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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, University of 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 of CHEMISTRY We accept t h i s thesis as conforming to the required standard September, 1966 UNIVERSITY OF BRITISH COLUMBIA In presenting t h i s thesis i n p a r t i a l f u l f i l m e n t of the requirements for an advanced degree at the University of B r i t i s h Columbiaj I agree that the Library s h a l l make i t f r e e l y aval]able f o r reference and study. I further agree that permission-for extensive copying of t h i s thesis for scholarly purposes may he granted by the Head of my Department or by his representatives. I t i s understood that copying or publication of t h i s thesis for f i n a n c i a l gain s h a l l not be allowed without my written permission. Department of Chemistry The University of B r i t i s h Columbia Vancouver 8, Canada Date October 17th. 1966, - i i - ABSTRACT The infrared absorption spectra of single c r y s t a l s of strontium formate and strontium formate dihydrate have been recorded between 4000 and 500 cm""1. Crysta l s l i c e s cut perpendicular to the c r y s t a l axes were employed; the spectra were recorded using polarized radiation, the e l e c t r i c vector being p a r a l l e l to the d i r e c t i o n defined by the c r y s t a l axis i n question. For Sr(CH02)2 i t was possible to assign 20 of the 36 infrared active i n t e r n a l fundamentals. In addition l a t t i c e modes at: 10, 12, 15, 20, 23, 70, 155, 130 and 200 cnT 1 were infered from combinations with i n t e r n a l fundamentals. For Sr(CH02)2»2H20 i t was possible to observe only 10 of the 36 i n t e r n a l fundamentals associated with the formate ions as the absorbing species. Of the 13 i n t e r n a l fundamentals associated with the water molecules as the absorbing species only one mode could be unambiguously assigned. L a t t i c e modes at: 642, 710, 750, 797, 340, 356 and 372 cm"1 were observed and two addi t i o n a l l a t t i c e modes at 13 and 110 cm""1 were infered from combinations with 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 cosines associated with each of the two c r y s t a l l o g r a p h i c a l l y non- equivalent formate ions contained i n the unit c e l l . - i - ACKNOWLEDGEMENT The author wishes to acknowledge with thanks Dr. K.B. Harvey's assistance i n carrying out t h i s work and i n i n t e r p r e t i n g the experimental r e s u l t s . Thanks are also due to Mr. R.W. Green f o r h e l p f u l discussions r e l a t i n g to experimental technique. Use of the f a c i l i t i e s of the University Computing Centre i s appreciated. - i i i - TABLE OF CONTENTS Page ACKNOWLEDGEMENT ± ABSTRACT i i TABLE OF CONTENTS i i i LIST OF TABLES v LIST OF FIGURES v i i CHAPTER I INTRODUCTION 1-1 Introductory Remarks 1 1-2 The Cryst a l Structure of Sr(CH0 2)2 2 1- 3 The Cr y s t a l Structure of Sr(CH0 2)2.2H 20 2 CHAPTER II EXPERIMENTAL 2^1 Materials 3 2- 2 Growth of Single Crystals 3 2-3 Sample Preparation 10 2- 4 Apparatus 15 CHAPTER I I I RESULTS 3- 1 Spectra of P o l y c r y s t a l l i n e 16 Strontium Formate 3- 2 Single Crystal Spectra of 16 Sr(CH0 2) 2 and Sr(CH0 2)2«2H 20 CHAPTER IV THEORY 4- 1 The Vibrations of Isolated 3$ Polyatomic Molecules 4-2 Selection Rules 41 4-3 S o l i d State Spectra and 43 Crystal Symmetry - i v - 4- 4 Factor Group Analysis of Vibrations i n Crystals CHAPTER V DISCUSSION - PART I 5- 1 V i b r a t i o n a l Analysis f o r Sr(CH0 2)2 5-2 The Internal Fundamentals of Sr(CH0 2) 2- Assignments 5-3 The Internal Fundamentals of Sr(CH02)2 - I n t e n s i t i e s 5-4 Overtones and Combinations of Internal Fundamentals - Sr(CH02)2 5- 5 Combinations of Internal Fundamentals and La t t i c e Modes - Sr(CH0 2)2 CHAPTER VI DISCUSSION - PART II 6- 1 V i b r a t i o n a l Analysis f o r Sr(CH0 2) 2.2H 20 6-2 The Internal Fundamentals of Sr(CH0 2)2« 2 H2° ~ Assignments 6-3 The Internal Fundamentals of Sr(CH0 2) 2.2H 20 - In t e n s i t i e s 6-4 Overtones and Combinations of Internal Fundamentals - Sr(CH0 2) 2.2H 20 6-5 Combinations of Internal Fundamentals and L a t t i c e Modes - Sr(CH0 2) 2.2H 20 CHAPTER VII CONCLUSION - V - LIST OF TABLES Page Table 1-1 C r y s t a l Structure of Sr(CH02)2 4 1-2 Cryst a l Structure of Sr(CH02)2»2H 20 5 2 Vi b r a t i o n a l Assignments f o r Spectra of 21 Po l y c r y s t a l l i n e Strontium Formate 3 V i b r a t i o n a l Assignments f o r Single 27 Cry s t a l Spectra of Sr(CH0 2)2 4-1 V i b r a t i o n a l Assignments f o r Single 3 5 Cry s t a l Spectra of Sr(CH0 2)2«2H 20 4-2 V i b r a t i o n a l Assignments f o r Single 37 Crystal Spectra of Sr(CH0 2)2» 2 H2 0 - Previous Work 5 Summary of Expressions f o r Characters of 46 the Group Operation, R 6 Character Table and Factor - Group 50 Analysis f o r Sr(CH0 2)2 7 Squares of Direction Cosines f o r 53 Formate Ions I and II of Sr(CH0 2)2 8 The Internal Fundamental Modes of 60 Sr(CH0 2) 2 9 Calculated and Observed Intensity 61 Ratios - Sr(CH0 2)2 10 Calculated and Experimental Direction 65 Cosines f o r Formate Ions I and II of Sr(CH0 2)2 11 Symmetry Species of Combinations 66 and Overtones 12 Character Table and Factor - Group 70 Analysis f o r Sr(CH0 2) 2.2H 20 13 Squares of the Direction Cosines f o r 72 Formate Ions I and II of Sr(CH0~)~.2H~0 - v i - The Internal Fundamental Modes of Sr(CH0 2) 2.2H 20 Calculated and Observed Intensity Ratios - Sr(CH0 2) 2.2H 20 - v i i - LIST OF FIGURES Pas;e Figure 1-1 C r y s t a l Structure of Sr(CH02)2 6 1- 2 Crystal Structure of Sr(CH0 2)2«2H 20 7 2- 1 Spectra of P o l y c r y s t a l l i n e Strontium 18 Formate, 4000-500 cm"1 2-2 Spectra of P o l y c r y s t a l l i n e Strontium 19 Formate, 1400-1320 crrr 1 2- 3 Spectra of P o l y c r y s t a l l i n e Strontium 20 Formate, 6*10-730 cm-1 3- 1 Polarized Spectra of Sr(CH0 2)2i 2 2 3300-2600 cm-1 3-2 Polarized Spectra of Sr(CH0 2)o, 23 2000-1200 cm-1 3-3 Polarized Spectra of Sr(CH0 2) 2, 24 1120-1040 cm-1 3-4 Polarized Spectra of Sr(CH0 2) 2, 25 310-7^0 cm-1 26 3- 5 Polarized Spectra of Sr(CH0 2)2, 310-730 cm"1 4- 1 Polarized Spectra of Sr(CH0 2) 2.2H 20, 31 3900-2500 cm-1 4-2 Polarized Spectra of Sr(CH0 2) 2.2H 20, 32 2500-1900 cm-1 4-3 Polarized Spectra of Sr(CH0 2) 2.2H 20, 33 2000-1200 cnT 1 4-4 Polarized Spectra of Sr(CH0 ?) ?.2H ?0, 34 1100-500 cm"1 - 1 - CHAPTER I INTRODUCTION 1-1 Introductory Remarks The v i b r a t i o n a l spectra of Sr(CH0 2) 2 and Sr(CH0 2) 2.2H 20 have been the subject of investigation of previous workers (1-5). Only i n the study of Sr(CH0 2) 2.2H 20 (4,5) were single c r y s t a l s and polarized radiation used. In t h i s work spectra of p o l y c r y s t a l l i n e strontium formate and strontium formate dj were studied as well as single c r y s t a l spectra of both Sr(CH0 2) 2 and Sr(CH0 2) 2.2H 20. The single c r y s t a l spectra were studied using polarized infrared r a d i a t i o n as a continuation of the study of i n  organic formates i n i t i a t e d i n t h i s laboratory by B.A. Morrow (6) and subsequently continued by T.L. Charlton (7). As w i l l be discussed l a t e r i t i s necessary when considering the spectra of single c r y s t a l s to take account of the orientation of the absorbing species with respect to the c r y s t a l axes. This orientation of the absorbing species with respect to the c r y s t a l axes i s d i r e c t l y related to the i n t e n s i t y of the i n t e r n a l fundamental modes of v i b r a t i o n associated with the absorbing species. Consequently information obtained from polarized spectra of single c r y s t a l s i s not only an aid i n making v i b r a t i o n a l assignments but can also a i d i n the determination 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 involved. - 2 - 1-2 The Cryst a l Structure of SrfCHC^)? The c r y s t a l structure of Sr(CH0 2) 2 i s described by -v. N i t t a and his co-workers (8-101) as being orthorhombic and belonging to the space group P2 12^2^(D^). The c e l l parameters and the co-ordinates of the generating atomic positions are l i s t e d i n Table 1-1 ( i ) . The hydrogen atom positions were calculated by the author on the assumption of a value of 1.09 A 0 f o r the C-H bond length. The formate ion parameters were also calculated and are given i n Table 1-1 ( i i ) . The c r y s t a l structure of Sr(CH0 2) 2 can be v i s u a l i z e d from the projection on to the (001) plane given i n F i g . 1-1. We see that the structure maybe described as consisting of complex chains along the screw p a r a l l e l to the C axis; the chains being linked l a t e r a l l y through the oxygen atoms of the formate ions. 1-3 The Cryst a l Structure of Sr(CH0o)o.2Ho0 A preliminary X-ray analysis of Sr(CH0 2) 2.2H 20 was reported by Ni t t a i n 1928 (&) with subsequent work being done by Osaki {&). I t was found that the dihydrate l i k e anhydrous strontium formate belongs to the space group P212^2-^ (D 2). The c e l l parameters and the co o r d i n a t e s of the generating atomic positions as given by Osaki are l i s t e d i n Table 1-2 ( i ) . Again the hydrogen atom positions 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 ) . Fig. 1-2 shows a projection of the structure onto the (001) plane. The structure i s similar to that of SrfCHOg^ and also maybe described as consisting of complex chains along the screw axis parallel to the C axis, with the chains being linked laterally through the water molecules and the oxygens of the formate ions. TABLE 1 - 1 - 4 - CRYSTAL STRUCTURE OP Sr(CH0 2)2 Space Group j P 2 1 2 i 2 i (D|) a = 6.874 A 0 b = 8.748 A° c - 7-267 A 0 ( i ) Generating Positions with Origin Halfway Between Three Pairs of Non Intersecting Screw Axest 4 S r 2 + Ions at (0.2500, 0.0915, 0.0000) FORMATE ION I 4 0 atoms at (0.005, 0.260, 0.420) 4 H atoms at (0.046, 0.298, O.558) * 4 0 atoms at (0.105, 0.154, O.558) 4 0' atoms at (-0.154, 0.550, O.550) FORMATE ION I I 4 C atoms at (0.118, 0.505,-0.906) 4 H atoms at (0.255, 0.501, 0.851) * 4 0 atoms at (-0.018, 0.255, 0.828) 4 0" atoms at (0.120, 0.570, 1.057) ( i i ) Formate Ion Parameters: FORMATE ION I r(C-O) = 1.24A° r(C-0') = 1.24A0 r(C-H) a 1.09A0 Z.