i d e o f r e s o n a n c e t o e s t a b l i s h t h a t t h e r e s o n a n c e was f i n e d t o t h e r e g i o n s t u d i e d i n expanded quency for 0.05  (He  scale.  The  f i e l d W u-as v a r i e d o v e r a wide  mgauss t o 45 mgauss.  w i d t h s remained  t  Ulhan an r f r e g i o n was  c o n s t a n t as the power was  con-  A l s o , a t each  f i e l d ) p r e l i m i n a r y s p e c t r a were r u n t o check  saturation.  on  fre-  the r f l e v e l  range  from  f o u n d where  about  line  l o w e r e d , f o r w a r d and r e -  25  v e r s e s c a n s mere r u n t o check t h a t l i n e directions.  shape was  Ufhen an a p p a r e n t l y s a t i s f a c t o r y  the r f l e v e l was  further  l i n e shape changes  reduced to a s c e r t a i n  occurred.  t h r e e s t e p s were n e c e s s a r y .  t h e same f o r b o t h  l e v e l had t h a t no  I n g e n e r a l , i t was  been f o u n d additional  found t h a t a l l  S i n c e a t l e a s t two c h e m i c a l l y  f l u o r i n e n u c l e i were p r e s e n t i n e a c h m o l e c u l e , s a t u r a t i o n p r o d u c e d sometimes  s u b t l e changes  e n t l y s a f e power l e v e l 0.5  to 1.0  mgauss  effects  i n t h e s p e c t r a a f t e r an a p p a r -  had e l i m i n a t e d  was  shifted  the gross e f f e c t s .  Around  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  a l w a y s c h e c k e d o v e r a r a n g e o f r f power f o r s i g n s o f s a t u r a t i o n , o At 77 K, t h e 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 p o o r p a c k i n g f a c t o r i n t h e r e c e i v e r c o i l .  Since  the s a t u r a t i o n l e v e l was t i m e the r f was was  fairly  low (Hi  under 1.5  r e d u c e d below s a t u r a t i o n ,  poor i n some c a s e s .  and sample s i z e , and  The  actual ratio  mgauss) by t h e  the s i g n a l  to noise  v a r i e d d e p e n d i n g on  on t h e RF u n i t u s e d and i t s o p e r a t i n g  ratio sample  condition.  A h i g h sweep m o d u l a t i o n c o u l d n o t be u s e d t o i m p r o v e t h e s i g n a l n o i s e r a t i o s i n c e m o d u l a t i o n b r o a d e n i n g would of s t r u c t u r e which would  have t o t a l l y  have c a u s e d a l o s s  f r u s t r a t e d attempts to r e s o l v e  t h e 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. a m p l i t u d e u s e d ( a p p r o x i m a t e l y 0.5  At t h e low m o d u l a t i o n  gauss peak t o p e a k ) , m o d u l a t i o n  c o r r e c t i o n t o t h e s e c o n d moment was  negligible,  s i g n a l t o n o i s e r a t i o had o f t e n t o bs t o l e r a t e d . about 4:1  to  but a r e l a t i v e l y Ratios varied  i n some u n f a v o u r a b l e c a s e s a t 77°K t o 45:1  under  good  low from  -  26  -  c o n d i t i o n s a t room temperature. No r e f e r e n c e sample urns used i n the runs w i t h v a r i a b l e tempe r a t u r e equipment or w i t h the l a r g e dewar on the HA100, but a CF„C00H or C.F, r e f e r e n c e was used i n the Ho f i e l d dependence runs 3 6 6 at 77°K and 300°K.  S i n c e 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 c o n c l u s i o n of the experiments.  The s h i f t was + 7 6 2 1 0  Two sidebands were imposed on the r e f e r e n c e ' s f l u o r i n e w i t h a Hewlett Packard model 200CD Audio O s c i l l a t o r . H»was scanned proceeded,  ppm.  resonance The  field  through one of the sidebands and, while scanning  the r e f e r e n c e was  r e p l a c e d by the sample, the probe  rebalanced i f necessary and the spectrum  recorded.  The sample  was then r e p l a c e d by the r e f e r e n c e and the other sideband recorded. The p o s i t i o n of the r e f e r e n c e resonance was taken as the midpoint between the two s i d e b a n d s . A minimum of f o u r s p e c t r a were recorded at each i n the temperature dependence runs. runs, except at 94.1  IYIHZ  temperature  In the H» f i e l d dependence  where machine time was i n great demand,  at l e a s t four r e f e r e n c e d s p e c t r a were recorded at each frequency o o at 300 K and ten to twelve at 77 K, the temperature of g r e a t e s t interest.  In a d d i t i o n , a t l e a s t a dozen non-referenced s p e c t r a o  were run f o r each sample a t each frequency at 77 K and 300  o K.  CHAPTER IV  RESULTS & INTERPRETATION  Programs w r i t t e n f o r t h e U n i v e r s i t y o f B r i t i s h IBM  7040 computer p l a y e d  evaluating gether  the r e s u l t s  an e x t e n s i v e  obtained  with explanations  Samples o f a l l t h r e e SF^  • AsF^  or l i q u i d  o f wT  mentally  1.  The  programs a r e  and  listed  to-  I.  , IF  • AsF  ,  and  a p p e a r e d 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 a c e t o n e n i t r o g e n baths.  T h e r e was  s p e c t r a o f t h e same s a m p l e s t a k e n storage.  part i n determining  here.  i n Appendix  Columbia's  Spectra  no  change e x h i b i t e d between  a f t e r more than one  year  of  o f a l l s a m p l e s o f t h e same compound were e x p e r i -  c o n s i s t e n t w h e t h e r o l d or f r e s h l y  supplied.  Results Although  s a m p l e s w h i c h were doped w i t h p a r a m a g n e t i c  IrF o  could  be r u n  signal  at a higher  to n o i s e  identically  ratio,  r f ( H ^ ) w i t h a r e s u l t a n t more  b o t h p u r e and  within experimental  doped s a m p l e s o f UJF  error.  Therefore  i s made between pure or doped s a m p l e s i n the F i g u r e 1 d e m o n s t r a t e s the  favourable  no  results  behaved  distinction reported.  t e m p e r a t u r e dependence o f  the  19 F nmr  s p e c t r a of 'wT^  a common x - s c a l e and  a t 30 IYIH .  being  The  normalized  27  -  absorption spectra to c o n s t a n t  area,  having  were  To Follow Page 27  To F o l l o w Page 27  F i g u r e 2,  WF\/.  Temperature dependence o f 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  T E M P E R A T U R E  2  °K  4  0  2  8  0  -  obtained  by i n t e g r a t i o n  2, A p p e n d i x  I.  28  -  from t h e d e r i v a t i v e c u r v e s u s i n g  Program  R e p r o d u c t i o n s o f d e r i v a t i v e c u r v e s f o r tempera-  t u r e d e p e n d e n c e a t 30 MHz and a l s o a t 94.1 rnHz a r e 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 t h e  s e c o n d moment a t 30 MHz ( c a l c u l a t e d w i t h Program using  t h e method o u t l i n e d  and 9 4 . 1 MHz (between  1, A p p e n d i x I  t h e r e ) and t h e l i n e w i d t h a t 30 MHz  e x t r e m e maxima and minima o f t h e 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 o f t e m p e r a t u r e . 2 s e c o n d moment r e m a i n s c o n s t a n t a t 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 s e e n i n F i g u r e 1, t h r o u g h o u t The  this  r e g i o n t h e r e i s an asymmetry t o h i g h f i e l d w h i c h d i s a p p e a r s  o 2 as t h e s e c o n d moment d r o p s between 180 and 220 K t o 1.0+.05 gauss . During 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 t o a s y m m e t r i c d e r i v a t i v e c u r v e a t 205 t o 210°K.  The s e c o n d moment r e m a i n s c o n s t a n t a t 1.0 gauss  to 262°K.  Beyond t h i s  region  t h e r e i s a sudden  from 220  d r o p between 262  o and 265 K t o a v a l u e w h i c h c o u l d n e t be a c c u r a t e l y measured the  derivative The  from  curve.  b e h a v i o u r o f t h e l i n e w i d t h a t 30 MHz f o l l o w s t h e 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 g a u s s from 77 t o 180 K, d r o p p i n g t o 3.2+0.1 gauss by 2 z 0 K and dropping again (after  r e m a i n i n g c o n s t a n t a t 3.2 g a u s s ) around 262  o o t o 265 K t o a v a l u e o f 0.1 gauss as measured a t 269 K. the  Although  l i n e w i d t h measurement c a n be made between 265 and 287°K, i t  -  is  29  -  g o v e r n e d by the d e p t h o f m o d u l a t i o n w h i c h was  peak.  The  spectra i n this  or below the m e l t i n g  point  o a t 265.0 K,  transition  and  to c u b i c  o p o i n t a t 276.4 K,  a l l had  However, i n t e n s i t i e s  the  g a u s s peak to  whether taken  o f 276°K ( o r t h o r h o m b i c  melting  290.3-290.7°K ( 2 0 , 2 6 ) ) spectra.  r e g i o n were s i m i l a r  0.1  and  boiling  than and  lines  /  same f i e l d .  The  (CF^COOH a t 298  l i q u i d within this  range  V a r i a b l e t e m p e r a t u r e s p e c t r a a t 94.1 similar  b e h a v i o u r t o t h o s e a t 30 MHz.  of 12.0+0.3 gauss between 173 still has  present  although  n a r r o w e d t o 11.1  widths are  plotted  the t r a n s i t i o n s and 94.1  identical MHz  indicate  183°K.  l i n e width  i n Figure  3 there  are  MHz.  above the nmr  (111Hz ( A p p e n d i x  By  and  at ~  the 94.1  the samples i n t h e  two  the narrow l i n e r e g i o n  cases.  to f i x  and  185-205°K  there.  s p e c t r a appear to i n d i spectra.  This  temperature gradients  along  30 MHz  In a d d i t i o n a l l 94.1  appear to e x h i b i t  line  behaviour  a t 30 MHz  point  to d i f f e r e n t ,  Although  similar  taken  line  derivative  The  Above the m a l t i n g  be due  order  the  enough p o i n t s  dependent broadening  d i f f e r e n c e may  and  not  field  than- the  l i b ) show  i s o f the  270°K the  absence of  c a t e more l i q u i d - l i k e c h a r a c t e r  the  193°K, asymmetry i s  transition  MHz  in  (265-2B7°K).  3.1+0.1 gauss.  l i n e w i d t h s of the s p e c t r a region  K)  to disappear,  Between 223  a c c u r a t e l y a t 94.1  i n the the  with  were  r e a l l y more l i k e  Line width  i t i s beginning  gauss.  curve i s symmetrical  and  point  o \  a p p e a r a n c e o f the s p e c t r u m was  that of a v i s c o u s  crystal  appearance of l i q u i d - l i k e  were l e s s  broader than t h a t of a l i q u i d s i g n a l  above  MHz  spectra in  a s m a l l amount o f d i s p e r -  30  s i o n which  could not  be b a l a n c e d  t h i s m i g h t be a l o w , c u l e s undergoing  less  t h e narrow l i n e . brought  i t was  MHz  may  t o remove c o m p l e t e l y  The  MHz  of moleproducing be  t h a t the e f f e c t was  prob-  o f a s m a l l amount of d i s p e r s i o n mode i n was  n o t p r e s e n t a t 30 MHz, i t s  l i e i n an i n a b i l i t y  i n t h i s width region  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  to provide modulation. t h e 94.1  thought  components" c o u l d n o t  decided  S i n c e the d i f f i c u l t y  a t 94.1  i t was  peak i n d i c a t i n g a p e r c e n t a g e  However, t h e "two  to the presence  the s i g n a l .  Initially  f r e q u e n t r e o r i e n t a t i o n than those  i n t o phase and  a b l y due  origin  broad  out.  At t e m p e r a t u r e s  below t h e nmr  transition  s p e c t r a were q u i t e satisfactory„  r e s u l t s a g r e e w e l l , w i t h one  tained independently  by B l i n c  F i g u r e 8) p l a c e s t h e low  (41).  temperature  e x c e p t i o n , with, those  H i s second nmr  ob-  moment p l o t ( h i s  t r a n s i t i o n a t the same 2  p o i n t as found is  here.  His r i g i d  l a t t i c e second  o f c o u r s e somewhat h i g h e r due  higher f i e l d  of h i s experiment  a t 30 MHz).  I t i s even s l i g h t l y  obtained  by i n t e r p o l a t i n g  certainly within line  moment of 9 5  gauss  0  t o the i n c r e a s e d a n i s o t r o p y a t  the  (9500 gauss as a g a i n s t 7500 gauss h i g h e r t h a n the v a l u e o f 9„1  our r e s u l t s a t 9500 g a u s s ,  tha r e p r o d u c i b i l i t y  o f an nmr  gauss  but i s  experiment.  His  w i d t h o f about 10 gauss a t 7250 gaus's f i e l d i s t h e same as  our  v a l u e i n t e r p o l a t e d a t t h e same f i e l d and h i s 3 gauss l i n e w i d t h a t o . -41 C a t 9500 gauss i s a g a i n i n a g r e e m e n t . ( B l i n c ' s l i n e widths «<  were e s t i m a t e d  from  his Figure 5).  However h i s v a l u e o f about  31  1.8 gauss  (estimated  200°K nmr t r a n s i t i o n  from h i s F i g u r e i s significantly  8) F o r t h e r e g i o n above t h e higher  than o u r v a l u e o f  2 1.0+0.05 gauss .  Since  the anisotropy  has been a v e r a g e d o u t 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 broadening. it  Since  i s unlikely  line  widths  from f i e l d  a p p e a r t h e same i n b o t h s t u d i e s ,  t h a t t h e 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 o r  modulation broadening i n B l i n c ' s s p e c t r a . s a t u r a t i o n narrowing great  The s p e c t r a o b t a i n e d  have an e x c e l l e n t s i g n a l  to noise  f r o m them a r e t h e r e f o r e c o n s i d e r e d  since  the r f ( H ) . l e v e l .  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  of the s p e c t r a . and  The a l t e r n a t i v e t h a t  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  c a r e was e x e r c i s e d i n c o n t r o l l i n g  discrepancy  dependent  The  the t a i l s  here a r e i n expanded s c a l e ratio.  The s e c o n d moments  quite accurate.  The  lower  s e c o n d 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 be d i s c u s s e d  temperature r e g i o n .  This  later.  F i g u r e 4 shows t h e f i e l d UJFg s p e c t r u m a t 77°K.  dependence o f t h e c e n t r o i d o f t h e  The c h e m i c a l  shift,  measured w i t h  respect  t o an e x t e r n a l sample o f C F ^ O O H a t 295°K, i s -255+40 ppm. culated relative value  will  Cal-  t o HF i t i s -380+40 ppm compared w i t h B l i n c ' s  o f -440+20ppm  o  This i s not r e a l l y  when t h e method u s e d t o o b t a i n  the s h i f t  a significant difference (see Chapter I I I ) i s  considered,, In F i g u r e 2 t h e c o n s t a n t  o o s e c o n d moment from 77 K t o ~ 180 K  S S f l V O ± d l H S OldOd-LOSI  NV3IAI  -  32  s u g g e s t s t h a t , e x c e p t f o r w h a t e v e r z e r o p o i n t m o t i o n o f t h e atoms o may be p r e s e n t ,  t h e wT^. l a t t i c e  i s rigid  a t 77 K.  o f t h e s e c o n d moment i s i n i t s e l f no a b s o l u t e but  as w i l l  calculated  be s e e n below i t i s s u p p o r t e d theoretical  rigid  lattice  The c o n s t a n c y  guarantee of r i g i d i t y ,  by c o m p a r i s o n w i t h t h e  s e c o n d moment.  The a n i s o o  tropy  o f t h e UiF^ s p e c t r u m c a n t h e r e f o r e be s a f e l y  s t u d i e d a t 77 K, some  o  100  below t h e t r a n s i t i o n where m o t i o n a v e r a g e s o u t t h e e f f e c t .  field in  dependence o f t h e average a b s o r p t i o n  Figure  curves  5 a t 2, 16, 30, 40, 56.4, and 94.1 MHz.  derivatives  typical  s o r p t i o n curves  of the spectra recorded  have a common x - s c a l e  The  a t 77°K i s shown Appendix l i e g i v e s  f o r Figure  and a r e n o r m a l i z e d  5.  The abto constant  area. The 16 MHz s p e c t r a n o t q u i t e c o n s i s t e n t w i t h t h e o t h e r s . I n c o n t r a s t t o UF ( 3 8 , 39, 41) t h e r e i s v i r t u a l l y no r e s o l u t i o n o f t h e b s p e c t r a e x c e p t a t 94.1MHz. A t t h i s f r e q u e n c y , t h e s p e c t r a were o  actually  taken  a t 173-175 K.  However, as i s a p p a r e n t below,  seems t o have been s u f f i c i e n t l y o b t a i n a v a l i d spectrum. i d e n t i c a l with Blincs. 40 and  little  lattice frequency  a r e very s i m i l a r  appear  t o h i s 7250  As o u r s p e c t r a and the p l o t o f t h e f i e l d a t 77°K i n F i g u r e 6 i n d i c a t e ,  change i n l i n e w i d t h  there  over the e n t i r e range of f i e l d s  0.5;.Kgauss a t 2 MHz up t o 2 3 . 5 i K g a u s s a t 94.1 MHz. one has  region to  The d e r i v a t i v e s a t 30 MHz (7500 g a u s s ) and  MHz ( 1 0 , 0 0 0 g a u s s ) i n A p p e n d i x H e 9500 g a u s s s p e c t r a .  the r i g i d  The s p e c t r a a t lower  dependence o f the l i n e width is  into  this  from  The change as  goes t o l o w e r f r e q u e n c y i s r e a l l y o n l y a s l i g h t n a r r o w i n g w h i c h t h e e f f e c t o f f i l l i n g i n t h e s h o u l d e r on t h e h i g h f i e l d s i d e  To F o l l o w Page 32  To F o l l o w Page 3 2  F i g u r e 6.  O'  WF^.  F i e l d dependence o f l i n e w i d t h a t 77°K  5000  15,000  FIELD (H ) Q  GAUSS  25,000  33  o f the s p e c t r a w i t h s c a r c e l y stages of the i n v e s t i g a t i o n  -  any change i n h e i g h t . i t was t h o u g h t  that saturation  might be i n v o l v e d , b u t t h i s was l a t e r r u l e d shown t o be g e n u i n e  by c a r e f u l  2.- R e s o l u t i o n a t t e m p t s I t was e x p e c t e d  checks  At i n i t i a l effects  o u t and t h e e f f e c t  of the r f (^)  level.  - 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  t h a t \11F l i k e U C  would probably  C  b  have a d i s -  o  t o r t e d s t r u c t u r e a t low t e m p e r a t u r e s .  T h e r e would l i k e l y  s h o r t e q u a t o r i a l bonds and two l o n g a x i a i s h i f t tensors e x h i b i t i n g  axial  be f o u r  bonds w i t h t h e c h e m i c a l  symmetry a l o n g t h e bond  f o r such a m o l e c u l e 6 , = fi„ = 6 „ = <S. = €> and 6 1 = 1 2 3 4 e 5 E q u a t i o n ( 1 9 ) t h a n becomes  direction. = ^ . 6 a  vj^^^r^-^^fe-^*jf4-«-)*J €  a  and &  e  correspond r  ••  <2o)  t o t h e c e n t e r s o f z e r o f i r s t moment o f t h e  r e s o l v e d a x i a l and e q u a t o r i a l inside  Shifts  final  term  the square  shift  of t h e components.  components o f t h e t o t a l b r a c k e t s i s the r e l a t i v e  curve.  The  chemical  T h i s e q u a t i o n i s g i v e n w i t h an i n c o r r e c t  f a c t o r o f 6 i n s t e a d o f 2/3 b e f o r e  this  term  by B l i n c  (41).  It is  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 gives aoproximately  The a v e r a g e d  second  h i s reported results  f o r IIF . 