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Crystal structures of some group V compound Zobel, Tessa 1965

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CRYSTAL STRUCTURES OF SOME GROUP V COMPOUNDS by TESSA ZOBEL B.Sc.(Hons.), University of B r i s t o l , 1963 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE i n the Department of CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA A p r i l , 1965 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t o f t h e r e q u i r e m e n t s f o r an a d v a n c e d d e g r e e a t t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e L i b r a r y s h a l l make i t f r e e l y a v a i l a b l e f o r r e f e r e n c e and s t u d y , I f u r t h e r a g r e e t h a t p e r -m i s s i o n f o r e x t e n s i v e c o p y i n g o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by t h e Head o f my D e p a r t m e n t o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t . c o p y i n g o r p u b l i -c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l n o t be a l l o w e d w i t h o u t my w r i t t e n p e r m i s s i o n . D e p a r t m e n t o f CAg-A^iYT The U n i v e r s i t y o f B r i t i s h C o l u m b i a , V a n c o u v e r 8, C a n a d a Date 2*^ /M^t AST ABSTRACT The c r y s t a l and molecular structure of cacodylic acid, (CH^^AsO.OH, has been determined by X-ray d i f f r a c t i o n of a single c r y s t a l . The crystals belong to the- t r i c l i n i c system with a = 6.53, b = 6.82, c = 6.61 A, a = 77°30», P = 78°45», if = 55°9 1, z = 2, space group Pl". The structure was determined from v i s u a l intensity data by Patterson and Fourier methods, and the positional and anisotropic thermal parameters were refined by least-squares. The f i n a l discrepancy factor i s 0,149 for 806 observed r e f l e c t i o n s . The structure consists of centrosymmetrical, hydrogen-o bonded dimers, with 0-H...0 distances of 2.57A, the arsenic atoms having a tetrahedral configuration with bond angles i n the range 106° - 115°. Crystals of antimony t r i i o d i d e , Sbl^, are rhombohedral o o _ with ay = 7.48 A, Cjj = 20.90 A, z = 6, space group R3. The structure was determined from h0.£ Patterson, Fourier and difference projections, the f i n a l discrepancy factor being 0,1314. The antimony atoms are s i g n i f i c a n t l y displaced from the centres of iqdine octahedra, and have three near- neighbour 0 o iodine atoms at 2.868 + 0.010 A, with I-Sb-I = 95.8 + 0.3 , o and three further off at 3.316 + 0,010 A, The structure i s thus intermediate between that of a molecular c r y s t a l , as i n A s l ^ , and an ionic arrangement. o o Crystals of B i l 3 have a R = 7.52 A, c H = 20.72 A« Com-parison of measured and calculated povder i n t e n s i t i e s suggests that the bismuth atom i s situated at the centre of an iodine octahedron, so that the structure i s probably largely i o n i c . Lone-pair s t e r i c e f f e c t s , as well as changes i n bonding character, are thought responsible for the differences i n the c r y s t a l structures of A s l - , Sbl- and B i l - . i i i ACKNOWLEDGEMENT S It i s my pleasant duty to express my thanks to Dr« James Trotter for his guidance and constant encouragement throughout the course of this work. I would also l i k e to thank Dr» W.R, Gullen, who suppli the c r y s t a l sample of cacodylic acid, and made his laboratory f a c i l i t i e s available to me for preparative work* iv TABLE OP CONTENTS Page TITLE PAGE ....••»•••••*«••••»•.••• i ABSTRACT . , i i ACKNOWLEDGEMENTS • iv TABLE OF' CONTENTS v LIST OF FIGURES • • v i LIST OF TABLES v i i I» THE STRUCTURE OF CACODYLIC ACID A. Introduction ............................ 1 B. Experimental » . . . . » • • • » a . . . . . . . . . . 1 C. Structure Analysis ...................... 2 D. Discussion .............................. 8 I I . THE STRUCTURES OF ANTIMONY AND BISMUTH TRIIODIDES A. Introduction I ........... 11 B. Experimental 12 C. Structure Analysis .............. 13 D. Discussion 19 APPENDIX. CALCULATION OP THE LATTICE CONSTANTS OF BISMUTH TRIIODIDE ......... 24 REFERENCES ....•••••••«».««»».«»«*».»... »•»«•«»<»«>» 26 v LIST OF FIGURES Figure Page CACODYLIC ACID 1 Superimposed sections of the three dimensional electron-density d i s t r i b u t i o n through the atomic centres p a r a l l e l to (OOl), and a perspective view of the molecule. 4 2 Packing of the molecules, projected along the b-axis. 10 ANTIMONY TRIIODIDE 3 Electron density projection along the b-axis. 14 v i LIST OP TABLES CACODYLIC ACID Fin a l measured and calculated structure factors Positional parameters, with standard deviations, and temperature factors Bond lengths and valency angles, with standard deviations Shorter intermolecular distances ANTIMONY AND BISMUTH TBIIODES Crystal data Fi n a l measured and calculated structure factors. (Antimony t r i i o d i d e ) Fractional positional parametersj i n t e r -atomic distances and bond angles 2 Fi n a l measured and calculated F values. (Bismuth t r i i o d i d e ) v i i I. CACODYLIC ACID 1 A. Introduction The structure of cacodylic acid, dimethylarsinic acid, (CH^)2As0.0H was determined i n order to investigate the stereochemistry of the arsenic atom, and the hydrogen-bonding p o s s i b i l i t i e s i n the c r y s t a l . It was expected that the structure would involve either hydrogen—bonded dimers as i n carboxylic acids, or endless sp i r a l s of molecules, and that the arsenic atom would have a tetrahedral configuration as i n other As compounds. B. Experimental Crystals of cacodylic acid are colourless prisms elongated along the a-axis, with (100), (010), and (001) developed. The density was measured by f l o t a t i o n i n a chloroform-bromoform mixture, and the unit c e l l dimensions and space group were determined from rotation films about the a—axis, 0k£ Veissen-berg, and h0£ and hkO precession photographs. Crystal Data (X, Cu - Ka = 1.5418A; X, Mo - Ka = 0.7107A) Cacodylic acid, C 2H 70 2As; M, 138,0; m.p. 200°C T r i c l i n i c , a = 6.53 + 0.01, b = 6.82 +0.01, c = 6.61 + 0.01A • a =. 