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Effect of crystal anisotropy and crystal defects on dissolution Burt, Helen Mary 1980

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EFFECT OF CRYSTAL ANISOTROPY AND CRYSTAL DEFECTS ON DISSOLUTION by HELEN MARY BURT B. Pharm., U n i v e r s i t y of Bath, 1975 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY \ ^ — i n \ THE FACULTY OF GRADUATE STUDIES ( Facu l t y of Pharmaceutical Sc iences) D i v i s i o n of Pharmaceutics We accept t h i s t h e s i s as conforming to the requ i red standard THE UNIVERSITY OF BRITISH COLUMBIA August, 1980 Q Helen Mary Bu r t , 1980 In present ing t h i s t he s i s i n p a r t i a l f u l f i l m e n t of the requirements f o r an advanced degree at the U n i v e r s i t y of B r i t i s h Columbia, I agree t ha t the 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 re fe rence and study. I f u r t h e r agree that permiss ion f o r ex tens i ve copying of t h i s t he s i s f o r s c h o l a r l y purposes may be granted by the Head of my Department or by h i s r e p r e s e n t a t i v e s . I t i s understood that copying or p u b l i c a t i o n of t h i s t he s i s f o r f i n a n c i a l ga in s h a l l not be a l lowed without my w r i t t e n permi s s ion . Department of PHrfVg. H ( r C ^ k T C C r t r C S Cj CAES The U n i v e r s i t y o f B r i t i s h Columbia 2075 Wesbrook P lace Vancouver, Canada V6T 1W5 D E - 6 B P 75-51 1 E - i i -ABSTRACT There are a number of i n t e r e s t i n g and as y e t unresolved problems concerning the d i s s o l u t i o n ra tes and s o l u b i l i t i e s of var ious drugs. I t seems c l e a r tha t the inherent p r ope r t i e s of c r y s t a l s ( i . e . su r face and bulk s t r u c t u r e and p r ope r t i e s ) and t h e i r r e l a t i o n s h i p to s o l u b i l i t y and d i s s o l u t i o n r a t e need to be more c l e a r l y understood before exp lanat ions f o r these observat ions can be o f f e r e d . The approach taken i n t h i s study to the problem of d i s s o l u t i o n i s to cons ider the method of p repa ra t i on and i t s e f f e c t on c r y s t a l s t r u c t u r e . Th i s study attempts to show t h a t , i n a d d i t i o n to p rope r t i e s o f . t h e s o l i d s t a t e such as polymorphism, s o l v a t i o n and degree of c r y s t a l ! i n i t y , the d i s s o l u t i o n k i n e t i c s may be a f f e c t e d by: a) the a n i s o t r o p i c nature of c r y s t a l l i n e s o l i d s and hence c r y s t a l hab i t b) the type and number of c r y s t a l de fect s i nco rpo ra ted i n t o a c r y s t a l dur ing growth. Inorganic s a l t s such as n i c ke ! s u l f a t e hexahydrate (NiSO^ a 6H2O) and potassium pe r ch l o r a te (KCIO^) provided s u i t a b l e model, c r y s t a l l i n e ma te r i a l s as they grew as l a r g e , we l l - fo rmed c r y s t a l s w i th d i s t i n c t h a b i t s . KCIO^ c r y s t a l s cou ld be e a s i l y c leaved and etched and grew wi th r e l a t i v e l y low d i s l o c a t i o n d e n s i t i e s . The d i s s o l u t i o n an i so t ropy of NiSO^ a 6 ^ 0 c r y s t a l s was s tud ied us ing a s i n g l e c r y s t a l d i s s o l u t i o n method by measuring the movement o f the (111) and (112) c r y s t a l faces w i th time i n a f l ow ing so l ven t us ing a t r a v e l l i n g microscope. The observed apparent r a te con s tan t , KQ^S f o r the (112) face was g rea te r than f o r the (111) face at a l l f l ow ra te s but an i so t ropy was l e s s pronounced at the lower f low r a t e s , The apparent r a te constants f o r the t r an spo r t and sur face c o n t r o l l e d r e a c t i o n s , K t and K p were of the same order of magnitude suggest ing tha t the o v e r a l l d i s s o l u t i o n r e a c t i o n was under mixed con t r o l at the lower f l ow r a t e s . A c t i v a t i o n energ ies were s l i g h t l y h igher than the normal range f o r t r an spo r t processes. K r (112) > K r (111) i n d i c a t i n g tha t an i so t ropy was probably due to d i f f e r e n c e s i n the r a t e o f the su r face r e a c t i o n . At high f l ow ra te s the re was a change to a predominantly su r face c o n t r o l l e d r e a c t i o n . I t i s l i k e l y t ha t d i s s o l u -t i o n an i so t ropy i s due to the d i f f e r e n c e s i n a c t i v a t i o n energy f o r the two faces . The e f f e c t o f hab i t m o d i f i c a t i o n on the d i s s o l u t i o n r a te of NiSO^ a 6 ^ 0 i n 60% v/v ethanol was s tud ied us ing a r o t a t i n g basket method. B ipyramidal c r y s t a l s were grown i n a f l u i d i z e d - b e d c r y s t a l l i z e r and p l a t y c r y s t a l s were r e c r y s t a l l i z e d from supersaturated s o l u t i o n s of n i c k e l s u l f a t e con ta i n i n g small amounts of g e l a t i n . A c i c u l a r c r y s t a l s were prepared by the t o p o t a c t i c dehydrat ion of a c i c u l a r c r y s t a l s of N i S O ^ h ^ O . DSC thermograms of p l a t y and a c i c u l a r hab i t s were s i m i l a r but d i f f e r e d from the b ipyramidal hab i t probably due to d i f f e r e n c e s i n vapor pressures exer ted by the h a b i t s . The observed d i s s o l u t i o n r a te cons tant , K ' 0 | 3 S 7. T " o r the b ipyramida l and a c i c u l a r c r y s t a l s was s i m i l a r and g rea te r than the p l a t y hab i t a t both low and high r o t a t i o n r a t e s , the d i f f e r e n c e being l e s s pronounced at the lower r o t a t i o n speed. At the high r o t a t i o n speed d i s s o l u t i o n was under mixed t r a n s p o r t -sur face c on t r o l . The d i f f e r e n c e i n K' .„ must be due to d i f f e r e n t values obs of the o v e r a l l su r face energy of the c r y s t a l s . KCIO^ c r y s t a l s were grown i n s i l i c a ge l s and the c r y s t a l s from three growth l e v e l s (and hence grown at d i f f e r e n t r a t e s ) were c l e a v e d , etched and the d i s l o c a t i o n etch p i t s counted us ing a d i f f e r e n t i a l i n t e r f e r e n c e - i v -con t r a s t microscope. C r y s t a l s grown at the f a s t e s t r a te had the h ighest mean d i s l o c a t i o n d e n s i t i e s and the h ighest K' 0| 3 S va lues as determined us ing the r o t a t i n g basket method. Converse ly , c r y s t a l s grown at the i lowest r a te had a low mean d i s l o c a t i o n den s i t y and low K Q ^ va lue s . The d i f f e r e n c e s i n w e r e n o t due to i m p u r i t i e s but to d i f f e r e n c e s i n the energy content of c r y s t a l s r e s u l t i n g from the i n c o r p o r a t i o n of d i f f e r i n g numbers of d i s l o c a t i o n s i n t o the c r y s t a l s . - V -TABLE OF CONTENTS Page Ab s t r a c t i i L i s t of Tables x i i L i s t of F igures x i v L i s t of Schemes x v i i Symbols x v i i i Acknowledgements x x i i INTRODUCTION 1 LITERATURE SURVEY 5 A. C r y s t a l S t r uc tu re 5 1. L a t t i c e S t r u c t u r e 5 2. I s o t r o p i c and a n i s o t r o p i c c r y s t a l s 7 3. C r y s t a l hab i t s and polymorphic forms 7 •4. C r y s t a l de fec t s ( imper fec t i on s ) 8 4.1 Po in t de fec t s 8 4.2 L a t t i c e de fec t s 10 4.21 L ine de fec t s 10 4.22 Gra in boundaries 11 4.23 Twins 11 4.24 S tack ing f a u l t s 11 B. C r y s t a l growth 13 1. Theor ies of c r y s t a l growth 13 1.1 D i f f u s i o n t heo r i e s 14 1.2 Adsorpt ion l a y e r 16 2. O r i g i n of d i s l o c a t i o n s 20 3. Growth r a te and d i s l o c a t i o n den s i t y 21 - v i -Page 4. Growth of c r y s t a l s i n s i l i c a ge l s 23 4.1 Gel s t r u c t u r e and p r ope r t i e s 23 4.2 Growth mechanism 24 C. D i s s o l u t i o n k i n e t i c s 24 1. Transport c o n t r o l l e d d i s s o l u t i o n 25 2. Mixed t r a n s p o r t - s u r f a c e c o n t r o l l e d d i s s o l u t i o n 26 3. Surface r e a c t i o n c o n t r o l l e d d i s s o l u t i o n 27 D. Factors a f f e c t i n g d i s s o l u t i o n r a t e 30 1. Degree of a g i t a t i o n 31 2. Temperature 35 3. S o l u b i l i t y and concen t ra t i on g rad ient 35 4. pH of d i s s o l u t i o n medium 36 5. Surface area 36 6. V i s c o s i t y 36 7. S o l u b i l i z a t i o n and sur face a c t i v i t y 37 E. C r y s t a l S t r u c tu re and r e a c t i v i t y 37 1. C r y s t a l l i n e c h a r a c t e r i s t i c s 38 1.1 Polymorphism, hydrates and so l va te s 38 1.2 Degree of c r y s t a l l i n i t y 38 2. An i so t ropy 39 2.1 D i s s o l u t i on an i so t ropy 40 2.2 Habi t m o d i f i c a t i o n 42 3. C r y s t a l de fec t s 46 3.1 Energet ic s of d i s l o c a t i o n s 46 3.2 Defects and c r y s t a l r e a c t i v i t y 47 3.3 Defects and d i s s o l u t i o n 48 3.31 Nuc lea t i on a t d i s l o c a t i o n s 51 3.32 D i s l o c a t i o n etch p i t s 51 3.33 I n t e r r e l a t i o n s h i p s between growth r a t e , i m p u r i t i e s , d i s l o c a t i o n s and d i s s o l u t i o n r a t e 53 - v i i -Page EXPERIMENTAL 55 A. Apparatus 55 B. M a t e r i a l s 5 7 C. D i s s o l u t i o n an i so t ropy 58 1. Growth of n i c k e l s u l f a t e a hexahydrate c r y s t a l s 58 2. P repa ra t i on of ethanol d i l u t i o n s 58 3. S i n g l e c r y s t a l d i s s o l u t i o n measurements 59 3.1 Apparatus . 59 3.11 S e l e c t i o n of tub ing f o r the pump 59 3.2 Measurement 61 3.21 S e l e c t i o n o f d i s s o l u t i o n medium 61 3.22 Co r r e c t i on f a c t o r s 62 3.23 Measurement of length of c r y s t a l faces 62 3.3 Test f o r su r face c o n t r o l l e d d i s s o l u t i o n 62 D. Habit m o d i f i c a t i o n and d i s s o l u t i o n r a te 65 1. Growth of c r y s t a l hab i t s 65 1.1 B ipyramidal hab i t 65 1.2 Habi t m o d i f i c a t i o n t r i a l s 65 1.3 P l a t y hab i t 66 1.4 A c i c u l a r hab i t 66 2. Bulk d i s s o l u t i o n 67 3. I n t r i n s i c d i s s o l u t i o n 68 E. C h a r a c t e r i z a t i o n of n i c k e l s u l f a t e ; 7H 2 0, 36H 20 and hab i t s of a6H 20 69 1. Growth of NiS04 3 6H 20 c r y s t a l s 69 2. S o l u b i l i t y determinat ion 69 2.1 S o l u b i l i t y of NiS04 a 6H 20 i n ethanol d i l u t i o n s 69 2.2 S o l u b i l i t y of c r y s t a l hab i t s i n 60% v/v ethanol 69 3. X-ray d i f f r a c t i o n 69 4. X-ray energy a n a l y s i s 69 - v i n -5. Thermal a n a l y s i s 6. Surface area 7. Dehydration of N i S0 4 . 7H 2 0 Ana l y s i s of n i c k e l s u l f a t e hexahydrate 1. P repa ra t i on of standards 2. Operat ing c ond i t i o n s C r y s t a l de fect s and d i s s o l u t i o n r a te 1. N i cke l s u l f a t e hexahydrate c r y s t a l s 1.1 Growth of b ipyramidal c r y s t a l s of NiSO^ 1.2 E f f e c t of f low r a t e on the growth r a te 1.3 C r y s t a l c h a r a c t e r i z a t i o n 1.31 Flow c e l l grown c r y s t a l s 1.32 F l u i d i z e d - b e d grown c r y s t a l s 1.4 S i n g l e c r y s t a l d i s s o l u t i o n 2. Calc ium t a r t r a t e c r y s t a l s 3. Potassium pe r ch l o r a t e c r y s t a l s 3.1 Gel growth of c r y s t a l s 3.11 E f f e c t of gel den s i t y 3.12 E f f e c t of pH of ge l s 3.13 E f f e c t of temperature 3.14 Harvest ing of c r y s t a l s 3.2 C r y s t a l c h a r a c t e r i z a t i o n 3.21 C r y s t a l de fec t s 3.22 X-ray d i f f r a c t i o n 3.23 X-ray energy a n a l y s i s 3.24 Thermal a n a l y s i s 3.25 S o l u b i l i t y determinat ion 3.26 Surface area 3.3 Bulk d i s s o l u t i o n - i x -Page H. Ana l y s i s of potassium pe r ch l o r a te 80 1. P repara t ion of standards 80 2. Operat ing c ond i t i o n s 81 RESULTS AND DISCUSSION 82 A. D i s s o l u t i o n an i so t ropy 82 1. Choice of model 82 2. C a l c u l a t i o n of observed apparent r a t e constant 82 3. D i s s o l u t i o n from a f l a t p l a t e ( c r y s t a l face) 84 3.1 D i f f u s i o n c o e f f i c i e n t - 84 3.2 Kinematic v i s c o s i t y 87 3.3 L inea r f l ow ra te s and Reynolds numbers 90 4. Hydrodynamics of the system and d i s s o l u t i o n an i so t ropy 92 5. Determinat ion of apparent t r an spo r t and sur face r e a c t i o n r a t e constants 97 6. A c t i v a t i o n energ ies f o r d i s s o l u t i o n 100 7. A l t e r a t i o n s i n under sa tu ra t ion l e v e l s 104 B. Habi t m o d i f i c a t i o n and d i s s o l u t i o n r a te 104 1. Choice of model 104 2. C h a r a c t e r i z a t i o n of hab i t s 106 2.1 X-ray d i f f r a c t i o n 106 2.2 X-ray energy a n a l y s i s 113 2.3 Thermal a n a l y s i s 113 2.4 S o l u b i l i t y 120 3. D i s s o l u t i o n of hab i t s 120 4. A c t i v a t i o n energ ies f o r d i s s o l u t i o n 130 C. Polymorphism and thermochemistry of NiS0^.6H20 133 1. Polymorphism 133 - X -Page 2. Thermochemistry 138 2.1 Hydrat ion energy 138 2.2 L a t t i c e energy 139 2.3 D i s s o l u t i o n of N i S0 4 . 6H 2 0 i n 60% v/v ethanol 139 2.4 A c t i v a t i o n energy f o r d i f f u s i o n 140 D. S i ng le c r y s t a l growth and d i s s o l u t i o n 140 1. Choice of N i S 0 4 a 6H 20 140 2. Growth k i n e t i c s 140 3. E f f e c t of f l ow ra te on the growth r a te 142 4. M i c r o s cop i ca l examination of c r y s t a l s 142 4.1 F l u i d i z e d - b e d grown b ipyramidal c r y s t a l s 142 4.2 Flow c e l l grown b ipyramida l c r y s t a l s 147 5. S i n g l e c r y s t a l d i s s o l u t i o n 147 5.1 F l u i d i z e d - b e d grown c r y s t a l s 147 5.2 Flow c e l l grown c r y s t a l s 151 E. C r y s t a l de fec t s and d i s s o l u t i o n 151 1. Choice o f potassium pe r ch l o r a t e 151 2. C h a r a c t e r i z a t i o n 153 2.1 X-ray d i f f r a c t i o n 153 2.2 Thermal a na l y s i s 153 2.3 Impur ity a n a l y s i s 153 2.31 X-ray energy a n a l y s i s 156 3. D i s l o c a t i o n content of KCIO^ c r y s t a l s 156 3.1 D i s l o c a t i o n s and etch p i t s 156 3.2 Etch ing of KC10 4 c r y s t a l s 156 3.3 D i s l o c a t i o n den s i t y 158 3.4 D i s l o c a t i o n den s i t y and growth r a t e 160 4. D i s s o l u t i o n of KC10 A c r y s t a l s 162 - x i -Page SUMMARY AND CONCLUSIONS 170 REFERENCES 174 APPENDIX I 187 APPENDIX II 192 APPENDIX I I I 194 - x i i -LIST OF TABLES Table Page I C l a s s i f i c a t i o n of c r y s t a l s 6 II E f f e c t s of c r y s t a l de fec t s on var ious p r ope r t i e s 49 I I I Phy s i ca l constants of 60% v/v ethanol and N i S0 4 a 6H 20 64 99 IV Apparent r a t e constants and f i l m th i cknes s f o r the d i s s o l u t i o n of N i S 0 4 a 6H 20 i n 60% v/v ethanol V A c t i v a t i o n energ ies of d i s s o l u t i o n f o r the (111) and (112) c r y s t a l faces of N i S 0 4 a 6H 20 102 VI X-ray data f o r NiSO* a 6H 2 0; b i p y r a m i d a l , p l a t y and a c i c u l a r hab i t s 111 VII X-ray data f o r N i S0 4 . 7H 2 0 r e c r y s t a l l i z e d and s tored at 4 ° . Samples ground and held a t room temperature f o r about 45 min. 112 VI I I Thermal a n a l y s i s and X-ray d i f f r a c t i o n of hab i t s of N i S 0 4 a 6H 20 and N i S0 4 . 7H 2 0 116 IX S o l u b i l i t i e s and su r face areas of hab i t s of N i S 0 4 a 6H 20 122 X I n t r i n s i c d i s s o l u t i o n ra tes o f hab i t s of N i S 0 4 a 6H 20 129 XI A c t i v a t i o n energ ies of d i s s o l u t i o n f o r the b i p y r a -midal and p l a t y hab i t s o f N i S 0 4 a 6H 20 132 XII Changes i n thermograms and X-ray d i f f r a c t i o n of emerald green c r y s t a l s of n i c k e l s u l f a t e on storage a t 58° 134 XI I I X-ray data f o r N i S0 4 . 6H 2 0 r e c r y s t a l l i z e d and s tored 5 days a t 58° 135 XIV Changes i n thermograms and X-ray d i f f r a c t i o n of emerald green c r y s t a l s of n i c k e l s u l f a t e on storage a t room temperature 137 XV Growth data f o r N i S 0 4 a 6H 20 i n water a t 37° and a f l ow ra te of 3.02 crrus" 1 145 XVI Growth and d i s s o l u t i o n r a te s o f f l u i d i z e d - b e d grown N i S 0 4 a 6H 20 c r y s t a l s 149 - x i i i -Table Page XVII Growth and d i s s o l u t i o n ra te s of f l u i d i z e d - b e d grown NiSG^ a 6H2O c r y s t a l s i n the presence and absence of i n h i b i t o r 150 XVIII X-ray data f o r KC104 c r y s t a l s grown at 0-1 cm, 2-3 cm and 4-6 cm growth l e v e l s 154 XIX Thermal a n a l y s i s of KCIO4 c r y s t a l s 155 XX D i s l o c a t i o n d e n s i t i e s , s o l u b i l i t y , su r face areas and d i s s o l u t i o n r a t e constants f o r KCIO^ c r y s t a l s 164 XXI Ana l y s i s of va r iance of K ' 0 5 S data f o r KCIO^ c r y s t a l s grown at d i f f e r e n t growth l e v e l s 167 XXII A c t i v a t i o n energ ies f o r t r an spo r t and su r face c o n t r o l l e d d i s s o l u t i o n f o r the (111) and (112) c r y s t a l faces of N i S 0 4 a 6H 20 193 - x i v -LIST OF FIGURES Figure Page 1 An edge d i s l o c a t i o n (upper diagram) and screw d i s l o c a t i o n ( lower diagram) 12 2 S t r u c t u r e of a low index face f o r a p e r f e c t c r y s t a l on the Ko s se l - S t r an sk i model 17 3 React ion path f o r a growth u n i t 19 4 D i f f u s i o n and hydrodynamic boundary l a ye r s f o r laminar f l ow over a f l a t p l a t e 32 5 D i s s o l u t i o n apparatus and diagram of a s i n g l e NiS04 a 6H2O c r y s t a l showing geometry and p o s i t i o n of c r y s t a l f a c e s , c h a r a c t e r i z e d by t h e i r M i l l e r i nd i ce s 60 6 Co r r e c t i on f a c t o r s f o r the (111) and (112) faces of N i S 0 4 a 6H o0 63 7 Diagram of a s i n g l e KC104 c r y s t a l showing the geometry and p o s i t i o n of c r y s t a l f a ce s , c h a r a c t e r i z e d by t h e i r M i l l e r i nd i ce s 78 8 Movement of the (111) c r y s t a l face of N i S 0 4 a 6 H 2 0 as a f u n c t i o n of t ime at 37° 83 9 E l i m i n a t i o n of the i n i t i a l surge i n the movement of the (111) face of NiS04 a 6 H 2 0 a t 37° and a f low r a t e of 3.7 cm.s~l 85 10 D i f f e r e n t i a l i n t e r f e r e n c e c on t r a s t micrograph of a (111) c r y s t a l face of N i S 0 4 a 6H2O before d i s s o l u t i o n 86 11 P l o t of v i s c o s i t y (n) versus temperature f o r 60% v/v ethanol 88 12 P l o t of den s i t y (p) versus temperature f o r 60% v/v ethanol 89 13 D i s s o l u t i o n an i so t ropy of N i S 0 4 a 6H0O at 3 7° . Po in t s expe r imenta l , curves p red i c ted us ing Eqn. 23 91 14 Movement of the (111) c r y s t a l face of N i S 0 4 a 6 H 2 0 versus time to show sur face c o n t r o l l e d d i s s o l u t i o n 93 15 Dependence of K 0 b s f o r the (111) face of NiS04 a 6H 20 on f low r a t e 94 - XV -F igure Page 16 Dependence of KQ^S f o r the (111), face of NiSC>4 a 6 H 2 O on f low r a te us ing 55% v/v ethanol as the d i s s o l u t i o n medium 9 5 17 Ang l ing of a N i S 0 4 a 6 H 2 O c r y s t a l on the tungsten w i re support 96 18 P l o t of the r e c i p r o c a l of K 0 5 S aga in s t r e c i p r o c a l of square root of f low r a t e f o r the (111) and (112) faces of N i S 0 4 a 6H 20 at 37° 98 19 Ar rhen ius p l o t s f o r the (111) and (112) faces of N i S 0 4 a 6H 20 101 20 D i s s o l u t i o n r a te of the (111) face of N i S 0 4 a 6H 20 as a f unc t i on of the under sa tu ra t ion of the d i s s o l u -t i o n medium at 37° and f low r a t e of 4.68 cm. s - ! 105 21 Hab i t m o d i f i c a t i o n s of N i S 0 4 a 6H 2 0. a) B ipyramidal hab i t b) P l a t y hab i t c) A c i c u l a r hab i t 107-110 22 Dehydration and moisture uptake of N i S0 4 . 7H 2 0 c r y s t a l s at 22° 114 23 X-ray energy a n a l y s i s of N i S 0 4 a 6H 20 c r y s t a l s a) b ipyramida l b) p l a t y and c) a c i c u l a r hab i t s 115 24 V a n ' t Hoff p l o t of s o l u b i l i t y data f o r N i S 0 4 a 6H 20 i n d i f f e r i n g ethanol d i l u t i o n s 121 25 P l o t of the change i n bulk concen t ra t i on as a f u n c t i o n of time f o r the b ipyramida l NiSO* a 6H0O c r y s t a l s a t 22° 124 26 P l o t of K'obs a s a f u n c t i o n of the r o t a t i o n r a t e f o r the three hab i t s of N i S 0 4 a 6H 20 125 27 P l o t of the change in•bu lk concen t ra t i on as a f u n c t i o n of time f o r r o t a t i n g d i s c s of N i S 0 4 a 6H 20 (at 300 rpm) 128 28 Dependence of K i n t on r o t a t i o n speed at 3 0 ° , f o r r o t a t i n g d i s c s of the b ipyramidal N i S 0 4 a 6H 20 c r y s t a l s 131 29 Movement of the (001) c r y s t a l face of N i S 0 4 a 6H 20 as a f u n c t i o n of time at 37° dur ing growth 141 30 P l o t of growth r a t e , measured as the r a t e of movement of the (001) face of N i S 0 4 a 6H 2 0, versus supe r sa tu ra -t i o n a t 37° 143 - x v i -F igure Page 31 P l o t of growth r a t e , measured as the o v e r a l l r a te of i nc rease i n weight of a NiSO^ a 6 H 2 O s i n g l e c r y s t a l , versus supe r sa tu ra t i on a t 37° 144 32 Movement o f the (001) c r y s t a l face of N i S 0 4 a 6H 20 versus time to show su r face c o n t r o l l e d growth at 37° 146 33 a) D i s l o c a t i o n etch p i t s on the c leaved and etched (001) plane of a N i S 0 4 a 6H20. c r y s t a l b) Growth " s p i r a l " on the (001) face of NiS04 a 6H 20 148 34 P l o t s of K 0 k s as a f u n c t i o n of the growth r a t e f o r s i n g l e c r y s t a l s of N i S 0 4 a 6 H 2 O , a t 30° and a f low r a te of 5.43 cm.s-1 152 35 X-ray energy a n a l y s i s of KC104 c r y s t a l s from a) 0-1 cm and b) 4-6 cm growth l e v e l s 157 36 D i s l o c a t i o n etch p i t s on the c leaved and etched (001) plane of a KCIO^ c r y s t a l 159 37 Number of K C I O 4 c r y s t a l s w i th a given d i s l o c a t i o n den s i t y range from the a) 0-1 cm b) 2-3 cm and c) 4-6 cm growth l e v e l s 161 38 P l o t of concen t ra t i on i n the bu lk/sur face area versus time f o r K C I O 4 c r y s t a l s a t 10.5° and a r o t a t i o n speed of 500 rpm 163 39 P l o t of the mean K'obs as a f unc t i on of the mean d i s l o c a t i o n den s i t y f o r K C 1 O 4 c r y s t a l s 166 - xv i i -LIST OF SCHEMES Scheme Page 1. C l a s s i f i c a t i o n o f c r y s t a l de fec t s 9 2. P red i c ted behavior of c r y s t a l l i n e faces and hab i t s on d i s s o l u t i o n r a te 44 - x v i i i -SYMBOLS AA energy r equ i red to remove a s o l u te molecule from the s o l i d su r face ( l a t t i c e energy) A r c o l l i s i o n frequency f a c t o r f o r a su r face c o n t r o l l e d r e a c t i o n Aj. c o l l i s i o n frequency f a c t o r f o r a t r an spo r t c o n t r o l l e d r e a c t i o n a d i s t ance measured i n a v e r t i c a l d i r e c t i o n by the t r a v e l l i n g microscope a ' , b' constants i n Eqn. 25 A, B complex, temperature dependent constants AB energy of s o l v a t i o n ABcat energy of s o l v a t i o n of the c a t i o n ABan energy of s o l v a t i o n of the anion b d i s t ance measured i n a d i r e c t i o n pe rpend icu la r to the c r y s t a l face by the t r a v e l l i n g microscope b Q Bu rge r ' s vec to r AC a c t i v a t i o n energy f o r d i f f u s i o n C concen t ra t i on i n the bulk s o l u t i o n a t time t C g s a t u r a t i o n s o l u b i l i t y C* bulk supersaturated concen t ra t i on C.j concen t ra t i on i n the i n t e r f a c i a l l a ye r dur ing d i s s o l u t i o n C.j supersaturated concen t ra t i on a t the c r y s t a l su r face D d i f f u s i o n c o e f f i c i e n t D c d i f f u s i o n c o e f f i c i e n t of the c a t i o n D= d i f f u s i o n c o e f f i c i e n t of the anion a AE net energy change per mole between molecules i n the c r y s t a l and so l va ted i n s o l u t i o n E r energy of a c t i v a t i o n f o r a su r face c o n t r o l l e d r e a c t i o n - x i x -E^ . energy of a c t i v a t i o n f o r a t r an spo r t c o n t r o l l e d r e a c t i o n E s s t r a i n energy per u n i t length of d i s l o c a t i o n E c core energy per u n i t length of d i s l o c a t i o n F mean range of KQ^S AG Gibbs f r e e energy A G c j e L | ( t ( j e n ) a c t i v a t i o n f r e e energy and r e l a x a t i o n time f o r a growth u n i t en te r i ng the su r face l a y e r ^ d e a d s ^ d e a d s ) a c t i v a t i o n f r e e energy and r e l a x a t i o n time f o r a growth u n i t l eav i ng the su r face AG s u i f f ( t s d i f f ) a c t i v a t i o n f r e e energy and r e l a x a t i o n time f o r a ' growth u n i t making the d i f f u s i o n jump on the su r face M>kink(tkink) a c t i v a t i o n f r e e energy and r e l a x a t i o n time f o r a growth u n i t en te r i ng the k ink s i t e AGj f r e e energy of fo rmat ion of a two-dimensional nucleus a t an i d e a l su r face AG^ f r e e energy of fo rmat ion of a two-dimensional nucleus a t an emergent d i s l o c a t i o n G e l a s t i c shear modulus of the c r y s t a l AH energy (enthalpy) change AH S heat of s o l u t i o n h th i cknes s of the s t a t i o n a r y l i q u i d f i l m ( d i f f u s i o n l a y e r ) h 0 hydrodynamic boundary l a ye r th i cknes s h-| depth of two-dimensional nucleus K R apparent su r face r e a c t i o n r a t e constant K T apparent t r an spo r t r a t e constant K Q ^ S observed apparent r a t e constant f o r d i s s o l u t i o n of s i n g l e faces of a c r y s t a l K ' 0 . observed apparent r a t e constant f o r bulk d i s s o l u t i o n of d i f f e r e n t c r y s t a l hab i t s - XX -i n t r i n s i c d i s s o l u t i o n r a t e constant o v e r a l l growth r a t e constant su r face r e a c t i o n r a t e constant ( d i s s o l u t i o n ) t r an spo r t r a t e constant su r face i n t e g r a t i o n r a t e constant (growth) observed r a t e constant f o r mixed con t r o l d i s s o l u t i o n constant i n Eqn. 14 c h a r a c t e r i s t i c length i n Reynolds number determinat ion order of r e a c t i o n number of bonds to be ruptured between two neighbor ing p a r t i c l e s gas cons tant Boltzmann ' s cons tant rad ius of the c r y s t a l r a t e of a g i t a t i o n or s t i r r i n g r a t e o f abso rp t ion of s o l u t e per u n i t area Reynolds number growth r a t e r a t e o f a r r i v a l of s o l u t e a t the su r face by d i f f u s i o n from the bulk s o l u t i o n r a t e of i n t e g r a t i o n i n t o the s o l i d l a t t i c e d i s s o l u t i o n r a t e rad ius of two-dimensional nucleus rad iu s of the core of the d i s l o c a t i o n su r face area of a s o l i d s upe r sa tu ra t i on r a t i o entropy change f r a c t i o n a l r a t e of su r face replacement of an element of l i q u i d - xx i -abso lu te temperature time energy of d i s s o c i a t i o n of a p a r t i c l e from a c e r t a i n s i t e on the c r y s t a l su r face l i n e a r f l ow r a t e of s o l ven t molecu la r volume volume of d i s s o l u t i o n medium k inemat ic v i s c o s i t y angular v e l o c i t y of a r o t a t i n g d i s c length of (111) face length of (112) face d i s t ance p ropo r t i ona l to (111) face measured by t r a v e l l i n g microscope d i s t ance p r opo r t i o na l to (112) face measured by t r a v e l l i n g microscope den s i t y of s o l ven t dynamic v i s c o s i t y of s o l ven t Po i s s on ' s r a t i o c r y s t a l - 1 i q u i d i n t e r f a c i a l energy change i n chemical p o t e n t i a l accompanying d i s s o l u t i o n i n t e r a c t i o n energy between two neighbor ing p a r t i c l e s time o f exposure of element of l i q u i d to the su r face mo lecu la r r ad iu s i n t e r f a c i a l angles of a c r y s t a l r e l a t i v e s upe r sa tu ra t i on weight ing f a c t o r ( f o r weighted l e a s t squares f i t t i n g o f data) - x x i i -ACKNOWLEDGEMENTS I wish to thank Dr. A.G. M i t c h e l l f o r h i s guidance and encouragement throughout the course of t h i s study. I am g r a t e f u l t o : Dr. T. A lden , N. Ep s t e i n , J . Or r , J . McNe i l l f o r t h e i r help and va luab le adv i ce . Mr. R. B u t t e r s , Department of Me ta l l u r g y , f o r the X-ray d i f f r a c t i o n a n a l y s i s . Mr. A. Lac i s and Mr. P. M u s i l , Department of Me t a l l u r g y , f o r the scanning e l e c t r o n microscopy and d i f f e r e n t i a l i n t e r f e r e n c e c on t r a s t microscopy. Dr. R. P h i l l i p s and Dr. N. E p s t e i n , Department of Chemical Eng ineer ing , f o r the n i c k e l s u l f a t e c r y s t a l s . Mr. M. F r i e s e n , f o r t e c h n i c a l he lp . Mr. R. Bur ton, f o r computer a n a l y s i s . Dr. R. Venkataramanan, f o r h i s help and encouragement. F i n a n c i a l support from the U n i v e r s i t y of B r i t i s h Columbia, S tan ley Drugs Products and the Medical Research Counc i l of Canada i s g r a t e f u l l y acknowledged. - 1 -INTRODUCTION Both the r a t e and extent of abso rp t ion ( b i o a v a i l a b i l i t y ) of many drugs admin i s tered i n s o l i d dosage forms may be r a t e - l i m i t e d by the d i s s o l u t i o n process. The r a te of d i s s o l u t i o n depends on the f o r m u l a t i o n , the manufactur-ing process and the phy s i ca l s t a t e of the drug. I t i s w e l l recogn ized tha t f a c t o r s such as p a r t