6  moments o f t h e s p e c t r a t a k e n a t 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 t h e s q u a r e field  (H )„  of. t h e  F i g u r e 7 sho ws t h a t , as p r e d i c t e d by e q u a t i o n ( 2 0 ) ,  the p l o t g i v e s a s t r a i g h t the z e r o f i e l d  line.  The e x p e r i m e n t a l v a l u e o f g ( h ) ,  broadening," o b t a i n e d from  the i n t e r c e p t i n Figure 7  To F o l l o w Page 33  F i g u r e 7.  WF^*  F i e l d squared dependence o f second moment a t 77  A  O  I O O  FIELD  2  0  0  SQUARED  3  0  0  (H|)  =  B L I N C  4  0  0  ( 4 1 )  5  0  KILOGAUSS  0  2  34  is  8.2+0.2 gauss .  lattice  This i s considerably  s e c o n d moments p u b l i s h e d  fluorides  2 (4 t o 5 gauss , but no  Initial the 2 and  B l i n c (41)  v a l u e mas  94.1  MHz  spectra. 16  I t was  t o 56.4  of ths p r o b a b l e  MHz  two  given  chemical  shift  and  over the  Spectra  of  deter-  components would be u n l i k e l y .  an a v e r a g e a n i s o t r o p y  could  Since  would l i k e l y  be  be  relative  determined.  s e r i e s o f r e s o l u t i o n a t t e m p t s w h i c h showed  most p l a u s i b l e a t one  satisfactory  running  lack  s p e c t r a t h a t an e x a c t  t h a t a l a r g e v a r i e t y o f r e s o l u t i o n s was and  to  hoped, h o w e v e r , t h a t a t l e a s t a  Thus began a t i r e s o m e  hexa-  f o r WF -). o  o b v i o u s from the  t h e a n i s o t r o p i e s o f the c o m p o n e n t s , i f p r e s e n t , q u i t e s i m i l a r i t was  rigid  for other  a t t e m p t s a t r e s o l u t i o n mere made p r i o r  r e s o l u t i o n i n the mination  by  l a r g e r t h a n the  full  p o s s i b l e , some  or more f i e l d s ,  promising  but none o f w h i c h  was  range.  were run a t 2 MHz  t o d e t e r m i n e a good  approximation  to  the z e r o f i e l d l i n e s h a p e . The a v e r a g e s e c o n d moment was 2 2 8.25 gauss , i n s p l e n d i d a g r e e m e n t w i t h the 8-. 2 gauss extrapolated value. height  The  or w i d t h  HA100 and a t 94.1  line  shape was  but w i t h l i t t l e  from the shape a t h i g h e r  i t s 23.5  fflHz.  symmetrical  fields.  These s p e c t r a c o m p l e t e d f i e l d squared.  ths s t r a i g h t l i n e The  Warian  one  from t h e  other.  run  p l o t of  improved r e s o l u t i o n i n  t h e s p e c t r u m gave p r o m i s e t h a t t h e r e were two be s e p a r a t e d  When the  Kgauss f i e l d became a v a i l a b l e , s p e c t r a were  s e c o n d moment a g a i n s t  could  change i n  components w h i c h  There was  some c o n c e r n  that  35  since  t h e s p e c t r a were r u n a t 173 K, they m i g h t n o t be w i t h i n t h e  rigid  lattice  line  r e g i o n , b u t t h e a v e r a g e d second moment l i e s  of Figure  7 and t h e s p e c t r a seem  Unfortunately at a l l  0  whose a r e a  (high  The c h e m i c a l  I f i n equation  zero, the slope maximum v a l u e  symmetrical  about i t s midpoint  r a t i o s are a q u i t e precise 4 (low f i e l d ) to 2  field).  270+5 ppm.  matters  8) t o d e f i n e two w e l l r e s o l v e d  p e a k s each o f w h i c h i s v i r t u a l l y and  valid.  t h e 94.1 MHz s p e c t r a do n o t c l a r i f y  They a p p e a r ( s e e F i g u r e  on t h e  shift  between t h e peaks i s a b o u t  (20) the anisotropy  i s put equal to  o f t h e s e c o n d moment l i n e i n f i g u r e 7 g i v e s a  o f 220+10 ppm.  The agreement between t h e s h i f t s i s  p e r h a p s h o t t o o bad, b u t i f t h e UJFg s p e c t r u m i s composed o f two, symmetrical, should  isotropically  by s h i f t i n g  to low r a t h e r  ratios  experimental fails  area  i s main-  F i g u r e 0 shows c u r v e s  As t h e f i g u r e i n d i c a t e s t h e c o n s t r u c t e d  agree w e l l w i t h  resolves  i s lowered.  ( i f constant  curve  constructed  t h e two components r e s o l v e d a t 94.1 MHz by 270 ppm a t  each f i e l d .  area  peaks, t h e e x p e r i m e n t a l  n a r r o w and i n c r e a s e i n h e i g h t  t a i n e d ) as t h e f i e l d  and  shifted  the experimental  than high  field.  t h e 2 IVIHz c u r v e  curves  two s i m i l a r  ( F i g u r e 9) a c o n s t r u c t e d curve  at higher  dc n o t  and even i n d i c a t e t a i l i n g  I f one a c c e p t s  into  curves  curve  t h e 220 ppm  shift  components o f 4:2  can be f i t t e d  to the  a t 15 and 30 MHz w i t h q u i t e good agreement but  fields.  I f a 220 ppm r e s o l u t i o n i s a t t e m p t e d a t  To F o l l o w Page 35 F i g u r e 8. WF^. S y m m e t r i c a l component r e c o n s t r u c t i o n f r o m 94.1 MHz spectra  HIGH FIELD —5*0  5G  > i « t i i  Solid Una experimental Broken line  constructed  To Follow Page 35  Figure 9. WF^.  Symmetrical component r e c o n s t r u c t i o n from 2 KHz spectra  36  94.1  MHz, t h e 4:2 a r e a Prior  r a t i o c a n n o t be m a i n t a i n e d  to running  t h e 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 o f t h e f a i l u r e cal  shift  t o r e s o l v e t h e components, t h e c h e m i -  between t h e 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 m i g h t be s o  s m a l l t h a t t h e r e were s i x e s s e n t i a l l y In  t h i s case e q u a t i o n  345+20 ppm.  (20) reduces  equivalent fluorines  t o equation  presentc  ( 1 8 ) and  =  As i n d i c a t e d i n B l o e m b e r g e n ( 7 2 ) , Andrew ( 7 1 ) and  Abragam ( 5 2 , p„ 2 0 6 , 2 2 0 ) a c u r v e comparison with the experimental  F ( H ) may be s y n t h e s i z e d f o r curve.  The form o f t h e f u n c t i o n  is + 09  HH)--  J -f(Ho-H*)s(H-H>JH< 0  where f (Ho-H ) = - f ( h ) as d e f i n e d i n e q u a t i o n applied  field  a t the c e n t r o i d o f the spectrum, H  meter and Ho i s t h e a p p l i e d f i e l d . curves The  to high f i e l d .  i s the  i s a general  para-  The a s y m m e t r i e s o f t h e e x p e r i m e n t a l  Therefore  t h e s i g n o f |<5^j-6jJ i s p o s i t i v e .  d e t e r m i n a t i o n o f (is^-6j) d e f i n e s f (Ho-H ) and f o r t h e b r o a d -  ening Use  tail  (16), H  f u n c t i o n , S(H-Ho), t h e e x p e r i m e n t a l  of the experimental  mation t o the f i e l d a gaussian  curve  should  c u r v e a t 2 MHz i s u s e d .  p r o v i d e a much b e t t e r a p p r o x i -  independent broadening  l i n e shape h a v i n g  as has been done p r e v i o u s l y .  f o r computing.  the assumption of  the e x t r a p o l a t e d zero f i e l d The f u n c t i o n was c a l c u l a t e d  Program 3, A p p e n d i x I where i t i s e x p r e s s e d suitable  than  s e c o n d moment using  i n a form  The c o n s t r u c t e d c u r v e s  a r e shown i n  37  F i g u r e 10.  B e c a u s e o f the r e l a t i v e l y  (8.2 gauss ) e x p e r i m e n t a l  broadening  curves are n e a r l y s y m m e t r i c a l Trials  -  MHz)  approximation  function.  t h e observed  l i n e shape.  symmetry o f t h e i r  w i t h i n i t s r a n g e and account the  non-equivalent  f o r the l i n e shape.  MHz  of s i x l i k e  s p e c t r a were fluorines  The  94 1  MHz  0  f l u o r i n e s must be p r e s e n t  N a t u r a l l y as t h e  b e t t e r from 30 MHz  experimental  (21) c a n n o t have a minimum  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  progressively  field  is  c u r v e i n F i g u r e 10  down u n t i l a t 2 MHz  fit  of Rigny's  (39)  to  decreased becomes  i t fits exactly.  T h i s a t l e a s t d e m o n s t r a t e s t h a t t h e computer program w o r k s . e f f e c t i v e n e s s o f t h e program was  0  incompatible with  s h i f t tensors.  s p e c t r a show a minimum, b u t e q u a t i o n  shoulder  by u s i n g a much  t h e 94.1  completely at v a r i a n c e w i t h the concept exhibiting axial  to the  T h i s however was Finally  the l a r g e  synthesized  even a h i n t o f a  c o u l d be o b t a i n e d  smaller broadening 2 MHz  f u n c t i o n , the  without  showed t h a t a r e a s o n a b l e  l i n e shape (up t o 56.4  s m a l l a n i s o t r o p y and  The  f u r t h e r c h e c k e d by i t s q u i t e good  r e s o l v e d components o f UF  . D  The most p r o b a b l e non-equivalent  axial  and  o f a l l p o s s i b i l i t i e s was equitorial  considered  f l u o r i n e s w h i c h showed  s h i f t anisotropy.  However, when r e s o l u t i o n was  the only frequency  a t w h i c h i t was  t i o n , the c o n t o u r s  of ths composite curve produced  a r e a r a t i o 4:2,  truly  w h i c h were o n l y v e r y  r e l a t i v e s h i f t o f a b o u t 265  ppm.  to  Tho  attempted  feasible  chemical a t 94.1  to attempt two  be  MHz,  resolu-  components  f a i n t l y asymmetrical,  and  s h i f t e x c e e d s t h e maximum  had  of a  value  To Follow Page 37  Figure 10. WF,.  Asymmetrical reconstruction for 6-like fluorines  38  o f 220  ppm  which  i s o b t a i n e d i n the a b s e n c e o f a n i s o t r o p y .  resolution i s scarcely different symmetrical t h e 4:2  peaks.  from  the attempted  I f t h e r e l a t i v e s h i f t was  area r a t i o s t i l l  maintained,  components r e s u l t e d w h i c h if  -  were d i s r e g a r d e d .  ppm.  resolution  k e p t below 220  I f two  ppm  slightly, relative  s i m i l a r c u r v e s o f 4:2  area  r a t i o a r e a g a i n c o n s t r u c t e d from  t h e e x p e r i m e n t a l 2 MHz  u s i n g t h e 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 t o the  p e r i m e n t a l c u r v e can increasingly symmetrical little  bad  a g a i n be made w h i c h  above.  The  f o r the case  broadening  F i g u r e 11.  The  94.1  of s i x l i k e  MHz  at high f i e l d  and  ex-  t o 30 MHz  but  a r e so n e a r l y  Indeed,  the  con-  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 fluorines.  a l s o attempted  an a r e a 4 c u r v e a t low curve  curve.  f u n c t i o n i s dominant i n b o t h  R e s o l u t i o n was  then  t h e i r d i r e c t i o n s o f asymmetry makes  change i n the shape o f the t o t a l  F i g u r e 10  curve  computed component c u r v e s  t h a t even o p p o s i n g  s t r u c t e d curves are almost  i s tolerable  and  shaped  To a n t i c i p a t e  i s assumed, the  into  ppm  some v e r y i m p l a u s i b l y  an a v e r a g e a n i s o t r o p y o f about 300  s h i f t must be a b o u t 105  The  spectrum field  and  tailing  experimental 2  MHz  cases.  u s i n g opposed a s y m m e t r i e s as i n  was  resolved into  tailing t o low  but c l e a r l y  two  to high f i e l d  field.  a t 94.1,  h o p e f u l a t 56.4,  at lower  f r e q u e n c i e s , even i f the maximum 220  I n view o f the above f a i l u r e s ,  The  failing  components and  an a r e a 2  T h i s seemed  promising  a t 40 MHz, ppm  and  s h i f t was  hopeless used.  n o n - a x i a l symmetry o f the  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  shift  To F o l l o w Page 38  39  certainly  not  sufficient  more c o m p l i c a t e d than  i n the  line  preceding  Resolutions of  the  than there  resolution  exist  is  sufficient  and  the  distinct  The  doublet  the  minor high  peak  i n the  broad  doublet  94.1  which  c e n t r o i d of the  attempted  nuclei  t o do  so  with  5:1  and  less  There  the  two  m e r e no  s y m m e t r y mas  conspicuously  last  i n the  is' also  these  better  assumed.  3:3  area  ratios  successful  even  possibility  components.  If this  attempt  that  can  molecule  to  change i n l i n e field  MHz  might the  Attempts  r e s o l u t i o n of  that,  i s the  case  hopeless.  component must  field  between  than  distortion  both  the  more  RlHz t o p e r m i t  inhere a x i a l  i s h o w e v e r one  action,  of  cases  attempts.  i s utterly  There  shapes.  They were  preceding  might  94.1  mere a l s o  components.  the  at  peak be  to  width  a t 94.1 high  spectrum.  field One  made.  a doublet  as  field  the  be  could  not  (from  inter-  i s varied  the  high  have a  very  o f moments t o  small  there  explained.  to produce  T h a t w o u l d make r ,  involved impossibly  If  permit  If]Hz m i g h t  have i t s c e n t e r  spectrum.  be  low  the  field  separation  reference  52,  -3 p.  220,  the  doublet  13  show  two  p o s s i b l e r e s o l u t i o n s at  and  two  like  produce which  the  in  the  i n gauss  do  not  have  shift  absence  any  i s 220 of  apparent ppm,  MHz  ).  Figures  involving  That i n Figure of  12  sets  components  has  chemical  what i s p r e d i c t e d  The  12  and  of  four  Both r e s o l u t i o n s , i n p a r t ,  anisotropy  just  anisotropy.  i s 3^r  94.1  components.  q u i t e p l a u s i b l e numbers.  isotropic in  nuclei  splitting  can  by be  two  components  shift,,  Their  equation used  as  (20)  indicated  To Follow Page 39 Figure 12. WF^.  Reconstruction with doublet and symmetric singlet  $  To Follow Page 39  Figure 13. WF,.  Resolution w i t h doublet and asymmetric s i n g l e t  -  40  in  the figure  t o c o n s t r u c t c u r v e s 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 t h e experiment no  curves  worse t h a n i n o t h e r a t t e m p t s .  and w h i c h  The o t h e r d o u b l e t  shown i n F i g u r e 13, i n v o l v e s a l o w f i e l d asymmetry i n d e e d . If  t h e low f i e l d ,  and  Putting  peak w i t h a v e r y  a n i s o t r o p i c component's s e c o n d of the f i e l d  this  a value of  strange ppm.  moment i s p l o t t e d  (^~^j_)  =  +  ^3 PP  3  m  value 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  i s  term  r e m e m b e r i n g t h a t t h e o t h e r a n i s o t r o p i c term i s z e r o s i n c e t h e  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 s h i f t o f a b o u t 135 ppm. found  experimentally.  d o u b l e t s cannot let  resolution,  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 a b o u t 115  a g a i n s t the square found.  agreement i s c e r t a i n l y  splitting  equation  (20) a r e l a t i v e  T h i s i s n o t bad agreement w i t h t h e 115 ppm Obviously  be c o r r e c t .  both o f the r e s o l u t i o n s  involving  I n f a c t n e i t h e r o f them i s .  i s t h e same i n each c a s e .  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  Estimated  from  The doub-  the.94,1 MHz  i n t e r n u c l e a r separations of  o a b o u t 2.4  and 2„0 A r e s p e c t i v e l y .  tances i n the doublet w i l l r e s t of the molecule was  verified  doublet  be l i t t l e  different  and a d i s t i n c t d o u b l e t  procedure  (52, p. 220).  Using  Finally  o f t h e UJF  spectrum  This  i s based on Abragam's the parameters  avail-  There was  structure.  i t may be s t a t e d t h a t t h e d i f f i c u l t y  the r e s o l u t i o n  dis-  those i n the  t h i s work, t h e d o u b l e t c o u l d n o t be r e p r o d u c e d .  o n l y a r o u n d e d c u r v e w i t h no s i g n o f d o u b l e t  attempting  from  c o u l d n o t be s e e n .  u s i n g Program 4, A p p e n d i x I w h i c h  fitting  a b l e from  In s h o r t , the i n t e r n u c l e a r  experienced i n  C3n n o t be a t t r i b u t e d  41  t o e l e c t r o n c o u p l i n g o f the ~^F b u t i o n to the second  and  moment from  *^UJ  i n the s o l i d .  The  contri-  t h i s s p l i t t i n g according to  Gutowsky ( 6 3 ) i s  -  ( 2 2 )  The  coupling constant X  0.011  gauss.  The  m i l l t h e r e f o r e be The  measured by R i g n y  a d d i t i o n t o t h e second  trials  g i v e s a s u r e r e s u l t and  t h a n any  of the o t h e r s .  Blinc  f o r , a l t h o u g h he  source  Mone o f  encountered  similar  4:2  area r a t i o  f o r UJF , he  gives  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 a zero f i e l d  measurements he does g i v e a v a l u e o f s t a t e s t h a t t h i s agrees  within  second =  J 6 „ " £ > J  moment.  chemical From  500+200 ppm  l i n e width data.  The  range 500  t o 700  ppm  is  o b t a i n e d by a s s u m i n g s i x l i k e f l u o r i n e s . ppm  quite feasible.  if  the  I t i s not s u r p r i s i n g  t h i s i s the case.  Orders  ppm  as  t h a t the curve i s d i f f i c u l t  o f m a g n i t u d e a r e a l l t h a t can  (20).  of  T h i s makes  U i i t h our d a t a t h i s  r e l a t i v e s h i f t between the components o f a b o u t 105 earlier.  clearly  of  An upper l i m i t t o the a v e r a g e a n i s o t r o p y i s s e t by the v a l u e  l o w e r l i m i t o f 300  (  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  c h e m i c a l s h i f t when a p p l i e d t o our d a t a u s i n g e q u a t i o n  345+20 ppm  T  and  t o o h i g h s i n c e i t would g i v e a n e g a t i v e v a l u e t o the s q u a r e relative  the  does show examples o f r e s o l v e d , a s y -  s h i f t f o r t h e components, nor  from  or  none i s r e a l l y any more p l a u s i b l e  (41) seemingly  mmetric c u r v e s w i t h approximate  determined  this  a r e most u n s a t i s f a c t o r y .  attempts  neither values  moment from  Hz  negligible.  resolution  difficulty  ( 4 2 ) i s 43.8  Blinc's  gives a noted to r e s o l v e be  expected.  42  Our  data  g i v e an u p p e r l i m i t  there i s zero a n i s o t r o p y .  o f 220+10 ppm t o t h e r e l a t i v e s h i f t i f  The v a l u e s  ) and ( 6 -€> ) a r e o f a r e s o n a b l e They do n o t , u n f o r t u n a t e l y , p e r m i t experimental  curves.  o f 300 ppm and 105 ppm f o r order of magnitude t h e r e f o r e .  accurate r e c o n s t r u c t i o n of the  Moreover, i f the chemical s h i f t  some t h r e e t i m e s g r e a t e r ' than t h e i s o t r o p i c s h i f t c o m p o n e n t s , w i t h b o t h phenomena b e i n g prising lution  field  between t h e  dependent, i t i s s u r -  t h a t t h e 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 r a t h e r than merely  a change i n l i n e shape.  