77°30' + 5 ' , P = 78°45' ± 5 \ V= 55°9 * + 5 1 03 Volume of the unit c e l l = 234.9A -3 -3 Dm = 1 , 9 5 g* c m* » z = 2, D x = 1.95 g.cm. Absorption c o e f f i c i e n t for X-rays, A = 1.5418A, o t- -1 u = 95 cm. P(000) = 136 No absent r e f l e c t i o n s ; space group Pl or P l ; Pl from structure analysis The i n t e n s i t i e s of the reflections were measured v i s u a l l y from Cu-Koc equi-inclination Veissenberg films of the 0k£ .. . 5k£ layers. Two sets of films were taken for each layer to record the whole of reciprocal space, and the various layers were correlated by ca r e f u l l y timed exposures. The cry s t a l cross-section was 0.2 x 0.2 mm., so that absorption errors are small, and. no corrections were applied. The structure amplitudes were derived as usual for the 806 observed r e f l e c t i o n s . C. Structure Analysis The arsenic position was determined from the three axial Patterson projections, and the carbon and oxygen atoms were located on a three-dimensional electron-density d i s t r i b u t i o n computed with signs based on the arsenic contributions alone. The map could be interpreted i n terms of space group P l . Structure factors were calculated using standard scattering 1 °2 factors , and an isotropic temperature factor, B = 4.OA for a l l atoms. The discrepancy fac tor , R = ^ - l F 0 ~ F c l / 2 F Q was 0.270 for the observed r e f l e c t i o n s . The positional and thermal parameters, and an overall scale factor, were refined by (block—diagonal) least-squares; the function minimized was 2 w ( F - P ) , with s/w = IF | /l8 o c ' o when |F q|<18, and V"w = 18/|FJ when | F Q| ^  18. Three cycles with isotropic thermal parameters and three cycles with aniso-tropic thermal parameters completed the refinement. R, for the 806 observed r e f l e c t i o n s , was reduced from 0.270 to 0.149, and A F was reduced from 6.9 x 10 to 2.9 x 10 . F i n a l measured and calculated structure factors are l i s t e d i n Table 1, and a f i n a l electron density d i s t r i b u t i o n i s shown i n F i g . 1 Co-ordinates and Molecular Dimensions The f i n a l positional and anisotropic thermal parameters are given i n Table 2. x, y and z are f r a c t i o n a l co-ordinates referred to the t r i c l i n i c c r y s t a l axes; <f (x), ^ ( y ) , and C^(z) o are their standard deviations (in A) computed from the l e a s t -squares residuals (see Appendix); X', J\ and Z' are co-ordinat i n A referred to orthogonal axes a' (= a.sincf), b, and c* (normal to a' and b); b.. are the thermal parameters i n the expression: exp - ^b-j^-j^h2 + b 1 2hk + b 1 3 h £ + b 2 2 k 2 + b 2 3 k ^ + b^C2 "j. and are the components of the mean—square vibratio n tensors The bond lengths and valency angles i n the molecule are given, with their standard deviations, i n Table 3. The shorter intermolecular contacts are l i s t e d i n Table 4, and the packing of the molecules i s shown i n F i g . 2. o i zK P i g . 1» Superimposed sections of the three-dimensional electron—density-d i s t r i b u t i o n through the atomic centres p a r a l l e l to. (OOl), contours at arbitrary i n t e r v a l s , arsenic omitted for c l a r i t y . A perspective drawing of the molecule i s also shown. 5 Table 1 Pinal measured and calculated structure factors, h> k » * > Fobs. a n d F c a l c . respectively. Columns are 0 0 l 2 7.3 34.2 0 0 2 45.2 - 4 9 . 2 0 0 1 2 3.7 - 3 0 . 7" 0 0 4 1.6 - 0 . 8 0 0 5 9.8 11.9 0 0 6 9.3 11.3 0 0 7 0 . - 0 . 3 0 0 8 6.6 - 8 . 1 0 1 - 7 2 .9 "3.0 a 1 -6 9.6 11.5 0 1 - 5 5 .6 7.6 0 1 -4 13.2 - 1 6 . 6 0 1 - 3 55.4 - 4 4 . 5 0 1 -2 18.0 - 2 3 . 1 0 1 -1 48 .2 52.7 0 1 0 74.1 74.3 0 1 1 13.3 8.0 0 1 7 8. 3 - 5 . 9 0 1 8 8.4 - 9 . 1 0 2 - 7 3.2 4 .6 0 2 -6 ' 9 . ; " 1 1 . 0 0 2 - 5 5.0 5.1 0 2 -4 27 .5 - ? 5 . 4 0 2 -3 37 .7 - 4 1 . 7 0 2 -2 2.5 3.4 0 2 -1 45 .4 50.0 o ' 2" 0 17.5 22 .9 0 2 1 20 .6 - 1 8 . 1 0 2 2 37.6 - 2 9 . 1 0 2 3 17. 3 - 1 2 . 4 0 2 4 22.0 19.0 0 2 5 31 .9 26.2 0 2 6 9 .3 7.1 0 2 7 10.1 - 8 . 3 0 2 8 9 .0 - 8 . 4 0 3 -6 8.4 8.6 0 3 - 5 2.0 - 2 . 1 0 3 -4 19.2 - 2 0 . 4 0 3 - 3 2 3.8 - 2 1 . 2 0 3 -2 8.7 9.3 0 3 -1 42 . 3 34. 1 0 3 0 12.8 10.2 0 3 1 40.3 - 3 4 . 0 0 3 2 44 .9 - 3 5 . 9 "0" 3 3 1.7 1 ; r 0 3 4 29.4 24 .9 0 3 5 20.1 18.8 0 3 6 3.4 2 .5 0 3 7 8.1 - 7 . 8 0 4 - 6 3.5 5.3 0 4 - 5 5. 3 - 6 . 6 0 4 -4 13. 1 - 1 3 . 9 0 4 -3 4.5 - 3 . 5 0 4 -2 16.1 14.8 0 4 -1 19.3 20 .5 0 4 0 0 . - 1 . 8 0 4 1 37.3 - 3 2 . 8 0 4 2 30.4 - 2 6 . 6 0 4 3 6.2 6.2 0 4 4 25.5 20.2 0 4 5 16.2 12. 1 0 4 6 2.5 - 1 . 7 0 4 7 10.2 - 9 . 2 0 5 - 5 4 .6 - 5 . 7 0 5 -4 15.4 - 9 . 4 0 5 -3 2.6 2.7 0 S -2 18.0 19.3 0 5 -1 16.5 13.1 0 5 0 14.4 - 1 2 . 5 0 5 1 31.3 - 2 3 . 7 0 5 2 11.7 - 1 0 . 8 0 5 3 6.4 6.2 0 5 4 16.7 13.9 0 5 5 8.8 7.3" 0 5 6 6.8 - 6 . 9 0 6 -3 3.4 4.7 0 6 -2 13.3 14.6 0 6 -1 7.9 6. 7 0 6 0 14.8 -11 .8 0 6 1 16:7 - 1 5 . 0 0 6 2 3.1 - 3 . 0 0 6 3 8.7 8.7 0 6 4 8.6 11.0 0 7 0 5.8 - 7 . 4 0 7 1 7.7 - 8 . 4 0 1 2 27.4 -36.6" 0 I 3 15.6 - 2 2 . 4 0 1 4 6.4 9 .5 0 1 5 18.2 23.0 0 1 b 9.3 10.6 0 I -8 2 .6 - 4 . 6 0 3 -7 4 .3 6.6 V 0 1 19.9 - 2 6 . 4 1 0 2 21.6 -37 .1 1 0 3 1.7 - 3 . 