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Infrared study of crystalline strontium formate and strontium formate dihydrate McQuaker, Neil Robert 1966

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AN INFRARED STUDY OF CRYSTALLINE STRONTIUM FORMATE AND STRONTIUM FORMATE DIHYDRATE by NEIL ROBERT MCQUAKER B.Sc,  U n i v e r s i t y o f B r i t i s h Columbia,  196$  A THESIS SUBMITTED IN PARTIAL FUFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF  MASTER OF SCIENCE i n the Department o f CHEMISTRY We accept t h i s t h e s i s as conforming t o the required  standard  September,  1966  UNIVERSITY OF BRITISH COLUMBIA  In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree a t the U n i v e r s i t y of B r i t i s h Columbiaj I agree that the L i b r a r y s h a l l make i t f r e e l y aval]able f o r reference and study.  I f u r t h e r agree that permission-for  extensive  copying of t h i s  t h e s i s f o r s c h o l a r l y purposes may he granted by the Head of my Department or by h i s representatives.  I t i s understood that copying  or p u b l i c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission.  Department of  Chemistry  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date  October 17th. 1966,  - i iABSTRACT  The i n f r a r e d a b s o r p t i o n s p e c t r a o f s i n g l e c r y s t a l s o f s t r o n t i u m formate and s t r o n t i u m formate d i h y d r a t e have been recorded between 4000 and 500 cm"" . 1  C r y s t a l s l i c e s cut  p e r p e n d i c u l a r t o the c r y s t a l axes were employed; were r e c o r d e d u s i n g p o l a r i z e d  radiation,  the s p e c t r a  the e l e c t r i c  vector  being p a r a l l e l t o the d i r e c t i o n d e f i n e d by the c r y s t a l a x i s in  question. For  Sr(CH02)2 i t was  infrared active  i n t e r n a l fundamentals.  modes a t : 10, 12, 15, 20, were i n f e r e d For  p o s s i b l e to a s s i g n 20 o f the 36  23,  In addition  70, 155, 130 and 200  lattice cnT  1  from combinations w i t h i n t e r n a l fundamentals.  Sr(CH02)2»2H20  i t was  p o s s i b l e to observe o n l y 10  of the 36 i n t e r n a l fundamentals a s s o c i a t e d w i t h the formate i o n s as the a b s o r b i n g s p e c i e s .  Of the 13 i n t e r n a l  fundamentals  a s s o c i a t e d w i t h the water molecules as the a b s o r b i n g s p e c i e s o n l y one mode c o u l d be unambiguously 340, 356  assigned.  L a t t i c e modes  a t : 642, 710, 750,  797,  and two a d d i t i o n a l  l a t t i c e modes a t 13 and 110 cm""  and 372 cm"  1  were observed 1  were  i n f e r e d from combinations w i t h i n t e r n a l fundamentals. From the i n t e n s i t y r a t i o s of the i n t e r n a l fundamentals of Sr(CH02)2 i t  w  a  s  possible to calculate  the d i r e c t i o n  a s s o c i a t e d w i t h each o f the two c r y s t a l l o g r a p h i c a l l y e q u i v a l e n t formate i o n s contained i n the u n i t  cell.  cosines  non-  - i -  ACKNOWLEDGEMENT  The author wishes t o acknowledge w i t h  thanks  Dr. K.B. Harvey's a s s i s t a n c e i n c a r r y i n g out t h i s work and i n i n t e r p r e t i n g t h e experimental r e s u l t s . due  Thanks are a l s o  t o Mr. R.W. Green f o r h e l p f u l d i s c u s s i o n s r e l a t i n g t o  experimental technique.  Use o f the f a c i l i t i e s o f the  U n i v e r s i t y Computing Centre i s a p p r e c i a t e d .  - iii  -  TABLE OF CONTENTS Page ACKNOWLEDGEMENT  ±  ABSTRACT  i i  TABLE OF CONTENTS  i i i  LIST OF TABLES  v  LIST OF FIGURES CHAPTER I  v  i  i  INTRODUCTION  1-1  I n t r o d u c t o r y Remarks  1  1-2  The C r y s t a l S t r u c t u r e o f Sr(CH0 )2  1- 3  The C r y s t a l S t r u c t u r e o f Sr(CH0 )2.2H 0  2  2  2  CHAPTER I I  2  2  EXPERIMENTAL  2^1  Materials  3  2- 2  Growth o f S i n g l e C r y s t a l s  3  2-3  Sample P r e p a r a t i o n  10  2- 4  Apparatus  15  CHAPTER I I I  RESULTS  3- 1  Spectra o f P o l y c r y s t a l l i n e Strontium Formate  16  3- 2  Single C r y s t a l Spectra of S r ( C H 0 ) and S r ( C H 0 ) 2 « 2 H 0  16  2  CHAPTER IV  2  2  2  THEORY  4- 1  The V i b r a t i o n s o f I s o l a t e d Polyatomic Molecules  3$  4-2  S e l e c t i o n Rules  41  4-3  S o l i d S t a t e Spectra and C r y s t a l Symmetry  43  - iv 4- 4  F a c t o r Group A n a l y s i s o f Vibrations i n Crystals  CHAPTER V  DISCUSSION - PART I  5- 1  V i b r a t i o n a l Analysis  5-2  The I n t e r n a l Fundamentals o f S r ( C H 0 ) - Assignments 2  f o r Sr(CH0 )2 2  2  5-3  The I n t e r n a l Fundamentals o f Sr(CH02)2 - I n t e n s i t i e s  5-4  Overtones and Combinations o f I n t e r n a l Fundamentals - Sr(CH02)2  5- 5  Combinations o f I n t e r n a l Fundamentals and L a t t i c e Modes - S r ( C H 0 ) 2 2  CHAPTER VI  DISCUSSION - PART I I  6- 1  Vibrational Analysis  6-2  The I n t e r n a l Fundamentals o f S r ( C H 0 ) 2 « 2 ° ~ Assignments  f o r Sr(CH0 ) .2H 0 2  2  2  2 H  2  6-3  The I n t e r n a l Fundamentals o f Sr(CH0 ) .2H 0 - Intensities 2  6-4  2  2  Overtones and Combinations o f I n t e r n a l Fundamentals - S r ( C H 0 ) . 2 H 0 2  6-5  2  2  Combinations o f I n t e r n a l Fundamentals and L a t t i c e Modes - S r ( C H 0 ) . 2 H 0 2  CHAPTER V I I  CONCLUSION  2  2  -  V  -  LIST OF TABLES Page Table  1-1  C r y s t a l S t r u c t u r e o f Sr(CH02)2  4  1-2  C r y s t a l S t r u c t u r e o f Sr(CH02)2»2H 0  2  V i b r a t i o n a l Assignments f o r S p e c t r a o f P o l y c r y s t a l l i n e Strontium Formate  21  3  V i b r a t i o n a l Assignments f o r S i n g l e C r y s t a l Spectra of Sr(CH0 )2  27  V i b r a t i o n a l Assignments f o r S i n g l e C r y s t a l Spectra of Sr(CH0 )2«2H 0  35  V i b r a t i o n a l Assignments f o r S i n g l e C r y s t a l Spectra of S r ( C H 0 ) 2 » 2 - Previous Work  37  5  Summary o f E x p r e s s i o n s f o r C h a r a c t e r s o f the Group Operation, R  46  6  C h a r a c t e r Table and F a c t o r - Group A n a l y s i s f o r Sr(CH0 )2  50  Squares o f D i r e c t i o n Cosines f o r Formate Ions I and I I o f Sr(CH0 )2  53  The I n t e r n a l Fundamental Modes o f Sr(CH0 )  60  C a l c u l a t e d and Observed I n t e n s i t y Ratios - Sr(CH0 )2  61  C a l c u l a t e d and Experimental D i r e c t i o n Cosines f o r Formate Ions I and I I o f Sr(CH0 )2  65  11  Symmetry S p e c i e s o f Combinations and Overtones  66  12  C h a r a c t e r Table and F a c t o r - Group Analysis f o r Sr(CH0 ) .2H 0  70  Squares o f the D i r e c t i o n Cosines f o r Formate Ions I and I I o f Sr(CH0~)~.2H~0  72  2  5  2  4-1  2  4-2  2  2 H  0  2  2  7  2  8  2  9  2  2  10  2  2  13  2  2  - vi The I n t e r n a l Fundamental Modes o f Sr(CH0 ) .2H 0 2  2  2  C a l c u l a t e d and Observed I n t e n s i t y Ratios - Sr(CH0 ) .2H 0 2  2  2  - viiLIST OF FIGURES Pas;e Figure  1-1  C r y s t a l S t r u c t u r e o f Sr(CH0 )2  6  1- 2  C r y s t a l S t r u c t u r e o f Sr(CH0 )2«2H 0  2- 1  Spectra o f P o l y c r y s t a l l i n e Strontium Formate, 4000-500 cm"  18  S p e c t r a o f P o l y c r y s t a l l i n e Strontium Formate, 1400-1320 c r r r  19  2- 3  Spectra o f P o l y c r y s t a l l i n e Strontium Formate, 6*10-730 cm-1  20  3- 1  P o l a r i z e d Spectra o f Sr(CH0 )2i 3300-2600 cm-1  2  3-2  P o l a r i z e d S p e c t r a o f Sr(CH0 )o, 2000-1200 cm-1  23  3-3  P o l a r i z e d Spectra o f S r ( C H 0 ) , 1120-1040 cm-1  24  3-4  P o l a r i z e d Spectra o f S r ( C H 0 ) , 310-7^0 cm-1  25  3- 5  Polarized Spectra of Sr(CH0 )2, 310-730 cm"  26  2  2  7  2  1  2-2  1  2  2  2  2  2  2  2  2  1  4- 1  P o l a r i z e d Spectra o f S r ( C H 0 ) . 2 H 0 , 3900-2500 cm-  31  4-2  Polarized Spectra of Sr(CH0 ) .2H 0, 2500-1900 cm-1  32  4-3  Polarized Spectra of Sr(CH0 ) .2H 0, 2000-1200 c n T  33  P o l a r i z e d Spectra o f S r ( C H 0 ) . 2 H 0 , 1100-500 cm"  34  2  2  2  1  2  2  2  2  2  2  1  4-4  ?  1  ?  ?  - 1 CHAPTER I  1-1  INTRODUCTION  I n t r o d u c t o r y Remarks The v i b r a t i o n a l s p e c t r a o f S r ( C H 0 ) 2  and  2  Sr(CH0 ) .2H 0 2  2  2  have been the s u b j e c t o f i n v e s t i g a t i o n of previous workers (1-5).  Only i n the study of S r ( C H 0 ) . 2 H 0 (4,5) 2  2  were  2  s i n g l e c r y s t a l s and p o l a r i z e d r a d i a t i o n used. In t h i s work s p e c t r a of p o l y c r y s t a l l i n e formate and  strontium formate dj were s t u d i e d as w e l l as  s i n g l e c r y s t a l s p e c t r a of both S r ( C H 0 ) 2  The  strontium  2  and  Sr(CH0 ) .2H 0. 2  2  2  s i n g l e c r y s t a l s p e c t r a were s t u d i e d u s i n g p o l a r i z e d  i n f r a r e d r a d i a t i o n as a c o n t i n u a t i o n of the study of i n organic formates i n i t i a t e d i n t h i s l a b o r a t o r y by B.A. (6) and  subsequently  continued  by T.L.  Morrow  Charlton ( 7 ) .  As w i l l be d i s c u s s e d l a t e r i t i s necessary when c o n s i d e r i n g the s p e c t r a of s i n g l e c r y s t a l s to take o f the o r i e n t a t i o n of the absorbing to the c r y s t a l axes.  species with  T h i s o r i e n t a t i o n of the  account  respect  absorbing  s p e c i e s w i t h r e s p e c t to the c r y s t a l axes i s d i r e c t l y r e l a t e d t o the i n t e n s i t y of the i n t e r n a l fundamental modes o f v i b r a t i o n a s s o c i a t e d w i t h the absorbing  species.  Consequently  i n f o r m a t i o n obtained from p o l a r i z e d s p e c t r a of s i n g l e c r y s t a l s i s not o n l y an a i d i n making v i b r a t i o n a l assignments but can a l s o a i d i n the d e t e r m i n a t i o n  of c r y s t a l structures-  p a r t i c u l a r l y where hydrogen atoms are i n v o l v e d .  - 2 1-2  The C r y s t a l S t r u c t u r e o f SrfCHC^)? The  crystal structure of Sr(CH0 ) 2  2  i s d e s c r i b e d by -v.  N i t t a and h i s co-workers (8-10 ) as b e i n g orthorhombic  and  1  belonging t o the space group P2 2^2^(D^). The c e l l parameters 1  and t h e c o - o r d i n a t e s o f the g e n e r a t i n g atomic l i s t e d i n Table 1-1 ( i ) .  p o s i t i o n s are  The hydrogen atom p o s i t i o n s were  c a l c u l a t e d by the author on the assumption o f a value o f 1.09 A  0  f o r the C-H bond l e n g t h .  The formate i o n parameters  were a l s o c a l c u l a t e d and a r e g i v e n i n Table 1-1 The  c r y s t a l structure of Sr(CH0 ) 2  2  (ii).  can be v i s u a l i z e d  from the p r o j e c t i o n on t o the (001) plane g i v e n i n F i g . 1-1. We see t h a t the s t r u c t u r e maybe d e s c r i b e d as c o n s i s t i n g o f complex chains along the screw p a r a l l e l t o the C a x i s ; the chains b e i n g l i n k e d l a t e r a l l y through the oxygen atoms o f the formate i o n s .  1-3  The C r y s t a l S t r u c t u r e o f Sr(CH0o)o.2Ho0 A p r e l i m i n a r y X-ray a n a l y s i s o f S r ( C H 0 ) . 2 H 0 was 2  2  2  r e p o r t e d by N i t t a i n 1928 (&) w i t h subsequent work b e i n g done by Osaki  {&).  I t was found t h a t the d i h y d r a t e  anhydrous strontium formate belongs P2 2^2-^ ( D ) . 1  2  like  t o the space group  The c e l l parameters and the c o o r d i n a t e s o f  the g e n e r a t i n g atomic i n Table 1-2 ( i ) .  p o s i t i o n s as g i v e n by Osaki are l i s t e d  Again the hydrogen atom p o s i t i o n s were  calculated by the author, a value of 1.09 A° being assumed for the C-H bond length.  The formate ion parameters are  given i n Table 1-2 ( i i ) . F i g . 1-2 shows a projection of the structure onto the (001) plane.  The structure i s similar to that of S r f C H O g ^  and also maybe described as consisting of complex chains along the screw axis p a r a l l e l to the C axis, with the chains being linked l a t e r a l l y through the water molecules and the oxygens of the formate ions.  - 4 -  TABLE 1 - 1  CRYSTAL STRUCTURE OP Sr(CH0 )2 2  Space Group j a (i)  =  6.874 A  b  0  P 2 2 i 2 i (D|) 1  8.748 A°  =  c - 7-267 A  Generating P o s i t i o n s with O r i g i n Halfway Between Three P a i r s of Non I n t e r s e c t i n g Screw Axest 4 Sr  Ions a t (0.2500, 0.0915, 0.0000)  2 +  FORMATE ION I 4 4 4 4  0 H 0 0'  atoms atoms atoms atoms  at at at at  (0.005, (0.046, (0.105, (-0.154,  0.260, 0.298, 0.154, 0.550,  0.420) O.558) * O.558) O.550)  FORMATE ION I I 4 4 4 4 (ii)  C H 0 0"  atoms atoms atoms atoms  at at at at  (0.118, (0.255, (-0.018, (0.120,  0.505,-0.906) 0.501, 0.851) * 0.255, 0.828) 0.570, 1.057)  Formate I o n Parameters: FORMATE ION I r(C-O) = 1.24A° r(C-H) 1.09A 0  a  r(C-0') = 1.24A Z.(d-C-0') - 150°  0  FORMATE ION I I r(C-O) = 1.24A r(C-H) » 1.09A  0  *  0  0  r(C-O') = 1.24A RO-C-O') - 129°  Assuming r(C-H) - 1.09 A° as Indicated i n ( i i )  I i 1  0  - 5 TABLE  1-2  CRYSTAL STRUCTURE OP Sr(CH0 ) .2H 0 2  Space Group: a (i)  s  7.352 A°  b  2  P212J2! (D ) 2  12.040 A  =  2  c  0  =  7.144 A  Generating P o s i t i o n s with O r i g i n Halfway Between Three P a i r s Non I n t e r s e c t i n g Screw Axes: 4 H 0 j Molecules a t 2  ( 0 . 4 l l , 0.092, -0.469)  4 HgOj Molecules a t (-0.025, 0.221, 4 Sr  2 +  0.24l)  at (0.2500, 0.0715, 0.1970)  Ions  FORMATE ION I 4 4 4 4  C H 0 0'  atoms atoms atoms atoms  at at at at FORMATE ION I I  4 4 4 4 (ii)  C H 0 0'  atoms atoms atoms atoms  at at at at  (-0.142, -0.012, 0.417) (-0.201, -0.095, 0.429)* ;(0.022, - 0 . 0 0 5 , 0.450) (-0.247, 0.063, 0.372)  Formate Ion Parameters: FORMATE ION I r(C-O) - 1.21A° r(O-H) = 1.09A 0  r(O-O') =:.1.20A° /.(O-C-0 ) - 125° 1  FORMATE ION I I r(C-O) = 1.23A° r(C-K);= 1.09A° r  *  0  r(C-O') = 1.23A L(O-C-O') =128°  Assuming r(C-H) . 1.09 A° as Indicated i n ( i i )  0  - 6 -  FIG M  CRYSTAL STRUCTURE OF Sr(CH0 ) 2  (i) Proj ec t i on of Structure  (ii)Symmetry  2  on(OOl)  Elements of the Unit  Cell  1  4  O  I\r  L  j  >  /  4  -o f  j. • 4  1  ' 4  FIG  1-2  - 7CRYSTAL STRUCTURE OF S r(C H 0 ) 2  (i) Pro j ec t i on of Structure  (ii) Symmetry  1  2  2H O 2  on(OOl)  Elements of the Unit C e l l  o  i1  •  i  \  1  ;  4  ! 4  -o < '  - g CHAPTER I I  2-1  Materials The  of  EXPERIMENTAL  strontium formate used was prepared  f o r m i c a c i d w i t h s t r o n t i u m carbonate.  The product  f i l t e r e d and r e c r y s t a l l i z e d from s o l u t i o n . s t r o n t i u m carbonate  by n e u t r a l i z a t i o n was  Both the  and formic a c i d were o f reagent  grade  and were obtained from the B r i t i s h Drug Houses L t d . The  s t r o n t i u m formate d, was prepared  i n a similar  manner u s i n g formic a c i d - d j .  2-2  Growth of S i n g l e C r y s t a l s The  c r y s t a l s were grown from aqueous s o l u t i o n by slow  e v a p o r a t i o n a t constant temperature;  the hydrated  crystals  being grown a t 60°C and the anhydrous a t 6*5°C. C r y s t a l growth was c a r r i e d out i n l i t e r vacuum f l a s k s ; the f o l l o w i n g procedure  was f o l l o w e d .  n e a r l y saturated s o l u t i o n was prepared temperature,  I n i t i a l l y a l i t e r of a t the growing  care being taken t h a t t h e r e were no i m p u r i t i e s  in.the solution.  The s o l u t i o n was then maintained  growing temperature and allowed t o evaporate  a t the  s l o w l y - slow  e v a p o r a t i o n was achieved by p l a c i n g a c o t t o n plug i n the mouth of the f l a s k .  The f l a s k was watched c a r e f u l l y so  - 9 t h a t the f i r s t  s i g n of seed c r y s t a l s forming on the bottom  of the f l a s k could be d e t e c t e d . of two  procedures was  of seed c r y s t a l s was  When t h i s o c c u r r e d one  f o l l o w e d depending  on whether a h a r v e s t  d e s i r e d or whether i t was  s t a r t the growth of a l a r g e s i n g l e  desired to  crystal.  I f seeds were d e s i r e d the slow e v a p o r a t i o n was u n t i l they had reached a s i z e o f about 3-5  mm.  continued  i n length.  They were then h a r v e s t e d . I f i t was c r y s t a l was  d e s i r e d t o grow a s i n g l e c r y s t a l a seed  p l a c e d i n the s a t u r a t e d s o l u t i o n suspended  a t h i n nylon filament. was  by  The f r e e end of the n y l o n f i l a m e n t  secured on the arm p r o j e c t i n g from the vacuum f l a s k .  T h i s process was  c a r r i e d out i n minimumal time so t h a t as  l i t t l e vapour as p o s s i b l e escaped from the f l a s k . A f t e r s u f f i c i e n t growth had taken p l a c e ( u s u a l l y a p e r i o d of about 3-4 weeks) the c r y s t a l was the s a t u r a t e d s o l u t i o n .  removed from  However, when removing  from the s a t u r a t e d s o l u t i o n i t was  the  s u f f i c i e n t t o s e v e r e l y crack the c r y s t a l .  temperature  was  In order t o  circumvent t h i s problem N u j o l at the temperature  The c r y s t a l was  crystals  found t h a t the thermal  s t r a i n imposed by the sudden change i n temperature  s a t u r a t e d s o l u t i o n was  after  o f the  p l a c e d on top of the s a t u r a t e d s o l u t i o n .  then drawn up i n t o the N u j o l l a y e r and the  lowered t o room temperature  over a p e r i o d o f  about 3 hours.  10 -  The c r y s t a l s so obtained were l a r g e l y f r e e  from c r a c k s and i n t e r n a l f l a w s . Both the hydrated and anhydrous c r y s t a l s when grown i n the above manner were o f s p h e n o i d a l h a b i t , 10 t o 15 wide, 20 t o 30 mm.  long and 7 t o 10 mm.  f a c e o f both c r y s t a l s was the (010)  thick.  mm.  The p r i n c i p a l  f a c e elongated i n the  C direction.  2-3  Sample P r e p a r a t i o n The most d i f f i c u l t p a r t of the experimental work was  preparing spectroscopically t h i n c r y s t a l s l i c e s from the s i n g l e c r y s t a l . developed The  ( i . e . 20-30n)  The f o l l o w i n g technique  was  d u r i n g the course of the experimental work. s i n g l e c r y s t a l was f i r s t mounted w i t h epoxy r e s i n  ( A r a d i t e Adhesive,  Ciba L t d . ) , on a s p e c i a l l y  designed  support, care being taken t h a t the d e s i r e d c r y s t a l a x i s was mounted p e r p e n d i c u l a r t o the base o f the support.  The  c r y s t a l and i t s support were then mounted i n a c r y s t a l c u t t i n g d e v i c e so t h a t the d e s i r e d c r y s t a l a x i s was perp e n d i c u l a r t o the c u t t i n g plane. The  c u t t i n g plane c o n s i s t s o f a 3 by 6 i n c h t a b l e w i t h  r o l l e r s a t e i t h e r end. a l|  I n the centre o f t h i s t a b l e there i s  i n c h c i r c u l a r opening below which i s the c r y s t a l  support.  P r o v i s i o n i s made t o e l e v a t e , r o t a t e and t i l t  this  - 11 support  so t h a t the c r y s t a l maybe a p p r o p r i a t e l y p o s i t i o n e d  with r e s p e c t t o the c u t t i n g plane. Once the c r y s t a l was a p p r o p r i a t e l y mounted i n the c r y s t a l c u t t e r , c u t t i n g began.  I n o r d e r t o cut the c r y s t a l a piece  of No. 40 c o t t o n thread was h e l d a g a i n s t the c r y s t a l and p u l l e d back and f o r t h a c r o s s the r o l l e r s a t e i t h e r end o f the c u t t i n g t a b l e .  A carborundum-water s l u r r y was placed on  the c u t t i n g t a b l e t o a c t both as a l u b r i c a n t and as an a i d to  the c u t t i n g process.  U s i n g t h i s method i t was p o s s i b l e  to  cut a c r o s s s e c t i o n o f 600 mm.  i n about o n e - h a l f  hour.  A f t e r the c r y s t a l was cut the f a c e o f the p o r t i o n o f the c r y s t a l remaining  on the c r y s t a l support was p o l i s h e d .  T h i s p o l i s h i n g process was c a r r i e d out i n two s t e p s . first  step made use of a p o l i s h i n g d i s c .  d i s c was covered  The  The s u r f a c e o f t h i s  w i t h No. 36O-A carborundum paper and i t  was mounted so t h a t i t r o t a t e d h o r i z o n t a l l y a t about 3000 R.P.M.  The c r y s t a l f a c e t o be p o l i s h e d was held a g a i n s t  the r o t a t i n g d i s c ; care b e i n g taken t o r o t a t e the c r y s t a l at  evenly  spaced i n t e r v a l s so as t o ensure as f l a t a s u r f a c e  as p o s s i b l e . Once a f l a t u n i f o r m l y smooth surface had been obtained the second step i n the p o l i s h i n g process was c a r r i e d o u t . T h i s process, which brought the c r y s t a l f a c e t o an extremely h i g h p o l i s h , c o n s i s t e d o f rubbing the c r y s t a l f a c e on a piece o f v e l v e t l a p s t r e t c h e d over a f l a t g l a s s p l a t e ;  - 12 -  dampened jewellers rouge being used as the polishing compound. After the c r y s t a l face had been s a t i s f a c t o r i l y polished the c r y s t a l face was G.C.  coated with s i l v e r paint (Silver Print;  Electronics Co.) except f o r an area of 3 x 11 mm.,  this  area being the size of the s l i t on the sample holders.  When  the s i l v e r paint had dried the whole of the c r y s t a l face was covered with a coat of p l a s t i c cement (Radio Service Cement; General Cement Mfg. Co.).  After the p l a s t i c cement  had dried epoxy resin was used to glue a piece of glass plate measuring £ x 1| x l i inches to the c r y s t a l face. Care was taken that no a i r bubbles were trapped under the small glass plate. The purpose of the epoxy was to provide a firm backing f o r the c r y s t a l which contained no glue-free pockets. a backing was were reached. c r y s t a l was about 0.5 mm.  Such  c r u c i a l once the f i n a l stages of polishing After,the epoxy had been allowed to set the  so positioned i n the c r y s t a l cutter that a s l i c e thick could be cut.  This s l i c e which was  mounted on the small;glass plate was then ground on the polishing disc i n the manner outlined previously. Where the c r y s t a l was  coated with s i l v e r paint i t was  possible to  measure the thickness of the c r y s t a l d i r e c t l y with a Zeiss Light Section Microscope as the polishing process progressed. I t should be noted that the purpose of the p l a s t i c cement as w i l l be mentioned l a t e r was to allow f o r the action of  i  - 13 acetone t o f r e e the c r y s t a l s l i c e from the g l a s s p l a t e once the p o l i s h i n g process was  completed.  When the c r y s t a l s l i c e reached a t h i c k n e s s of about 50 ja the 6 cm.  p o l i s h i n g d i s c was  r e p l a c e d by a 7 mm.  disc  and the p o l i s h i n g process continued u n t i l a t h i c k n e s s of 3 5 - 4 0 ja had been reached.  The f i n a l  stage of p o l i s h i n g  was  c a r r i e d out by r e p l a c i n g the carborundum s u r f a c e on the s m a l l d i s c by a chamois s u r f a c e w e l l impregnated rouge- n u j o l b e i n g used as a l u b r i c a n t .  with jewellers  I t was  found  that  the c r y s t a l s l i c e showed no tendency t o crack or c h i p d u r i n g the p o l i s h i n g p r o c e s s . A f t e r the c r y s t a l s l i c e had been p o l i s h e d t o the d e s i r e d t h i c k n e s s (about 25M) the c r y s t a l was  the g l a s s p l a t e s u p p o r t i n g  p l a c e d i n a P e t r i d i s h and covered w i t h a  bath o f anhydrous acetone.  The P e t r i d i s h was  i n a d e s s i c a t o r f o r about two hours which was  then  left  sufficient  time f o r the acetone t o d i s s o l v e the p l a s t i c cement and enable the c r y s t a l s l i c e t o f l o a t  free.  The next step i n the sample p r e p a r a t i o n was the c r y s t a l s l i c e t o the sample h o l d e r . was  transferring  (The sample h o l d e r  simply a brass d i s c designed t o f i t the keys on the  spectrometer mounting so t h a t the sample could be p l a c e d as c l o s e as p o s s i b l e t o the entrance s l i t ) .  In o r d e r t o  t r a n s f e r the c r y s t a l s l i c e t o the sample h o l d e r , the sample h o l d e r was  placed i n the acetone bath and a f i n e h a i r brush  - u was  used t o g e n t l y p o s i t i o n the c r y s t a l s l i c e over the 3 x 11  mm.  slit  i n the sample h o l d e r .  