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 very s i m i l a r will  anisotropy i s  to the experimental  spectra.  The  doublet  i n a fashion  Therefore,  although i t  be assumed t h a t t h e r e a r e two a s y m m e t r i c components o f a r e a  r a t i o 4:2 c o r r e s p o n d i n g a t low and h i g h f i e l d ting  t o f o u r e q u i t o r i a l and two a x i a l  r e s p e c t i v e l y , i t would s t i l l  fluorines  be v e r y  interes-  t o see t h e UJFg s p e c t r u m a t 77°K and 200 MHz. Even i f an e x p e r i m e n t  solve the r e s o l u t i o n  were done a t 200 MHz, i t m i g h t n o t  p r o b l e m i n UJF , however. C  The a t t e m p t s  have  D  all  been based on t h e p r e m i s e t h a t i f a r e s o l u t i o n can be made a t  one  field,  other  t h e components w i l l  fields  and.using  g i v e the" e x p e r i m e n t a l chemical s h i f t . a s and  another  at high lower  retain  the observed curves  fields,  c h e m i c a l s h i f t can be summed t o  a t those  fields.  f o r ona "component" a r i s i n g  from hydrogen n u c l e i ,  fields,  their d i s t i n c t i d e n t i t i e s at  curve"  from f l u o r i n e  t h e r e would be a c l e a r  t h e "components" would r e t a i n  and a " t o t a l  I n t h e case  o f extreme nuclei  resolution  their identities at  c o u l d be d e r i v e d from t h e  43  -  "components" u s i n g t h e o b s e r v e d c h e m i c a l s h i f t . of i d e n t i c a l shift  nuclei,  there u/ill  In the o t h e r  be no change a r i s i n g  and t h e e x p e r i m e n t a l c u r v e s c a n a g a i n be r e p r o d u c e d  t h e range o f f i e l d s a v a i l a b l e . i n which s i m i l a r shifted  amount w h i c h i s n o n e t h e l e s s s m a l l e r  b r o a d e n i n g , t h e component l i n e shapes  entangled.  F o r Uj'Fg a t low f i e l d s  case  t h e r e appear  cases.  fields  than  c a n n o t be d i s -  t o be s i x e s s e n t i a l l y  f l u o r i n e s and a t h i g h f i e l d s two more o r l e s s  components w i t h a t i n t e r m e d i a t e two e x t r e m e  throughout  n u c l e i a r e i n components w h i c h a r e c h e m i c a l l y  by a s i g n i f i c a n t  equivalent  isotropic  However, f o r t h e i n t e r m e d i a t e  the d i p o l a r  in  from  extreme  distinct  a confusing mixture of the  The r e s o l u t i o n a t t e m p t s above have been p r e s e n t e d  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 n o t  p r e s e n t i n t h e e x p e r i m e n t a l s p e c t r a i t cannot reasonable attempts.  The d i f f i c u l t y  be f o u n d by making  a r i s e s n o t from d e f i c i e n c i e s i n  t h e e x p e r i m e n t b u t from t h e n a t u r e o f t h e 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 c a s e s o f mixed  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  shifts. 3.  Proposed C r y s t a l A theoretical,  comparison w i t h moment. The  Structure rigid  lattice  second moment c a n be computed f o r  the observed zero f i e l d  No X - r a y s i n g l e c r y s t a l  or f i e l d  independent  s t u d y o f UJF has been 6  s t r u c t u r e s u g g e s t e d , h e r e was based  second  published.  on the IJJ-F bond l e n g t h o f  o 1.833A from U i e i n s t o c k Table 1 s u p p l i e d Siegei.  ( 3 7 a ) 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  by B a r t l e t t  ( 3 7 b ) from a p r i v a t e c o m m u n i c a t i o n  from  44  -  Table 1 Cell  2  7  3  °  K  cell  cubic  cell  orthorhombic  253°K  Parameters  o f UJF 6  o a=6„28A ,  03 VX247.7A  ,  „ ^ c a l c = 3.99  o a=9.68A , b=8.Bl c=5.09  o3 V=434.1A  ,  / ' c a l c = 4.56  Z=4 s p a c e g r o u p Pmma?  -  >9  -  o Attempts  t o f i t t h e f o u r UJFg m o l e c u l e s i n t o t h e u n i t c e l l  produced  what a p p e a r e d  t o be u n r e a s o n a b l e d i s t o r t i o n s and a s u s p i -  c i o n a r o s e t h a t Pmma m i g h t UJeinstock  ( 7 7 ) may a c t u a l l y  q u i t e c l e a r whether  a t 253 K  be a t r a n s c r i p t i o n  e r r o r f o r Pnma.  s t a t e t h a t UJF i s Pnma, but i t i s n o t  he means t h a t a l l t h e h e x a f l u o r i d e s he d i s c u s s e s  a r e Pnma o r o n l y t h a t t h e y a r e a l l o r t h o r h o m b i c . I n any c a s e i t was d e c i d e d t o base t h e UJFg s e c o n d 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 for UF . o C  Hoarde and 5 t r o u p e dimensions  (36) give the atomic coordinates,  and band l e n g t h s  f o r UFg w h i c h a r e r e p r o d u c e d  cell  i n T a b l e 2.  -  45  -  Table 2 Atomic C o o r d i n a t e s ,  C e l l D i m e n s i o n s , and Bond  •  V F  2 3  F  V F  5  F  6  UF  C  a t 293°l  D  O  y  z  0.2500 0.093  0.081 0.250  U-F A  0.014  0.407  0.250  2.01  0.246  0.407  - 0.083  2.01  0.246  0.093  - 0.083  2.01  0.003  0.250  —  0.250  2.13  • .250  0.250  0.417  2.12  X  U  L e n g t h s of  .  0.1295 0.014  t  2.05  average Orthorhombic,  Pnma, Z = 4 , s c a l e = 5.06 o a=9.80 , b=9.00, c=5.2GA S i n c e the  ratios  dimensions for  of the c e l l  UIF^ and UF a r e a p p r o x i 6 o 8.81 5.09 0.98-0.99^) and • ~ 9.00 ~ 5.20 ~  m a t e l y e q u a l f o r e a c h d i r e c t i o n f^r • Z = 4 f o r b o t h m o l e c u l e s , the able.  same s p a c e  The r a t i o o f UJF. t o UF. c e l l 6  group  f o r b o t h may be r e a s o n -  volume i s 0.95.  The r a t i o o f t h e  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 c r u d e , s p h e r i c a l including  f l u o r i n e van d e r UJaals r a d i i  "spherical"  volume e x c e e d s  i s 0.82.  the u n i t c e l l  the  excess i s r e l a t i v e l y  less  the  UJFg m o l e c u l e r e l a t i v e l y mora freedom  molecules  In both cases the  volume, but i n t h e UJF^ c a s e  than i n t h e UF^ c a s e .  T h i s would  give  t o 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 t e m p e r a t u r e nmr t r a n s i t i o n a t 200 K. In  computing  t h e 'JJF s t r u c t u r e ,  t h e c o o r d i n a t e s o f a uranium  o  atom were chosen as a m o l e c u l a r o r i g i n . the  The a t o m i c c o o r d i n a t e s f o r  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 t o t h i s  a c c o r d i n g t o the f o l l o w i n g  origin  formulae to g i v e c o o r d i n a t e s f o r the  -  f l u o r i n e p o s i t i o n s i n UJF b  46  -  .  ( f l u o r i n e a t o m i c c o o r d , i n WFgo r i g i n atomic coord.) ( c e l l d i m e n s i o n MF  )  ( f l u o r i n e atomic coord, i n UF o r i g i n atomic coord.) ( c e l l d i m e n s i o n UF ) C  a v e r a g e Ui-F bond average.U-F  length  bond l e n g t h  D  1.833  .  ISO)  ~0.\M5)(  ~o-Z5'O0)(8.8j)  Z05~  .  1.833 Z  -o.o8/;($-.20)  oS  •  as)  1833  Z 0 5 "  0  i v a l u e 1.833A g i v e n by UJeinstock was the  average  of the p o s s i b l y non-equal  t u r e phase o f \ilf  r  .  bond l e n g t h s .in t h e low  The a t o m i c 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  o equations  temperafrom  o  ( 2 3 ) a r e g i v e n i n T a b l e 3. Table 3  Calculated  F: F'  A t o m i c C o o r d i n a t e s and Bond L e n g t h s X  y  .1295 .0250 ,0250 .2349 .2349 .0150 . 2386  .2500 . 1065 „3935 .3935 . 1065 .2500 .2500  z  .0810 .2354 .2 554 ~ .0688 —.0688 —„2213 . 3879 average  f o r UiF^ a t "253°K" Ui-F A t _  1.80 1„80 1.80 1. 80 1.90 1.90 1. 83  Orthorhornbi c, Pnma, Z-4 68, b=8.81, c=5.09R  9 r , 9  0  The p o s i t i o n s a r e n o t o f c o u r s e a c c u r a t e t o t h e number o f s i g n i f i c a n t figures retained i n this table.  To Follow Page J+6  Figure L+. WF^. Proposed u n i t c e l l (along c-axis)  '  1  a  ATOMIC C O O R D I N A T E S  Pnma  a = 9.68 A b = 8.8 I A c = 5.09A  OF TUNGSTEN I 0.13,0.25,0.08 2-0.13,0.75,-0.08 3  0.37, 0.75,0.58  A-  0 . 6 3 , 0.25, Q 4 2  Q  5  ' ' — C I R C L E S INDICATE FLUORINE Van d e r Waals radii  1  1  l  J  °  -  The  symmetry o p e r a t i o n s o f t h e Pnma s p a c e group g i v e t h e o t h e r 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 . of 4.  47  F i g u r e 14 shows the p r o p o s e d  iJJFg v i e w e d a l o n g t h e c - a x i s . T h e o r e t i c a l R i g i d L a t t i c e Second To p r o v i d e n u c l e a r p o s i t i o n s  a simple linear  t r a n s f o r m program  It  translates  in  a block of u n i t  of.the r i g i d to  structure  Moment  f o r t h e second moment (Program  5, A p p e n d i x  t h e 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 cells  lattice  the assumption  around  the o r i g i n a l c e l l .  calculation  I.) was w r i t t e n .  into  positions  In the computation  t h e o r e t i c a l s e c o n d moment t h e r e i s i n a d d i t i o n  o t h a t a r e a s o n a b l e UJFg s t r u c t u r e a t 253 K can be  o derived  from t h e UFg s t r u c t u r e a t 298 K, the a d d i t i o n a l  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.  assumption  The two h o x a l u c r i d e s a r e  s i m i l a r m o l e c u l e s and t h e t e m p e r a t u r e s a t w h i c h t h e X - r a y r e s u l t s a r e quoted  a r e i n each c a s e r a t h e r r o u g h l y t h e same d i s t a n c e  melting  p o i n t s o f t h e r e s p e c t i v e compounds.  reasonable approximation.  The assumed UJF^ s t r u c t u r e ,  a t e m p e r a t u r e above t h e nmr t r a n s i t i o n below  the t r a n s i t i o n .  The f i r s t  below t h e  i s n o t an unhowever, i s f o r  but i s used a t t e m p e r a t u r e s  This too i s .acceptable.  X - r a y s p e c t r o s c o p y and  nmr s p e c t r o s c o p y . a r e s e n s i t i v e t o 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 . far  as X - r a y i s c o n c e r n e d , t h e s t r u c t u r e i s e s s e n t i a l l y  As  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 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  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  As w i l l bility  be n o t e d l a t e r ,  thermodynamic  o f the l a t t i c e  i s not too g r e a t i  evidence r u l e s out the p o s s i -  o f 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 a rigid,  (2) gives the t h e o r e t i c a l d i p o l a r  polycrystalline solid.  The f i r s t  s e c o n d moment f o r  term a p p l i e s  i n t e r a c t i o n s , t h e s e c o n d t o t h e UJ— F i n t e r a c t i o n s . n u m e r i c a l c o e f f i c i e n t s a r e 316.8 and 0.27.  t o t h e F-F  The r e s p e c t i v e  When t h e 1 4 ^ n a t u r a l  183 abundance o f  UJ, t h e o n l y i s o t o p e  o f tungsten with  moment, i s c o n s i d e r e d , t h e UJ—F f a c t o r bution  from UJ-F i n t e r a c t i o n s  actions  need  a magnetic  becomes ~ 0.04.  The c o n t r i -  i s n e g l i g i b l e and o n l y F-F i n t e r -  be summed i n e q u a t i o n ( 2 ) .  o u t on t h e IBM 7040 u s i n g Program  The summation was c a r r i e d  6, Appendix  I using the nuclear  5 and was e x t e n d e d  c o o r d i n a t e s g e n e r a t e d by Program  to a radius of  o 6A from m o l e c u l e number one ( a n y one o f t h e f o u r ; i n t h e u n i t c e l l o -6 Because  o f the r  dependence o f t h e s e c o n d moment, i t i s s u f f i c i e n t  t o assume t h e r e m a i n d e r o f t h e n u c l e i known d e n s i t y  are uniformly d i s t r i b u t e d  t h r o u g h o u t t h e r e s t o f t h e sample  with  ( 5 1 , p. 1 6 0 ) . I f  2  the  number o f n u c l e i  between r and r + d r i s 4 P r ^ d r , i n h e r e ^ i s t h e ,o3 i s g i v e no f by number n u c l e i p e r u n i t volume (A ) , t h e a d d i t i o n a l c o n t r i b u t i o n /  x  CO  S  n 4  . ,  C-i.  ' Ciuimeritol { ^ c ^ y i t  t o the t o t a l , 2  s e c o n d moment o f 8.14 gauss  fe/..8)4$*  3r  ' *• The c o n t r i b u t i o n s  s  (24) 3  theoretical rigid  • a r e g i v e n i n T a b l e 4.  lattice  dipolar  -  49  Table 4  Rigid  Dipolar  Second Moments o f UiF  a t 77°K  g  2 T o t a l I n t r a m o l e c u l a r .Second Moment „ o z T o t a l Second Moment w i t h i n 6K 7.80 G 6A " ^ C o n t r i b u t i o n O u t s i d e 6A .34 G' T o t a l T h e o r e t i c a l Second Moment E x p e r i m e n t a l Second Moment 3  2  M o d e r a t e d i s t o r t i o n makes l i t t l e Ths  intramolecular  bonds o f l e n g t h for four  short  4.40 G  difference  8.14 G ^ 8.2+0.2 G  t o the s e c o n d moment.  moment c a l c u l a t e d on t h e b a s i s o f s i x e q u a l ii'-F  1.833A e a c h i s 4.31 g a u s s ^ . . The moment 3  equatorial  ( l . 8 o S ) and two l o n g  axial  calculated  ( l , 9 o S ) bonds  2 i s 4.40 gauss The  only  slightly different.  c r y s t a l s t r u c t u r e assumed h e r e r e c e i v e s  some  s u p p o r t from t h e c o u n t o f i n t e r n u c l e a r i n t e r a c t i o n s .  passive The t h e o r e t i c a l  s e c o n d moment program i n d i c a t e s t h a t w i t h i n a range o f 6.5 from t h e m o l e c u l e chosen as o r i g i n , 12 i n t e r a c t i o n s i n v o l v e twice are  there  a r e 152 F-F i n t e r a c t i o n s .  nuclei with  separations  t h e f l u o r i n e van d e r UJaals r a d i u s .  a l l intramolecular.  radius.  This  favourable  o f l e s s t h a n 2.70°,  However, t h e s e i n t e r a c t i o n s  At l e a s t the s t r u c t u r e  h a v i n g no i n t o r m o l e c u l a r  Of t h e s e ,  has t h e a d v a n t a g e o f  i n t e r a c t i o n s l e s s than t h e van o'er UJaals  o f c o u r s e does n o t say t h a t  other s t r u c t u r e s  equally  do n o t e x i s t .  X-ray r e s u l t s o b t a i n e d o  C o n s i d e r i n g t h a t t h e s t r u c t u r e i s based on o o a t 298 K, a d j u s t e d t o 253 K, and a p p l i e d a t  .77 K where t h e r m a l c o n t r a c t i o n  m i g h t be s i g n i f i c a n t ,  the vary  close  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 s e c o n d moments i s  50  perhaps f o r t u i t o u s . 5,,  Nonetheless  -  i t i s encouraging.  R e o r i e n t a t i o n i n the S o l i d Above t h e nmr t r a n s i t i o n  a r o u n d 180-210°K, t h e 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  transition  and t h e  n e x t around 265°K, the l i n e w i d t h has a c o n s t a n t v a l u e o f a b o u t 3.2 gauss a t b o t h 30 and 94.1 MHz. dent broadening second  existed  C l e a r l y whatever f i e l d  below 200°K, i t i s now a v e r a g e d  moment p l o t i n F i g u r e 2 shows a drop from 2  9 gauss  depen-  o u t . The  approximately  2 ( 8 . 2 gauss  at zero  f i e l d ) below t h e l o w e r t r a n s i t i o n t o  2 1.05+0.05 gauss approximately  above t h e t r a n s i t i o n .  sperical,  this  S i n c e t h e w'Fg m o l e c u l e i s  d r o p i n second  moment t o about 1  2  gauss  may be due t o t h e o n s e t  of i s o t r o p i c  c u l e about i t s c e n t e r o f g r a v i t y . second is  moment a v e r a g e s  5, . °X  of equation  « 3/4.AW SN; R." 0  tV3.t«er>-  0  fry  *  Since this c a l c u l a t i o n  In t h i s case  the i n t r a m o l e c u l a r  t o z e r o and t h e o n l y r e m a i n i n g  from t h e i n t e r r n o l e c u l a r s e c o n d  the a p p r o p r i a t e form  r o t a t i o n o f t h e mole-  1  contribution  moment ( 5 1 , p. 1 7 3 ) . F o r UJF., 5 (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  (25)  fc  *  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  a t t h e molec-  u l a r c e n t e r s , t h e sum i s computed u s i n g Program 6 w i t h t h e c o ordinates of the tungsten n u c l e i corrected  for nuclei  as t h e c e n t e r s .  a t d i s t a n c e s g r e a t e r than  The r e s u l t  6A i s 1.06 5  gauss . 2  T h i s i s e x c e l l e n t agreement w i t h t h e e x p e r i m e n t a l v a l u e o f 1.05+.05 2 gauss , b u t S m i t h  ( 6 4 b ) p o i n t s o u t 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 g i v e a s e c o n d moment d i f f e r e n t from t h e i s o t r o p i c v a l u e experimental positively  by as l i t t l e  value i t s e l f  (37a, 77) c o n s i d e r s  a t the s o l i d - s o l i d  r o t a t i o n i n the s o l i d  phase  transition  believes that f o r a l l the h e x a f l u o r i d e s between the c u b i c s o l i d -  phase  0  (255 K f o r '<HF ).  there i s l i t t l e  and the l i q u i d ,  The nmr r e s u l t s , however, a p p e a r  c u b i c phase.  Admittedly  He  difference ,  a b e l i e f which our  to i n d i c a t e a very  r e o r i e n t a t i o n n o t o n l y i n t h e c u b i c phase,  i s un»  r e s u l t s s u p p o r t , 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  rhombic phase, same 65° below  to s t a t e  reorientation i s taking place.  .  likely  S i nee t h e  v a r i e s by 5%, i t i s i m p o s s i b l e  t h a t an i s o t r o p i c  UJeinstock  as 5 t o 15%.  phase.  considerable  but a l s o i n the o r t h o -  the s o l i d - s o l i d  transition  to the  t h e r e a p p e a r s no s i g n o f t h e t r a n s i t i o n  o i n t h e v i c i n i t y o f 200 K from thermodynamic d a t a . The h e a t c a p a c i t y c u r v e f o r UJF_ i s smooth w i t h no break from 4°K t o t h e p o i n t a t w h i c h fa the t r a n s i t i o n t o t h e c u b i c s t r u c t u r e t a k e s p l a c e ( 2 8 ) . S i n c e t h e r e is  no change i n thermodynamic  p r o p e r t i e s , t h e s e c o n d moment d r o p c a n -  o n o t be due t o a change o f c r y s t a l s t r u c t u r e a t 200 K.  I t must  arise  from r e o r i e n t a t i o n s w h i c h , c o n s i d e r i n g t h e a p p r o a c h o f t h e s e c o n d moment t o a v a l u e 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 n o t only  the two d i f f e r e n t  but a l s o t o a c o n s i d e r a b l e  the l o c a l  degree  fields  fluorine'sites, as w e l l .  