i c l e s i z e and the nature of the s o l i d s t a t e of the drug (eg. whether c r y s t a l l i n e or amorphous; the degree of s o l v a t i o n i n c l u d i n g h yd r a t i on ; i t s polymorphic form) may exer t a s i g n i f i c a n t e f f e c t on d i s s o l u t i o n r a t e . The important r o l e played by the c r y s t a l l i n e nature o f a s o l i d on i t s d i s s o l u t i o n r a te i s evidenced by the l a rge volume of work pub l i shed on the i d e n t i f i c a t i o n and c h a r a c t e r i z a t i o n of s o l va te s and polymorphic forms of many drugs and t h e i r e f f e c t on d i s s o l u t i o n and b i o a v a i l a b i l i t y . However, examination o f t he l i t e r a t u r e revea l s many anomalies and unanswered ques t i on s . There has been a great deal of cont rover sy over observat ions made by severa l workers t ha t there are s i g n i f i c a n t d i f f e r e n c e s i n the d i s s o l u t i o n ra te s o f d i f f e r e n t commercial samples o f a s p i r i n and a s p i r i n r e c r y s t a l l i z e d from d i f f e r e n t s o l v e n t s . Tawashi (1968a) and Summers e t a l . (1970) reported the ex i s tence of severa l polymorphic forms of a s p i r i n which were s a i d to account f o r the d i f f e r e n c e s i n d i s s o l u t i o n r a t e s . M i t c h e l l and S a v i l l e (1967) found tha t samples of commercial a s p i r i n had d i f f e r e n t i n t r i n s i c d i s s o l u t i o n ra tes but from c r y s t a l l o g r a p h i c s tud ie s concluded t ha t the v a r i a t i o n i n d i s s o l u t i o n rates was not a r e s u l t of polymorphism. Fur ther s tud ie s ( M i t c h e l l and S a v i l l e , 1969) showed t ha t the samples had d i f f e r e n t thermo-dynamic a c t i v i t i e s and t ha t the metastable form was capable of r a p i d r eve r s i on to a more s t a b l e form. G r i f f i t h s and M i t c h e l l (1971) demonstrated - 2 -t ha t the r e ve r s i on occurs i n the su r face l a ye r s of the c r y s t a l on ly but found no evidence f o r a change i n c r y s t a l s t r u c t u r e . S a v i l l e (1968), P f e i f f e r (1971), and M i t c h e l l e t a l . (1971) proposed tha t the v a r i a b i l i t y i n d i s s o l u t i o n ra te s may be due to d i f f e r e n c e s i n the type and number of c r y s t a l de fec t s i n the l a t t i c e s or hab i t m o d i f i c a t i o n . Jamal i and M i t c h e l l (1973) r e c r y s t a l l i z e d a s p i r i n us ing a wide v a r i e t y of techniques and so l vent s and showed tha t the d i s s o l u t i o n r a te was independent of c r y s t a l growth r a t e , s a l i c y l i c a c i d content (up to 3.9% w/w), hab i t m o d i f i c a t i o n and p a r t i c l e s i z e . However, hab i t m o d i f i c a t i o n or the i n f l u e n c e o f growth r a te on the numbers of c r y s t a l de fec t s and t h e i r subsequent e f f e c t on the d i s s o l u t i o n r a te cannot be r u l ed out as the i n t r i n s i c d i s s o l u t i o n ra tes were measured using a r o t a t i n g d i s c method. I t i s probable tha t the inherent p r ope r t i e s of the i n d i v i d u a l c r y s t a l s (such as the nature and content of c r y s t a l de fec t s and su r face c h a r a c t e r i s t i c s ) w i l l be destroyed on g r i nd i ng and compress ion. Another i n t e r e s t i n g and as y e t unresolved problem concerns the d i s s o l u t i o n and apparent e q u i l i b r i u m s o l u b i l i t i e s of var ious samples of d i g o x i n . Severa l re fe rence samples of d i gox in were found to have d i f f e r e n t e q u i l i b r i u m s o l u b i l i t i e s (F lo rence and S a l o l e , 1976) and i t was suggested tha t the commercial samples d i f f e r e d i n thermodynamic p r o p e r t i e s . Powder d i s s o l u t i o n s tud ie s showed a corresponding dependence of i n i t i a l d i s s o l u t i o n ra te on s o l u b i l i t y . On comminution of the samples, d i g ox i n underwent a phase t r a n s i t i o n to an amorphous s t a t e and the apparent e q u i l i b r i u m s o l u b i -l i t i e s were g r e a t l y i nc reased . Black and Lover ing (1978) attempted to c o r r e l a t e the degree o f c r y s t a l l i n i t y of d i gox i n w i th the apparent e q u i l i b r i u m s o l u b i l i t y and d i s s o l u t i o n r a t e but found i n s tead a r ap i d r e c r y s t a l l i z a t i o n of the amorphous to the c r y s t a l l i n e s t a t e . They a l s o observed t ha t drug samples having the same degree of c r y s t a l ! i n i t y d i f f e r e d i n apparent - 3 -e q u i l i b r i u m s o l u b i l i t y . Chiou and Kyle (1979) c a r r i e d out thermal a na l y s i s and s o l u b i l i t y s tud ie s on d i f f e r e n t commercial samples of d i gox i n and d i g i t o x i n , and d i gox i n r e c r y s t a l l i z e d from ch lo ro form and e thano l . Although marked d i f f e r e n c e s i n s o l u b i l i t i e s were r epo r t ed , i n severa l i n s t ance s , the s o l u b i l i t i e s had been determined before the samples had reached e q u i l i b r i u m . The authors found t ha t both d i gox i n and d i g i t o x i n melted over a very wide temperature range which v a r i ed f o r d i f f e r e n t commercial samples. The study made no attempt to determine a po s s i b l e reason f o r the observed behavior of d i gox i n samples. I n s tead, they pos tu -l a t ed tha t the v a r i a t i o n i n me l t i ng range could be due to the presence of polymorphic and amorphous forms, c r y s t a l d e f e c t s , i m p u r i t i e s or s o l v a te format ion (or any combination of these four f a c t o r s ) . I t seems c l e a r tha t the inherent p r ope r t i e s of c r y s t a l s ( i . e . su r face and bulk s t r u c t u r e and p r o p e r t i e s ) and t h e i r r e l a t i o n s h i p to s o l u b i l i t y and d i s s o l u t i o n r a t e w i l l have to be more c l e a r l y understood before exp lanat ions f o r the observat ions o u t l i n e d above can be o f f e r e d . The r a t e of the i n t e r -f a c i a l d i s s o l u t i o n r e a c t i o n depends on the type of f o r ce s t ha t e x i s t between the atoms or molecules making up the p a r t i c u l a r c r y s t a l s t r u c t u r e . S ince the b ind ing energy of an atom i n a su r face depends s t r ong l y on i t s l o c a l environment (Bassett e t a l . , 1959) i t i s important to know as much as po s s i b l e about the d e t a i l e d geometry of the i n t e r f a c e . The approach taken i n t h i s study to the problem of d i s s o l u t i o n i s to cons ider the method of p repa ra t i on and the process of c r y s t a l growth and t h e i r e f f e c t s on c r y s t a l s t r u c t u r e . There i s evidence tha t the cond i t i on s of growth and the growth r a te can have a pronounced e f f e c t on both the ex te rna l appearance (hab i t ) and on the type and number of de fec t s i ncorporated i n t o the c r y s t a l . Even though var ious commercial sources of a p a r t i c u l a r mate r i a l may appear i d e n t i c a l i n t h e i r - 4 -c r y s t a l l i n e form, as evidenced by techniques such as X-ray d i f f r a c t i o n , they may c o n s i s t of d i f f e r e n t hab i t m o d i f i c a t i o n s and a l s o vary w ide l y i n the type and number of c r y s t a l d e f e c t s . In a d d i t i o n to p r ope r t i e s of the s o l i d s t a t e such as polymorphism, s o l v a t i o n and degree of c r y s t a l 1 i n i t y , the v a r i a t i o n i n d i s s o l u t i o n k i n e t i c s observed w i th c e r t a i n drugs may be due t o : a) the a n i s o t r o p i c nature of c r y s t a l l i n e s o l i d s and hence c r y s t a l hab i t b) the type and number of c r y s t a l de fec t s i nco rpora ted i n t o a c r y s t a l dur ing growth. For a number of reasons ( o u t l i n e d i n the D i scus s ion s e c t i o n s ) , i no rgan i c s a l t s such as n i c k e l s u l f a t e hexahydrate and potassium pe r ch l o r a te prov ide the most s u i t a b l e model, c r y s t a l l i n e m a t e r i a l s f o r our s t u d i e s . The s p e c i f i c aims of the p r o j e c t were as f o l l o w s : 1. To determine the d i s s o l u t i o n k i n e t i c s of d i f f e r e n t faces of s i n g l e c r y s t a l s under cond i t i on s o f t r a n s p o r t , mixed t r a n s p o r t - s u r f a c e and sur face c o n t r o l l e d d i s s o l u t i o n . 2. To make d i f f e r e n t hab i t m o d i f i c a t i o n s of a c r y s t a l l i n e ma te r i a l by va ry ing c ond i t i o n s of growth and i n v e s t i g a t e the d i s s o l u t i o n k i n e t i c s under a t r a n s p o r t , mixed t r a n s p o r t - s u r f a c e and su r face c o n t r o l l e d d i s s o l u t i o n . 3. To grow s i n g l e c r y s t a l s a t d i f f e r e n t growth ra te s i n a s i l i c a gel medium and to quant i f y ; . , the number of d i s l o c a t i o n s . 4. To i n v e s t i g a t e the p o s s i b i l i t y of a c o r r e l a t i o n between the number of d i s l o c a t i o n s and the d i s s o l u t i o n r a t e s . - 5 -LITERATURE SURVEY A. CRYSTAL STRUCTURE 1. L a t t i c e S t r u c t u r e The s o l i d s t a t e i s c h a r a c t e r i z e d by a r i g i d i t y of form and a tendency to mainta in a d e f i n i t e shape. A c r y s t a l l i n e s o l i d i s c h a r a c t e r i z e d by long-range order extending over many atom d iameters . The i n t e r n a l s t r u c t u r e of a c r y s t a l l i n e s o l i d i s made up of a r e gu l a r arrangement of u n i t c e l l s which form the space l a t t i c e . The space l a t t i c e may be regarded as a three-d imens iona l pa t te rn of po in t s i n space, where each po i n t i n the l a t t i c e has e x a c t l y the same environment as any other po i n t r ep re sen t i ng the same atom or i o n . The po in t s i n a space l a t t i c e can be arranged i n a number of ways as a s e r i e s of p a r a l l e l and e q u i d i s t a n t planes c a l l e d l a t t i c e p lanes . The ex te rna l faces of a c r y s t a l are p a r a l l e l to these p lanes , the most f r e q u e n t l y o c cu r r i n g types of faces being those corresponding to planes con ta i n i n g the l a r g e s t number of p o i n t s , r e f e r r e d to as a high r e t i c u l a r dens i t y (Law of B r a v a i s ) . When a c r y s t a l i s subjected to an ex te rna l s t r e s s , rupture occurs along one or more d i r e c t i o n s which bear a s imple geometric r e l a t i o n s h i p to the o r i g i n a l faces of the c r y s t a l and the new sur faces so exposed are a l s o p l ana r . Th i s phenomenon i s known as c leavage. A c r y s t a l may possess severa l c leavage planes or none. The q u a l i t y of c leavage may range from poor to p e r f e c t (Wahlstrom, 1979). C r y s t a l s have been c l a s s i f i e d i n t o seven systems (Table I) (G lasstone and Lewis, 1978). a, 3 , y are the angles between axes of re fe rence c a l l e d c r y s t a l l o g r a p h i c axes. The axes are g e n e r a l l y chosen to correspond w i th the edges of the u n i t c e l l , a , b and c are the i n t e r c e p t s made by the u n i t - 6 -Table I C l a s s i f i c a t i o n of c r y s t a l s System Angles between axes Length of axes Examples Cubic ( i s omet r i c ) Tetragonal Orthorhombic (rhombic) Monoc l i n i c T r i c l i n i c Hexagonal Rhombohedral a = 8 = y = 90° a = b = c a = 3 = y = 90° a = b * c a = B = Y = 90° a ^ b ^ c a = Y = 9 0 ° , 6 + 90° i / b ^ c a f 6 * Y i 90° a ^ b ^ c a = 6 = 9 0 ° , Y = 120° a = b t c a = B = Y ^ 9 0 ° a = b = c NaC l , CaF 2 N i S 0 4 a 6H 20 KCIO^, a c e t a n i l i d N i S 0 4 66H 20, sucrose CuS0 4 5H 20 S i 0 2 CaCOg, c o r t i s o n e - 7 -c e l l a long these 3 axes. C r y s t a l planes and faces are i d e n t i f i e d by a system devised by W.H. M i l l e r (Laud i se , 1970). The M i l l e r i n d i c e s of a plane or face are the r e c i p r o c a l s of the i n t e r c e p t s o f the plane or face w i th the c r y s t a l l o g r a p h i c axes. 2. I s o t r o p i c and a n i s o t r o p i c c r y s t a l s Except f o r those belonging to the cub i c system a l l c r y s t a l s have c e r t a i n p r ope r t i e s t ha t vary w i th the d i r e c t i o n . Such substances are s a i d to be a n i s o t r o p i c , to d i s t i n g u i s h them from cub ic c r y s t a l s and amorphous ma te r i a l s which are i s o t r o p i c , having i d e n t i c a l c h a r a c t e r i s t i c s i n a l l d i r e c t i o n s . The a n i s o t r o p i c p r o p e r t i e s of c r y s t a l s may o r i g i n a t e i n two ways (Bunn, 1961) a) The molecules may themselves be a n i s o t r o p i c . b) The o r d e r l y arrangement, of atoms or ions i n a c r y s t a l g ives r i s e to d i f f e r e n t atomic d i s t r i b u t i o n s i n d i f f e r e n t d i r e c t i o n s and confers p r ope r t i e s va ry ing w i th c r y s t a l d i r e c t i o n . 3. C r y s t a l hab i t s and polymorphic forms The ex te rna l shape or hab i t depends on the r e l a t i v e development of the d i f f e r e n t f a ce s , but the i n t e r f a c i a l angles are always cons tant . Habi t m o d i f i c a t i o n s normal ly a r i s e when the environment of a growing c r y s t a l a f f e c t s i t s e x te rna l shape wi thout changing i t s i n t e r n a l s t r u c t u r e . These mod i f i c a t i o n s i n c l ude v a r i a t i o n s i n s i z e , the r e l a t i v e development of c e r t a i n faces and the k ind and number of faces present . Polymorphism i s the a b i l i t y of any element or compound to c r y s t a l l i z e as more than one d i s t i n c t c r y s t a l s pec i e s . D i f f e r e n t polymorphs of a g iven compound a r e , i n g e n e r a l , as d i f f e r e n t i n s t r u c t u r e and p r o p e r t i e s as the c r y s t a l s of two d i f f e r e n t compounds (Ha l eb l i an and McCrone, 1969). - 8 -4. C r y s t a l de fec t s ( imper fec t i on s ) C r y s t a l s may be c h a r a c t e r i z e d as p e r f e c t or imper fec t . The p e r f e c t c r y s t a l however i s an i d e a l i z e d concept. A p e r f e c t c r y s t a l would have a r egu l a r arrangement of u n i t c e l l s where the space l a t t i c e was p e r f e c t l y formed w i th no i r r e g u l a r i t i e s or deformat ions. Real c r y s t a l s i n nature are always imper fec t i n some sense and these l a t t i c e imper fec t ions can confer some important chemical and mechanical p r ope r t i e s on c r y s t a l l i n e m a t e r i a l s . A c l a s s i f i c a t i o n of c r y s t a l imper fec t i on s i s g iven i n Scheme 1. 4.1 Po in t de fec t s Po in t de fec t s may be c l a s s i f i e d i n t o phonons, e l e c t r on s and ho l e s , e x c i t o n s , vacancies and ex t r a atoms ( i n t e r s t i t i a l s and s u b s t i t u t i o n a l atoms). Po in t de fect s are l o c a l i z e d imper fec t ions (zero d imens iona l ) and a r e , i n gene ra l , thermodynamical ly s t a b l e i . e . the energy expended i n t h e i r forma-t i o n i s compensated f o r by the c o n f i g u r a t i o n a l entropy a s soc i a ted wi th t h e i r presence. Vacancies are holes or vacant l a t t i c e s i t e s i n the c r y s t a l l a t t i c e caused by the absence of atoms. Two major types of vacancy de fec t s can occur ; Frenkel d e f e c t s , i n which c e r t a i n of the atoms or ions have migrated to i n t e r s t i t i a l p o s i t i o n s l e a v i n g behind the holes t ha t they vacated, and Schottky d e f e c t s , where the atoms tha t might occupy the vacancies are not present i n the c r y s t a l (Laud i se, 1970). I n t e r s t i t i a l s occur where ex t r a atoms ( f o r e i g n or of the same spec ie s ) occupy p o s i t i o n s i n the i n t e r s t i c e s between the atoms i n the c r y s t a l . I t i s a l s o po s s i b l e f o r f o r e i gn atoms ( impur i t y atoms) to s u b s t i t u t e f o r the normal atoms. Phonon de fec t s are r e l a t e d to thermal v i b r a t i o n s of i n d i v i d u a l atoms i n the l a t t i c e and e l e c t r on s and holes and exc i ton s are e l e c t r o n i c d e f e c t s . These de fec t s w i l l not be d i scussed f u r t h e r . Scheme 1. C l a s s i f i c a t i o n of c r y s t a l defect s DEFECTS POINT DEFECTS Phonons E lec t rons and Holes LATTICE DEFECTS Exc i tons Vacancies Ext ra Atoms Schottky X Frenkel Twins S tack ing Fau l t s L ine Defects Gra in Boundaries lO I Same Substance 1 Foreign Atoms - 10 -4.2 L a t t i c e de fec t s 4.21 L ine de fec t s L ine defect s or d i s l o c a t i o n s are one dimensional de fec t s which are thermodynamical ly unstab le ( C o t t r e l l , 1953). Hence most s o l i d s even when c r y s t a l l i n e , are not a t t rue e q u i l i b r i u m . The concept of d i s l o c a t i o n s as l a t t i c e de fect s was in t roduced independent ly by Tay l o r (1934) and Orowan (1934) to account f o r the f a c t t ha t i n s i n g l e c r y s t a l s , deformat ion occurs along we l l de f ined s l i p planes r a t he r than i n a random manner and tha t the f o r ce requ i red to produce the s l i p i s s i g n i f i c a n t l y l e s s than the t h e o r e t i c a l . In the i dea l case, a c r y s t a l deforms by planes of atoms s l i d i n g over one another, l i k e cards i n a deck. There i s one u n i t of s l i p on a s l i p plane i f every atom on one s i de of t ha t plane has moved i n t o a p o s i t i o n o r i g i n a l l y occupied by i t s nearest neighbor i n the d i r e c t i o n of s l i p . Thus, u n i t s l i p leaves the atoms i n r e g i s t e r across the s l i p plane and does not d i s t u r b the c r y s t a l p e r f e c t i o n . In most c r y s t a l s however, s l i p i s not uniform over a s l i p plane because the atoms are not r i g i d l y bound to each o ther . They are e l a s t i c a l l y coup led, so tha t thermal v i b r a t i o n and l o c a l i r r e g u l a r i t i e s make the fo rce s a c t i n g over the g l i d e planes n o n u n i f o r m . S l i p occurs by d i f f e r e n t amounts on e i t h e r s i de of the s l i p plane and the boundary between the two reg ions of s l i p i s a l i n e . I t i s a reg ion where the atoms are not p roper l y surrounded by neighbors (an i m p e r f e c t i o n ) . S ince the impe r fec t i on i s conta ined w i t h i n a few atomic diameters of a l i n e , i t i s c a l l e d a l i n e imper fec t i on or d i s l o c a t i o n (Read, 1953). There are two types of d i s l o c a t i o n , the edge d i s l o c a t i o n and the screw d i s l o c a t i o n which rep re sen t , not d i s c r e t e types , but s pec i a l o r i e n t a t i o n s . A d i s l o c a t i o n can be de f ined w i th the a i d of a Bu rge r ' s c i r c u i t . . Th i s i s - '11 -any atorn-to-atorn path made i n a c r y s t a l which forms a c l o sed loop. I f the c i r c u i t i s made i n an i dea l d i s l o c a t i o n - f r e e c r y s t a l , the vec to r to complete the c i r c u i t i s ze ro . I f the Bu rge r ' s c i r c u i t encloses a d i s l o c a t i o n , the c l o su re f a i l u r e i s the Bu rge r ' s vec to r ( b Q ) . In edge d i s l o c a t i o n s the Bu rge r ' s vec to r i s pe rpend icu la r to the d i s l o c a t i o n and i n screw d i s l o c a t i o n s , i t i s p a r a l l e l ( F i g . 1 ) . Imperfect ions i n t e r a c t w i th each other e .g . some types of imper fec t i on generate others and the group forms an i n t e r l o c k i n g f a m i l y . Often they make complexes, such as vacancy c l u s t e r s or a d i s l o c a t i o n surrounded by an impur i t y atmosphere. Impurity atoms d i f f u s e towards d i s l o c a t i o n s . Overs ized atoms are a t t r a c t e d to the reg ion of tens ion around a d i s l o c a t i o n ; unders ized s u b s t i t u t i o n a l atoms are a t t r a c t e d to the reg ion of compress ion. 4.22 Grain boundaries In many s o l i d m a t e r i a l s , the i n d i v i d u a l c r y s t a l s are smal l and the m a t e r i a l s conta in many of these c r y s t a l l i t e s . Each of the c r y s t a l l i t e s i s m i so r i en ted w i th respect to i t s neighbors to a g rea te r or l e s s e r degree. When the angle between adjacent c r y s t a l l i t e s i s s m a l l , the r e s u l t a n t low-angle g r a i n boundary c o n s i s t s of an a r ray of d i s l o c a t i o n s . T i l t boundaries c o n s i s t of a l i n e . o f edge d i s l o c a t i o n s and t w i s t boundaries of a l i n e of p a r a l l e l screw d i s l o c a t i o n s . 4.23 Twins Composite c r y s t a l s i n which the i n d i v i d u a l par t s are r e l a t e d to one another i n a d e f i n i t e c r y s t a l l o g r a p h i c manner are twinned c r y s t a l s . 4.2.4 S tack ing f a u l t s There are a number of imper fec t i on s t ha t can r e s u l t i n c r y s t a l s of c e r t a i n symmetries because of the improper order of the s t ack i ng sequence. For example, a t h i n l a ye r o f ma te r i a l of one s t r u c t u r e can become "sandwiched" - 12 -Dislocation line Dislocation line F i g . 1. An edge d i s l o c a t i o n (upper diagram) and screw d i s l o c a t i o n ( lower diagram). - 13 -between l aye r s of ma te r i a l of another s t r u c t u r e . B. CRYSTAL GROWTH The depo s i t i on of a s o l i d c r y s t a l l i n e phase from l i q u i d and gaseous s o l u t i o n s , pure l i q u i d s and pure gases, can on ly occur i f some degree of supe r sa tu ra t i on or supercoo l i ng has been achieved i n the system. The degree of s upe r sa tu ra t i on or d e v i a t i o n from the s a t u r a t i o n s o l u b i l i t y i s the main f a c t o r c o n t r o l l i n g the depo s i t i o n of the s o l i d phase. The c r y s t a l l i z a t i o n process can be cons idered to comprise three bas ic s teps : 1. achievement of s upe r sa tu ra t i on or s upe r coo l i n g , 2. format ion of c r y s t a l n u c l e i , 3. growth of the c r y s t a l s . For growth to occur , there must be s t a b l e n u c l e i i . e . p a r t i c l e s l a r g e r than a c r i t i c a l s i z e , present i n the s o l u t i o n . As i n a l l chemical r e a c t i o n s , there e x i s t s an energy b a r r i e r f o r n u c l e a t i o n . I n i t i a l l y , by molecu la r aggregat ion, c r y s t a l nuc l e i are formed i n the supersaturated s o l u t i o n s , some of which r e d i s s o l v e . Others , however, due to the s t a t i s t i c a l f l u c t u a -t i o n e f f e c t , can i nco rpo ra te more atoms or molecules to . fo rm the c r i t i c a l n uc l e i and a t t a i n s u f f i c i e n t energy to pass over the energy b a r r i e r . C r y s t a l growth then ensues. Nuc lea t i on may occur spontaneously (homogeneous nuc l ea t i on ) or i t may be induced by f o r e i g n p a r t i c l e s (heterogeneous nuc lea t i on ) (Walton, 1965). 1. Theor ies of c r y s t a l growth M u l l i n (1972) and P h i l l i p s (1973) have broadly c l a s s i f i e d the t heo r i e s on the mechanism of c r y s t a l growth under the three general headings, " s u r f a ce energy " , " ad so rp t i on l a y e r " and " d i f f u s i o n " t h e o r i e s . The su r face - 14 -energy t heo r i e s are based on the p o s t u l a t i o n of Gibbs (1928) and Cur ie (1885) tha t the shape a growing c r y s t a l assumes i s t ha t which has a minimum sur face energy. This po s t u l a t e was based on con s i de ra t i on s of the su r face f r e e energy of a l i q u i d d r o p l e t . However, Gibbs recogn ized the l i m i t a t i o n s of the analogy s i nce i n a l i q u i d d r o p l e t the atoms or molecules are randomly d i sper sed and i n a c r y s t a l , are r e g u l a r l y arranged i n a l a t t i c e . Wul f f (1901) suggested that the c r y s t a l would grow at ra tes p ropo r t i ona l to t h e i r re spec -t i v e su r face energ ie s . There i s l i t t l e q u a n t i t a t i v e evidence to support the su r face energy t heo r i e s and they have been l a r g e l y abandoned. 1.1 D i f f u s i o n t h e o r i e s The d i f f u s i o n t heo r i e s cons ide r the processes occur ing i n the s o l u t i o n surrounding the c r y s t a l as we l l as those a t the c r y s t a l s u r f a ce . Noyes and Whitney (1897) were the o r i g i n a t o r s of the d i f f u s i o n t h e o r i e s . They assumed t h a t d i f f u s i o n i s f r e q u e n t l y the r a t e determing step i n the case of a s o l i d -l i q u i d r e a c t i o n due to the r e l a t i v e l y slow r a t e of t h i s process i n s o l u t i o n . The depo s i t i on of s o l i d on the face of a growing c r y s t a l cou ld be regarded as a d i f f u s i o n a l p rocess , the r a t e of the process being governed by the d i f f e r e n c e between the concen t ra t i on a t the s o l i d su r face and i n the bulk of the s o l u t i o n . The equat ion f o r the growth r a te i s g iven by, r = k t S (C* - C s ) (1) where r i s the growth r a t e , S i s the su r face area of the c r y s t a l , C* i s the bulk supersaturated c o n c e n t r a t i o n , Cs i s the s a t u r a t i o n s o l u b i l i t y and kt the t r an spo r t r a t e cons tant . Nernst (1904) int roduced the concept of a t h i n , stagnant f i l m of l i q u i d adjacent to the c r y s t a l face through which molecules would have to d i f f u s e . He concluded from the f i l m theory t h a t , - 15 -where D i s the d i f f u s i o n c o e f f i c i e n t and h i s the f i l m t h i c kne s s . The term h v a r i e s i n v e r s e l y w i th the v e l o c i t y of the s o l u t i o n past the c r y s t a l and the growth r a te i s expected to i nc rease wi th s o l u t i o n v e l o c i t y . However, Marc (1908) observed tha t k t d i d not i nc rease i n d e f i n i t e l y w i th i n c r ea s i n g s o l u t i o n v e l o c i t y , but reached some l i m i t i n g va lue . Hence f i l m d i f f u s i o n alone i s not s u f f i c i e n t to e x p l a i n the mechanism of c r y s t a l growth. Berthoud (1912) then suggested tha t c r y s t a l growth takes p lace by d i f f u s i o n of s o l u t e to the c r y s t a l su r face fo l l owed by a f i r s t .order " r e a c t i o n " where s o l u te molecules are incorporated, i n t o the l a t t i c e . - The ra te s o f the two processes can be w r i t t e n , r t = k t S (C* - C i * ) (3) r s = k s S ( C i * - C s ) (4) where C-j* i s the supersaturated concen t ra t i on a t the c r y s t a l s u r f a c e , r^ i s the r a te of a r r i v a l of s o l u te a t the su r face by d i f f u s i o n from the bulk s o l u t i o n , r s i s the r a te of i n t e g r a t i o n i n t o the s o l i d l a t t i c e ( su r face r eac t i on ) and k s i s the su r face i n t e g r a t i o n r a te cons tant . At steady s t a t e , r t = r s = r a n c * ^ i * can be e l i m i n a t e d . r = KS (C* - C s ) (5) where 1 =i^ +k7 (6) and K i s the o v e r a l l growth r a te cons tant . - 16 -Marc (1908) i n v e s t i g a t e d the r a t e of c r y s t a l l i z a t i o n of a number of s a l t s and found t ha t i n many cases the dependence of growth r a t e on super-s a t u r a t i o n was g rea te r than f i r s t o rder . Th is g i v e s , r = KS (C* - C s ) n (7) where n may be g rea te r than one imply ing t ha t d i f f u s i o n i s f i r s t order and the su r face r e a c t i o n may have a h igher order than one. 1.2 Adsorpt ion l a y e r t heo r i e s These prov ide t heo r i e s f o r the mechanism of i n c o r p o r a t i o n of s o l u te molecules i n t o the c r y s t a l l a t t i c e , the su r face r e a c t i o n process. Verma and Kr i shna (1966) have reviewed the theory of the growth of an i d e a l l y p e r f e c t c r y s t a l and an imper fect c r y s t a l . The growth of a p e r f e c t c r y s t a l can be i l l u s t r a t e d by the Ko s se l - S t r an sk i model ( F i g . 2) where the molecules are represented as cubes. The cubes are stacked face to face and each cube i s a t t r a c t e d e q u a l l y by a l l s i x of i t s neighbors. Volmer (1939) thought t ha t c r y s t a l s grew i n l a ye r s and t ha t f o r a new l a y e r to grow,two-dimensional n u c l e a t i o n , where a c r i t i c a l number of adsorbed ions or molecules form a nuc leus , had to take p l a ce . Kossel (1934) mod i f i ed t h i s and s a i d t ha t adsorbed ions or molecules would migrate along the su r face of the c r y s t a l and be i nco rpora ted i n t o the c r y s t a l a t k ink s i t e s i n the monomolecular s tep. Two-dimensional nuc l ea t i on on a p e r f e c t su r face r equ i r e s a l a r ge degree of s upe r sa tu ra t i on .(50%). However, i t was observed expe r imen ta l l y t ha t growth can occur a t super sa tu ra t i on s of 1%. Frank (1949) suggested that the observed cont inued growth at low supe r sa tu ra t i on cou ld occur i f the c r y s t a l conta ined screw d i s l o c a t i o n s . The sur face step cannot then be e l im ina ted as atoms a t t a ch to the s tep . The step r o t a t e s about the screw d i s l o c a t i o n and the c r y s t a l grows up a " s p i r a l ramp". Bu r ton , Cabrera . - 17 -MONOMOLECULAR STEP F i g . 