(d-C-0') - 150° FORMATE ION I I r(C-O) = 1.24A0 r(C-O') = 1.24A0 r(C-H) » 1.09A0 RO-C-O') - 129° * Assuming r(C-H) - 1.09 A° as Indicated i n ( i i ) I i 1 - 5 - TABLE 1 - 2 CRYSTAL STRUCTURE OP Sr(CH0 2) 2.2H 20 Space Group: P212J2! (D 2) a s 7.352 A° b = 12.040 A 0 c = 7.144 A 0 ( i ) Generating Positions with Origin Halfway Between Three Pairs Non Intersecting Screw Axes: 4 H 2 0j Molecules at ( 0 . 4 l l , 0.092, -0.469) 4 HgOj Molecules at (-0.025, 0.221, 0.24l) 4 S r 2 + Ions at (0.2500, 0.0715, 0.1970) FORMATE ION I 4 C atoms at 4 H atoms at 4 0 atoms at 4 0' atoms at 4 C atoms at 4 H atoms at 4 0 atoms at 4 0' atoms at FORMATE ION I I (-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) ( i i ) Formate Ion Parameters: FORMATE ION I r(C-O) - 1.21A° r(O-O') =:.1.20A° r(O-H) = 1.09A 0 /.(O-C-01) - 125° FORMATE ION I I r(C-O) = 1.23A° r(C-O') = 1.23A 0 r(C-K);=r1.09A° L(O-C-O') =128° * Assuming r(C-H) . 1.09 A° as Indicated i n ( i i ) - 6 - FIG M CRYSTAL STRUCTURE OF Sr(CH0 2) 2 (i) Proj ec t i on of Structure on(OOl) (ii)Symmetry Elements of the Unit Cell 1 4 L O I r j \ > / 4 - o f j. • 4 1 ' 4 - 7 - FIG 1-2 CRYSTAL STRUCTURE OF S r(C H 0 2 ) 2 2 H 2 O (i) Pro j ec t i on of Structure on(OOl) (ii) Symmetry Elements of the Unit Cell o 1 • i 1 i \ 4 ! 4 -o '< 1 ; - g - CHAPTER II EXPERIMENTAL 2-1 Materials The strontium formate used was prepared by n e u t r a l i z a t i o n of formic acid with strontium carbonate. The product was f i l t e r e d and r e c r y s t a l l i z e d from solu t i o n . Both the strontium carbonate and formic acid were of reagent grade and were obtained from the B r i t i s h Drug Houses Ltd. The strontium formate d, was prepared i n a similar manner using formic acid- dj. 2-2 Growth of Single Crystals The c r y s t a l s were grown from aqueous solution by slow evaporation at constant temperature; the hydrated c r y s t a l s being grown at 60°C and the anhydrous at 6*5°C. Crystal growth was carried out i n l i t e r vacuum f l a s k s ; the following procedure was followed. I n i t i a l l y a l i t e r of nearly saturated solution was prepared at the growing temperature, care being taken that there were no impurities in.the solution. The solution was then maintained at the growing temperature and allowed to evaporate slowly- slow evaporation was achieved by placing a cotton 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 - that the f i r s t sign of seed cr y s t a l s forming on the bottom of the f l a s k could be detected. When t h i s occurred one of two procedures was followed depending on whether a harvest of seed c r y s t a l s was desired or whether i t was desired to star t the growth of a large single c r y s t a l . I f seeds were desired the slow evaporation was continued u n t i l they had reached a size of about 3-5 mm. i n length. They were then harvested. I f i t was desired to grow a single c r y s t a l a seed c r y s t a l was placed i n the saturated solution suspended by a t h i n nylon filament. The free end of the nylon filament was secured on the arm projecting from the vacuum f l a s k . This process was car r i e d out i n minimumal time so that as l i t t l e vapour as possible 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 place (usually a f t e r a period of about 3-4 weeks) the c r y s t a l was removed from the saturated solution. However, when removing the c r y s t a l s from the saturated solution i t was found that the thermal s t r a i n imposed by the sudden change i n temperature was s u f f i c i e n t to severely crack the c r y s t a l . In order to circumvent t h i s problem Nujol at the temperature of the saturated solution was placed on top of the saturated solution. The c r y s t a l was then drawn up into the Nujol layer and the temperature lowered to room temperature over a period of - 10 - about 3 hours. The c r y s t a l s so obtained were l a r g e l y free from cracks and i n t e r n a l flaws. Both the hydrated and anhydrous cr y s t a l s when grown i n the above manner were of sphenoidal habit, 10 to 15 mm. wide, 20 to 30 mm. long and 7 to 10 mm. thick. The p r i n c i p a l face of both c r y s t a l s was the (010) face elongated i n the C d i r e c t i o n . 2-3 Sample Preparation The most d i f f i c u l t part of the experimental work was preparing spectroscopically t h i n c r y s t a l s l i c e s ( i . e . 20-30n) from the single c r y s t a l . The following technique was developed during the course of the experimental work. The single c r y s t a l was f i r s t mounted with epoxy r e s i n (Aradite Adhesive, Ciba Ltd.), on a s p e c i a l l y designed support, care being taken that the desired c r y s t a l axis was mounted perpendicular to the base of 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 cutting device so that the desired c r y s t a l axis was per pendicular to the cutting plane. The cutting plane consists of a 3 by 6 inch table with r o l l e r s at e i t h e r end. In the centre of t h i s table there i s a l | inch c i r c u l a r opening below which i s the c r y s t a l support. Provision i s made to elevate, rotate and t i l t t h i s - 11 - support so that the c r y s t a l maybe appropriately positioned with respect to the cutting plane. Once the c r y s t a l was appropriately mounted i n the c r y s t a l cutter, cutting began. In order to cut the c r y s t a l a piece of No. 40 cotton thread was held against the c r y s t a l and pulled back and f o r t h across the r o l l e r s at eithe r end of the cutting table. A carborundum-water s l u r r y was placed on the cutting table to act both as a lubricant and as an aid to the cutting process. Using t h i s method i t was possible to cut a cross section of 600 mm. i n about one-half hour. After the c r y s t a l was cut the face of the portion of the c r y s t a l remaining on the c r y s t a l support was polished. This polishing process was carried out i n two steps. The f i r s t step made use of a polishing d i s c . The surface of t h i s disc was covered with No. 36O-A carborundum paper and i t was mounted so that i t rotated h o r i z o n t a l l y at about 3000 R.P.M. The c r y s t a l face to be polished was held against the r o t a t i n g disc; care being taken to rotate the c r y s t a l at evenly spaced i n t e r v a l s so as to ensure as f l a t a surface as possible. Once a f l a t uniformly smooth surface had been obtained the second step i n the polishing process was carried out. This process, which brought the c r y s t a l face to an extremely high polish, consisted of rubbing the c r y s t a l face on a piece of velvet lap stretched over a f l a t glass plate; - 12 - dampened jewellers rouge being used as the polishing compound. After the crystal face had been satisfactorily polished the crystal face was coated with silver paint (Silver Print; G.C. Electronics Co.) except for an area of 3 x 11 mm., this area being the size of the s l i t on the sample holders. When the silver paint had dried the whole of the crystal face was covered with a coat of plastic cement (Radio Service Cement; General Cement Mfg. Co.). After the plastic cement had dried epoxy resin was used to glue a piece of glass plate measuring £ x 1| x l i inches to the crystal face. Care was taken that no air bubbles were trapped under the small glass plate. The purpose of the epoxy was to provide a firm backing for the crystal which contained no glue-free pockets. Such a backing was crucial once the f i n a l stages of polishing were reached. After,the epoxy had been allowed to set the crystal was so positioned in the crystal cutter that a slice about 0.5 mm. thick could be cut. This slice which was mounted on the small;glass plate was then ground on the polishing disc i n the manner outlined previously. Where the crystal was coated with silver paint i t was possible to measure the thickness of the crystal directly with a Zeiss Light Section Microscope as the polishing process progressed. It should be noted that the purpose of the plastic cement as w i l l be mentioned later was to allow for the action of i - 13 - acetone to free the c r y s t a l s l i c e from the glass plate once the polishing process was completed. When the c r y s t a l s l i c e reached a thickness of about 50 ja the 6 cm. polishing disc was replaced by a 7 mm. disc and the polishing process continued u n t i l a thickness of 35-40 ja had been reached. The f i n a l stage of polishing was carried out by replacing the carborundum surface on the small disc by a chamois surface well impregnated with jewellers rouge- nujol being used as a lub r i c a n t . I t was found that the c r y s t a l s l i c e showed no tendency to crack or chip during the polishing process. After the c r y s t a l s l i c e had been polished to the desired thickness (about 25M) the glass plate supporting the c r y s t a l was placed i n a P e t r i dish and covered with a bath of anhydrous acetone. The P e t r i dish was then l e f t i n a dessicator f o r about two hours which was s u f f i c i e n t time f o r the acetone to dissolve the p l a s t i c cement and enable the c r y s t a l s l i c e to f l o a t free. The next step i n the sample preparation was t r a n s f e r r i n g the c r y s t a l s l i c e to the sample holder. (The sample holder was simply a brass disc designed to f i t the keys on the spectrometer mounting so that the sample could be placed as close as possible to the entrance s l i t ) . In order to transfer the c r y s t a l s l i c e to the sample holder, the sample holder was placed i n the acetone bath and a fi n e hair brush - u - was used to gently position the c r y s t a l s l i c e over the 3 x 11 mm. s l i t i n the sample holder. The s i l v e r paint which s t i l l adhered to the c r y s t a l s l i c e could be used as a convenient guide i n aligning the c r y s t a l and the s l i t i n the sample holder. Once the c r y s t a l had been co r r e c t l y positioned on the sample holder, the