As  F i g u r e 14 and t h e count o f i n t e r n u c l e a r d i s t a n c e s i n t h 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  demonstrate,  t h e m o l e c u l e s i n t h e UJF  unit  52  cell  interlock  siderable as  do  restricted  not  overlap.  3  gives a separation  clearance. and  The  4 are  8.92A ; 3-4,  separations  1-2,  o f 6.36A  5  o r i e n t a t i o n would not  van  the  molecules  der UJaals F r a d i u s  between m o l e c u l e s f o r c o m p l e t e  5.60A ; 1-4, 3  overlap  5.14$; 2-3,  5.9o8;  encountered during i s o t r o p i c  be i m p o s s i b l y  Uieinstock's (77)  +  room f o r c o n -  between t h e c e n t e r s o f m o l e c u l e s 1,  3  The  Approximating  (UJ-F =.1.83  5.68A ; 1-3,  5.7oS.  5  There i s c l e a r l y  reorientation.  s p h e r e s o f r a d i u s 3.18A  s 1.35)  3,  but  He  and  12.8,  PuFg as  13.6,  concludes  these as  1.45  eu.  and  13.7  limit  eu  respectively.  o f 5 eu  for p l a s t i c  t h a t r o t a t i o n below the m e l t i n g  This  Cady ( 2 5 )  gives  has  &  the e n t r o p y  an e n t r o p y  o f f u s i o n o f 3.2  values  g l o b u l a r compounds, for  o f f u s i o n f o r UJF  change a s s o c i a t e d w i t h the two  eu and  transitions,  al  entropy  eu  this  basis  and  l e s s t h a n the  vapour phase (22.1  total will  out  t r a n s i t i o n might  solid-solid  o n l y 7.7+3.2=10.9 eu w h i c h i s c o n s i d e r a b l y o f the m o l e c u l e i n the  w o u l d on  points  However, the t o t a l  is  t h e 10.9  UJeinstock  i t s solid-solid  a c o n s e q u e n c e o f the o n s e t o f r o t a t i o n .  Since  these  v a l u e , w h i c h i s w e l l w i t h i n the Timmermans' l i m i t ,  q u a l i f y as a p J a s t i c c r y s t a l and  point).  Since  NpF^,  point i s u n l i k e l y  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 . that PtF  thermo-  g i v e s the. e n t r o p i e s o f f u s i o n f o r UF^,  hexafluorides.  re-  evidence a g a i n s t a high degree of motion i n  e x c e e d Timmermans' (78) he  2-4,  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 .  t h e s o l i d s t a t e s o f the h e x a f l u o r i d e s i s based i n p a r t on dynamic grounds.  2,  entropy fusion, rotation-  eu a t the  i n c l u d e o t h e r as w e l l  be  as  fusion  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 s m a l l e r than 10.9 eu.  He b e l i e v e s t h a t 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 , w i t h 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 t h a t free r o t a t i o n does not occur i n e i t h e r case. even l e s s  R o t a t i o n at a lower t r a n s i t i o n would be  l i k e l y then.  Hence f o r 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 f u s i o n i s 1.45 eu f o r a t o t a l of 6.73 eu a g a i n s t a vapour phase r o t a t i o n a l entropy of 21.8 eu, the same o b j e c t i o n s would apply. However, both the 5d t r a n s i t i o n s e r i e s h e x a f l u o r i d e s , UJF^ and PtFg, f o r 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 t i 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 respectively. B l i n c (41) places the UJF. t r a n s i t i o n a t about 200 K, b  as do we, and the P t F  b c  (7) or (8) average f r e q u e n c i e s V be o b t a i n e d .  o  t r a n s i t i o n at about 250 K. t  From equation  of molecular r e o r i e n t a t i o n may  From an A r r h e n i u s - t y p e p l o t of In. (  ) a g a i n s t */T°K,  an a c t i v a t i o n energy f o r 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 a t 200 K there i s an a c t i v a t i o n energy o f 10.0+0.4 K c a l from second moment data and 15„0+0 9 K c a l from l i n e width data. o  In accord w i t h Powles (65), the value d e r i v e d 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 u s i n g  Program 7, Appendix I which was m o d i f i e d from Smith program gives a l e a s t squares  (79).  The  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 v a l u e 10.0 K c a l w i l l i n c l u d e  a s l i g h t e r r o r due t o the a n i s -  otropy o f the second moment, but i t seems a very reasonable a c t i v a t i o n energy 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 . ment w i t h  the v a l u e of about 9 Kcal o b t a i n e d by B l i n c w i t h  measurements. 265  I t i s i n good agreeT  (  Because of the abrupt nature of the t r a n s i t i o n a t  K n e i t h e r e q u a t i o n (7) nor (8) gives a meaningful a c t i v a t i o n  energy f o r that change. The thermodynamic and nmr r e s u l t s are not c o n t r a d i c t o r y . The phenomena a r e r e s p o n s i v e to d i f f e r e n t frequencies of r e o r i e n t ation.  For the nmr experiment, a h i g h degree of r e o r i e n t a t i o n  i m p l i e s a frequency o f r e o r i e n t a t i o n o f the order of t h 9 nmr l i n e 5 - 1  4  w i d t h , i . e . 10  - ID  sec  ; whereas the frequency of the r e -  o r i e n t a t i o n s must be of the order of 10"*- l O * thermodynamic p r o p e r t i e s .  I t i s consistent  2  s e c " * to a f f e c t the  therefore  f o r 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 t a k i n g place above 200°K i n WF . 2 of 1.05+0.05 gauss  obtained here suggests t h a t a s . f a r as an nmr  experiment can d e t e c t ,  i s o t r o p i c r o t a t i o n can not be r u l e d 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 o c c u r r i n g hindering  The value  p o t e n t i a l b a r r i e r of 10 K c a l per mole.  through a  55  The A s F  5  Adducts  In the case o f the two AsF adducts, there w i l l o b v i o u s l y b be n o n - e q u i v a l e n t f l u o r i n e n u c l e i p r e s e n t . As w i l l be seen below, the  e q u i v a l e n t f l u o r i n e s are grouped as I F * 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 n o n - e q u i v a l e n t 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 s m a l l compared t o d i p o l a r broadening. A. 1.  I F • AsF ?  5  Results F i g u r e 15 shows the temperature dependence of the IF^.» AsF^  f l u o r i n e a b s o r p t i o n spectrum a t 30 MHz.  As f o r the previous com-  pound, the c u r v e s have a common 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 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  p l o t of the averaged second moments o f the d e r i v a t i v e c u r v e s . 2 second moment i s constant a t l l 6 + 0 . 6 gauss o  The  o from 77 K up to about  205°K a t which p o i n t the moment begins dropping u n t i l 2.1+0.2 gauss^ o i s reached a t 235 K.  o I t then remains constant up to 295 K, the  h i g h e s t temperature recorded.A p r e l i m i n a r y l i n e width study i n d i cated no o t h e r t r a n s i t i o n from 77° t o 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 a p p r o x i m a t e l y s y m m e t r i c a l and a t 217°K, w i t h i n 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  To  Follow  Page 55  T E M P E R A T U R E  °K  56  r e g i o n , 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  field  o s p e c t r a a t 77 and 295 K , t h i s e f f e c t i s indeed r e a l . however, present  I t does,  a d i s t i n c t d i f f i c u l t y i n d e c i d i n g 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,^ R e s o l u t i o n i n t o Components. Chemical S h i f t s Figures 17a and 17b  I s o t r o p i c and ;  show the f i e l d dependence of the  o IF^  <»  "sFg a b s o r p t i o n  Anisotropic .  s p e c t r a a t 300  o and 77 K.  Typical deri-  v a t i v e s of the s p e c t r a are given i n Appendices I H b F i g u r e 17a demonstrates the spectrum at 94.1  MHz  at h i g h F i e l d .  broad component to low The  IIIc. o  and 300  r e s o l v e d i n t o two q u i t e symmetrical components. comparatively  and  As  K can  be  There i s . a :  f i e l d and a narrow component  r e l a t i v e areas of the components are 1.1:1  the i s o t r o p i c chemical  s h i f t between them i s 153+10 ppm.  The  nents are e q u i d i s t a n t on e i t h e r s i d e of the c e n t r o i d of the curve, which, from F i g u r e 18, has a chemical r e s p e c t to our CF^OOH standard  and compo-  total  s h i f t of -54+8 ppm  at 295-300°K.  The  with  figure indicates  that the s h i f t of the c e n t r o i d w i t h respect to the reference  o  at  o  300 K i s the same whether the adduct i s at 77 or 300 The 1.1:1  K.  r a t i o of the areas of the components i m p l i e s t h a t  twelve f l u o r i n e s known to be present  i n the IF  • AsF  adduct are  the  To F o l l o w Page 56  F i g u r e 17a.  I  F  A 0  s  F 6  •  F i e l d dependence o f a b s o r p t i o n  s p e c t r a a t 295°K  To Follow Page 56  Figure 17b.  IFTAsF, . F i e l d dependence of absorption spectra a t 77°K ' b  b  To Follow Page 56  Figure 18. IF*AsF£ . Chemical shift of centroid of spectrum relative to CF^COOH  CO  if) D <  1.5  h  O  =  2  A =  9  7  5  7  °  K  °  K  LL  I CO  o Q_ O cc h o  -IO  <?"=-54t 8 ppm  -0.5  CO  z <  o o  5  0  0  0  1 5 , 0 0 0  LU F I E L D (H ) o  GAUSS  2  5  ,  0  0  0  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 a t 300 K. (For  I F ^ and AsF^ the r a t i o would have been 1.4:1).  supports the i o n i c f o r m u l a t i o n I F ! A S F . suggested 6 o Detmer ( 5 ) and confirmed  This  by S e e l and  by Beaton ( 1 0 ) .  F i g u r e 19 g i v e s the f i e l d dependence o f the l i n e width at 77 and 295°K.  For the 295°K s p e c t r a the s l o p e of the p l o t  i s 140+25 ppm i n agreement w i t h the chemical s h i f t  determined  from the r e s o l v e d curves a t 94.1 MHz. • This confirms t h a t the r e s o l u t i o n does i n v o l v e components which are not completely overlapped and which have no: asymmetry.  For I F * AsF D  we may  O  take e = a = e = a = a = s = * and 5 .= e = § = e €T, , = C, = C» where 6„ and 6T denote the mean i s o t r o p i c 11 Li. 1 As I x  z  2  5  4  6  A s  7  g  Q  1 0  T  s h i f t s f o r f l u o r i n e atoms bonded to a r s e n i c and i o d i n e respectively.  I f , as the r e s o l u t i o n a t 94.1 MHz and Figure 19  suggest, the asymmetry i n the components i s averaged out, equation (19) becomes *  Jf(<s -S,)  1  ............  As  The r e l a t i v e p o s i t i o n s of <T  and 6" w i t h respect to high or  MS  low f i e l d cannot be determined  (26)  1  '  from t h i s e q u a t i o n , but may be  deduced from other c o n s i d e r a t i o n s .  I t w i l l be i n d i c a t e d l a t e r  t h a t 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 c h e m i c a l s h i f t between the components i s (**"pj - € 1 ) = 135 + 8 ppm. S  This i s q u i t e reasonable agreement w i t h  To F o l l o w Page 57  F I E L D (H ) Q  GAUSS  To Follow Page 57  FIELD  SQUARED. (Hf)  KILOGAUSS  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 a n i s o t r o p y 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 c o n s t r u c t e d by shifting  the two components r e s o l v e d at 94.1 RlHz r e l a t i v e to each  other w i t h a s h i f t of 153 ppm.  Although  at low f i e l d s the con-  s t r u c t e d curve i s t a l l e r than the e x p e r i m e n t a l curve, l i n e i s about the same and the c o n s t r u c t e d and experimental  width  curves have o  very s i m i l a r shapes.  E v i d e n t l y , i n the r e g i o n 235-295 K, the  trum i s composed of two d i s t i n c t q u i t e d e f i n i t e 1.1:1.  spec-  curves whose area r a t i o s are a  From comparison of the l i n e shapes of the  components w i t h those of the SF^, • 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 s h o r t component (second moment 2.0 6  2  ^  gauss ) to low f i e l d i s the I F ^ grouping.Confirmation  comes from  C h r i s t e et a l (80), from whom a chemical s h i f t of -126.6 ppm respect to HF can be o b t a i n e d f o r AsF^ i n HF s o l u t i o n . 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 0  -54+8 ppm  w i t h respect to CF„C00H.  The AsF  with  In our  curve i s D  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  -100+20 ppm  D  O  r e l a t i v e to HF i n f a i r agreement w i t h C h r i s t e ' s v a l u e .  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 s p e c t r a to t a i l i n the opposite d i r e c t i o n to the high temperature s p e c t r a , a n i s o t r o p y of chemical s h i f t almost  -  certainly seen  59  must be p r e s e n t a t t h e l o w e r t e m p e r a t u r e .  b e l o w when t h e I F * AsF o  in  be  c r y s t a l s t r u c t u r e i s mentioned, the b  I-F and A s - F bond l e n g t h s a r e q u i t e s i m i l a r . nearly  As w i l l  The groups a r e  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  distortion  the As-group).  constancy presumably  When t h e y a r e a t 77°K where^ because o f t h e o o o f s e c o n d moment between 77 and 205 K, t h e y a r e both rigid,  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 o f about polated  10.7 g a u s s  zero f i e l d ,  e a c h , t h e same v a l u e as t h e e x t r a -  d i p o l a r s e c o n d moment.  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 of the second  moment.  This i s v e r i f i e d  rigid  lattice  below  calculations  ( 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 s e c o n d moment b e c a u s e o f  t h e g r e a t e r m a g n i t u d e o f t h e F-I t h a n t h e F-As i n t e r a c t i o n . ) o line  shapes too w i l l  of a n i s o t r o p i c s h i f t , direction  be q u i t e s i m i l a r  The  a t 77 K and, i n t h e absence  t h e t o t a l c u r v e would  o f t h e asymmetry - t o h i g h f i e l d  be s y m m e t r i c a l .  The  - gives a p o s i t i v e  value t o the . a n i s o t r o p i e s or a t l e a s t to t h e i r net e f f e c t . They w i l l a l m o s t 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 t h e r e l a t i v e s h i f t o f t h e c e n t r o i d o o f t h e t o t a l c u r v e w i t h r e s p e c t t o CF^COOH was t h e same a t 77 o and 300 K. I f we make t h e r e a s o n a b l e a s s u m p t i o n t h a t t h e r e l a t i v e s h i f t b e t w e e n t h e components r e m a i n s t h e same a t both t e m p e r a t u r e s o an e s t i m a t e c a n be made o f t h e c h e m i c a l 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 t h e e q u a t i o n .... ( 2 7 )  60  to  t h s 77  line  i n F i g u r e 20.  -  From t h e upper  shift  o f 153+10 ppm, t h e a v e r a g e s h i f t  limit  o f 135-8 ppm, a v e r a g e a n i s o t r o p i c s  355  ppm r e s p e c t i v e l y  of  the i n d i v i d u a l  to  say.  are obtained.  groups approach  limit  o f 143+10 ppm, and t h e l o w e r o f about 310, 333, and  How c l o s e l y the average  The a v e r a g e i t s e l f a p p e a r s  of the r e l a t i v e  the a n i s o t r o p i c s  value i s d i f f i c u l t  t o be o f a r e a s o n a b l e  s i n c e i t i s q u i t e s i m i l a r t o t h e a p p r o x i m a t e 300 ppm  magnitude  forU J .  The  b r o k e n c u r v e i n F i g u r e 17b shows c u r v e s r e c o n s t r u c t e d from two 2 e q u a l components o f 10.7 gauss otropies,  s e c o n d moment, h a v i n g 333 ppm  and w i t h r e l a t i v e s h i f t  broadening function  o f 143 ppm.  has been a p p l i e d  s t r u c t e d curve i s perhaps  anis-  Since a gaussian  t o e q u a t i o n ( 1 6 ) , the con-  too narrow.  Compared t o t h e g a u s s i a n  c u r v e o f t h e same s e c o n d moment, t h e e x p e r i m e n t a l z e r o f i e l d c u r v e f o u n d f o r UJF^ was r a t h e r w i d e r t o w a r d s e x t e n s i v e wings.  T h i s would  the t o p , but w i t h o u t such  make t h e c o n s t r u c t e d c u r v e s i n F i g u r e  17b i n somewhat b e t t e r agreement w i t h t h e o b s e r v e d s h a p e s .  How-  e v e r , t h e q u a l i t a t i v e agreement w i t h t h e e x p e r i m e n t a l l i n e  shape  is 3.  n o t bad c o n s i d e r i n g Crystal Beaton  the assumptions  involved,  Structure ( 1 0 ) has d e t e r m i n e d t h e s t r u c t u r e o f I F * ' A s F . from C  powder X - r a y d a t a , p r e s u m a b l y is  summarized  i n T a b l e 5.  a t room t e m p e r a t u r e .  D  His information  61  -  Table 5 X-Ray Powder S t r u c t u r e  S p a c e Group Pa3  cubic atomic  As I F F  i n 4(a) i n 4(b) i n 24(d) i n 24(d)  ( 0 , 0, 0) ( i , A, i ) ( x , y, z ) ( x , y, z )  Z  Q  =  9.4935+0.0005A  parameters  x=0.0980; y=0.1377; x=0.6001; y=0.6431;  bond d i s t a n c e s As-F  o f IF* A s F ~ ~ 295°K o o  z=-0.0489 z=0 4411 e  and a n g l e s  1.678*  F-As-F = 86.5° .0C  1 -F 1.75^*  F- 1-F = 9 0 intermolecular  distances  ( 3 ) F...F a t 2.81.8  These d i s t a n c e s  Beaton p o i n t s data  the  (3)  F...F  a t 2.978  (3)  F...F  a t 3„048  out that  short,  below  derived  c  from h i s X - r a y  t h e As-F l e n g t h i n p a r t i c u l a r . o f t h e r m a l m o t i o n when  He  determining  and s u g g e s t s t h a t s u c h a c o r r e c t i o n m i g h t be  o r more. As e v i d e n c e he c i t e s  a salt  See t e x t  t h e bond l e n g t h s  to h i s neglect  bond l e n g t h s  0.l8 in  this  F...F a t 2.95.8  may be t o o s m a l l .  may be r a t h e r  ascribes  (3)  C o p e l a n d e t a l ( 8 l ) who found  o f A s F ~ t h a t t h e As-F bond l e n g t h c o r r e c t e d 6  m o t i o n was 1.77^8 and u n c o r r e c t e d  was 1.65A.  siders  large c o r r e c t i o n f o r thermal  that t h i s appears a r a t h e r  Trotter  f o r thermal ( 8 2 ) con-  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  to each o f B e a t o n ' s bond l e n g t h s , both o f them a r e s t i l l the r a n g e s g i v e n i n t h e I n t e r a t o m i c D i s t a n c e s  o f O.lR within  Supplement ( 8 3 ) .  T h e r e , v a l u e s o f 1.71, 1.85, 1,80, and 1.83 a r e g i v e n f o r bond l e n g t h s i n I F AsF  -  •  o  In t h i s  In T a b l e  ?  