9 1 0 4 28.8 26.5 1 0 5 24.8 25 .9 1 b 6 0. 1.9 1 0 7 10.4 - 1 2 . 7 1 0 8 6 .5 - 7 . 8 1 0 - 8 0. 0.1 1 0 - 7 9 .6 9.8 1 0 - 6 10.7 9.1 1 0 - 5 6.1 - 7 . 7 1 0 -4 27. 1 - 2 7 . 1 1 0 - 3 27.4 - 3 1 . 3 1 0 -2 0. 3 .0 1 0 -1 56.9 58.4 1 0 0 35.7 40.4 1 1 - 7 9.2 10.4 1 1 - 6 5.6 5 .0 1 1 -5 9 .0 - 1 0 . 3 1 1 - 4 25.2 -24 .4 1 1 -3 22 .9 - 2 4 . 7 1 1 -2 5 .6 10.4 1 1 -1 42.9 52.3 1 1 0 10.2 13.5 1 1 1 50.8 - 5 6 . 1 1 1 2 44 . 5 - 4 5 . 6 1 1 3 10.4 12.2 1 1 4 35.6 41 .5 1 1 5 21.4 23.7 1 1 6 8. 1 - 5 . 8 1 1 7 12.0 - 1 2 . 8 1 1 8 3 .7 - 4 . 0 1 2 - 7 8.7 9.1 1 2 " -6 4 . 2 4. 1 1 2 - 5 11.4 - 1 2 . 9 1 2 - 4 16.4 - 2 1 . 7 1 2 -3 0. - 0 . 9 1 2 -2 19.1 25.5 1 2 -1 15.4 20.9 1 2 0 6 .7 - 1 1 . 6 1 2 1 46.6 - 5 5 . 9 1 2 2 54.7 - 4 9 .4 1 2 3 16.4 20.6 1 2 4 35. 1 46 .0 1 2 5 13.8 12.1 1 2 6 17.9 -13.1" 1 2 7 10.4 - 9 . 5 1 2 8 0 . - 0 . 1 1 3 - 7 5.0 6.0 1 3 -6 2 .2 0.6 1 3 - 5 10.7 - 1 1 . 3 1 3 - 4 12.0 -12.8" 1 3 -3 9 .7 9.8 1 3 -2 29 .0 32.5 1 3 -1 15.3 17.3 1 3 0 31.4 - 3 1 . 5 1 3 1 64 .9 - 5 8 . 7 1 3 " 2" 25T4 - 2 1 . 3 1 3 3 45.2 30.7 1 3 4 36.4 , 27 .6 1 3 5 0 . - 2 . 3 1 3 6 14.6 - 1 3 . 7 1 3 7 8 .6 - 7 . 6 1 3 8 0 . 2 .0 1 4 - 6 2 .8 - 4 . 2 1 4 - 5 8.8 - 8 . 4 1 4 - 4 3.6 - 2 .4 1 4 - 3 11.3 12. 1 1 4 -2 29. 7 27 .5 1 4 -1 14.0 13.8 1 4 0 35.4 - 3 4 . 1 1 4 1 51.8 - 4 3 . 8 1 4 2 8.3 5.2 1 4 3 37.1 30.0 1 4 4 11.0 9.7 1 4 " 5 " "10.8 - 10'. 1 1 4 6 12.3 -14 .1 1 4 7 6.2 - 6 . 9 1 4 8 0.5 4 . 7 1 5 - 5 5.5 - 7 .4 1 5 -4 0. 1.7 1 5 - 3 17.4 15.4 1 5 -2 19.5 17.9 1 5 -1 0. - 2 . 0 I 5 0 31.0 - 2 5 . 3 1 5 1 19.9 - 1 6 . 3 i 5 2 14.2 13.7 1 5 3 22 .9 21.5 1 5 4 ' 5.7 4 . 6 1 5 5 12.4 -13 .1 1 5 6 14.7 - 1 5 . 8 1 5 7 2.0 - 3 . 5 I 6 - 3 15.9 13.7 1 6 -2 10.2 9.4 1 6 -1 12.4 -11 .1 1 6 0 21.6 - 1 7 . 1 1 6 1 0. - 0 . 0 1 6 2 16. 1 15.9 1 6 V 14.0 """ 15.7 1 6 4 2. 3 0.8 1 6 5 12.6 - 1 4 .4 1 6 6 9.0 - 1 1 . 9 I 7 -2 1.1 2.0 1 7 -1 9 .9 - 9 . 7 " 1 7 " 0 "" "9.2 - 1 0 . 9 1 7 1 3.4 3.4 1 7 2 13.7 16.0 1 7 1 10.4 11.4 I 7 4 4 . 3 - 4 . 5 1 -1 8 0. - 7 . 8 1 -1 1 9.2 - 8 . 5 " 1 -1 b 3.5 3 .9 I -1 5 20.4 21.2 11.5 27.9 37.0 2~2"."2 48 .6 19.6 1.6 16.3 21. 1 15.2 -25 .4 - 3 9 . 2 ~ f 7 3 ~ 55.8 30.6 2.9 -21 .1 - 2 6 . 9 3.5 12.8 6 .0 3.2 3 .6 5.1 - 2 . 5 14.8 6 .7 - 4 . 6 - 3 . 5 6.2 14.6 0. 29 .9 24 .9 18.4 39.1 " 15.8 1.9 18.3 12.2 5.7 T l . 7 " 0. 8.1 9.1 9.2 21 .5 1.0 - 3 0 . 2 - 2 8 . 2 21.2 44.6 23.7 - 2 . 8 - 2 2 . 4 - 1 5 . 7 9 .0 14.9 2 .0 9 .2 7.6 - 1 1 . 0 - 2 3 . 2 9.1 9 .9 23.0 19.6 8. 1 J.8-3_ 2 .5 12.1 7.0 3 .5 10.1 12.0 - 1 0 . 7 11.6 26.6 18.8 - 1 2 . 5 -24 .3 2.6 11.3 14.4 3.5 11.9 11.4 - 5 - 5 - 5 - 5 - 5 -5 - 5 3 .5 10. 1 5.6 5.6 8.8 _ _ 0 . 1173 9 .5 6.0 11.6 4 .6 5. I 8. 7 2.1 7.7 3.1 6 .5 8.8 1.5 26 .9 25.5 10.3 14.8 32.8 12.6 15.3 14.8 2. 7 10.9 0. 18.3 18.1 9 .1 24.6 2 .6 7.2 3.4 17.4 10.6 22.8 30.2 10.1 41.4 34.9 7.6 21 .7 33 .9 18.4 8.2 7. 3 2.8 8.6 - 1 . 4 17.0 11.5 3 .7 - 1 1 . 4 ^16.8 -37 0 12.8 16.2 1.9 - 1 7 . 9 - 1 5 . 6 " 5.5" 16.1 8.8 - 6 . 9 - 9 . 8 0.1 13.9 9.8 - 9 . 2 -17 .1 - 7 . 1 7.5 7 1 12 9.6 3.7 - 9 . 3 - 1 3 . 0 - 3 . 2 - 3 0 . 5 - 3 7 . I - 1 4 . 3 18.7 32.2 11.0 - 1 1 . 8 - 1 0 . 3 1.7 9 .3 - 0 . 9 - 1 8 . 2 -18 .4 8 .5 28.9 7. 1 5.8 - 3 . 7 - 1 4 . 9 - 1 0 . 5 19.6 36.5 - 7 . 9 - 5 4 . 3 - 4 0 . 0 - 9 . 8 22.5 30.7 1.2 - 1 8 . 1 - 6 . 7 6 .5 2 .7 2 2 - 5 15.0 - 1 2 . 3 2 2 -4 5.2 4 .8 2 2 - 3 26 .7 27.2 2 2 -2 19.6 22.9 2 2 -1 6.0 - 6 . 4 2 2 0 34.6 - 4 0 . 1 2 2 1 56.3 - 5 0 . 7 2 2 2 5.1 - 4 . 7 2 2 3 38.3 39.0 2 2 4 17.9 17.7 2 2 5 23.1 - 1 9 . 2 2 2 6 21.2 - 1 9 . 5 2 2 1 0. - 0 . 9 2 2 8 10.2 8.8 2 3 -6 10.8 - 9 . 6 2 3 - 5 11.5 - 9 . 3 2 3 -4 14.7 12.2 2 3 -3 28.2 28.3 "2 3 " -2 "'" 12."8 13.3 2 3 -1 8.0 - 9 . 5 2 3 0 25. 1 - 2 9 . 5 2 3 1 37.2 - 3 0 . 5 2 3 2 18.6 15.6 2 3 3 50.3 38.4 2 3 4 0 . - 0 . 3 2 3 5 32.0 - 2 8 . 4 2 3 6 21.2 - 1 8 . 0 2 3 7 4 .5 2.0 2 3 8 13.1 10.2 2 4 - 6 9 .0 - 7 . 8 2 4 - 5 5.1 " - 4 . 0 2 4 -4 13.7 9.6 2 4 -3 21 .9 20.7 2 4 -2 13.4 12.0 2 4 -1 17.2 - 1 7 . 6 2 4 0 34.1 - 2 9 . 7 "2" 4 1 0 . 2.8 2 4 2 46.2 35. 3 2 4 3 32. 1 22 .6 2 4 4 14.2 - 1 1 . 6 2 4 5 29. 7 - 2 6 . 2 "2 4 "6 "15.1 - 1 4 . 9 2 4 7 7.2 4 .7 2 4 8 13.1 10.5 2 5 - 5 0. 0.2 2 5 -4 8.5 8.2 2 5 -3 14.9 11.1 2 5 -2 5.0 1.8 2 5 -1 22.6 - 1 8 . 7 2 5 0 22.8 - 1 8 . 8 2 5 1 16.6 15. 7 2 5 2 47.8 35.6 2 5 3 16.0 14.5 2" 5 4 18.2 -15 .1 2 5 5 27.8 -23 .1 2 5 6 6.4 - 6 . 9 2 5 7 10.4 9.4 2 6 -4 10.0 8.7 2 6 -3 5.6 5 . 1 "i" 6 -2 8.9 - 9 . 5 2 6 -1 21.1 - 1 6 . 5 2 6 0 5.6 - 4 . 8 2 6 1 21.2 15.9 2 6 2 30.0 24.9 2 6 3 9 .3 8.2 2 6 4 22 .9 - 1 6 . 4 2 6 5 21.0 - 1 6 . 4 2 6 6 3.1 2.9 2 7 -2 11.6 - 1 0 . 5 2 7 -1 15.0 - 1 3 . 3 2 7 0 0 . 0 .5 2 7 1 19. 1 15.6 2 7 2 1 7. 7 15. 1 2 7 3 3.7 - 2 . 5 2 7 4 17.3 - 1 5 . 3 2 7 5 6.2 - 6 . 3 2 8 3 7.8 - 8 . 8 2 6 2 7.1 6 .7 2 8 1 13.8 12.8 2 -1 - 7 9 .3 9.9 2 -1 -6 3.3 3.0 2 -1 -5 16.8 - 1 6 . 9 2 -1 -4 20.7 - 2 1 . 9 2 -1 -3 2.1 - 2 . 7 2 -1 -2 22.3 19.9 2 -1 -1 21.1 25.6 2 -I 0 5.4 - 1 . 5 2 -1 1 28.4 - 3 3 . 4 2 -1 2 14.5 - 1 8 . 1 2 -1 3 '15.0 16.7 2 -1 4 28.2 25.2 2 -1 5 11.7 10.9 2 - 1 6 8.8 - 5 . 1 2 -1 7 12.6 - 9 . 7 2 -2 - 7 6. 1 7.1 2 "-2" - 6 8 . 1" "7.6 2 -2 - 5 6.0 - 8 . 6 2 -2 -4 21.0 - 2 4 . 5 2 -2 - 3 11.5 - 1 1 . 1 2 -2 -2 20 .7 20.9 Table 1 - Continued 6 2 -2 -1 27.5 29.6 2 -2 0 3.5 6. 7 2 -2 1 23.2 -17.1 2 -2 2 16.2 -16.2 2 -2 3 tt. 1 2.4 2 -2 tt 17.5 15.3 2 -2 5 9.6 10.9 2 -2 6 0. -1 .7 2 -2 7 7.4 -7 .9 2 -3 -6 7.7 B . 7 2 -3 -5 0. - 0 . 1 2 -3 -4 15. 1 -18.5 2 -3 -3 15.0 -14.9 2 -3 -2 .12. B 13.3 2 -3 -1 30.7 25.3 2 -3 0 11.2 11.3 2 -3 I 8.0 -5 .9 2 -3 2 16.7 -15.2 2 " -3 3 6. 1 -8 . 3 2 -3 tt 9. 1 7. 7 2 -3 5 13.9 10.1 2 -3 6 0. 0.2 2 -4 -5 3.3 4.2 2 -4 -tt 7.2 -8.0 2 "-tt ~ i ' 12.7 -14. 