2. S t r u c tu re of a low index face f o r a pe r f e c t c r y s t a l on the Ko s se l - S t r an sk i model. - 18 -and Frank (1951) developed a k i n e t i c theory of growth based on the screw d i s l o c a t i o n mechanism o f c r y s t a l growth and which p r ed i c t ed r a te s much c l o s e r to exper imental r a te s than the e a r l i e r t h e o r i e s . In t h i s they assumed tha t the d i f f u s i o n a long the su r face determined the r a t e of the growth process and the f o l l o w i n g equat ion was d e r i v e d : r = A a 2 tanh ( | ) (8) C* where a i s the r e l a t i v e supe r sa tu ra t i on = S 1 - 1 and S 1 = 7 — ( supe r sa tu ra t i on L s r a t i o ) . A and B are complex, temperature dependent constants which i n c l ude parameters which depend on step spac ings . At low s u p e r s a t u r a t i o n , the equat ion approximates to m a 2 , but a t high s upe r s a tu r a t i on s , ma. There i s a change . f r o m a pa r abo l i c to a l i n e a r growth law as the supe r sa tu ra t i on i nc rea se s . Th is theory was der i ved f o r c r y s t a l growth from the vapor. However, Bennema (1967a) adapted the Bur ton , Cabrera , Frank model to growth from s o l u t i o n by i n t r oduc i ng r e l a x a t i o n t imes . He proposed fou r a c t i v a t i o n f r e e ene rg ie s , as represented i n F i g . 3 A G ^ , A G ^ g ^ , AG S u i f f > and AGkink> which def ined the corresponding fou r r e l a x a t i o n t imes t ^ - p , t c j e a c | s , t s > c j - j f f , t^-jpk f o r en te r i n g the su r face l a y e r , f o r l e a v i n g the s u r f a c e , f o r making the d i f f u s i o n jump on the su r face and f o r en te r i ng the kink r e s p e c t i v e l y . I t was shown (Bennema, 1967b) tha t t h i s su r face d i f f u s i o n model gave the most s a t i s f a c t o r y exp l ana t i on of a c c u r a t e l y measured growth r a te vs. r e l a t i v e s upe r sa tu ra t i on (a) cu rves . Konak (1973) c r i t i c a l l y examined the main fea tu re s of the t heo r i e s of growth from s o l u t i o n which had been put forward up to 1973 and showed them to be who l l y o r p a r t l y incompat ib le with exper imental ob se r va t i on s . S ince there was no u n i f i e d c r y s t a l growth theory , a s e t o f f i v e t heo r i e s each dea l i ng w i th a c e r t a i n aspect of the growth process , were surveyed and - 19 -(1) Hydra ted growth u n i t in s o l u t i o n . (2) Dehydra ted growth u n i t in a d s o r p t i o n l a y e r . (3) Growth u n i t on s t e p s i t e . (h) Growth u n i t i n c o r p o r a t e d in k i n k s i t e . F i g . 3. React ion path f o r a growth u n i t . - 20 -shown to be compat ib le w i th each other (Bennema, 1974). Another approach to mode l l i ng c r y s t a l growth r a te k i n e t i c s i s t ha t of computer s imu l a t i on (Gi lmer and Bennema, 1972). The growth r a t e of a c r y s t a l i s r e l a t e d to a number of f a c t o r s which determine the c o n d i t i o n of the c r y s t a l - f l u i d i n t e r f a c e . Among these are the atomic bonding i n the su r face l a y e r , the m o b i l i t y of the atoms a t the i n t e r f a c e , the degree of p e r f e c t i o n of the growing c r y s t a l , su r face roughness and i m p u r i t i e s . I t i s very d i f f i c u l t to examine each of these f a c t o r s i n i s o l a t i o n ; f o r example, small q u a n t i t i e s of i m p u r i t i e s may have a major e f f e c t on the k i n e t i c s and f a c t o r s such as su r face atom m o b i l i t y cannot be a l t e r e d w i thout changing the temperature and hence the d r i v i n g f o r c e . By us ing computer and Monte-Carlo s imu l a t i on models, each parameter can be v a r i ed independent ly (G i lmer , 1976; G i lmer , 1980; Bennema e t a l , 1973). 2. O r i g i n of d i s l o c a t i o n s There are severa l mechanisms whereby d i s l o c a t i o n s are formed i n c r y s t a l s . D i s l o c a t i o n s w i l l propagate i n t o the growing c r y s t a l from the nucleus or seed (Johnston, 1962). Frank (1949) proposed severa l ways i n which d i s l o c a t i o n s cou ld a r i s e dur ing the growth of a c r y s t a l and these have been reviewed by Nabarro (1967) and Albon (1963). a) D i s l o c a t i o n s are formed when two po r t i on s of a c r y s t a l d i f f e r i n g s l i g h t l y i n o r i e n t a t i o n impinge on one another eg. i n d e n d r i t i c growth. b) I f a growing c r y s t a l meets a p a r t i c l e of f o r e i g n mat te r , m i s f i t d i s l o c a t i o n s may o r i g i n a t e a t the i n t e r f a c e . c) Rows of d i s l o c a t i o n s are formed along a plane when the su r face of a hard c r y s t a l i s damaged. - 21 -d) When c r y s t a l s are grown at high temperature, the thermal s t re s se s which occur as i t begins to cool to room temperature may cause p l a s t i c f low and the m u l t i p l i c a t i o n of d i s l o c a t i o n s i n the c r y s t a l (Hopkins, 1969). e) Po in t de fec t condensat ion ( u s ua l l y vacant l a t t i c e s i t e s ) r e s u l t s i n the format ion of d i s l o c a t i o n loops . f ) D i s l o c a t i o n s can form as a consequence o f the inhomogenous d i s t r i b u t i o n of i m p u r i t i e s (Ma l i c sko and Szomor, 1971). Changes i n l a t t i c e parameter, a s soc i a ted w i th inhomogeneit ies cause s t re s se s i n the growing c r y s t a l . These s t re s se s may be compen-sated by the format ion of d i s l o c a t i o n s . g) P l a s t i c y i e l d under mechanical s t r e s s does not c r ea te d i s l o c a t i o n s but m u l t i p l i e s those a l ready present . 3. Growth r a t e and d i s l o c a t i o n d e n s i t y There i s evidence to show tha t the den s i t y of d i s l o c a t i o n s depends on the c r y s t a l growth r a t e . In a general d i s cu s s i on on c r y s t a l growth, Garner (1949) and Frank (1949) s ta ted t ha t c r y s t a l s grow more r e g u l a r l y , the lower the supe r sa tu ra t i on (and hence, lower growth r a t e s ) . Ma l i c sko and Szomor (1971) s t a t e tha t inhomogenous impur i t y d i s t r i b u t i o n i s a consequence of f l u c t u a t i o n s of growth c o n d i t i o n s . Experimental i n v e s t i g a t i o n s show the ex i s t ence of a r e l a t i o n s h i p between the concen t r a t i on of i m p u r i t i e s b u i l t i n to the c r y s t a l and the den s i t y of d i s l o c a t i o n s (Kun et a l , 1968). Ma l i c sko and Szomor (1971), grew KC1 s i n g l e c r y s t a l s from aqueous s o l u t i o n con ta i n i n g Sn and Pb ion a d d i t i v e s and found tha t the d i s l o c a t i o n den s i t y increased w i th growth r a t e . I z r ae l e t a l (1972) c a r r i e d out a d e t a i l e d X-ray topographic study of the growth de fec t s i n t r i g l y c i n e s u l f a t e c r y s t a l s i n r e l a t i o n to t h e i r growth c o n d i t i o n s . They s t a ted tha t i n - 22 -c r y s t a l s grown from s o l u t i o n , the d i s l o c a t i o n s are u s u a l l y nea r l y p a r a l l e l to the growth d i r e c t i o n and terminate a t the su r face of the c r y s t a l . Comparison of samples of c r y s t a l s grown from the same s o l u t i o n showed that the den s i t y of d i s l o c a t i o n s decreased w i th decreas ing s upe r sa tu ra t i on and growth r a t e , even a t very small r a t e s . Other growth cond i t i o n s i n f l u e n c i n g the den s i t y of d i s l o c a t i o n s were a l s o d i s cu s sed . Samples grown wi th a temperature s t a b i l i t y of 0.05°C gave a high den s i t y of d i s l o c a t i o n s p a r t i c u l a r l y along the p r o j e c t i o n of the seed i n the d i r e c t i o n of growth. At h igher temperature s t a b i l i t y , a lower den s i t y of d i s l o c a t i o n s was produced. Any abrupt change i n growth cond i t i o n s ( a g i t a t i o n , tempera-tu re c on t r o l e t c . ) w i l l cause i n c l u s i o n s (foreign i m p u r i t i e s , which may be s o l i d , l i q u i d or gas, the pockets of impur i t y being termed i n c l u s i o n s ) to be embedded and d i s l o c a t i o n s to be formed. In a d d i t i o n to i n t e r r u p t e d growth, a f a s t e r growth r a te w i l l a l s o lead to i n c l u s i o n s (Brooks e t a l . , 1968). Small amounts of s p e c i f i c i m p u r i t i e s in t roduced i n t o the mother s o l u t i o n induced a high d i s l o c a t i o n d e n s i t y . A correspondence between growth r a te and d i s l o c a t i o n den s i t y was a l s o shown by von Batche lder and Vaughan (1967). S i ng l e c r y s t a l s of sodium c h l o r i d e and potassium c h l o r i d e were grown from s o l u t i o n a t d i f f e r e n t growth ra te s and the c r y s t a l s c leaved and etched. The c leaved sur faces were observed under an o p t i c a l microscope and photographs taken of the sur faces to show the d i s l o c a t i o n etch p i t den s i t y . The photographs c l e a r l y demonstrated the inc rease i n d i s l o c a t i o n den s i t y brought about by increases i n the growth r a t e . Mel ikhov and Vukovic (1974) have developed a complex equat ion to represent the c r y s t a l de fec t generat ion dependence on the growth r a t e . Henisch et a l . (1965a) grew c r y s t a l s of ca l c ium t a r t r a t e i n sodium m e t a s i l i c a t e g e l . In gel systems, the growth r a t e i s c o n t r o l l e d by the d i f f u s i o n process i n the - 23 -gel and not by i n t e r f a c i a l processes. Hence, i n a system where one reagent d i f f u s e s through a gel charged w i th another reagent, the average c r y s t a l growth r a te i s g r ea te s t near the top of the d i f f u s i o n column where the concent ra t i on g rad ient s are high and small near the bottom where the g rad ient s are s m a l l . . They found t h a t , corresponding to the d i s t r i b u -t i o n of growth r a t e s , there was a l s o a d i s t r i b u t i o n i n the number of etch p i t s on any c r y s t a l f a c e . They suggested t ha t the growth r a t e i t s e l f determines the number of de fec t s b u i l t i n t o the c r y s t a l , even i n the absence of foreign i m p u r i t i e s . Pa te l and Rao (1979) have grown potassium pe r ch l o r a te c r y s t a l s i n s i l i c a ge l s and shown tha t the d i s l o c a t i o n den s i t y decreases w i th the depth below the g e l - s o l u t i o n i n t e r f a c e ( i . e . decreas ing growth r a t e ) . 4. Growth of c r y s t a l s i n s i l i c a ge l s Large, w e l l - d e f i n e d c r y s t a l s can be grown i n s i l i c a ge l s and i n recent years the technique has been w ide l y used i n the p repa ra t i on of a v a r i e t y of m a t e r i a l s , s u i t a b l e f o r s o l i d - s t a t e exper imenta t ion . 4.1 Gel s t r u c t u r e and p r ope r t i e s When sodium m e t a s i l i c a t e goes i n t o s o l u t i o n m o n o s i l i c i c a c i d i s p ro -duced, which then polymer izes w i th the l i b e r a t i o n of water (Hen i sch, 1970). E ven tua l l y a th ree -d imens iona l network of S i - 0 l i n k s i s e s t a b l i s h e d . Gels have the mechanical p r ope r t i e s of s o l i d s and i t i s be l i e ved t ha t they have a r i g i d phase which possesses the c h a r a c t e r i s t i c s of a s o l i d . In ge l s of the s i l i c i c a c i d t ype , the s o l i d phase i s c r y s t a l l i n e ( L l o y d , 1926). Ge l a t i on i s a process c l o s e l y p a r a l l e l to c r y s t a l l i z a t i o n and i s accompanied i n most cases by e v o l u t i o n of heat. The time requ i red f o r g e l a t i o n i s very s e n s i t i v e to pH. A pH of 8 g ives the minimum g e l l i n g t ime. - 24 -4.2 Growth mechanism One reagent i s mixed w i th the sodium m e t a s i l i c a t e s o l u t i o n and the s o l u t i o n a l lowed to g e l . The second reagent d i f f u s e s through the g e l , the concent ra t i on g rad ient s being high near the top of the d i f f u s i o n column and small near the bottom. From observat ions of the growth proces s , i t has been t e n t a t i v e l y concluded t ha t there e x i s t s i n the immediate neighborhood of the c r y s t a l s u r f a ce , a supe r sa tu ra t i on which remains constant dur ing growth. The gel a l s o supports the c r y s t a l and, a t the same t ime, y i e l d s to i t s growth w i thout e x e r t i n g major f o rce s upon i t . Th is r e l a t i v e freedom from c o n s t r a i n t and the s t a b l e pa t te rn of concen t ra t i on g rad ient s are important f a c t o r s i n the achievement of high s t r u c t u r a l p e r f e c t i o n i n the c r y s t a l s . Another important f u n c t i o n of the gel i s t ha t of suppress ing nuc l ea t i on thereby reducing the compet i t i ve nature of the growth. Pate l and Rao (1977, 1978) have s tud ied the n u c l e a t i o n and growth of potassium pe r ch l o r a te c r y s t a l s i n s i l i c a g e l s . They have assessed the e f f e c t s of va ry ing the concent ra t i ons of reagents , ageing of g e l s , gel den s i t y and pH and temperature. Other c r y s t a l s grown i n gel systems i n c l ude ca lc ium oxa l a te ( B i s a i l l o n and Tawashi, 1975), ca l c ium pyrophosphate ( P r i t z k e r e t a l . , 1978), lead c h l o r i d e (Abdulkhadar and I t t yachen , 1980), d i c a l c i u m phosphate (Lefaucheux e t al„ 1979). C. DISSOLUTION KINETICS C r y s t a l d i s s o l u t i o n comprises hydrat ion a t k i n k s , motion of ma te r i a l a long step l i n e s and on the c r y s t a l su r face and de so rp t i ve t r a n s f e r f o l l owed by mass t r an spo r t of m a t e r i a l i n t o the aqueous environment (Jones and L inge , 1975). D i s s o l u t i o n can be cons idered as a s p e c i f i c type of heterogeneous r e a c t i o n i n which a mass t r a n s f e r i s e f f e c t e d through the net r e s u l t of - 25 -escape and depo s i t i on of s o l u te molecules a t a s o l i d s u r f ace . Var ious models of the d i s s o l u t i o n process have been reviewed by Higuchi (1967). Of these , the "double b a r r i e r " model has been va l uab le i n d e s c r i b i n g va r ious d i s s o l u -t i o n phenomena (Wurster and T a y l o r , 1965a, b; M i t c h e l l and S a v i l l e , 1969; Nogami e t a l . , 1969a; Donbrow and Tou i t ou , 1977). Th is model cons ider s d i s s o l u t i o n as occur ing i n two consecut i ve s teps : 1) an i n t e r f a c i a l or su r face r e a c t i o n which r e s u l t s i n the l i b e r a t i o n of s o l u te molecules from the s o l i d phase, and 2) the subsequent t r an spo r t of s o l u te away from the i n t e r f a c e under the i n f l u e n c e of d i f f u s i o n . Depending on the r e l a t i v e magnitudes of these two s t ep s , d i s s o l u t i o n r eac t i on s can be d i v i ded i n t o three types : a) Transport c o n t r o l l e d d i s s o l u t i o n : The r e a c t i o n a t the i n t e r f a c e occurs much f a s t e r than the r a t e of t r an spo r t of products from the i n t e r f a c e . The re fo re , the r a te i s d e t e r -mined by the t r an spo r t processes i . e . d i f f u s i o n and convec t i on . b) Surface r e a c t i o n c o n t r o l l e d d i s s o l u t i o n : The su r face or i n t e r f a c i a l r e a c t i o n i s much s lower than the t r an spo r t processes and hence determines the r a t e . c) Mixed su r face r e a c t i o n and t r an spo r t c o n t r o l l e d d i s s o l u t i o n : The ra tes o f the su r face r e a c t i o n and the t r an spo r t processes are of the same order o f magnitude, so t ha t the o v e r a l l r a t e i s a f u n c t i o n o f both processes. 1. Transport c o n t r o l l e d d i s s o l u t i o n This i s o f ten r e f e r r e d to as the d i f f u s i o n l a y e r model or Noyes-Nernst model. In most cases d i s s o l u t i o n has been t r e a t ed as being c o n t r o l l e d by d i f f u s i o n from a f i l m at the i n t e r f a c e through a s t a t i o n a r y boundary l a y e r . The r a t e of d i s s o l u t i o n i s g iven by the Noyes-Whitney equat ion or subsequent - 26 -modi f i cat ions of i t (Noyes and Whitney, 1897; Nernst and Brunner, 1904). r a te = S k t ( C s - C) (9) where k f , the t r an spo r t r a te constant = D/h and D i s the d i f f u s i o n c o e f f i -c i e n t i n the sa tu ra ted l a y e r , h i s the th i cknes s of the s t a t i o n a r y l i q u i d f i l m , C s i s the e q u i l i b r i u m concen t ra t i on i n the sa tu ra ted l a y e r , C i s the concen t ra t i on i n the bulk s o l u t i o n a t t ime t , and S i s the su r face area of the s o l i d . The assumption which unde r l i e s Eqn. 9 i s t ha t molecules of s o l u te are l i b e r a t e d r a p i d l y a t the s o l i d - s o l v e n t i n t e r f a c e to form the sa tu ra ted f i l m ; the observed r e a c t i o n v e l o c i t y i s the r a te a t which s o l u te molecules d i f f u s e from t h i s f i l m through the boundary l a y e r i n t o the bulk s o l u t i o n . Van Name and H i l l (1913) po inted out tha t the d i f f u s i o n l a y e r would not be s t a t i o n a r y but tha t i t s outer po r t i on s would possess a con s i de rab le motion i n a plane p a r a l l e l to the s u r f a ce . They def ined the th i cknes s of the d i f f u s i o n l a y e r as the average d i s t ance from the su r face of the s o l i d to the po in t a t which the s t i r r i n g e f f e c t o f the eddies and c r o s s - c u r r en t s p r e v a i l i n g i n the main body of l i q u i d becomes s i g n i f i c a n t . Eqn. 9 r e p r e -sents a t h e o r e t i c a l l y sound equat ion f o r d i f f u s i o n a l f l ow i n a s t a t i c medium but should be regarded as emp i r i c a l when app l i ed to a f l u i d i n motion ( L e v i c h , 1962). Boundary l a y e r theory i s developed i n Sec t i on D . l . 2. Mixed t r a n s p o r t - s u r f a c e c o n t r o l l e d d i s s o l u t i o n The Noyes-Nernst equat ion has been extended to i n c l ude r eac t i on s of the in te rmed ia te type and the o v e r a l l d i s s o l u t i o n r a te i s g iven by r a te = S k o b s ( C s - C) (10) where kQ^s i s the observed r a t e constant f o r mixed c o n t r o l l e d d i s s o l u t i o n and i s equal to - 27 -k r k t k o b s = l c 7 T - k 7 where k r ; i s the f i r s t order su r face r e a c t i o n r a te 1 constant.When k r » k t the over -a l l r a te i s de te rm ined . so l e l y by the t r an spo r t .p roce s s and Eqn. 10 becomes the Noyes-Nernst equat ion . The c o n d i t i o n k^ » k r represents the case of su r face c o n t r o l l e d d i s s o l u t i o n i n which the concen t ra t i on i n the i n t e r -f a c i a l l a y e r , C i , i s l e s s than the e q u i l i b r i u m s o l u b i l i t y (Van Name and H i l l , 1916). Th is i s analagous to Eqns.\5 and 6 der i ved f o r c r y s t a l growth k i n e t i c s ( Sect ion B . l . l ) . 3. Surface r e a c t i o n c o n t r o l l e d d i s s o l u t i o n This i s a l s o r e f e r r e d to as the i n t e r f a c i a l b a r r i e r model. The assumption tha t the t r an spo r t process i s r a t e - l i m i t i n g , i s v a l i d on ly under c e r t a i n c o n d i t i o n s . I f the s o l i d i s very i n s o l u b l e or the v e l o c i t y of s o l ven t f low over the su r face i s very high (and hence h i s very s m a l l ) , s o l u te molecules are t ranspor ted away from the i n t e r f a c e at a r a te f a s t e r than they can be rep laced by l i b e r a t i o n of molecules from the s o l i d s u r f a ce . In t h i s case, d i s s o l u t i o n i s c o n t r o l l e d by the su r face r e a c t i o n process . S ub s t an t i a l exper imental evidence f o r the p a r t i c i p a t i o n o f the su r face r e a c t i o n i n the c on t r o l of the d i s s o l u t i o n r a t e has accumulated i n the l a s t 15 years f o r an i n c r ea s i n g number of i o n i c c r y s t a l s (Campbell and Nanco l l a s , 1969; L i t t l e and Nanco l l a s , 1970; Bovington and Jones, 1970; Jones e t a l , 1973; L i u and Nanco l l a s , 1976). These s tud ie s have shown, r a te = S k r ( C s - C ) n (12) where n i s a p o s i t i v e i n t ege r g rea te r than u n i t y . Davies and Jones (1955) proposed an " ad so rp t i on l a ye r model" where the hydrat ion a t kink s i t e s was - 28 -the r a te l i m i t i n g step and a hydrated ion l a y e r immediately adjacent to the c r y s t a l su r face was formed. This adsorpt ion l a y e r theory p red i c ted the expe r imenta l l y observed dependence of n on s a l t s t o i c h i ome t r y . Thus, f o r the l a t t i c e AgB^, n = a + b. The order of the su r face c o n t r o l l e d r e a c t i o n i s 2 f o r s a l t s such as PbS04, SrSO^, BaSG^ and 3 f o r Ba( I03)2 3 ^9^2 ' Ag2Cr04. S z i n a i and Hunt (1972) po inted out the importance of deve lop ing t h e o r i e s which are not l i m i t e d to d i f f u s i o n as the r a te l i m i t i n g s t ep , and take i n t o account energy changes dur ing the d i s s o l u t i o n process . They gave the f o l l o w -ing general equat ion f o r d i s s o l u t i o n , r a t e = k o b s S ( C s - C) (13) where k 0 b s i s the observed r a te constant f o r d i s s o l u t i o n , k g ^ i s a f u n c t i o n of the temperature a t the i n t e r f a c e , the l a t t i c e energy of molecules a t the s u r f a ce , energy of s o l v a t i o n and the su r face energy of the s o l i d under d i s s o l u t i o n c o n d i t i o n s , i . e . AE k obs = k o e " R T (14) where k 0 i s a cons tant , R i s the gas con s tan t , T i s the temperature (°K) and AE i s the net energy change per mole between a molecule i n the c r y s t a l a t the i n t e r f a c e and a molecule s o l va ted i n s o l u t i o n . The pr imary energy f a c t o r s f o r d i s s o l u t i o n a r e ; a) the energy requ i red to remove a s o l u t e molecule from the s o l i d su r face (AA(T) ) b) the energy of s o l v a t i o n (AB(T) ) c) the a c t i v a t i o n energy of d i f f u s i o n (AC(T) ) - 29 -S u b s t i t u t i n g terms i n t o Eqn. 14 "obs • ko ( e - M f T ) / R T > ( e - A B < T > / R T ) ( e - A C < T ' / R T ) (15) I f d i s s o l u t i o n i s c o n t r o l l e d by the su r face r e a c t i o n , then the d i f f u s i o n energy term can be neglected and the d i s s o l u t i o n r a t e i s g iven by, _ AA(T) _ AB(T) r a t e = k 0 (e R T ) (e R T ) S ( C s . - C) (16) Hsia e t a l (1977) q u a n t i f i e d the energ ies a s soc i a ted wi th the d i s s o l u t i o n process us ing a s i m i l a r approach to tha t of S z i n a i and Hunt (1972). These energ ies con s i s t ed of a) su r face i n t e r a c t i o n (heat o f wet t i ng ) b) heat of s o l v a t i o n g iven by s u b t r a c t i n g the heats of wet t i ng and fu s i on from the heat of s o l u t i o n c) mass t r a n s f e r ( a c t i v a t i o n energy of d i f f u s i o n ) . They found tha t the sum of terms i n a) and b) were g rea te r than i n c) and concluded tha t the energy b a r r i e r f o r d i s s o l u t i o n was the s o l i d - s o l v e n t i n t e r a c t i o n and not the mass t r a n s f e r of s o l u te i n t o the bulk s o l u t i o n . The two major models d e s c r i b i n g the mechanism o f mass (and heat) t r a n s f e r between two phases are the f i l m theory and the sur face renewal theory . The f i l m theory assumes that there i s a reg ion i n which steady s t a t e molecu la r t r a n s f e r i s c o n t r o l l i n g . Danckwerts (1951) abandoned the idea of the stagnant f i l m and int roduced the sur face renewal theory which assumes tha t macroscopic packets or elements of l i q u i d reach the i n t e r f a c e by random eddy d i f f u s i o n . At the su r f a ce , each element of l i q u i d absorbs s o l u t e , the r a t e being dependent on the time f o r which i t i s exposed to the s o l u t e . Two r a t e equat ions have been proposed depending on the way i n which the sur face - 30 -i s rep laced (Danckwerts, 1971). I f each element i s exposed to the s o l u te f o r the same length of time before being r e p l a c e d , the r a te of abso rp t ion (per u n i t area) i s g iven by where $ i s the time of exposure. I f i t i s assumed tha t there i s no c o r r e l a -t i o n between the chance of an element being rep laced and the length of t ime f o r which i t has been at the s u r f a ce , then R' = / D S 1 ( C s - C) (18) where S-] i s the f r a c t i o n a l r a te of su r face replacement. Danckwerts (1951) der i ved these equat ions f o r the process of abso rp t ion of a gas i n t o an ag igated l i q u i d . Johnson and Huang (1956) showed t ha t the su r face renewal theory could a l s o be app l i ed to the s o l i d - l i q u i d i n t e r f a c e . Toor and Marche l lo (1958) showed tha t the f i l m theory and pene t ra t i on ( su r face renewal) theory are not separa te , un re la ted concepts but r a t he r are l i m i t i n g cases of a more general model, r e f e r r e d to as the f i l m - p e n e t r a t i o n model. Goyan (1965) used the Danckwerts model to de r i ve equations f o r the d i s s o l u -t i o n of s o l i d s i n a m u l t i p a r t i c u l a t e system. D. FACTORS AFFECTING DISSOLUTION RATE The phys.lcochemical f a c t o r s which i n f l u e n c e the r a t e of d i s s o l u t i o n have been reviewed by Wurster and Tay l o r (1965c)and i n c l ude temperature, a g i t a t i o n , compos i t ion of the d i s s o l u t i o n medium (pH, i o n i c s t r eng t h , v i s c o s i t y , s o l u b i l i z a t i o n and sur face a c t i v i t y ) , s o l u b i l i t y , c oncen t r a t i on - 31 -g rad ient and sur face a rea . The e f f e c t of c r y s t a l s t r u c t u r e (polymorphic forms, hydrates , hab i t m o d i f i c a t i o n s , imper fec t i on s ) on c r y s t a l r e a c t i v i t y and d i s s o l u t i o n w i l l be reviewed i n Sec t i on E. 1. Degree of a g i t a t i o n Lev ich (1962) de r i ved an equat ion f o r h, the th i cknes s of the d i f f u s i o n l a y e r i n terms of fundamental, phy s i ca l q u a n t i t i e s f o r laminar f l ow along a f l a t p l a t e , where the dimensions of the system are such t ha t other wa l l and edge e f f e c t s are n e g l i g i b l e : where x i s the d i s t ance from the upstream edge of the p l a t e measured along an ax i s p a r a l l e l to the d i r e c t i o n of f low, v i s the k inemat ic v i s c o s i t y of the so l ven t and u i s the l i n e a r f low r a te at a d i s t ance f a r from the p l a t e ( F i g . 4 ) . The f l u i d i n contact w i th the su r face i s assumed to have zero v e l o c i t y and f r i c t i o n a l r e s i s t a n c e re ta rd s the moving f l u i d i n a t h i n l a y e r near the wa l l (Knudsen and Katz , 1958). This r e s u l t s i n a hydrodynamic boundary l a y e r , h 0 , which i s de f ined as the d i s t ance from the sur face of the p l a t e to the po in t where the f low v e l o c i t y a t t a i n s a va lue approx imately 99% of u (the f low r a te of the undisturbed main s t ream). S i m i l a r equations have been developed f o r laminar f l ow of a l i q u i d over a r o t a t i n g d i s c . Far from the r o t a t i n g d i s c the f l u i d moves towards the d i s c and, i n a t h i n l a y e r immediately adjacent t o i t s s u r f a c e , the l i q u i d acqu i re s a r o t a t i n g mot ion. The angular v e l o c i t y of the f l u i d , w, inc reases as the su r face of the d i s c i s approached, u n t i l the angular v e l o c i t y of the r o t a t i n g h - 3 x ] / 2 D 1 / 3 v 1 / 6 u " 1 / 2 (19) h - 0.6 ( £ ) (20) - 32 -U U FLAT PLATE F i g . 4. D i f f u s i o n and hydrodynamic boundary l a ye r s f o r l am ina r . f l ow over a f l a t p l a t e . - 33 -d i s c i s f i n a l l y a cqu i red . A s i g n i f i c a n t c h a r a c t e r i s t i c of h i s t ha t i t i s constant over the whole su r face of the d i s c (except i n a zone a t the edge of the d i s c ) . h = 1.61 D 1 / 3 v 1 / 6 w _ 1 / 2 - 0 . 