acetone was c a r e f u l l y removed from the Pet r i dish. F i n a l l y the c r y s t a l s l i c e was glued sparingly at the edges to the sample holder. P l a s t i c cement was used f o r t h i s purpose. Now that the c r y s t a l was mounted a f i n a l measurement was made of the thickness of the c r y s t a l using the Zeiss Light Section Microscope. The thickness of the cryst a l s used i n t h i s work were found to be of the order of 25/<W. In most cases i t was found that the surfaces of the c r y s t a l were not planar ( i . e . , over the 11 mm.'length of the crystal' exposed to the sample beam the c r y s t a l s l i c e usually tapered from about 30 to 20M) . In order to check the r e l a t i v e o rientation of the cr y s t a l axes a Zeiss Pol a r i z i n g Microscope was used. Observation of interference figures also made i t possible to confirm that the crys t a l s were ground to one or two degrees of the perpendicular. - 15 - 2-4 A p p a r a t u s The s p e c t r a were r e c o r d e d i n t h e r e g i o n o f 4000 t o 500 c m " u s i n g a P e r k i n E l m e r 421 s p e c t r o m e t e r w i t h two d u a l g r a t i n g i n t e r c h a n g e s , t h e e r r o r o f measurement b e i n g e s t i m a t e d as t 2 cm"-1- 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 , c o n s i s t e d o f two t h r e e - s h e e t s t a c k s o f 0.5 mm. s i l v e r c h l o r i d e p l a t e s mounted i n t h e f o r m o f a V (12) t o p r e v e n t d i s p l a c e m e n t o f t h e s p e c t r o m e t e r beam. M e a s u r e m e n t s i n t h e 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 p r i s m i n d i c a t e t h a t l e s s t h a n 5$ o f t h e 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 p a s s e d . M e a s u r e m e n t s o f t h e c o n v e r g e n c e o f t h e sample beam showed t h a t l e s s t h a n Ifo of t h e 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 c o n v e r g e n c e . - 16 - CHAPTER III RESULTS This Chapter contains reproductions of spectra obtained during the course of the experimental work. For convenience they are divided into three groups; spectra of p o l y c r y s t a l l i n e strontium formate; single c r y s t a l spectra of Sr(CH0 2) and single c r y s t a l spectra of Sr(CHC"2)2«2H2' The Chapter also contains Tables giving v i b r a t i o n a l assignments of the respective groups of spectra. Discussion of the basis for the assignments i s l e f t u n t i l Chapters Y and VI. 3-1 Spectra of P o l y c r y s t a l l i n e Strontium Formate The samples used to obtain the spectra i n F i g . 2 were obtained using the t h i n f i l m technique which consists of mechanically depositing a thi n f i l m of the sample on an appropriate support. In t h i s work KBr windows were used. V i b r a t i o n a l assignments along with the res u l t s of previous workers (1-3) are given i n Table 2. 3-2 Single Crystal Spectra of Sr(CH0 2)2 and S r ( C H O o ) 2 » 2 H 2 ° The samples used to obtain the spectra i n F i g . 3 and Fi g . 4 were obtained using the techniques outlined i n section 2-3; as already indicated the samples were approx imately 25A thick. The v i b r a t i o n a l assignments f o r the polarized single c r y s t a l spectra of Sr(CH0 2)2 and - 1 7 - Sr(GH0 2)2» 2H20 are given i n Tables 3 and 4-1 respectively. The r e s u l t s f o r single c r y s t a l s of Sr(CH02)2« 2H20 obtained by Vierne (4,5) using 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; the assignments are h i s . I t should be noted that f o r the polarized single c r y s t a l spectra the reference to p o l a r i z a t i o n p a r a l l e l (11) to a certain crystallographic axis r e f e r s to the e l e c t r i c vector being p a r a l l e l to the d i r e c t i o n defined by the c r y s t a l axis. In the tables and i n subsequent discussion v i b r a t i o n a l modes w i l l be referred to as X(a), Y(c) or Z(c) active; a, b and c re f e r i n g to the c r y s t a l axis to which the e l e c t r i c vector i s p a r a l l e l . For the polarized spectra of Sr(CH0 2)2 i n "the 310-730 cm"-1- region (Fig. 3-4 and 3-5) the c r y s t a l face i s noted on the spectra. For the remainder of the polarized spectra the observed spectra did not appear to be dependent upon the c r y s t a l face. FIG 2-1 SPECTRA OF POLYCRYSTALLINE STRONTIUM FORMATE (i) Sr(CHQ2)2 4000-500 cm-' w 8 0 - ~ 6 0 E M c 4 0 D 2 0 J 1 I I I I L J I I L I I ' I I (ii) Sr(CD0 2) 2 4000-500 cm- 0 £ 8 0 D . t 6 0 E M c 4 0 - 2 0 - IHI i t I * I i ! I I I I I I I I I 1 I I I I I L J I I I I I 1 I L 3500 3000 2500 2000 Frequency cm'1 1500 1000 - 19 - FIG 2-2 SPECTRA OF POLYCRYSTALLINE STRONTIUM FORMATE (i) Sr(CH02)2 1400-1320 em- 90H * 80H ° 70 6 0 H i- 50H 4 0 (30H (ii) Sr(CD02)2 1400-1320 cm- 90H 2 H G - 7 0 E v, 6 0 i c D 50-1 4 0 - 3 0 - 1400 1360 1320 Frequency cm"' - 20 - FIG 2-3 SPECTRA OF POL YCR YSTAL LIN E STRONTIUM FORMAT E (i) Sr(CH02)2 810-730 em' 90H * 80H ° 70H I 6<H c D ». 50 40- 30- (ii) Sr(CD02)2 810-730 cm-' 90 Z 80 c D - 70-1 w 60-| c I 50H 40- 30- 1 1 810 770 730 Frequency cm*1 TABLE 2 - 21 - VIBRATIONAL ASSIGNMENTS FOR SPECTRA OF POLYCRYSTALLINE STRONTIUM FORMATE (WAVENUMBERS IN. CM"1) Harvey Schutte Donaldson Sr(CH02)2 Sr(CD02)2 Mode et a l and Buijs et a l This Work This Work 763 765 763 763 755 Z / 5 ( 6 0 C O ) a i 780 781 781 779.5 772 784 785 786 783-5 776 -fy 1070 */6(/>CH)b2 1082 IO85 1087 1084 919 1350 1351 1349 1360 1359.5 ^ 2 ( ^ C 0)ai 1362 1364 1362.5 1340 1369 1374 1374 1368 ^ / 5(^CH)b 1 1581 1397 1399 1393.5 1013 1387.5 1401 1404 1399 1039 Z/^COyb! 1580 1572 1572 1570 1 562 1590 . 1593 1593 1653 1651 I65O 2720 2720 2775 2775 2872 2849 2874 . 2872 2160 ^ / 1(^CH)a 1 2183 2925 2925 0.(H - 24 - FIG 3-3 POLARIZED SPECTRA OF Sr(CH0 2) 2 1120-1040 cm1 o.o- a> w c 0 . 2 D ° 0.4-1 < 0 . 6 1 . 0 - oo - Polarized II to b axis 1120 1080 1040 Frequency cm -' - 25 - FIG 3-4 POLARIZED SPECTRA OF Sr(CH0 2) 2 810-730 cm*' o.oH u c 0 . 2 -o J 2 ° 0 . 4 - < 0 . 6 - 1.0- oo • Polarized II to b axis ab face 0.0 i 0 . 2 H a> u C o ° 0 . 4 - < 0 . 6 1.0- oo • Polarized II to c axis ac face 4 - 810 770 730 Frequency cm'1 - 26 - FIG 3-5 POLARIZED SPECTRA OF Sr(CH0 2) 2 810-730 em-' 0 . 0 H r\f~ 0) u c 0 .2 - o I 0.4" Jl < 0 .6H Polarized II to b axis be face 1 . 0 - oo • TABLE 3 - 27 - VIBRATIONAL ASSIGNMENTS FOR SINGLE CRYSTAL SPECTRA OF Sr(CH02)2 (WAVENUMBERS IN CM"1) Assignments X Y Z Active Modes Active Modes Active Modes 748 756 763 766 775 779.5 786 787 (sh) 1067 ^ 3 - 15 748 ^ 3 - 23 756 ^ 3 - 1 2 761 ^ 3 2/3' 766 ^ 3 + 1 2 775 783.5 ^ 3 + 23 6 1070 K 1084 6 1363 2 ^ ' + 10 1084 1070 1085 1360 1359 1374 1 - 23 - TABLE 3 cont'd. Assignment* X Y Z Active Modes Active Modes Active Modes - 10 1383 ^ 5 1393 1393 1399 1399 + 10 H03 Vk , 1580 1580 - 1580 ^ + 70 ' 1650 Vk + 155 1735 (sh) 1735 (sh) + 180 1760 (sh) + 200 1780(sh) V2 + ^ 3 2130 ^ / 2'+^ / 2152 2 ^ + ^ 5 2165 ! 2165 2165 V^^Vh 2334 2334 2334 2^2+>6 2434 2434 - 2434 £-2 + ^ ' 2458 2458 - 29 - TABLE 3 cont'd. Assignment* X Y Z Active Modes Active Modes Active Modes 2V2 2702 2702 21^ 2721 2721 vz + ^ 5 2735 ^'+ ^ ' 2753 zv5 2760 2>£' 2775 2775 2 ^ - 20 2852 Z ' i , 2 ^ ' 2872 J 2872 2872 -V2 + 2925 2925 2925 2944 (sh) 2944 (sh) ^4' 2957 2957 (eh) ^4 + ^ 5 2975 2988 Z^'+Z^' 2998 (sh)" 2998 (sh) ZV^ 3128 3128 3143 (sh) 3143 (sh) 3192 -Vx + V3 3631 3631 ^ V ^ ' 3648 * The 7S and ^  r e f e r respectively to formate ions I and II. - 31 - FIG 4-1 POLARIZED SPECTRA OF Sr (C H 02)2-2H20 3900-2500 cm'1 i I I I I I l I I I I I 3700 3500 3300 3100 2900 2700 Frequency cm*1 i - 32 - FIG 4-2 . POLARIZED SPECTRA OF S r(C H 02)2-2H20 2500-1900 cm o.o- u c 0.2- Polarized II \ / JI to a axis \ / I 0.4- JI • < 0.6- i.o- i i i i oo - , 1 , 1 , 1 , 1 o.o- c 0.2- n Polarized II \ / w J3 la to b axis N w - ~ ^ > / S 0-4- JI < 0.6- 1.0- i i I l oo - i 1 i 1 i 1 i 1 i o.o- V u c 0.2- Polarized II \ / D JQ to c axis / 2 0.4- Jl < 0.6- 1-0- 1 t 1 1 oo - • 1 . 1 , 1 . 1 , 2500 2300 2100 1900 Frequency cm*1 - 33 - FIG 4-3 POLARIZED SPECTRA OF S r (C H02)2-2H20 2000-1200 cm-' TABLE 4 - 1 - 35 - VIBRATIONAL ASSIGNMENTS FOR SINGLE CRYSTAL SPECTRA OF Sr(CH02)2.2H20 (WAVENUMBERS IN CM-1) Assignment* X Y Z Active Modes Active Modes Active Modes 7^(H 20) 1 642 642 642 7/R(H20)2 710 710 710 ^R ( H2 0 )3 7 5 0 ( s h> 7 5 0 7 5 3 <sh> ^ R ( H 2 0 ) 4 797 (sh) 797 (sh) ^ ( H 2 0 ) 5 840 838 (sh) Z i ( H 2 0 ) 6 856 ^ R ( H 2 0 ) ? 872 872 , 1064 1064 2^R(H20); 1225 1255 1255 ^ - 18 1337 1337 1337 ^ 1355 ^ 2 * ^ 5 1 3 6 4 1 3 6 4 l/J 1383 1383 (sh) 1383 >5 + 18 1392 I 1392 1392 - 36 - TABLE 4-1 cont'd. Assignment* X Y Z Active Modes Active Modes Active Modes Z£ - 110 1476 (sh) 1476 (sh) 1476 (sh) V 2(H 20) ^ !545 Vh 1590 1590 5^' 1612 1^ + 110 1700 (sh) Z-2(H20)-»-7^(H20)1 2170 (sh) 2170 2170 ^(H 20)4.^ R(H 20) 2 2250 2250 2250 (sh) ZV2 2718 2718 2Z^ 2740 2740 2740 22^' 2763 y-l 2 8 5 8 2 85S 2858 ^l(H20),Z^3(H20) 3150 3150 3150 * The V and V'refer respectively to formate ions I and I I , - 37 - TABLE 4-2- VIBRATIONAL ASSIGNMENTS FOR SINGLE CRYSTAL SPECTRA OF Sr(CH02)2.2H20 - PREVIOUS WORK*(WAVENUMBERS IN CM-1) • X . Y Z Assignment Active Modes Active Modes Active Modes 662 662 662 ^ 5 714 714 714 ^ 5 . 