1 2 -4 -2 0. 0.1 2 -4 -1 18.1 18.7 2 -tt 0 17. 3 15.7 2 -tt 1 3.5 - 3 . 1 2 -tt 2 15.8 -14.0 2 -tt'" "3" 8.3 - a . 6 2 -tt * 3.5 2.3 2 -5 -3 10.7 - l o . a 2 -5 -2 6.5 -6.3 2 -5 -1 9. 1 9.6 2 -5 0 14.5 13. 3 2 -5 ' 1 0. " -0 .0 2 -5 2 10. 1 -9.1 3 0 0 46.0 -43.2 3 0 1 11.5 - 18.2 J 0 2 15.5 16.9 3 0 3 16.8 20.2 3 0 tt 1.7 3.3 3 0 5 11.0 -10.9 3 0 6 9.8 -10.3 3 0 7 2.0 0.8 3 1 -5 8.3 -7.1 3 1 -4 12.2 12.8 3 i -3 32.5 •" 32.1 3 1 -2 B . 6 8.2 3 1 -1 33.7 -34. 1 3 I 0 25.7 -29.3 3 1 1 4.5 -0 .5 3 I 2 12.9 14.6 3 1 3 12.3 16.6 3 1 tt 4.2 - 3 . 1 3 1 5 22.4 -21.3 3 1 6 12. 1 -12.5 3 1 7 5.3 5. 3 3 1 e a.2 9.4 3 2 -6 9.5 -8.5 3 2 -5 4.5 -2.4 3 2 -tt 16.a 1 7.0 3 2 -3 29.4 26. 7 3 2 -2 0. 0.3 3 2 - I 32. 1 -31.5 3 2 0 13.6 -19.3 3 2 1 21.a 15.5 3 2 2 19.9 29.2 3 2 3 a.o 11. 1 3 2 18.5 -17.7 3 2 5 26.5 -25.7 3 2 6 7.2 -9.2 3 2 7 7.5 7.3 2 8 7.9 9.1 3 -6 9.0 -7 .9 3 -5 1.8 3.6 3 -tt 16.0 16.9 3 -3 11.1 10.9 3 -2 9.1 - B . 6 3 -1 22. 1 -20. 1 3 0 1 5.8 21.a -10.3 25.8 "'3 2 38.2 42.0 3 3 3.9 6.4 23.4 -26.5 3 5 22.6 -23. 1 3 6 1.9 -3.8 3 7 11.7 9.3 3 B 7.8 7. 7 4 -6 5.3 -4.8 <t -5 4.3 5.0 -tt 12.9 13.7 4 -3 i . a 2.8 -2 20.2 -19.0 4 -1 22. 1 -20.5 0 1 6.2 36.6 6.1 33.1 2 30.5 29.7 3 0. 0.7 tt 25. 3 -21.8 tt 5 20. 7 -17.8 tt 6 2.6 2.7 I 7 a 17.5 4.3 13.5 4.5 5 -5 5.1 5.0 5 -tt 8.7 7.8 5 -3 0. -1 .5 5 -2 21.6 -20.5 5 -1 18.9 -18.9 5 0 13.3 12.8 5 1 33. 1 31.0 5 2 16.9 16.0 5 3 7.3 -6 .3 3 5 4 22. > -18.7 3 5 5 11.0 -9.1 3 5 6 12.7 12. 1 3 5 7 15.8 14.5 3 6 -4 3.9 3.5 3 6 -3 6.6 -7.1 3 6 -2 16.2 -15.0 3 6 -1 18.7 -8 .6 3 6 0 '9.8 9 .7 3 6 1 22.5 20.0 3 6 2 10. 7 8.4 3 6 3 15.0 -14. 1 3 6 4 20.9 -18.7 3 6 5 0. 2.1 3 6 6 1 7.6 17.9 3 6 7 7.2 . 9.9 3 7 -3 9.4 - a . 4 3 7 -2 10.6 - 1 0 . 5 3 7 -1 0. - 0 . 2 3 7 0 10.2 9 . 9 3 7 1 11.7 1 1 . 2 3 7 2 1.8 - 1 . 3 3 7 3 16.0 - 1 7 . 7 3 7 4 12.9 -12.4 3 7 5 6.9 8.7 3 7 6 12.5 15.0 3 8 0 11.4 11.0 3 a 1 7 .2 6.2 3 a '2" 9.0 - 9 . 1 3 a 3 15.3 -15. 3 3 - l 7 1.7 -2.8 3 - i 6 7.3 - / . 6 3 - l 5 4.8 - 3 . 1 3 - l 4 5.2 8.2 3 - i 3 "" 18.3 20.2 3 - l 2 11.2 12.7 3 - i 1 20.9 -22. 7 3 - l 0 32.4 -36.1 3 -2 0 15.7 - 1 6 .a 3 -2 1 19.3 -18.8 3 " -2 2 0. 0.2 3 -2 3 15.0 16. 7 3 -2 4 10.0 12.9 3 -2 5 0. - 0 . 3 3 -2 6 6. 1 -6 .5 3 -3 4 11.9 11.4 "3" -3" "3' "8.6 10.3 3 -3 2 5.7 -5.6 3 -3 1 14.0 -14.8 3 -3 0 4. 7 -5 .0 3 -3 - I 8.0 10.3 3 -3 -2 10.5 13. 7 3 - 3 -3 0". " 1.6 3 -3 -4 8.0 -10.4 3 -3 -5 .6.5 -8 .5 3 -4 -4 ] 5 .1 -8.6 3 -4 -3 2.6 -3.2 3 -4 -2 7. 3 10.0 3 -4 -1 12.3 12.9 3 -4 0 2.3 -0.3 3 -4 1 10.0 -10.3 3 -4 2 5.2 -5.8 3 -tt 3 3.2 3.4 3 -1 -1 2.2 -4.4 3 -1 -2 20.0 20. 7 3 -1 -3 10.7 13.1 3 -1 -4 2.7 - 3 . 7 3 -1 -5 a . i -10 . 7 3 -1 -6 2 . 9 -5.3 3 -2 -6 0 . -2.2 3 -2 -5 7.8 -11.9 3 -2 -4 5.2 -8 .9 3 - 2 -3 5.4 8.3 3 -2 -2 13.3 17.0 3 -2 -1 2.6 3.3 3 2 - 7 3.6 -4.1 3 0 -7 0. 0.5 3 0 -6 7.5 -7 .5 3 0 -5 .a.o -8.4 3 0 -4 3.8 4.7 3 0 -3 2 0 . 7 22. 1 ... ^ _ - j ~"18.4 17.9 3 0 -1 15.2 -18.2 3 1 -6 7.7 -8.2 4 -3 -3 6.7 7.0 4 -3 -2 4.0 5.5 4 -3 -1 2.5 -4 .0 4" -3 "0 9.9 - 1 1 . 3 4 — 3 1 6.1 -6.2 4 -3 2 4.6 5.7 4 -3 3 8.6 9.3 4 0 0 11.6 -14.0 4 0 1 13.0 15. 1 4 0 — j - '" 19. 1 "19:5 4 0 3 2.3 -0.1 4 0 4 1 2 . a -14.6 4 0 5 1 0 . 9 -12.9 4 0 6 0 . -1.6 4 0 7 5.8 6.5 4 1' 7 7 . 7 7.7 4 1 6 5.2 3.0 4 1 5 12.0 -14.5 4 1 4 22.6 -23. 1 4 1 3 2.5 -3 .6 4 1 2 19.0 23.3 4 ~"i ...... 16.7 " 23.0 4 i 0 0. -0 .9 4 i -1 19.1 -18.5 4 i -2 8.2 -10.9 4 i -3 7.4 8.2 4 l -4 12.4 13.8 "4 ""7 ~"7".7 7.6 4 2 6 8.2 7.0 4 2 5 6.2 -8.8 4 2 4 24.0 -24.0 4 2 3 12. 1 -10.2 4 2 2 16.5 20.8 4 2 1 33.6 32.5 tt 2 0 11.7 14. 1 4 2 - 1 17.3 -14.8 4 2 - 2 21.3 -20.3 4 2 - 3 0. 0.4 4 2" - 4 14. 3 13~.0 4 2 - 5 5.6 6. 1 4 3 7 8.0 8.0 4 3 6 9.4 10.3 4 3 5 2.4 1 . 5 4 3 4 14.2 -15.9 ' 4 ' 3 . . . . . . 15.2" -20. 1 4 3 2 6.0 11.1 4 3 1 32. 1 40. 1 4 3 0 14.5 20.5 4 3 -I 13.1 -15.0 4 3 -2 20. 1 -21.3 4 3 -3 5.0 -6 .0 4 3 -4 6.5 6.4 4 3 -5 6.3 7.0 4 4 8 5.3 -5.1 4 4 7 8.2 8.3 4 4 6 16. 1 15.9 ' 4" 4 5 " 7. 7 8.2 4 4 4 9.9 -10.1 4 4 3 22.9 -20.8 4 4 2 4.3 -1 .2 4 4 1 20.8 27.a 4 4 0 17.B 21.5 4 "4 -1 6.5 -6 .5 4 4 -2 20.4 -19. 1 4 4 -3 11.1 -12.3 4 4 -4 1.7 1.4 4 4 -5 7.9 7.7 4 5 7 4.3 4.9 4 5 6 18.7 19. 1 4 5 5 11.1 13.0 4 5 4 8.3 -7 .2 4 5 3 18.5 -18. 1 4 5 2 11.1 -12.1 4 5 1 7.7 8. 1 "4 '"" 5" "0 21.0 11.3 4 5 - 1 4.0 5.2 4 5 -2 17.5 -16.6 4 5 -3 14.2 -14.2 4 5 -4 0. 0.5 4 5 -5 6.9 6.5 "4 '6 7 0." -0 .6 4 6 6 13.4 14.2 4 6 5 15. 1 16.5 4 6 4 1.7 -1 .7 4 6 3 19.4 -19.5 4 6 2 18.3 -18.3 ' 4 6 "1 0. " 0.9 4 6 0 18.0 16.3 4 6 -1 9.2 a.6 4 - z 9.3 - a . 5 4 6 -3 12.7 -10.2 4 -4 0. -1 .7 4 7 6 6.1 6 .4 4 7 5 15.0 14.7 4 7 4 4.7 4.4 4 7 3 16.9 -16.1 4 7 2 17.8 -18.4 4 7 1 2.4 -1 .7 4 7 0 9.7 10.4 4 7 -1 10.1 9. 1 4 7 -2 0. 0.5 4 7 -3 6.8 -6.2 4 8 5 7.0 9. 7 4 8 4 5.9 6.8 4 8 3 5.4 -6 .9 4 8 2 14.5 -14.3 4 8 1 5. 7 -6 .3 4 8 0 6. 1 6.2 4 8 -1 9. 7 10.3 4 -1 0 14.4 -17.3 4 -1 1 2.4 2. 1 4 - I 2 13.6 14.6 4 -1 3 5.2 6.9 4 -1 4 6.6 -6.3 4 -1 5 9.4 -10. 1 4 ' - i " 6 2.9 -3.2 4 - 2 1 6.0 -6.2 4 - 2 2 9.9 10.3 4 -2 3 10.2 1 1.4 4 -2 4 0. -1.2 4 - 2 5 7.8 -7 .0 4 0 -6 3.1 -4 .2 4 0 -5 2.6 2. 1 4 0 -4 7.9 10.8 4 0 -3 1 0 . a 13.5 4 0 -2 0. -1 .5 4 0 -1 16.4 -22.6 4 1 -5 3.9 4.6 4 1 -6 4. 1 -4 .0 4 - I -5 0. -0 .7 4 -1 -4 6.8 a.7 4 -1 -3 9.0 12.4 4 -1 - 2 0. 1.4 "4" -1 -1 "12.7 "-16.6 4 - 2 0 12.4 -15.4 4 - 2 -5 1.4 -3.3 4 - 2 -4 7.3 5.2 4 - 2 -3 9.0 9.3 4 - 2 -2 4.1 3.0 "4~" - 2 " -1 6;t -8.4 5 0 1 15.0 15.2 5 0 2 4.4 4.9 5 0' 3 6.6 -7.8 5 0 4 11.1 -11.6 5 0 5 2.6 -3 .7 5 0 6 6.0 5. 1 5 1 6 11.4 a . 3 5 1 5 4 . 3 2 . 7 5 1 4 11.9 - 1 1 . 2 5 1 3 12.4 -13.5 5 1 2 3 . a 3.4 5 1 I 15.0 19.4 5 1 0 a.2 15. 1 5 2 7 2. 1 1 .0 5 2 6 14.4 10.9 5 2 5 12.3 10.9 5 2 4 7.9 -6.6 5 2 3 18.4 -17.  