and 1.80+Q.05A  f o r t h e A s - F bond l e n g t h s i n  5  0  l a s t , t h e F-As-F a n g l e  6 the f i r s t  I-F  0  i s g i v e n as 88.3 +2.1 .  column o f a t o m i c  —  coordinates  contains  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 0.1A  i n c r e a s e i n bond l e n g t h .  the u n i t  cell  5  Only t h e f i r s t " m o l e c u l e " i n  i s g i v e n , t h e symmetry o p e r a t i o n s w i l l  give the other  of course  three. Table  6  A t o m i c C o o r d i n a t e s f o r I F * A s F " ~ 295°K 0 b x  As  I F F  1 0  1 1  12  (1)  (2)  Beaton  Thermally Adjus ted Beaton  0.0000 0.0980 • 0.0489 0.1377 0.0980 0.0489 0.1377 0.5000 0.6001 0.4411 0.6431 0.3999 0.5589 0.3569  0.0000 0.1039 -0.0518 0.1460 -0.1039 0.0518 -0.1460 0.5000 0.6058 0.4377 0.6513 0.3942 0.5623 0.3487  y Beaton 0.0000 0.1377 0.0980 -0.0489. -0.1377 -0.0980 0.0481 0.5000 0.6431 0.6001 0.4411 0.3569 0,3999 0.5589  Thermally Adjusted Beaton 0.0000 0.1460 0.1039 -0.0518 -0.1460 -0.1039 0.0518 0.5000 0.6513 0.6058 0.4377 0.3487 0.3942 0.5623  2 Beaton 0.0000 -0.0489 0.1377 0.098.0 0.0489 -0.1377 -0.0980 0.5000 0.4411 0.6431 0.6001 0.5589 0.3569 0.3999  Thermally Adjusted Beaton 0.0000 -0.0518 0.1460 0.1039 0.0518 -0.1460 -0.1039 0.5000 0.4377 0.6513 0.6058 0.5623 0.3487 0.3942  " T h e r m a l l y a d j u s t e d B e a t o n " means t h a t t h e c o o r d i n a t e l i s t e d under " B e a t o n " h a s been i n c r e a s e d t o a l l o w f o r an e s t i m a t e d +0.lS t h e r m a l c o r r e c t i o n t o t h e bond l e n g t h . I t i s n o t meant t o i m p l y a c c u r a c y t o f o u r s i g n i f i c a n t f i g u r e s in this table.  63  4.  Theoretical Rigid For  L a t t i c e 5econd  Moment  I F * AsF,. , e q u a t i o n ( 2 ) f o r t h e 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 s e c o n d moment w i l l second.  -  have a t h i r d  The n u m e r i c a l f a c t o r s w i l l  term s i m i l a r t o t h e  be 316.8, 23.4, and 74.3  for  t h e F-F, F-As, and F-I sums r e s p e c t i v e l y .  the  s e c o n d moment c o n t r i b u t i o n s  Table 7 gives  from c a l c u l a t i o n s  based  both  on B e a t o n ' s a t o m i c c o o r d i n a t e s a d j u s t e d f o r t h e r m a l m o t i o n and on h i s u n a d j u s t e d c o o r d i n a t e s .  F o r Beaton's u n c o r r e c t e d  v a l u e s o n l y t h e t o t a l s e c o n d moment i s shown. the  s e c o n d moments i t has been assumed t h a t t h e c o o r d i n a t e s o 295 K w i l l  at  In c a l c u l a t i n g  o ba i n 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 t h o s e a t 77 K. Table 7  Rigid Lattice  Second Moment C o n t r i b u t i o n s t o I F 6  From B e a t o n ' s a d j u s t e d c o o r d i n a t e s I F  6  A s F  Total  6  (including integral c o n t r i b u t i o n s over 6A o f 0.35, O.fJO, and 0.01 gauss )  +  AsF o  Second Moment Gauss F-F F-As F-I Total 0.98 10.40 8.78 0.39  5  IF+  6  A s F  INTRA  6  AsF* o AsF" o  4.75  0.38-  0.93  6.06  TOTAL ( t c 6A )  4.71  0.38  0.04  5.13  INTRA  2.71  0.38  0.00  3.09  TOTAL ( t o 68)  4.07  0.01  0.93  5.01  INTRA  2.04  0.00  0.93  2.97  10 68  0.54  1.34  1 2 56  5  K  From B e a t o n ' s c o o r d i n a t e s ( l O ) I F  6  A s F  TOTAL ( i n c l u d i n g above integral contributions)  6  E x t r a p o l a t e d Zero Second Moment  o  0  Field 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 a r e based on a 1 2 - f l u o r i n e IF AsF" u n i t . N i n e q u a t i o n ( 2 ) has been t a k e n as 12 f o r 6 6 . a l l groups. +  Zero p o i n t 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 c o n t r a c t i o n of the c r y s t a l l a t t i c e between o 295  o K, where the s t r u c t u r e was  determined  and 77 K where i t was  a p p l i e d 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 i n c r e a s e 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 second moment i n d i c a t e s t h a t the "thermal c o r r e c t i o n " was of the r i g h t order.  field  probably  The probable bond lengths t h e r e f o r e are of the  same order as those l i s t e d i n the I n t e r a t o m i c Distances Supplement as Beaton suggested,  and are longer than those he reported,.  The c o n t r i b u t i o n s of the IF* and AsF groups to the t o t a l o o second moment (up to 6A r a d i u s from the center of the r e l e v a n t 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 o b t a i n the second moments the i n d i v i d u a l components would have i f they could be o 2 r e s o l v e d 'out at 77 K. This gives 10.20 and 10.44 gauss r e s p e c t i v e l y 5  when the c o n t r i b u t i o n f o r d i s t a n t n u c l e i i s i n c l u d e d .  Both values are  2 i n good agreement w i t h the 10.7  gauss  assumed above f o r the  r e c o n s t r u c t i o n of the experimental curves i n Figure 5.  17b  attempted  0  R e o r i e n t a t i o n s i n the S o l i d Above t h e i r r e s p e c t i v e nmr  t r a n s i t i o n s a l l three of the  IF* , AsF^. , and UJF^ groups e x h i b i t symmetrical s p e c t r a .  Below the  t r a n s i t i o n the UJFg s p e c t r a e x h i b i t asymmetry presumably both because of a n i s o t r o p y 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 e q u a t o r i a l 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 a n i s o t r o p y and the mean i s o t r o p i c s h i f t between the n o n - e q u i v a l e n t 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 I F * AsF which i s a l s o b  o around 200 K.  fa  In the case of t h a s a l t , there are two s y m m e t r i c a l ,  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 a n i s o t r o p i c s h i f t and non-equival e n c e s ( i f p r e s e n t ) w i t h i n each d i f f e r e n t i o n . The d i f f e r e n c e s between  t h e f l u o r i n e s a t t a c h e d to the c a t i o n and those attached to  the a n i o n a r e a consequence  o f t h e i r bonding to the r e s p e c t i v e 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 i o n s t h e r e f o r e remains r e g a r d l e s s of the degree of r e o r i e n t a t i o n . UJith regard t o the a c t u a l r e o r i e n t a t i o n s which are o c c u r r i n g above t h e t r a n s i t i o n , i t appears that t h a t AsF^ i s undergoing mora + o e x t e n s i v e motion than the IF i o n . I t s second moment a t 295 K i s D  2  about 0.7 gauss , a value q u i t e c o n s i s t e n t w i t h i s o t r o p i c r e o r i e n t a t i o n about i t s c e n t e r o f mass.  The I F * component, however, 2  has a broader l i n e and a g r e a t e r second moment, 2.0 gauss .  In ex-  p l a i n i n g or a t 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 s t a t e d t h a t both the I F * and AsF^ component l i n e shapes would probably b  b  be s i m i l a r s i n c e the two ions were s i m i l a r i n s i 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 a l s o a t h i g h e r temperatures s i n c e the two groups presumably w i l l e x p e r i e n c e and be i n f l u e n c e d e q u a l l y by the same b a r r i e r to r e o r i e n t a t i o n . more f r e q u e n t 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  The  than the  66  IFg group may About any  be a consequence of the shorter  As-F  bond  length  a x i s of r o t a t i o n , the moment of i n e r t i a of the AsF  a  ion 6  is  some 10%  l e s s than that f o r the IF* i o n . This estimate mas o made using r e g u l a r octahedra. In f a c t the AsF. octabedra are b  distorted (10).  The  compression, however, i s along a 3 a x i s .  e f f e c t merely squeezes the  The  faces of the octahedra together and  centers of mass s t i l l c o i n c i d e  w i t h those of the As atoms so  the As atoms s t i l l make no c o n t r i b u t i o n  the that  to the moments of i n e r t i a .  Although the moment of i n e r t i a i s i n c r e a s e d 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 a x i s at r i g h t angles to the 3 a x i s along which compression occurs. one  expects a r e o r i e n t a t i o n  Since q u a l i t a t i v e l y  to occur p r e f e r e n t i a l l y about the  axis  w i t h 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 a x i s where the moment i s even l e s s than i n the case. 2 9 5 ° K  Hence the AsF than the The  IF*  b  i o n undergoes more frequent r e o r i e n t a t i o n ion.  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  (84) who  p o i n t s out  that  p o t e n t i a l w e l l to the  next  barrier i s W  where  at  b  above view i s confirmed by Das  .over an n - f o l d  undistortad  r W  t  + W  '  T  (28)  and \A^. 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 pectively. only protons  ww c  quantum mechanical t u n n e l i n g  through the  barrier  res-  Since f o r a l l r o t a t i n g groups other than those i n v o l v i n g 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  sL[y±\  e  / M  (29)  67  where I vation  err  i s t h e e f f e c t i v e moment o f i n e r t i a and where Vo, t h e a c t i '  energy or height o f the hindering  determined that  -  from e q u a t i o n  the smaller I f f  (8).  From e q u a t i o n ( 2 9 ) , i t i s o b v i o u s  » the g r e a t e r i s the p r o b a b i l i t y o f r e o r i e n t a t i o n .  e  Hence t h e A s F g r o u p c a n l o g i c a l l y o quent r e o r i e n t a t i o n vided that  p o t e n t i a l b a r r i e r , may be  be e x p e c t e d t o undergo more f r e -  than t h e I F * group a t a g i v e n t e m p e r a t u r e , p r o fa  t h e t e m p e r a t u r e i s h i g h enough f o r t h e m o t i o n t o occur,.  A l t h o u g h t h e above  q u a l i t a t i v e l y predicts  AsFg r e o r i e n t a t i o n , I t may be t h a t ,  the a c t u a l  contrary  a higher p r o b a b i l i t y f o r  p r o b a b i l i t i e s d i f f e r by l e s s  t h a n 10%„  t o t h e a s s u m p t i o n a b o v e , t h e g r o u p s do en-  c o u n t e r d i f f e r e n t b a r r i e r s w i t h t h e AsF.. b a r r i e r t o r e o r i e n t a t i o n o being the l e s s e r . 2 The n a r r o w A s F l i n e w i t h i t s 0„7 gauss s e c o n d moment c a n be o o a c c o u n t e d f o r a t 295 K by a s s u m 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 o f t h e g r o u p as n o t e d e a r l i e r .  The b r o a d e r l i n e  o f the I F * component has o  2 a s e c o n d moment o f 2„0 g a u s s , however,  w h i c h i s c l e a r l y much h i g h e r  2 t h a n t h e 1 gauss is  too high also  value predicted forreorientation  of t h e o c t a h e d r a l g r o u p .  forisotropic reorientation.  a t random 'about t h e symmetry axes  T h i s would have t h e e f f e c t t h a t  r i n e s p e n t l / 6 o f i t s t i m e a t each p o s i t i o n s e c o n d moment t o a v a l u e o n l y s l i g h t l y reorientation a single dipolar angle  (63).  r e d u c e each c o n t r i b u t i o n  the i n t e r n u c l e a r  vector  for isotropic  (5), reorientations  b r o a d e n i n g by a f a c t o r t ( 3 C o s ^ ^ - t  between  each f l u o -  and would r e d u c e t h e  l a r g e r than t h a t  As n o t e d i n e q u a t i o n  symmetry a x i s  It  )  about  to the i n t r a g r o u p 2  where  and t h e a x i s  Vj^  i s the  of r o t a t i o n .  68  This  factor holds f o r stepwise r e o r i e n t a t i o n  with the  -  H-3  and f o r c l a s s i c a l  a b o u t an n - f o l d  r o t a t i o n about any a x i s  (57). For  I F * i o n t h e r e a r e two - , t h r e e - , and f o u r f o l d  about which r e o r i e n t a t i o n  might o c c u r . 0  reorientations  about t h e  intragroup contribution  0  »  and  there w i l l  symmetry  The i n t r a g r o u p  moments f o r I F ^ a r e 2.04, 2 1 7 , and 1 9 3 gauss axes.  axes  second  respectively for In addition  be an i n t e r g r o u p  to this  contribution.  The AsFg group a p p e a r s t o be u n d e r g o i n g an i s o t r o p i c i n w h i c h i t s i n t r a g r o u p s e c o n d moment would  axis  reorientation  be a v e r a g e d t o zero,,  2 T h e r e f o r e i t s 0.7 gauss group i n t e r a c t i o n s  s e c o n d moment i s due e n t i r e l y  to i n t e r -  and can be u s e d t o e s t i m a t e an i n t e r g r o u p  moment f o r t h e s i m i l a r I F * g r o u p .  T h i s makes t h e t o t a l  second  second  •  2 moments o f t h e c a t i o n 2.74, 2.87, and 2.63 gauss for , , ^ reorientations. A l l t h e s e e x c e e d t h e e x p e r i m e n t a l v a l u e o f 2.0 a n <  2 gauss  + by more t h a n 30%.  The a c t u a l m o t i o n w h i c h I F  i s undergoing  b  must t h e r e f o r e be l e s s t h a n r e o r i e n t a t i o n random but g r e a t e r t h a n r e o r i e n t a t i o n the  a b o u t o c t a h e d r a l axes a t  about a s i n g l e a x i s .  motion i s a c o m b i n a t i o n o f r e o r i e n t a t i o n  simultaneous o s c i l l a t i o n  about  another.  Perhaps  a b o u t one a x i s and  This implies  that  different  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 t h e I F * and A s F . i o n s 6 6 The a v e r a g e a c t i v a t i o n e n e r g y determined mole.  from an A r r h e n i u s p l o t  This energy i s v e r y . h i g h .  of t h e p o i n t s j u s t below  0  f o r t h e combined m o t i o n s was  o f e q u a t i o n ( 8 ) t o be 19+4 K c a l p e r Because  o f t h e s c a t t e r i n F i g u r e 16  the t r a n s i t i o n ; i t i s possible  i n second moment as drawn i s s h a r p e r t h a n i t r e a l l y i s .  that  t h e change  A less  -  a b r u p t t r a n s i t i o n would  69  -  have a l o w e r a c t i v a t i o n e n e r g y .  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 n o t be v a l i d o of f i x e d crystal  found  I n s t e a d o f a change i n m o t i o n w i t h i n a s o l i d  crystal structure,  the t r a n s i t i o n may  mark an  may  phase  actual  transition,, B.  1»  I f the  SF^ • AsF<-  Results F i g u r e 21 shows the t e m p e r a t u r e dependence o f t h e SF^ • A s F ^  a b s o r p t i o n spectrum  a t 30  x - s c a l e and a r e i n t e g r a t e d derivative curves.  ffiHz.  The  a b s o r p t i o n c u r v e s have the same  to a c o n s t a n t , a r b i t r a r y  Appendix  a r e a from  the  IVa c o n t a i n s r e p r o d u c t i o n s o f t h e  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 t e m p e r a t u r e s h i g h e r than h i g h e s t v a l u e shown i n F i g u r e 2 1  c  F i g u r e 22 i s a p l o t o f t h e tem-  p e r a t u r e dependence o f the a v e r a g e d second moments a t 30 fslHz. s e c o n d moment does n o t appear  the  to achieve a r i g i d  The  l a t t i c e v a l u e by  o 77 K, t h e l o w e s t t e m p e r a t u r e r e a c h e d i n the s t u d y .  o At 77 K t h e  2 s e c o n d moment i s 5 9 + 0 3 gauss  From t h a t t e m p e r a t u r e i t d r o p s 2 o g r a d u a l l y i n a smooth c u r v e t o 1.85+0.1 gauss a r o u n d 200 K. The 0  0  .  b s e c o n d moment r e m a i n s c o n s t a n t a t t h i s v a l u e u n t i l 336 K. Througho out t h e 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 a r e o almost symmetrical, with a s l i g h t  tailing  t o low  field.  Above 336 K  t h e a b s o r p t i o n s were so narrow t h a t t h e i n t e g r a t e d s p e c t r a were n o t plotted. The d e r i v a t i v e c u r v e s i n A p p e n d i x IVa show a marked i n c r e a s e i n motion  o b e g i n n i n g a t 336 K.  o t h a t a t 295 K  9  The  d e r i v a t i v e a t 320  o  w h i c h shows a s h o u l d e r on the low f i e l d  i s similar  to  h a l f of the  To Follow Page 69  TOTAL SECOND  69  sS^d  M O T T O i oj,  MOMENT  G A U S S  2  70  derivative.  The s p e c t r a a t 336  shape and a s i m i l a r  have a v e r y  s e c o n d moment t o those  general  similarity i n  o a t 320 , but t h e s h o u l d e r o  has  now become a n a r r o w component.  value  o f a b o u t 0.1 gauss  highest  2  o by 342 K.  temperature recorded,  Second moment d r o p s a t 336 Between 342  o  to a  o and 373 K, t h e  t h e s e c o n d moment r e m a i n s  constant,  o  By 342 K t h e r e two  i s an a l m o s t c o m p l e t e r e s o l u t i o n o f t h e s p e c t r u m  components w i t h an i s o t r o p i c c h e m i c a l  resolution exactly  i s slightly  s h i f t o f 97 5+5 ppm. Q  b e t t e r a t 373°K, b u t t h e c h e m i c a l  into The  shift i s  t h e same.  A p p e n d i x I V a as n o t e d above shows t h e t e m p e r a t u r e dependence o f t h e d e r i v a t i v e l i n e a t 30 MHz. shoulder  towards high  makes i t d i f f i c u l t , to peak l i n e  width  field  as w i t h  is  chemical  g i v e n i n F i g u r e 23.  For t h i s  f o r the t o t a l curve Although  s c a t t e r i s so g r e a t  determined 2  0  with respect  t o CF^COOH a t 300 K ,  t h a t i t c a n n o t be e s t a b l i s h e d .  24a and b show t h e f i e l d  f o r these  I s o t r o p i c and  dependence o f t h e a b s o r p t i o n  o  s p e c t r a a t 300 K and 77 K. curves  The s h i f t  ppm.  R e s o l u t i o n w i t h Components ( s e e R e s u l t s a l s o ) . Anisotropic Chemical S h i f t .  o  t o CF C00H  i t a p p e a r s t h a t t h e r e m i g h t be a o  from F i g u r e 23 i s -40+15  Figures  r e a s o n no p l o t o f  i s given.  t e m p e r a t u r e dependence o f t h e s h i f t r e l a t i v e the  field  I F * A s F ^ , t o d e f i n e a c o n s i s t e n t peak  from t h e d e r i v a t i v e .  shift  s h i f t o f t h e low  changes t h e l i n e shape i n a manner w h i c h  variable' temperature l i n e width The  The g r a d u a l  spectra  A p p e n d i c e s IVb and I V c g i v e  the d e r i v a t i v e  F i g u r e 24a d e m o n s t r a t e s t h a t one can make a  To Follow Page 70  F i g u r e 23. SFoAsF, . Chemical shift of centroid of spectrum relative to CF C00H J  O  6  5000  15,000  F I E L D (H ) Q  GAUSS  25,000  To Follow Page 70  To F o l l o w Page 7 0  Solid line experimental Broken line constructed  71  r e s o l u t i o n o f t h e c u r v e a t 300 K and 94.1 area under the t a l l , field  high f i e l d  IYIHZ.  