The s i l v e r p a i n t which  still  adhered t o the c r y s t a l s l i c e could be used as a convenient guide i n a l i g n i n g the c r y s t a l and the s l i t  i n the sample  holder. Once t h e c r y s t a l had been c o r r e c t l y sample h o l d e r , the acetone was c a r e f u l l y Petri dish.  p o s i t i o n e d on the removed from t h e  F i n a l l y the c r y s t a l s l i c e was glued s p a r i n g l y  at the edges t o the sample h o l d e r . f o r t h i s purpose.  P l a s t i c cement was used  Now t h a t the c r y s t a l was mounted a f i n a l  measurement was made o f the t h i c k n e s s o f the c r y s t a l the Z e i s s L i g h t S e c t i o n Microscope. crystals  using  The t h i c k n e s s o f t h e  used i n t h i s work were found t o be o f the order o f  25/<W. I n most cases i t was found t h a t the s u r f a c e s o f the c r y s t a l were not p l a n a r  ( i . e . , over the 11 mm.'length o f the  c r y s t a l ' exposed t o the sample beam the c r y s t a l s l i c e u s u a l l y tapered  from about 30 t o 20M) .  In o r d e r t o check the r e l a t i v e o r i e n t a t i o n o f the c r y s t a l axes a Z e i s s P o l a r i z i n g Observation  Microscope was used.  o f i n t e r f e r e n c e f i g u r e s a l s o made i t p o s s i b l e t o  confirm t h a t the c r y s t a l s were ground t o one o r two degrees of the p e r p e n d i c u l a r .  - 15 2-4  Apparatus  4000  The s p e c t r a w e r e r e c o r d e d i n t h e r e g i o n o f 500  c m " u s i n g a P e r k i n E l m e r 421  grating interchanges, e s t i m a t e d as t  s p e c t r o m e t e r w i t h two d u a l  t h e e r r o r o f measurement  being  2 cm"- - w i t h a r e p r o d u c i b i l i t y o f 1 1 cm - -. 1  -  The p o l a r i z e r c o n s t r i c t e d i n t h e M e c h a n i c a l s h o p , o f two t h r e e - s h e e t  stacks  o f 0.5  mounted i n t h e f o r m o f a V (12) the  s p e c t r o m e t e r beam.  against  to  1  consisted  mm. s i l v e r c h l o r i d e  plates  to prevent displacement  Measurements i n the v i s i b l e  a Wollaston prism i n d i c a t e that less  of  region  t h a n 5$ o f  the  component p e r p e n d i c u l a r t o t h e d e s i r e d component and t h e beam i s  passed.  Measurements o f the convergence  s a m p l e beam showed t h a t l e s s  t h a n Ifo of t h e  of  the  component  p a r a l l e l t o t h e beam d i r e c t i o n w o u l d be i n t r o d u c e d by t h e convergence.  - 16 CHAPTER I I I  RESULTS  T h i s Chapter contains r e p r o d u c t i o n s of s p e c t r a obtained d u r i n g the course o f the experimental work. For convenience they are d i v i d e d i n t o three groups; s p e c t r a of p o l y c r y s t a l l i n e strontium formate; s i n g l e c r y s t a l s p e c t r a o f Sr(CH0 ) and s i n g l e c r y s t a l s p e c t r a o f Sr(CHC"2)2«2H2' The Chapter a l s o contains Tables g i v i n g v i b r a t i o n a l assignments of the r e s p e c t i v e groups o f s p e c t r a . D i s c u s s i o n of the b a s i s f o r the assignments i s l e f t u n t i l Chapters Y and V I . 2  3-1  S p e c t r a of P o l y c r y s t a l l i n e Strontium Formate The  samples used t o o b t a i n the s p e c t r a i n F i g . 2  were obtained u s i n g the t h i n f i l m technique which c o n s i s t s of  m e c h a n i c a l l y d e p o s i t i n g a t h i n f i l m o f the sample on an  a p p r o p r i a t e support.  I n t h i s work KBr windows were used.  V i b r a t i o n a l assignments along w i t h the r e s u l t s o f p r e v i o u s workers (1-3) are g i v e n i n Table 2.  3-2  S i n g l e C r y s t a l S p e c t r a o f S r ( C H 0 ) 2 and 2  The Fig.  Sr(CHOo)2»  2 H  2°  samples used t o o b t a i n the s p e c t r a i n F i g . 3 and  4 were obtained u s i n g the techniques o u t l i n e d i n  s e c t i o n 2-3; as a l r e a d y i n d i c a t e d the samples were approxi m a t e l y 25A t h i c k .  The v i b r a t i o n a l assignments f o r the  p o l a r i z e d s i n g l e c r y s t a l s p e c t r a o f S r ( C H 0 ) 2 and 2  -  Sr(GH0 )2»  2H 0  2  The  2  17  -  a r e g i v e n i n Tables 3 and 4-1 r e s p e c t i v e l y .  r e s u l t s f o r s i n g l e c r y s t a l s o f Sr(CH02)2« 2H 0 o b t a i n e d 2  by V i e r n e  (4,5) u s i n g i n f r a r e d r e f l e c t i o n techniques are  contained i n Table 4-2; t h e assignments a r e h i s . I t should be noted t h a t f o r the p o l a r i z e d spectra  single crystal  t h e r e f e r e n c e t o p o l a r i z a t i o n p a r a l l e l (11) t o a  certain crystallographic  a x i s r e f e r s t o the e l e c t r i c  being p a r a l l e l t o the d i r e c t i o n d e f i n e d  vector  by the c r y s t a l a x i s .  In the t a b l e s and i n subsequent d i s c u s s i o n v i b r a t i o n a l modes w i l l be r e f e r r e d t o as X ( a ) ,  Y(c)  o r Z(c)  a c t i v e ; a, b and c  r e f e r i n g t o the c r y s t a l a x i s t o which the e l e c t r i c is  vector  parallel. For the p o l a r i z e d  cm"-- r e g i o n 1  spectra  o f Sr(CH0 )2 i n "the 310-730 2  ( F i g . 3-4 and 3-5) the c r y s t a l f a c e  the  spectra.  F o r the remainder o f the p o l a r i z e d  the  observed s p e c t r a  the  crystal face.  i s noted on spectra  d i d not appear t o be dependent upon  FIG  2-1 SPECTRA (i)  w  ~  Sr(CHQ ) 2  OF POLYCRYSTALLINE  STRONTIUM  FORMATE  4000-500 cm-'  2  8060  E M  c D  40 20  J  (ii)  1  I  I I  Sr(CD0 ) 2  I  L  J  I  I  L  I  I  '  I  I  4000-500 cm-  2  0 £ D  80  .t E  60  IHI  M  c  4020-  i  t  I  * I  i  3500  !  I  I  I  3000  I  I  I  I  I  I  2500  1  I  I  I  I  2000  Frequency cm'  1  I  L  J  1500  I  I  I  I I  1000  1  I  L  - 19 FIG 2-2 SPECTRA OF  (i)  Sr(CH0 ) 2  POLYCRYSTALLINE  STRONTIUM  1400-1320 em-  2  90H  * 80H 70  °  60H  50H  i-  40 (  30H  (ii)  Sr(CD0 ) 2  2  1400-1320 cm-  90H  2 H G  -  70  E  v, 6 0 i  c D  50-1 4030-  1400 1360 1320 Frequency cm"'  FORMATE  - 20 -  FIG 2-3  (i)  SPECTRA OF  Sr(CH0 ) 2  POL YCR YSTAL LIN E STRONTIUM  810-730 em'  2  90H * 80H ° 70H  I  6<H  c D  ». 50 4030-  (ii)  Sr(CD0 ) 2  2  810-730 cm-'  90  Z  80  c D  - 70-1  w 60-|  c  I  50H 4030-  1  1  810 770 730 Frequency cm* 1  FORMAT E  - 21 -  TABLE 2  VIBRATIONAL ASSIGNMENTS FOR SPECTRA OF POLYCRYSTALLINE STRONTIUM FORMATE (WAVENUMBERS IN. CM" ) 1  Mode  Z/ (60CO)ai 5  -fy  * 6(/>CH)b /  2  Harvey et a l  Schutte and Buijs  Donaldson et a l  763 780 784  765 781 785  763 781 786  1070 1082  IO85  1087  1084  1351  1349  1369  1362 1374  1364 1374  1359.5 1362.5 1368  1340  1581 1387.5  1397 1401  1399 1404  1393.5 1399  1013 1039  1580  1572 1590  1572  1570 1593  1 562 1593  1651  I65O  1350  ^2(^C0)ai  ^ (^CH)b /  5  1  Z/^COyb!  1360  .  1653  ^ (^CH)a  Sr(CH02)2 This Work 763 779.5 783-5  2720  2720  2775  2775  2872  2849  2874 .  2872  /  1  1  2925  2925  Sr(CD02)2 This Work 755 772 776  919  2160 2183  0.(H  - 24 -  FIG 3-3 POLARIZED  SPECTRA OF Sr(CH0 ) 2  o.o-  a> w  c 0.2  D  ° <  Polarized II to b axis  0.4-1 0.6  1.0oo -  1120 1080 1040 Frequency cm ' -  2  1120-1040 cm  1  FIG 3-4 POLARIZED  - 25 SPECTRA OF  Sr(CH0 ) 2  o.oH  u  c 0.2o  J2  ° 0.4-  Polarized II to b axis ab face  < 0.61.0-  oo •  0.0  a> u C  i  0.2H  o ° 0.4-  Polarized II to c axis ac face  < 0.6 1.0-  oo •  4-  810  770  730  Frequency cm'  1  2  810-730 cm*'  - 26 FIG 3-5 POLARIZED  c 0.2o  I  Jl <  0.4" 0.6H 1.0-  oo •  Sr(CH0 )  r\f~  0.0H  0) u  SPECTRA OF  Polarized II to b axis be face  2  2  810-730 em-'  - 27 TABLE 3  VIBRATIONAL ASSIGNMENTS FOR SINGLE CRYSTAL SPECTRA OF Sr(CH0 ) (WAVENUMBERS IN CM" ) 1  2  2  Y Active Modes  Z Active Modes  Assignments  X Active Modes  ^ 3 - 15  748  748  ^ 3 - 23  756  756  ^3-12  761  ^3  763  2/3'  766  ^3+12  775  766 775 779.5  783.5 ^  3  786  + 23  787 (sh)  1067  6  1070  1070 1084  K  1084 1085  6  1360 1363  2 ^ ' + 10  1374  1  1359  - 23 TABLE 3 cont'd.  Assignment*  X A c t i v e Modes  - 10 ^  Z A c t i v e Modes  1383 1393  5  Y A c t i v e Modes  1393 1399  + 10  V , ^  + 70  V  V ^  H03 1580  k  k  + 155  1580  / 2  -  ' 1735 (sh)  1580 1650  1735 (sh)  + 180  1760 (sh)  + 200  1780(sh) 2130  + ^3  2  1399  '+^  2^+^  /  2152 2165  ! 2165  2165  V^^V  2334  2334  2334  2^2+>6  2434  2434  - 2434  2458  2458  5  h  £-2 + ^ '  - 29 TABLE 3 cont'd. Assignment*  X A c t i v e Modes  Y A c t i v e Modes  2702  2702  2V  2  2721  21^  v  +^  z  2753 2760  5  2>£' 2 ^ -  2721  2735  5  ^'+ ^ ' zv  Z A c t i v e Modes  2775  20  2775 2852  Z'i , 2^'  2872  -V +  2925  2925  2944 (sh)  2944 (sh)  2  ^4'  957  2  J 2872  2872  2925  2957 (eh)  ^4 + ^5  2975 2988  Z^'+Z^' ZV^  2998 (sh)"  2998 (sh)  3128  3128  3143 (sh)  3143 (sh) 3192  -V ^ *  x  +  V  3  V ^ '  3631 3648  The 7S and ^ r e f e r r e s p e c t i v e l y t o formate ions I and I I .  3631  FIG  - 31 -  4-1 POLARIZED  i  I 3700  SPECTRA OF  I  I 3500  I  I 3300  Sr (C H 0 ) -2H 0 2  l  2  I  I  3100  I 2900  Frequency cm*  1  i  2  3900-2500 cm'  I  I 2700  1  - 32 FIG 4-2. POLARIZED  SPECTRA OF  S r(C H 0 ) -2H 0 2  2  2  2500-1900 cm  o.ou  c JI  I  JI  0.2-  Polarized II to a axis  \  / \  /  0.4•  0.6-  <  i.ooo -  i  ,  i  i  1  ,  1  ,  i  ,  1  1  o.oc  n w J3 la  0.2-  Polarized II to b axis  \  / Nw-~^>/  S 0-4-  JI <  0.61.0oo -  i  i  i  1  I  1  i  l  1  i  1  i  i  o.oV u  c D  0.2-  JQ  2  Polarized II to c axis  \  / /  0.4-  Jl  < 0.61-0oo -  t  1  •  1  2500  .  1  1  ,  1  1  .  2300 2100 Frequency cm*  1  1  1900  ,  FIG 4-3 POLARIZED  - 33 SPECTRA OF S r (C H0 ) -2H 0 2  2  2  2000-1200 cm-'  - 35 TABLE 4 - 1  VIBRATIONAL ASSIGNMENTS FOR SINGLE CRYSTAL SPECTRA OF Sr(CH0 ) .2H 0 (WAVENUMBERS IN CM ) -1  2  Assignment*  2  X Active Modes  2  Y Active Modes  Z Active Modes  7^(H 0)  1  642  642  642  7/ (H 0)  2  710  710  710  2  R  2  ^R 2 3 (H  0)  ^ (H 0) R  2  7  5  Zi(H 0)  6  2  2  ^ (H 0) R  2  0 (sh  >  7  5  840  3  < > sh  838 (sh)  872  ?  872 1064  1064  1225 ;  1255 ^  5  856  2^ (H 0) 2  7  797 (sh)  ,  R  0  797 (sh)  4  ^(H 0)  5  - 18  1255  1337  1337  ^ ^2*^5  l/J >5 + 18  1337 1355  1  3  6  4  1383 1392  1  3  6  4  1383 (sh)  I 1392  1383 1392  - 36 TABLE 4 - 1 cont'd.  Assignment*  X Active Modes  Z£ - 110 V 2  Y Active Modes  1476 (sh)  (H 0)  Z Active Modes  1476 (sh)  1476 (sh)  ^  2  !545 1590  V  h  1590  5^' 1^  1612  + 110  1700 (sh)  Z- (H 0)-»-7^(H 0)  2170 (sh)  2170  2170  ^(H 0)4.^ (H 0)  2250  2250  2250 (sh)  2  2  2  2  R  2  1  2  ZV  718  2  2  2Z^  2740  2718  2740  2740  22^'  2763  y-l  2 8  ^l(H 0),Z^ (H 0) 2  *  3  2  The V and V'refer  5  8  3150  28  5S  2858  3150  respectively to formate ions I and I I ,  3150  - 37 TABLE 4-2-  VIBRATIONAL ASSIGNMENTS FOR SINGLE CRYSTAL SPECTRA OF Sr(CH0 ) .2H 0 - PREVIOUS WORK*(WAVENUMBERS IN CM ) • -1  2  Assignment  ^5 ^5  2  2  X Active Modes  .Y Active Modes  Z Active Modes  662  662  662  714  714  714  757  757  .  855 865  ^2  1570  1567  ^4  1577  1578  ^4  1587.5  1587.5  ^5  1614  ^5  *  Vierne et a l .  1605  1566  - 33 CHAPTER IV  THEORY  S e c t i o n s 1 and 2 of t h i s Chapter b r i e f l y d i s c u s s the v i b r a t i o n s o f a p o l y atomic system and the a s s o c i a t e d s e l e c t i o n r u l e s , and are used as an a i d i n i n t r o d u c i n g the more complex theory o f s o l i d s t a t e s p e c t r a contained i n s e c t i o n s 3 and 4«  4-1  The V i b r a t i o n s o f I s o l a t e d Polyatomic M o l e c u l e s In o r d e r t o study the motions o f an i s o l a t e d  n-atomic  system, a s e t o f 3n c o o r d i n a t e s i s r e q u i r e d to d e s c r i b e its' the  configuration.  Of these 3n c o o r d i n a t e s , three d e s c r i b e  t r a n s l a t i o n a l motion and t h r e e more d e s c r i b e the r o t a t -  i o n a l motion o f the system, l e a v i n g 3n-6  c o o r d i n a t e s to  d e s c r i b e the systems' v i b r a t i o n a l degrees o f freedom. W i l s o n , Decius and Cross (13)  d i s c u s s a g e n e r a l method  whereby the equations o f motion may a chosen c o o r d i n a t e system.  be w r i t t e n i n terms o f  The set o f equations thus  d e r i v e d y i e l d s a s e r i e s o f s o l u t i o n s corresponding t o the normal modes o f v i b r a t i o n o f the system. The 3n x 3n s e c u l a r determinant which must be s o l v e d i n order t o determine the normal frequences can o f t e n be simplified. the of  T h i s s i m p l i f i c a t i o n a r i s e s from the f a c t  that  system under i n v e s t i g a t i o n u s u a l l y possesses some form symmetry.  