5 2 2 1.5 -1.4 5 2 1 10.5 17.9 5 2 -1 1.8 2.3 5 2 -2 10.6 -10.9 5 2 -3 17.2 -12.2 5 2 - 4 4 . 2 -1.3 5 3 7 0. 0.3 5 3 6 13.4 11.7 5 3 5 16.2 15.4 5 3 4 0. 2.0 5 3 3 18.0 -16.5 5 3 2 '9.2 -14.4 5 3 0 17.2 19.4 5 3 -1 4.5 6.6 5 3 -2 12.2 -10.8 5 3 -3 15.4 -13.3 5 3 -4 ' "" 5.1 -3.2 5 3 -5 6.0 4.4 5 4 7 4. 7 -2.4 5 4 6 10.3 10.3 5 4 5 20.9 1 7.2 5 4 4 7.7 7.8 5 4 3 12.0 -14.3 5 4 2 25.2 -24.8 5 4 1 0. -3.3 5 4 0 17.0 17.9 5 4 -1 7.9 9.5 5 4 -2 7.0 -6.8 5 ' ' 4 -3 10.3 -9 .8 5 4 -4 5. 3 -4.6 5 4 -5 2.1 1.9 5 5 7 9 . a -7.0 5 5 6 4 . 5 5.1 5 5 5 2 1 . 3 17. 1 5" 5 "4 '" 1 2 . 4 9.4 5 5 3 13. 1 -12.5 5 5 2 24.0 -23.0 5 5 1 8.9 -10.3 5 5 0 9.9 8.9 5 5 - 1 13.4 13.2 5 " 5" - 2 0. 2.5 5 5 -3 a.8 -7 .3 5 5 -4 6.9 -6.2 5 6 7 8.9 -9.3 5 6 6 3 . 6 -2.4 5 6 5 12.8 12.0 5 "6 " 4 14.1 11.7 5 6 3 4.4 -5.8 5 6 2 18.0 -18.6 5 6 1 15.8 -14.2 5 6 0 4.9 3.2 5 6 - I 17.6 14.9 5 6 -2 7. 7 7.5 5 6 -3 6.2 -4 .9 5 6 -4 6.4 -5 .5 5 7 6 7.4 -7.1 S 7 5 4.4 4.7 5 7 4 15.2 13.3 5 7 3 4 . 8 3.5 5 7 2 16.8 -13.5 5 7 1 16.4 -13.7 5 7 0 3.0 1.7 5 7 -1 14.0 11.4 5" " 7 -2 '9. 7" 7.1 5 a 4 1 0 . a 11.2 5 8 3 a.6 a.3 5 8 2 6.2 -5.6 5 8 1 12.2 -10.4 5 a 0 2.8 -2.0 5 8 -1 7.4 5.8 5 -1 5 4.8 -4.8 5 -1 4 10.8 -10.1 5 -1 3 4.0 -4.3 5 -1 2 6.4 7 .3 5 -1 1 10.9 10.2 5"' -1 0" " i . e ""1.4" 5 -1 -1 6.4 -7.2 5 -1 -2 9.4 -6 .6 5 -1 -3 3.2 0.9 5 - I - 4 8. 3 6.4 5 -2 3 0. -1.2 5 -2 2 9.5" 7.0 5 -2 1 7.6 5.9 5 -2 0 0. -3.3 5 -2 -1 8.5 -7 .7 5 -2 -2 4. 7 -3 .7 5 0 0 10.5 10.2 5 0 -5 6. 1 4.9 5 0 -4 5.5 5.9 5 0 -3 3.7 -1 .7 5 0 -2 12.1 -10.9 5 0 -1 3.H -5 .8 5 1 -1 0. -2.8 5 "1 -2 12.3 -12.2 5 1 -3 8.5 -6.4 5 1 - 4 0. 2.8 5 1 -5 7.2 5. 3 5 2 0 12.8 16.1 5 2 -5 0. 1 5.8 7 Table 2 Pinal p o s i t i o n a l parameters (fractional) with standard deviations, and temperature factors. Atom X y z <T ( x ) *(y) < ^ ( z A s ( l ) 0.1667 0.0602 0.1785 0.007A 0.006A 0.006A C(2) 0.4072 -0.2732 0.2794 0.066 0.056 0.068 C(3) 0.1953 0.2660 0.3049 0.069 0.057 0.054 0(4) 0.1879 0.1290 -0.0726 0.033 0.030 0.030 0(5) -0.1089 0.1157 0.2543 0.060 0.047 0.043 Atom X' T' Z' As ( l ) 0.997A 0 1.288A 1.147A C(2) 2.345 0.059 1.795 C(3) 1.223 2.978 1.959 Q(4) 0.966 1.477 -0.466 0(5) -0.437 0.746 1.634 Atom b l l b12 b13 b22 b23 b32 i x 104 A s ( l ) 325 • -268 - 82 183 -118 192 C(2) 452 --426 -110 250 160 381 0(3) 629 • -414 -114 320 -273 251 0(4) 398 --3 57 -140 272 - 71 200 0(5) 700 • -420 -232 304 -263 222 Atom U l l u 1 2 u 1 3 u 2 2 U23 U 3 3 x 10 2 A s ( l ) 5.09 -2.00 -0. 71 2.85 -1.06 4.00A^ C(2) 6.53 -3.20 -0.95 3.89 1.45 7.97 C(3) 9.10 -3.10 -0. 99 4.98 -2.46 5.24 0(4) 5.75 -2.68 -1. 21 4.23 -0.64 4.18 0(5) 10.12 -3.15 -2.02 4.73 -2.37 4.63 D. Discussion The analysis has established that the arsenic atom i n cacodylic acid has the expected tetrahedral configuration. The As-C bond lengths do not d i f f e r s i g n i f i c a n t l y , and the mean o value of 1.91 + 0.04A i s not s i g n i f i c a n t l y d i f f e r e n t from the v 0 usual As-C distance (1.955 + 0.018A i n (Me 2AsS) 2 for 2 example ). The As-0 bond lengths are also, surprisingly, equal within experimental error, the mean value being 1.62 + 0.03A. Although information about As—0 bond lengths i s sparse, p a r t i c u l a r l y for As , this value i s comparable to that reported for the As V-0 4and for the A s 1 1 1 — 0 single bonds 3. angles, and standard deviations Bond distances As(l)-C(2) As(l)-C(3) As(l)-0(4) As(l)-0(5) 0(4)...(5') Table 3 o (A) and valency 1.937 ± 0.06 1.890 + 0.06 1.625 ± 0.03 1.609 + 0.05 2.567 + 0.06 C(2)-As(l)-C(3) C(2)-As(l)-0(4) C(2)-As(l.)-0(5) C(3)-As(l)-0(4) C(3)-As(l)-0(5) 0(4)-As(l)-0(5) 109.9° + 2.5° 114.8 + 2.0 107.8 + 2.3 109.0 + 2.0 106.1 + 2.3 108.9- +1.8 The cr y s t a l isi b u i l t up from centrosymmetrical hydrogen-o bonded dimers (Pig. 2), with 0-H...0 = 2.57A, so that the structure i s similar to that of carboxylic acids, rather than to arsonic acids, RAsO^H^, where the two replaceable hydrogen atoms give r i s e to more complex hydrogen bonding schemes 4 involving endless chains of molecules • The fact that the 9 As—0 bond lengths i n cacodylic acid are found to be equivalent could imply a more completely resonating structure than i n carboxylic acids. However, another p o s s i b i l i t y i s that the difference between the As=0 and As-0 bond lengths i s too small to be detected in th i s analysis. This seems the more l i k e l y explanation i n the l i g h t of covalent r a d i i measurements^. A l l the other intermolecular contacts correspond to 5 van der Yaals interactions , the shortest involving oxygen atoms (Table 4); the shortest As...As and C»*.C contacts are o o 3.98A and 3.88A. Table 4 Shorter intermolecular distances ( A l l distances ^ 4A between molecule 1 and neighbouring molecules were calculated; only contacts 0 < 3.5A are l i s t e d ) . Atom (in molecule l ) to Atom i n Molecule d(2) As(l) 0(4) 2 3.46 As(l) 0(5) 2 3.49 C(2) 0(4) 3 3.29 0(2) 0(5) 4 3.34 0(4) 0(5) 2 2.57 0(5) 0(4) 2 2.57 0(5) 0(5) 4 3.48 Molecule 1 at x y z 2 at -x -y -z 3 at 1-x -y -z 4 at -x -y 1-z 10 Pi g . 2. Projection of the structure along the b-axisj i l l u s t r a t i n g the molecular packing. The hydrogen bonds are shown as broken l i n e s . I I . ANTIMONY AND BISMUTH TRIIODIDES A. Introduction The t r i h a l i d e s of arsenic, antimony and bismuth have a l l been reported as having the "bismuth triiodide structure" . This has the arsenic, antimony and bismuth atoms situated at the centres of iodine octahedra, the iodine atoms being i n a hexagonal close-packed array. Such a structure would indicate that a l l three compounds form ionic c r y s t a l s , and while this i s probable for B i l ^ , i t seems unlikely for the other compounds. 