757 757 865 855 ^2 1570 1567 1566 ^ 4 1577 1578 ^ 4 1587.5 1587.5 ^ 5 1614 ^ 5 1605 * Vierne et al. - 33 - CHAPTER IV THEORY Sections 1 and 2 of t h i s Chapter b r i e f l y discuss the vibrations of a poly atomic system and the associated selection rules, and are used as an aid i n introducing the more complex theory of s o l i d state spectra contained i n sections 3 and 4« 4-1 The Vibrations of Isolated Polyatomic Molecules In order to study the motions of an i s o l a t e d n-atomic system, a set of 3n coordinates i s required to describe i t s ' configuration. Of these 3n coordinates, three describe the t r a n s l a t i o n a l motion and three more describe the r o t a t  i o n a l motion of the system, leaving 3n-6 coordinates to describe the systems' v i b r a t i o n a l degrees of freedom. Wilson, Decius and Cross (13) discuss a general method whereby the equations of motion may be written i n terms of a chosen coordinate system. The set of equations thus derived y i e l d s a series of solutions corresponding to the normal modes of v i b r a t i o n of the system. The 3n x 3n secular determinant which must be solved i n order to determine the normal frequences can often be s i m p l i f i e d . This s i m p l i f i c a t i o n arises from the fact that the system under invest i g a t i o n usually possesses some form of symmetry. I f , i n a molecule, a symmetry operation i s - 39 - c a r r i e d out which transforms the molecule into an equivalent position, the k i n e t i c and potential energies w i l l remain unchanged. The set of symmetry operations that a molecule possesses which carry i t into equivalent positions i s known as a group. Each symmetry operation associated with the group maybe represented a n a l y t i c a l l y by a l i n e a r transformation connecting the old coordinates with coordinates of the molecule i n i t s new po s i t i o n . The set of l i n e a r transform ations so obtained i s said to be a representation of the group of symmetry operations; while the coordinates, i n terms of which the transformation are written are said to form a basis of the representation. I t i s usually possible, by choosing a suitable set of coordinates to reduce the 3n x 3 n transformation matrices to a comparatively simple form; i n eff e c t separating these coordinates into sets which do not mix with each other i n any of the transformations. When a coordinate system has been found such that i t i s impossible to break the coordinates down into any smaller non-mixing sets, the representation f o r which these coordinates form a basis i s said to be completely reduced. When i t i s possible to do t h i s , the o r i g i n a l representation i s said to be reducible. The equations involving the members of any one non-mixing set can be considered by themselves as making up transformations - 40 - which form a representation of the group. Such a represent ation i s i r r e d u c i b l e and i t i s seen that a completely reduced representation i s made up of a number of i r r e d u c i b l e representations. I t i s usually possible to choose several sets of coordinates to form a basis f o r the representations, but i n each case the res u l t s would be the same. Any two represent ations, are said to be equivalent when they d i f f e r only i n the choice of the basis coordinates. The fundamental, theorem concerning i r r e d u c i b l e represent ations states that f o r each point group there are only a d e f i n i t e number of non-equivalent i r r e d u c i b l e representations possible. I t i s possible to show that the number of times an ir r e d u c i b l e representation appears i n a reduced representation i s Where h i s the order of the group (equal to the number of character of the i th ir r e d u c i b l e representation of the operation R . The sum i s taken over a l l the operations of the group. The character i s defined as the sum of the diagonal elements of the transformation matrix, the characters of equivalent representations being i d e n t i c a l . These (1) symmetry operations contained i n the group), X g i s the character of the reducible representation and i s the - 41 - quantities on the ri g h t hand side of {1)> are e a s i l y deter mined using a simple set of ru l e s . Associated with each non-mixing set of normal coordinates i s a set of normal modes of vi b r a t i o n , the number of normal modes being equal to the number of normal coordinates i n the set. Since each normal coordinate transforms according to one of the i r r e d u c i b l e representations of the group, we can use (1) to determine the number of normal modes of vi b r a t i o n belonging to each i r r e d u c i b l e representation. 4-2 Selection Rules Group theory maybe used to derive the selection rules 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 . For a fund amental t r a n s i t i o n to occur by absorption of infrared radiation i t i s necessary that one or more of the i n t e g r a l s : h i M t Y-jdr, Y; Mr, J V ^ H i d T have a non zero value. Here, ^ i s the v i b r a t i o n a l ground state, *\Ay i s the excited state and A*.^ , y^Ly , and XA. ^  are the components of the e l e c t r i c dipole moment operator. I t maybe determined whether the above in t e g r a l s vanish i f the symmetry properties of , Yy , ^  , ^ and are known. Since these are d e f i n i t e i n t e g r a l s over the whole configuration space of the molecule, they should be - 42 - unchanged by a symmetry operation R, i n as much as such an operation merely produces a transformation of coordinates. That i s , either 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 of the species V,* , //>- and V j must contain the t o t a l l y symmetric species. Since a l l wave functions for normal vibrations i n t h e i r ground states ( ) are bases f o r the t o t a l l y symmetric representation of the symmetry species 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 (from the ground state to the f i r s t excited state) w i l l be symmetric of the dipole moment operator and the f i r s t excited state belong to the same species ( i . e . the dir e c t product of a represent ation with i t s e l f i s symmetric). I t can be shown (10) that the components of the dipole moment operator transform i n the same manner as the t r a n s l a t i o n a l coordinates, T x , T y and T 2 . Thus a normal mode of v i b r a t i o n w i l l be i n f r a r e d active i f Vj belongs to the same symmetry species as one of the t r a n s l a t i o n a l coordinates. Similar symmetry arguments may be applied to determine the a c t i v i t y of overtone and combination absorption. I t should be noted that the above discussion considers dipole selection rules only- other interactions are assumed n e g l i g i b l e . - 43 - 4-3 S o l i d State Spectra and Crystal Symmetry The discussion of the vibrations of polyatomic molecules i n 4-1 pertained to i s o l a t e d molecules. In c r y s t a l s where molecules are i n close proximity to one another i t i s necessary to consider the nature of the intermolecular interactions when seeking to determine se l e c t i o n rules f o r o p t i c a l t r a n s i t i o n s . Procedures f o r determining these selection r u l e s , have been devised by Bhagavantam and Venkatarayudu (14) and also by Halford (15). In the f i r s t of these procedures the motions of the crystallographic unit c e l l are considered whereas i n that of Halford attention i s focused upon the motions of i n d i v i d u a l molecules. I t i s the work by Bhagavantam and Venkatarayudu that s h a l l be referred to most. However, before proceeding i t i s convenient to b r i e f l y consider the r e l a t i o n of various groups to the description of 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 of symmetry operations including trans l a t i o n s , proper and improper rotations and combinations of these. There are a limited number of ways of combining such operations to form the 230 space groups. The symmetry of a c r y s t a l maybe described by assigning i t to the space group which contains as i t s elements the symmetry operations associated with the c r y s t a l . I t should be noted that c r y s t a l s - 44 - on the basis of t h e i r external symmetry can be d i s t r i b u t e d among 32 c r y s t a l classes, each class being i d e n t i f i e d with a c o l l e c t i o n of symmetry elements and an unique point group of operations concerned with them. Each point group generates a c h a r a c t e r i s t i c number of space groups which, as indicated above, are descriptive 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 that any space group may be regarded as the product of an invariant subgroup, known as a t r a n s l a t i o n group, and a factor group. The t r a n s l a t i o n group as i t s name suggests consists of the elements of the space group corresponding to pure t r a n s l a t i o n s . As already indicated the cosets of the t r a n s l a t i o n group i n the space group form what i s known as a factor group. The factor groups are always isomorphous with one of the 32 crystallographic point groups, although some of them may involve cosets containing other than purely point operations combined with l a t t i c e translations ( i . e . screw r o t a t i o n or glide r e f l e c t i o n . ) The l a s t group with which we w i l l be concerned i s the s i t e group. A s i t e i s defined as a point which i s l e f t invariant by certain operations of the space group and i s equivalent to 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 spec i a l position. These operations may be shown to form a group which i s known as a s i t e group. Every point 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 associated with at lea s t the t r i v i a l s i t e group C^. A s i t e group i s necessarily isomorphous with some subgroup of the factor group and, of course, involves only point symmetry operations since no gli d e r e f l e c t i o n or screw rotation can leave any point inv a r i a n t . The two procedures previously mentioned f o r determining 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 precisely described by s t a t i n g the type of group used i n the analysis of the motion; i . e . Bhagavantam and Venkatarayudu analyse the motion of the unit c e l l under the fa c t o r group and Halford analyses the molecular unit i n the c r y s t a l according to the group associated with i t s s i t e . In the following section the factor group analysis of Bhagavantam and Venkatarayudu which i s generally more sa t i s f a c t o r y than the s i t e group analysis of Halford w i l l be considered. 