I f , i n a molecule, a symmetry o p e r a t i o n i s  -  39 -  c a r r i e d out which transforms  the molecule i n t o an e q u i v a l e n t  p o s i t i o n , the k i n e t i c and p o t e n t i a l e n e r g i e s w i l l remain unchanged. The  s e t o f symmetry o p e r a t i o n s t h a t a molecule  possesses  which c a r r y i t i n t o e q u i v a l e n t p o s i t i o n s i s known as a group.  Each symmetry o p e r a t i o n a s s o c i a t e d w i t h the group  maybe r e p r e s e n t e d  a n a l y t i c a l l y by a l i n e a r  transformation  connecting the o l d c o o r d i n a t e s w i t h c o o r d i n a t e s o f the molecule i n i t s new p o s i t i o n .  The s e t o f l i n e a r  transform-  a t i o n s so obtained i s s a i d t o be a r e p r e s e n t a t i o n o f the group o f symmetry o p e r a t i o n s ; while the c o o r d i n a t e s , i n terms o f which the t r a n s f o r m a t i o n are w r i t t e n are s a i d t o form a b a s i s o f the r e p r e s e n t a t i o n . I t i s u s u a l l y p o s s i b l e , by choosing a s u i t a b l e s e t o f coordinates t o reduce the 3 n x 3 n t r a n s f o r m a t i o n to a comparatively  matrices  simple form; i n e f f e c t s e p a r a t i n g these  c o o r d i n a t e s i n t o s e t s which do not mix w i t h each other i n any o f the t r a n s f o r m a t i o n s . been found  When a coordinate system has  such t h a t i t i s i m p o s s i b l e t o break the c o o r d i n a t e s  down i n t o any s m a l l e r non-mixing s e t s , the r e p r e s e n t a t i o n f o r which these completely  c o o r d i n a t e s form a b a s i s i s s a i d t o be  reduced.  When i t i s p o s s i b l e t o do t h i s , the  o r i g i n a l r e p r e s e n t a t i o n i s s a i d t o be r e d u c i b l e . equations  The  i n v o l v i n g the members o f any one non-mixing s e t  can be considered by themselves as making up t r a n s f o r m a t i o n s  - 40 which form a r e p r e s e n t a t i o n o f the group.  Such a r e p r e s e n t -  a t i o n i s i r r e d u c i b l e and i t i s seen t h a t a completely  reduced  r e p r e s e n t a t i o n i s made up o f a number o f i r r e d u c i b l e representations. I t i s u s u a l l y p o s s i b l e t o choose s e v e r a l s e t s o f c o o r d i n a t e s t o form a b a s i s f o r the r e p r e s e n t a t i o n s , but i n each case the r e s u l t s would be the same.  Any two r e p r e s e n t -  a t i o n s , are s a i d t o be e q u i v a l e n t when they d i f f e r only i n the choice o f the b a s i s The  coordinates.  fundamental, theorem concerning  irreducible  represent-  a t i o n s s t a t e s t h a t f o r each p o i n t group there are o n l y a d e f i n i t e number o f non-equivalent possible.  irreducible  representations  I t i s p o s s i b l e t o show t h a t the number o f times an  i r r e d u c i b l e r e p r e s e n t a t i o n appears i n a reduced r e p r e s e n t a t i o n is (1)  Where h i s the order o f the group (equal t o the number o f symmetry o p e r a t i o n s  contained  i n the group), X g i s the  c h a r a c t e r o f the r e d u c i b l e r e p r e s e n t a t i o n and  i s the  c h a r a c t e r o f t h e i t h i r r e d u c i b l e r e p r e s e n t a t i o n o f the operation the group.  R .  The sum i s taken over a l l the o p e r a t i o n s o f  The c h a r a c t e r i s d e f i n e d as the sum o f the  d i a g o n a l elements o f the t r a n s f o r m a t i o n matrix,  the c h a r a c t e r s  of e q u i v a l e n t r e p r e s e n t a t i o n s being i d e n t i c a l .  These  - 41 on the r i g h t hand s i d e o f {1)> are e a s i l y d e t e r -  quantities  mined u s i n g a simple s e t o f r u l e s . A s s o c i a t e d w i t h each non-mixing s e t o f normal c o o r d i n a t e s i s a s e t o f normal modes o f v i b r a t i o n , the number o f normal modes being equal t o the number o f normal c o o r d i n a t e s i n the set.  Since each normal coordinate transforms a c c o r d i n g t o  one o f the i r r e d u c i b l e r e p r e s e n t a t i o n s o f the group, we can use (1) t o determine the number o f normal modes o f v i b r a t i o n belonging t o each i r r e d u c i b l e r e p r e s e n t a t i o n .  4-2  Selection  Rules  Group theory maybe used t o d e r i v e the s e l e c t i o n f o r v i b r a t i o n a l t r a n s i t i o n s i n the i n f r a r e d .  rules  F o r a fund-  amental t r a n s i t i o n t o occur by a b s o r p t i o n o f i n f r a r e d r a d i a t i o n i t i s necessary  h  i  M  t  t h a t one o r more o f the i n t e g r a l s :  Y  Y-jdr,  have a non zero v a l u e .  Here, ^  s t a t e , *\Ay i s the e x c i t e d  ;  Mr,  J V ^ H i d T  i s the v i b r a t i o n a l ground  s t a t e and A*.^ , y^Ly , and XA. ^  are the components o f the e l e c t r i c d i p o l e moment I t maybe determined  whether the above i n t e g r a l s v a n i s h i f  the symmetry p r o p e r t i e s o f are known.  operator.  , Yy  ,^  , ^  and  Since these are d e f i n i t e i n t e g r a l s over the  whole c o n f i g u r a t i o n space o f the molecule,  they should be  - 42 unchanged by a symmetry o p e r a t i o n R, i n as much as such an o p e r a t i o n merely produces a t r a n s f o r m a t i o n of  coordinates.  That i s , e i t h e r the i n t e g r a l s must be t o t a l l y  symmetric,  or the t r i p l e d i r e c t product Vj  of the species  , //>-  V,*  and  must c o n t a i n the t o t a l l y symmetric s p e c i e s . Since a l l wave f u n c t i o n s f o r normal v i b r a t i o n s i n t h e i r  ground s t a t e s (  ) are bases f o r the t o t a l l y  symmetric  r e p r e s e n t a t i o n of the symmetry s p e c i e s of the molecule, the i n t e g r a l f o r fundamental t r a n s i t i o n s s t a t e to the f i r s t  e x c i t e d s t a t e ) w i l l be symmetric o f the  d i p o l e moment o p e r a t o r and to  (from the ground  the f i r s t  excited state  the same species ( i . e . the d i r e c t product  a t i o n w i t h i t s e l f i s symmetric).  belong  of a r e p r e s e n t -  I t can be shown (10)  that  the components of the d i p o l e moment o p e r a t o r t r a n s f o r m the same manner as the t r a n s l a t i o n a l c o o r d i n a t e s , and  T  2  .  a c t i v e i f Vj  T  Thus a normal mode of v i b r a t i o n w i l l be  in ,  x  T  y  infrared  belongs t o the same symmetry s p e c i e s as  one  of the t r a n s l a t i o n a l coordinates. S i m i l a r symmetry arguments may  be a p p l i e d to determine the a c t i v i t y of overtone  combination a b s o r p t i o n .  and  I t should be noted t h a t the above  d i s c u s s i o n c o n s i d e r s d i p o l e s e l e c t i o n r u l e s onlyi n t e r a c t i o n s are assumed n e g l i g i b l e .  other  - 43 4-3  S o l i d S t a t e Spectra and C r y s t a l  Symmetry  The d i s c u s s i o n o f the v i b r a t i o n s of polyatomic i n 4-1 p e r t a i n e d t o i s o l a t e d molecules. molecules  molecules  I n c r y s t a l s where  are i n c l o s e p r o x i m i t y t o one another i t i s  necessary t o c o n s i d e r the nature o f the i n t e r m o l e c u l a r i n t e r a c t i o n s when seeking t o determine s e l e c t i o n r u l e s f o r optical transitions.  Procedures  f o r determining  these  s e l e c t i o n r u l e s , have been d e v i s e d by Bhagavantam and Venkatarayudu (14) and a l s o by H a l f o r d (15). of these procedures  I n the f i r s t  the motions o f the c r y s t a l l o g r a p h i c  u n i t c e l l are considered whereas i n t h a t o f H a l f o r d a t t e n t i o n i s focused upon the motions o f i n d i v i d u a l molecules.  Iti s  the work by Bhagavantam and Venkatarayudu t h a t s h a l l be r e f e r r e d t o most. convenient  However, before proceeding i t i s  t o b r i e f l y c o n s i d e r the r e l a t i o n of v a r i o u s  groups t o the d e s c r i p t i o n o f c r y s t a l  symmetry.  I f a c r y s t a l were i n f i n i t e i n extent, i t would admit an i n f i n i t e number o f symmetry o p e r a t i o n s i n c l u d i n g t r a n s l a t i o n s , proper and improper r o t a t i o n s and combinations these.  of  There are a l i m i t e d number o f ways o f combining  such o p e r a t i o n s t o form the 230 space groups.  The symmetry  of a c r y s t a l maybe d e s c r i b e d by a s s i g n i n g i t t o the space group which c o n t a i n s as i t s elements the symmetry o p e r a t i o n s a s s o c i a t e d w i t h the c r y s t a l .  I t should be noted t h a t c r y s t a l s  - 44 on the b a s i s o f t h e i r e x t e r n a l symmetry can be d i s t r i b u t e d among 32 c r y s t a l c l a s s e s ,  each c l a s s being i d e n t i f i e d w i t h  a c o l l e c t i o n of symmetry elements and an unique p o i n t group of o p e r a t i o n s concerned w i t h them.  Each point group  generates a c h a r a c t e r i s t i c number o f space groups which, as i n d i c a t e d  above, are d e s c r i p t i v e  of the i n t e r n a l c r y s t a l  structure. I t i s shown i n standard works on space group theory t h a t any space group may be regarded as the product o f an invariant  subgroup, known as a t r a n s l a t i o n group, and a  f a c t o r group. consists  The t r a n s l a t i o n group as i t s name suggests  o f the elements o f the space group c o r r e s p o n d i n g  to pure t r a n s l a t i o n s . the  As a l r e a d y i n d i c a t e d  the cosets o f  t r a n s l a t i o n group i n the space group form what i s known  as a f a c t o r group.  The f a c t o r groups are always  w i t h one o f the 32 c r y s t a l l o g r a p h i c  isomorphous  point groups, although  some o f them may i n v o l v e c o s e t s c o n t a i n i n g o t h e r than p u r e l y p o i n t o p e r a t i o n s combined w i t h l a t t i c e ( i . e . screw r o t a t i o n o r g l i d e  translations  reflection.)  The l a s t group w i t h which we w i l l be concerned i s the s i t e group. invariant  A s i t e i s d e f i n e d as a p o i n t which i s l e f t  by c e r t a i n o p e r a t i o n s o f the space group and i s  e q u i v a l e n t t o what i s c r y s t a l l o g r a p h i c a l l y known as a special position.  These o p e r a t i o n s may be shown t o form a  group which i s known as a s i t e group.  Every p o i n t i n the  - 45 c r y s t a l l a t t i c e i s thus a s i t e , and i s a s s o c i a t e d w i t h a t l e a s t the t r i v i a l s i t e group C^.  A s i t e group i s n e c e s s a r i l y  isomorphous w i t h some subgroup o f the f a c t o r group and, o f course, i n v o l v e s o n l y p o i n t symmetry o p e r a t i o n s  s i n c e no  g l i d e r e f l e c t i o n o r screw r o t a t i o n can leave any p o i n t invariant. The two procedures p r e v i o u s l y mentioned f o r d e t e r m i n i n g selection rules associated with o p t i c a l t r a n s i t i o n s i n c r y s t a l s , may now be more p r e c i s e l y d e s c r i b e d  by s t a t i n g  the type o f group used i n the a n a l y s i s o f the motion; i . e . Bhagavantam and Venkatarayudu analyse the motion o f the u n i t c e l l under the f a c t o r group and H a l f o r d analyses molecular u n i t i n the c r y s t a l a c c o r d i n g associated with i t s s i t e .  the  t o the group  I n the f o l l o w i n g s e c t i o n the  f a c t o r group a n a l y s i s o f Bhagavantam and Venkatarayudu which i s g e n e r a l l y more s a t i s f a c t o r y than the s i t e group a n a l y s i s o f H a l f o r d w i l l be  4-4  considered.  F a c t o r Group A n a l y s i s o f V i b r a t i o n s i n C r y s t a l s As p r e v i o u s l y mentioned the f a c t o r group a n a l y s i s  considers  the u n i t c e l l or more c o r r e c t l y the p r i m i t i v e  u n i t c e l l o f the c r y s t a l which by d e f i n i t i o n c o n t a i n s  the  s m a l l e s t r e p e a t i n g u n i t of p a t t e r n found w i t h i n the c r y s t a l ( i . e . t h i s u n i t o f p a t t e r n i s r e l a t e d t o i d e n t i c a l u n i t s of  -  46  -  p a t t e r n i n a l l neighbouring u n i t c e l l s by simple  translation.)  