7 A reinvestigation of the c r y s t a l structure of arsenic t r i i o d i d e indicated that the structure was not as previously reported^. Preliminary examination of the h0.-£ structure factors indicated that the iodine atoms were situated close to (y, j , Y2") in space group R3, as previously found*', but that better agreement between observed and calculated structure factors was obtained for zk about — rather than the As 5 previous value of ^ , referred to a hexagonal unit c e l l . These 7 changes were confirmed by refinement of the analysis. Although the iodine atoms are i n an approximate hexagonal close-packed array, the arsenic atoms are displaced from the centres of iodine octahedra and the structure may therefore be considered as b u i l t up from discrete A s l ^ molecules. Knowing t h i s , a similar reinvestigation of the cr y s t a l structures of antimony and bismuth t r i i o d i d e s was made. B. Experimental Crystals of antimony t r i i o d i d e were prepared by re-fluxing iodine and powdered antimony i n benzene, according 8 to the method of Bailar and Cundy . They are orange-red hexagonal plates with (OO.l) developed, and have a strong tendency to twin on this face. The unit c e l l parameters were o determined from an h0.£ precession f i l m (A, MoKoc = 0.7107A). Single crystals of bismuth t r i i o d i d e could not be obtained; sublimation i n vacuo, and various c r y s t a l l i z a t i o n techniques yielded only conglomerates of very small c r y s t a l s . The unit c e l l dimensions were therefore determined by least-squares g treatment, with the inclusion of a Nelson—Riley extrapolation term, of the sin 0 values from a powder f i l m (A, CuKa = 1.5418 A) — see Appendix. The powder lines were indexed by comparing their measured 0 values with ones calculated using previously reported c e l l dimensions . The c r y s t a l data for Asl-j (included for comparison), Sbl^ and B i l ^ are summarized i n Table 5. For Sbl^ the i n t e n s i t i e s of the h0«-£ re f l e c t i o n s were recorded on precession films with MoKoc radiation, estimated v i s u a l l y , corrected for Lorentz and polarization factors, and the structure amplitudes were derived. The c r y s t a l used was a very small hexagonal plate with edge 0.1 mm. and thickness 0.02 mm., and absorption corrections were not considered necessary. The c r y s t a l was twinned with the volumes of the two parts i n the ratio 1.2:1, and the i n t e n s i t i e s of r e f l e c t i o n s such as 303 and 303 were derived by assuming that, as found i n A s l - , they had equal F values. (Such r e f l e c t i o n s were super-imposed on the f i l m s ) . For B i l ^ , for which single crystals could not be obtained, the i n t e n s i t i e s were recorded, with CuKoc radiation, on a powder f i l m which was photometered, and the integrated i n t e n s i t i e s were then measured with a planimeter. The sample was mounted i n a thin-walled Lindemann glass c a p i l l a r y , of diameter 0.3 mm. The appropriate Lorentz and p o l a r i z a t i o n factors, and c y l i n d r i c a l absorption corrections 2 (uR = 24) were applied, and the F values for each powder line were derived. The photograph showed evidence of some preferred orientation, which was p a r t i c u l a r l y marked for the 00.£ r e f l e c t i o n s . C. Structure Analysis For. Sbl^, the h0.£ Patterson projection indicated a structure similar to that of A s l ^ , but with Z g ^ = 0.18. An electron density map showed the antimony and iodine atoms well resolved with s i g n i f i c a n t changes i n iodine positions also indicated (Fig. 3). The value of Z g ^ = 0.18 was con-firmed by computing structure factors f o r Z g ^ = 0.16, 0.17, 0*18, 0.19, 0.20, the F c's with z = 0.18 giving s i g n i f i c a n t l y better agreement (R = 0.2l) with the measured values than any of the other sets. Scattering factors from the International Tables, 1, corrected for anomalous dispersion and with °2 B = 4.5 A for a l l atoms, were used i n the calculations. Refinement of the positional and isotropic temperature para-meters was achieved by computing four Fourier (P ) and Difference (F - F ) syntheses successively; the discrepancy o c factor R, was thus f i n a l l y reduced to 0.131. With z, taken as \ t a n d a l l other parameters as their f i n a l values, R 14 F i g . 3. Electron-density projection along the b-axis, with contours at intervals of 10 electrons about Sb and I. Table 5 Crystal data for Asl-j, Sbl^ and B i l ^ 15 Formula Mol. wt. m.p. Crystal system aH H U, H a a R R R 2R D m x u(CuKa) u(MoKa) F(OOO) (hexagonal c e l l ) Space group As l ^ 455.7 146 Rhombohedral 7.208 + 0.001 21.436 + 0.001 964.5 6 8.269 51°41' 321.5 2 4.75 4.71 1220 200 1152 R3 Sbl . L3 502.5 170.5 Rhombohedral 7.48 + 0.02 20.90 + 0.05 1012.7 6 8,20 54°18» 337.6 2 4.85 4.94 1423 178 1260 B i l 3 589.8 439 °C Rhombohedral 7.516 + 0X.003 A 20.718 + 0.02 A °3 1013.5 A J 8.156 A 54°52' o-337.8 A' 2 5.7 g.cm -3 -3 R3 5.80 g.cm. 1600 cm - 1 386 cm"1 1452 electrons R3 Table 6 Measured and calculated structure factors for Sbl^, h0,4> reflec tions. i K l F c h I K l F c h i l Fol F c 3 227 -223 2 13 46 -59 T 23 52 6 6 528 -551 16 49 65 5 2 51 -34 9 247 -224 19 54 -66 5 74 47 12 517 519 22 56 42 8 117 -99 15 75 78 25 54 -19 11 76 80 18 233 -241 3 0 761 754 14 35 -29 21 65 -37 3 139 -139 17 24 22 24 54 74 6 343 -358 20 55 -26 1 98 99 9 171 -151 23 53 10 4 28 -22 12 306 361 7 1 73 72 7 33 -18 15 53 55 4 64 -37 10 63 65 18 148 -176 7 37 -41 13 84 -95 21 38 -27 10 84 44 