5 ( £ ) 1 / 3 h o (21) In a t r an spo r t c o n t r o l l e d d i s s o l u t i o n process kt = D/h and s u b s t i t u t i o n f o r h via Eqn; .19 g ives kt = 0.33x 1/2 D 2/3 v - l / 6 J / 2 ( 2 2 ) For a mixed c o n t r o l l e d d i s s o l u t i o n r e a c t i o n the i n d i v i d u a l r a t e constants kt and k r can be obta ined by rear rang ing Eqn. 11, 1 - 1 + T 7 - (23) ^obs ^ t k r assuming k r i s a f i r s t order r a t e cons tant . S u b s t i t u t i n g f o r k t from Eqn. 22 J — 3 X 1 ' 2 D " 2 ' 3 v 1 / 6 u " 1 / 2 + 1 (24) K obs K r Levy (1963) showed that the p r o p o r t i o n a l i t y between d i s s o l u t i o n r a te and the square root of r o t a t i o n r a te app l i ed to r o t a t i n g d i s c s of organ ic weak a c i d s . He gave the f o l l o w i n g general equa t i on , r a te = a ' ( R * ) b (25) where R* i s the r a te of a g i t a t i o n or s t i r r i n g and a ' and b' are constants . - 34 -This may be expressed i n l o ga r i t hm i c form l o g ( r a t e ) = log a ' + b' log R* (26) I f d i s s o l u t i o n i s t r an spo r t c o n t r o l l e d , ' b' _< 1. I f d i s s o l u t i o n i s s u r f ace c o n t r o l l e d R* should exe r t l i t t l e or no i n f l uence on d i s s o l u t i o n r a t e and b' should be c l o se to ze ro . The value of b' w i l l depend on the type of a g i t a t i o n , ( l aminar or t u r b u l e n t ) , the c h a r a c t e r i s t i c s of f l u i d motion i n the boundary l a y e r , the geometry of the s t i r r e r and vesse l and the p o s i t i o n of the s t i r r e r w i th respect to the d i s s o l v i n g substance (Bircumshaw and R i d d i f o r d , 1952; B i s a i l l o n and Tawashi, 1971; G o l l e t t e t a l . , 1972). Fee et a l . (1976) s tud ied the e f f e c t of s o l ven t f l ow Reynolds,, number (Re) on the d i s s o l u t i o n r a te of KC1. They found tha t the i n t r i n s i c d i s s o l u -t i o n r a te was a l i n e a r f u n c t i o n of Re from Re = 360-3000. At Re > 3000 there was a t r a n s i t i o n from laminar to t u r bu l en t f l ow . Nelson and Shah (1975) and Shah and Nelson (1975) have developed and expe r imenta l l y conf irmed a convect i ve d i f f u s i o n model to de sc r i be the i n i t i a l d i s s o l u t i o n ra te s from a su r face of a r ec tangu l a r t a b l e t and a d i s c . So lvent f low was p a r a l l e l to the plane of the s o l i d and d i s s o l u t i o n r a t e was a r e l a t i v e l y weak f unc t i on of the s t i r r i n g r a t e i . e . r a te a R* 1 / 3 (27) Langenbucher (1974) has reviewed the r e l a t i o n s h i p s between l i q u i d a g i t a t i o n and mass t r a n s f e r . Reported values of h f o r d i f f e r e n t systems are g iven eg. f r e e c o n v e c t i o n a l , r o t a t i n g d i s c , s t i r r e d - t a n k , r o t a t ed - t ank , r o t a t i n g basket. - 35 -2. Temperature An inc rease i n temperature w i l l i nc rease both the r a te of the su r face r e a c t i o n and the r a t e of the t r an spo r t process (Bircumshaw and R i d d i f o r d , 1952). A f t e r separat ion of the r a te cons tan t s , the dependence of k r and k t on temperature may be expressed by means of the Arrhen ius equat i on s : and kj-where A r and A t a re c o l l i s i o n frequency f a c t o r s and E r and E^ are energ ies of a c t i v a t i o n f o r the su r face c o n t r o l l e d and t r an spo r t c o n t r o l l e d processes r e s p e c t i v e l y . A change i n temperature has a g rea te r e f f e c t on su r face c o n t r o l l e d d i s s o l u t i o n than on t r an spo r t c o n t r o l l e d d i s s o l u t i o n . For the former, the 10° temperature c o e f f i c i e n t i s about 2.0 and f o r the l a t t e r i s about 1.3 (Wurster and T a y l o r , 1965). 3. S o l u b i l i t y and concen t ra t i on g rad ien t Accord ing to the Noyes-Nernst equa t i on , the d i s s o l u t i o n r a te i s propor-t i o n a l to ( C s - C ) . Therefore by i n c r ea s i n g C s ( s a t u r a t i o n s o l u b i l i t y ) or decreas ing C, the d i s s o l u t i o n r a t e may be i nc rea sed . Hamlin et a l . (1965) used cond i t i on s where C s » C and showed tha t the d i s s o l u t i o n r a t e was d i r e c t l y p ropo r t i ona l to C s . However, Hamlin and Higuchi (1966) reported dev i a t i on s from t h i s r e l a t i o n s h i p due to the much g rea te r d i f f u s i o n c o e f f i -c i e n t f o r the s o l ven t than the s o l u t e . The value of C can be mainta ined c l o se to zero by s tudy ing on ly i n i t i a l d i s s o l u t i o n r a t e s , us ing l a r ge volumes of d i s s o l u t i o n medium or ma in ta in ing s ink c o n d i t i o n s . Accord ing to G i b a l d i A r e RT = At e Et RT (28) (29) - 36 -and Feldman (1967), s ink cond i t i on s can be assumed i f the t o t a l amount of s o l i d i n s o l u t i o n does not exceed 10-20% of C s . For s o l i d s having only a very low s o l u b i l i t y i n the d i s s o l u t i o n medium, t h i s can r e s u l t i n the use of very l a rge volumes of f l u i d . G i b a l d i and Feldman (1967) used an organ ic so l vent phase to f u n c t i o n as a r e s e r v o i r f o r d i s s o l v e d s o l i d and mainta in s ink c o n d i t i o n s . Wurster and P o l l i (1961) used an adsorbent i n the aqueous phase to remove s o l u te and mainta in s ink c o n d i t i o n s . 4. pH of d i s s o l u t i o n medium The s a t u r a t i o n s o l u b i l i t y of a weak a c i d or weak base w i l l vary w i th the pH of the d i s s o l u t i o n medium. In both cases i t i s po s s i b l e to inc rease C$ and consequent ly , the r a te of d i s s o l u t i o n . 5. Surface area From the Noyes-Nernst equat i on , d i s s o l u t i o n r a t e i s d i r e c t l y propor-t i o n a l to the su r face a r e a , S. Any method whereby the p a r t i c l e s i z e of the s o l u te i s reduced, w i l l i nc rease the su r face area and hence inc rease the d i s s o l u t i o n r a te eg. mechanical comminution, format ion of e u t e c t i c mixtures and s o l i d s o l u t i o n s ( R o l l e r , 1931; Goldberg e t a l . , 1965). Enhanced d i s s o l u -t i o n ra tes i n the presence of s u r f a c t an t below the c r i t i c a l m i c e l l e concent ra -t i o n have been a t t r i b u t e d to an inc rease i n e f f e c t i v e su r face a r ea , r e s u l t i n g from a lower ing of i n t e r f a c i a l tens ion and increased wet t i ng (Weintraub and G i b a l d i , 1969). 6. V i s c o s i t y The ra te s of t r an spo r t c o n t r o l l e d d i s s o l u t i o n processes decrease wi th an increase i n v i s c o s i t y whereas v i s c o s i t y has l i t t l e e f f e c t on su r face c o n t r o l l e d d i s s o l u t i o n . Decreases i n k^ wi th an inc rease i n v i s c o s i t y are due to an inc rease i n k inemat ic v i s c o s i t y of the medium and a decrease i n - 37 -d i f f u s i o n c o e f f i c i e n t (Nogami e t a l . , 1966; Wurster and P o l l i , 1964). 7. S o l u b i l i z a t i o n and sur face a c t i v i t y The enhanced s o l u b i l i t y of a compound i n a m i c e l l a r s o l u t i o n of s u r f a c t a n t r e s u l t s i n an inc rease i n the d i s s o l u t i o n r a te and t h i s has been reviewed by G i b a l d i and Feldman (1970). Singh et a l . (1968) developed equations de s c r i b i n g the i n f l u e n c e of m i c e l l e - d r u g s o l u b i l i z a t i o n on the d i s s o l u t i o n r a t e . M i c e l l e s o l u b i l i z e d drug has a lower d i f f u s i o n c o e f f i c i e n t than f r ee drug, so t ha t changes i n d i s s o l u t i o n r a t e due to a d d i t i v e w i l l be r e l a t e d to the magnitude of dependence of d i s s o l u t i o n r a t e on d i f f u s i o n c o e f f i c i e n t s of the d i f f u s i n g spec ies ( C o l l e t t and Rees, 1975). E. CRYSTAL STRUCTURE AND REACTIVITY The ra tes of s o l i d - s t a t e r eac t i on s may depend on 1. The c r y s t a l l i n e c h a r a c t e r i s t i c s of the s o l i d eg. i t s polymorphic form, degree of s o l v a t i o n and degree of c r y s t a l ! i n i t y . 2. The immediate " h i s t o r y " of the s o l i d , t ha t i s a) the method of p repa ra t i on and storage b) ageing c) p r e l i m i n a r y mechanical treatment ( f r i c t i o n , deformat ion, b reak ing , aggregat ion) d) p r e l i m i n a r y i r r a d i a t i o n by l i g h t , X-rays e t c . Each of the f a c t o r s i n a) to d) may a f f e c t the de fec t content of c r y s t a l s . Changes i n the method of p repa ra t i on and c o n d i t i o n s of growth can a l s o r e s u l t i n m o d i f i c a t i o n s of the c r y s t a l hab i t (Bo ldyrev, 1975a; Boldyrev e t a l . , 1979). Hence c r y s t a l r e a c t i v i t y ( i n c l u d i n g c r y s t a l d i s s o l u t i o n r a te s ) may be s i g n i f i c a n t l y . a f f e c t e d by the f o l l o w i n g f a c t o r s - 38 " a) c r y s t a l l i n e c h a r a c t e r i s t i c s b) an i so t ropy and hab i t m o d i f i c a t i o n s c) de fec t content . 1. C r y s t a l l i n e c h a r a c t e r i s t i c s 1.1 Polymorphism, hydrates and so l va te s Many compounds e x h i b i t d i f f e r e n t polymorphic forms, which can be e i t h e r s t a b l e or metastab le . Metastab le polymorphs u s u a l l y have g rea te r s o l u b i l i t i e s and f a s t e r d i s s o l u t i o n r a te s than the s t a b l e form ( M i l o s o v i c h , 1964; Higuchi e t al., 1963; H a l e b l i a n , 1975). In the process of d i s s o l u t i o n , the metastable form may be transformed to the s t a b l e form and r e s u l t i n a decreased d i s s o l u -t i o n r a te (Carstensen, 1977; Higuchi et al„ 1967). The s o l u b i l i t y and r a te of d i s s o l u t i o n of a s o l v a te (or hydrate) may be s i g n i f i c a n t l y d i f f e r e n t from the non-so lvated (or anhydrous) form. F requent l y , the d i s s o l u t i o n r a te of the non-so lvated form i s g rea te r than the so l va ted a lthough i t does depend on the nature of the s o l v a t e and d i s s o l u t i o n medium ( She f te r and H i g u c h i , 1963; Poole and Baha l , 1968). 1.2 Degree of c r y s t a l l i n i t y Several re fe rence samples of d i g ox i n were found to have d i f f e r e n t e q u i l i b r i u m s o l u b i l i t i e s . On comminution of the samples, d i gox i n underwent a phase t r a n s i t i o n to an amorphous s t a t e and the e q u i l i b r i u m s o l u b i l i t i e s were g r e a t l y increased (F lorence and S a l o l e , 1976). B lack and Lover ing (1978) attempted to c o r r e l a t e the degree of c r y s t a l l i n i t y of d i g ox i n w i th the apparent e q u i l i b r i u m s o l u b i l i t y and d i s s o l u t i o n r a t e but found i n s tead a r ap id r e c r y s t a l l i z a t i o n of the amorphous to the c r y s t a l l i n e s t a t e . They a l s o observed tha t drug samples having the same degree of c r y s t a l l i n i t y d i f f e r e d i n apparent e q u i l i b r i u m s o l u b i l i t y . - 39 -2. An i so t ropy In con s i de r i ng an i d e a l l y p e r i o d i c l a t t i c e , i t i s apparent tha t the abrupt te rm ina t i on of the l a t t i c e a t the su r face must r e s u l t i n unique c r y s t a l l i n e c o n f i g u r a t i o n s of atoms. A s o l i d su r face may be cons idered to be a g i an t l a t t i c e de fec t (Gato.s, 1962). The su r face of a s o l i d i s c h a r a c t e r i z e d by a su r face f r e e energy (or su r face t e n s i o n ) , the work spent i n forming u n i t area of su r face and a sur face s t r e s s , the work spent i n s t r e t c h i n g the s u r f ace . Un l i ke the s i t u a t i o n w i th l i q u i d s , the su r face f r e e energy of s o l i d s i s not n e c e s s a r i l y equal to the su r face s t r e s s . The sur face tens ion i n a l i q u i d i s always p o s i t i v e or t e n s i l e which produces the tendency of the l i q u i d su r face to c o n t r a c t , whereas the su r face s t r e s s of c r y s t a l l i n e s o l i d s can be e i t h e r t e n s i l e ( p o s i t i v e ) or compressive ( nega t i ve ) . The ex i s t ence of a su r face s t r e s s does not i n i t s e l f imply tha t the arrangement of atoms i n the su r face reg ion i s d i f f e r e n t from tha t i n . t h e i n t e r i o r o f the c r y s t a l . The c o n d i t i o n f o r such rearrangements i n a c r y s t a l " a t e q u i l i b r i u m i s t ha t they correspond to a m in im i za t i on of the t o t a l f r e e energy or of the t o t a l i n t e r n a l energy ( B l a k e l y , 1973). Arrays of d i s l o c a t i o n s , or vacancies i n su r face planes can lead to changes i n the sur face s t r e s s from tha t c h a r a c t e r i s t i c of an i dea l plane (Adamson, 1967). A study of the arrangements of atoms i n d i f f e r e n t planes of a c r y s t a l w i l l suggest t h a t most p r ope r t i e s a s soc i a ted w i th s o l i d sur faces w i l l vary w i th the c r y s t a l l o g r a p h i c o r i e n t a t i o n of the su r face p l ane ,o f ten r e f e r r e d to as an i so t ropy (see Sec t i on A .2 ) . Experimental s tud ie s of such d i ve r se phenomena as thermal expans ion, e l e c t r o n emi s s ion , r e f r a c t i v e index, cohes ion , sur face atomic d i f f u s i o n and chemical r eac t i on s between sur faces and s o l u t i o n s have conf irmed t h i s . - 40 -The sur face s t r e s s , and hence the su r face energy, v a r i e s w i t h o r i e n t a -t i o n s ince the b ind ing energ ies and v i b r a t i o n a l modes of the su r face atoms w i l l depend on the l o c a l atomic arrangement. The f i r s t q u a n t i t a t i v e t r e a t -ment of su r face f r e e energy of c r y s t a l faces was made by Wu l f f (1901). He suggested a convenient way of p l o t t i n g the d i r e c t i o n a l dependence of the sur face f r ee energy i n a c r y s t a l , the r e s u l t i n g p l o t being known as a "Wu l f f p l o t " . Attempts have been made to p r e d i c t which faces w i l l have the lowest s p e c i f i c su r face f r e e energy by d i r e c t c a l c u l a t i o n of the r e t i c u l a r den s i t y • of the atoms i n a g iven plane (Donnay and Harker,1937). While high den s i t y c lose-packed faces do have low values of su r face energy the d i r e c t i o n a l nature of bond format ion and the s p a t i a l arrangement of atoms must be taken i n t o account. Some improvement i n compensating f o r c e r t a i n of these f a c t o r s i s obta ined i n the p e r i o d i c bond cha in method o f Hartman and Perdok (1955). In t h i s method every c r y s t a l i s d i v i ded i n t o p e r i o d i c bond chains and growth i s p red i c ted to be f a s t e s t i n the d i r e c t i o n of s t ronges t cha in s . 2.1 D i s s o l u t i o n an i so t ropy I t i s g e n e r a l l y accepted tha t the var ious c r y s t a l f a c e s , p lanes , or axes of a n i s o t r o p i c c r y s t a l s may d i s s o l v e a t d i f f e r e n t ra te s ( R o l l e r , 1932; Bunn, 1961). A p p l i c a t i o n of the k i n e t i c t heo r i e s of heterogeneous r eac t i on s (see Sec t i on C) to t h i s phenomenon o f d i s s o l u t i o n an i s o t ropy suggest th ree p o s s i b i l i t i e s : a) where d i s s o l u t i o n i s c o n t r o l l e d by the t r an spo r t p rocess , under the same hydrodynamic c o n d i t i o n s , the d i s s o l u t i o n r a te should be the same f o r each face of both i s o t r o p i c and a n i s o t r o p i c c r y s t a l s . b) where d i s s o l u t i o n i s su r face c o n t r o l l e d , u n l i k e faces of a n i s o t r o p i c c r y s t a l s should d i s s o l v e a t d i f f e r e n t i a t e s due to the d i f f e r e n c e s i n su r face f r e e energy of d i f f e r e n t f ace s . - 4T -c) Under mixed t r a n s p o r t - s u r f a c e c o n t r o l l e d d i s s o l u t i o n , u n l i k e faces of a n i s o t r o p i c c r y s t a l s should d i s s o l v e a t d i f f e r e n t r a t e s . Although d i s s o l u t i o n an i so t ropy i s a fundamental property of a l l non-i s omet r i c c r y s t a l s , t h i s aspect of d i s s o l u t i o n has r ece i ved l i t t l e a t t e n t i o n . Indeed M u l l i n (1972) has s t a ted " d i f f e r e n t c r y s t a l l o g r a p h i c faces may grow at d i f f e r e n t ra te s they may even d i s s o l v e a t d i f f e r e n t ra tes but r e l i a b l e measurements of t h i s behavior have not been r e p o r t e d " . Although perhaps an overstatement, a l i t e r a t u r e search has revea led few papers comparing the d i s s o l u t i o n ra tes of d i f f e r e n t c r y s t a l f a ce s . S i ng l e c r y s t a l s tud ie s of a n i s o t r o p i c c r y s t a l s of MgS04.6H20 have shown tha t d i s s o l u t i o n ra te s along two c r y s t a l l o g r a p h i c axes are equal when d i s s o l u t i o n i s t r an spo r t c o n t r o l l e d ( T re i vu s , 1964). S i m i l a r l y Karsh in and Gr igoryan (1970) found no d i f f e r e n c e i n the d i s s o l u t i o n r a t e of two c r y s t a l l o -graph ic planes of gypsum s i n g l e c r y s t a l s when the r e a c t i o n was under t r an spo r t con t r o l but under su r face c on t r o l there was a t h r e e - f o l d d i f f e r e n c e i n d i s s o -l u t i o n r a t e s . Hinzner and Stevenson (1963) found tha t s i n g l e c r y s t a l s of z i n c showed a more r ap i d r a t e of d i s s o l u t i o n f o r planes pe rpend i cu la r to the basal plane than f o r the more c l o s e l y packed basal p lanes , when d i s s o l u t i o n was under mixed t r a n s p o r t - s u r f a c e c o n t r o l . Ravdel and Moshkevich (1971) obta ined s i m i l a r r e s u l t s to H inzer and Stevenson (1963) us ing s i n g l e c r y s t a l s of z i n c , but they found d i s s o l u t i o n to be t r an spo r t c o n t r o l l e d . They pos tu -l a t e d the ex i s t ence of a su r face c o n c e n t r a t i o n , l e s s than the s a t u r a t i o n c oncen t r a t i o n , which had d i f f e r e n t values f o r the two c r y s t a l planes s t ud i ed . Haussuhl and Mu l l e r (1972) demonstrated d i s s o l u t i o n an i so t ropy from three faces of ca l c ium formate and two faces of s t ront ium formate d i h yd ra te . Two d i f f e r e n t faces of goe th i te ( aFe^H)^ ) c r y s t a l s d i s s o l ved at d i f f e r e n t ra te s under su r face c o n t r o l l e d d i s s o l u t i o n (Corne l l et a l . , 1974). - 42 -2.2 Habi t m o d i f i c a t i o n Fuhrer (1978) be l i e ve s tha t most of the unsolved problems concern ing the d i s s o l u t i o n p r ope r t i e s of a drug which a r i s e dur ing the p repara t ion and storage of s o l i d dosage forms are due to c r y s t a l l o g r a p h i c changes. These changes i n c l ude polymorphic t r a n s i t i o n s , changes i n the sur face c h a r a c t e r i s -t i c s and hab i t m o d i f i c a t i o n s . Carstensen (1973) has s t a ted tha t " s i n c e d i s s o l u t i o n ra tes d i f f e r f o r d i f f e r e n t hab i t s t h i s aspect i s of great pharmaceutical s i g n i f i c a n c e " and " c r y s t a l s of d i f f e r e n t hab i t s may e x h i b i t b i o l o g i c a l d i f f e r e n c e s " . However, there i s l i t t l e exper imental evidence to support these statements concerning the e f f e c t of c r y s t a l hab i t on d i s s o l u t i o n . Cons ide ra t i on of the a n i s o t r o p i c d i s s o l u t i o n from d i f f e r e n t faces of a c r y s t a l , leads to the p r e d i c t i o n t ha t the bulk d i s s o l u t i o n ra te s should d i f f e r f o r d i f f e r e n t c r y s t a l ! i n e h a b i t s . In g e n e r a l , d i f f e r e n c e s i n d i s s o l u t i o n r a t e , expressed as an observed r a te constant (see Eqn. 10, Sect ion C.2) , both f o r the d i s s o l u t i o n of s i n g l e f a c e s , K 0 b s , and f o r the bulk d i s s o l u t i o n of d i f f e r e n t h a b i t s , K 1 o b s , w i l l depend on: a) the nature of the r a te c o n t r o l l i n g step i n the d i s s o l u t i o n r e a c t i o n , b) whether the c r y s t a l s are i s o t r o p i c or a n i s o t r o p i c . Depending on such v a r i a b l e s as the degree of a g i t a t i o n , temperature or the d i s s o l u t i o n medium, the d i s s o l u t i o n r e a c t i o n may be t r an spo r t c o n t r o l l e d , su r face c o n t r o l l e d or mixed t r a n s p o r t - s u r f a c e c o n t r o l l e d (see Sec t i on C ) . Where d i s s o l u t i o n i s pu re l y t r an spo r t c o n t r o l l e d , then , f o r both i s o t r o p i c and a n i s o t r o p i c c r y s t a l s , K 0 u S should have the same value f o r each face of a g iven c r y s t a l , and K ' 0 u S f o r bulk d i s s o l u t i o n should be independent of c r y s t a l h ab i t . Where the r e a c t i o n i s under su r face c o n t r o l or mixed t r a n s p o r t -su r face c o n t r o l , i t i s expected t h a t , i n most cases , K ' 0 b s w i l l depend on c r y s t a l h ab i t . However, the r e l a t i o n s h i p between hab i t and K* Q ^ s w i l l depend - 43 -on whether the c r y s t a l s are i s o t r o p i c or a n i s o t r o p i c . For i s o t r o p i c c r y s t a l s , K 0 b s w i l l be the same f o r each face and where d i f f e r e n t hab i t s have equ i va l en t c r y s t a l l o g r a p h i c faces then K ' 0 ^ s should be independent of c r y s t a l h ab i t . However, where d i f f e r e n t hab i t s have d i f f e r e n t c r y s t a l l o -graphic faces then K'0^s f o r the bulk d i s s o l u t i o n of i s o t r o p i c c r y s t a l s w i l l be d i f f e r e n t . For a n i s o t r o p i c c r y s t a l s , K 0 b s w i l l d i f f e r f o r each c r y s t a l l o -graphic face and d i f f e r e n t hab i t s w i l l e x h i b i t d i f f e r e n t values of K ' 0 b s . The above p r e d i c t i o n s are summarized i n Scheme 2 but there i s l i t t l e con f i rmatory evidence i n the l i t e r a t u r e . Sodium c h l o r i d e , an i s o t r o p i c c r y s t a l belonging to the i s ome t r i c system, normal ly forms cub ic c r y s t a l s but when grown i n a s o l u t i o n con ta i n i n g 10% urea forms octahedra l c r y s t a l s . The atomic arrangement on a l l faces of each hab i t i s i d e n t i c a l but the cub ic faces c o n s i s t of" a l t e r n a t i n g N a + and C I " ions whereas the octahedra l faces c o n s i s t of a l l ions of l i k e charge (Bunn, 1961). Van Hook (1961) reviewed e a r l y work on the two hab i t s of NaCl. Although somewhat c o n t r a d i c t o r y , the r e s u l t s show tha t the octahedra l faces d i s s o l v e f a s t e r than the cub ic faces and t ha t t h i s r e l a t i o n s h i p i s reversed in the presence of urea. Although there have been few sys temat ic s tud ie s of the e f f e c t of hab i t m o d i f i c a t i o n on bulk d i s s o l u t i o n , the l i m i t e d data a v a i l a b l e from s i n g l e c r y s t a l s tud ie s suggests that the e f f e c t s o f hab i t m o d i f i c a t i o n w i l l become apparent on ly when d i s s o l u t i o n i s under su r face or mixed c o n t r o l . Chakrabart i e t a l , (1977) s tud ied the e f f e c t of cub ic and needle shaped hab i t s of phenytoin on d i s s o l u t i o n r a t e . D i f f e r e n t s i z e f r a c t i o n s of the two hab i t s were obta ined by s i e v i n g and the d i s s o l u t i o n ra te s of the var ious f r a c t i o n s compared. Small d i f f e r e n c e s were found f o r the l a r g e r s i z e range m a t e r i a l . However, s i z e c l a s s i f i c a t i o n by s i e v i n g does not permit an accurate comparison of the Scheme 2. Pred icted behavior of c r y s t a l l i n e Faces and Habits on D i s so lut ion Rate. ISOTROPIC CRYSTALS ANISOTROPIC CRYSTALS ISOMETRIC ALL OTHER SYSTEMS Transport Control Surface Reaction and Mixed Control Transport Control same hab i t ; K obs = d i f f e r e n t hab i t s ; K ' o b s = same h a b i t ; K obs = d i f f e r e n t habits Surface Reaction and Mixed Control same hab i t ; Kobs = d i f f e r e n t hab i t s ; K obs = same hab i t ; Kobs t d i f f e r e n t habits K ' o b s * wi th equ iva lent f ace s ; K ' o b s = with d i f f e r e n t faces ; K ' o b s f K o t ) S = observed r a t e constant f o r the d i s s o l u t i o n of d i f f e r e n t faces on a given c r y s t a l K ' . = observed r a te constant f o r bulk d i s s o l u t i o n - 45 -su r face area of the two hab i t s and d i s s o l u t i o n r a t e . In a d d i t i o n , the nature of the r a te c o n t r o l l i n g step was not cons idered. Tawashi (1968b) has suggested t ha t p a r t i c u l a r c r y s t a l l i n e hab i t s have a p re fe r r ed o r i e n t a t i o n which, on compaction i n t o t a b l e t s may i n f l u e n c e the d i s s o l u t i o n k i n e t i c s . Th i s p r e f e r r ed o r i e n t a t i o n has been demonstrated by She l l (1963) and Nakai e t a l . (1978) to a f f e c t the tab - l e t t i ng behavior of c r y s t a l l i n e m a t e r i a l s . Most organ ic compounds possess an i so t ropy o f cohesion and a d i f f e r e n c e i n o r i e n t a t i o n of c r y s t a l s of d i f f e r e n t hab i t may i n f l u e n c e the s t rength of t a b l e t s produced. Ha l eb l i a n (1975) d i scussed hab i t m o d i f i -c a t i o n of c r y s t a l s by dyes and the i n h i b i t i o n of d i s s o l u t i o n by adsorbed dye. We be l i e ve tha t there are two main reasons f o r the dearth of i n fo rmat ion on any r e l a t i o n s h i p between c r y s t a l hab i t and d i s s o l u t i o n , and e s p e c i a l l y so, i n the pharmaceutical l i t e r a t u r e : a) d i f f i c u l t i e s i n the cho ice of a s u i t a b l e c r y s t a l l i n e ma te r i a l b) d i f f i c u l t i e s i n methodology. I t i s o f ten very d i f f i c u l t to produce we l l - fo rmed c r y s t a l s of o rgan ic compounds. Large, complex molecules have d i f f i c u l t y , i n forming c r y s t a l s , e s p e c i a l l y when they have a s p e c i a l arrangement of po in t s of a t t r a c t i o n (Bunn, 1964). The c r y s t a l s when formed tend to be s m a l l , f r a g i l e and of w ide ly d i f f e r i n g s i z e and shape. Apart from s i n g l e c r y s t a l methods, methods f o r measuring the d i s s o l u -t i o n r a te f a l l i n t o two c a t e g o r i e s , namely constant su r face methods and m u l t i p a r t i c u l a t e bulk d i s s o l u t i o n methods. In constant su r face methods the s o l i d i s u s u a l l y ground to form small p a r t i c l e s which are then compressed i n t o a d i s c . S i z e reduc t i on and compression probably o b l i t e r a t e any e f f e c t due to the o r i g i n a l h ab i t . In the bulk d i s s o l u t i o n method eva l ua t i on f o r any e f f e c t due to d i f f e r e n t hab i t s i s d i f f i c u l t or imposs ib le because of - 46 -d i f f e r e n c e s i n s i z e and shape. 3. C r y s t a l de fec t s The format ion and s t r u c t u r e of c r y s t a l de fec t s or imper fec t i on s have been reviewed i n Sec t i on A.4. Po in t de fec t s are g e n e r a l l y thermodynamical ly s t a b l e but d i s l o c a t i o n s have a l o c a l i z e d energy a s soc i a ted wi th them made up of an e l a s t i c s t r a i n energy and core energy (Johnston, 1962). 3.1 Energet ic s of d i s l o c a t i o n s Atoms near the core or cent re of the d i s l o c a t i o n are r a t he r f a r from t h e i r e q u i l i b r i u m p o s i t i o n s and thus g ive r i s e to the core energy. Atoms f u r t h e r away from the core are e l a s t i c a l l y d i s p l a ced from t h e i r e q u i l i b r i u m p o s i t i o n s and e l a s t i c i t y theory may be used to determine the e l a s t i c s t r a i n f i e l d about the d i s l o c a t i o n and the d i s l o c a t i o n energy due to the e l a s t i c s t r a i n f i e l d . A s t r a i n energy i s a s s o c i a t ed w i th both edge and screw d i s l o -ca t i on s and an express ion f o r the s t r a i n energy per u n i t length of d i s l o c a t i o n , E s , i s g iven by G b 0 ? R 0  E s ^ = 4 - , r ( l - : v ) l n r0 (3°) G b 0 2 R 0 E s (screw) = ^ — In — (31) where G i s the e l a s t i c shear modulus of the c r y s t a l , b 0 i s the length of the Burger ' s v e c t o r , R 0 i s the rad ius of the c r y s t a l , r 0 i s the rad ius of the core and v i s Po i s s on ' s r a t i o which i s g e n e r a l l y about 0.3. The re fo re , the energy of an edge d i s l o c a t i o n i s approx imately one t h i r d l a r g e r than tha t of the screw d i s l o c a t i o n . The t o t a l energy i s g iven by the sum of the s t r a i n energy and core energy ( E c ) . - 47 -Core energy i s g iven by G b 0 2 Ec * - I T T ( 3 2 ) and i s 10-20% of the s t r a i n energy ( F i ne , 1975). The f r ee energy of f o rmat i on , AG, of a d i s l o c a t i o n can be determined from the Gibbs-HelmhoTtz equat ion AG = AH - TAS (33) where AH i s g iven by the t o t a l energy of a d i s l o c a t i o n . The presence of a d i s l o c a t i o n inc reases the d i s o r de r and entropy of a c r y s t a l . The entropy term, TAS, i s made up of a c o n f i g u r a t i o n a l entropy which e x i s t s because the d i s l o c a t i o n may be arranged i n the c r y s t a l i n a v a r i e t y of ways and a v i b r a t i o n a l entropy ( d i s l o c a t i o n s a f f e c t the thermal v i b r a t i o n s of a c r y s t a l ) . The e n t i r e entropy term i s n e g l i g i b l e i n comparison to the t o t a l energy. There fo re , i n a c r y s t a l a t room temperature the f r ee energy due to a d i s l o c a -t i o n i s almost the same as the t o t a l energy, which, being endothermic, s i g n i f i e s t ha t d i s l o c a t i o n s are thermodynamical ly uns tab le ( C o t t r e l l , 1953; Thomas, 1969). 