For n atoms i n the p r i m i t i v e u n i t c e l l there w i l l be 3n v i b r a t i o n s o f which three correspond t o v i b r a t i o n s w i t h t r a n s l a t i o n o f the u n i t c e l l .  The remaining 3n-3  v i b r a t i o n a l modes are c l a s s i f i e d as being e i t h e r or i n t e r n a l v i b r a t i o n s .  associated  external  The e x t e r n a l v i b r a t i o n s o r l a t t i c e  v i b r a t i o n s are f u r t h e r c l a s s i f i e d as a r i s i n g from  trans-  l a t o r y or r o t a t o r y motions o f the molecules i n the u n i t The  e x t e r n a l v i b r a t i o n s u s u a l l y e x h i b i t low  w h i l e the i n t e r n a l v i b r a t i o n s o r v i b r a t i o n s  frequencies; involving  movements o f the i n d i v i d u a l atoms i n each molecule themselves w i l l g e n e r a l l y By c o n s i d e r i n g  e x h i b i t high  cell.  against  frequencies.  the group o f n non-equivalent  points,  corresponding t o the n non-equivalent atoms contained i n the p r i m i t i v e u n i t c e l l and a p p l y i n g  the p r i n c i p l e s o f group  theory, we can f i n d an e x p r e s s i o n f o r nj_ , the number o f Pj  times a p a r t i c u l a r i r r e d u c i b l e r e p r e s e n t a t i o n contained i n the r e d u c i b l e  representation  P  .  is The debited  expression i s :  >i,^lh 16 (R)Y-(R) J  Where ~j£-(R) and  ( 2 )  j  ")£(R) a r e the characters  o f the o p e r a t i o n  J  R i n the r e p r e s e n t a t i o n s the  P  order o f the group and  and hj  o p e r a t i o n s f a l l i n g under the  P  respectively;  Al i s  i s the number o f group j t h class.  A l l terms i n ( 2 )  - 47 except group.  c  a  n  D e  obtained from the a p p r o p r i a t e  A n a l y t i c a l e x p r e s s i o n s f o r the  have been  ")C(R)  devised by Bhagavantam and Venkatarayudu (14) summarized i n Table  factor  and  are  5«  By s u i t a b l e choice of the r e d u c i b l e r e p r e s e n t a t i o n and u t i l i z i n g the c h a r a c t e r s  X(R)  a p p r o p r i a t e to i t we  can c o n f i n e o u r s e l v e s to one or the other of the s e v e r a l types of normal v i b r a t i o n s mentioned p r e v i o u s l y . o f normal v i b r a t i o n a s s o c i a t e d w i t h each of the i n d i c a t e d i n Table The  The  type  JC{TL) i s  5»  f a c t o r group a n a l y s i s f o r Sr(CHC>2)2 *d ar  Sr(CHC>2)2»2H 0 are g i v e n r e s p e c t i v e l y i n chapters V and 2  VI.  - us -  TABLE 5  SUMMARY OF EXPRESSIONS FOR CHARACTERS OF THE GROUP OPERATIONS, R  Type of Vibration  Expression for the Corresponding Characters of the Group Operation R i n the Reducible Representation,P  n^ - Total number of vibrations of symmetry species i  X(R)  = U (n)(±l+2 Cos0 )  ni(T) - Number of purely Translational vibrations of symmetry species i  X(R)  * (±1+2 Cos0)  X(R)  ="[u (s)-l](±l+2 Cos^ )  X(R)  = 'U (s-v)(l±2 Cos?*)  X(R)  =[u (n)-U (s)](±l+2 COB0 )  ni(T') - Number of Lattice vibrations of Translational origin of symmetry species i n^R' ) - Number of Lattice vibrations of Rotational origin of symmetry species i n^' - Number of Internal vibrations of symmetry species i  R  R  R  R  R  -U (s-v)(l±2 Coatf ) R  U (n)  - the number of atoms i n variant under the operation R  R  U (s) R  a  the number of groups occupying lattice sites which are invariant under the operation R ^  U (s-v) R  0  =  =  the number of groups occupying lattice sites which are i n variant under the operation R less the number of atoms occupying lattice sites which are invariant under the operation R '  the angle of rotation associated with the operation R.  - 49 CHAPTER V  DISCUSSION - PART I  T h i s chapter d i s c u s s e s the e x p e r i m e n t a l l y observed i n f r a r e d spectrum o f c r y s t a l l i n e Sr(CH02)2 i n r e l a t i o n t o the v i b r a t i o n a l modes p r e d i c t e d by the f a c t o r group a n a l y s i s . In addition, information obtained from the p o l a r i z e d s i n g l e c r y s t a l s p e c t r a i s d i s c u s s e d i n r e l a t i o n t o the v i b r a t i o n a l assignments and the c r y s t a l s t r u c t u r e o f Sr(CH02)2« L a t t i c e modes and combination modes a r e a l s o d i s c u s s e d .  5-1  Vibrational Analysis  f o r Sr(CH02)?  As i n d i c a t e d i n Chapter I the p r i m i t i v e u n i t c e l l o f s t r o n t i u m formate c o n t a i n s 36 atoms; t h i s means there w i l l be a t o t a l o f 108 v i b r a t i o n s .  Using equation (2) we f i n d  t h a t under the f a c t o r group Dj-fr, which i s isomorphous w i t h t h e p o i n t group D2, the s t r u c t u r e o f the r e p r e s e n t a t i o n  of  c a r t e s i a n c o o r d i n a t e s i s r • 27a 4. 27b]_ + 27b2 + 27b^ .  By  f u r t h e r a p p l i c a t i o n o f e q u a t i o n (2) the types o f normal vibrations associated can be determined.  w i t h each i r r e d u c i b l e  representation  The r e s u l t s are summarized i n the  f a c t o r group a n a l y s i s contained i n Table 6. Reference t o Table 6 shows t h a t there a r e a t o t a l o f 48 i n t e r n a l v i b r a t i o n s : 12a ,12b! , 12b2 12bj. t  This  leaves  57 e x t e r n a l v i b r a t i o n s which a r e d i s t r i b u t e d i n the f o l l o w i n g manner; 36 l a t t i c e v i b r a t i o n s o f r o t a t o r y o r i g i n :  -  50 -  TABLE 6  CHARACTER TABLE AND FACTOR-GROUP ANALYSIS FOR Sr(CH02)  D  b  2  x  b  2  b^  E  0 ( z ) 0 (y) 2  2  C (x) 2  n i  n^T)  2  n^(T')  ni(R') n ' i  1  1  1  1  27  0  9  6  12  1  1  -1  -1  27  1  8  6  12  T  z  1  -1  1  -1  27  1  8  6  12  T  y  1  -1  -1  1  27  1  8  6  12  T  x  - 51 6a , 6b^ origin:  t  6b  , 6b^  2  and 33 l a t t i c e v i b r a t i o n s o f t r a n s l a t o r y  9a , 6"b^ , 8 b  2  , Sbj .  The remaining t h r e e v i b r a t i o n s  correspond t o t r a n s l a t i o n on the u n i t c e l l and are o f symmetry s p e c i e s b^ , b  5-2  2  and b^ .  The I n t e r n a l Fundamentals o f SrfCHC^lgThe  Assignments  s i g n i f i c a n c e o f the s p l i t t i n g a s s o c i a t e d w i t h the  i n t e r n a l modes i n r e l a t i o n t o the f r e e i o n modes i s understood by c o n s i d e r i n g the r e l a t i o n s h i p between the formate i o n s i n the u n i t o f p a t t e r n .  For Sr(CH0 )2 2  t  n  e  u n i t of  p a t t e r n c o n t a i n s e i g h t formate i o n s composed o f two s e t s o f four c r y s t a l l o g r a p h i c a l l y equivalent u n i t s .  I n each s e t  of f o u r i o n s the i o n s may execute the same v i b r a t i o n i n phase o r 16*0° out o f phase r e l a t i v e t o one o f t h e i r number arbitrarily  chosen.  Thus, f o r each s e t o f f o u r i o n s  there  are f o u r p o s s i b l e combinations; each combinations c o r r e s ponding t o one o f the i r r e d u c i b l e r e p r e s e n t a t i o n s D a  4  factor-group > ^1 , ^2  a  n  d  o f the  and thus g i v i n g r i s e t o c r y s t a l modes o f  ^3  symmetry.  I t i s r e a d i l y seen t h a t when  t h i s f o u r - f o l d s p l i t t i n g a s s o c i a t e d w i t h each s e t o f f o u r i o n s i s considered  w i t h the t w o - f o l d  the two s e t s o f non-equivalent  s p l i t t i n g a r i s i n g from  i o n s t h a t we have an e i g h t f o l d  s p l i t t i n g a s s o c i a t e d w i t h each o f the s i x f r e e i o n fundamentals.  Thus accounting  f o r the 43 i n t e r n a l fundamentals  - 52 predicted  by the  s p e c i e s of b i , b the  -  factor-group analysis. and  2  b^ symmetry are a c t i v e i n the  i n f r a r e d spectrum of the  fundamental a s s o c i a t e d  However, since  c r y s t a l should r e v e a l  w i t h the  only  infrared each  free ion s p l i t into six  components; g i v i n g r i s e to the 36  infrared active  internal  fundamentals. I t i s r e a d i l y seen from the f a c t o r group a n a l y s i s f o r p o l a r i z e d r a d i a t i o n along any c r y s t a l l o g r a p h i c axes o n l y two a l l o w e d ; these two equivalent  one  of the  of the  principal  s i x components  components corresponding to the  s e t s of formate i o n s  that  contained i n the  are  two  unit  nonof  pattern. Although the r e l a t i v e i n t e n s i t i e s of the fundaments are not  d i s c u s s e d i n d e t a i l u n t i l the  s e c t i o n ; i t i s convenient t o note t h a t  the  between the v a r i o u s components a s s o c i a t e d fundamentals can c o s i n e s of the  be understood i f we  o s c i l l a t i n g dipoles  i o n fundamentals- t o a f i r s t the  internal next  intensity relation w i t h the  c o n s i d e r the  free  ion  direction  g i v i n g r i s e to the  free  approximation the r a t i o s of  r e l a t i v e i n t e n s i t i e s of the v a r i o u s components should  be i n the direction  same r a t i o as the  squares of the  appropriate  cosines.  Values f o r the  squares of the  d i r e c t l y o b t a i n e d from the  d i r e c t i o n c o s i n e s can  c r y s t a l structure.  g i v e n i n Table 7 are based upon the  The  values  c r y s t a l structure  of  be  - 53 -  TABLE 7  SQUARES OF THE DIRECTION COSINES FOR FORMATE IONS I AND II of Sr(CH0 ) 2  Symmetry Species of Associated Free Ion Fundamentals a  1  2  0.0659  0.0908  bj_  0.5320  0.4673  b  0.4039  0.4398  x  2  i  2  2  &  0.7510  0.0001  bi  0.1777  0.2754  b  0.0711  0.7237  x  *  2  2  2  The subscripts 1 and 2 refer to formate ions I and II respectively.  - 54 N i t t a (9).  In the following discussion  i t w i l l be i n d i c a t e d  where r e l a t i v e i n t e n s i t i e s have been used i n making the assignments; r e f e r e n c e being made t o the s p e c t r a  shown i n  F i g u r e s 2 and 3 and a l s o t o Tables 7 and 9 (Table 9- which i s i n t r o d u c e d l a t e r gives c a l c u l a t e d and observed intensityratios. ) The s i x f r e e i o n fundamentals o f the formate i o n have been w e l l c h a r a c t e r i z e d  (1-3), and as has been  mentioned  p r e v i o u s l y we expect each o f the s i x f r e e i o n fundamentals to s p l i t i n t o s i x i n f r a r e d a c t i v e components i n the s i n g l e c r y s t a l spectrum- thus g i v i n g r i s e t o the 3 6 i n f r a r e d a c t i v e fundamentals p r e d i c t e d convenient t o d i s c u s s  by the f a c t o r group a n a l y s i s .  the i n t e r n a l fundamentals i n terms  of the f r e e i o n fundamentals.  F i r s t o f a l l we w i l l  the f r e e i o n fundamental l/^i^CE) a-^_ c r y s t a l spectrum.  It i s  consider  as r e l a t e d t o the  Both the spectrum o f p o l y c r y s t a l l i n e  Sr(CH02)2 ( F i g * 2-1) and the s i n g l e c r y s t a l spectrum ( F i g . 3-1) i n d i c a t e only a s i n g l e a b s o r p t i o n corresponding to  i t h i s absorption occurring  a t 2872 cm~^.  That no  observable s p l i t t i n g occurs i s f u r t h e r v e r i f i e d by the f a c t t h a t the i n t e n s i t y r a t i o s expected f o r v a r i o u s  polarizations,  assuming no s p l i t t i n g are i n good agreement w i t h t h e r a t i o s observed e x p e r i m e n t a l l y (Table 9). For  (^CO)a^ the p o l y c r y s t a l l i n e spectrum ( F i g . 2-2)  shows three components o c c u r r i n g  a t 1359.5, 1362.5 and  - 55 1363 cm"-'-; t h e two h i g h frequency w e l l defined shoulders.  components appearing as  The p o l y c r y s t a l l i n e spectrum a l s o  shows another a b s o r p t i o n i n t h i s r e g i o n a t 1349*5 cm"-*-. However, c o n s i d e r a t i o n o f the spectrum o f p o l y c r y s t a l l i n e strontium formate - d ^ ( F i g . 2-2) and the i n t e n s i t i e s shown by the p o l a r i z e d s i n g l e c r y s t a l s p e c t r a ( F i g . 