16 86 84 24 26 54 13 54 -15 19 50 -58 *3 3 139 -139 16 55 27 22 55 42 6 343 -3 58 19 55 -40 2 236 . -196 9 171 -151 22 52 23 5 194 218 12 306 361 6 0 256 263 8 135 -178 15 53 55 3 59 -49 11 92 149 18 148 -176 6 142 -127 14 104 -120 21 38 -27 9 52 -56 17 81 73 24 26 54 12 140 137 20 55 -32 4 1 48 26 15 37 22 23 50 13 4 48 10 18 83 -70 2 103 -124 7 49 10 21 48 -11 5 153 153 10 26 23 24 44 22 8 180 -190 13 82 -69 *6 3 59 -50 11 120 150 16 56 56 6 142 -127 14 69 -85 19 55 -26 9 52 -56 17 52 56 22 55 23 12 140 137 20 55 -41 T 2 158 -119 15 37 21 23 56 16 5 109 129 18 83 -70 26 55 1 8 75 -75 21 48 -11 Table 6 - Continued / l P o l F c h I l P o l F h c I 1 116 126 11 84 71 24 4 114 -53 14 60 -83 7 30 -54 17 68 48 10 93 78 20 56 -12 increases to 0.270. Measured and calculated structure factors are l i s t e d i n Table 6. The f i n a l positional parameters are given i n Table 7, and th e i r standard deviations, calculated from Cruickshank' s formulae 1^, are : <f(x), d'(y), (f(z) = 0, 0, 0.014A for Sb, 0.007, 0.007, 0.009A for Ii °2 The f i n a l thermal parameters are B = 4.5A for a l l atoms. Interatomic distances and angles are also given i n Table 7, together with the corresponding parameters for A s l ^ which are included for comparison. Extrapolation of the atomic positional parameters for A s l ^ and Sbl^ to bismuth t r i i o d i d e , based on v a r i a t i o n of a parameter such as covalent radius, suggests that i n B i l ^ , z_. must be about \. Structure factors were calculated for Bi 6 a l l the three—dimensional re f l e c t i o n s of B i l ^ , using the same posi t i o n a l parameters as for Sbl^, but with z^^ = The 2 F values for each powder line were then derived by summing , c the values for the r e f l e c t i o n s contributing to the l i n e , with allowance for m u l t i p l i c i t y p. An overall thermal parameter 2 and the F scale factor were determined from a plot of o r (' 2 2\ 2 Ffi / F Q Jagainst sin 0. The slope of the li n e indicated °2 2 2 B = 0 A • The values of F and F are compared i n Table 8; o c the agreement i s quite good, the only poor agreement being for 2 the 00.<£ r e f l e c t i o n s , for which the F values are too high as o a result of preferred orientation. Unfortunately, the powder data do not allow a more precise determination of the para-meters, since the accuracy of intensity measurement i s not s u f f i c i e n t l y high to detect the small differences i n S p F c produced by small changes i n , for example, Z g ^ . The positional parameters used to calculate F 's i n Table 8 are included with c the Asl-j and Sbl^ values i n Table 7. D. Discussion The present analyses of Sbl^ and B i l ^ , and the 7 corresponding redetermination of the Asl-j structure , show that i n a l l three compounds the iodines are i n an approximately hexagonal close-packed array. In B i l ^ , Z i g ^ does not d i f f e r s i g n i f i c a n t l y from ^, so that each bismuth atom i s at the centre of an octahedron of iodine atoms. This arrangement i s t y p i c a l of a compound which i s largely ionic i n character. In Asl-j, zAs = and, the structure i s b u i l t up from discrete A s l ^ molecules, which have dimensions i d e n t i c a l with those of the molecules i n the vapour phase. In Sbl^, Zgk = 0.1820, so that, as with the arsenic atoms i n A s l ^ , the antimony atoms are displaced from the centres of iodine octahedra, and have only three near neighbour iodine atoms, at 2.868 + 0.010 A, with I - Sb - I = 95.8° + 0.3°. The next o three iodine neighbours are at 3.316 + 0.010A. Each iodine atom has six iodine neighbours i n a plane p a r a l l e l to (00.l); two of these are i n the same Sbl-j molecule and are at 4.25. A, and the other four are at 4.29A (two), and 4.41 A (two). In addition there are six other near neighbours, three above o the plane at 4.40, 4.37, 4,37 A and three below at 4.12, 4.22, o 4.22 A. The intermolecular I...I contacts i n Sbl^ and B i l ^ (Table 7) are quite similar to those i n Asl-j, and a l l correspond 5 to normal van der Vaals interactions . The dimensions of the Sbl^ molecule i n the vapour phase 1 1 20 o are Sb — I = 2.67 ± 0.03 A, I - Sb - I = 99 + 1 , indicating that the structure i n the crys t a l i s intermediate between a purely molecular cr y s t a l and an ionic one. The structures of A s l ^ , Sbl^ and B i l ^ , as summarized i n Table 7, exemplify the change from molecular, through i n t e r -mediate, to ionic arrangement as would be expected from similar compounds of elements i n the same group. In a l l these compounds there i s a lone-electron pair on the central atom. 3 In A s l ^ , this lone-pair, having almost sp character, i s s t e r i c a l l y active and could explain the displacement of the arsenic atom from the centre of the iodine octahedron. The effect lessens i n proceeding down the group and i n B i l ^ , the lone—pair would be expected to have almost s—character and consequently, a negligible s t e r i c e f f e c t . The bismuth atom could then be situated at the centre of the iodine octahedron. A theory based on lone-pair p a r t i c i p a t i o n alone requires no change i n the character of the "metal" — iodine bond, but some change towards ionic character i n B i l ^ i s expected. A combination of the two eff e c t s , changes i n lone-pair bond and "metal" — iodine bond character, rather than either one considered alone i s preferred as an explanation of the observed differences i n crys t a l structures. 