3.2 Defects and c r y s t a l r e a c t i v i t y On a q u a l i t a t i v e bas i s i t can be argued t ha t there should be g reate r r e a c t i v i t y a t a d i s l o c a t i o n than at an und i s t o r t ed reg ion of a c r y s t a l due to s tereochemica l d i f f e r e n c e s at the d i s l o c a t i o n co re . In a d d i t i o n , the chemical p o t e n t i a l of spec ies a t the core should be d i f f e r e n t from tha t of spec ies elsewhere i . e . there i s g rea te r chemical un sa tu ra t i on a t the d i s l o -c a t i o n core . P a r t l y because of t h i s u n s a t u r a t i o n , i m p u r i t i e s tend to congre-- 48 -gate a t the d i s l o c a t i o n thereby c o n t r i b u t i n g f u r t h e r to enhanced (sometimes to suppressed) r e a c t i v i t y . The l o c a l i z e d energy of d i s l o c a t i o n s i s a l s o r e spon s i b l e f o r enhanced r e a c t i v i t y a lthough i t i s s t i l l a matter of s pecu l a -t i o n whether the core energy or the e l a s t i c s t r a i n energy i s the p r i n c i p l e ene rge t i c f a c t o r (Thomas, 1969). Some of the e f f e c t s of de fec t s on v a r i e t y of c r y s t a l l i n e p r ope r t i e s are summarized i n Table I I . 3.3 Defects and d i s s o l u t i o n The d i s s o l u t i o n phenomenon w i l l depend on the type of f o r c e t ha t e x i s t s between the atoms or molecules which are r e spon s i b l e f o r the p a r t i c u l a r c r y s t a l s t r u c t u r e . The nature of the cohes ive fo rce s and t h e i r s t rength i n the c r y s t a l w i l l determine the d i s s o l u t i o n r a t e . C r y s t a l imper fec t ions or c r y s t a l de fect s are fundamental matters i n d i s cu s s i n g the s t rength and cohesion fo rce s i n c r y s t a l s . Tawashi (1968a)bel ieves tha t the nature of d e v i a t i o n from pe r f e c t c r y s t a l s can probably e x p l a i n the anomalies i n d i s s o l u -t i o n ra tes of c r y s t a l s exposed to the same s o l ven t . Bur ton, Cabrera and Frank (1951) showed tha t thermal energy f l u c t u a t i o n s would cause the arrangement of the su r face l a ye r on a c r y s t a l face to depart from a p e r f e c t a r r ay . A r ea l su r face would look l i k e a se t of steps i n t e r -rupted by k inks and separated by p lanar p o r t i o n s . For such a su r face the energy of d i s s o c i a t i o n from a c e r t a i n s i t e Uj would be approx imate ly ; Uj = n ' ty (34) where ty i s the i n t e r a c t i o n energy between two neighbor ing p a r t i c l e s and n' i s the number of bonds to be ruptu red . Assuming the Ko s se l - S t r an s k i model (see Sec t i on B.1.2) , n ' has va lues of 3 f o r a k ink s i t e , 4 f o r a step s i t e - 49 -Table II E f f e c t s of c r y s t a l de fec t s on va r ious p r ope r t i e s PROPERTY CRYSTAL EFFECT REFERENCE Hardness KBr Increased growth r a t e , decreased hardness due to g rea te r number of d i s l o c a t i o n s * . Ridgway and Au l ton (1971) C a t a l y t i c a c t i v i t y Phase t r a n s i t i o n s Dehydration D i s s o l u t i o n E l e c t r i c a l p r ope r t i e s L i F D i c h l o r o -benzene Polymorphic changes N i S0 4 . 6H 2 0 Decomposition CaC03 Hydroxya -p a t i t e L i F N i S0 4 . 6H 2 0 A s p i r i n Si 1 icon Increased number of d i s -l o c a t i o n s , increased c a t a l y t i c a c t i v i t y . T r a n s i t i o n from a to 3 nuc leates a t d e f e c t s . Transformat ions are nuc leated a t d e f e c t s * . P r e f e r e n t i a l dehydra-t i o n a t emergent d i s -l o c a t i o n s . P r e f e r e n t i a l decomposit ion a t emergent d i s l o c a t i o n s . P r e f e r e n t i a l d i s s o l u t i o n at emergent d i s l o c a t i o n s . V a r i a t i o n s i n o v e r a l l d i s s o l u t i o n due to d e f e c t s * . Defects r e s u l t i n enhanced number of conduct ion e l e c t r on s i n semiconductors. Ha l l and Rase (1964) K i t a r g o r o d s k i i e t a l (1965) Bryn (1976) Thomas and Renshaw (1969) Thomas and Renshaw (1967) Jongebloed et a l (1974) Ives and H i r t h (1960) Thomas et a l (1971) P f e i f f e r (1971) M i t c h e l l et a l (1971) Jamal i and M i t c h e l l (1973) Moore (1967) Fluorescence Pho to l y s i s Anthracene Anthracene Po l ymer i za t i on Tr ioxane Defects p lay a s i g n i f i -cant r o l e i n f l uo re scence . P r e f e r e n t i a l photod imer i -z a t i o n at d i s l o c a t i o n s . Defects p lay a s i g n i f i -cant r o l e i n po l ymer i z a -t i o n . H e l f r i c h and L i p s e t t (1965) W i l l i ams and Thomas (1967) Bas set t (1967) * Suggested; no d i r e c t exper imental ev idence. - 50 -and 5 f o r a plane s i t e . Therefore from energy c o n s i d e r a t i o n s , atoms w i l l be more l i k e l y to be removed from a k ink than from other p laces on the c r y s t a l f a ce . Frank (1958) has developed an ex tens i ve theory where d i s s o l u t i o n i s t r ea ted as a process of kink movement along the steps and the progress ion of u n i t steps across a face of a c r y s t a l . He assumes t ha t the speed w i th which the steps move depends on ly .on;the den s i t y of other s teps . The methods he employs are those app l i ed by L i g h t h i l l and Whitham (1955) to problems of road t r a f f i c and r i v e r f l o o d s , i n which a l s o the f l ow ( c a r s , or ga l l on s per minute) may o f ten be assumed to depend on ly on the l i n e a r den s i t y ( c a r s , or g a l l on s per m i l e ) . When a reced ing step reaches the edge of the c r y s t a l , i t i s e l i m i n a t e d . However, where a step terminates a t a screw d i s l o c a t i o n , i t w i l l not be e l i m i n a t e d , as the screw d i s l o c a t i o n i s a source of s teps . In d i s s o -l u t i o n , the edges of the c r y s t a l a l s o ac t as sources of steps (observed v i s u a l l y as rounding of the edges of the c r y s t a l ) . On a p e r f e c t s u r f a c e , new steps may on ly be formed by a two-dimensional nuc l ea t i on process ( i . e . format ion of a ho le i n the c r y s t a l su r face) and t h i s on l y occurs i f the under sa tu ra t i on i s s u f f i c i e n t l y l a r g e . I f two-dimensional nuc l ea t i on can occur more r a p i d l y a t a d i s l o c a t i o n s i t e than e l sewhere, an etch p i t may form. An etch p i t i s a steep s ided p i t formed by succes s i ve nuc l ea t i on a t d i s l o c a t i o n s i t e s . Th is mechanism f o r d i s s o l u t i o n was in t roduced by Bur ton, Cabrera and Frank (1951) and has been reviewed by Johnston (1962). I t would appear l i k e l y t ha t the s p i r a l depress ion formed at a screw d i s l o c a t i o n should c o n s t i t u t e a v i s i b l e etch p i t . The e a r l y work assumed tha t a l l etch p i t s were formed at screw d i s l o c a t i o n s . However, i t i s known tha t etch p i t s can be produced at edge as we l l as screw d i s l o c a t i o n s and i t i s now w ide l y accepted t ha t a l l d i s l o c a t i o n etch p i t s are produced by a two-dimensional nuc l ea t i on process and not as a r e s u l t o f d i s s o l u t i o n by a s p i r a l mechanism. 3.31 Nuc leat ion a t d i s l o c a t i o n s Two-dimensional nuc l ea t i on occurs more r a p i d l y a t a d i s l o c a t i o n s i t e than elsewhere on the c r y s t a l su r face due to the enhanced r e a c t i v i t y a t d i s l o c a t i o n s . Thomas et a l (1971) have compared the ene rge t i c s of d i s s o l u -t i o n a t d i s l o c a t i o n s i t e s and at an i d e a l s u r f ace . At an i d e a l s u r f a ce , the f r ee energy of f o rmat i on , AGj of a two-dimensional nucleus of r a d i u s , r-j and depth, h-| i s g iven by 2 , IT r 1 h-, AGj = ^ — — Ay + 2TT r-, h-, y (35) where y i s the c r y s t a l - l i q u i d i n t e r f a c i a l energy, V-| i s mo lecu la r volume and Ay i s the change i n chemical p o t e n t i a l accompanying d i s s o l u t i o n . At an emergent d i s l o c a t i o n , the f r e e energy, of format ion of a two-dimensional nuc leus , AGj i s g iven by 2 , TT r, h, AG d = f L Ay + 2TT r ] h ] y - h ] ( E s + E_) (36) The l a s t term takes i n t o account the c o n t r i b u t i o n of the energy of the d i s l o -c a t i o n . Eqn.. 36 p r e d i c t s t ha t the a c t i v a t i o n energy f o r the format ion of a nucleus a t a d i s l o c a t i o n should be lower than the corresponding a c t i v a t i o n energy a t an i d e a l su r face to an extent d i c t a t e d by the magnitude of the d i s l o c a t i o n energy. 3.32 D i s l o c a t i o n etch p i t s The p r o f i l e of an e t ch p i t depends on the r a t e a t which i t deepens by nuc l ea t i on of steps a t the d i s l o c a t i o n and the v e l o c i t y of steps across the s u r f ace . The l a t t e r process may be con s i de rab l y reduced or even prevented - 52 -by c r y s t a l " po i sons " or etchants which adsorb onto the su r face steps and r e t a r d t h e i r movement across the s u r f a ce . Gilman et a l (1958) have developed a s imple etchant c o n s i s t i n g of a d i l u t e s o l u t i o n of f e r r i c f l u o r i d e i n d i s t i l l e d water , which produces we l l def ined etch p i t s a t d i s l o c a t i o n - s u r f a c e i n t e r s e c t i o n s on the (100) faces 3+ of l i t h i u m f l u o r i d e . Less than 1 ppm Fe a f f e c t s etch p i t format ion i n L i F . Most reagents con ta in more than t h i s amount of impur i t y and t h e r e f o r e , a c c i den t a l i m p u r i t i e s may ac t as a step po i son. There are severa l other methods f o r de t e c t i n g d i s l o c a t i o n s besides t ha t of e tch ing and these are mentioned b r i e f l y below. 1. Decorat ion D i s l o c a t i o n s are de l i n ea ted by forming a p r e c i p i t a t e on them. 2. E l e c t r on microscopy A.specimen i s th inned to severa l thousand Angstroms th i cknes s so t ha t i t can be examined i n a t ransmi s s i on e l e c t r o n microscope. 3. X-ray d i f f r a c t i o n An X-ray beam i s d i f f r a c t e d from a c r y s t a l which i s o r i e n t a t e d to ob ta in a Bragg r e f l e c t i o n . The beam i s recorded on a photographic p l a t e . Wherever the p e r i o d i c i t y of the d i f f r a c t i n g planes i s d i s t u rbed e.g . a t a d i s l o c a t i o n , the d i f f r a c t i o n i n t e n s i t y inc reases and a dark spot appears on the p l a t e . There i s a l s o a t ransmi s s i on X-ray technique which i s s i m i l a r to the r e f l e c t i o n technique desc r ibed above. 4. Other methods i ) d i r e c t r e s o l u t i o n of the l a t t i c e planes by e l e c t r o n microscopy. This has been c a r r i e d out on copper. i i ) two t h i n c r y s t a l s are superimposed and examined by t ran smi s s i on e l e c t r o n microscopy. Moire" pa t te rns are produced i n which d i s l o c a t i o n s appear - 53 -magn i f i ed . i i i ) s t r e s s b i r e f r i n g e n c e - a c r y s t a l i s examined i n t r a n s m i t t e d , p o l a r i z e d l i g h t and b i r e f r i n g e n c e due to the s t r a i n f i e l d of the d i s l o c a t i o n - produces a p h o t o e l a s t i c p a t t e r n . i v ) thermal e t ch i ng - thermal e tch p i t s are formed by evaporat ion when c r y s t a l s are heated to high temperatures. However, c o r r e l a t i o n between thermal etch p i t s and d i s l o c a t i o n s has not been we l l e s t a b l i s h e d . Other techniques i n c l ude f i e l d i on microscopy and e t ch i ng by i on bombard-ment. 3.33 I n t e r r e l a t i o n s h i p s between growth r a t e , i m p u r i t i e s , d i s l o c a t i o n s and  d i s s o l u t i o n r a t e Stud ies of the i n t e r r e l a t i o n s h i p s between i m p u r i t i e s , d i s l o c a t i o n s and . the d i s s o l u t i o n r a te may be d i v i ded i n t o a) those where the importance o f de fec t s i n the d i s s o l u t i o n process has been shown expe r imen ta l l y , and b) those where the r o l e of de fec t s i s suggested but there i s no d i r e c t exper imental evidence (see Table I I ) . In the l a t t e r group, severa l workers have s tud ied the c r y s t a l po i son ing and subsequent i n h i b i t i o n of d i s s o l u t i o n r a te by i m p u r i t i e s (or poisons) added to the d i s s o l u t i o n medium ( P i c c o l o and Tawashi, 1970, 1971; B i s a i l l o n and Tawashi, 1976; M a g r i l l , 1975). They suggested tha t i m p u r i t i e s were adsorbed onto the "pr imary sources " or " a c t i v e s i t e s " of the c r y s t a l su r face thus r e t a r d i n g the r a t e of s o l u t e removal from k inks and s teps . L i u e t a l (1976) prepared three sets of seed barium s u l f a t e c r y s t a l s under d i f f e r i n g cond i t i on s f o r d i s s o l u t i o n s t ud i e s . They found t ha t there was a 3 - f o l d d i f f e r e n c e i n su r face area between two set s of seeds but a corresponding 12 - f o l d d i f f e r e n c e i n the su r face r e a c t i o n r a t e cons tant . They concluded - 54 " t ha t the d i f f e r e n t seed c r y s t a l s may con ta i n qu i t e d i f f e r e n t numbers of " a c t i v e s i t e s " per u n i t area f o r growth or d i s s o l u t i o n . In the former category , the d i s s o l u t i o n k i n e t i c s a t d i s l o c a t i o n s i t e s has been the sub jec t o f . e x t e n s i v e research (Gilman et a l . , 1958; Ives, 1963; Sears , 1960; Ives and H i r t h , 1960; Thomas et a l . , 1971; Gal 1 i l y and F r i e d l a n d e r , 1965) but there has been l i t t l e attempt to r e l a t e these to the o v e r a l l d i s s o -l u t i o n r a te of the c r y s t a l . The r e l a t i o n s h i p s between i m p u r i t i e s , d i s l o c a t i o n den s i t y and growth r a t e of c r y s t a l s have been reviewed i n Sec t i on B.3. C o r r e l a t i o n o f these f a c t o r s w i t h d i s s o l u t i o n k i n e t i c s r e s u l t s i n a number of complex i n t e r r e l a t i o n s h i p s . These may be summarized as f o l l o w s : ( i ) Impur i t i e s ( po in t de fec t s ) present i n the c r y s t a l can enter i n t o s o l u t i o n and ac t as a poison thereby decreas ing the d i s s o l u t i o n r a te ( s e l f - p o i s o n i n g ) (Sears, 1960; Bundgaard, 1973). ( i i ) Impur i t i e s i n c r y s t a l s tend to segregate a t d i s l o c a t i o n s and i n h i b i t d i s s o l u t i o n (Gilman et a l , 1958). O c c a s i o n a l l y , impur i t y atoms enhance d i s s o l u t i o n (Johnston, 1962; Ives and PI ewes, 1965). ( i i i ) D i s l o c a t i o n s are thermodynamical ly un s tab le , having an a s soc i a ted l o c a l i z e d energy which r e s u l t s i n an inc rease i n f r ee energy and a reduc t i on i n the a c t i v a t i o n energy f o r d i s s o l u t i o n at po in t s where they emerge on the c r y s t a l f a c e . Hence, i t may be specu lated that a c r y s t a l w i th a h igher d i s l o c a t i o n den s i t y should have a h igher thermodynamic a c t i v i t y ( i . e . metastable w i t h re spec t to a c r y s t a l w i t h a lower d i s l o c a t i o n den s i t y ) which may r e s u l t i n a g rea te r o v e r a l l d i s s o l u t i o n r a te when the process i s under su r face c o n t r o l . EXPERIMENTAL APPARATUS Constant temperature bath , Magni W h i r l , Blue M. E l e c t r i c Company. Constant temperature c i r c u l a t o r , Haake Models FT and FE. P e r i s t a l t i c pump, M a n o s t a t , . V a r i s t a l t i c , Advanced Model. Diaphragm pump, Model 920, Mace Co rpo ra t i on . F i she r Stedispeed ad ju s t ab l e s t i r r e r . Flow meter, Gi lmont, S i ze 4 f lowmeter. Heating tape. Temperature probe, YSI s e r i e s 400. Temperature c o n t r o l l e r , Thermistemp model 71A. Va r i ab l e autot rans former. U.S.P. d i s s o l u t i o n apparatus. Rotat ing d i s c apparatus. Hydrau l i c p res s , C30 Research and I n d u s t r i a l Instruments Company. E l e c t r o n i c s t roboscope, F lash Tac, E l e c t r o n i c A p p l i c a t i o n s L t d . T r a v e l l i n g microscope, Sw i f t and Son. D i f f e r e n t i a l i n t e r f e r e n c e con t r a s t microscope, Model R, Nikon and Ze i s s U l t r aphot I I I -M. Scanning e l e c t r o n microscope, ETEC Autoscan. X-ray energy ana l y ze r , ORTEC, Model 6200. X-ray d i f f r a c t o m e t e r , wide ang le , P h i l i p s . Cahn Gram e l e c t r o b a l a n c e . D i f f e r e n t i a l scanning c a l o r i m e t e r w i th e f f l u e n t gas a na l y ze r , Pe rk in Elmer DSC-1B. Atomic absorpt ion spectrophotometer, Var ian Techtron Models 4 and 5. - 56 -N i cke l hol low cathode lamp, Var ian Techtron L t d . Potassium hol low cathode lamp, Cathodeon L t d . U l t r a - v i o l e t spectrophotometer, Coleman, H i t a ch i pH meter, Radiometer, Model 26. Mi H i pore sy r inge and f i l t e r s . - 57 -B. MATERIALS N i cke l s u l f a t e hexahydrate, C e r t i f i e d ACS, F i s he r S c i e n t i f i c Company. G e l a t i n B.P., B r i t i s h Drug Houses. 95% v/v e t h a n o l , commercial grade and r e d i s t i l l e d i n f r a c t i o n a l d i s t i l l a t i o n apparatus. Cyanoacry late g l ue , Krazy Glue. Na i l enamel, Rimmel ( c o l o r l e s s ) . P e r c h l o r i c a c i d 60%, A n a l y t i c a l reagent, M a l l i n c k r o d t Company. Potassium c h l o r i d e , A n a l y t i c a l reagent, B r i t i s h Drug Houses. Sodium m e t a s i l i c a t e , C e r t i f i e d , F i s he r S c i e n t i f i c Company. Sodium s u l f i t e , Baker analyzed reagent, J .T . Baker Chemical Company. Su lphu r i c a c i d ( concent ra ted ) , reagent grade, American S c i e n t i f i c and Chemica l . T a r t a r i c a c i d ( d e x t r o ) , B r i t i s h Drug Houses. Calc ium c h l o r i d e d i h yd r a t e , C e r t i f i e d ACS, F i s he r S c i e n t i f i c Company. Cesium c h l o r i d e , C e r t i f i e d ACS, F i s he r S c i e n t i f i c Company. Sodium t r i p o l ypho spha te , Mackenzie and Feimann L t d . Veegum suspens ion, 6% w/v. Carbopo l , 0.15% w/v. G l a c i a l a c e t i c a c i d , reagent ACS, A l l i e d Chemical Canada. Urea, Baker analyzed reagent, J .T . Baker Chemical Company. B r i l l i a n t blue dye, F.D. and C. Blue #1. Water, d i s t i l l e d . - 58 -C. DISSOLUTION ANISOTROPY 1. Growth of n i c k e l s u l f a t e a hexahydrate c r y s t a l s The c h a r a c t e r i z a t i o n of the NiSO^ a 6 ^ 0 b ipyramida l c r y s t a l s i s g iven i n s e c t i on E. The b ipyramida l c r y s t a l s were grown i n a f l u i d i z e d - b e d c r y s t a l l i z e r by P h i l l i p s and Eps te in (1973, 1974). "Seed" c r y s t a l s were used i n the d i s s o l u t i o n s tud ie s s i nce these were a v a i l a b l e i n s u f f i c i e n t numbers. The seed c r y s t a l s were prepared under known, h i gh l y c o n t r o l l e d cond i t i on s from "sub-seeds" of s i z e range 600-710 urn. Growth of the " sub-seeds" i n t o seed c r y s t a l s was c a r r i e d out i n severa l growth stages at the same temperature and i n i t i a l s upe r s a tu r a t i on . C r y s t a l s s e l e c ted f o r the s i n g l e c r y s t a l d i s s o l u t i o n s tud ie s were between 4.0-4.8 mm i n width and 4.5-5.0 mm i n length w i t h w e l l - d e f i n e d c r y s t a l l i n e f a ce s . 2. P repara t ion of ethanol d i l u t i o n s Ethanol s o l u t i on s of va r ious s t rengths were prepared by d i l u t i n g 95% ethanol w i th water i n the p ropor t ions g iven i n the f o l l o w i n g t a b l e . Before the mixture was f i n a l l y adjusted to volume, i t was cooled to room temperature. Strength of ethanol (% v/v) Volume of 95% ethanol (nt) F i na l volume of mixture (mL) 70 737 1000 60 632 1000 55 579 1000 50 526 1000 - 59 -3. S i ng l e c r y s t a l d i s s o l u t i o n measurements 3.1 Apparatus The d i s s o l u t i o n f low c e l l ( F i g . 5) was designed by M u l l i n and Gars ide (1967) to measure the growth ra tes of i n d i v i d u a l c r y s t a l f a ce s . The so l ven t r e s e r v o i r was a 600 ml_ j acke ted g las s beaker connected to a constant temperature c i r c u l a t o r and f i t t e d w i th a cover to min imize so l ven t evapora t i on . Ethanol i n the j acke ted beaker was s t i r r e d us ing a magnetic s t i r r e r and a 3.5 cm Te f l on - coa ted s t i r r e r bar. The so l ven t was drawn from the beaker by a v a r i a b l e speed p e r i s t a l t i c pump f i t t e d w i th s i l a s t i c 1 cm i n t e r n a l diameter t ub i n g , through a c a l i b r a t e d g la s s f l ow meter (range 10-850 mL.min"^) i n t o the f low c e l l and back to the beaker. The d i s t ance d, of the f low c e l l was 10.5 cm wi th an i n t e r n a l diameter of 1.5 cm. The requ i red temperature i n the c e l l was mainta ined by heat ing tape wound around the lower h a l f of the c e l l and was monitored i n i t i a l l y by a thermometer placed i n the top. The temperature was c o n t r o l l e d to ±0.05° us ing a s t a i n l e s s s t e e l probe and a temperature c o n t r o l l e r connected through a v a r i a b l e autotransformer to the heat ing tape. 3.11 S e l e c t i o n of tub ing f o r the pump Three types of tub ing were a va i l abe f o r the p e r i s t a l t i c pump. a) Te f l on tub ing (Manostat, Versatube) Although chem ica l l y i n e r t , t h i s tub ing was found to be un su i t ab l e s i nce i t s i n f l e x i b i l i t y r e s u l t e d i n an exaggerated " p u l s i n g " s o l ven t f l ow . This produced v i b r a t i o n of the c r y s t a l . b) Tygon tub ing 55% v/v e t h a n o l , held i n t h i s tub ing f o r up to 6 hours, was analyzed i n an u l t r a - v i o l e t spectrophotometer scanning over the wavelength range 370-190 my. Severa l l a r g e , broad peaks were observed i n d i c a t i n g the - 60 -CRYSTAL F i g . 5 . D i s s o l u t i o n apparatus and diagram of a s i n g l e N i S O 4 a 6 H 2 O c r y s t a l showing geometry and p o s i t i o n of c r y s t a l f a c e s , c h a r a c t e r i z e d by t h e i r M i l l e r i n d i c e s . - 61 -presence of i m p u r i t i e s re leased by the tub ing , c) S i l a s t i c tub ing S i l a s t i c tub ing was soaked overn ight i n 55% v/v ethanol fo l l owed by au toc l a v i ng a t 121° i n water f o r 5 hours. The tub ing was f i t t e d i n the p e r i s t a l t i c pump and 55% v/v ethanol pumped through the d i s s o l u t i o n apparatus f o r approx imately 3 hours. Ana l y s i s of samples of the s o l ven t i n a scanning u l t r a - v i o l e t spectrophotometer d i d not revea l any impur i t y peaks. This tub ing was used i n a l l subsequent d i s s o l u t i o n t r i a l s . 3.2 Measurement The (001) face of the c r y s t a l was f i x e d us ing one drop of cyanoacry la te glue to a tungsten w i r e , 1 mm diameter and 8 cm l eng t h , sealed i n t o a ground g las s s topper . When temperature and f low r a te had been s t a b i l i z e d at the des i red c o n d i t i o n s , the thermometer was removed and rep laced by the g lass stopper c a r r y i n g the c r y s t a l . The movement of the (111) or (112) c r y s t a l face was measured w i th a t r a v e l l i n g microscope reading ±0.0005 cm. The ob se r ve r ' s head was po s i t i oned i n a head r e s t attachment from a gonioscope to prevent p a r a l l a x e r r o r s . 3.21 S e l e c t i o n of d i s s o l u t i o n medium D i s s o l u t i o n t r i a l s were c a r r i e d out us ing 500 ml of 50%, 55%, 60% and 70% v/v ethanol to s e l e c t a s u i t a b l e s o l v en t . Movement of the c r y s t a l faces was too small to permit accurate measurement a t low f l ow r a t e s , us ing 70% v/v ethanol as the d i s s o l u t i o n medium. 50% v/v ethanol caused a very r ap i d d i s s o l u t i o n which was undes i r ab le . D i s s o l u t i o n ra tes f o r the (111) face were measured at 37° and 45.5° a t f low ra te s of between 100-800 mi.min"^ us ing 55% v/v ethanol as the s o l v e n t , but aga in , d i s s o l u t i o n was too r a p i d . 60% v/v ethanol was found to be the opt imal so l vent and was used i n a l l subsequent experiments on d i s so lu t i on an i s o t ropy . D i s s o l u t i o n was fo l l owed - 62 -a t f l ow rates of between 100-800 mL.min - 1 at temperatures of 3 0 ° , 3 7 ° , 41° and 45.5° f o r 50-60 minutes dur ing which time there was n e g l i g i b l e change i n su r face a rea. D i s s o l u t i o n occurred under s ink cond i t i on s s i nce at no time d i d the concen t ra t i on o f n i c k e l s u l f a t e exceed 1.5 per cent of i t s 3 -1 s a t u r a t i o n s o l u b i l i t y . The experimental f l ow ra tes (cm .s ) were converted to l i n e a r f low r a t e s , u, (cm.s~^)by d i v i d i ng by the c r o s s - s e c t i o n a l area (cm ) of the f low c e l l and corresponded to Reynolds numbers of between 100-800 which i s i n the range of laminar f l ow. C a l c u l a t i o n of Reynolds number i s de sc r ibed i n s e c t i o n A.3.3 of the r e s u l t s and d i s c u s s i o n . 3.22 Co r rec t i on f a c t o r s The t r a v e l l i n g microscope measured the movement of the observed c r y s t a l face i n a v e r t i c a l d i r e c t i o n i . e . d i s t ance a_ i n F i g . 6 whereas b_, the movement i n a d i r e c t i o n pe rpend icu la r to the face was r e q u i r e d . Hence a l l readings were c o r r e c t e d accord ing to Eqn. 37. b = a cos 6 (37) where the values of 0 , obta ined from the geometry of the c r y s t a l ( F i g . 5) were 70%. 54' and 59° 16' f o r the (111) and (112) faces r e s p e c t i v e l y ( P h i l l i p s and E p s t e i n , 1974). 3.23 Measurement of length of c r y s t a l faces The lengths of the (111) and (112) c r y s t a l s are x and x ' r e s p e c t i v e l y . The lengths y and y ' ( F i g . 5) were measured w i th the t r a v e l l i n g microscope and x and x ' (Table I I I ) c a l c u l a t e d from x = y / s i n 6 (38) 3.3 Test f o r su r face c o n t r o l l e d d i s s o l u t i o n Several experiments were c a r r i e d out i n which the movement of the (111) - 63 -(111) f a c e , b = a . 0 - 3 2 7 2 (112) f a c e , b = a . 0 - 5 1 1 0 F i g . 6. Co r r e c t i on f a c t o r s f o r the (111) and (.112) faces of NiSO, a 6H-0. Table I I I Phy s i ca l constants of 60% v/v ethanol and NiSO, a 6H ?0 Dynamic Dens i t y , Kinematic D i f f u s i o n Temperature v i s c o s i t y , v i s c o s i t y , c o e f f i c i e n t (°C) n x 10^ p v x 10 z D x 10 x x ' ( g . cm " 1 . s ~ 1 ) ( g . c n f 3 ) ( e m 2 . s _ 1 ) ( c m 2 . s _ 1 ) (111) face (112) face (cm) (cm) 37 1.56. 0.886 1.76 3.38 0.135 a 0.114 a 41 1.40 0.883 1.59 3.82 (0.109-0.159) b (0.111-0.118) ' a Mean of 6 c r y s t a l s b Range - 65 -face was measured at a high f l ow r a t e . At time t = 30 or 40 min the f low r a t e was increased and the movement of the (111) face measured f o r an a d d i t i o n a l 30 min. Temperatures of 37° and 40.5° were used i n the exper iments. 3.4 A l t e r a t i o n s i n l e v e l of under sa tu ra t i on of d i s s o l u t i o n medium Increas ing amounts of N i S 0 4 a 6H2O (0.9-3.4 g . 1000 g""*. s o l ven t ) were d i s s o l v ed i n the d i s s o l u t i o n medium and d i s s o l u t i o n of the (111) face f o l l owed at 37° and a f l ow r a te of 4.68 cm.s - ^ . D. HABIT MODIFICATION AND DISSOLUTION RATE 1. Growth of c r y s t a l hab i t s C h a r a c t e r i z a t i o n of the hab i t s i s g iven i n s e c t i o n E. 1.1 -B ipyramidal hab i t The c r y s t a l s were grown from seed c r y s t a l s , s i z e range 1.00-1.18 mm at 40° at s i m i l a r i n i t i a l super sa tu ra t i on s ( P h i l l i p s and E p s t e i n , 1973, 1974). The f i n a l growth ra te s of the c r y s t a l s were between 22.3 x 10" - 27.4 x 10" - 2 - 1 g.cm .s . C r y s t a l s s e l e c t e d f o r the bulk d i s s o l u t i o n s tud ie s were between 2.1-2.4 mm i n width and 2.4-2.8 mm in l eng th . 1.2 Habit m o d i f i c a t i o n t r i a l s Supersaturated s o l u t i o n s of N i S O ^ H g O i n water were prepared and the f o l l o w i n g methods of modi fy ing the c r y s t a l hab i t c a r r i e d out. a) Change of s upe r sa tu ra t i on So l u t i on s of va ry ing s upe r sa tu ra t i on were prepared and r e c r y s t a l l i z e d at 33° f o r 18 hours. However, b ipyramida l c r y s t a l s on ly were formed. b) Change of so l vent Supersaturated s o l u t i o n s of NiS04.6H20 i n 15% v/v e t h a n o l , 10% v/v methanol and 0.1 N h yd ro ch l o r i c a c i d were prepared and r e c r y s t a l l i z e d at 35° f o r 16 hours. C r y s t a l s grown i n 15% v/v ethanol and 0.1 N h yd roch l o r i c - 66 -a c i d formed on ly the b ipyramidal h a b i t . R e c r y s t a l l i z a t i o n i n 10% v/v methanol produced a f i n e p r e c i p i t a t e , c) A d d i t i v e s Supersaturated s o l u t i o n s of NiSO^.eHgO i n water were prepared and small amounts of the f o l l o w i n g compounds added. In a l l cases r e c r y s t a l l i z a -t i o n was c a r r i e d out a t 35° f o r between 48-56 hours. B r i l l i a n t blue dye, urea, veegum suspension and carbopol a d d i t i v e s d id not change the c r y s t a l h ab i t from tha t of the b ipyramidal h ab i t . Sodium t r i po l ypho spha te added to the r e c r y s t a l l i z a t i o n medium produced c r y s t a l s resembl ing the b ipyramida l h a b i t , but e longated and mis s ing the (001) f a ce . The most pronounced m o d i f i c a t i o n o f c r y s t a l hab i t was produced on a d d i t i o n of a small amount of g e l a t i n to the r e c r y s t a l l i z a t i o n medium, as desc r ibed below. 