The r a t i o o f t h e  peak t o t h a t under t h e s h o r t , low  peak i s 2.2:1, from w h i c h  i t i s concluded  that there 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 t h e h i g h f i e l d low  field.  ionic  peak as i n t h e  Hence a t 300°K t h e SF^ • A s F ^ a d d u c t i s p r o b a b l y t h e  s a l t SF* ^ s F g f o r t h e e x p e r i m e n t a l r a t i o o f a r e a s u n d e r t h e  components i s g r e a t e r t h a n 6:3, n o t between 6:3 and 5:4.  The h i g h  2 field  component has a second  moment o f about 0.9 gauss 2  field  component one o f 1.1 g a u s s .  The r e l a t i v e  and t h e low  chemical  shift  between t h e two components as r e s o l v e d a t 94.1 MHz and 300°K i s 105+10 ppm i n agreement w i t h t h e v a l u e d e t e r m i n e d o s p e c t r a a t 342 K and above. the r e s o l u t i o n their broken 100 at  The components a t 300 K o b t a i n e d  o f t h e 94.1 MHz s p e c t r u m ,  shift.between  about  As shown by t h e  i n F i g u r e 24a t h e components, w i t h a s h i f t o f a b o u t  ppm, g i v e a r e a s o n a b l e each l o w e r  from  a r e each s y m m e t r i c a l  c e n t e r s w i t h no s u g g e s t i o n o f asymmetry. lines  i n t h e 30 Y!1 Hz o  frequency  r e p r o d u c t i o n of the experimental  investigated.  From t h e a p p r o x i m a t e  spectrum 100 ppm  t h e components and t h e -40+15 ppm s h i f t o f t h e t o t a l o  c u r v e w i t h r e s p e c t t o CF^COOH a t 300 K, t h e s h i f t s o f t h e components w i t h r e s p e c t t o any s t a n d a r d high f i e l d  Relative  component i s a t -107+20 ppm and t h e low f i e l d  a t -207+20 ppm. it  c a n be d e t e r m i n e d .  i s undoubtedly  t o HF t h e component  S i n c e t h e A s F ~ i o n i s common t o b o t h t h e A s F t h e peak found  c a t i o n i n each a d d u c t i s t h e n  5  a t about -100+20 ppm i n e a c h .  t h e low f i e l d  component i n e a c h  adducts, The case.  72  -  I t i s a l s o p o s s i b l e to make a r e s o l u t i o n i n t o components a t 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 t h a t 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 o b t a i n e d w i t h a r e l a t i v e shi'ft of 185+20 ppm which might be "squeezed" t o 160+20 ppm but no more.  As i n d i c a t e d  later  even t h i s value may be too g r e a t The area of the t a l l e r , high f i e l d curve (AsF ) t o t h a t of the s h o r t e r , low f i e l d curve (SF*) i s b -J 0  1 9 : 1 , again p r o v i d i n g support f o r the 2:1 area r a t i o r e q u i r e d by 0  t h e i o n i c f o r m u l a t i o n of the adduct. 2  The AsF component has a second b  +  2  moment of 2.8 gauss , the SF^ component one of 4 7 gauss .  Shifting  0  t h e two curves a p p r o p r i a t e l y g i v e s a reasonable r e p r o d u c t i o n of the l i n e shapes a t lower f r e q u e n c i e s as i n d i c a t e d by the broken curves i n F i g u r e 24b. F i g u r e 25 shows the f i e l d squared dependence of the second o moment at 300  o and 77 K.  Since there was no asymmetry evident i n  the r e s o l v e d components a t 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 S i n c e C. = 6  chemical s h i f t .  1  n  = G  £  = § and 6. = O  5  4  = 6 3  C  = 6 „ = 5_ = 0  (  0  6„ = <>„ where the S and As r e f e r to the f l u 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 d e t e c t a b l e a n i s o t r o p y present, e q u a t i o n (19) becomes  = j x ( k ) + ^-\U(G>U-6S  . (30)  From equation (30) the 300°K l i n e g i v e s a value of the r e l a t i v e of 87+10 ppm i  n  shift  good agreement w i t h the two other values f o r 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 s m a l l slope of the second moment l i n e , 2  a change o f only +0.2 gauss  i n the average second moment a t 94.1 MHz  would b r i n g t h i s s h i f t up t o about 100 ppm i n even c l o s e r agreement w i t h the values  o From the 77 K  found by r e s o l u t i o n of the s p e c t r a .  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. o w i t h the value a t 300 K confirms  This agreement  o t h a t there i s no a n i s o t r o p y a t 77 K. o  I t a l s o suggests t h a t the r e s o l u t i o n a t 77 the shape of the experimental  may be i n e r r o r .  Although  curve appears to d i c t a t e components w i t h  a s h i f t o f a t 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 f o r 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 S t r u c t u r e No X-ray study i s a v a i l a b l e f o r SF*. AsF^. .  a v a i l a b l e f o r SF^ • SbF^ SF* AsFg._  f  Some i n f o r m a t i o n i s  enough to make a guess a t the s t r u c t u r e of  In the absence of a r i g i d l a t t i c e second moment f o r comparison  w i t h the t h e o r e t i c a l moment f o r the model, the guess must be r a t h e r t e n t a tive. B a r t l e t t (6) has determined a c r y s t a l s t r u c t u r e from powder data f o r SF^ ° SbFj. .  The d e t e r m i n a t i o n  was not f u l l y completed but the  symmetry suggested an i o n i c f o r m u l a t i o n SF* SbF. . j  M u e t t e r t i e s (85)  b  a l s o suggested the i o n i c f o r m u l a t i o n f o r 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 . Table 8.  B a r t l e t t ' s i n f o r m a t i o n i s summarized i n  -  74  Table  8  X-Ray D a t a f o r SF*  Simple cubic  = The  1 7 8  Interatomic Distances  0.0028  3  '  * °  1  • /calc.=  a  i n the  ( p o w d e r ) l e n g t h o f I.808.  n e a r l y the same symmetry and  atomic  The  SbF  and  c  t o the SF*  J>  simple  cubic c e l l .  A s F g g r o u p s may  They c o u l d  s e c o n d moment c a l c u l a t i o n octahedra use  i n the c e l l  is The  SF*  crystal)  earlier  an  have  SbF^  structure  may  However the  b  SbF-  and  a f u r t h e r approxima-  b  be p l a c e d a t t h e c o r n e r s  of  the  f o r the p u r p o s e s o f a the  However, Program 6 i s d e s i g n e d  to  (0,  0,  was  and  e r r o r w i t h a model.  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 f o u r c o r n e r s  group w i l l  unlikely group was  (82)  and  the  be i n the c e n t e r  t h a t the s u l f u r  placed  t r i a n g l e centered cell.  (single  as s p h e r e s ( 8 6 ) s i n c e the o r i e n t a t i o n s o f  chosen a f t e r c o n s i d e r a b l e t r i a l  The  the SF*  be a p p r o x i m a t e d  a r e unknown.  nuclear coordinates  having  1  AsF,, s t r u c t u r e .  •J  The  Z =  b  c o o r d i n a t e s a r e n o t known f o r SF*  0  '  AsF,. g r o u p s w i l l  volume t h e n and  approximation  t i o n must be made  3  bond l e n g t h r a n g e n o t e d  b  be a r e a s o n a b l e  '°  3  S u p p l e m e n t (83) g i v e s an Sb-F  bond l e n g t h o f 1.788, and As-F  a t 291°K  a = 5,625 +  • Abs.=  83  SbF~  on  \  y  \)  v e r t i c a l axis passing  through  o f the c e l l  three  and  Then t h e s u l f u r atom and  AsF^  atom w i l l  so t h a t t h e (^-,  0)  g r o u p from T'F^+AsFg  be a t t h e e x a c t  y  \).  cell  0  center.  f l u o r i n e s were i n an  parallel  \  o f the  a t (•??, - j , 5 ) , but i t  t o the a-b  i t s l o n e p a i r can  (£,  Octahedra  plane  f i t along  equilateral of  the  tha  In t h e model i t a p p e a r e d t hat  -  75  -  t h e SF* g r o u p c o u l d r o t a t e q u i t e f r e e l y a b o u t t h e 5 atom and ( 5 , - j , for  .  Table 9 gives the atomic coordinates  t h e assumed SF* A s F  determining 1 778, 0  a x i s through the  c  calculated  u n i t c e l l a t "291°K" and a p p l i e d a t 77°K  the coordinates  as f o r t h e p r e v i o u s  0  In  f o r t h e A s F ^ g r o u p s , As-F bond l e n g t h s o f a d d u c t , were u s e d .  F i g u r e 26 shows a view  Table 9 Estimated  Atomic C o o r d i n a t e s  As F,  0.0000 0.1754 -0.0S74 0.2464 -0.1754 0.0874 -0.2464 0.5000 0.3693 0.7614 0.3693  down t h e a - a x i s f o r t h e p r o p o s e d Theoretical Rigid Solid. The  theoretical  0.0000 -0.0874 0.2464 0.1754 0.0874 -0.2464 -0.1754 0.4074 0.5000 0.5000 0.5000  0.0000 0.2464 0.1754 -0.0874 -0.2464 -0.1754 0.0874 0.5000 0.2736 0.5000 0.7264  I t i s n o t meant t o i m o l y a c c u r a c y  4.  f o r SF* A s F ~ a t "291°K" 0 0  to four s i g n i f i c a n t  figures.  structure.  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 t h e  rigid  lattice  s e c o n d moment f o r SF* AsF~ c a l c u l a t e d 3 6 2 by Program 6 from t h e 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 t h e n a t u r a l abundance 33 of  S, t h e o n l y s t a b l e , m a g n e t i c i s o t o p e o f 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 .  T h e r e a r e a g r e a t many a s s u m p t i o n s i n -  v o l v e d i n t h e 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 F o l l o w Page 75  F i g u r e 26. SF*AsF£ .  Proposed u n i t c e l l ( a l o n g  a-axis)  c  A  P  23  PROPOSED  POSITION  OF  PROPOSED  POSITION  O F "S  Qo = 5.6 A  O  As AT CORNERS A T ( 1/  2  1/ , 1 / ) 2  2  5A  CIRCLES INDICATE FLUORINE Von  d e r W o o l s radii  check. can  Indeed the count o f i n t e r n u c l e a r d i s t a n c e s  provide  shows t h a t t h e SF* i o n i s somewhat crowded i n i t s  assumed p o s i t i o n .  There a r e f o u r SF* i n t e r g r o u p  surrounding AsF^ ions. but  w h i c h Program 6  with  Two a r e n o t t o o s e v e r e b e i n g 2.5 and 2.68 ,  the o t h e r two a r e 2.2A w e l l u n d e r t w i c e  d e r UJaals r a d i u s .  contacts  Inspite of t h i s  of a r e a s o n a b l e m a g n i t u d e . s e c o n d moment a r e l i s t e d  t h e 1.358 f l u o r i n e van  t h e c a l c u l a t e d s e c o n d moment seems  The v a r i o u s  contributions  to the t o t a l  i n T a b l e 10. T a b l e 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  t o SF* AsFg 2  S F  S F  3  A S F  3  6  flsF  AsF~ 0  AsF"  0  6  Second Moment Gauss F-F F-As TOTAL-  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 o v e r s8 o f 0.31 g a u s s ^ t o F-F)  8.80  0.52  9.42  4.72  0.51  5.23  5.96  0.51  6.47  3.62  0.50  4.12  •2.63  0.01  2.64  0.77  0.00  0.77  INTRA TOTAL ( t o  e8) •  INTRA TOTAL ( t o  68)  INTRA  Note:  56  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 a r e based on a 9 - f l u o r i n e u n i t SF+ A s F " . N i n e q u a t i o n ( 2 ) J D has been t a k e n as 9 f o r a l l o r o u p s .  Reorientations One t h i n g  i n the S o l i d  to n o t i c e  i n T a b l e 10 i s t h a t  f o r the component SF* c u r v e , i f i t c o u l d  t o t a l second  be r e s o l v e d  out,  moment is  9 2.64  -  2  w h i l e i t s i n t r a g r o u p s e c o n d moment i s o n l y 9 2 + 0.77 x = 2.3 gauss . I n d e t e r m i n i n g p o s i t i o n s i n t h e SF^ i o n ,  it  x  77  gauss  =  was assumed  i n agreement  with Bartlett  ( 6 ) t h a t because o f t h e  e l e c t r o n l o n g p a i r on t h e s u l f u r ,  t h e 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 .  T h e r e f o r e S-F bond l e n g t h s o f  1.56$  a lone p a i r w i l l  of a  ( 8 3 ) and F-S-F a n g l e s o f 109° 28' were u s e d .  bond p a i r  (7).  The p r e s e n c e  r e p e l t h e t h r e e bond p a i r s somewhat more t h a n  The bond a n g l e w i l l  than the t e t r a h e d r a l a n g l e .  t h e r e f o r e be somewhat  less  T h i s would r e d u c e t h e 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 w o u l d hence r e d u c e t h e r a t h e r  heavy  2 proportion of i n t e r  (7.9 - 2.3 = 5.6 gauss ) t o i n t r a - g r o u p ' s e c o n d  2  +  moment ( 2 . 3 gauss ) i n t h e SF^ i o n . which t i l t e d  t h e i o n away from i t s assumed  change t h e s e c o n d moment.  p o s i t i o n would  cell  also  However, r e d u c i n g t h e t e t r a h e d r a l a n g l e  w o u l d r e d u c e t h e e f f e c t i v e volume in  A p o s i t i o n i n the u n i t  o f t h e i o n and g i v e . i t mors freedom  the AsF^. " c a g e " 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 m o t i o n as l o w as o  0  77 K.  The most p r o b a b l e m o t i o n a t 77  axis.  The s h r i n k a g e o f t h e i o n due t o t h e s m a l l e r bond a n g l e would  a l s o r e d u c e t h e moment o f i n e r t i a the  ion's -ability  enhance  zero f i e l d  rigid  lattice  s e c o n d moment i s a b o u t 0  y e t t h e e x p e r i m e n t a l moment a t 30 fflHz and 77 K, w h i c h i n -  cludes a contribution The  a b o u t t h i s a x i s and f u r t h e r  to r e o r i e n t .  The c a l c u l a t e d 2 9.4 gauss  i s r e o r i e n t a t i o n about the  t h e o r e t i c a l zero  from i s o t r o p i c  chemical s h i f t ,  field  i s o n l y 5 9 gaus 0  a n i o n and c a t i o n r e s o l v e d c u r v e s would 9 , 2 2 have s e c o n d moments o f about 6.47 x /6 = 9 7 gauss and 7.9 gauss r e s p e c t i v e l y i f t h e y c o u l d be measured a t t h e i r r i g i d lattice 0  78  temperature.  Their a c t u a l resolved  components a t 77°K and 30 MHz  2 have moments o f 2.8 gauss  2 and 4.7 gauss .  m o t i o n i n t h e groups i s s u f f i c i e n t n o t only  O b v i o u s l y by 77°, t h e to average out tha  anisotropy  ( s i n c e t h e components a r e s y m m e t r i c a l ) , b u t a l s o t o 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 t h e t o t a l s e c o n d moment o f t h e e x p e r i m e n t a l 30 MHz c u r v e has f a l l e n  2 t o a b o u t 1.9 gauss .  S i 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  above the t r a n s i t i o n ;  t h e r e s o l u t i o n i n t o components made a t  94.1 IYIHz and 300°K w i l l change i n l i n e  shape  be v a l i d  h e r e t o o ( t h e r e i s v i r t u a l l y no  from 200 t o 295°K a t 30 MHz).  2 moments a r e 1.1 gauss respectively.  2 and 0.9 gauss  The s e c o n d  +  —  f o r t h e SF„ and A s F ~ i o n s  The a n i o n s u r e l y and t h e c a t i o n  undergoing i s o t r o p i c  region  very l i k e l y a r e  or n e a r i s o t r o p i c r e o r i e n t a t i o n above t h e  transition. In the absence of a r i g i d possible  to o b t a i n a r e l i a b l e  l a t t i c e s e c o n d moment, i t i s i m -  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 c a n o f c o u r s e e s t i m a t e a r e a s o n a b l e v a l u e f o r t h e e x p e r i m e n t a l rigid  lattice  s e c o n d moment a t 30 MHz ( a t w h i c h f r e q u e n c y t h e  t e m p e r a t u r e dependence s t u d i e s were made) and e v e n t u a l l y a t an a c t i v a t i o n e n e r g y . 1 K c a l per mole o b t a i n e d . t h a n one n o r m a l l y o b t a i n s The  transition  arrive  T h i s was done and an e n e r g y o f a b o u t I t i s o f c o u r s e an even c r u d e r e s t i m a t e from s e c o n d moment s t u d i e s , ,  between  meaningful a c t i v a t i o n energy.  336 and 342°K i s t o o a b r u p t t o g i v e a The v a l u e o f t h e t o t a l s e c o n d  moment  i s about 0.1 gauss  which i n c l u d e s the c o n t r i b u t i o n from  relative  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 p r o b a b l y t a k i n g  place through the s o l i d .  Although the sample i s rather" p l a s t i c  • l o o k i n g a t 373 K, i t remains s o l i d and does not melt even when h e l d a t that temperature f o r s e v e r a l hours.  CHAPTER \l SUMMARY AMD It i s difficult studied.  to o b t a i n p r e c i s e r e s u l t s  This i s p a r t i c u l a r l y  t i o n o f t h a t compound i s i n t o t r o p i c s h i f t o f 105 ppm 300 ppm.  so w i t h 'wTg  .  The most p r o b a b l e r e s o l u -  two components s e p a r a t e d by a mean i s o -  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  rigid  f o r the t h r e e compounds  and each w i t h an a v e r a g e a n i s o t r o p i c s h i f t  quoted f o r t h e z e r o f i e l d , retical  DISCUSSION  of  be made, no v a l u e s were  d i p o l a r broadening of each.  From t h e t h e o -  l a t t i c e s e c o n d moment, the c o n t r i b u t i o n s o f t h e 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 t o t h e t o t a l second moment f o r t h e m o l e c u l e a r e 2 2.71  gauss  2 and 5.44  gauss  respectively.  r e l a t i v e numbers o f f l u o r i n e s  Weighted  a c c o r d i n g t o the  i n v o l v e d i n e a c h , they w o u l d  give  2 8.14  gauss  f o r each component i f t h e y c o u l d  second moments a r e v i r t u a l l y  identical  out.  These  t o t h e s e c o n d moment o f t h e  observed z e r o f i e l d  c u r v e ( a c t u a l l y a t 2 MHz)  broadening f u n c t i o n  (components  reconstruction  be r e s o l v e d  w e i g h t e d 4:2  w h i c h was  used as a  by a r e a ) i n t h e a t t e m p t e d  based on the s h i f t s m e n t i o n e d , i m m e d i a t e l y above.  assumed t h a t the i n d i v i d u a l  l i n e shapes would  t o t a l curve at zero f i e l d .  The  about l i n e s h a p e .  L i n e shapes  be s i m i l a r  I t was  t o t h a t o f the  second moment, however, s a y s n o t h i n g a r e much more d i f f i c u l t  to p r e d i c t  a r e s e c o n d moments, w h i c h , o f c o u r s e , i s the d i f f i c u l t y  than  here.  F o r t h e two AsF,. a d d u c t s 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 determined.  However, even  f o r IF* AsF. D  average a n i s o t r o p i c s reliable  could  value at a l l could  only  o  be e s t i m a t e d f o r t h e two components. be o b t a i n e d f o r SF* AsF~ s i n c e a -  80  -  No  rigid  81  l a t t i c e mas not found w i t h i n the temperature range of the i n v e s t i g a t i o n . A l l t h r e e o f 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 e n e r g i e s of v a r y i n g r e l i a b i l i t y were determined f o r the probable r e o r i e n t a t i o n s o c c u r r i n g . 