4-4 Factor Group Analysis of Vibrations i n Crystals As previously mentioned the fa c t o r group analysis considers the unit c e l l or more c o r r e c t l y the primitive unit c e l l of the c r y s t a l which by d e f i n i t i o n contains the smallest repeating unit of pattern found within the c r y s t a l ( i . e . t h i s unit of pattern i s related to i d e n t i c a l units of - 46 - pattern i n a l l neighbouring unit c e l l s by simple translation.) For n atoms i n the primitive u n i t c e l l there w i l l be 3n vibrations of which three correspond to vibrations associated with t r a n s l a t i o n of the unit 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 either external or i n t e r n a l v i b r a t i o n s . The external vibrations or l a t t i c e vibrations are further 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 rotatory motions of the molecules i n the unit c e l l . The external vibrations usually exhibit low frequencies; while the i n t e r n a l vibrations or vibrations involving movements of the i n d i v i d u a l atoms i n each molecule against themselves w i l l generally exhibit high frequencies. By considering the group of n non-equivalent points, corresponding to the n non-equivalent atoms contained i n the primitive unit c e l l and applying the p r i n c i p l e s of group theory, we can f i n d an expression f o r nj_ , the number of times a p a r t i c u l a r i r r e d u c i b l e representation Pj i s contained i n the reducible representation P . The debited expression i s : > i , ^ l h J 1 6 j ( R ) Y - ( R ) ( 2 ) Where ~j£-(R) and ")£(R) are the characters of the operation J R i n the representations P and P respectively; Al i s the order of the group and hj i s the number of group operations f a l l i n g under the j t h cl a s s . A l l terms i n (2) - 47 - except c a n D e obtained from the appropriate factor group. A n a l y t i c a l expressions f o r the ")C(R) have been devised by Bhagavantam and Venkatarayudu (14) and are summarized i n Table 5« By suitable choice of the reducible representation and u t i l i z i n g the characters X(R) appropriate to i t we can confine ourselves to one or the other of the several types of normal vibrations mentioned previously. The type of normal v i b r a t i o n associated with each of the JC{TL) i s indicated i n Table 5» The factor group analysis f o r Sr(CHC>2)2 a r*d Sr(CHC>2)2»2H20 are given respectively i n chapters V and VI. TABLE 5 - us - SUMMARY OF EXPRESSIONS FOR CHARACTERS OF THE GROUP OPERATIONS, R Type of Vibration n^ - Total number of vibrations of symmetry species i ni(T) - Number of purely Translational vibrations of symmetry species i 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 Expression for the Corresponding Characters of the Group Operation R in the Reducible Representation,P X(R) = UR(n)(±l+2 Cos0 ) X(R) * (±1+2 Cos0) X(R) ="[uR(s)-l](±l+2 Cos^ ) X(R) = 'UR(s-v)(l±2 Cos?*) X(R) =[uR(n)-UR(s)](±l+2 COB0 ) -UR(s-v)(l±2 Coatf ) UR(n) - the number of atoms in variant under the operation R U R(s) a the number of groups occupying lattice sites which are invariant under the operation R ^ UR(s-v) = the number of groups occupying lattice sites which are in variant under the operation R less the number of atoms occupying lattice sites which are invariant under the operation R ' 0 = the angle of rotation associated with the operation R. - 49 - CHAPTER V DISCUSSION - PART I This chapter discusses the experimentally observed i n f r a r e d spectrum of c r y s t a l l i n e Sr(CH02)2 i n r e l a t i o n to the v i b r a t i o n a l modes predicted by the factor group analysis. In addition, information obtained from the polarized single c r y s t a l spectra i s discussed i n r e l a t i o n to the v i b r a t i o n a l assignments and the c r y s t a l structure of Sr(CH02)2« L a t t i c e modes and combination modes are also discussed. 5-1 V i b r a t i o n a l Analysis f o r Sr(CH02)? As indicated i n Chapter I the primitive unit c e l l of strontium formate contains 36 atoms; t h i s means there w i l l be a t o t a l of 108 vibr a t i o n s . Using equation (2) we f i n d that under the fac t o r group Dj-fr, which i s isomorphous with the point group D2, the structure of the representation of cartesian coordinates i s r • 27a 4. 27b]_ + 27b2 + 27b^ . By further application of equation (2) the types of normal vibrations associated with each i r r e d u c i b l e representation can be determined. The r e s u l t s are summarized i n the factor group analysis contained i n Table 6. Reference to Table 6 shows that there are a t o t a l of 48 i n t e r n a l v i b r a t i o n s : 12a ,12b! , 12b2 t12bj. This leaves 57 external vibrations which are dis t r i b u t e d i n the following manner; 36 l a t t i c e vibrations of rotatory o r i g i n : TABLE 6 - 50 - CHARACTER TABLE AND FACTOR-GROUP ANALYSIS FOR Sr(CH02) 2 D2 E 0 2(z) 02(y) C2(x) n i n^T) n^(T') ni(R') n'i 1 1 1 1 27 0 9 6 12 bx 1 1 -1 -1 27 1 8 6 12 T z b 2 1 -1 1 -1 27 1 8 6 12 T y b^ 1 -1 -1 1 27 1 8 6 12 T x - 51 - 6a , 6b^ t 6 b 2 , 6b^ and 33 l a t t i c e vibrations of translatory o r i g i n : 9a , 6"b^  , 8 b 2 , Sbj . The remaining three vibrations correspond to t r a n s l a t i o n on the unit c e l l and are of symmetry species b^ , b 2 and b^ . 5-2 The Internal Fundamentals of SrfCHC^lg- Assignments The significance of the s p l i t t i n g associated with the i n t e r n a l modes i n r e l a t i o n to the free ion modes i s under stood by considering the r e l a t i o n s h i p between the formate ions i n the unit of pattern. For Sr(CH0 2)2 t n e unit of pattern contains eight formate ions composed of two sets of four c r y s t a l l o g r a p h i c a l l y equivalent units. In each set of four ions the ions may execute the same v i b r a t i o n i n phase or 16*0° out of phase r e l a t i v e to one of t h e i r number a r b i t r a r i l y chosen. Thus, f o r each set of four ions there are four possible combinations; each combinations corres ponding to one of the ir r e d u c i b l e representations of the D 4 factor-group and thus giving r i s e to c r y s t a l modes of a > ^ 1 , ^2 a n d ^3 symmetry. I t i s re a d i l y seen that when t h i s four-fold s p l i t t i n g associated with each set of four ions i s considered with the two-fold s p l i t t i n g a r i s i n g from the two sets of non-equivalent ions that we have an eight f o l d s p l i t t i n g associated with each of the s i x free ion fund amentals. Thus accounting f o r the 43 i n t e r n a l fundamentals - 52 - predicted by the factor-group analysis. However, since only species of b i , b 2 and b^ symmetry are active i n the infrared the infrared spectrum of the c r y s t a l should reveal each fundamental associated with the free ion s p l i t i n t o s i x components; giving r i s e to the 36 i n f r a r e d active i n t e r n a l fundamentals. I t i s r e a d i l y seen from the f a c t o r group analysis that f o r polarized r a d i a t i o n along any one of the p r i n c i p a l crystallographic axes only two of the s i x components are allowed; these two components corresponding to the two non- equivalent sets of formate ions contained i n the unit of pattern. Although the r e l a t i v e i n t e n s i t i e s of the i n t e r n a l fundaments are not discussed i n d e t a i l u n t i l the next section; i t i s convenient to note that the i n t e n s i t y r e l a t i o n between the various components associated with the free ion fundamentals can be understood i f we consider 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- to a f i r s t approximation the r a t i o s of the r e l a t i v e i n t e n s i t i e s of the various components should be i n the same r a t i o as the squares of the appropriate d i r e c t i o n cosines. Values f o r the squares of the d i r e c t i o n cosines can be d i r e c t l y obtained from the c r y s t a l structure. The values given i n Table 7 are based upon the c r y s t a l structure of TABLE 7 - 53 - SQUARES OF THE DIRECTION COSINES FOR FORMATE IONS I AND II of Sr(CH0 2) 2 Symmetry Species 2 2 of Associated 1 Free Ion Fundamentals a x 0.0659 0.0908 bj_ 0.5320 0.4673 b 2 0.4039 0.4398 i 2 2 &x 0.7510 0.0001 bi 0.1777 0.2754 b 2 0.0711 0.7237 * 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 indicated 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; reference being made to the spectra shown i n Figures 2 and 3 and also to Tables 7 and 9 (Table 9- which i s introduced l a t e r gives calculated and observed intensity- r a t i o s . ) The six free ion fundamentals of the formate ion have been well characterized (1-3), and as has been mentioned previously we expect each of the s i x free ion fundamentals to s p l i t into s i x i n f r a r e d active components i n the single c r y s t a l spectrum- thus giving r i s e to the 36 i n f r a r e d active fundamentals predicted by the fact o r group analysis. I t i s convenient to discuss the i n t e r n a l fundamentals i n terms of the free ion fundamentals. F i r s t of a l l we w i l l consider the free ion fundamental l/^i^CE) a-^_ as related to the c r y s t a l spectrum. Both the spectrum of p o l y c r y s t a l l i n e Sr(CH02)2 (Fig* 2-1) and the single c r y s t a l spectrum (Fi g . 