21 Table 7 o Fractional positional parameters, interatomic distances (A) and angles i n A s l ^ , Sbl^ and B i l ^ . M = As Positional parameters 6M i n 6 c 181 i n 18 f z = x = y = z •'*= 0.1985 0.3485 0.3333 0.0822 Sb 0.1820 0.3415 0.3395 0.0805 Bi 0.1667 (0.3415) (0.3395) (0.0805) Interatomic distances Intramolecular M - I 2.556 + 0.004 2.868 + 0.010 3.1 I - M - I 102.0° + 0.1° 3.97 95.8° + 0.3° 4.25 Intermolecular M ... I 3.50 3.32 I ... I 4.26(2x),4.26(2x) 4,29(2x),4.41(2x) 4.21,4.30(2x), 4.12,4i22(2x) 4.29,4.38(2x) 4.37,4.40(2x) 3.1 Dimensions of gaseous molecules M - I 2.55 +0.03 I — M - I 101° + 1.5° 2.67 + 0.03 99° + 1° Table 8 2 Measured and calculated F values for B i l ^ F 2 x IO" 6 0 meas 0 (CuKoc) 1.0 6*57 1.1 13.06 8.3 13.66 7.6 17.78 1.6 19*70 8.0 20,95 1.2 22.00 6.6 23.27 6.8 25.30 h k £ P c 2 P P c 2 x 10 0 0 3 -431 0.37 0 1 5 237 0.62 0 0 6 -378 1 1 3 244 8.96 1 1 3 -1171 2 0 1 251 2 0 5 182 7.95 1 1 6 872 1 1 % 729 0 0 9 -527 0.55 0 2 7 167 7.74 3 0 0 1123 3 0 3 -355 1.52 3 0 T -355 1 1 9 -933 5.65 1 1 9 269 3 0 6 -300 7.50 3 0 6 -300 2 2 3 -984 2 2 T 191 0 1 n 178 1 3 l 187 0 0 12 1029 2.12 3 1 5 244 6.02 2 2 6 625 2 2 r 744 2 1 10 -138 2.65 3 0 9 -460 3 0 -460 2 2 9 277 4.56 2 2 -821 0 1 14 -186 5.1 26,65 5.5 27.97 4.4 29.31 3.8 32.09 T a b l e 8 - C o n t i n u e d 23 h k € F £ p P 2 x I O " 6 c c 4 1 3 1 6 0 9.41 1 4 3 1 6 0 4 1 5 - 8 7 1 1 4 3 - 8 7 1 1 3 1 0 - 2 2 6 1 0 . 4 6 3 0 1 2 9 1 5 3 0 1 2 9 1 5 2 0 14 - 1 4 0 4 1 6 6 7 3 9.28 1 4 6 6 7 3 4 1 Z 5 6 6 1 4 3" 5 6 6 3 1 1 1 1 0 9 5.52 0 5 1 2 2 7 1 1 1 5 8 1 1 1 13 - 8 9 3 2 3 8 - 2 2 7 3 3 0 8 8 7 4 . 7 2 3 2 1 0 - 1 5 7 7 . 2 0 4 1 9 - 7 4 1 1 4 9 _ 7 4 i A \ \ 1 9 7 1 4 9 1 9 7 2 2 1 5 - 8 1 3 4 . 0 5 2 2 1 5 68 4 2 8 - 9 2 0 5 1 0 - 1 1 3 6.01 3 3 9 - 3 8 5 3 3 9 — 3 8 3 1 1 1 8 6 9 6 1 1 IS 4 0 7 4 1 1 2 - 5 0 1 4 1 2 - 5 0 4 1 1 2 1 4 2 1 4 1 2 1 4 2 F x 1 0 e meas 0 (CuKoc) 9.5 3 3 . 7 5 1 0 . 4 3 4 * 8 9 5.7 3 6 . 0 2 8.2 3 6 . 5 9 2.4 3 8 . 1 1 6.0 3 9 . 7 4 3.9 4 4 . 0 2 7.2 4 4 , 5 8 24 APPENDIX 12 Calculation of the l a t t i c e constants of bismuth t r i i o d i d e An accurate redetermination of the l a t t i c e constants of bismuth t r i i o d i d e using information from a povder f i l m o (A, CuKoc = 1.5418A) i s described below. The systematic errors i n d, the interplanar spacing, were taken as proportional to ^£cos 2©/sin © + cos2©/©J - the o Nelson—Riley function - and the best values of the u n i t - c e l l 13 parameters, a and c, were obtained by the least-squares method * using the measured 0 values of a l l the d i f f r a c t i o n l ines which could be unambiguously indexed. 2 For the hexagonal and trigonal system the sin © equation i s s i n ^ O ^ = A(h 2 + hk + k 2) + Ct 2 where A = A 2/3a 2, C = A 2/4c 2 . With systematic errors i n d values proportional to ^[cos 2©/sin © + cos2©/©3 , i t can be shown that the errors i n .2 2 si n © are proportional to this expression multiplied by sin ©. Putting 5 equal to 10 times this l a t t e r expression (the factor 10 being introduced to make the S values more nearly equal to the other terms involved, thus f a c i l i t a t i n g computation), and allowing for random observational errors, then for each d i f f r -action l i n e , k(h±2 + h ^ + k i 2 ) + Cl i 2 + D 6 i - sinV = £ i 25 where D i s the proportionality constant. The best results of A, C and D are those which minimize 2J£^ , the sum of the squares of the differences between the 2 calculated and observed values of sin 0 . This i s the pri n c i p l e of the least-squares method. The f i r s t derivatives of with respect to A, C and D are equated to zero, and the resul t i n g three simultaneous equations (the normal equations) are solved for the three unknowns. The unit c e l l parameters may then be calculated by means of the relationships already given. Standard deviations of these parameters may be obtained from the least-squares residuals: E r 2 - - - 1 _ i e . x a cT^x) = (number of planes - number of parameters) where a ^ - 1 i s the appropriate diagonal element i n the inverse of the matrix used i n the calc u l a t i o n of the unit c e l l para-meters. The method of least-squares i s extensively used for the refinement of atomic positional and thermal parameters. There are, of course, usually many more parameters, and the calculation involved can only be handled e f f e c t i v e l y by a computer. How-ever, the calculation i s ess e n t i a l l y the same as that described here. REFERENCES 26 1. "International Tables for X-ray Crystallography", V o l . I l l , Kynoch Press, Birmingham, 1962. 2. N. Camerman and J . Trotter, J . Chem. Soc., 1964, 219. 3* V.R. Cullen and J . Trotter, Canad. J . Chem.. 1962, 40. 1113; 1963, 41, 2983. 4. A.Shimada, B u l l , Chem. Soc. Japan, 1959, 32, 309; 1960, 33, 301; 1961, 34, 639; 1962, 35, 1600. 5m L. Pauling, "The Nature of the Chemical Bond", 3rd. Edii., Cornell University Press, Ithaca, 1960. 6. Strukturbericht. 2. 25, 294; Structure Reports. 11. 272. 7. J . Trotter, Z. K r i s t a l l o g r . , 1965 (in press). 8. J.C. B a i l a r and P.F. Cundy i n "Inorganic Syntheses", V o l . I, McGraw-Hill Book Company, 1939, Ed. H. S. Booth, p. 104. 9. J.B. Nelson and D.P. Riley, Proc. Phys. S o c , 1945, 57, 160. 10. D»¥.J. Cruickshank, Acta. Cryst., 1949, 2, 65. 11. "Tables of Interatomic Distances and Configuration i n Molecules and Ions", Chem. Soc. Spec. Publ. No. 11, 1958. 12. J . Trotter, Acta. Cryst.. 1960, 13. 86. 13. M.U. Cohen, Rev. S c i . Instr.. 1935, 6, 68; 1936, 7, 155. 14. L.V. Az&roff and M.J. Buerger, "The Powder Method i n X-ray Crystallography", McGraw-Hill, New York, 1958. 

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