3-2) i n d i c a t e t h a t t h i s a b s o r p t i o n i s not a s s o c i a t e d w i t h the  7^2 r e g i o n i n the spectrum o f p o l y c r y s t a l l i n e  formate -d]_ we see t h a t no corresponding  Considering strontium  a b s o r p t i o n appears  which immediately suggests t h a t the a b s o r p t i o n under c o n s i d e r a t i o n i s not a s s o c i a t e d w i t h  7^2 •  i  s  also interesting  to note t h a t even though the spectrum o f p o l y c r y s t a l l i n e strontium formate -d-^ shows no evidence  o f s p l i t t i n g i n the  r e g i o n - t h e band envelope i n d i c a t e s t h a t the same s p l i t t i n g i s present as f o r p o l y c r y s t a l l i n e s t r o n t i u m Although the 1^2  r e  formate.  g i ° n i s not very w e l l r e s o l v e d i n the  s i n g l e c r y s t a l s p e c t r a , the use o f p o l a r i z e d r a d i a t i o n shows t h a t the 1359*5 cm"-*- component i s due t o i o n I w h i l e the components o c c u r r i n g a t 1362.5 cm"-*- and 1368 cm"-*- a r e due t o ion  II.  I n the s i n g l e c r y s t a l s p e c t r a , under X p o l a r i z a t i o n  the most i n t e n s e a b s o r p t i o n o c c u r r i n g i n t h i s r e g i o n i s found a t 1362 cm"- - r e f e r e n c e t o Table 7 shows t h a t i o n I I 1  i s indicated.  F o r Y p o l a r i z a t i o n the most i n t e n s e  absorption  occurs a t 1359 cm"-* which i n d i c a t e s i o n I . Under Z p o l a r -  i z a t i o n we have the appearance o f a broad a b s o r p t i o n which  - 56 has a peak a t  1359.5  I36O  cm"^; t h i s i n d i c a t e s the presence  of the  cm~l component a s s o c i a t e d w i t h i o n I , which we expect  t o be s t r o n g l y absorbing and a l s o the presence 1368 cm~l component observed  o f the  i n the p o l y c r y s t a l l i n e spectrum,  which we can a s s i g n t o i o n I I . The  (eSoCOja^ r e g i o n i s w e l l r e s o l v e d i n both the  p o l y c r y s t a l l i n e and s i n g l e c r y s t a l s p e c t r a ( F i g s . 2-3 and 3-4,  3-5 r e s p e c t i v e l y ) .  The p o l y c r y s t a l l i n e spectrum  three w e l l resolved absorptions o c c u r r i n g at  783.5  cm--. -  1  763, 779.5  and  The i n t e n s i t y r a t i o o f t h e two h i g h wave  number a b s o r p t i o n s i s approximately o n e - t h i r d . Table 7 immediately  779.5  a c t i v e component and the a c t i v e component.  Reference t o  i n d i c a t e s that i o n I I i s involved; the  l e s s strongly absorbing  cm"-- a b s o r p t i o n being the X  733.5  1  cm""-- a b s o r p t i o n b e i n g t h e Z 1  As shown i n Table 9 the i n t e n s i t y  o b t a i n e d from the s i n g l e c r y s t a l s p e c t r a support assignment.  shows  ratios  this  The remaining component o f the t r i p l e t , o c c u r r -  i n g a t 763 c m  - 1  i s thus due t o i o n I and r e f e r e n c e t o Table 7  i n d i c a t e s i t should be most a c t i v e under Z p o l a r i z a t i o n . Reference  t o the s i n g l e c r y s t a l s p e c t r a show t h a t under Z  p o l a r i z a t i o n a doublet unexpectly appears  i n this region.  F o r the Z p o l a r i z e d be f a c e a peak occurs a t 766 cm""l w i t h a shoulder o c c u r r i n g a t 761 cm"--; f o r the Z p o l a r i z e d ac 1  f a c e the s i t u a t i o n i s r e v e r s e d .  I t i s p o s s i b l e t h a t the  peaks occur because o f the Y a c t i v e 766 cm-- a b s o r p t i o n and -  1  761  the X a c t i v e  cm"  57  -  absorption.  1  manner enables us to place the as i n d i c a t e d  by the  ratios  the  i n Table 9 the  f o r t h i s r e g i o n are  i n the ~}/^ r e g i o n i n the 2  The  2  and  and  cm"  1  Consideration  less strongly  i n excellent  a l s o i n t e r e s t i n g to note t h a t  Sr(CH0 )  spectrum.  calculated  in this  component at 763  components both occur at 766  Y active  indicated  Z active  polycrystalline  of i n t e n s i t y r a t i o s show t h a t X and  Rationalizing  absorbing  cm"-*-.  observed  As  intensity  agreement.  It is  i d e n t i c a l s p l i t t i n g i s observed  polycrystalline  s p e c t r a of both  Sr(CD0 ) . 2  2  most i n t e n s e r e g i o n of a b s o r p t i o n observed i n  the  spectrum of c r y s t a l l i n e s t r o n t i u m formate i s a s s o c i a t e d w i t h the  f r e e i o n fundamental 3^(.« C0)b-j_ • i/  r e s o l v e d i n the  polycrystalline  T h i s r e g i o n i s best  s p e c t r a ; i n the  both p o l y c r y s t a l l i n e  s t r o n t i u m formate and  s t r o n t i u m formate d^  (Fig. 2-1)  i n t o a doublet i s observed. s t r o n t i u m formate the at 1570  and  1593  cm" . 1  single  three polarizations  ( F i g . 3-2)  at about 1580  as expected the  cm" ; 1  a s s i g n e i t h e r member of the  that  polarized  f o r both *^  2  and  polycrystalline  doublet are  observed  c r y s t a l spectra f o r a l l  i n t e n s i t y of t h i s absorpI t was  not  possible  doublet to i o n I or I I on  spectra. the  splitting  show o n l y a s t r o n g a b s o r p t i o n  t i o n i s l e a s t under Z p o l a r i z a t i o n .  b a s i s of the  spectrum of  components of the The  polycrystalline  almost i d e n t i c a l  In the  spectrum of  However, i t has  to  the  been seen  h i g h wave number member of  the  - 53 doublet  has  been a s s o c i a t e d w i t h i o n I and  t h i s order i s preserved b a s i s we ion  f o r the  5 and  5, and  can t e n t a t i v e l y a s s i g n the 1570  I and  the 1593  cm"  1  as w i l l be  cm"  1  on  seen  this  component t o  component to i o n I I .  Reference to the spectrum of p o l y c r y s t a l l i n e s t r o n t i u m formate ( F i g . 2-2)  shows a w e l l r e s o l v e d doublet  w i t h the f r e e i o n fundamental7/^[CO CHjb-^; the of t h i s doublet the  occur at 1393.5 and  1399  ( F i g . 3-2)  single c r y s t a l spectra  r e s o l v e d i n t h i s r e g i o n i t can be  cm" .  i s a strong a b s o r p t i o n  are not v e r y  cm"  1399  cm"  F i n a l l y we  ( F i g . 3-3)  IO84 cm"  1070  cm" . 1  i n the  spectrum  When i t i s observed  o c c u r r i n g at 1034 show a doublet  Under X p o l a r i z a t i o n the members o f  o c c u r at 1070  and  appearance  J  single c r y s t a l spectra  1067  which  -1  c o n s i d e r the f r e e i o n fundamental ^5(/ CH)b2.  i t appears as a v e r y weak a b s o r p t i o n  doublet  cm  expected.  of p o l y c r y s t a l l i n e Sr(CH02)2 ( F i g . 2-1).  t h i s region.  Reference  For Z p o l a r i z a t i o n a sharp peak at  T h i s mode i s observed o n l y w i t h d i f f i c u l t y  The  polar-  Under I p o l a r i z a t i o n  i n d i c a t i n g the  appears i n d i c a t i n g i o n I I as  1  well  appears.  1  o c c u r r i n g at 1396  appears to be s p l i t i n t o a doublet o f both components.  Although  1  t o Table 7 shows t h i s i n d i c a t e s i o n I . there  components  seen t h a t f o r X  at 1393  i z a t i o n a strong absorption  associated  1  and  and  1034  cm" , 1  1  in  the  under Y p o l a r i z a t i o n a t  under Z p o l a r i z a t i o n at 1035  As shown i n the  cm" .  s p e c t r a there are marked  and  -  differences  59  -  i n i n t e n s i t y f o r the various components and  reference to Table 7 allows us to assign the high wave number component to ion I I and the low wave number component to ion I . Table 3 gives a complete summary of the r e s u l t s discussed above.  From the table we can see the magnitude of the  various s p l i t t i n g s .  The s p l i t t i n g associated with the doublet  i s a d i r e c t measure of the s t a t i c f i e l d e f f e c t while the s p l i t t i n g associated with the t r i p l e t s i s a d i r e c t measure of the dynamic c r y s t a l effect or c o r r e l a t i o n f i e l d  5-3  splitting.  The Internal Fundamentals of Sr(CHOp)p- I n t e n s i t i e s The  r e l a t i o n of the i n t e n s i t y of the i n t e r n a l fund-  amentals to the d i r e c t i o n cosines of the o s c i l l a t i n g dipoles giving r i s e to the free-ion fundamentals was mentioned i n the previous section.  In t h i s section observed i n t e n s i t y  r a t i o s are presented along with the corresponding calculated ratios.  For each of IV^ and ^  two sets of r a t i o s  corres-  ponding to the i n t e n s i t i e s a r i s i n g from formate ions I and II were obtained.  While f o r each of " - ^ j «^2» fc^and f ^  i t was only possible to obtain a single set of i n t e n s i t y r a t i o s ; the r a t i o s corresponding to the combined i n t e n s i t i e s a r i s i n g from formate ions I and I I .  The r e s u l t s are  contained i n Table 9 and especially f o r the well resolved  -  TABLE 8  60  -  THE INTERNAL FUNDAMENTAL MODES OF Sr(CH0 )2 (WAVENUMBERS IN CM" ) 1  2  Free Ion Fundamental* Z (Z/CH)a  Associated Doublett  Magnitude of Splitting  2872  0  /  1  1  y (60C0)a 5  ?  1559.5 1565  5.5  2  Z Active b^ Modest  2872  2872  ? ?  1559 1568  1565 766  765  1  ?  Y Active b Modes  2872  2872 '  X Active Modes  766  765  5.5 781.5 1570 25 1  1595  ?  ?  ?  ?  1595 5.5 1599 ^ (/ 0H)b 6  ,  2  ? 1084  1084 15 1069  779.5  785.5  1595  ? 1084  —  ? —  1599  ,  IO85  i 1070  1067  *  The ^ a n d ^ ' r e f e r to'formate ions I and I I r e s p e c t i v e l y .  t  The frequencies f o r the components o f the doublet are given as averages o f the X, Y and Z a c t i v e components where necessary.  1070  *  \ j  ~f The dashes (—,) i n d i c a t e that the corresponding a c t i v i t y i s too weak t o be observed experimentally, while the question marks (?) i n d i c a t e that no conclusive assignments could be made from the observed spectra. 1  TABLE 9  CALCULATED AMD OBSERVED INTENSITY RATIOS - S r ( C K 0 ) 2  2/2  Associated Free Ion Fundamental  1  ,  /  Calc.  f  Obs.  0.726  0.712  0.91S  1.000  f  i  * Error  8.9*  i  /  i  Calc.  0.9*  2.81  2.67  5.056  Calc.  0.0845 2/2.  14*  2/2  2  2  2  9.156  mj+m /n,+n  2  Calc.  Obs.  0.375  Obs.  0.332  0.375-  2.89  2.72  n +n /l +l Calc.  Obs.  2  3.1*  0.945  3.1*  1.001  2  Calc.  I  * Error  Product o f Obs. Ratios  )  13* 5.9*  0.885  2  Obs.  -  0.0832  0.0833  0.055  1.34  1.30  3.056  0.998  2.20  0.0832  0.314  280$  1.3^  1.25  6.7*  0.864  0.956  1.12  1.36  1.51  1156  0.772  0.597  23*  1.010  0.956  1.35  1.36  1.30  U.U*  0.772  0.592  23*  1.040  2^1 (a-,)  8.99  9.22  ^ (  2.99  ^U(bi)  0.387  2  3.85  2  2  1?+1 /m,+m  12.U  n /l Obs.  3.53  Obs.  12.8  2  0.0004  2  Calc.  2/ 2  Obs.  ""070982  )  * Error  0.107  2  7500  a i  Obs.  m /n  Calc.  2  2/2  0.108  111  Calc.  2/2  i  r 2  2  2.6*  4l*  - 62 r e g i o n s o f the spectrum, there i s remarkably  good agreement  between the experimental and c a l c u l a t e d r a t i o s .  Since  each r a t i o was o b t a i n e d from the p o l a r i z e d s p e c t r a o f a s i n g l e sample no e r r o r i s i n t r o d u c e d i n t o the r a t i o s by having t o a l l o w f o r sample t h i c k n e s s . However, p o s s i b l e e r r o r s do a r i s e from the f o l l o w i n g sources: (i)  the c r y s t a l s l i c e s were not ground a b s o l u t e l y  p e r p e n d i c u l a r t o the c r y s t a l axes-  the maximum d e v i a t i o n  being estimated a t 2° by o b s e r v a t i o n o f i n t e r f e r e n c e f i g u r e s . (ii)  the p o l a r i z e r was not 100$ e f f i c i e n t -  i t was  estimated t h a t l e s s than 5% o f the component p e r p e n d i c u l a r to the d e s i r e d component was passed; measurements being made i n the v i s i b l e r e g i o n a g a i n s t a W o l l a s t o n (iii)  the i n c i d e n t r a d i a t i o n was not p a r a l l e l due t o  convergence o f the sample beamvergence  prism.  measurements o f the con-  showed t h a t l e s s than 1% o f the component  parallel  to the beam would be i n t r o d u c e d . (iv)  the p o l a r i z e r was not c o r r e c t l y a l i g n e d w i t h  r e s p e c t t o the sample f a c e -  i t was estimated t h a t the e r r o r  i n alignment was l e s s than 2 ° . C o n s i d e r a t i o n o f the above sources o f e r r o r  suggest  t h a t the experimental e r r o r i n t r o d u c e d i n t o the observed i n t e n s i t y r a t i o s c o u l d correspond t o as much as 8% o f the component p e r p e n d i c u l a r t o the d e s i r e d component being  passed.  - 63 However, i t would appear from t h i s study t h a t i f c a r e f u l experimental procedure  i s f o l l o w e d the t o t a l e r r o r should  correspond t o l e s s than 5% o f the component p e r p e n d i c u l a r t o the d e s i r e d component being passed.  Even so, i t can be  r e a d i l y a p p r e c i a t e d t h a t i f a c e r t a i n component i s s t r o n g l y a b s o r b i n g a t a c e r t a i n frequency under one p o l a r i z a t i o n and i s o n l y v e r y weakly a b s o r b i n g a t the same frequency under a d i f f e r e n t p o l a r i z a t i o n ; c o n s i d e r a b l e e r r o r c o u l d be i n t r o d u c e d i n t o the observed  intensity  ratio.  I n Table 9 the % e r r o r f o r each r a t i o i s g i v e n as w e l l as the product o f the three r a t i o s making up each s e t of r a t i o s .  T h i s product should e q u a l u n i t y and the d e v i a t i o n  from u n i t y i s a measure o f the i n t e r n a l c o n s i s t e n c y possessed by the experimental i n t e n s i t i e s .  Since the  ^4  a  n  d  1S^ r e g i o n s are not very w e l l r e s o l v e d i n the s i n g l e c r y s t a l s p e c t r a we expect the g r e a t e r e r r o r a s s o c i a t e d w i t h the observed^ i n t e n s i t y r a t i o s - the e r r o r being l a r g e l y i n t r o d u c e d by o v e r l a p p i n g w i t h combination  modes.  One o f the most i n t e r e s t i n g aspects o f an i n f r a r e d  study  o f the c r y s t a l l i n e s t a t e i s the p o s s i b i l i t y o f e x p e r i m e n t a l l y o b t a i n i n g the d i r e c t i o n c o s i n e s a s s o c i a t e d w i t h the a b s o r b i n g species. for  Reference  "^l^l)*  t o Table 9 shows t h a t the i n t e n s i t y data  fji&i)  and  ^ 6 ^ 2 ) should a l l o w d i r e c t  c a l c u l a t i o n o f the d i r e c t i o n c o s i n e s a s s o c i a t e d w i t h symmetry species  a^ and b£ f o r both formate i o n s I and I I .  The o n l y  problem which presents  64 -  i t s e l f i s t h a t i n some cases t h e  product o f the s e t o f r a t i o s i s not i n t e r n a l l y ( i . e . the product does not equal u n i t y ) .  consistent  I f t h i s product  i s not equal t o u n i t y i t can be r e a d i l y a p p r e c i a t e d  t h a t the  d i r e c t i o n c o s i n e s we c a l c u l a t e from the r a t i o s w i l l not be i n t e r n a l l y c o n s i s t e n t themselves ( i . e . the sumrof t h e i r squares w i l l not equal u n i t y ) .  I n o r d e r t o circumvent  this  problem each r a t i o i n a s e t was m u l t i p l i e d by a common f a c t o r so as t o b r i n g t h e product o f t h e r a t i o s t o u n i t y . I t i s noted t h a t t h i s procedure i s not j u s t i f i a b l e mathem a t i c a l l y but s i n c e t h i s common f a c t o r i n a l l cases was c l o s e to u n i t y the e r r o r i n t r o d u c e d The  i s very  small.  s i g n s o f the d i r e c t i o n cosines a s s o c i a t e d w i t h the  symmetry s p e c i e s a^ and \>2 f o r both formate i o n s a r e obtained by a p p l y i n g t h e o r t h o g o n a l i t y requirement. a t i o n o f the o r t h o g o n a l i t y r e l a t i o n allows  Further a p p l i c calculation for  both i o n s I and I I o f the d i r e c t i o n cosines a s s o c i a t e d  with  symmetry s p e c i e s b i . The contained  c a l c u l a t e d and experimental d i r e c t i o n c o s i n e s a r e i n Table 10 and i t can be seen t h a t the agreement  i s e x c e p t i o n a l l y good.  TABLE 1 0 CALCULATED AND EXPERIMENTAL DIRECTION COSINES FOR FORMATE IONS I AND II OF Sr(CHD ) 2  Symmetry Species of Associated Free Ion Fundamentals  m  Calc.  Expt'l  2  l  Calc.  Expt'l  Calc.  Expt'l  0.301  0.297  0.918  0.916  0.684  0.699  -0.026  -0.025  -O.663  -0.649  0.395  0.397  1  -0.257 -0.259 0.729 0.715 O.636 0.649  n  m  2  Calc.  Expt'l  2  Expt'l  Calc.  Expt'l  Calc.  0.045  -0.^99  -O.M92  -O.S67  -0.874  0.008  -O.I421  -0.1*05  0.525  0.501  0.740  O.765  -O.267  -O.256  -0.851  -0.864  o. 53  o>3i  u  - 66 5-4  Overtones and Combinations o f I n t e r n a l Sr(CHQ?)  Fundamentals-  ?  As noted p r e v i o u s l y each f r e e - i o n fundamental i s s p l i t i n t o 8 components under the D2 f a c t o r group.  Of these 8  components 4 are a s s o c i a t e d w i t h formate i o n s I and 4 are a s s o c i a t e d w i t h formate i o n s I I .  Reference to Table 11  shows t h a t the overtones a s s o c i a t e d w i t h the i n t e r n a l fundamentals a r i s i n g from formate i o n I and a l s o formate i o n I I c o n s i s t o f 16 components (4a , 4bi, 4b2> 4b3). these 16 components 12 are i n f r a r e d a c t i v e Hence, we  (4b]_, 4b2,  Of 4b3).  expect t o observe 4 components f o r both i o n s I  and I I under each o f X, Y and Z p o l a r i z a t i o n s .  Considerations  s i m i l a r t o the above a l s o a p p l y t o combination modes. From the observed s p e c t r a i t was p o s s i b l e t o a s s i g n a number o f overtones and combinations o f i n t e r n a l fundamentals. These assignments were g i v e n p r e v i o u s l y i n Table 3.  5-5  Combinations o f I n t e r n a l Fundamentals  and L a t t i c e Modes-  SrtCHOp)? Sum  and d i f f e r e n c e modes o f the low frequency l a t t i c e  v i b r a t i o n s and the i n t e r n a l fundamentals w i l l g i v e r i s e t o a s e r i e s o f weaker peaks on the h i g h and low frequency s i d e s of the a b s o r p t i o n peak a s s i g n e d t o the i n t e r n a l fundamental. The t r a n s i t i o n p r o b a b i l i t i e s f o r the d i f f e r e n c e modes are the same as those o f the corresponding: sum modes but the  - 67 i n t e n s i t i e s are expected t o be l e s s because o f the s m a l l e r p o p u l a t i o n s o f the e x c i t e d l a t t i c e mode energy l e v e l s a t which the t r a n s i t i o n s  originate.  Reference t o Table 6 shows t h a t the l a t t i c e are  vibrations  d i s t r i b u t e d i n the f o l l o w i n g manner: (153^, 14bj, 14b2,  14b3).  I f we  c o n s i d e r the p o s s i b l e combinations o f these  l a t t i c e modes w i t h the i n t e r n a l fundamentals we f i n d by r e f e r i n g t o Table 11 t h a t f o r i n t e r n a l fundamentals o f symmetry s p e c i e s , a, b i , \>2 and b  3  the r e s p e c t i v e combination  modes p o s s i b l e a r e : (15a, 1 4 b i , 14b2, ^ b ^ ) , (15b]_, 14a, 1 4 b ) , ( 1 5 b , 14b , 2  2  3  14a, 14b!)  and (15b , 14b , 3  2  14b , x  3  14a).  Remembering t h a t c r y s t a l modes o f symmetry s p e c i e s are  14b ,  a  not i n f r a r e d a c t i v e i t can be r e a d i l y seen from the above  t h a t f o r each o f X, Y and Z p o l a r i z e d s p e c t r a we would, i n p r i n c i p l e , expect the s a t e l l i t e s t r u c t u r e of each o f the 6 i n t e r n a l fundamental d o u b l e t s t o e x h i b i t 114 peaks.  Of these  114 peaks 57 w i l l correspond t o combination modes and the remaining 57 w i l l correspond t o d i f f e r e n c e modes. From the observed s p e c t r a i t was a s s i g n a few l a t t i c e modes (Table 3 ) .  possible to t e n t a t i v e l y These assignments are  based on the r e c u r r e n c e o f i d e n t i c a l peak s e p a r a t i o n s between the v a r i o u s i n t e r n a l fundamentals and the modes associated with t h e i r s a t e l l i t e  structures.  Reference t o Table 3 shows t h a t the observed spectrum i n d i c a t e s l a t t i c e modes o c c u r r i n g a t 10, 12, 15, 20, 23, 155, 130 and 200  cm" . 1  70,  - 63 -  SYMMETRY SPECIES OP COMBINATIONS AND OVERTONES  b  l  1 \  a  b  2  b  5  2  5 b  b 5  2  -  CHAPTER VI  -  69  DISCUSSION - PART I I  T h i s c h a p t e r d i s c u s s e s the e x p e r i mentally observed i n f r a r e d spectrum o f c r y s t a l l i n e Sr(CHOg^^KteO i n r e l a t i o n t o the v i b r a t i o n a l modes p r e d i c t e d by the f a c t o r group a n a l y s i s . I n a d d i t i o n i n f o r m a t i o n o b t a i n e d from the p o l a r i z e d s i n g l e c r y s t a l s p e c t r a i s d i s c u s s e d , where p o s s i b l e i n r e l a t i o n t o the v i b r a t i o n a l assignments and c r y s t a l s t r u c t u r e o f Sr(CH02)2»2H20. L a t t i c e modes and combination modes are a l s o d i s c u s s e d .  6-1  V i b r a t i o n a l A n a l y s i s f o r Sr(CHOg)2.2H2O The v i b r a t i o n a l a n a l y s i s f o r Sr(CH0 )2»2H20 i s 2  contained i n Table 1 2 . 2 H 0 and S r ( C H 0 ) 2 2  2  a  r  e  S i n c e the space group f o r Sr(CH02)2» b  °th P 2 2 2 1  1  1  (D2) l i t t l e  can be  added t o the d i s c u s s i o n c o n t a i n e d i n s e c t i o n 5-1•  We  do  note however t h a t f o r each o f the IS i n t e r n a l fundamental v i b r a t i o n s a s s o c i a t e d w i t h each symmetry s p e c i e s , the 12 modes- n i ' ( C H 0 2 ) w i l l be due t o the formate i o n s and the remain s i x modes- n i ' ( H 2 0 ) w i l l be due t o the water m o l e c u l e s . The i n t e r n a l fundamentals a s s o c i a t e d w i t h the two  non  e q u i v a l e n t water molecules contained i n the u n i t o f p a t t e r n can be d i s c u s s e d i n a manner e n t i r e l y e q u i v a l e n t t o the d i s c u s s i o n o f the two non e q u i v a l e n t formate i o n s .  TABLE 12  CHARACTER TABLE AND FACTOR-GROUP ANALYSIS FOR Sr(CH0 ) .2H 0 2  D  2  « 1  CsU) 1  0 (y) 2  C (x) 2  ni  ni(T) ni(T«)  2  2  ni(fi')  nj'  (CH0 ) 2  1  1  45  0  15  12  18  12  nj'(EgO)  b  x  1  1  -1  -1  45  1  14  12  18  12  6  T  z  b  2  1  -1  1  -1  45  1  14  12  18  12  6  T  y  1  -1  -1  1  45  1  14  12  18  12  6  Tx  - 71 6-2  o f S r ( C H 0 ? ) ? . 2 H ? 0 - Assignments  The I n t e r n a l Fundamentals  The method o f assignment used f o r the formate i o n s o f Sr(CH02)2 w i l l a l s o be used i n the assignment o f the i n t e r n a l fundamentals o f Sr(CH02)2«2H20.  The i n t e r n a l fundamentals  a s s o c i a t e d w i t h the formate i o n as the a b s o r b i n g considered  s p e c i e s are  first.  Reference t o the s i n g l e c r y s t a l s p e c t r a contained i n F i g . 4-1 shows t h a t i n the r e g i o n 3 4 0 0 - 2 9 0 0 c m  - 1  there i s  u n f o r t u n a t e l y t o t a l a b s o r p t i o n due t o the 0-H s t r e t c h i n g f r e q u e n c i e s o f the water m o l e c u l e s .  However, t h i s r e g i o n o f  t o t a l a b s o r p t i o n i s not so broad so as t o t o t a l l y obscure the appearance o f the i n t e r n a l fundamentals a s s o c i a t e d w i t h fCH)ai  which appears a t 2 8 5 8 cm"  there appears t o be no observable  1  .  As f o r S r ( C H 0 2 ) 2  s p l i t t i n g under v a r i o u s  polarizations. In the 1 4 0 0 - 1 3 0 0  cm"  1  r e g i o n o f the spectrum  (Fig.4-3)  t h e r e appears t o be c o n s i d e r a b l e o v e r l a p p i n g o f the v a r i o u s modes.  However, c o n s i d e r a t i o n o f the r e l a t i v e  p r e d i c t e d by the squared d i r e c t i o n c o s i n e s w i t h the i n f o r m a t i o n obtained  intensities  (Table 13) along  from the p o l a r i z e d s p e c t r a  a l l o w us t o make some f a i r l y c o n c l u s i v e assignments.  Under  X p o l a r i z a t i o n we f i n d the appearance o f two s t r o n g absorpt i o n s o c c u r r i n g a t 1 3 8 3 and 1 3 6 4 cm" . 1  Assuming t h a t the  o r d e r o f the modes a s s o c i a t e d w i t h the f r e e - i o n fundamentals  - 72  TABLE 13  SQUARES OF THE DIRECTION COSINES FOR FORMATE IONS I AND I I o f Sr(CH0 ) .2H 0 2  Symmetry Species of Associated Free Ion FundamentIs a  x  2  2 1^  2 m^  2  0.0055  0.0011  0.9956  b  1  0.5518  0.6482  0.0001  b  ?  0.6455  0.5505  0.0061  2 °i  2  0.1599  0.8559  O.O065  0.7987  0.1576  O.0658  0.0405  0.0294  0.9501  , 2 i 2  a  l  b b  *  2  x  2  ' j  2  The s u b s c r i p t s 1 and 2 r e f e r t o formate ions I and I I respectively.  *  *  -  7^2 and  -  73  f ^ i s not r e v e r s e d - r e f e r e n c e t o Table 1 3  i n d i c a t e s t h a t the a b s o r p t i o n o c c u r r i n g a t 1 3 8 3 cm" a s s o c i a t e d w i t h the f r e e i o n fundamental The  a b s o r p t i o n o c c u r r i n g a t 1 3 6 4 cm"  1  2 '^(tVCH)b^ - i o n I I . /  a l s o appears under Y  p o l a r i z a t i o n along w i t h a shoulder a t 1 3 3 3 cm" ,  - i t would  1  appear t h a t the 1 3 6 4 cm" a b s o r p t i o n s a r i s i n g from  1  is  1  a b s o r p t i o n i s due t o a mixing o f "Z^-  i o n I and  3^2"  i  o  n  1  1  •  Under Z p o l a r i z a t i o n a s t r o n g a b s o r p t i o n appears a t 1 3 5 5 cm" - r e f e r e n c e t o Table 1 3 c l e a r l y i n d i c a t e s As might be expected  of  1  i  o  n  The two  1  1  •  Z^-  due t o  remaining  i n t h i s r e g i o n a t 1 3 9 2 and 1 3 3 7 cm"  appear t o be due t o combination The  a  t h e a b s o r p t i o n a t 1 3 8 3 cm"  i o n I I a l s o appears under Z p o l a r i z a t i o n . a b s o r p t i o n s appearing  ) l ~  1  1  modes.  s p e c t r a contained i n F i g . 4 - 4 show the appearance  -^(fCH)b-2  at 1 0 6 4 cm"  1  - no s p l i t t i n g i s observed.  Unexpectedly no a c t i v i t y was observed polarization.  f o r t h i s mode under X  However, f o r both Y and Z p o l a r i z a t i o n where  a c t i v i t y i s observed  i t i s noted the base l i n e s l o p e s "up"  r e l a t i v e t o the a b s o r p t i o n i n q u e s t i o n w h i l e f o r X p o l a r i z a t i o n the base l i n e s l o p e s "down". b a s e l i n e p o s i t i o n may account The  This difference i n  f o r the observed  results.  s p e c t r a contained i n F i g . 4 - 4 a l s o show the r e g i o n o f the  spectrum where we would expect  t o f i n d the appearance o f the  modes a s s o c i a t e d w i t h the f r e e i o n mode  ^(^OCO)a]_.  However, i t i s found t h a t the s t r o n g l y a b s o r b i n g  .lattice': -  - 74 modes observed  i n t h i s r e g i o n t o t a l l y obscure the appearance '^(o'OCOjai.  of the i n t e r n a l fundamentals a s s o c i a t e d w i t h The r e g i o n o f the spectrum i o n fundamental  2V^(^C0)bi  a s s o c i a t e d w i t h the f r e e  ( F i g . 4-3)  l i k e the other r e g i o n s  where i n t e r n a l fundamentals are observed considerable overlapping.  i s complicated  Under both X and Y  by  polarizations  a v e r y i n t e n s e a b s o r p t i o n occurs at 1590  cm~l.  under Z p o l a r i z a t i o n we f i n d t h a t we now  have an i n t e n s e  a b s o r p t i o n o c c u r r i n g at 1545 shows t h a t we  cm . -1  expect l i t t l e  Reference  However,  t o Table  13  i n t e n s i t y to be a s s o c i a t e d w i t h  ^ under Z p o l a r i z a t i o n .  Hence, the above i n t e n s i t y  c o n s i d e r a t i o n when considered w i t h the r a t h e r l a r g e s h i f t of 45  cm  i n d i c a t e s the 1545  -1  Z^tf^Hjaj-  l a r g e l y due to  absorbing s p e c i e s .  t  cm" n  e  1  a b s o r p t i o n as being  water molecules  Intensity r a t i o s f o r t h i s region-  c o n s i d e r i n g the s t r o n g a b s o r p t i o n s at 1590 g i v e n i n Table 15. t i o n s observed  I f we  and 1545  cm"  are  1  c o n s i d e r the t h r e e s t r o n g absorp-  f o r the r e s p e c t i v e p o l a r i z a t i o n s as being  "Z^^(CH02) and  due only to  being the  2^2 ^2^)  we  can, i n p r i n c i p l e ,  use the experimental i n t e n s i t y r a t i o s to c a l c u l a t e v a l u e s  2 f o r the sums o f the squared d i r e c t i o n c o s i n e s ( i . e . 1^ 0 m  l  0 m  2  0 a n (  *  n  l  +  2 4-  1  2  0 n  2  ' a s s o c i a t e d with symmetry s p e c i e s  a^ f o r water molecules I and I I .  However, when these sums  were c a l c u l a t e d they were not c o n s i s t e n t w i t h the r e q u i r e ment t h a t t h e i r t o t a l sum  should equal two.  T h i s , of course,  - 75 i n d i c a t e s t h a t other components are i n v o l v e d . it  None the l e s s  can be s a i d w i t h a good d e a l o f c e r t a i n t y t h a t the  observed i n t e n s i t y r a t i o s show  ^2^2^  t  0  m  o  s  strongly  t  a c t i v e under Z p o l a r i z a t i o n and i n d i c a t e s t r o n g Y a c t i v i t y . F i n a l l y we c o n s i d e r the r e g i o n o f a b s o r p t i o n a s s o c i a t e d w i t h the 0-H  sketching frequencies.  In discussing t h i s  r e g i o n we can o n l y c o n s i d e r the "dimensions" o f the r e g i o n s of t o t a l absorption.  They are g i v e n below:  (i)  X p o l a r i z a t i o n - 2375, 3100 and 3325  cm"  (ii)  Y p o l a r i z a t i o n - 2925, 3175 and 3425  cm"  ( i i i ) Z p o l a r i z a t i o n - 2375, 3150 and 3425  cm"  In each o f ( i ) ,  1  1  1  ( i i ) and ( i i i ) above the c e n t e r wave number  r e f e r s t o the centre o f the r e g i o n o f t o t a l a b s o r p t i o n , w i t h the two o u t s i d e wave numbers r e f e r r i n g t o the outer extremi t i e s o f the r e s p e c t i v e r e g i o n s o f t o t a l a b s o r p t i o n . assume  I f we  l ^ f ^ O ) t o be most s t r o n g l y a c t i v e under Y and Z  p o l a r i z a t i o n s , then c o n s i d e r a t i o n o f the o u t e r e x t r e m i t i e s o f the r e g i o n s o f t o t a l a b s o r p t i o n tends t o p l a c e - H0  *' (l'0K)a 1  2  1  a t a h i g h e r frequency than  V ^ Q R ) ^ -  The r e s u l t s d i s c u s s e d above are completely  H 0. 2  summarized  i n Table 14. 6-3  The I n t e r n a l Fundamentals o f Sr(CH0p)p.2H?0- I n t e n s i t i e s Even though the p o l a r i z e d s i n g l e c r y s t a l s p e c t r a o f  Sr(CH0 ) .2H 0 o f f e r l i t t l e i n t e n s i t y information of a 2  2  2  TABLE 1 4  THE INTERNAL FUNDAMENTAL MODES OF Sr(CH02)2*2H20 (WAVENUMBERS IN CM"*)  (i)  The Internal Fundamentals - nj_'(C3H02)2 Free Ion * Fundamental  ^'(CHOs) 2858  (^CH)  ai  X,Y,Z  2858  vl Z (SOCO)a /  5  Observed Activity  1  1555  Z  ~1564  X,Y  —  —  1590  ^(^CH)^  ;  X,Y  1612  Z  ~1564  X,Y  1585  X,Y,Z  1064 x,z  1064  *  They and "V'refer to formate ions I and II respectively,  (ii)  The Internal Fundamentals - ^'(HgO) * Free H2O Fundamental  n^'^O)  2^ (?'0H)a  -5150  Y,Z  1545  Z  1  1  ^2(SH0H)ai  vypv&yo\ *  ~ 5150  Observed Activity  —  As noted i n the text 1/-^(2^0H)a^ i s believed to be of highe frequency than ^ ( Z A J H ^ .  TABLE If CALCULATED AND OBSERVED INTENSITY RATIOS - Sr(CH0 )2-SH^ 2  Ratios *  Calc.  Obs.  Calc.  Obs.  0.815  0.947  0.153  0.995  *  1.47  4  1.80  0.803  2.42  0.907  3  Sale.  12.3 0.4o6  Obs.  0.987  0.930  0.426  0.935  0.555 0.411  1.37  1 — The ratios refer to the combined intensities due to formate ions I and II for both ^ (CH0 ) and 5^(CH0 ) . 2  2  Product of Obs. Ratios  2  2 - The ratios refer to the combined intensities due to formate ions I and II for ^%(CH0 ) and water molecules I and II for ^(HgO). 2  3 - The ratios refer to the intensities due to formate ions I and II for J^(CE0 ). 2  4 - The ratios refer to the intensities due to formate ions I and II for >£(CH0 ). 2  - 73 q u a n t i t a t i v e n a t u r e - i t was  p o s s i b l e t o compare observed and  c a l c u l a t e d i n t e n s i t y r a t i o s i n a few c a s e s .  These are  summarized i n Table 15.  6-4  Overtones and Combinations o f I n t e r n a l Sr(CH0?)2.2H?0  Fundamentals-  For Sr(CH02)2»2H 0 we must c o n s i d e r the combinations and 2  overtones o f the i n t e r n a l fundamentals n j / f C I K ^ ) and n ^ ' f l ^ O ) . I n both cases the d i s c u s s i o n o f overtones and  combinations  i s completely e q u i v a l e n t t o t h a t contained i n s e c t i o n From the observed s p e c t r a i t was assignments- these are g i v e n i n T a b l e  6-5  5-4.  p o s s i b l e t o make some 4-1.  Combinations o f I n t e r n a l Fundamentals  and L a t t i c e Modes  Reference t o Table 12 shows t h a t the l a t t i c e  vibrations  are d i s t r i b u t e d i n the f o l l o w i n g manner: (27a, 26b-^, 26b2, 26b-j) I f we  c o n s i d e r the p o s s i b l e combinations o f these l a t t i c e  modes w i t h the i n t e r n a l fundamentals we f i n d by r e f e r i n g t o Table 9 t h a t f o r i n t e r n a l fundamentals o f symmetry s p e c i e s a  >  d  1J 2 d  a n c  *  D  3  are: ( 2 7 a , 2 6 b  the r e s p e c t i v e combination modes p o s s i b l e 1}  26b , 26b3), 2  (27b!, 26a, 2 6 b , 2 6 b ) , 3  2  (27b , 2  26b3, 26a, 26bi) and (27b3, 26b , 2 6 b i , 26a). 2  Remembering t h a t c r y s t a l modes o f symmetry s p e c i e s  a  are not i n f r a r e d a c t i v e the above i n d i c a t e s t h a t f o r each o f  -  79  -  X, I and Z p o l a r i z e d s p e c t r a we would, i n p r i n c i p l e , expect the  s a t e l l i t e s t r u c t u r e o f each o f the 6 i n t e r n a l fundamental  d o u b l e t s - nj/(CH02) and each o f the 3 i n t e r n a l fundamental d o u b l e t s - n-j/fR^O) t o e x h i b i t 210 peaks.  Of these 210 peaks  105 w i l l correspond t o combination modes and the remaining 105 w i l l correspond t o d i f f e r e n c e modes. From the observed s p e c t r a i t was p o s s i b l e t o a s s i g n some o f the l a t t i c e modes. i n the 900-600 cm"  1  a s s o c i a t e d w i t h the  The i n t e n s e a b s o r p t i o n s observed  r e g i o n o f the spectrum appear t o be ^ mode observed i n the spectrum o f i c e  and hence can be a s s i g n e d as l a t t i c e modes o f r o t a t i o n a l origin  ("^(h^O) - see Table 4-1).  Further tentative  assignments o f l a t t i c e modes a t 18 and 110 cm"  1  a r e based on  peak s e p a r a t i o n s between the v a r i o u s i n t e r n a l fundamentals and the modes a s s o c i a t e d w i t h t h e i r s a t e l l i t e  structures.  - 30 CHAPTER V I I  CONCLUSIONS  I t can be seen from t h i s work t h a t the i n f o r m a t i o n obtained  from p o l a r i z e d i n f r a r e d s p e c t r a o f s i n g l e c r y s t a l s  can be an important a i d i n determining c r y s t a l  structures-  t h i s i s p a r t i c u l a r l y t r u e where hydrogen atoms or other l i g h t atoms are i n v o l v e d .  The f a c t o r which most determines  the amount and q u a l i t y o f t h e i n f o r m a t i o n s p e c t r a i s the t h i c k n e s s o f the c r y s t a l s .  obtained  I t would appear  t h a t f o r optimum r e s u l t s - e s p e c i a l l y where s t r o n g l y modes are i n v o l v e d - t h a t the c r y s t a l s l i c e s should about 5-10 A*  thick.  This thickness  from the  absorbing be  can no doubt be reached  as more s o p h i s t i c a t e d g r i n d i n g techniques are developed. T h i s work has shown t h a t the s p e c t r a o f c r y s t a l l i n e materials analysis.  can be e x p l a i n e d  on the b a s i s o f f a c t o r - group  Future i n f r a r e d work w i l l , no doubt i n part be  concerned w i t h attempting t o observe the low frequency l a t t i c e modes.  Raman Spectroscopy a l s o o f f e r s important  possibilities i n this  area.  - 3l BIBLIOGRAPHY  1.  K.B. Harvey, B.A. Morrow and H.F. S h u r v e l l , Can. J . Chem. £1, 1181  (1963).  2.  C.J.H. Schutte and K. B u i j s , Spectrochim A c t a 20, 187 (1964).  3.  J.D. Donaldson, J . F . K n i f t o n and S.D. Ross, Spectrochim Acta 20, 347 (1964).  4.  R. V i e t n e , Rev. Univ Mines 15_, 510 (1959).  5.  A.M. Vergnoux and R. V i e r n e , Comptes Rendus  6.  B.A. Morrow, M.Sc. T h e s i s (U.B.C.), 1962.  7.  T.L. C h a r l t o n , M.Sc. T h e s i s (U.B.C.), 1964.  3.  I . N i t t a , S c i . Papers I n s t . Phys Chem. Research (Tokyo) 2, 151 (1923).  9.  I N i t t a and Y. S a i t o , X-Rays  261 (6), 1236 (1965).  39 (1949).  10. T. Sugawara, M. Kakudo, Y. S a i t o and I . N i t t a , X-Rays 6, 35 (1949). 11. K. O s a k i ,  Ann Rept S c i . Works, F a c . S c i . ,  Osaka U n i v . 6,  13 (1953).  1  12. E. Charney, J.O.S.A. Z^, 930 (1955). 13. E.B. W i l s o n , J.C. D i c i u s and P.C. C r o s s . M o l e c u l a r Y i b r a t i o n s , McGraw-Hill (1955). 14. S. Bhagavantam and T. Venkataryudu, Theory o f Groups and i t s A p p l i c a t i o n t o P h y s i c a l Problems, Andhra U n i v e r s i t y , W a l t a i r (1951). 15. R.S. H a l f o r d , J . Chem Phys. 14, 3 (1946).  

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