3-1) indicate only a single absorption corresponding to i t h i s absorption occurring at 2872 cm~^. That no observable s p l i t t i n g occurs i s further v e r i f i e d by the fac t that the i n t e n s i t y r a t i o s expected f o r various p o l a r i z a t i o n s , assuming no s p l i t t i n g are i n good agreement with the r a t i o s observed experimentally (Table 9). For (^CO)a^ the p o l y c r y s t a l l i n e spectrum (Fig. 2-2) shows three components occurring at 1359.5, 1362.5 and - 55 - 1363 cm"-'-; the two high frequency components appearing as well defined shoulders. The p o l y c r y s t a l l i n e spectrum also shows another absorption i n t h i s region at 1349*5 cm"-*-. However, consideration of the spectrum of p o l y c r y s t a l l i n e strontium formate -d^ (Fig. 2-2) and the i n t e n s i t i e s shown by the polarized single c r y s t a l spectra (Fig. 3-2) indicate that t h i s absorption i s not associated with Considering the 7^2 region i n the spectrum of p o l y c r y s t a l l i n e strontium formate -d]_ we see that no corresponding absorption appears which immediately suggests that the absorption under consider ation i s not associated with 7^2 • i s also i n t e r e s t i n g to note that even though the spectrum of p o l y c r y s t a l l i n e strontium formate -d-^ shows no evidence of s p l i t t i n g i n the region- the band envelope indicates that 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 strontium formate. Although the 1^2 r e g i ° n i s not very well resolved i n the single c r y s t a l spectra, the use of polarized r a d i a t i o n shows that the 1359*5 cm"-*- component i s due to ion I while the components occurring at 1362.5 cm"-*- and 1368 cm"-*- are due to ion I I . In the single c r y s t a l spectra, under X p o l a r i z a t i o n the most intense absorption occurring i n t h i s region i s found at 1362 cm"-1 - reference to Table 7 shows that ion II i s indicated. For Y po l a r i z a t i o n the most intense absorption occurs at 1359 cm"-*- which indicates ion I. Under Z polar i z a t i o n we have the appearance of a broad absorption which - 56 - has a peak at I36O cm"^; t h i s indicates the presence of the 1359.5 cm~l component associated with ion I, which we expect to be strongly absorbing and also the presence of the 1368 cm~l component observed i n the p o l y c r y s t a l l i n e spectrum, which we can assign to ion I I . The (eSoCOja^ region i s well resolved i n both the po l y c r y s t a l l i n e and single c r y s t a l spectra (Figs. 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 shows three well resolved absorptions occurring at 763, 779.5 and 783.5 cm--1-. The i n t e n s i t y r a t i o of the two high wave number absorptions i s approximately one-third. Reference to Table 7 immediately indicates that ion II i s involved; the less strongly absorbing 779.5 cm"-1- absorption being the X active component and the 733.5 cm""-1- absorption being the Z active component. As shown i n Table 9 the i n t e n s i t y r a t i o s obtained from the single c r y s t a l spectra support t h i s assignment. The remaining component of the t r i p l e t , occurr ing at 763 cm - 1 i s thus due to ion I and reference to Table 7 indicates i t should be most active under Z p o l a r i z a t i o n . Reference to the single c r y s t a l spectra show that under Z pol a r i z a t i o n a doublet unexpectly appears i n t h i s region. For the Z polarized be face a peak occurs at 766 cm""l with a shoulder occurring at 761 cm"-1-; f o r the Z polarized ac face the sit u a t i o n i s reversed. I t i s possible that the peaks occur because of the Y active 766 cm--1- absorption and - 57 - the X active 761 cm"1 absorption. Rationalizing i n t h i s manner enables us to place the Z active component at 763 cm"1 as indicated by the p o l y c r y s t a l l i n e spectrum. Consideration of i n t e n s i t y r a t i o s show that the less strongly absorbing X and Y active components both occur at 766 cm"-*-. As indicated i n Table 9 the calculated and observed i n t e n s i t y r a t i o s f o r t h i s region are i n excellent agreement. I t i s also i n t e r e s t i n g to note that i d e n t i c a l s p l i t t i n g i s observed i n the ~}/^  region i n the p o l y c r y s t a l l i n e spectra of both Sr(CH0 2) 2 and Sr(CD0 2) 2. The most intense region of absorption observed i n the spectrum of c r y s t a l l i n e strontium formate i s associated with the free ion fundamental 3^(.«i/C0)b-j_ • This region i s best resolved i n the p o l y c r y s t a l l i n e spectra; i n the spectrum of both p o l y c r y s t a l l i n e strontium formate and p o l y c r y s t a l l i n e strontium formate d^ (Fig. 2 - 1 ) almost i d e n t i c a l s p l i t t i n g into a doublet i s observed. In the spectrum of p o l y c r y s t a l l i n e strontium formate the components of the doublet are observed at 1570 and 1593 cm"1. The single c r y s t a l spectra for a l l three polarizations (Fig. 3-2) show only a strong absorption at about 1580 cm"1; as expected the i n t e n s i t y of t h i s absorp t i o n i s least under Z p o l a r i z a t i o n . I t was not possible to assign either member of the doublet to ion I or II on the basis of the polarized spectra. However, i t has been seen that f o r both *^2 and the high wave number member of the - 53 - doublet has been associated with ion I and as w i l l be seen t h i s order i s preserved for the 5 and 5, and on t h i s basis we can t e n t a t i v e l y assign the 1570 cm"1 component to ion I and the 1593 cm"1 component to ion I I . Reference to the spectrum of p o l y c r y s t a l l i n e strontium formate (Fig. 2-2) shows a well resolved doublet associated with the free ion fundamental7/^[CO CHjb-^; the components of t h i s doublet occur at 1393.5 and 1399 cm"1. Although the single c r y s t a l spectra (Fig. 3-2) are not very well resolved i n t h i s region i t can be seen that f o r X polar i z a t i o n a strong absorption at 1393 cm"1 appears. Reference to Table 7 shows t h i s indicates ion I. Under I p o l a r i z a t i o n there i s a strong absorption occurring at 1396 cm - 1 which appears to be s p l i t into a doublet i n d i c a t i n g the appearance of both components. For Z p o l a r i z a t i o n a sharp peak at 1399 cm"1 appears i n d i c a t i n g ion II as expected. F i n a l l y we consider the free ion fundamental ^5(/JCH)b2. This mode i s observed only with d i f f i c u l t y i n the spectrum of p o l y c r y s t a l l i n e Sr(CH02)2 (Fig. 2-1). When i t i s observed i t appears as a very weak absorption occurring at 1034 cm"1. The single c r y s t a l spectra (Fig. 3-3) show a doublet i n t h i s region. Under X p o l a r i z a t i o n the members of the doublet occur at 1070 and 1034 cm"1, under Y p o l a r i z a t i o n at 1067 and IO84 cm"1 and under Z p o l a r i z a t i o n at 1035 and 1070 cm"1. As shown i n the spectra there are marked - 59 - differences i n intensity for the various components and reference to Table 7 allows us to assign the high wave number component to ion II and the low wave number component to ion I. Table 3 gives a complete summary of the results discussed above. From the table we can see the magnitude of the various splittings. The splitting associated with the doublet is a direct measure of the static f i e l d effect while the spli t t i n g associated with the t r i p l e t s i s a direct measure of the dynamic crystal effect or correlation f i e l d s p l i t t i n g . 5-3 The Internal Fundamentals of Sr(CHOp)p- Intensities The relation of the intensity of the internal fund amentals to the direction cosines of the oscillating dipoles giving rise to the free-ion fundamentals was mentioned i n the previous section. In this section observed intensity ratios are presented along with the corresponding calculated ratios. For each of IV^ and ^ two sets of ratios corres ponding to the intensities arising from formate ions I and II were obtained. While for each of " - ^ j «^2» fc^and f ^ i t was only possible to obtain a single set of intensity ratios; the ratios corresponding to the combined intensities arising from formate ions I and II. The results are contained in Table 9 and especially for the well resolved - 60 - TABLE 8 THE INTERNAL FUNDAMENTAL MODES OF Sr(CH02)2 (WAVENUMBERS IN CM"1) Free Ion Associated Magnitude X Active Y Active Z Active Fundamental* Doublett of S p l i t t i n g Modes b 2 Modes b^ Modest Z/1(Z/CH)a1 2872 0 ? 2872 2872 2872 2872 ? ' 1559.5 ? ? 1559 1565 5 . 5 1565 1568 y 5 ( 6 0 C 0 ) a 1 765 766 766 765 781 .5 5 . 5 7 8 5 . 5 7 7 9 . 5 1570 ? ? — 1 1595 25 ? ? ? 1595 1595 — 1599 5 . 5 ? ? 1599 , ^ 6 ( / , 0 H ) b 2 1084 1084 1084 IO85 1069 15 1070 1067 i 1070 * * The ^ and ^ ' r e f e r to'formate ions I and I I respectively. t The frequencies for the components of the doublet are given as \ averages of the X, Y and Z active components where necessary. j ~f The dashes (—,) indicate that the corresponding a c t i v i t y i s too weak to be observed experimentally, while the question marks (?) indicate that no conclusive assignments could be made from the observed spectra. 1 TABLE 9 CALCULATED AMD OBSERVED INTENSITY RATIOS - Sr(CK0 2) 2 2 / 2 2/2 2/2 Associated 1 , / f f i i / i i Product Free Ion of Obs. Fundamental Calc. Obs. * Error Calc. Obs. * Error Calc. Obs. * Error Ratios 0 . 7 2 6 0.712 0.108 0.107 0 . 9 * 12.8 12.U 3.1* 0.945 0.91S 1.000 8 . 9 * 2.81 2 . 6 7 5 . 0 5 6 0.387 0.375 3.1* 1.001 111 r 2 2/ 2 m2/n2 n 2 / l 2 Calc. Obs. Calc. Obs. Calc. Obs. 7500 0 . 0 0 0 4 0 . 3 3 2 0.375- 1 3 * ""070982 0.0845 14* 3.53 3.85 9 . 1 5 6 2.89 2 . 7 2 5 . 9 * 0.885 1?+12 2/2. 2 /m,+m2 2 2/2 2 mj+m2/n,+n2 n I+n 2/l )+l 2 Calc. Obs. Calc. Obs. Calc. Obs. - 2^ 1 (a-,) 8 . 9 9 9.22 2 . 6 * 0.0832 0.0833 0.055 1.34 1 . 3 0 3 . 0 5 6 0.998 ^ 2 ( a i ) 2 . 9 9 2.20 0.0832 0.314 280$ 1 .3^ 1 . 2 5 6 . 7 * 0.864 ^U(bi) 0.956 1.12 1 . 3 6 1 . 5 1 1156 0 . 7 7 2 0.597 2 3 * 1.010 0.956 1 . 3 5 4 l * 1 . 3 6 1 . 3 0 U.U* 0 . 