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 r e s o l v e d component,, "Table 11 summarizes  what are considered t o be the best values  obtained here f o r the 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 , second moments, t r a n s i t i o n temperatures, and p o s s i b l e 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 d i s c u s s e d i n d e t a i l  earlier.  F i n a l l y , i t i s p o s s i b l e from the a n 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 t o draw some c o n c l u s i o n s about bond c h a r a c t e r i n the h e x a f l u o r i d e 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 t o  chemical s h i f t i s from the paramagnetic term i n equation (10) a c c o r d i n g to Saika and S l i c h t e r (70) and K a r p l u s and Das ( 8 8 ) .  Following  their  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 * / ^ , and s which are r e s p e c t i v e l y the i o n i c 7  c h a r a c t e r , double bond c h a r a c t e r , 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 f o r 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 o f 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 Group  A ppm  B ppm  -300+40  ^6  GAUSS  D . GAUSS'  8.25+0.2  1.0+0.05  180-210  10.0+0.4  10.7+0.2  2.1+0.2  205-235  19+4'  equatorial F  -435+40  ~300  » .. 1  axial  -325+40  ~300  8.14  F  -170+8  "I  -245+20  ~333  10.20  1  2-.0  AsF~  -100+20  ~333  10.44  1  0.7  -155+15 -205+20  5.9+0.3 9.4l 4.7 7.9 2. 8 9.7l 2  I s o t r o p i c or near i s o t r o p i c  1  IF* AsF" o o  6  Kcal/mole  1.9+0.1  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. I s o t r o p i c or near i s o t r o p i c <77-200  ~1  1.1  I s o t r o p i c or near i s o t r o p i c  0.9  Isotropic  342-373°K 336-342 Q.l  Diffusion  1  AsF~ o SF* AsF" o o  B. C.  0. £. F. G.  -105+20  2  lYlean i s o t r o p i c c h e m i c a l s h i f t to n e a r e s t 5 ppm r e l a t i v e to HF. A n i s o t r o p y of Chemical s h i f t [S Zero f i e l d second moment 77°K. 11 Second moment a t 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. P o s s i b l e 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. 2.  C a l c u l a t e d f o r theoretical, rigid lattice. Not a r i g i d l a t t i c e .  -  The  K  r e l a t e t o ff - b o n d i n g  expressionsand  i n t h e xz and yz  S u c h fT-bonds may be formed by t h e o v e r l a p o f t h e f l u o r i n e  planeso p x  83  and p y  o r b i t a l s with the d xz  K  chemical s h i f t i s expected o f t h e bond, from Although  and d yz  c e n t r a l atom o r b i t a l s  to vary, according t o the i o n i c c h a r a c t e r  HF t h e most i o n i c down t o F^ t h e most c o v a l e n t o  hybridization  c o u l d have t h e 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 b e c a u s e o f t h e d i f f i c u l t y a numerical estimate. z a t i o n , we s h a l l  The  0  Although  Andrew has t a k e n a c c o u n t  o f making of hybridi-  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 R i g n y  (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 , t h e n , i n t h e c a s e symmetry o f t h e c h e m i c a l s h i f t : t e n s o r where 6  =  ZZ = ^ ±  » equations  .  and &  IJ  = XX  (31) reduce t o  e„-is (y-/> )  <  z  c  of a x i a l  32)  ,  6 j . =f 6 o ( l - I ^ D where Das  =  /^y  =  a n d  the c o e f f i c i e n t  the exact value o f ^ trends calculated are o f primary The  ^ q  /^  a  n  d  1  a  r  e  as'above.  = -863 ppm.  q  From K a r p l u s and  They p o i n t o u t , however, t h a t  i s n o t i m p o r t a n t s i n c e i t does n o t a f f e c t t h e  and i t i s t h e t r e n d s , n o t t h e a c t u a l  values,  significance.  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)  which  or  for a x i a l  symmetry  of  the  shift  tensor  S:i(Z6 .+<5„)  ( 3 4 )  J  If  §  i s measured  enables  individual  stitution are  into  available  670+50 f o r U F and  relative values  equations here, and  &  but  Blinc  the i n d i v i d u a l  27  as  groups  then  the  knowledge  and  ^j,  to  Only (41)  1300+100 and  e q u a t o r i a l components  fluoride  6„  of (32).  average a n i s o t r o p i e s are for  t o HF,  reports values  respectively. probably  components  s t u d i e d here  0  good  F i g u r e 27,  f o r UF  estimated  f o r the  t h a t such  plots  compounds. groups.  5-F  be  Figure  Indeed  = ^  bond i n SF*  .  considered  only  27  taken  even  will the  value  nor  fitted  to  components  shifts  found  here  Blinc  and  (41)  components i n PuF^  although  , he  unable was  I = ~  applying  ths  as  to  holding  value  to determine  able  to  estimate  values  Figure  HF.  0.8  can  and  be  Das of  caution similar  axial  component  f o r I i s i n good  of  the  the  for hexafluoride  of  l i e far outside values  axial  hexain  to  groups  e q u a t o r i a l component  give meaningless  was  and  the  plotted  respect  f o r t h e UF^  Also neither axial Both  0.01  only  of  ment.  plot.  plot  as  widely  the  the  be  with  to  I f o r the  are  and  therefore,  However, K a r p l u s  viates  although  from  shift  (oL )  f o r the  f i  case,  and  Gx.)  for sub-  640+50  approximations  also  of ^  values  In our  o f ^  and  of  ~  ( <3,,  of  for PtF  Values  a f u n c t i o n o f mean i s o t r o p i c From  values  1 3 8 0 + 1 0 0 ppm  (€5,,  obtained  0 8  average  of  PtF^ the  and  deagree  can  be  range  of  I.  However,  a n i s t r o p i e s of  mean i s o t r o p i c  the  chemical  To  O  -200  -400  M E A N  Follow  Page 84  -600  ISOTROPIC  -800  -IOOO  SHIFT  P P M  -1200  8 5  shifts  o f -440 and -1070 ppm  torial  components  range of s h i f t s  respectively.  i n F i g u r e 27.  0.1, I = 0.6 I = 0.03  relative  These s h i f t s  do l i e w i t h i n t h e  From t h e f i g u r e we can  f o r the a x i a l  f o r the e q u a t o r i a l  t o HF f o r t h e a x i a l and equa-  predict  f l u o r i n e bonds a n d ^ ^ = 0.38,  bonds.  APPENDIX I  COMPUTER  AH adapted  the programs i n t h i s to Fortran  Columbia's  a p p e n d i x have been w r i t t e n i n o r  IV as c o m p a t i b l e w i t h  IBM 7040 (now t e m p o r a r i l y  p r o g r a m s have been t i d i e d were u s e d .  PROGRAMS  However t h i s  the U n i v e r s i t y o f B r i t i s h  7044) c o m p u t e r .  up s l i g h t l y  from t h e form i n w h i c h t h e y  merely i n v o l v e d changing n o t a t i o n  might  have been c o n f u s i n g .  input  as d a t a s t i l l  Some q u a n t i t i e s w h i c h r e a l l y  t o adapt  that  c o u l d be  a p p e a r i n s t e a d i n t h e programs t h e m s e l v e s .  T h e s e a r e o b v i o u s , however, and c a n e a s i l y wishing  Some o f t h e  be changed  t h e programs f o r h i s own u s e .  86  -  by any one  87  Program 1.  C a l c u l a t i o n o f 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 p r o g r a m i s f o r t h e g e n e r a l case o f an a s y m m e t r i c d e r i vative  curve.  F o r an a s y m m e t r i c c u r v e  the second  moment i s  2 Sffl = S - (Fiil) .  SM i s t h e s e c o n d  moment a b o u t t h e c e n t r o i d  of the  c u r v e , S i s t h e second  moment computed about any p o i n t ( t a k e n a t  the e s t i m a t e d  to minimize  centroid  e r r o r ) , and F!K1 i s t h e f i r s t  moment computed a b o u t t h e same p o i n t . the second  For the d e r i v a t i v e  moment i s  sxy  3  U  £  »y >  ——-  where s c a l e = g a u s s p e r d i v i s i o n .  The l a s t term  for  f o r modulation  is  Sf(l i s Andrew's ( 8 9 ) c o r r e c t i o n  o n e - h a l f t h e peak t o peak m o d u l a t i o n .  experimental curves, convenient,  the x - a x i s  i n the equation broadening,  I n t h e measurement o f t h e  o f t h e spectrum  e q u a l d i v i s i o n s , f o r which  m i n e d , and t h e c o r r e s p o n d i n g The  curve  i s divided  into  a c a l i b r a t i o n has been d e t e r -  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  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 d a t a s h e e t s and t h e  remainder  o f t h e d e t e r m i n a t i o n o f t h e second  moment i s c a r r i e d o u t  by t h e c o m p u t e r . : t h e i d e n t i f i c a t i o n number o f t h e d e r i v a t i v e c u r v e or TRACE = t o t a l number o f d a t a p o i n t s on t r a c e N = t o t a l number o f d a t a p o i n t s on t h e f i r s t h a l f o f t h e c u r v e 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. SCALE := g a u s s p e r d i v i s i o n  N Nl N2  PfflOD :: A Km = \ peak t o peak "modulation  TEMP IY  sm,  :: t e m p e r a t u r e i n d e g r e e s r y amplitude i n a r b i t r a r y units d i v i s i ons s, and Ffil a r e as d e s c r i b e d above.  f o r each o f t h e M l e q u a l  88  It  i s i m m a t e r i a l a t w h i c h end o f t h e s p e c t r u m measurement i s com-  menced.  However t o a v o i d  Program 2 , i f i n t e g r a t i n g  c o n f u s i o n as to f i e l d derivatives  m m e t r i c , i t i s recommended  that  S t a r t a l w a y s a t t h e low f i e l d t i v e i n that  direction in  which are only s l i g h t l y  a consistent  policy  be  end and choose t h e s i g n  h a l f of the spectrum.  asy-  followed. o f IY p o s i -  s  • I; i " S F O R T  R A N  C  S E C O N D  1  F O R M A T  ( J. 9  I 4  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  F O R M A T  5 R  E  A  ( I X ,  D  I 5 »F6  (IY  ( 5 » 1 )  K F M  =  1 » F9  {' I  ) , I  I S  T o ~ I  1 0  J  = 1 »  I Y ( J K  +  = ~ I A =  +  "" . 2 > . 1 X  ,F8  ""  . 2 » 5 X , F6  . 2 » 5X  , 8 A 6  )  }  _  l7Nl )  .  _  _  ^  .  ~  K F M  " f*  _ I  YTJ )  .;_  F M =",< F M =  =  „  I S  _ A.= I A  F M  )  _  I =  S U M  '.  N 1  = K * I + I S _ _  A  __  !  I = J - N 2 < = I *  _  »J_HS »_1 OA? 2 H£M » 1 OX»?HSM)  ,4X»1HT>5X  """  .  _  K F M  _  0  . D O  .  . ( 5 » 2 . ) N.» HI »N2 > SCAL E » PMOD » TEMP » ( C ( I ) » I = 1» 8 )  ,. R E A D 6  E  WRITE'"'("6737  4  ./.i  X 5  IX » 5 H J R _ A C  J  •  j.  I.Yi..2 0 J D . J . . » C..L9,.,) ,  "  M O M E N T  D.I M E N S J . 0 N  ..  "  "  E X P E R I M E N T A L  _  _..  ;  _  '"  .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  .  )  _  '_  _  _  ~ SM=S-FM*"'FNr-7'2 5*PM _  W R I T E G O  S E N T R Y  E  (6»4)  T O  N  D  5 -  N » T E M P » S » F M » S M » ( C (  "  ~  _ ~  _____  •  I ) »1 = 1>  8 )  _ - -  —  __ '  -  ___'  . —--  •  _  '  90  Program 2.  I n t e g r a t i o n o f D e r i v a t i v e Curves t o A b s o r p t i o n  T h i s program i n t e g r a t e s t h e d e r i v a t i v e s p e c t r a u s i n g t h e d a t a punched The  integration  i s performed  curves  f o r the second  = = = =  to absorption  moment c a l c u l a t i o n s .  using rectangular strips  s m a l l e n o u g h ^ a r e s u f f i c i e n t l y a c c u r a t e f o r broad NWBR N SCALE IY  which,when  l i n e nmr.  i d e n t i f i c a t i o n number o f d e r i v a t i v e c u r v e t o t a l number o f d a t a p o i n t s gauss p e r d i v i s i o n (on t h e d e r i v a t i v e c u r v e ) y a m p l i t u d e s o f t h e N p o i n t s on t h e d e r i v a t i v e  I n t h e body o f t h e program t h e G ( l ) ' s a r e t h e a m p l i t u d e s absorption  curve a t p o i n t s separated  t a n c e SCALE. sure  one from  another  I t i s expressed  maximum a m p l i t u d e  as a p e r c e n t a g e  punch i n s t r u c t i o n  l a s t program o u t p u t s  which  the data  curves.  were w r i t t e n  FNORfil n o r m a l i z e s t h e  area f o r comparison  from  w i t h each o t h e r .  Program 2 on an X-Y  c o u l d be made d i r e c t l y  plotter.  between t h e  S i n c e t h e program c a l l s s p e c i a l r o u t i n e s  e x p r e s s l y f o r t h e computer here  c e n t e r s t a f f , i t cannot  This  to give a constant x-scale to a l l the absor-  c u r v e s so t h a t c o m p a r i s o n  area-normalized  of the i n t e g r a -  p r o d u c e s d a t a f o r use i n Program 2 .  program was w r i t t e n  ption  by t h e d i s -  i n terms o f G(N) and X t h e  of the a b s o r p t i o n curve.  spectra to constant a r b i t r a r y  The  of the  of the i n t e g r a t i o n .  Z, t h e DEVIATION, g i v e s an e s t i m a t e o f t h e a c c u r a c y  The  curve  BL i s a c o r r e c t i o n p a r a m e t e r a p p l i e d t o G ( l ) t o en-  t h a t G ( l ) approaches zero a t both l i m i t s  tion.  Curves.  be used  elsewhere.  by t h e c o m p u t i n g •  $ FORT RAN C I N T E G R A T I O N OF D E R I V A T I V E C U R V E DIME N S J O N G(100) » T I T L E ( 9 ) > I Y ( 1 0 0 ) 20 " R E A D ( 5 > 1 ) NMBR J N « S C A L E > (~TITLE( I ) » I = 1 »9 1 F0RMAT(A4»I<+»4X»F7o4*6X»9A6) READ ( 5 * 2 ) ( I Y ( I ) »_ I = 1 »N ) F O R M A T ! 1 9 14> 4 X ) H = 0. Dp 1 0 . : = .:..». N H = H +FLOAT( I Y( I ) ) 10 G(I)=H*SCALE . ._Z = G..(. NJ : WR I ' E ( 6 » 1 2 ) N M B R » ( T I T L E ( I ) , I1.9) BL = G ( N ) / F L O A T ( N ) DO„.2_9. _ _ I _ 1 »N_ 29 G ( I =) G ( I ) - F L O A T ( I ) # B L X=0 Y=0 DO'"3'0 I=1 , N I F ( G ( I ! .GT.X)X =G ( I ) I F ( Y . G T . G f I ) ) Y = G { I.!. 30 "CONTINUE I F ( X. LT . ( -Y )Y ) X = Z=Z*100./x " A R E A = O'C DO 1 0 0 1=1,M 100 A R E A = A R E A + G ( I •SCALE ) FNORM=1000./AREA DO 1 1 0 1 = 1 , N 110 G ( I ) =G (_I Hi-FNORM ^ "WRITE; 6 »40)AR'EAVZ 40 FORMAT(70X>5HAREA=,F10.1»5X*10HDEVIATION=»F10.4) WRITE ( 6 . 1 1 ) ( G ( I ) » I_= 1_» N J ' " P U N C H 1 > NMBR >N > S C A L E * PUNCH 11* ( G ( I ) » I = 1 » N ) 11 FORMAT ( 1 0 F 8 . 2 ) _ ~i2 ~FbRiMATr'3X\T4TrOX 79 K&) ~ " ~ " SENTRY  GO TO END  20  o  I  -vO-  L  a  $ IB F T C • ' C  1 2 •• 3 4  REMEMBER  LAST  S P E C , N, S C A L E  CARD  MUST  BE  BLANK.  TO  CALL  PLOTND  DIMENSION X(100)»Y(100) CALL PLOTS  READ (5,2) SPEC,N,SCALE FORMAT (F4.0,I4,4X,F7.4) IF(N.LE.O) GO TO 1 0 0 READ (5,4) <Y(I),I=1,N) FORMAT (10F8.2) DEEX=SCALE/2.54 DEEY=0.03  •-  —  10  11  12  100  SENTRY  S=FLOAT(N-l>*DEEX DO 1 0 I = 1 , N X( I ) = F L O A T ( I ) * D E E X  o  DO 11 I = 1 • N Y ( I ) =Y ( I ) * D E E Y .  I F ( Y ( I ) . L T . (-0 . 2 5 . ) )  Y(I)  C A L L NUMBER' DO 12 I=1,N  ( 5 . , 8 . , 0 . 14 ,  CALL  (X(  SYMBOL  I ) ,Y(  END  SPEC,0.,-1)  I ) ,0.14,3,0.,-I  vO  ^  '  1  = (-0.25)  CALL PLOT ( (S+2. ) , 0 . , - 3 ) GO T O 1 CALL PLOTND STOP  CP5 4  )  ro  -  P r o g r a m 3.  93  L i n e Shape F u n c t i o n F ( H ) .  T h i s program s y n t h e s i z e s a c u r v e determined moment.  values of  - ^)  a r |  d the zero f i e l d  I t i s w r i t t e n f o r the case  a x i a l symmetry o f t h e i r are present,  shift  and  I f non-equivalent  two o r more s y n t h e s i z e d c u r v e s  F(H) i s given  0  may  be c h o s e n e q u a l F(H)  =  curve, to zero  H  will  second exhibiting nuclei  appropriately shifted  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  t h a t of the experimental  dipolar  of equivalent n u c l e i  tensors.  r e l a t i v e t o each o t h e r may be u s e d Since  F(H) u s i n g e x p e r i m e n t a l l y  by e q u a t i o n ( 2 1 ) ,  be s u p e r i m p o s e d on  be i d e n t i c a l i n each  f o r t h e program.  case  Therefore  f(H0)S(H-H0)DH0  (A)  where  f (HO) * and will  (I  HO  VI  ALPHA J  the constant i n equation itself  be n o r m a l i z e d  () Q  (B) i s omitted s i n c e the f u n c t i o n F(H)  i n t h e program.  Two p r o g r a m s , 3a and 3b, a r e g i v e n below. mental l i n e  shape a t 2 MHz has been used as t h e b r o a d e n i n g  S(H-HO) and f o r 3b t h e b r o a d e n i n g having  F o r 3a t h e e x p e r i function  f u n c t i o n i s a gaussian f u n c t i o n  t h e same s e c o n d moment as t h e e x t r a p o l a t e d z e r o " f i e l d  moment.  The f o r m e r  mas u s e d w i t h UiF_ and t h e l a t t e r w i t h I F * AsF 6 6  Program 3 a . ALPHA SCALE  second  = the " a " d e f i n e d under e q u a t i o n (16) = s e p a r a t i o n i n . g a u s s between t h e d a t a p o i n t s on the e x p e r i m e n t a l b r o a d e n i n g f u n c t i o n ( e b f . ) .  D  94  Program 3a  Contd.  NY  = t h e number o f d a t a p o i n t s ^ i n c l u d i n g t h e c e n t r o i d _ , on t h e l e f t h a l f o f e b f . Nffl = t o t a l number o f d a t a p o i n t s on e b f . Y(l) = an a m p l i t u d e on e b f . H and DHO = (where DHO = dHo) a r e as d e f i n e d u n d e r e q u a t i o n ( 2 1 ) . AlflP = t h e maximum a m p l i t u d e o f the e x p e r i m e n t a l c u r v e . I f t h e c u r v e c o n s i s t s o f two o r more components, t h e s y n t h e s i z e d c u r v e must be n o r m a l i z e d t o t h e a r e a , not the h e i g h t o f the e x p e r i m e n t a l curve. Program 3b. ALPHA i s a s f o r 3 a . BETA i s t h e s q u a r e r o o t o f t h e e x t r a p o l a t e d z e r o f i e l d r i g i d l a t t i c e s e c o n d moment. H, DHO, and Amp a r e as f o r 3 a . B o t h programs o u t p u t of  H - labelled  values o f F(H) - l a b e l l e d  dipolar  F ( K ) here - f o r v a l u e s  C(K) here.  Note t h a t i n t h e a c t u a l programs SH(H-HO) i s w r i t t e n as SH(HO).  SIBFTC C  ANISOTROPIC FUNCTION WITH EXPERIMENTAL BROADENING FUNCTION ..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") = 1 »~NM ) FORMAT ( 1 0 F 8 . 1 ) _WR I T E j_6>_2_..) ! Y_(_I_)__»_I = 1 ._NMJ. READ (5.4) ALPHA .SCALE .NY.AMP FORMAT ( 4 X . 2 F 1 2 . 4 . 4 X . I 3 . 4 X . F 1 2 . 4 ) .WRITE. (.6... 4 ) + L.PH A...S.C AJ=.E i N Y _ AM.E H=-20. DH=0.5 DHO=0.1 __ DC 11 K = T » 8 0 F(K ) =0. H= H+DH ' GTK )' = H ~ ' " ~ ™ " " ~ HO=-ALPHA+0.01 I F ( H . G T . 2 0.) GO TO_3_ "bo1 o" L = 1 .?000* HO=HO+DHO I F ( H O . G T . ( 2 . A L P H A ) ) GO TO 1 1 'F ( K )"=F (;< ) +F'HVH'OT^SHI H'O'T FMAX=0. DO 2 0 N= 1.8 0 _ (N )) FMAX= F ( N ) IF(FMAX.LT CONTINUE FMAX=AMP/FMAX  Ti  .T  3 4  L  t  10 11 20 21 22  DC21N=T,'80  F ( N ) = F ( N ) *FM + X F ( K ) » K=l» 80 ) WR I TE. ( 6 , 22 ) ( G ( K) "FORMAT"" ( 1X Y 2 F 12". 