1.3 P l a t y hab i t A supersaturated s o l u t i o n of N iS04 . 6 H 2 0 i n water was prepared a t 48° and a small amount (approx. 0.2 mg.mL"^) of g e l a t i n B.P. i n water was added. The very high concent ra t i on of s o l ub l e e l e c t r o l y t e ( n i c k e l s u l f a t e ) r e s u l t e d i n the " s a l t i n g out " of the g e l a t i n . The s o l u t i o n was f i l t e r e d through g lass wool and r e c r y s t a l l i z e d a t 38° i n a constant temperature bath. The c r y s t a l s were washed i n water and s to red at 84% r e l a t i v e humidity p r i o r to use (See Tab l e , s e c t i o n E.7). C r y s t a l s s e l e c t e d f o r the d i s s o l u t i o n s tud ie s were between 1.7-3.0 mm i n length and width w i th a t h i ckne s s of between 0 . 6 -1 .2 mm. 1.4 A c i c u l a r hab i t A c i c u l a r c r y s t a l s of NiSO^./h^O measuring 6.0-10.00 mm i n length and 1.0-2.0 mm i n width were grown from a supersaturated s o l u t i o n at 2 2° . On storage overn ight i n a d e s i c c a t o r , the c r y s t a l s dehydrated t o . g i v e NiS04 a 6H2O. Rehydrat ion d i d not occur r e a d i l y as shown by storage at a - 67 -r e l a t i v e humidity of 90%.(25°) (see Tab l e , s e c t i o n E.7). 2. Bulk D i s s o l u t i o n The d i s s o l u t i o n r a t e of the var ious hab i t s was determined us ing the U.S.P. d i s s o l u t i o n t e s t apparatus. For each d i s s o l u t i o n exper iment, a number of c r y s t a l s were taken to g ive approx imate ly constant weights and su r face areas. Between 9-15 c r y s t a l s : f o r the b ipyramidal and p l a t y hab i t s and between 3-7 c r y s t a l s f o r the a c i c u l a r hab i t were used. Before each d i s s o l u t i o n exper iment, the c r y s t a l s were washed i n 10 mL of 60% v/v ethanol f o r 1 minute to remove su r face p a r t i c u l a t e matter and then d r i e d and weighed. 900 mL of 60% v/v ethanol was p laced i n a covered, 1000 ml g las s vesse l and e q u i l i b r a t e d at the de s i r ed temperature i n a constant temperature bath. The c r y s t a l s were p laced i n the w i re basket, lowered i n t o the d i s s o l u t i o n medium and r o ta ted by.means of a constant speed motor. The r o t a t i n g v e l o c i t y ( i n rpm) was measured us ing an e l e c t r o n i c stroboscope and constant checks on the r o t a t i n g v e l o c i t y were made throughout the d i s s o l u t i o n t r i a l . 1 mL samples of the d i s s o l u t i o n medium were removed from a po in t 4-5 cm below the su r face of the d i s s o l u t i o n medium at s u i t a b l e time i n t e r v a l s , made up to 5 ml w i th water and s to red i n a i r t i g h t , b o r o s i l i c a t e g la s s v i a l s p r i o r to a n a l y s i s . At the end of each exper iment, the c r y s t a l s were reweighed and the weight l o s s dur ing d i s s o l u t i o n used as a mass balance check. D i s s o l u t i o n was fo l l owed at r o t a t i o n speeds of between 150-750 rpm at temperatures of 9 . 9 ° , 22° and 30° f o r 50-90 minutes dur ing which time there was n e g l i g i b l e change i n su r face a rea . D i s s o l u t i o n occurred under s ink cond i t i on s s i nce a t no time d i d the concen t ra t i on of NiS04 a 6H2O exceed 1.8% of i t s s a t u r a t i o n s o l u b i l i t y . - 68 -3. I n t r i n s i c D i s s o l u t i o n I n t r i n s i c d i s s o l u t i o n ra te s of the b i p y r a m i d a l , p l a t y and a c i c u l a r c r y s t a l s were measured us ing the r o t a t i n g d i s c method of Nogami e t a l . (1966). The c r y s t a l s were ground i n a g las s mortar and p e s t l e and compressed i n t o 1.3 cm diameter d i s c s a t 5 tons pressure us ing a h yd r au l i c p res s . The d i s c was a f f i x e d to a s t a i n l e s s s t e e l ho lder of the same diameter us ing non-perfumed, c o l o r l e s s n a i l enamel as an adhes ive. So t ha t on ly the bottom face of the d i s c was exposed to the s o l v e n t , the edges of the d i s c were covered w i th the adhes ive. 500 mL of 60% v/v ethanol was placed i n a 600 mL j acke ted g la s s beaker connected to a constant temperature c i r c u l a t o r and f i t t e d w i th a cover to min imize so l vent evapora t i on . The j acke ted beaker was p laced on a l abo r a to r y j ack which was r a i s ed to immerse the d i s c to a f i x e d depth (2 cm from the bottom of the beaker) and r o ta ted by means of the constant speed motor checked w i th the e l e c t r o n i c stroboscope. 1 mL samples of the d i s s o l u t i o n medium were removed from a po in t 6 to 7 cm below the su r face of the d i s s o l u t i o n medium at s u i t a b l e time i n t e r v a l s , made up to 5 mi i n water and s to red as above p r i o r to a n a l y s i s . D i s s o l u t i o n was c a r r i e d out a t a r o t a t i o n speed of 300 rpm a t temperatures of 30° and 45° f o r 120 minutes. In a d d i t i o n , the r o t a t i o n speed was v a r i ed from 75-750 rpm f o r d i s c s of the b ipyramida l c r y s t a l s a t 30° . - 69 -E. CHARACTERIZATION OF NICKEL SULFATE; 7H 20, 3 6H9O AND HABITS OF g 6H 20 1. Growth of N i S 0 4 3, 6H 20 c r y s t a l s A supersaturated s o l u t i o n of NiS04.6H 2 0 i n water was prepared at approx imately 70° and r e c r y s t a l l i z e d at 58° fo l l owed by storage at 58° i n a t i g h t l y c l o sed b o t t l e to prevent dehydrat ion . 2. S o l u b i l i t y determinat ion 2.1 S o l u b i l i t y of NiSO^ a 6H 20 i n ethanol s o l u t i o n s An excess of N i S0 4 . 6H 2 0 was added to vo lumet r i c f l a s k s conta ing 50%, 60% and 70% v/v e thano l . These were e q u i l i b r a t e d by r o t a t i o n i n a water bath t h e r m o s t a t i c a l l y c o n t r o l l e d a t the requ i red temperature f o r 48-56 hours. 10 mL of each s o l u t i o n was f i l t e r e d i n t o vo lumet r i c f l a s k s through a Mi 11ipore sy r inge f i t t e d w i th a 0.45 micron f i l t e r and weighed on an a n a l y t i c a l balance. So l u t i on s were made up to 100 g w i th water and f u r t h e r d i l u t i o n s made where necessary, p r i o r to a n a l y s i s . Samples were analyzed f o r Ni content us ing atomic absorpt ion spectrophotometry. 2.2 S o l u b i l i t y of c r y s t a l hab i t s i n 60% v/v ethanol A f t e r g r i n d i n g , excess amounts of each hab i t were e q u i l i b r a t e d w i th 60% v/v ethanol by r o t a t i o n i n a water bath t h e r m o s t a t i c a l l y c o n t r o l l e d a t the requ i red temperature. Samples were f i l t e r e d and analyzed as above. 3. X- ray d i f f r a c t i o n Approximately 300 mg of the ground samples was exposed to CuKa r a d i a t i o n i n a wide angle X-ray d i f f r a c t o m e t e r . The l o c a t i o n and i n t e n s i t y of the peaks a t d i f f e r e n t va lues of the g l anc ing angle C-28) were s t ud i ed . 4. X-ray energy a n a l y s i s C r y s t a l s of the b i p y r a m i d a l , p l a t y and a c i c u l a r hab i t s were.coated - 70 -w i th spectre-graphic g r a p h i t e . The c r y s t a l s were p laced i n the specimen ho lder of a scanning e l e c t r o n microscope, connected to an X-ray energy ana l y ze r . X-rays i n the 0-20 KeV energy range were ana lyzed. 5. Thermal a n a l y s i s Thermal a n a l y s i s was performed us ing a d i f f e r e n t i a l scanning c a l o r i -meter equipped f o r e f f l u e n t gas a n a l y s i s . C r y s t a l s were ground i n a g la s s p e s t l e and mortar and 1-5 mg samples were weighed us ing a Cahn Gram e l e c t r oba l ance d i r e c t l y i n t o aluminum v o l a t i l e sample pans. Scans were made a t 10°/minute us ing c lo sed pans and pans w i th a 0.1-0.2 mm p i nho l e . Vapo r i z a t i on of the water of c r y s t a l l i z a t i o n from the pans w i th a p inho le was detected us ing the e f f l u e n t gas ana l yze r and was est imated q u a n t i t a t i v e l y by weighing the pan a f t e r each endothermic peak. 6. Surface area The b i p y r a m i d a l , p l a t y and a c i c u l a r hab i t s have r e g u l a r , w e l l - d e f i n e d c r y s t a l f a ce s . The dimensions of each face were measured us ing a t r a v e l l i n g -4 microscope reading ±5 .0 x 10 cm and used to c a l c u l a t e the t o t a l su r face a rea . 7. Dehydration of N i S O ^ H o O Saturated s o l u t i o n s of the f o l l o w i n g s a l t s were prepared i n g las s de s i c ca to r s at room temperature to g i ve d i f f e r e n t r e l a t i v e h u m i d i t i e s . - 71 -S a l t R e l a t i v e Humidity % NaHS0 4.H 20 52 NaN0 2 66 NH4C1 79.5 KBr 84 Z-nS0 4.7H 20 90 Na 2 HP0 4 .12H 2 0 95 500 mg of the a c i c u l a r N i S0 4 . 7H 2 0 c r y s t a l s were p laced i n each of the d e s i -c c a t o r s , i n c l u d i n g one con ta i n i n g fused C a C l 2 granules to remove water vapor. The c r y s t a l s were weighed at i n t e r v a l s over a per iod of 9 days. F. ANALYSIS OF NICKEL SULFATE HEXAHYDRATE Ana l y s i s f o r Ni was c a r r i e d out by atomic abso rp t ion spectrophotometry us ing a n i c k e l hol low cathode lamp. 1. P repa ra t i on of standards A 1000 ppm Ni stock s o l u t i o n was f u r t h e r d i l u t e d w i th water to g ive a 100 ppm Ni s o l u t i o n . Standards of 1-5 ppm were prepared by p i p e t t i n g the appropr i a te volume of 100 ppm Ni s o l u t i o n i n t o 100 mL vo lumet r i c f l a s k s . 20 mL of 60% v/v ethanol was added to each f l a s k before making up to volume w i th d i s t i l l e d water. The standards and d i l u t e d samples of d i s s o l u t i o n medium both conta ined f i n a l concent ra t i ons of 12% v/v e t hano l . - 72 -2. Operat ing cond i t i on s The s o l u t i o n s were vapor i zed i n an a i r - a c e t y l e n e (ethyne) mixture flame and absorbances measured under the f o l l o w i n g c o n d i t i o n s . F i r s t and second most s e n s i t i v e wavelengths were s e l e c t e d , the l a t t e r being used on ly a t the h igher sample concen t ra t i on s . Wavelength (nm) S e n s i t i v i t y (ppm) Lamp cu r ren t (mA) SI i t width (urn) Fuel gas Support gas 232.2 0.066 5 50 ethyne a i r 341.7 0.34 5 50 ethyne a i r The standard curve f o r Ni was l i n e a r over the range of 0-6 ppm N i . A s imple check on the assay f i g u r e s was p rov ided , by reco rd ing the weight l o s s o f the c r y s t a l s a f t e r each d i s s o l u t i o n t r i a l . Hence the t o t a l amount of N i S0 4 . 6H 2 0 i n the d i s s o l u t i o n medium was known and cou ld be compared w i th the assay va lue . The d i f f e r e n c e between these two values was always l e s s than 5%.. - 73 -G. CRYSTAL DEFECTS AND DISSOLUTION RATE A number of c r y s t a l l i n e m a t e r i a l s have been used i n t r i a l s to determine a s u i t a b l e model c r y s t a l system f o r s tudy ing the e f f e c t of de fect s on the d i s s o l u t i o n r a t e . 1 . N i c ke l s u l f a t e hexahydrate c r y s t a l s 1 . 1 Growth of b ipyramida l c r y s t a l s of NiSQ^ g 6 H Q O The apparatus desc r ibed i n s e c t i o n C.3.1 was used to grow the c r y s t a l s w i th the f o l l o w i n g m o d i f i c a t i o n s . A diaphragm-type pump w i th good f low con t r o l rep laced the p e r i s t a l t i c pump. A l l par t s i n con tac t w i th s o l u t i o n were t e f l o n thus reducing the l i k e l i h o o d of i m p u r i t i e s en te r i ng s o l u t i o n . The f l ow meter was removed as the supersaturated s o l u t i o n c r y s t a l l i z e d out i n the narrow o r i f i c e a t the entrance to the f l ow meter. A supersaturated s o l u t i o n of NiSO^ g 6 1 ^ 0 i n water was prepared and f i l t e r e d a t 4 5 ° i n an oven. The ( 0 0 1 ) face of a seed c r y s t a l was f i x e d us ing one drop of cyanoacry la te glue to the tungsten w i r e . The b ipyramida l c r y s t a l s used as seed c r y s t a l s were the same as those desc r ibed i n s e c t i o n D . l . l . S o l u t i on s of va ry ing s upe r sa tu ra t i on were c i r c u l a t e d through the apparatus a t a temperature of 3 7 ° and f l ow r a t e of 3 2 0 mL .m in " 1 . The move-ment of the (001) f ace was measured w i th a t r a v e l l i n g microscope. The c r y s t a l s were weighed before and a f t e r growth to determine the growth r a t e as an o v e r a l l r a t e of i nc rease i n weight. Ana l y s i s of the supersaturated s o l u t i o n s was by atomic abso rp t ion spectrophotometry. 1 . 2 E f f e c t of f l ow r a t e on the growth r a t e Several c r y s t a l s were grown as p r e v i ou s l y desc r ibed except tha t a t time > = '\15 and 4 0 min the f l ow r a te was i nc rea sed . Movement of the ( 0 0 1 ) - 74 -face was measured as be fo re . 1.3 C r y s t a l c h a r a c t e r i z a t i o n 1.31 Flow c e l l grown c r y s t a l s The c r y s t a l s were examined us ing a r e f l e c t e d l i g h t microscope and a Ze i s s U l t r aphot 111-M w i th d i f f e r e n t i a l i n t e r f e r e n c e c o n t r a s t . 1.32 F l u i d i z e d - b e d grown c r y s t a l s Two samples of b ipyramida l c r y s t a l s , grown i n a f l u i d i z e d - b e d c r y s t a l l i -zer w i th a 40 f o l d d i f f e r e n c e i n growth r a t e , average s i z e 1.01 mm, were c leaved along the (001) plane w i th a s c a l p e l b lade. The c r y s t a l s were etched by immersing them in warm, 100% ethanol f o r approx imately 1 min. The c leavage faces were examined m i c r o s c o p i c a l l y as desc r ibed i n s e c t i o n G.1.31. 1.4 S i n g l e c r y s t a l d i s s o l u t i o n The d i s s o l u t i o n r a te s o f the (001) face of the c r y s t a l s were measured us ing the apparatus desc r ibed i n s e c t i o n C.3.1 w i th 60% v/v ethanol as the s o l ven t . D i s s o l u t i o n was c a r r i e d out a t 30° and 37° w i th a f l ow r a t e of 576 mL.min"^. The d i s s o l u t i o n r a te s of the c r y s t a l s grown i n the f l u i d i z e d - b e d were -5 a l s o determined i n the presence of 7 x 10 M sodium t r i p o l y p h o s p h a t e , a d i s s o l u t i o n i n h i b i t o r , added to the d i s s o l u t i o n medium. 2. Calc ium t a r t r a t e c r y s t a l s S i ng l e c r y s t a l s of ca lc ium t a r t r a t e were grown i n a s i l i c a gel medium accord ing to a method desc r ibed by Henisch et a l . (1965). 24 g sodium m e t a s i l i c a t e was d i s s o l v e d i n 100 mL water and mixed w i th an equal volume of 1 M t a r t a r i c a c i d . The mixture was p laced i n g las s tubes 20 cm long and 2.5 cm i n t e r n a l diameter and a l lowed to gel at constant temperature f o r 24-48 hours. 1 M ca lc ium c h l o r i d e d ihyd ra te was added over the su r face - 75 -of the g e l . A f t e r a pe r i od of severa l days the c r y s t a l s were harvested from the d i f f e r e n t l a ye r s of the g e l . However, the c r y s t a l s were found to be un su i t ab l e f o r f u r t h e r s t ud i e s because, a) the c r y s t a l s showed wide v a r i a t i o n i n h a b i t . b) many c r y s t a l s were d i s c o l o r e d due to an i n co rpo r a t i o n of i r on i m p u r i t i e s . c) c r y s t a l s were hard, b r i t t l e and d i f f i c u l t to c l e a ve . d) many c r y s t a l s con s i s ted of l a r ge aggregates of dend r i t e s which, due to t h e i r s i z e and weight f r e q u e n t l y f e l l through the gel caus ing i t to crack and form l a r ge channe l s , thereby a f f e c t i n g the growth of adjacent c r y s t a l s . 3. Potassium perch !o ra te c r y s t a l s 3.1 Gel growth of c r y s t a l s S i n g l e c r y s t a l s of potassium pe r ch l o r a te were grown i n a s i l i c a gel medium accord ing to a method desc r ibed by Pate l and Rao (1977, 1978, 1979). 3.11 E f f e c t of gel den s i t y I t was observed that a t h igher gel d e n s i t i e s the c r y s t a l s became le s s t ransparent and we l l - fo rmed due to the i n c o r p o r a t i o n of s i l i c a gel i n t o the c r y s t a l s . S o l u t i on s each con ta i n i n g 16 g, 14 g, 13 g, 12 g, 10 g sodium m e t a s i l i c a t e were d i s s o l v ed i n 100 mL water , f i l t e r e d and 20 mL placed i n g las s tubes, 20 cm in length and 2.5 cm i n t e r n a l d iameter . 10 mL IN p e r c h l o r i c a c i d was added and the s o l u t i o n s mixed on a vor tex mixer . The tubes were kept a t 30° f o r 24-48 hours i n a constant temperature water bath. 13 g sodium m e t a s i l i c a t e i n 100 mL water was the opt imal c oncen t r a t i on f o r growth and was used i n a l l f u r t he r , s t u d i e s . Below t h i s c o n c e n t r a t i o n , s o l u t i o n s would not gel w i t h i n 10-14 days, and a t h igher c oncen t r a t i o n s , the - 76 -ge l s were very dense. 3.12 E f f e c t of pH of ge l s As the pH i n c rea se s , the t ransparency of ge l s decreases. The pH of the gel was va r i ed by adding 1, 2 or 3 drops of g l a c i a l a c e t i c a c i d to the g e l l i n g s o l u t i o n from a Pasteur p i p e t t e . drops CH3C00H pH of gel 0 6.95 1 5.15 2 4.53 3 3.91 Two drops of g l a c i a l a c e t i c a c i d were added to the g e l l i n g s o l u t i o n i n a l l growth s t u d i e s . Three or more drops produced very f r a g i l e g e l s . 3.13 E f f e c t of temperature Gels were prepared as p r e v i ou s l y de s c r i bed . Approx imate ly 30 mL IN potassium c h l o r i d e was c a r e f u l l y p laced over the ge l s and kept a t constant temperature f o r 7-10 days. Growth s tud ie s were conducted a t 2 3 ° , 3 0 ° , 35° and 40° . More c r y s t a l s nuc leated at lower than at h igher temperatures. At 35° and 40° very few c r y s t a l s formed i n the ge l and no c r y s t a l s grew at depths g rea te r than 3 cm below the su r face of the g e l . At 2 3 ° , the c r y s t a l s were small and l a rge numbers grew i n the g e l . The opt imal growth temperature was 30° . - 77 -3.14 Harvest ing of c r y s t a l s The tubes were marked o f f from the g e l - s o l u t i o n i n t e r f a c e i n 1 cm increments down the length of the gel columns. C r y s t a l s from each growth l e v e l ( i . e . 0-1 cm, 1-2 cm, 2-3 cm e t c . ) were removed and p laced i n beakers. The c r y s t a l s were separated from the gel by repeated washings i n water. A f t e r a i r d ry ing a t room temperature the c r y s t a l s a t each growth l e v e l were s tored i n t i g h t l y stoppered g la s s j a r s . 3.2 C r y s t a l c h a r a c t e r i z a t i o n 3.21 C r y s t a l de fec t s a) C leav ing and e t ch i ng KC10 4 c r y s t a l s w i th the octahedra l hab i t shown i n F i g . 7 were c leaved by p l a c i n g a s c a l p e l blade pe rpend i cu la r to the (210) face and tapping sha rp l y on the upper edge of the b lade. Th is exposed the (001) plane of the c r y s t a l . The c r y s t a l s were.etched by s w i r l i n g gen t l y i n a mixture of 5 mL 0.25 M sodium s u l f i t e and 5 mL concentrated s u l phu r i c a c i d . The c r y s t a l s were etched f o r 3 minutes f o l l owed by washing i n ether f o r 1 minute. b) Microscopy A net g r a t i c u l e marked o f f i n 100 squares was p laced i n the eyepiece of a sur face i l l u m i n a t i o n , d i f f e r e n t i a l i n t e r f e r e n c e con t r a s t microscope. The etched (001) plane of the c r y s t a l was viewed and the number of d i s l o c a t i o n etch p i t s noted i n the squared g r a t i c u l e . The d i s l o c a t i o n etch p i t s over the whole area of the (001) plane were counted. The etch p i t s on 12-17 c r y s t a l s from three d i f f e r e n t growth l e v e l s ( 0 -1 , 2-3 and 4-6 cm) were counted. The lengths of the edges of the exposed (001) plane were measured us ing a t r a v e l l i n g microscope and the area of the plane c a l c u l a t e d . Hence the d i s l o c a t i o n den s i t y (number of d i s l o c a t i o n s per cm ) was determined. - 78 -( 1 0 1 ) ( 1 0 1 ) F i g . 7, Diagram of a s i n g l e KCIO4 c r y s t a l showing the geometry and p o s i t i o n of c r y s t a l f a c e s , c h a r a c t e r i z e d by t h e i r M i l l e r i n d i c e s . - 79 -3.22 X-ray d i f f r a c t i o n Th i s was c a r r i e d out as desc r ibed i n s e c t i o n E.3, us ing ground samples of KCIO^ from growth l a ye r s 0 -1 , 2-3 and 4-6 cm. 3.23 X-ray energy ana l y s i s Octahedral c r y s t a l s of K C I O 4 from the 0-1 and 4-6 cm growth l e v e l s were coated w i th s p e c t r o g r a p h s g r aph i t e . The c r y s t a l s were p laced i n the specimen ho lder of a scanning e l e c t r o n microscope, connected to an X- ray energy ana l y ze r . X-rays i n the 0-20 KeV energy range were ana lyzed. 3.24 Thermal a na l y s i s Th i s was c a r r i e d out as desc r ibed i n s e c t i on E.5. The scanning r a t e was va r i ed and open pans and v o l a t i l e sample pans w i th a p inho le were used. 3.25 S o l u b i l i t y determinat ion A f t e r g r i n d i n g , excess amounts of potassium pe r ch l o r a te from the three d i f f e r e n t growth l e v e l s were e q u i l i b r a t e d w i th 95% v/v ethanol by r o t a t i o n i n a water bath t h e r m o s t a t i c a l l y c o n t r o l l e d a t 1 0 . 5 ° . Samples were f i l t e r e d us ing a s y r inge f i t t e d w i th a M i l l i p o r e f i l t e r and a f t e r app rop r i a te d i l u t i o n , were analyzed f o r K content us ing atomic abso rp t ion spectrophotometry. 3.26 Surface area The octahedra l hab i t of KC104 has r e g u l a r , w e l l - d e f i n e d c r y s t a l f a ce s . The dimensions o f each face were measured us ing a t r a v e l l i n g microscope and used to c a l c u l a t e the t o t a l su r face a rea . 3.3 Bulk d i s s o l u t i o n The d i s s o l u t i o n r a t e of c r y s t a l s grown a t three growth l e v e l s ( 0 - 1 , 2-3 and 4-6 cm) was determined us ing the apparatus desc r ibed i n s e c t i on D.2. For each d i s s o l u t i o n exper iment, a number of c r y s t a l s were taken to g i ve -approx imate l y constant weights and su r face a reas . Between - 80 -7-11 c r y s t a l s f o r the octahedra l hab i t were used. Before each d i s s o l u t i o n exper iment, the c r y s t a l s were washed i n 5 mL of 95% v/v ethanol f o r 30-60 seconds to remove su r face p a r t i c u l a t e matter and then d r i e d and weighed. 800 mL of 95% v/v ethanol was p laced i n the 1000 mL g la s s vesse l and e q u i l i b r a t e d at 10.5° i n a constant temperature bath. 2.5 mL samples o f the d i s s o l u t i o n medium were removed from a po i n t 4-5 cm below the su r face of the d i s s o l u t i o n medium at s u i t a b l e time i n t e r v a l s , made up to 5 mL w i th a s o l u t i o n of 2 mg.mL"^ cesium in water and s tored i n a i r t i g h t , b o r o s i l i c a t e g la s s v i a l s p r i o r to a n a l y s i s . D i s s o l u t i o n was f o l l owed a t a r o t a t i o n speed of 500 rpm f o r 120 minutes dur ing which t ime there was n e g l i g i b l e change i n su r face a rea . H. ANALYSIS OF POTASSIUM PERCHLORATE Samples were analyzed f o r K by atomic absorpt ion spectrophotometry us ing a potassium hol low cathode lamp. I. P repara t ion of standards Approximately 3.5 g of KCIO^ a c c u r a t e l y weighed was d i s s o l v e d i n water and made up to 1000 mL. Th i s 1000 ppm K s o l u t i o n was f u r t h e r d i l u t e d w i th water to g ive a 10 ppm K stock s o l u t i o n . Standards of 0.4-1.4 ppm were prepared by p i p e t t i n g the app rop r i a te volume of 10 ppm K s o l u t i o n i n t o 100 mL vo lumet r i c f l a s k s . 50 mL 95% v/v ethanol was added to each f l a s k . Potassium i s p a r t i a l l y i o n i z ed i n the a i r - e t h y n e f lame and to suppress i o n i z a t i o n , an excess of a cesium s a l t i s added to a l l s o l u t i o n s . A 20 mg.mL -^ Cs stock s o l u t i o n was prepared by d i s s o l v i n g 2.526 g cesium c h l o r i d e i n water and making up to 100 mL i n a vo lumet r i c f l a s k . 5 mL of t h i s stock s o l u t i o n was added to each of the 100 mL f l a s k s f o r the s tandards. - 81 -A l l f l a s k s were made up to volume w i th water. The standards and d i l u t e d samples of d i s s o l u t i o n medium both conta ined f i n a l concent ra t i on s of 47.5 % v/v ethanol and 1 mg.mi -^ Cs. 2. Operat ing cond i t i on s The s o l u t i o n s were vapor i zed i n an a i r - e t h y n e mixture flame and absorbances measured under the f o l l o w i n g c o n d i t i o n s . The f i r s t most s e n s i t i v e wavelength was s e l e c t e d . Wavelength S e n s i t i v i t y Lamp cu r ren t SI i t width Fuel Support (nm) (ppm) (mA) (uni) gas gas 766,4 0.01 5 100 ethyne a i r The standard curve f o r K was l i n e a r over the range of 0-1.4 ppm K. - 82 -RESULTS AND DISCUSSION A. DISSOLUTION ANISOTROPY 1. Choice of model D i s s o l u t i o n an i so t ropy i s most e a s i l y s tud ied us ing a s i n g l e c r y s t a l technique which permits d i r e c t measurement o f the d i s s o l u t i o n of var ious c r y s t a l l o g r a p h i c f ace s . N i cke l s u l f a t e ( N i S O 4 a 6 H 2 O ) grows as a we l l - fo rmed c r y s t a l , i t s shape being a combination of two te t ragona l bipyramids and i s an i d e a l model f o r s i n g l e c r y s t a l s t u d i e s . Due to i t s symmetrical shape and f l a t (001) faces ( F i g . 5 ) , i t cou ld be e a s i l y mounted on the tungsten wi re support i n the s i n g l e c r y s t a l d i s s o l u t i o n c e l l . In a d d i t i o n , the (111) and (112) faces were w e l l - d e f i n e d and f l a t and t h e i r lengths v a r i ed w i t h i n a very narrow range (Table I I I ) . 2. C a l c u l a t i o n o f observed apparent r a te constant When C s » C and S i s cons tant , the o v e r a l l d i s s o l u t i o n r a te i s p ropo r t i ona l to k g ^ (Eqn. 10). F i g . 8 shows t y p i c a l p l o t s of d i s t ance moved as a f unc t i on of time f o r a c r y s t a l f a ce . The s l ope s , ( c m . s _ l ) , cl determined us ing l i n e a r reg re s s i on ana l y s i s , are p ropo r t i ona l to the - 3 - 1 d i s s o l u t i o n r a te (g.cm .s ) and were used as a measure of an observed apparent r a te cons tan t , An i n i t i a l surge i n the movement o f the face was o f ten observed between t = 0-10 min and the s lope was t he re fo re c a l c u l a t e d from the l i n e a r po r t i on of the curve a f t e r t = 10 min. On repeat ing an experiment on the same c r y s t a l under i d e n t i c a l c ond i t i on s the i n i t i a l surge was not observed and a Us i n g a Wang 600 programmable c a l c u l a t o r . - 83 -M I N U T E S F i g . 8. Movement of the (111) c r y s t a l face of NiS04 a 6H2O as a f u n c t i o n of t ime at 37°C. Flow r a t e s : • , 1.70 cm.s -1 ; • , 6 . 9 c m . s - 1 . - 84 -the r a te was equal to t ha t o f the i n i t i a l experiment a f t e r t = 10 min. - f i — l (see F i g . 9 ) . The i n i t i a l experiment had a s lope value of 1.77 x 10" cm.s" a f t e r t = 10 mins and the repeat experiment had a s lope value of 1.91 x 10" cm.s"" ' . When observed under a scanning e l e c t i o n microscope and a d i f f e r e n -t i a l i n t e r f e r e n c e c on t r a s t microscope the o r i g i n a l c r y s t a l faces showed m ic roc rack s , d i s l o c a t i o n etch p i t s and i n c l u s i o n s ( F i g . 10). The i n i t i a l surge was probably due to the e l i m i n a t i o n of the " d i s t u r b e d " s u r f a ce . 3. D i s s o l u t i o n from a f l a t p l a t e ( c r y s t a l face) The equat ions d e s c r i b i n g d i s s o l u t i o n from a f l a t p l a t e have been developed i n s e c t i o n D.l of the l i t e r a t u r e survey. The mixed r a te constant equat ion (Eqn. 23) was combined w i th the Lev i ch equat ion f o r laminar f low over a . f l a t p l a t e (Eqn. 19). T h e . f l a t p l a te s de f ined i n Eqn. 19 were assumed to be the lengths of the (111) and (112) faces as presented to the d i r e c t i o n of f l ow and are des ignated x and x ' r e s p e c t i v e l y . Values of x and x ' are g iven i n Table I I I . Determinat ion of other terms def ined i n Eqn. 24 are given below. 