7 7 2 0.592 2 3 * 1.040 - 62 - regions of the spectrum, there i s remarkably good agreement between the experimental and calculated r a t i o s . Since each r a t i o was obtained from the polarized spectra of a single sample no error i s introduced into the r a t i o s by having to allow f o r sample thickness. However, possible errors do arise from the following sources: (i) the c r y s t a l s l i c e s were not ground absolutely perpendicular to the c r y s t a l axes- the maximum deviation being estimated at 2° by observation of interference f i g u r e s . ( i i ) the po l a r i z e r was not 100$ e f f i c i e n t - i t was estimated that l e s s than 5% of the component perpendicular to the desired component was passed; measurements being made i n the v i s i b l e region against a Wollaston prism. ( i i i ) the incident radiation was not p a r a l l e l due to convergence of the sample beam- measurements of the con vergence showed that less than 1% of the component p a r a l l e l to the beam would be introduced. (iv) the polar i z e r was not cor r e c t l y aligned with respect to the sample face- i t was estimated that the error i n alignment was les s than 2°. Consideration of the above sources of error suggest that the experimental error introduced into the observed i n t e n s i t y r a t i o s could correspond to as much as 8% of the component perpendicular to the desired component being passed. - 63 - However, i t would appear from t h i s study that i f careful experimental procedure i s followed the t o t a l error should correspond to les s than 5% of the component perpendicular to the desired component being passed. Even so, i t can be re a d i l y appreciated that i f a certa i n component i s strongly absorbing at a certain frequency under one p o l a r i z a t i o n and i s only very weakly absorbing at 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 ; considerable error could be introduced into the observed i n t e n s i t y r a t i o . In Table 9 the % error f o r each r a t i o i s given as well as the product of the three r a t i o s making up each set of r a t i o s . This product should equal unity and the deviation from unity i s a measure of the i n t e r n a l consistency possessed by the experimental i n t e n s i t i e s . Since the ^ 4 a n d 1S^ regions are not very well resolved i n the single c r y s t a l spectra we expect the greater error associated with the observed^ i n t e n s i t y r a t i o s - the error being l a r g e l y introduced by overlapping with combination modes. One of the most i n t e r e s t i n g aspects of an inf r a r e d study of the c r y s t a l l i n e state i s the p o s s i b i l i t y of experimentally obtaining the d i r e c t i o n cosines associated with the absorbing species. Reference to Table 9 shows that the i n t e n s i t y data for " ^ l ^ l ) * fji&i) and ^ 6 ^ 2 ) should allow d i r e c t c a l c u l a t i o n of the d i r e c t i o n cosines associated with symmetry species a^ and b£ f o r both formate ions I and I I . The only - 64 - problem which presents i t s e l f i s that i n some cases the product of the set of r a t i o s i s not i n t e r n a l l y consistent ( i . e . the product does not equal u n i t y ) . I f t h i s product i s not equal to unity i t can be r e a d i l y appreciated that the di r e c t i o n cosines we calculate from the r a t i o s w i l l not be i n t e r n a l l y consistent themselves ( i . e . the sumrof t h e i r squares w i l l not equal u n i t y ) . In order to circumvent t h i s problem each r a t i o i n a set was multiplied by a common factor so as to bring the product of the r a t i o s to unity. I t i s noted that t h i s procedure i s not j u s t i f i a b l e mathe matically but since t h i s common factor i n a l l cases was close to unity the error introduced i s very small. The signs of the d i r e c t i o n cosines associated with the symmetry species a^ and \>2 f o r both formate ions are obtained by applying the orthogonality requirement. Further applic ation of the orthogonality r e l a t i o n allows c a l c u l a t i o n f o r both ions I and II of the d i r e c t i o n cosines associated with symmetry species b i . The calculated and experimental d i r e c t i o n cosines are contained i n Table 10 and i t can be seen that the agreement i s exceptionally good. TABLE 1 0 CALCULATED AND EXPERIMENTAL DIRECTION COSINES FOR FORMATE IONS I AND II OF Sr(CHD2)2 Symmetry Species of Associated Free Ion Fundamentals Calc. - 0 . 2 5 7 0.729 O.636 Calc. Expt'l 1 - 0 . 2 5 9 0.715 0.649 Expt'l - O . S 6 7 - 0 . 8 7 4 -O.I421 -0.1*05 m l Calc. Expt'l 0.301 0.297 0.684 0.699 -O.663 - 0 . 6 4 9 m2 Calc. 0.008 Expt'l 0.045 Calc. Expt'l 0.918 0.916 - 0 . 0 2 6 - 0 . 0 2 5 0.395 0.397 n 2 Calc. Expt'l 0.525 0.501 -0.^99 -O.M92 0.740 O.765 - O . 2 6 7 - O . 2 5 6 -0.851 -0.864 o.u53 o>3i - 66 - 5-4 Overtones and Combinations of Internal Fundamentals- Sr(CHQ?) ? As noted previously each free-ion fundamental i s s p l i t into 8 components under the D2 factor group. Of these 8 components 4 are associated with formate ions I and 4 are associated with formate ions I I . Reference to Table 11 shows that the overtones associated with the i n t e r n a l fundamentals a r i s i n g from formate ion I and also formate ion II consist of 16 components (4a , 4bi, 4b2> 4b3). Of these 16 components 12 are infrared active (4b]_, 4b2, 4b3). Hence, we expect to observe 4 components f o r both ions I and II under each of X, Y and Z p o l a r i z a t i o n s . Considerations similar to the above also apply to combination modes. From the observed spectra i t was possible to assign a number of overtones and combinations of i n t e r n a l fundamentals. These assignments were given previously i n Table 3. 5-5 Combinations of Internal Fundamentals and L a t t i c e Modes- SrtCHOp)? Sum and difference modes of the low frequency l a t t i c e v ibrations and the i n t e r n a l fundamentals w i l l give r i s e to a series of weaker peaks on the high and low frequency sides of the absorption peak assigned to 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 difference modes are the same as those of the corresponding: sum modes but the - 67 - i n t e n s i t i e s are expected to be less because of the smaller populations of the excited l a t t i c e mode energy l e v e l s at which the t r a n s i t i o n s o r i g i n a t e . Reference to Table 6 shows that the l a t t i c e vibrations are d i s t r i b u t e d i n the following manner: (153^, 14bj, 14b2, 14b3). I f we consider the possible combinations of these l a t t i c e modes with the i n t e r n a l fundamentals we f i n d by r e f e r i n g to Table 11 that f o r i n t e r n a l fundamentals of symmetry species, a, b i , \>2 and b 3 the respective combination modes possible are: (15a, 14bi, 14b2, ^ b ^ ) , (15b]_, 14a, 14b 3, 14b 2), (15b 2, 14b 3, 14a, 14b!) and (15b 3, 14b 2, 14b x, 14a). Remembering that c r y s t a l modes of symmetry species a are not infrared active i t can be r e a d i l y seen from the above that f o r each of X, Y and Z polarized spectra we would, i n p r i n c i p l e , expect the s a t e l l i t e structure of each of the 6 i n t e r n a l fundamental doublets to exhibit 114 peaks. Of these 114 peaks 57 w i l l correspond to combination modes and the remaining 57 w i l l correspond to difference modes. From the observed spectra i t was possible to t e n t a t i v e l y assign a few l a t t i c e modes (Table 3 ) . These assignments are based on the recurrence of i d e n t i c a l peak separations between the various 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 to Table 3 shows that the observed spectrum indicates l a t t i c e modes occurring at 10, 12, 15, 20, 23, 70, 155, 130 and 200 cm"1. - 63 - SYMMETRY SPECIES OP COMBINATIONS AND OVERTONES b l b2 b5 1 2 5 \ a b 5 b2 - 6 9 - CHAPTER VI DISCUSSION - PART II This chapter discusses the experi mentally observed infrared spectrum of c r y s t a l l i n e Sr(CHOg^^KteO i n r e l a t i o n to the v i b r a t i o n a l modes predicted by the factor group analysis. In addition information obtained from the polarized single c r y s t a l spectra i s discussed, where possible i n r e l a t i o n to the v i b r a t i o n a l assignments and c r y s t a l structure of Sr(CH02)2»2H20. L a t t i c e modes and combination modes are also discussed. 6-1 V i b r a t i o n a l Analysis f o r Sr(CHOg)2.2H2O The v i b r a t i o n a l analysis f o r Sr(CH0 2 )2»2H20 i s contained i n Table 1 2 . Since the space group f o r Sr(CH02)2» 2 H 2 0 and S r ( C H 0 2 ) 2 a r e b°th P 2 1 2 1 2 1 (D2) l i t t l e can be added to the discussion contained i n section 5-1• We do note however that f o r each of the IS i n t e r n a l fundamental vibrations associated with each symmetry species, the 12 modes- ni ' ( C H 0 2 ) w i l l be due to the formate ions and the remain s i x modes- n i ' ( H 2 0 ) w i l l be due to the water molecules. The i n t e r n a l fundamentals associated with the two non equivalent water molecules contained i n the unit of pattern can be discussed i n a manner e n t i r e l y equivalent to the discussion of the two non equivalent formate ions. TABLE 12 CHARACTER TABLE AND FACTOR-GROUP ANALYSIS FOR Sr(CH0 2) 2.2H 20 D2 « CsU) 02(y) C 2(x) n i ni(T) ni(T«) ni(fi') nj' (CH02) nj'(EgO) 1 1 1 1 45 0 15 12 18 12 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 T x - 71 - 6-2 The Internal Fundamentals of S r ( C H 0 ? ) ? . 2 H ? 0 - Assignments The method of assignment used f o r the formate ions of Sr(CH02)2 w i l l also be used i n the assignment of the i n t e r n a l fundamentals of Sr(CH02)2«2H20. The i n t e r n a l fundamentals associated with the formate ion as the absorbing species are considered f i r s t . Reference to the single c r y s t a l spectra contained i n F i g . 4-1 shows that i n the region 3 4 0 0 - 2 9 0 0 cm - 1 there i s unfortunately t o t a l absorption due to the 0-H stretching frequencies of the water molecules. However, t h i s region of t o t a l absorption i s not so broad so as to t o t a l l y obscure the appearance of the i n t e r n a l fundamentals associated with fCH)ai which appears at 2 8 5 8 cm"1 . As f o r S r ( C H 0 2 ) 2 there appears to be no observable s p l i t t i n g under various pol a r i z a t i o n s . In the 1 4 0 0 - 1 3 0 0 cm"1 region of the spectrum (Fig.4-3) there appears to be considerable overlapping of the various modes. However, consideration of the r e l a t i v e i n t e n s i t i e s predicted by the squared d i r e c t i o n cosines (Table 13) along with the information obtained from the polarized spectra allow us to make some f a i r l y conclusive assignments. Under X p o l a r i z a t i o n we f i n d the appearance of two strong absorp tions occurring at 1 3 8 3 and 1 3 6 4 cm"1. Assuming that the order of the modes associated with the free-ion fundamentals TABLE 13 - 72 SQUARES OF THE DIRECTION COSINES FOR FORMATE IONS I AND I I of Sr(CH0 2) 2.2H 20 Symmetry Species 2 2 2 of Associated 1^ m^  * Free Ion FundamentIs a x 0.0055 0.0011 0.9956 b1 0.5518 0.6482 0.0001 b ? 