4 ) GO TO 3 END  o  n ... ^  ..  _vO.  S I B F T C  FH F U N C T I O N  FH(HO)  C ,OMMQN.._. A L P H A... S C A. L £ A . N . X ...N. K . » Y.vrd..»±LO__ DIMENSION  Y(  00)  FH= 1 . +HO./ALPHA • FH_= 1 . Z.SQ..R I I F H . . ) RETURN END S 1 3 F 7 C  SH.._ F U N C T I O N '  COMMON _  SH(HO) 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 )  GO  TO  1 1 0  I F ( J . G E . N M )  GO  TO  1 1 0  BE LOW =  ,;0-  Y(J)  A 3 0 V E = Y ( J + l ) _ FT N K = ( A B O V E - B ' E L O W ) * (  i io_ 111  112 _  GO  TO  111  . G O  T0  112  SH = O.  SH=BELOW+FINK  „C  0 N T I NU.E  RETURN END  FE J - F L O A T  ;  ( J )  SFORTRAN C A N I S O T R O P I C F U N C T I O N WITH G A U S S I A N BROADENING PJ.MF.NS„lp^N_..XL.lO..Q.i.»Gixg^.L COMMON A L P H A , B E T A , H 1 READ ( 5 , 2 ) A L P H A , BET A,AMP FORMAT ( 1 X , 3 F 1 2 . 4 ) 2 "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 _ _ _ _ HO=-ALPHA+0.oi I F ( H . G T . 2 0 . ) GO TO 1 ...DO 10 J-1 ,2 0 0 0 ... . _ HO=HO+D'HO I F ( H O . G T . ( 2 . * A L P H A ) ) GO TO 11 F ( K ) = F ' ( K ) + F H (_HO ) * S H i H O ) _ :  10  I  I  ~  F  M A X "= 6 " . " " " " 2 0 N= 1,8 0  """""""  DO  I F ( F M A X . L T . F ( N  2  ) )  FMAX =  F(N)  0 C O N ' f l N U E , FMAX = A M P / F M A X  21 22  _..DO 2.1... NL=1 .'.8 0 F ( N ) =F ( N ) -»FMAX WRITE ( 6 , 2 2 ) ( G ( K ) » F ( K ) » K = 1 » 8 0 ) FORMAT ( 1 X , 2 F 1 2 . 4 ) GOTO1 END  FUNCTION  Oi  1!  -  -  ' ^ .  cq 3 '2  • _  '  "  °"  $ FORT RAN FUNCTION FH(HO) COMMON A L P H A , B E T A , H FH=1,+HO/ALPHA FH=1„/SORT(FH) ..REIURN.._ END SFORTRAN  SENTRY  3  . F U N C I J 0_N._.SH.(.HOJ...._.._ COMMON A L P H A , B E T A , H 5H=EXP(-(H-HO)*(H-HO .RETURN END  99  Program A.  Doublet F i t .  T h i s program i s from  D r . P. Raghunathan o f t h i s D e p a r t m e n t  and i s based on Abragam ( 5 2 , p. 2 2 0 ) . ALPHA and BETA a r e r e l a t e d by SiTl = ~ oL +/S * where Sffl i s t h e second moment o f t h e e x p e r i m e n t a l c u r v e and oC = ^ y t v t - " where r i s t h e e s t i m a t e d d o u b l e t splitting. H i s again a general f i e l d parameter. X i s t h e HO o f Program 3 and Abragam ( 5 2 , p . 2 2 0 ) . 2  3  The  program p u t s  o u t a m p l i t u d e s , 5Urn", f o r v a l u e s , H.  t h e e x i s t i n g program ( w h i c h was w r i t t e n put i n t o " p o l i s h e d "  form) a r e s c a l e d  the e x p e r i m e n t a l c u r v e values of r are t r i e d  f o r comparison  These i n  f o r a s i n g l e use and n e v e r  by hand t o t h e a m p l i t u d e o f of l i n e  u n t i l a f i t i s obtained.  shapes.  Different  $ I B r TC  r  21 22 10  DOUBLET F I T D I M E N S I O N C< 14) COMMON A L P H A , B E T A , X READ( 5,22>.<C( I ) » 1 =14 1) FORMAT(IX ,13A6,Al) W'RITE(6»22)(C(I)»I = 1»14) P R I N T 10 _F0RM AT ( J X . 3 4 H D 0 U B L E T _ L IjN ESHAP E FIT ABRAGAM READ(5,1) ALPHA,BETA DX= 0 o 0 1 2 5 .X = 2_,.JtALPHA H = 0. DO 1 0 0 1 = 1 , 1 0 0 0 H= H + ( 4 0 . * D X ) IF(H.EQ.ALPHA) H=(40.*DX H SUM = 0 . D. /- .-.3... * .ALPHA . DO 90 J= 1 , 4 0 0 0 D = D + DX I F ( D . G T . ( *A 3 LP HA) ) GO TO 91 f = H-D I F ( D . L T ( - A L P H A ) ) P = FH(D) I F ( D . G T .ALPHA)P=FO(D) _ I F( ABS ( D ) . LT . ALPHA ) P = FL ( D) SUM = P*SH(T)*DX+SUM CONTINUE. ___ . W R I T E ( 6 , 2 ) H, SUM FORMAT(2F12.8) FORMAT ( 1X»2HH=»F12_.8»10X,5HF »F13.4) I F ( h.GT . (3 . * 3 E Y A ) ) "GOT5To'l" CONTINUE CONTINUE _ _ GC T O 2 1 " " ' " " END _  90 91 1 2 100 101  01  Tl  v, A  P219)  "o"  S I B F T C FHD FUNC TION F H ( D ) ' COMMQN A L P H A , 3 E T A , X I F ( .D L T . X )'FH = 0. I F ( D . GT .X ) FH= ( - D / A L P H A + i . )- 0*>.•5 ) RELY. RN END S I B F T C SHT FUNC TI.ON_.SHJ_T )._ COMM ON A L P H A , B E T A , X SH = E X P ( - T * T * 0 . 5 / ( B E T A * B E T A ) ) / ( B E T A * 2 . 5 0 5 ) RETU RN END S I B F T C FLD FUNC T I ON F L ( D ) COMM ON A L P H A , B E T A , X A= D /ALPHA F L = ( - A + l . ) * * ( - 0 . 5 + ( A + l . ) ------ ( -0 , RETU RN END S I B F T C FQD FUNC TION F Q ( D ) COMM ON A L P H A , B E T A , X I F (.DG T . X ) F Q = 0 . I F ( .DL T . X ) F Q •= (6+1. **'( -0 . 5 RETU RN EN_D_ SENTRY"  -(-?  - 102 -  103  P r o g r a m .5  0  Transformation  of  Coordinates,,  T h i s program g e n e r a t e s b l o c k s  of u n i t c e l l s  around  [labelled  ( 0 , 0, 0 ) ] from w h i c h i t i s d e s i r e d t o compute  actions.  I t gives  the c o o r d i n a t e s  of a l l nuclei w i t h i n  a  cell  interthe  cells.  A I , B I , d l i s t h e d e s i g n a t i o n o f t h e c e l l from w h i c h t h e p r o g r a m s t a r t s ( n o t 0, 0, 0. S t a r t i n g from 0, 0, 0 w o u l d g i v e t h e 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 t h e d e s i g n a t i o n o f t h e c e l l a t w h i c h t h e program f i n i s h e s . XA, YB, zc a r e t h e u n i t c e l l d i m e n s i o n s i n a n g s t r o m s . XI, YI, ZI a r e t h e a t o m i c c o o r d i n a t e s o f the n u c l e i i n the u n i t c e l l . 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 . NUC The punched o u t p u t X,  Y,  Z ( t h e A,  B, C,and NUC  are merely  i n g ) i s u s e d i n Program 6 f o r t h e t h e o r e t i c a l second moment lation.  labellcalcu-  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 , B I , C I ,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,ZC W R I T E ( 6 , 3 ) XA , Y B , Z C __8 _ R E AD ( 5 _X l_» Y I , Z I >_NUC W R I T E ( 6 » 4 > X I ,YI , Z I ,NUC A = AI :  B = BI  10_  11  12  _.  C=C I GO TO 1 0 0 CONTINUE. C=C+1. I F ( C . G T . C M ) GO TO 11 GO....TO I C C , CONTINUE C = CI 3=3+1. I F ( B . G T . B M ) GO TO 12 •. GO TO 1 0 0 CONTINUE C = CI  B = BI  • . 100 v  101  A = A+1. I F ( A. GT . AM ) GO . TO 1 0 1 CONTINUE X=(XI+A)*XA " "Y =TY" I"+BY*"Y'B" Z=(ZI+C)*ZC WRITE ( 6 , 5 0 ) X»Y_,Z_,A»_B»_Cj_NUC ""'PUNCH'""50 ,X", Y ,Z , A , 3 , C V N U C GO TO 10 • CONTINUE WR I"T"E""("6','7'T GO TO 8 END  105  Program 6.  Theoretical  Rigid  -  L a t t i c e 5econd Moment  T h i s p r o g r a m computes t h e t h e o r e t i c a l r i g i d  Calculation  lattice  second  moment u s i n g t h e n u c l e a r c o o r d i n a t e s ( i n a n g s t r o m s ) g e n e r a t e d by Program 5. written  I t was a d a p t e d  from  UJ.R. Danzen's o r i g i n a l  program  f o r t h e IBM 1620.  1 i n s t r u c t s t h e computer t o r e a d i n a new s e t o f d a t a c a r d s 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 t o 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 . = d i s t a n c e i n angs troms up t o w h i c h t h e sum i s c a r r i e d . RMAX = the factor FACT i n e q u a t i o n ( 2 ) as i s a p p l i c a b l e . NN=DEN = N as i n e q u a t i o n ( 2 ) . = c o u n t o f i n t e r a c t i o n s between n u c l e i s e p a r a t e d by NVAN l e s s t h a n t h e van d e rUJaals r a d i u s . = t h e c o u n t o f i n t e r a c t i o n s w i t h i n t h e d i s t a n c e RMAX. NMB i s l i s t o f data cards read i n . N I , NM i s the l i s t o f parameters j i n r j k i n e q u a t i o n ( 2 ) . 3 1 , 3M i s the l i s t o f parameters k i n r j k i n e q u a t i o n ( 2 ) . K I , KM Y ( l ) , Z ( l ) a r e the n u c l e a r c o o r d i n a t e s i n angstroms X(I), g e n e r a t e d 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 s e c o n d moment. SM  LS  = 1, 2.  _  _  _  _•  _  _  __  _  SIBFTC C T H E O R E T I C A L SECOND. MOMENT ...C _ _ _ _ D I M E N S I O N X ( 2 00 0) »Y(2000 ) , Z ( ? 0 0 0) »A(?0 0 0 ) , 8 ( 2 0 0 0 ) , C ( 2 0 0 0 ) , N U C ( 2 0 0 0 ) 55. F O R M A T ( 1 H 1 , 7 X » 2 6 H T H E O R E T I C A L SECOND M O M E M T S » 2 2 X » 1 4 H P R 0 6 4 WRJ MRB) .7 4_ F..ORMAT.U_2....FJ_..0^^^ J. 75 FORMAT { I 5 , I 5 , r 1 1. 8 ) 88 FORMAT (5X , 3 F 8 . 4 » 5 X , 3 F 5 . 0 • A6 ) 99 FORMAT ( 10H0THEO SM = • F 6 . 2 » 8 X • I 5 »_i R_ L E S S _T H FJ41_,_2 H.... AJ ._. 1 0 0 F O R M A T ( 1H0") 101 F O R M A T ( 2 4 X , I 5 » 2 1 H R L E S S THAN 2.70 A///) _104 F0'RMAT__(_5X »Jj_l._0i.4ji WR I TE ! 6» 55! WRITE(6>100) 80 RE A D. ( 5..» 7±) L S , RMAX > FAC T , NN » N I »NM»JI ,JM»KI »KM RMS = RMAX*RMAX . DEN = NN  b 9  <• 8  :  5 0! i'l" Z\ r ..... j.  _  4H  A  1 10 2  15 16 17 ii. 10 9 a / 5 s 3  18 _ 40 20 30  =o  ;  NVAN=0 NMB =0 SUMR = ( 06.,07 4 ) L S , R M A X » F A C T » N N » N I » N M» J I »JM»KI»KM WRITE GO TO i 1 ,2 ) ,L'S DO 10 I = N l , N M READ(5,88) X ( I ) , Y ( I ) , 2 ( I ) , A ( I ) , 8 ( I ) , C ( I ) , N U C ( I ) DO 30 J = J I , J M D 0.._ 3 0....K ..=_..K.I.»!<M I F ( K . E Q . J ) GO TO 30 DZ = A B S ( Z ( K ) - Z ( J ) ) I F ( D Z . G E . R M A X ) GO TO 3 0 DY = A B S ( Y(K.) - Y ( J ) ) I F ( D Y . G E . R M A X ) GO TO 30 DX = ABS ( X ( K. > - X ( J ) ) I F ( D X . G E . R M A X ) GO TO 30 RS = DX*DX + DY-^DY + DZ*DZ _ I F ( R S . G E . R M S )_G0 TO_ 30 ____ T F T R S V G E Y 7 7 2 9 ) """GO TO 4 0 NVAN=NVAN+1 CONTINUE SUMR = SUMR + . 1 . / { R S * R S * R S ) NMB = NM3 + 1 CONTINUE  :  ;  i  o~~ O »  „  X  < CC cr 5:  co s: z  3 Z  <  10  >  •>  * s: z — CO z ~ UJ —• r-H Q.  \  0>  O  o> •—i  o  1— *  U vO CO <a; — — U_ L U U J — H - I—  o  \—  11  I-H  >->  o o z  cr. ex.  108  Program  7.  Activation Energies.  T h i s program activation  i s Smith's  e n e r g i e s from l i n e  I t i s l i s t e d h e r e as a d a p t e d I t i s , as n o t e d , w r i t t e n  ( 7 9 ) program w i d t h s i n nmr f o r the IBM  transition  7040 by D r .  Raghunathan. How-  f o r s e c o n d moments as i n  l ( 8 ) p r o v i d e d (Sffl) and SM a r e used i n s t e a d o f /\H and 2  of  regions.  f o r l i n e w i d t h s as i n e q u a t i o n (7.).  e v e r i t can be used w i t h o u t m o d i f i c a t i o n equation  f o r the c a l c u l a t i o n  /^H  2  S I B F T C  M  C  O  I F  C  _  C  DB  P  P  ' Y O UD O  S E E _W H A T M  O  A  L  I S  L T H E S E  G O I N G  D  O N . _  I F I E D  B  P  P  _  D I F F E R S  B P P _ E Q N _ P H Y _ S _ R E V _ 1 9 4 S _ _ V O L _ 7 3 P R O G R A M  C -  F R E Q U E N C Y  C  W H E N  "  C  C  O  R  R  C  E  U S E S  , M A K E S  P L O T T E D  L  .  F  R  E  Q  F  .  _'  T  A L P H A = D A T A  C '  T E M P .  C  I  ( L E S S  N  O  M  I  T  F  _ . _  C  C A S E  H  E  T  H  T O  T  H  E  C O M M E N T S  Y  I N C L U S I O N  B  P  S Q U A R E S  L I N E  N IT  E  .  G  F  N  D P L O T  P  E  I  O F  WID  T  O O  N F  T H E N  T H  V  S  T O  C >  G R E A T E R  T H A N  B  )  .  C  A  G  I  D E R I V E  T  I T  N  H  L N ( C O R . F R . Q )  S P E C I E S > = 7 6 7 . 6  F  O  R  H  .  D E L M I N =  R E V E R S E S  F I T , G R E A T E R  C C  D A T A  T  H  E  C O R R E L A T I O N A  S  A N D  I  R C P R T  C  _  D E R I V E D  C O R R E L .  = 1 / ( R - T E M P ) , W H E R E  E A C T  =  A  T  L I N E W  I N  I D T H  N L I N E W I D T H  L I N E W  C  TI V A T  I  N  I  N  I O N _ E N E R  T H E O R . F I T .  T H E O R .  F  D I M E N S ' I O ' N  2 T H F R Q (  I  T  . 5 0 0  F R E 0 .  R  E  N A R R O W I N G B E L O W  I  N  1 0  F O R M A T  1 5  R E A D '  O  "  '  "  "  F •( 6  F O R M A T  ' " 3 5 " R E A D " ' ' 4 0  1 . 9 8 6 9  R=  R E G I 0 5  F  O  R DO  M  A  O F  " " ~ "•  T H E O R E T I C  -C • vD  OF__ T H E O R E T I C F I T ,  F O R " T H E O R Y  F I T . N = N O .  O F  O  R )  PJ_5 0  ( 5 T  6 0  (  -  O F  M  A  ) , 1  T  ( A L P H A  1  2  E R E A C  T =  E R R O R  T H E O R . F I T .  I N  S A M E  T H F R Q =  " ( I  • F R Q M A X  =  C O R R E L . F R E O  D A T A  , R C P R T ( 5 0 0 )  THS_iNjj500_) , T  ,  5  T R E A T E D  H C O J  0 )  ,  , A L P H A ( 1 2  5 0 0 J  A C C O R D I N G  0  , T ' H T A N  T O  )  ,  ( 5 0 0 )  ^  G . W . S M I T H )  = 1 , 1 2 ) (  ) ,  5 0 0 ) , R E C I P T (  ) » X T A N ( 5 0 0 )  [ 500)  , T H D E L  " I = 1  "  l  2  A  6  "  )  "  "  "  "  "  "  "  "  "  "  ~  "  , 1 2 )  _  _  G  • ~ ~  TEMPj I ) >DE_L_TAH .  5  )  _  C O R F R Q .  '  "  "  "  "  "  '  , 3 F 1 5 . 5 )  , 5 0 ) ( 6  ._  N  F T 7 7 E R" F R O =Tf S E R R OR 7f H b E L = L IN E - " " " " " " ~ "  ) , C O R F R Q (  , X C O S ( 5 0 0 0 J  L I N E W I D T H .  X , 1 . 2 A 6 )  ( I 5  _.. X L N F R G = L  .  ( A.L P H A ( I  , 3 0  ( 1  F O R M A T  "  _____  ON 'NUCLR  C A L / D E G - M O L E . ) ,  T E M P . I N  ) , D E L f A H ( 5 0 0  ( 5 , 4 0 ) N * C * B » A  R E A D ""'5 0  ( I X , A - 9 H N M R  . ( 5 * 2 0 )  W R I T E 0  _ _  G I V E  T R A N S I T I O N .  R E G I O N  __ I N _ R E G I O N  CI P T = 1 / T E M P .  G Y( C _ A L / M O L E  T H T E M P =  > , X S I N ( 5 0 0 )  5 0 0 ) » T H T E M  '"'"PRINTlb  T  T E M P .  T O  _  T E M P (  1 X L N F R Q ( 5 0 0  3  I D T H  I N C R E M E N T  r  W I D T H  C  L I N E  C O M P O U N D » D A T E .  ' c " T N F ;" Y ;jp;" "cb R'RTL . F R E ' Q T f isr'TH FOR C  .  '  CALCULATED..QUMLTJJJAfc....Pl^ C 0 R F R Q =  C  T  _ _ I _ N F «  E P R O C E S S  P L O T .  O F  P O I N T S .  ...C C  T O  _  = A V G .  M  JHAN B . D E L M A X ~ M A X LESSTHAN77""D77T7C="T7NEWIDTH  C  E A S I E R  _  7"~~"'B"= A V G T L iTEwYbY77"_7v7TRAN'STTTONVAG="PARA'METER'""DE PEN DENT C  1 5  N U M E R A T O R  T O  O N . E N E R G Y  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 )  T H A N  T H E M  A G = 7 6 7 . 5  .T E M P . D A T A  N P U T _  NAME OF  T E R M  P R O T O N S  T H E _A C TI V A I . I  I O N S - I .  A  A N A L Y S I S  P 6 _ 7 _ ? . F O R  F I T . P R O G R A M  D E . F I  .  B  D E R I V E S  E  H A N D _  M O D I F I E D  L E A S T  V S . l / R T ,  T H E O R E T I C A L _  -C  T  A  Y  N A R R O W I N G  C  T H I S  O R I G I N A L  B  _  L I N E  C 7  F R O M  C A L C U L A T I O N S  ~  ( I  )  "  ~  ,  I = 1 _ , N ) "  "  "  '  "  '  '  "  "  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 ) )  "  """""  "  "  "  "  _  ..:  60 65 7.0 __8.0  i?.  _ 1  _  2 2 . 0 . .  F O R M  N  .  0 N  10 *  "  "  "  "  "  "  "  T  H  S  N  V  (  =  B  = '  T H C O  K  D  E  _  _  K_=  :<  )_  _  +  _  ( K  I N  ) /  5 EIT'N C"  + 0 . "  ~0  6Y  '  "  ( K ! = D E L M I N + (  )  ETM  1  1 _ » N S W  """"  C * * 2  .. _  L M A X " - ~ D  N O I N C  2 3 0 _ X  C  5  3  W =  T H D E L  7  4  S  A  A T ( 3 F 1 0 . 5  i' N C =  _DO_  a" " ~  _  —  -  l.RCP.RT ( i ) vL=.i.'._iJ_.: _ : _._ "" 9 0 • FORMAT ( 1H » 2 X , F 1 2 . 5 » 8 X » F l 2 « 5 » 7 X ? E l 4 . 6 » 9 X » F l 6 . 7 » 9 " x . SUMX = 0 . 0 SUMY = 0.0 DO 200 J = l ,N SUMX = SUMX+ RCPRT(J) .....SUMY . = 5 UM Y +, XLN F R OJ..J.) 2 00 "' CONfINUE CALL L S Q F I T ( N , R C P R T , X L N F R Q , S U M X , S U M Y , 0 , P , S T D E R O » S T D E R P , X A V , _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  _  1  _  XCOS( I ) =COS( 1. 5707*( DELTAH ( I ) **2-B**2 ) / ( C**2-B**2 ) ) XTAN( I )=XSIN( I ) /XCOSt I ) CORFRQXXif.AG*DELlAHJ.J.,i../i<I.AMI..L.._ - __ XLNFRQ ( I ) =AI_OG ( GORFRQ ( I ) ) RECI PT ( I ) = 1. /TEMP ! I ) _P_C P.R.I. n.J.=J_<^ : CONTINUE WRITE(6,70.).N,C,B,AG F.O.RMAX(.,.1H..O...,^ LATTICE _LjNE Wj..PJ.H._... =....,.£. 1 0. .5,, 5 ,X.,_2.QH INARROWED- LINEWIDTH = , F 1 0 . 5 , 5 X , A H A G =,F15.5) PRINT 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 ) »  A  K  -  1  .  ) - - - D E L I N G  - B * * 2  = SYN ( ' Y . " 5 Y o T * 7 f H D T L T ^ ) =COS ( 1 . 5 7 0 7 - - - ( T H D E L ( K )  T H T A N ( K ) = T H S N ( K ) / T H C O ( K )  * * 2 - B * * 2 )  /CB )  -  -  8 '  11 Z\ ;  , H I...  (.:  I  t •  '  •  •  5  THF RQ ( K ) = ( AG*THDEL MoT/THTANfflo  •  e  :  ' THTEMP ( K ) =EACT/( 1 . 9 8 6 9 * A L 0 G ( FRQMAX/THFRO ( K ) ) ) C.ON.II..N.UE  23.0 240  •  '  !  BPP LEAST SQUARES __ _  DATA _.  .  W  T  fit  _ D  T  '  H  G  T  _  __ ' " ' ~ ~ '" " SUBROUT INE L S Q F I T ( N , X , Y » S U M X , S U M Y , 3 » C , S T D E R 3 , S T D E R C , X A V , Y A V , N O G O ) _ DIMENSION X( 500) , YJ 500_) _ "IF('N-2)io5"d/fd5o',foob' " ' " " 1000 AN = N XAV = SUMX/AN YAV=SUMY'/AN'" ~ ~ ~ ~ ~ " " ~ '" ~ " " DIFXY=0. DI.FXSO = p. __ _ _ DO 10 10 J = 1 » N ~ DIFXY  = DIFXY  DIFXSQ= 1010  .. ' • _ . 0 < _ 1 ; \' : 3 .  .  + (X(J)  -  A  T  z  "  "  ~  "  "  K H » - - -.—  -  "" ™ ~ " ' " ' " ' " " " " " ' " " " " " " " " "  ~~~  Q0VRTD= Q / SQR T ( DEE ) STDE RC = QOVRTD*SQRT(AN) _ STDERB_= QOVRTD*SQRJ(XSQ) """""N'O"GO'"~"= " I " " ' " " " " " PRINT 1.040 1040 FORMAT(1H »52HNOGO = 1, THEREFORE L S Q F I T  ""  ~  '  >  i  D I FX SQ__+ J_X_U )- _XA_V_)j-»-2  'CONTINUE C=DIFXY/DIFXSQ B=YAV-C*XA'V DSQ=0  i  _______  XAV)*Y(J)  . 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 " " ~ DEE = AN*XSQ - ( AN*XAV ) * • _ _ _ I F ( D E E ) 1 0 5 O , 1 0 5 0 » 103 0 _ _ _ . 10 30  I ___ "'""  __  "" "  GO TO 15 END  :  _  *  3  6  FIT) :  " " F ' 0 R " M A T " ( T ' H 7 1 4 X 7 ? 1 1 . 5 t 3 0 X 7F 167 5 7 2 8 X , E 1 4 . 6 ) "  SI 3 F T C '.  „  1 U S S ) , 1 7 X , 2 7 H C O R R E L A T I O N FREQUENCY ( C P S ) ) 25C?F 7 "kTLVil^r»T7xViTHXYNE ' _' ' RW>R7IAT TE(( T 6H •T 2 60 ) ( TH TEMP' ( K ) » _TH DJEL (_KJ » THFRQ ( K ) , K = l ^_SW_)__  " " 2 6 6  •  - - - -  *  i  ..  PRINT 2 40 F O R M A T ( l , H 0 » 3 4 X » 4 7 H T H E O R E T I C A L MODIFIED _ _ . PRINT 2 50 _ _  s  f  ~ --  _  "  "  ~ -  HAS MADE A S U C C E S S F U L  " -  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 D e r i v a t i v e Curves f o r Temperature Dependence at 30 MHz•  - 114 -  - 115 -  Appendix l i e .  WF^ Derivative Curves for Field Dependence at 77 K  2 MHz  modulation amplitude R = reference  - 116 -  7 7  t  "K  I  '  '  0  Appendix I l i a .  IF^AsF^ D e r i v a t i v e Curves f o r Temperature Dependence a t 3 0 MHz  °K  2 6 8  = modulation amplitude 0  53  "K  4 5G  174  217  '  °K  R r reference  -  Appendix I I I c .  IF/ASFA.  56.4  40  l i s  -  D e r i v a t i v e Curves f o r F i e l d Dependence at 7 7 K  MHz  MHz  :  modulation amplitude  R = reference  30  MHz  Appendix IVb. 94.1  SF*AsF^ D e r i v a t i v e Curves f o r F i e l d Dependence a t 300"K  MHz  56.4  J__.«iV,H_  I  30 MHz = modulation R s reference  v  amplitude  MHz  -  122  -  References  W. 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