3.1 D i f f u s i o n c o e f f i c i e n t The d i f f u s i o n c o e f f i c i e n t , D, of NiS04 a 6H 20 was c a l c u l a t e d from the S t oke s - E i n s t e i n equat ion (Carstensen, 1977) 0 - JT • fck ( 3 9 ) where R/N i s Boltzmann ' s constant (1.38 x 10" e rg .deg " ), T i s abso lu te temperature and X i s the molecu la r r ad i u s . I t was assumed tha t the d i f f u s i n g 2+ spec ies were the hydrated, complex ion [N i ( 6H 2 0 ) ] and the hydrated s u l f a t e i o n , S0 A a n . Hydrated (and complex) ions may be regarded as • - 85 -M I N U T E S 9. E l i m i n a t i o n of the i n i t i a l surge i n the movement of the (111) face of N i S 0 4 a 6H 20 at 37° and a f l ow r a t e of 3.7 cm.s-" 1. • , i n i t i a l exper iment; O , repeat experiment. L ines f i t t e d by l i n e a r r eg re s s i on a n a l y s i s . - 86 -0.05mm 10. D i f f e r e n t i a l i n t e r f e r e n c e con t r a s t micrograph of a (111) c r y s t a l face of NiSO^ a 6 ^ 0 before d i s s o l u t i o n . - 87 -charged spheres the rad ius of which i s the sum of the i o n i c rad ius and the o diameter of the water molecule (2.76 A) (George and McCTure, 1959), g i v i n g i o n i c r a d i i of 3.54 A and 5.06 A f o r [ N i ( 6 H 9 0 ) J 2 * and S 0 „ 2 ~ r e s p e c t i v e -L. aCj . H aCj . l y . I t was a l so assumed tha t the e f f e c t of water-ethanol i n t e r a c t i o n s and of temperature change on the rad ius of the hydrated ions w i l l be small and w i l l not s i g n i f i c a n t l y a f f e c t the c a l c u l a t e d values of the i o n i c r a d i i . S u b s t i t u t i o n o f the constants i n t o Eqn. 39 g i v e s , a t 37° D [ N i ( 6 H 2 0 ) ] 2 + a Q = D c = 4.11 x 1 0 " 6 c m 2 . s _ 1 and D S 0 4 2 " a q = D a = 2.87 x 1 0 " 6 c m 2 . s _ 1 An average va lue , D a v , f o r the c a t i o n D c and the anion D a was obta ined from an equat ion der i ved by Nernst(Moore, 1972) 2 D c D a D av = D 7 T \ (40) D a v a t 41° was c a l c u l a t e d by the same method (Table I I I ) . 3.2 Kinematic v i s c o s i t y The k inemat ic v i s c o s i t y of the d i s s o l u t i o n medium, v, i s g iven by n/p where n and p are the dynamic v i s c o s i t y and den s i t y of 60% v/v ethanol r e s p e c t i v e l y (Table I I I ) . L i t e r a t u r e values of n and p were obta ined a t d i f f e r e n t temperatures ( I n t e r n a t i o n a l C r i t i c a l Tab le s , 1928; Lange, 1967), the values a t 37° and 41° being i n t e r p o l a t e d from p l o t s of n and p versus temperature ( F i g s . 11 and 12). - 88 -F i g . 11. P l o t of v i s c o s i t y ( n ) versus temperature f o r 60% v/v e thano l . - 89 -F i g . 12. P l o t of den s i t y ( p ) versus temperature f o r 60% v/v e thano l . - 90 -3.3 L inear f low ra te s and Reynolds numbers The l i n e a r f l ow r a t e s , u, were c a l c u l a t e d by d i v i d i n g the experimental f l ow ra te s by the c r o s s - s e c t i o n a l area of the f l ow c e l l . The diameter of 2 the f low c e l l was 1.5 cm and hence i t s c r o s s - s e c t i o n a l area was 1.7674 cm . The exper imental data f o r d i f f e r e n t kinds of f l u i d s , a t d i f f e r e n t v e l o c i t i e s and f l ow ing i n d i f f e r e n t geometries may be c o r r e l a t e d i n terms of d imens ion less numbers known as mass t r a n s f e r c o e f f i c i e n t s . One of these c o e f f i c i e n t s , the Reynolds number, Re, desc r i be s the e f f e c t of a g i t a t i o n or the degree of tu rbu lence . I t i s g iven by the r a t i o of the f l u i d momentum to the v i scous drag f o r ce (Geankop l i s , 1972) R e = ^ - ^ (41) where L i s a c h a r a c t e r i s t i c l e n g t h . For a c i r c u l a r p i pe , g iven here as the f l ow c e l l , L i s equal to the d iameter . Hence Re can be c a l c u l a t e d a t a g iven temperature and f l ow r a t e by s u b s t i t u t i o n of app rop r i a te va lues i n t o Eqn. 41. Reynolds numbers were found to vary between 100-800 which i s i n the range of laminar f l ow . b 1/2 F i g . 13 shows KQ^S p l o t t e d as a f u n c t i o n of u and inc ludes curves p red i c ted by s u b s t i t u t i n g va lues of the apparent r a t e constants f o r the t r an spo r t and su r face c o n t r o l l e d r e a c t i o n s , K^ . and K r r e s p e c t i v e l y (see l a t e r ) i n t o Eqn. 23. The curves are i n e x c e l l e n t agreement wi th the exper imental The un i t s of KQ^S (cm.s ) a re the same as k o b s Eqn. 10 but i t should be noted t ha t K o b s i s an apparent r a t e constant determined d i r e c t l y as the boundary movement of a c r y s t a l face w i t h t ime, wh i l e k0^s i s a r a t e constant f o r the d i s s o l u t i o n r e a c t i o n measured as a concen t ra t i on change w i t h t ime. - 91 -F i g . 13. D i s s o l u t i o n an i s o t ropy of NiSC^ a 6 H 2 O a t 3 7 ° : • , (111) f a c e ; o , (112) f a c e ; po in t s expe r imenta l , curves p red i c ted us ing Eqn. 23. - 92 -values of K Q B S a t the lower f low ra tes but d iverge at h igher f low r a t e s . A change i n s lope whereby KQ^S becomes independent of f low r a te i s u s u a l l y taken to i n d i c a t e a change to a su r face c o n t r o l l e d r e a c t i o n (Bircumshaw and R i d d i f o r d , 1952). Evidence tha t the r e a c t i o n i s e s s e n t i a l l y su r face c o n t r o l l e d at the h igher f low ra tes was obta ined by i n c r ea s i n g the f l ow r a t e a t t ime t = 40 or 50 min as shown i n F i g . 14. The absence of any change i n the r a te of movement of the c r y s t a l face showed tha t the r e a c t i o n was independent of f low r a t e . Never the le s s , the change i n s lope o f the exper imental va lues shown i n F i g s . 13 and 15 i s g rea te r than p red i c ted by Eqn. 10 and i t i s apparent tha t the mixed t r an spo r t su r face c o n t r o l l e d d i s s o l u t i o n model desc r ibes the r e s u l t s a t the lower f low ra te s on l y . F i g . 15 shows t ha t the 112 break i n the K ^ versus u curve occurs a t a lower f low r a te as the temperature i s reduced. Hence the d i sc repancy between the observed and p red i c ted values o f K Q ^ depends on both f low r a te and temperature and i s not s imply an e f f e c t o f non- laminar f l ow. The e f f e c t of a l t e r i n g the d i s s o l u t i o n medium i s shown i n F i g . 16. K O B S f o r the (111) face i s g rea te r at a l l f l ow ra tes i n 55% v/v ethanol and no s i g n i f i c a n t break i n the K 0 b s 112 versus u curve i s observed even at high f low r a t e s . 4. Hydrodynamics of the system and d i s s o l u t i o n an i so t ropy F i g . 13 shows t ha t K 0 t ) S f o r the (112) face was g reate r than f o r the (111) face a t a l l f l ow ra tes s t ud i ed . Because of d i f f e r e n c e s i n the angles at which the faces were presented to the f l ow ing s o l v e n t , i t was necessary to show tha t the observed d i s s o l u t i o n an i so t ropy was due to inherent c r y s t a l l i n e p rope r t i e s and not to a hydrodynamic e f f e c t . This was achieved by ang l i ng a c r y s t a l on the w i re support such :,.^that a (111) face occupied the (112) p o s i t i o n ( F i g . 17). K O B S f o r the (111) face was the same i n both - 93 -F i g . 14. Movement of the (111) c r y s t a l face of NiS04 a 6 H 2 ° versus time to show su r face c o n t r o l l e d d i s s o l u t i o n . C i r c l e s , 37°: • , 5.8 c m . s - 1 ; o , 8.1 c m . s - 1 . Squares, 4 0 . 5 ° : " , 4 . 9 c m . s - 1 ; • , 7.2 c m . s - 1 . Arrows i n d i c a t e change o f f low r a t e . - 94 -Fig. 15. Dependence of K 0bs for the (111) face of N i S 0 4 a 6H2O on flow rate: A , 30°; • , 3 7 ° ; • , 41°; Y , 45.5°. - 95 -F i g . 16. Dependence of K g bs f o r the (111) face of NiStfy a 6 H 2 ° on f low r a t e us ing 55% v/v ethanol as the d i s s o l u t i o n medium: • , 3 7 ° ; • , 4 5 . 5 ° . - 96 -(111) IN lfl2) POSITION DISSOLUTION RATE (1H) = DISSOLUTION RATE (Til) IN (112) POSITION F i g . 17. Ang l ing of a NiS04 a 6H2O c r y s t a l on the tungsten w i r e support. - 97 -6 1 - 6 —1 p o s i t i o n s , 4.96 x 10 cm.s" i n the normal p o s i t i o n and 4.94 x 10~ cm.s" i n the (112) p o s i t i o n . 5. Determinat ion of apparent t r an spo r t and su r face r e a c t i o n ra te constants F i g . 18 shows K Q b s versus u ' f o r the (111) and (112) faces p l o t t e d accord ing to Eqn. 24. Due to the d ivergence of KQ^S a t the h igher f low r a t e s , these values were not i nc luded i n the weighted l e a s t squares f i t t i n g of the data . E r ro r s i n (y) depend on the v a r i a b i l i t y of the su r faces of -1/2 i n d i v i d u a l c r y s t a l faces and observer e r r o r but are independent of u . -1/2 Hence a mean range, F, was c a l c u l a t e d from the range at each value of u , f o r a g iven face and temperature, and was used to c a l c u l a t e a weight ing f a c t o r 1/A where A = 1/ (y - \ F) - l / (y + \ F) (42) The weighted s lopes and i n t e r c e p t s were c a l c u l a t e d (Carstensen, 1972) and used 1/2 to c a l c u l a t e K t a t each f l ow r a t e from (1/slope) u ' and K r from 1/ i n te r cep t . For each c r y s t a l face i t might be expected t ha t K t , and hence the s lopes f o r the (111) and (112) faces would be the same. However from Eqn. 24 the s lope equals 3 x 1 / / 2 D - 2 ^ 3 v 1 / 6 and a lthough D and v are con s tan t s , there i s a s l i g h t d i f f e r e n c e i n x and x ' f o r the (111) and (112) faces r e s p e c t i v e l y (Table I I I ) and t he r e f o r e i n the values of h (Table IV) . The va lues of h were c a l c u l a t e d f o r each f low r a te by s u b s t i t u t i n g the appropr i a te constants i n t o Eqn. 19 and are comparable to those reported by Fee et a l . (1976). S ince i s i n v e r s e l y p ropo r t i ona l to h, a t any g iven f l ow r a te Kt (111). < K t (112), as shown i n Table IV. The values of Kt i nc rease wi th i n c rea s i n g f l ow r a te as expected from Eqn. 22 f o r a t r an spo r t c o n t r o l l e d r e a c t i o n . Although a c o n t r i b u t o r y f a c t o r , - 98 -0 - 2 0 - 4 0 - 6 0 * 8 1 - 0 1 * 2 u " 1 / 2 C c m . s - 0 F i g . 18. P l o t of r e c i p r o c a l of K 0 bs aga in s t r e c i p r o c a l of square root of f l ow r a t e f o r the ( 1 1 1 ) » and (112) O faces of N i S 0 4 a 6H 20 at 3 7 ° . Weighted l e a s t squares f i t t i n g of the data i nc ludes the f i r s t 4 data po in t s a t the lower f l ow r a t e s , f o r each f a ce . - 99 -Table IV Apparent r a t e constants and f i l m th i cknes s f o r the d i s s o l u t i o n of N i S 0 4 a 6H 20 i n 60% v/v e thano l . Temperature (°C) C r y s t a l face u ( cm. s " l ) K obs V°6 ( c m . s " ' ) a K t x 10 6 -1 (cm.s" ) K r x 10 6 (cm.s - ^) h x 10 3 (cm) 37 (111) 0.75 1.73 2.07 10.6 9.73 1.70 2.28 3.11 8.52 6.49 2.73 2.74 3.95 8.97 5.11 3.66 3.16 K o b s ± 0 . 0 9 b 4.56 10.3 9.51° 4.42 37 (112) 1.70 2.90 3.50 16.7 5.96 2.73 3.41 4.44 14.6 4.70 3.66 3.70 5.14 . 13.3 4.06 4.68 4.34 w°- 2 2 b 5.81 17.2 15.3 C 3.59 41 ( H I ) 1.79 3.11 3.82 16.8 6.45 2.83 3.85 4.79 19.4 5.13 3.89 4.38 5.62 19.8 4.38 4.90 4.69 6.31 18.3 3.90 5.96 4.96 6.96 17.3 18.3 C 3.54 41 (112) 1.79 3.60 4.43 19.1 5.93 2.83 4.41 5.57 21.1 4.72 3.89 5.09 6.53 23.1 4.03 4.90 5.26 K o b s ± 0 - 3 7 b 7.33 18.6 20 .4 . C 3.58 a Mean of two observat ions b K 0 [ 3 S ± j F, see t e x t c K r obta ined from i n t e r c e p t va lue s . - 100 -the d i f f e r e n c e between K t f o r the (111) and (112) f a c e s , i s too small to cause the d i s s o l u t i o n an i so t ropy shown i n F i g . 13. From Eqn. 11, K o b s approaches when K r approaches i n f i n i t y . Hence, the i n t e r c e p t on the o rd i na te of F i g . 18 w i l l approach the o r i g i n i f d i s s o -l u t i o n i s under pure t r an spo r t c o n t r o l . The p o s i t i v e i n t e r c e p t s i n d i c a t e tha t the d i s s o l u t i o n process f o r both the (.111) and (112) faces i s under mixed c o n t r o l . Values of K r obta ined from the i n t e r c e p t are g iven i n Table IV together w i th va lues c a l c u l a t e d from Eqn. 23. The va lues are g rea te r but are of the same order of magnitude as K t which supports the suggest ion t ha t the o v e r a l l d i s s o l u t i o n r e a c t i o n i s under mixed con t r o l even a t the lowest f l ow ra te s s t ud i ed . Table IV shows that K r i s independent of f l ow r a t e as expected f o r a su r face c o n t r o l l e d r e a c t i o n and i s g rea te r f o r the (112) face than f o r the (111) face a t both 37° and 41° i n d i c a t i n g tha t the observed d i s s o l u -t i o n an i so t ropy i s due main ly to d i f f e r e n c e s i n the r a t e of the su r face r e a c t i o n . 6. A c t i v a t i o n energ ies f o r d i s s o l u t i o n A c t i v a t i o n energ ies f o r d i s s o l u t i o n of the (111) and (112) faces a t f l ow ra te s of 1.89 and 6.60 cm.s"^ obta ined from Ar rhen ius p l o t s , F i g . 19, are g iven i n Table V. At the lower f l ow r a t e , the a c t i v a t i o n energ ies f o r both faces are s i m i l a r but are s l i g h t l y h igher than the range u s u a l l y accepted f o r t r an spo r t c o n t r o l l e d processes i . e . 2.8-7.0 k c a l . m o l - ^ (11.7-29.3 k J . m o l " ^ ) . The r e s u l t s are a d d i t i o n a l support f o r the suggest ion tha t d i s s o l u t i o n i s under mixed c o n t r o l even a t low f l ow r a t e s . At the f l ow r a t e o f 6.60 c m . s ~ \ the a c t i v a t i o n energ ies are w i t h i n the accepted l i m i t s f o r a su r face c o n t r o l l e d r e a c t i o n (10-20 k c a l . m o l ) but d i f f e r f o r the (111) - 101 -F i g . 19. Ar rhen ius p l o t s f o r the (111) and (112) faces o f NiS04 a 6 H 2 O . Flow r a t e s : 1.89 cm.s-" 1, o ( l l l ) f a c e , • (112) f a c e ; 6.60 c m . s - l , • (111) f a c e , • (112) f a c e . L ines f i t t e d by l i n e a r reg re s s i on a n a l y s i s . - 102 -Table V A c t i v a t i o n energ ies of d i s s o l u t i o n f o r the (111) and (112) c r y s t a l faces o f N i S 0 4 a 6H 20 u E J k c a l . m o l ' 1 ) 3 d ( c m . s - 1 ) (111) face (112) face 1.89 8.7 (36.4) 7.6 (31.8) 6.60 13.4 (56.1) 10.9 (45.6) a F igures i n brackets are Ea va lues i n kJ.mol - 103 -and (112) f a ce s . I t i s l i k e l y that the observed d i s s o l u t i o n an i so t ropy i s due to the d i f f e r e n c e i n magnitude between Ea f o r the two f a ce s . A c t i v a t i o n energ ies f o r su r face and t r an spo r t c o n t r o l l e d d i s s o l u t i o n , c a l c u l a t e d from the separated r a te constants K r and K^ . (at a g iven f low r a te ) f o r the (111) and (112) faces are g iven i n Appendix I I . As the temperature i s increased there i s a reduct ion i n an i so t ropy at the h igher f low r a t e . This i s l e s s ev ident a t the lower f low r a te where d i s s o l u t i o n i s under mixed con t r o l and the c o n t r i b u t i o n of the su r face r e a c t i o n towards i s sma l l e r than i n the case of a p re -dominantly su r face c o n t r o l l e d process. The po in t a t which the curves a t the h igher f low r a te converge, corresponds to a temperature of 4 9 ° . Th is i s c l o se to the temperature of 52-53° a t which te t ragona l NiSO^ a 6 ^ 0 undergoes a t r a n s i t i o n to monoc l i n i c N i S 0 4 3 61^0 ( N i c h o l l s , 1973). The s i g n i f i c a n c e of t h i s observat ion i s unc lea r . Further d e t a i l s on the p repa ra t i on and p rope r t i e s of NiSO^ B 6H2O are g iven i n s e c t i o n C l . The d i f f e r e n c e i n the values of su r face f r e e energy of the (111) and (112) faces presumably r e s u l t s from d i f f e r e n c e s i n the arrangement and packing den s i t y ( r e t i c u l a r den s i t y ) together w i t h the va r y i ng energy s t a t e s o f the su r face atoms. Th is i s analogous to the s i t u a t i o n which e x i s t s between po l y -morphic forms of the same c r y s t a l l i n e m a t e r i a l . Nogami et a l . (1969a) used a r o t a t i n g d i s c technique to i n v e s t i g a t e the d i s s o l u t i o n k i n e t i c s of b a r b i t a l polymorphs and t r ea ted the data i n a manner s i m i l a r to tha t g iven here, except tha t Eqn. 11 was combined w i th an equat ion g iven by Lev ich (1962) f o r the r e l a t i o n s h i p between h and the angular v e l o c i t y of the r o t a t i n g d i s c (Eqn. 21) r a the r than w i th Eqn. 19. The type of double r e c i p r o c a l p l o t shown i n F i g . 18 was o r i g i n a l l y in t roduced by Wilson i n 1915 f o r i n t e r p r e t i n g o v e r a l l c o e f f i -c i e n t s of heat t r a n s f e r i n su r face condensers (McAdams, 1954). The p l o t was known as a Wilson p l o t . - 104 -7. A l t e r a t i o n s i n under sa tu ra t i on l e v e l s - Decreasing the under sa tu ra t ion l e v e l of the d i s s o l u t i o n medium r e s u l t s i n a decrease i n the d i s s o l u t i o n r a t e . F i g . 20 i s p l o t t e d accord ing to Eqn. 10 and the data f i t t e d by l i n e a r r eg re s s i on a n a l y s i s , g i v i n g a s lope va lue of 2.39 x 10"^ cm.s"^ ( c o r r e l a t i o n c o e f f i c i e n t 0.970) wi th a s m a l l , p o s i t i v e i n t e r c e p t on the d i s s o l u t i o n r a t e a x i s . The s lope of the l i n e g ives a va lue p ropo r t i ona l to k o b s . As p red i c ted by Eqn. 10 and where d i s s o l u t i o n i s t r an spo r t or mixed c o n t r o l l e d , the d i s s o l u t i o n r a te s are l i n e a r w i th the degree of under sa tu ra t i on ( M u l l i n and Ga r s i de , 1968). However, there i s a l a r g e e r r o r a s soc i a ted w i t h the measurements a t the three lowest va lues of unde r s a tu r a t i on , s i n ce the d i s tances moved by the c r y s t a l face were very s m a l l . I f these po in t s are ignored i n the l i n e a r r eg re s s i on a n a l y s i s , the -4 -1 l i n e passes through the o r i g i n w i t h a s lope value of 2.50 x 10 cm.s ( c o r r e l a t i o n c o e f f i c i e n t 0.999). B. HABIT MODIFICATION AND DISSOLUTION RATE 1. Choice of model The e f f e c t on o v e r a l l d i s s o l u t i o n of va r ious hab i t m o d i f i c a t i o n s which a r i s e as a r e s u l t of c r y s t a l a n i s o t r o p y , i s most r e a d i l y s tud ied us ing c r y s t a l s w i t h w e l l - d e f i n e d shapes. NiSO^ a 6H2O was chosen as a model c r y s t a l l i n e m a t e r i a l s i n ce b i p y r a m i d a l , p l a t y and a c i c u l a r hab i t s could be grown as l a r g e , we l l - fo rmed c r y s t a l s . The d i s s o l u t i o n an i so t ropy of the b ipyramidal h ab i t i s reported i n s e c t i o n A. The su r face area of the three hab i t s may be r e a d i l y measured and t h e i r d i s s o l u t i o n ra te s can be determined w i th no a l t e r a t i o n of su r face c h a r a c t e r -i s t i c s . - 105 -O 1 0 2 0 3 0 4 0 50 U N D E R S A T U R A T I O N C C S - C 3 (g hexahydrate/g solvenOxlO F i g . 20. D i s s o l u t i o n r a t e of the (111) face of NiS04 a 6H 20 as a f u n c t i o n of the under sa tu ra t i on of the d i s s o l u t i o n medium at 37° and f l ow r a te of 4.68 c m . s - ! . Regress ion l i n e i nc ludes a l l data p o i n t s . - 106 -2. C h a r a c t e r i z a t i o n o f hab i t s The b i p y r am ida l , p l a t y and a c i c u l a r c r y s t a l hab i t s are shown in F i g . 21a-c. The f o l l o w i n g methods of c h a r a c t e r i z a t i o n were used to show that the three hab i t s were of a s i m i l a r chemical and c r y s t a l l i n e nature. 2.1 X-ray d i f f r a c t i o n X-ray d i f f r a c t i o n powder pat terns f o r the b i p y r a m i d a l , p l a t y and a c i c u l a r hab i t s were i d e n t i c a l w i th each other and w i th ACS n i c k e l s u l f a t e hexahydrate; a l l d values were c h a r a c t e r i s t i c of N1S04 a 6 H 2 O ( Se lec ted Powder D i f f r a c t i o n da ta , 1974) w i th the except ion of one l i n e which cou ld not be i d e n t i f i e d , (see Table V I ) . Success ive powder pat terns of the heptahydrate showed r ap i d dehydrat ion w i th d values corresponding to the i n i t i a l format ion of the 3 6 H 2 O polymorphic form (Se lected Powder D i f f r a c t i o n da ta , 1974) and t r a n s i t i o n to a 6 H 2 O w i t h i n approx imately 1 hr. X-ray d i f f r a c t i o n data f o r the heptahydrate a f t e r being ground and held a t room temperature f o r approx imately 45 min are shown in Table V I I . A mixture of the heptahydrate and two forms of the hexahydrate, a 6 H 2 O and 6 6 H 2 O were observed. Th is mixture i s converted e n t i r e l y to the a 6 H 2 O w i t h i n 60 min (see Table V I ) . The a c i c u l a r hab i t used i n t h i s work t he re fo re forms spontaneously a t room temperature from the t o p o t a c t i c r e a c t i o n : NiS0 4 . 7H 2 0 : > 3 6H 20 < »a6H20 t r a n s l u c e n t , opaque, g reen i sh -wh i te emerald green In topotaxy (a t o p o t a c t i c r e a c t i o n ) , a s i n g l e c r y s t a l of a s t a r t i n g mate r i a l i s converted i n t o a pseudomorph con ta i n i n g one or more products i n a d e f i n i t e c r y s t a l l o g r a p h i c o r i e n t a t i o n . A pseudomorph i s a c r y s t a l which has become converted i n t o another substance or mixture of substances, w i thout change i n - 107 -F igure 21: Habit m o d i f i c a t i o n o f NiS04 a 6H 2 0. a) B ipyramidal hab i t b) P l a t y hab i t c) A c i c u l a r hab i t x A f t e r d i s s o l u t i o n . - 108 -1mm F i g . 21a. i - 109 -1mm 21b. - n o -F i g . 21c. - m -Table VI X-ray data f o r N i S 0 4 a 6H' 20; b i p y r am ida l , p l a t y and a c i c u l a r hab i t s Sample data Standard d a t a a 0 .Re la t i ve R e l a t i v e d(A) I n t e n s i t y d(A)- I n t e n s i t y ^ 4.55 vs 4.57 s 4.24 vs 4.25 vs - 3.78 w 3.74 w 3.76 w 3.37 w 3.39 m 3.31 w 3.33 w 3.15 w 3.17 w 3.01 w 3.03 w 2.935 m 2.964 m 2.878 w 2.908 w 2.85 w 2.88 w 2.748 w 2.778 w 2.694 m 2.721 m 2.539 m 2.571 m 2.492 w 2.526 w 2.295 w 2.334 m 2.254 w -X-ray powder d i f f r a c t i o n data f i l e : card #8-470 k Abb rev i a t i on s : w, weak; m, medium; s, s t r ong ; v s , very st rong - 112 -Table VII X-ray data f o r N i S0 4 . 7H 2 0 r e c r y s t a l l i z e d and s to red a t 4 ° . Samples ground and held a t room temperature f o r about 45 min. Sample data Standard d a t a 9 o R e l a t i v e o R e l a t i v e Corresponding d(A) I n t e n s i t y d(A) I n t e n s i t y . TUT III 5.81 w 5.8 m e 6H 20 5.36 m 5.41 s 3 6H 20 5.26 s 5.3 s 7H 20 5.05 w 5.08 s 3 6H 20 4.87 m 4.89 s 3 6H 20 4.48 - - - -4.55 w 4.57 s a 6H 20 4.44 m 4.45 m 7H 20 4.35 s 4.35 vs 3 6H 20 4.19 vs 4.2 vs 7H 20 3.98 s 3.98 vs 3 6H 20 3.78 w 3.78 w a 6H 20 3.71 w 3.75 m 7H 20 3.42 s 3.45 m 7H 20 3.35 m 3.39 m a 6H 20 2.95 w 2.98 m 3 6H 20 2.93 w 2.96 w 7H 20 2.883 w 2.908 w a 6H 20 2.85 m 2.89/2.88 vs/w 3 /a6H 20 2.81 w 2.85 m 7H 20 2.71 s 2.75 w 7H 20 2.60 w 2.65 m 7H 20 2.45 w 2.49 w 7H 20 2.19 w 2.24 w 7H 20 3 X-ray powder d i f f r a c t i o n data f i l e : card #8-470 (N i S 0 4 a 6H 20); 18-891 (N i S0 4 3 6H 2 0 ) ; 1-403-(NiS0 4 .7H 2 0) - 113 -i t s ex te rna l form (G las ser e t a l . , 1 962 ) . In t o p o t a c t i c dehydra t ions , the pseudomorph sometimes has c r y s t a l l i n i t y comparable w i th t ha t of the s t a r t i n g mate r i a l or there may be a marked decrease i n the c r y s t a l l i n i t y . However, comparison of the X-ray peak heights and widths of the a c i c u l a r hab i t w i th those of the other two hab i t s revea led no d i f f e r e n c e s i n c r y s t a l l i n i t y . The dehydrat ion of the heptahydrate at d i f f e r e n t r e l a t i v e humid i t i e s i s shown in F i g . 22. On exposing the c r y s t a l s to a dry atmosphere there was a r ap i d decrease i n weight from 0-20 hours a f t e r which the weight remained r e l a t i v e l y constant . The weight l o s s corresponded to the lo s s of 1 mol of water. Del iquescence occurred a t RH 95. 2.2 X-ray energy a n a l y s i s X-ray energy spec t ra were obta ined f o r the three c r y s t a l hab i t s to check f o r p u r i t y of the c r y s t a l s ( F i g . 23). In a d d i t i o n to the energy peaks c h a r a c t e r i s t i c f o r n i c k e l s u l f a t e , the b ipyramida l c r y s t a l s conta ined a very small amount of potassium and a t r a ce amount of bromine. The p l a t y c r y s t a l s conta ined on ly a t r a ce of potassium and the a c i c u l a r c r y s t a l s showed no a d d i t i o n a l peaks. 2.3 Thermal a n a l y s i s Thermal a na l y s i s r e s u l t s are g iven i n Table V I I I . Each temperature i s the mean value of the peak maximum obta ined from severa l scans. S ince the de so l v a t i on of s o l va te s i s h i gh l y dependent on the exper imental c o n d i t i o n s , the sequence of peaks i s of more s i g n i f i c a n c e than the ac tua l temperature. The t o t a l water l o s s obta ined on heat ing each sample to about 500° conf irmed tha t each hab i t was the hexahydrate. Columns 1 and 2 show peaks w i thout an accompanying water l o s s and are i n t e r p r e t e d to be i n t e r n a l t r a n s i t i o n s . The peaks i n columns 3 and 4 i nc lude dehydrat ion and s imultaneous v a p o r i z a t i o n s i nce the peaks occurred both us ing c l o sed pans, which prevent water l o s s , - 114 -22. Dehydration and mo i s ture uptake of NiS04-7H20 c r y s t a l s a t 22° : o , RH 95%; A , R H 79%; RH 66%; • , RH 52%; • , dry atmosphere. - 115 -23. X-ray energy a n a l y s i s of NiS04 a 6H2O c r y s t a l s a) b ipyramidal b) p l a t y and c) a c i c u l a r h a b i t s . - 116 -Table VI I I Thermal a n a l y s i s and X-ray d i f f r a c t i o n of hab i t s of N i S 0 4 a 6H 20 and N i S0 4 . 7H 2 0 Endothermic Peak Maxima °C (moles H 20 vapor i zed per mole N i S 0 4 ) ' X- ray A.C.S.: C 90 3 119 P 96° 103 112(2) a6H 20 173(5) > 400(6) B ipyramid: C 97 P l a t y : A c i c u l a r : P 98 l P 96 l P 96 N i S0 4 . 7H 2 0 : P 97 l 103 106 108 107 110 107 174(5) >420(6) 118 118(2) -118 C 128 118 C 128(2) 159(5) > 450(6) 126 120 C 128(2) 162(5) > 400(6) a6H 20 a6H 20 a6H 20 122 c 131 160 > 450 7H20+86H2O+a6H20 C c l o sed pan P c lo sed pan w i th p inho le a va lues i n parentheses are to the nearest s t o i c h i o m e t r i c r a t i o small peak shoulder - 117 -and us ing pans w i th a p i n - h o l e . Peaks 5 and 6 are a l s o the r e s u l t of s i m u l -taneous dehydrat ion and v a p o r i z a t i o n but i t was not po s s i b l e to demonstrate the dehydrat ion i n a c l o sed pan s i nce the pressure exer ted by v a p o r i z i n g water d i s t o r t e d or even exploded the pan. The thermal behaviour of the c r y s t a l samples i n Table VI I I f a l l s i n t o two groups; the scans of the bipyramids are i d e n t i c a l w i th the o r i g i n a l ACS mate r i a l but d i f f e r s i g n i f i c a n t l y from the p l a t y and a c i c u l a r h a b i t s . In pans w i th a p i nho l e , a l l c r y s t a l s show t r a n s i t i o n peaks 1 and 2 wi th peak 2 as the major peak. In c lo sed pans, peak 1 becomes the major t r a n s i t i o n f o r the bipyramids and ACS c r y s t a l s w i th peak 2 m i s s i n g , whereas w i th the p l a t y and a c i c u l a r hab i t s the s i t u a t i o n i s reversed and the on ly t r a n s i t i o n corresponds to peak 2. Further d i f f e r e n c e s between the two groups o f c r y s t a l s are apparent on comparing peaks 3 and 4. The ACS and b ipyramida l c r y s t a l s undergo dehydrat ion between 113-119° (peak 3) w i th the s imultaneous v a p o r i z a t i o n o f 2H 20. The p l a t y and a c i c u l a r hab i t s undergo these r eac t i on s between 126-128° (peak 4) w i th on l y a shoulder a t about 118° to i n d i c a t e some dehydrat ion a t t h i s temperature. Dehydration r eac t i on s can be a f f e c t e d by changes i n the r a t i o between the su r face and volume of the c r y s t a l s i . e . m o d i f i c a t i o n of c r y s t a l hab i t (Bo ldyrev, 1975b). Boldyrev (1975a, c) found tha t f i v e " d i f f e r e n t c r y s t a l hab i t s of MgSO^h^O dehydrated at d i f f e r e n t ra tes and showed tha t the r a t e -c o n t r o l l i n g step i n the dehydrat ion of ZnSO^.f^O depends on the ex te rna l c o n d i t i o n s . When c a r r i e d out i n vacuum or at low p a r t i a l pressures of water vapor, the r e a c t i o n i s c o n t r o l l e d by the gaseous r e a c t i o n product i . e . by the water vapor p res sure , but when the vapor pressure i s i n c rea sed , c a t a l y s i s by the s o l i d product of the dehydrat ion r e a c t i o n becomes predominant. - 118 -Isothermal lo s ses of water vapor a t var ious temperatures below the t r a n s i t i o n temperature i n pans w i th a p i n h o l e , showed t ha t the b ipyramida l c r y s t a l s l o s t water more r a p i d l y than the p l a t y or a c i c u l a r h a b i t s . Hence i t seems l i k e l y t h a t the d i f f e r e n c e s i n the dehydrat ion r e a c t i o n , peaks 3 and 4, are due to the e f f e c t of a d i f f e r e n c e i n vapor pressure between the var ious h a b i t s . D i f f e rences i n vapor pressure may a l s o e x p l a i n the d i f f e r e n c e s i n the i n t e r n a l t r a n s i t i o n s , peaks 1 and 2 f o r the var ious hab i t s when compared i n c lo sed pans and pans wi th a p i nho le . Although the 6 H 2 0 — » 4H 20 dehydrat ion (peaks 3 or 4) occurs a t temperatures g rea te r than the t r a n s i t i o n temperatures, the hexahydrate w i l l l o se water at any temperature prov ided the vapor pressure of water surrounding the s o l i d i s l e s s than the e q u i l i b r i u m vapor pressure a t that temperature. Thus on heat ing a pan wi th a p i n h o l e , vapor l o s s w i l l occur a lthough the r a t e w i l l become app rec i ab le on ly when the vapor pressure w i t h i n the pan i s equal to the atmospheric pressure. On the other hand, water vapor cannot escape from a c lo sed pan and the vapor pressure inc reases w i th inc rease i n temperature. I t i s suggested tha t the lower t r a n s i t i o n temperature f o r the b ipyramida l and ACS c r y s t a l s i n a c lo sed pan i s r e l a t e d to the h igher vapor pressure of these h a b i t s . This obse rva t ion i s supported by the f a c t that when the e f f e c t of vapor pressure i s reduced by us ing a pan w i th a p i nho l e , both t r a n s i t i o n peaks 1 and 2 appear i n the thermograms of a l l hab i t s w i th peak 2 becoming the major peak i n each case. Chihara and Seki (1963) found s i m i l a r t r a n s i t i o n s above and below 100° us ing DTA and pos tu la ted the ex i s tence of two phases 6y and 6y' a lthough they noted that these may be the same. Rabbering e t a l . (1975) found no i n d i c a t i o n of the ex i s tence of a y phase or phases. Our r e s u l t s support Chihara and Seki but show tha t the t r a n s i t i o n s occur below 100°, above 100° or both , depending on - 119 -whether the system i s c l o sed or open and on the c r y s t a l h ab i t . Hence i t i s necessary to po s tu l a te the ex i s tence of on ly 6y. phase. The t r a n s i t i o n and dehydrat ion r eac t i on s f o r the two groups of c r y s t a l s are summarized below: N i S0 4 . 