0.6455 0.5505 0.0061 a l , 2 ' 2 2 i 2 j °i2 * 0.1599 0.8559 O.O065 b x 0.7987 0.1576 O.0658 b 2 0.0405 0.0294 0.9501 * The subscripts 1 and 2 refer to formate ions I and I I respectively. - 73 - 7^2 and f ^ i s not reversed- reference to Table 13 indicates that the absorption occurring at 1 3 8 3 cm"1 i s associated with the free ion fundamental 2/'^(tVCH)b^ - ion I I . The absorption occurring at 1 3 6 4 cm"1 also appears under Y po l a r i z a t i o n along with a shoulder at 1 3 3 3 cm"1, - i t would appear that the 1 3 6 4 cm"1 absorption i s due to a mixing of absorptions a r i s i n g from "Z^- ion I and 3 ^ 2 " i o n 1 1 • Under Z po l a r i z a t i o n a strong absorption appears at 1 3 5 5 cm"1 - reference to Table 13 c l e a r l y indicates ) a l ~ i o n 1 1 • As might be expected the absorption at 1 3 8 3 cm"1 due to Z ^ - ion II also appears under Z p o l a r i z a t i o n . The two remaining absorptions appearing i n t h i s region at 1 3 9 2 and 1 3 3 7 cm"1 appear to be due to combination modes. The spectra contained i n F i g . 4 - 4 show the appearance of -^(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 f o r t h i s mode under X po l a r i z a t i o n . However, f o r both Y and Z po 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 slopes "up" r e l a t i v e to the absorption i n question while f o r X polar i z a t i o n the base l i n e slopes "down". This difference i n baseline p o s i t i o n may account f o r the observed r e s u l t s . The spectra contained i n F i g . 4 - 4 also show the region of the spectrum where we would expect to f i n d the appearance of the modes associated with the free ion mode ^(^OCO)a]_. However, i t i s found that the strongly absorbing . l a t t i c e ' : -- 74 - modes observed i n t h i s region t o t a l l y obscure the appearance of the i n t e r n a l fundamentals associated with '^ (o'OCOjai. The region of the spectrum associated with the free ion fundamental 2V^(^C0)bi (Fig. 4-3) l i k e the other regions where i n t e r n a l fundamentals are observed i s complicated by considerable overlapping. Under both X and Y polarizations a very intense absorption occurs at 1590 cm~l. However, under Z p o l a r i z a t i o n we f i n d that we now have an intense absorption occurring at 1545 cm - 1. Reference to Table 13 shows that we expect l i t t l e i n t e n s i t y to be associated with ^ 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 consideration when considered with the rather large s h i f t of 45 cm - 1 indicates the 1545 cm"1 absorption as being larg e l y due to Z ^ t f ^ H j a j - t n e water molecules being the absorbing species. Intensity r a t i o s f o r t h i s region- considering the strong absorptions at 1590 and 1545 cm"1 are given i n Table 15. I f we consider the three strong absorp tions observed f o r the respective polarizations as being due only to "Z^ (^CH02) and 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 calculate values 2 2 f o r the sums of the squared d i r e c t i o n cosines ( i . e . 1^  4- 12 0 0 0 0 m l m2 a n (* n l + n2 ' associated with symmetry species a^ f o r water molecules I and I I . However, when these sums were calculated they were not consistent with the require ment that t h e i r t o t a l sum should equal two. This, of course, - 75 - indicates that other components are involved. None the less i t can be said with a good deal of certainty that 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 t strongly active under Z pol a r i z a t i o n and indicate strong Y a c t i v i t y . F i n a l l y we consider the region of absorption associated with the 0-H sketching frequencies. In discussing t h i s region we can only consider the "dimensions" of the regions of t o t a l absorption. They are given below: (i) X p o l a r i z a t i o n - 2375, 3100 and 3325 cm"1 ( i i ) Y p o l a r i z a t i o n - 2925, 3175 and 3425 cm"1 ( i i i ) Z p o l a r i z a t i o n - 2375, 3150 and 3425 cm"1 In each of ( i ) , ( i i ) and ( i i i ) above the center wave number ref e r s to the centre of the region of t o t a l absorption, with the two outside wave numbers r e f e r r i n g to the outer extrem i t i e s of the respective regions of t o t a l absorption. I f we assume l ^ f ^ O ) to be most strongly active under Y and Z pola r i z a t i o n s , then consideration of the outer extremities of the regions of t o t a l absorption tends to place *'1(l'0K)a1 - H 20 at a higher frequency than V ^ Q R ) ^ - H 20. The r e s u l t s discussed above are completely summarized i n Table 14. 6-3 The Internal Fundamentals of Sr(CH0p)p.2H?0- In t e n s i t i e s Even though the polarized single c r y s t a l spectra of Sr(CH0 2) 2.2H 20 o f f e r l i t t l e i n t e n s i t y information of a TABLE 14 THE INTERNAL FUNDAMENTAL MODES OF Sr(CH02)2*2H20 (WAVENUMBERS IN CM"*) (i) The Internal Fundamentals - nj_'(C3H02)2 Free Ion * Observed Fundamental ^'(CHOs) Activity (^CH)ai 2858 2858 X,Y,Z 1555 Z vl ~ 1 5 6 4 X,Y Z/5(SOCO)a1 — — 1590 ; X,Y 1612 Z ^ ( ^ C H ) ^ ~ 1 5 6 4 X,Y 1585 X,Y,Z 1064 1064 x , z * They and "V'refer to formate ions I and II respectively, (ii) The Internal Fundamentals - ^ '(HgO) * Free H2O Observed Fundamental n^'^O) Activity 2^1(?'0H)a1 - 5 1 5 0 Y,Z ^2(SH0H)ai 1545 Z vypv&yo\ ~ 5150 — * As noted in the text 1/-^(2^0H)a^ is believed to be of highe frequency than ^(ZAJH^. TABLE If CALCULATED AND OBSERVED INTENSITY RATIOS - Sr(CH02)2-SH^ Ratios * Calc. 3 4 0.815 1.47 1.80 Obs. Calc. Obs. Sale. Obs. 0.947 0.907 0.153 12.3 0.4o6 0.995 0.803 0.987 2.42 0.426 0.555 0.411 1.37 Product of Obs. Ratios 0.930 0.935 * 1 — The ratios refer to the combined intensities due to formate ions I and II for both ^2(CH02) and 5^(CH02) . 2 - The ratios refer to the combined intensities due to formate ions I and II for ^%(CH02) and water molecules I and II for ^(HgO). 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 >£(CH02). - 73 - quantitative nature- i t was possible to compare observed and calculated i n t e n s i t y r a t i o s i n a few cases. These are summarized i n Table 15. 6-4 Overtones and Combinations of Internal Fundamentals- Sr(CH0?)2.2H?0 For Sr(CH02)2»2H 20 we must consider the combinations and overtones of the i n t e r n a l fundamentals nj/fCIK^) and n^'fl^O). In both cases the discussion of overtones and combinations i s completely equivalent to that contained i n section 5-4. From the observed spectra i t was possible to make some assignments- these are given i n Table 4-1. 6-5 Combinations of Internal Fundamentals and L a t t i c e Modes Reference to Table 12 shows that the l a t t i c e vibrations are d i s t r i b u t e d i n the following manner: (27a, 26b-^, 26b2, 26b-j) I f we consider the possible combinations of these l a t t i c e modes with the i n t e r n a l fundamentals we f i n d by r e f e r i n g to Table 9 that f o r i n t e r n a l fundamentals of symmetry species a> d 1 J d2 a n c * D 3 the respective combination modes possible are: (27a , 2 6 b 1 } 26b 2, 26b3), (27b!, 26a, 26b 3 , 2 6 b 2 ) , (27b 2, 26b3, 26a, 26bi) and (27b3, 26b 2, 26bi , 26a). Remembering that c r y s t a l modes of symmetry species a are not in f r a r e d active the above indicates that f o r each of - 79 - X, I and Z polarized spectra we would, i n p r i n c i p l e , expect the s a t e l l i t e structure of each of the 6 i n t e r n a l fundamental doublets- nj/(CH02) and each of the 3 i n t e r n a l fundamental doublets- n-j/fR^O) to exhibit 210 peaks. Of these 210 peaks 105 w i l l correspond to combination modes and the remaining 105 w i l l correspond to difference modes. From the observed spectra i t was possible to assign some of the l a t t i c e modes. The intense absorptions observed i n the 900-600 cm"1 region of the spectrum appear to be associated with the ^ mode observed i n the spectrum of i c e and hence can be assigned as l a t t i c e modes of r o t a t i o n a l o r i g i n ("^(h^O) - see Table 4-1). Further tentative assignments of l a t t i c e modes at 18 and 110 cm"1 are based on peak separations between the various 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. - 30 - CHAPTER VII CONCLUSIONS It can be seen from t h i s work that the information obtained from polarized i n f r a r e d spectra of single 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 true where hydrogen atoms or other l i g h t atoms are involved. The factor which most determines the amount and quality of the information obtained from the spectra i s the thickness of the c r y s t a l s . I t would appear that f o r optimum r e s u l t s - e s p e c i a l l y where strongly absorbing modes are involved- that the c r y s t a l s l i c e s should be about 5-10 A* thick. This thickness can no doubt be reached as more sophisticated grinding techniques are developed. This work has shown that the spectra of c r y s t a l l i n e materials can be explained on the basis of fa c t o r - group analysis. Future infrared work w i l l , no doubt i n part be concerned with attempting to observe the low frequency l a t t i c e modes. Raman Spectroscopy also offers important p o s s i b i l i t i e s i n t h i s area. - 3 l - BIBLIOGRAPHY 1. K.B. Harvey, B.A. Morrow and H.F. Shurvell, Can. J . Chem. £1, 1181 (1963). 2. C.J.H. Schutte and K. Buijs, Spectrochim Acta 20, 187 (1964). 3. J.D. Donaldson, J.F. Knifton and S.D. Ross, Spectrochim Acta 20, 347 (1964). 4. R. Vietne, Rev. Univ Mines 15_, 510 (1959). 5. A.M. Vergnoux and R. Vierne, Comptes Rendus 261 (6), 1236 (1965). 6. B.A. Morrow, M.Sc. Thesis (U.B.C.), 1962. 7. T.L. Charlton, M.Sc. Thesis (U.B.C.), 1964. 3. I. N i t t a , S c i . Papers Inst. Phys Chem. Research (Tokyo) 2, 151 (1923). 9. I Ni t t a and Y. Saito, X-Rays 39 (1949). 10. T. Sugawara, M. Kakudo, Y. Saito and I. Ni t t a , X-Rays 6, 35 (1949). 11. K. Osaki, Ann Rept S c i . Works, Fac. S c i . , Osaka Univ. 6, 13 (1953). 1 12. E. Charney, J.O.S.A. Z^, 930 (1955). 13. E.B. Wilson, J.C. Dicius and P.C. Cross. Molecular Yibrations, McGraw-Hill (1955). 14. S. Bhagavantam and T. Venkataryudu, Theory of Groups and i t s Application to Physical Problems, Andhra University, Waltair (1951). 15. R.S. Halford, J. Chem Phys. 14, 3 (1946). 

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