6H 9 0 : A.C.S. and B ipyramidal N i S0 4 . 6H 2 0 ( s , a )—>N i S0 4 . 6H 2 0 ( s ,Y ) Peak 1 Peak 2 a Peak 3 Peak 3 3 Peak 5 b Peak 6 b NiS0, .6H 9 0: P l a t y and A c i c u l a r Peak l a Peak 2 Shoulder 3 Peak 4 Peak 4 a NiS0 4 . 4H 2 0 ^ N i S 0 4 .H 2 0 + 3H 2 0(g) Peak 5 b N i S 0 4 .H 2 0 ( s ) V N i S 0 4 + H 2 0(g) Peak 6 b a Only when us ing pans w i th a p inho le b D i s t o r t i o n of the c lo sed pan u s u a l l y prevents measurement of dehydrat ion temperature. - 120 -The DSC scan f o r the heptahydrate corresponds to t ha t o f the p l a t y and a c i c u l a r h a b i t s . Both DSC and X-ray r equ i r e the sample to be ground before a n a l y s i s . A r a p i d weight l o s s a f t e r g r i nd i ng and the subsequent DSC scan and X-ray d i f f r a c t i o n pa t te rn i n d i c a t e tha t the heptahydrate dehydrates very r a p i d l y and tha t the thermogram i s a c t u a l l y that of N i S 0 4 a 6H 2 0. 2.4 S o l u b i l i t y F i g . 24 i s p l o t t e d accord ing to the i n t eg r a ted form of the Van ' t Hoff equat ion (Eqn. 43) f o r N i S 0 4 a 6H 20 i n 50%, 60% and 70% v/v e thano l . AH S A S log C s - - Z 3 Q 3 R T + 2 > 3 0 3 R (43) where AS i s the entropy change and AH $ i s the heat of s o l u t i o n , assumed to be a constant over the temperature range used. The heats of s o l u t i o n were found to be +8.7, +6.3, +5.3 k c a l . m o l " 1 f o r 50%, 60% and 70% ethanol r e s p e c t i v e l y . Values of C s f o r the three hab i t s a t three d i f f e r e n t temperatures are g iven i n Table IX,and are i d e n t i c a l . 3. D i s s o l u t i o n of hab i t s The o v e r a l l bulk d i s s o l u t i o n r a te of the three hab i t s may be descr ibed by r a te = S . K ^ (C s - C) (44) where S i s the t o t a l su r face area of the c r y s t a l s , C $ i s the e q u i l i b r i u m s o l u b i l i t y i n the d i f f u s i o n l a y e r a t the s o l i d - l i q u i d i n t e r f a c e , C i s the concent ra t i on i n the bulk s o l u t i o n a t time t and K 1 q ^ s i s an observed r a t e constant . When C s » C and S i s cons tant , the o v e r a l l d i s s o l u t i o n r a te i s F i g . 24. V a n ' t Hoff p l o t of s o l u b i l i t y data f o r M S O 4 o 6 H 2 O i n d i f f e r i n g ethanol d i l u t i o n s : A , 50% v/v; • , 60% v/v; • , 70% v/v. L ines f i t t e d by l i n e a r r eg re s s i on a n a l y s i s . - 122 -Table IX S o l u b i l i t i e s and sur face areas of hab i t s of N i S 0 4 a 6H 20 Hab i t C s (mg.cm"3) S (cm 2) 9.9° 22° 30° B ipyramidal 1.64 2.56 3.26 2.4 ( 1 5 ) a P l a t y 1.64 2.56 3.22 2.2-2.8 ( 9 - 1 3 ) a A c i c u l a r 1.64 2.56 3.26 1.6-2.5 ( 3 - 7 ) a Number of c r y s t a l s f o r each experiment - 123 -p ropo r t i ona l to K ' o b s . F i g . 25 shows t y p i c a l p l o t s of concen t ra t i on change w i th time f o r the b ipyramida l c r y s t a l s a t d i f f e r e n t r o t a t i o n v e l o c i t i e s . 3 -1 The s lopes (mg.cm . s ) were determined us ing l i n e a r reg re s s i on a n a l y s i s and were used to c a l c u l a t e K . ( c m . s - 1 ) from the r e l a t i o n s h i p : . , where V i s the volume o f d i s s o l u t i o n medium. Values of S are g iven i n Table IX. Due to the very narrow s i z e range of the b ipyramidal c r y s t a l s , the t o t a l su r face area was the same f o r each de te rm ina t i on . However, the p l a t y and a c i c u l a r hab i t s possessed g reate r s i z e d i f f e r e n c e s and the t o t a l sur face area f o r d i f f e r e n t d i s s o l u t i o n experiments v a r i e d between the ranges g iven i n Table IX. Sample c a l c u l a t i o n s of su r face areas are g iven i n Appendix I. i F i g . 26 shows a p l o t of K ^ as a f u n c t i o n o f r o t a t i o n r a te f o r the b ipyramida l h ab i t . ^ 'obs ^ o r t b e P ^ a t ^ a n c ' a c 1 C L | l a r hab i t s are g iven at 150 rpm and 700 rpm. R e p r o d u c i b i l i t y f o r the b ipyramidal and p l a t y c r y s t a l s was good as i n d i c a t e d by the range of . The a c i c u l a r c r y s t a l s were l e s s we l l formed than the other hab i t s making the su r face area d e t e r -minat ion l e s s r e l i a b l e and the r e p r o d u c i b i l i t y was not as good at the lower r o t a t i o n r a t e . The observed r a t e constants f o r the b ipyramidal and p l a t y c r y s t a l hab i t s are s i g n i f i c a n t l y d i f f e r e n t . The d i f f e r e n c e inc reases w i th r o t a t i o n ra te as expected f o r a mixed t r a n s p o r t - s u r f a c e r e a c t i o n c o n t r o l l e d d i s s o l u -t i o n r e a c t i o n . I t i s we l l documented tha t the d i f f e r e n t faces of an a n i s o t r o p i c c r y s t a l have d i f f e r e n t values of the su r face f r ee energy. D i f f e r e n t hab i t s - 124 -F i g . 25. P l o t of the change i n bulk concen t r a t i on as a f u n c t i o n of t ime f o r the b ipyramida l NiS04 a 6H2O c r y s t a l s a t 2 2° . Ro ta t i on r a t e s : • , 150 rpm; • , 450 rpm; • , 650 rpm. - 125 -40f-ROTATION RATE (rpm) F i g . 26. P l o t of K ' 0 b S as a f u n c t i o n of the r o t a t i o n r a t e f o r the three hab i t s of NiS04 a 6H2O. Temperatures: 9 . 9 ° , b ipyramida l • , p l a t y A ; 2 2 ° , b ipyramida l • , p l a t y A ; 3 0 ° , b ipyramida l D , p l a t y A , a c i c u l a r Q . Each po i n t represents the mean o f 3 de te rm ina t i on s . Bars i n d i c a t e the range of K ' 0 b s « - 126 -w i l l vary i n the r e l a t i v e p ropor t i on of the var ious f ace s . The re fo re , i t seems l i k e l y t ha t the accompanying change i n o v e r a l l su r face energy i s r e spons i b l e f o r the d i f f e r e n c e s i n K * ^ . I t i s po s tu l a ted that the su r face energy of the p l a t y c r y s t a l s was lower than that of the b ipyramidal c r y s t a l s , although determinat ion of the su r face energ ies would be necessary to con f i rm t h i s . F i g . 26 shows t ha t K Q b s f o r the a c i c u l a r hab i t was of equal magni-tude to the b ipyramida l hab i t but g rea te r than f o r the p l a t y h a b i t . S ince the a c i c u l a r hab i t was formed so r e a d i l y by dehydrat ion of NiSO^^HgO, i t might be expected tha t rehydra t i on would occur dur ing d i s s o l u t i o n . However, there was no change i n the s lope of the concen t ra t i on vs time curves f o r e i t h e r bulk or i n t r i n s i c d i s s o l u t i o n (see below) as would be expected i f r ehydra t i on took p lace (Nogami e t a l . , 1969b). In a d d i t i o n , the s o l u b i l i t y of the a c i c u l a r c r y s t a l s i n 60% v/v ethanol was i d e n t i c a l to t ha t o f the o ther two hab i t s ( T a b l e i l X ) i n d i c a t i n g t h a t , over a per iod of 60 hours, there was no r eve r s i on to NiS0 4 .7H20. Although by d e f i n i t i o n , the a c i c u l a r c r y s t a l s are a t rue hab i t m o d i f i c a t i o n , t h e i r method o f p repa ra t i on d i f f e r e d markedly from the conven-t i o n a l technique of a l t e r i n g the environment o f the growing c r y s t a l , used i n the p repara t ion of the other two h a b i t s . The mechanism of the t o p o t a c t i c r e a c t i o n might be expected to a f f e c t the c h a r a c t e r i s t i c s of the c r y s t a l su r face (Bo ldyrev, 1975c). I t i s of i n t e r e s t t he re f o re that the b ipyramida l and a c i c u l a r hab i t s have s i m i l a r va lues f o r K* b but d i f f e r i n t h e i r thermo-grams, wh i l e the thermograms of the a c i c u l a r and p l a t y hab i t s are s i m i l a r but not t h e i r va lues of K o b s . X-ray powder d i f f r a c t i o n and DSC are amongst the techniques most w ide l y used to c h a r a c t e r i z e s o l i d s p r i o r to d i s s o l u t i o n s t ud i e s . S ince a l l three hab i t s have i d e n t i c a l X-ray powder d i f f r a c t i o n pat te rns i t i s apparent tha t - 127 -ne i t he r powder d i f f r a c t i o n pat terns nor DSC thermograms can be c o r r e l a t e d i n a s imple way w i th bulk d i s s o l u t i o n r a t e s . I t was necessary to show tha t the observed d i f f e r e n c e s i n K ' o b s f o r the b i p y r a m i d a l , p l a t y and a c i c u l a r c r y s t a l s were due to the e f f e c t of hab i t m o d i f i c a t i o n and not to d i f f e r e n c e s i n i n t r i n s i c d i s s o l u t i o n r a t e s , r e s u l t i n g , f o r example, from c r y s t a l po i son ing by i m p u r i t i e s . F i g . 27 shows a t y p i c a l p l o t of bulk concen t ra t i on versus time f o r r o t a t i n g d i s c s of the b ipyramidal and p l a t y h a b i t s . I n t r i n s i c d i s s o l u t i o n ra te s -3 -1 (mg.cm .s ) were c a l c u l a t e d from the s lopes of these p l o t s . The r e s u l t s i n Table X show that there i s no s i g n i f i c a n t d i f f e r e n c e i n the i n t r i n s i c d i s s o l u t i o n ra tes f o r each hab i t and that the t r a ce i m p u r i t i e s detected by X-ray energy ana l y s i s d id not a f f e c t the i n t r i n s i c d i s s o l u t i o n r a t e s . Furthermore the lower va lue f o r the p l a t y c r y s t a l s was u n l i k e l y to be due to c r y s t a l po i son ing s i n ce X-ray energy a n a l y s i s showed t h a t t h i s hab i t conta ined fewer t r a ce i m p u r i t i e s than the b ipyramidal c r y s t a l s . An experiment was a l s o c a r r i e d out i n which 2 ug .mL - 1 g e l a t i n was added to the d i s s o l u t i o n medium and the d i s s o l u t i o n r a t e of the b ipyramidal c r y s t a l s determined. K Q b s was the same i n the presence or absence of the added g e l a t i n , thus showing that t r a ce amounts o f g e l a t i n (such as might be present i n the p l a t y c r y s t a l s ) added to the d i s s o l u t i o n medium do not r e s u l t i n i n h i b i t i o n of d i s s o l u t i o n . These experiments support the conc lu s i on t ha t the marked d i f f e r e n c e s between K Q b s f o r the b ipyramida l and a c i c u l a r hab i t s and K ' o b s f o r the p l a t y hab i t were due to hab i t m o d i f i c a t i o n and not to d i f f e r e n c e s i n i n t r i n s i c d i s s o l u t i o n r a t e . I n t r i n s i c d i s s o l u t i o n ra te s f o r the b ipyramida l c r y s t a l s a t d i f f e r e n t r o t a t i o n speeds were used to c a l c u l a t e i n t r i n s i c d i s s o l u t i o n r a t e con s tan t s , K i n t ( c m . s - 1 ) from Eqn. 45 (where K-j nt rep laces K ' o b s ) . For t r an spo r t - 128 -F i g . 27. P l o t of the change i n bulk concen t r a t i on as a f u n c t i o n of t ime f o r r o t a t i n g d i s c s of NiS04 a 6H2O (at 300 rpm) c lo sed symbols 3 0 ° , open symbols 4 5 ° : • , b i p y r a m i d a l ; p l a t y h a b i t s . L ines f i t t e d by l i n e a r r eg re s s i on a n a l y s i s of the data f o r the b ipyramida l h a b i t . - 129 -Table X I n t r i n s i c d i s s o l u t i o n ra te s of hab i t s of NiSO^ a 6H 20 Temp. (°C) Habi t I n t r i n s i c d i s s o l u t i o n r a t e x 10 5 (mg.cnf 3 s - 1 ) 30° B ipyramidal 1.06 P l a t y 1.08 A c i c u l a r 1.05 45° B ipyramida l 2.77 P l a t y 2.58 A c i c u l a r 2.62 - 130 - i c o n t r o l l e d d i s s o l u t i o n , K i n t = D/h which can be s u b s t i t u t e d i n t o Eqn. 21 11? and K - j n t p l o t t e d aga in s t w ' as shown i n F i g . 28. A change i n s lope i n 1II the K n- n t versus w curve i s observed i n d i c a t i n g a change i n con t r o l of the d i s s o l u t i o n r e a c t i o n . Th is i s s i m i l a r to F i g . 15 d i scussed i n s e c t i o n A.3.3. 4. A c t i v a t i o n energ ies f o r d i s s o l u t i o n A c t i v a t i o n energ ies f o r d i s s o l u t i o n of the b ipyramidal and p l a t y c r y s t a l s a t r o t a t i o n speeds of 150 and 700 rpm obta ined from Arrhen ius p l o t s are g iven i n Table XI. Values of K ' Q b s f o r the bipyramidal c r y s t a l s a t 700 rpm were determined by i n t e r p o l a t i o n . At the lower r o t a t i o n speed the a c t i v a t i o n energ ies f o r the two hab i t s are s i m i l a r and are w i t h i n the range u s u a l l y accepted f o r t r a n s p o r t - c o n t r o l l e d processes i . e . 2.8-7.0 k c a l . m o l - 1 (11.7-29.3 k J . m o l - 1 ) . At the r o t a t i o n speed of 700 rpm the a c t i v a t i o n ene rg i e s , a lthough showing a small i n c r ea se , are 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 values a t 150 rpm. There i s evidence t ha t the p r e d i c t i o n of the r a te c o n t r o l l i n g step of a r e a c t i o n from a knowledge of i t s a c t i v a t i o n energy may be u n r e l i a b l e . Some reac t i on s w i th a low a c t i v a t i o n energy (4-7 k c a l . m o l - 1 ) are not t r an spo r t c o n t r o l l e d as expected, but sur face c o n t r o l l e d . Th i s has been demonstrated f o r both c r y s t a l growth (Tadros and Mayes, 1979) and d i s s o l u t i o n (James, 1943). The inc rease i n the d i f f e r e n c e i n K ' o b s f o r the b ipyramida l and p l a t y c r y s t a l s w i th r o t a t i o n speed i s c h a r a c t e r i s t i c of a mixed t r a n s p o r t - s u r f a c e c o n t r o l l e d d i s s o l u t i o n . Th is observat ion i s i n agreement w i th the p r e d i c t i o n s made i n Scheme 2. - 131 -F i g . 28. Dependence of K-jnt on r o t a t i o n speed at 3 0 ° , f o r r o t a t i n g d i s c s of the b ipyramidal NiSC>4 a 6H 20 c r y s t a l s . Bars i n d i c a t e the range of K-jnt» the po in t rep re sent ing the mean of 3 de te rmina t i on s . A l l other po in t s are s i n g l e de te rm ina t i on s . - 132 -Table XI A c t i v a t i o n energ ies of d i s s o l u t i o n f o r the b ipyramidal and p l a t y hab i t s of NiSO* a 6H 90 Rotat ion r a t e Ea(kcal .mol -l}a (rpm) B ipyramida l P l a t y Habi t Habit 150 6.2(5.2-6.7) 6.1(6.0-6.3) 700 6.4 6.6(6.5-6.8) Values i n parentheses are the range of Ea. - 133 -C. POLYMORPHISM AND THERMOCHEMISTRY OF N i S C y 6 H 2 0 1. Polymorphism The p r ope r t i e s of the a polymorph of N i S0 4 - 6H 2 0 and i t s var ious hab i t m o d i f i c a t i o n s have been d i scussed i n s e c t i o n B.2. In a d d i t i o n to the forma-t i o n of NiS04 3 6H 20 on dehydrat ion of the heptahydrate, the 3 form r e c r y s t a l l i z e s from aqueous s o l u t i o n above 53° ( N i c h o l l s , 1973). C r y s t a l s formed i n t h i s work a t 58° were an emerald green co l ou r c h a r a c t e r i s t i c of the 3 form but the X-ray d i f f r a c t i o n pa t te rn taken immediately a f t e r c r y s t a l l i -z a t i o n was c h a r a c t e r i s t i c of the a form w i t h on ly a t r a ce of 3 c r y s t a l s . The DSC scan, Table XII.;- however was d i f f e r e n t from any of the a forms i n Table VI I I and showed a 6 H 2 O — ) 1 H 2 0 dehydrat ion a t 129°. On storage i n an oven at 58° f o r two days the DSC scan changed to g ive a thermogram t y p i c a l of the a form but the X-ray pa t te rn became main ly that of the 3 form w i th some a form present. A f t e r f i v e days a t 5 8 ° , t r a n s i t i o n peaks 1 and 2 disappeared wh i l e the X-ray pa t te rn remained main ly tha t of the 3 form,. (Table X I I I ) . I t i s apparent tha t a lthough the mate r i a l c r y s t a l l i z i n g above 53° has the appearance of the 3 form, severa l days storage above the t r a n s i t i o n temperature are requ i red before the c r y s t a l s became t h i s form as c h a r a c t e r i z e d by X-ray and DSC. Un l i ke the a form, the 3 c r y s t a l s do not undergo i n t e r n a l t r a n s i t i o n p r i o r to dehydra t ion . The dehydrat ion r eac t i on s a re : N i S 0 4 . 6 H 2 0 ( s , 3 ) » N i S 0 4 . 4 H 2 0 ( s ) + 2H 20(g) peak 3 N i S0 4 . 4H 2 0 ( s ) >N i S0 4 .H 2 0 ( s ) + H 2 0(g) peak 5 On the removal from the oven, the c r y s t a l s turned b lue-green w i t h i n a day, the X-ray pa t te rn rever ted to main ly a and a t r a n s i t i o n endotherm reappeared i n the thermogram at 9 8 ° . - 134 -Table XII Changes i n thermograms and X-ray d i f f r a c t i o n of emerald green c r y s t a l s of n i c k e l s u l f a t e on storage at 58° Days Endothermic Peak Maxima, °C (moles vapor i zed per mole NiSC^) ' 2 X-ray 3 4 5 6 117 C 129(5) - > 400(6) main ly a; some 6. 119 168 116(2) - 171(5) > 400(6) 116 168 main ly 3; some a. 117(2) - 171(5) 114(2) - 171(5) 113 174 ... main ly 3; some a. 110(2) - 170(5) 0 2 5 8 C P C P P C 98 L 94 L 86 100 100 > 90 L C c lo sed pan P c l o sed pan w i th p inho le a values i n parentheses are to the nearest s t o i c h i o m e t r i c r a t i o b small peak 0 shoulder - 135 -Table XII I X-ray data f o r N i S0 4 . 6H 2 0 r e c r y s t a l l i z e d and s to red 5 days a t 58° Sampl d(A) e data R e l a t i v e I n t e n s i t y Standi d(A) i r d data R e l a t i v e I n t e n s i t y Corresponding form 5.81 m 5.8 m 3 6H20 5.42 m 5.41 s 3 6H20 5.05 m 5.08 s 3 6H 20 4.88 vs 4.89 s 3 6H 20 4.78 s - - -4.55 s 4.57 s a 6H 20 4.35 vs 4.35 vs 3 6H20 4.29 w - - -'4.23 s 4.25 vs a 6H 20 4.07 m 4.12 w 3 6H 20 3.98 vs 3.98 vs 3 6H20 3.85 w 3.89 vs 3 6H 20 3.75 w 3.78 w a.6H 20 3.59 w - - -3.52 m 3.57 s 3 6H 20 3.40 w 3.44 m 3 6H 20 3.37 w 3.39 m a 6H20 3.32 w 3.36 w 3; 6H 20 3.13 w 3.16 m 3 6H20 2.935 m 2.964 m a-. 6H 20 2.89 w 2.908 w a 6H20 2.86 s 2.89 vs 3 6H 20 2.78 w 2.83 w 3''.6H20 2.75 w 2.778 w a!'.6H20 2.69 m . 2.721 m a 6H 20 2.62 w 2.67 s 3 6H 20 2.54 w 2.57 m 3 6H 20 2.492 w 2.526 w a:.6H20 2.298 w 2.334 m a' 6H 20 2.22 m 2.27 vs 3. 6H 20 a X-ray powder d i f f r a c t i o n data f i l e : card #8-470 (N i S 0 4 a 6H ? 0 ) ; 18-891 (N i S0 4 3 6H 2 0 ) ; 1-403 (N iS0 4 .7H 2 0) - 136 -I f , a f t e r r e c r y s t a l l i z a t i o n and d ry ing a t 58° , the r e s u l t i n g emerald green c r y s t a l s were removed from the oven and s to red at room temperature, then the c r y s t a l s turned blue-green w i t h i n 5 hours. Accord ing to X-ray a n a l y s i s , the c r y s t a l s were mainly the a:'form w i th some 3 form present i n i t i a l l y but about 28 days storage at room temperature was necessary before the thermogram became c h a r a c t e r i s t i c of the a form, (Table XIV). For up to about 12 days the major dehyd ra t i on - vapo r i z a t i on r e a c t i o n was 6 s — » l s but w i th i n c r ea s i n g evidence of the 6 s— * 4 s—> l s pathway. DSC wi th e f f l u e n t gas a na l y s i s and weighing the sample pans a f t e r each endotherm were i n d i s p e n s i b l e techniques i n d i s t i n g u i s h i n g t h i s 6H 20 — ^ l l ^ O dehydrat ion from the 6 H 2 0 - * 4 H 2 0 dehydrat ion of the p l a t y and a c i c u l a r c r y s t a l s s i nce i n each case the endotherms occurred between 126-129° (peak 4 ) . I t i s apparent tha t when the c r y s t a l s are s to red at 58° u n t i l t r a n s i t i o n to the 3 form i s complete (about 5 days) then the Q—->a t r a n s i -t i o n occurs very r a p i d l y at room temperature ( < 1 day) . I f , however, the t r a n s i t i o n to the 3 form i s incomplete before removal from the oven, then the t r a n s i t i o n to the a form takes up to 28 days a t room temperature. Var ious workers have reported tha t the hexahydrate formed on the dehydrat ion of NiSO^.Z^O undergoes a phase t r a n s i t i o n ( C a i l l e r e and Pobeguin, 1962; Pannet ier e t a l . , 1964) or t r a n s i t i o n s (Chihara and S e k i , 1963) p r i o r to f u r t h e r dehydrat ion . S t a r t i n g w i th N i S 0 4 a 6H 2 0, Rabbering e t a l . (1975) a t t r i b u t e d peak 1 i n a DSC scan to an a — > 3 t r a n s i t i o n fo l l owed by the 6—>4 dehydrat ion of the 3 form, peak 2, and v a p o r i z a t i o n of the l i b e r a t e d water , peak 3. However, even i f peaks 1 were due to the a — > 3 t r a n s i t i o n , r a t he r than the a—>y t r a n s i t i o n , peaks 2 and 3 cannot be due to the consecut i ve dehydrat ion and v a p o r i z a t i o n o f the 3 form s i nce the thermograms of.NiSO^ 3 6H 20 show tha t dehydrat ion and v a p o r i z a t i o n occur - 137 -Table XIV Changes i n thermograms and X-ray d i f f r a c t i o n of emerald green c r y s t a l s of n i c k e l s u l f a t e on storage at room temperature Days Endothermic Peak Maxima, °C (moles HgO vapor ized per mole NiSO^)' X-ray 1 2 3 4 5 0 P 98 b - 117 C 129(5) - mainly a ; some g. 5 hours 0* P 94 b 106 121 C 129(5) -5 C - 102 120 126 158 rv P 94 b 105 119° 129(3-4) 156(5) Ut 12 P 94 b 104 114 C 126 165(5) 28 C - 101 120 - 164 a P 9 5 b 105 123(2) - 160(5) C c lo sed pan P c l o sed pan w i th p inho le a va lues i n parentheses are to the nearest s t o i c h i o m e t r i c r a t i o b smal l peak c shoulder emerald green—>blue green w i t h i n 5 hours - 138 -s imu l taneous l y , peak 3, Table X I I . 2. Thermochemistry The primary energy f a c t o r s f o r d i s s o l u t i o n , , as d i scussed i n s e c t i on C.3 of the l i t e r a t u r e survey, are the l a t t i c e energy (AA), the hydrat ion energy (AB) and the a c t i v a t i o n energy of d i f f u s i o n (AC). The thermodynamic c y c l e f o r the d i s s o l u t i o n of N i S0 4 . 6H 2 0 i n water i s g iven below; N i S 0 4 . 6 H 2 0 > [N i ( 6H 2 0 ) ] ^ + S 0 ^ " g ABan. [ N i ( 6 H 2 0 ) ] a 2 ; + S 0 4 2 - ^ ABcat . v 2.1 Hydrat ion energy I f hydrated, complex ions are regarded as charged spheres and the s o l u t i o n process as the i n t r o d u c t i o n of these spheres i n t o a continuous water d i e l e c t r i c , the hydrat ion energy, ABcat i s g iven by ABcat =. • (46) where X i s the rad ius i n Angstrom un i t s (George and McClure, 1959). I f X i s 3.54 A (see s e c t i o n A .3 .1 ) , ABcat = -189 kcal.mol .ABan = -265 k c a l . m o l " (Greenwood, 1970). Hence AB = ABcat + ABan = -454 k c a l . m o l " 1 - 139 -2.2 L a t t i c e energy The l a t t i c e energy, AA, can be c a l c u l a t e d i f AB and AH S are known, s i nce AH S = AA + AB (47) AH S was c a l c u l a t e d from a Van ' t Hoff p l o t of s o l u b i l i t y data f o r N i S 0 4 a 6H 20 i n water ( P h i l l i p s , 1973). AH S was found to be +1.2 k c a l . m o l - 1 . +1.2 = AA + (-454) Therefore AA = +455.2 k c a l . m o l " 1 Thi s va lue was i n good agreement w i th the pub l i shed f i g u r e of +476.6 kcal .mol c a l c u l a t e d f o r N i S0 4 . 6H 2 0 us ing a method of equat ing the e l e c t r o n e g a t i v i t i e s of c o n s t i t u e n t atoms (Kaganyuk, 1978). 2.3 D i s s o l u t i o n of NiS0/[.6Ho0 i n 60% v/v ethanol D i s s o l u t i o n of NiS04.6H 2 0 i n 60% v/v ethanol i s a spontaneous process and i s t he re fo re accompanied by a decrease i n Gibbs f r e e energy, AG. However, dur ing d i s s o l u t i o n , heat i s absorbed from the surroundings i . e . A H S i s p o s i t i v e and the r e a c t i o n i s endothermic. S ince A H s i s p o s i t i v e and AG i s nega t i ve , AS must be p o s i t i v e and la rge enough so t ha t TAS > AH $ . AS was c a l c u l a t e d from the Van ' t Hoff p l o t , Eqn. 43 and found to be +0.0234 kca l .deg m o l - 1 . S u b s t i t u t i n g values of AS and AH g i n t o the Gibbs-Helmholtz equa t i on , Eqn. 33, AG at 25° i s g iven by AG = 6.3 - (298 x 0.0234) = -0.697 k c a l . m o l " 1 Hence the spontaneous endothermic d i s s o l u t i o n r e a c t i o n occurs because of the increase i n entropy i . e . an entropy d r i ven process . - 140 -The hydrat ion energy, AB f o r [Ni (6H0O ) ] " " % „ and S O / " i n 60% v/v £ aq > aq ethanol may be c a l c u l a t e d by s u b s t i t u t i o n o f AH S = +6.3 k c a l . m o l " 1 i n t o Eqn. 47, and i s g iven by AB = -448.9 k c a l . m o l " 1 2.4 A c t i v a t i o n energy f o r d i f f u s i o n Values o f D a t d i f f e r e n t temperatures were c a l c u l a t e d (see s e c t i on A.3.1) and p l o t t e d i n an A r rhen iu s - t ype p l o t of log D versus 1/T. The s lope equals -AC/2.303 R and AC, the a c t i v a t i o n energy f o r d i f f u s i o n of NiSO^eh^O i n 60% v/v e t hano l , was found to be +6.4 k c a l . m o l - 1 . D. SINGLE CRYSTAL GROWTH AND DISSOLUTION 1. Choice of NiSO^ a 6H,,0 In the search f o r a s u i t a b l e model to study the e f f e c t of c r y s t a l de fec t s on the d i s s o l u t i o n r a t e , s i n g l e c r y s t a l s of N i S 0 4 a 6H£0 were chosen as a p o t e n t i a l l y usefu l model c r y s t a l l i n e m a t e r i a l . The c r y s t a l s are l a r g e , we l l - fo rmed and e a s i l y c leaved along the (001) p lane. 2. Growth k i n e t i c s F i g . 29 shows t y p i c a l p l o t s o f d i s t ance moved by the (001) face as a f u n c t i o n of time f o r the c r y s t a l s grown i n the f low c e l l . The s lopes ( cm.s " 1 ) determined us ing l i n e a r reg re s s i on a n a l y s i s are p ropo r t i ona l to the growth r a t e . Growth ra tes were a l s o measured as the o v e r a l l i nc rease i n weight i n a g iven t ime. The mean sur face area of a s i n g l e c r y s t a l exposed to the supersaturated s o l u t i o n was 0.155 cm (see Appendix I) and the growth -2 -1 ra tes were converted to un i t s of g.cm .s . The growth ra te s are averaged - 141 -s a X MINUTES F i g . 29. Movement of the (001) c r y s t a l face of N i S 04a6H 2 0 as a f u n c t i o n of t ime at 37° dur ing growth. - 142 -over the d i f f e r e n t faces present on the c r y s t a l , s ince the r a te s on each type of face cannot be determined sepa ra te l y from o v e r a l l weight inc reases of the c r y s t a l . P l o t s of the growth r a t e , r, versus the supe r sa tu ra t i on (C* - C s ) showed a p a r abo l i c r e l a t i o n s h i p a t low super sa tu ra t i on s which changed to a l i n e a r r e l a t i o n s h i p as the supe r sa tu ra t i on was i nc rea sed . Taking logar i thms of Eqn. 7 g i ve s log r = Tog K.+.n l og (C * - C s ) (48) F i g . 30 and 31 are p l o t t e d accord ing to Eqn. 48 corresponding to growth ra te s -1 -2 -1 measured as cm.s and g.cm .s r e s p e c t i v e l y . S ince n, g iven by the s lopes of the l i n e s i n F i g s . 30 and 31, i s g rea te r than one, the growth r a te i s not f i r s t order w i th respect to (C* - C s ) . The i n t e r c e p t va lue i s l og K and Table XV g ives the values o f n and K determined from F i g . 30 and 31. 3. E f f e c t of f l ow r a t e on.the growth r a t e Evidence that the growth i s e s s e n t i a l l y su r face c o n t r o l l e d a t u = 3.02 c m . s - 1 a t which growth ra te s were measured, was obta ined by i n c r ea s i n g the f low r a te a t time t = 15 and 40 min as shown i n F i g . 32. The absence of any change i n the r a t e of movement of the c r y s t a l face showed tha t the growth was independent of f l ow r a t e . 4. M i c ro s cop i ca l examination of c r y s t a l s 4.1 F l u i d i z e d - b e d grown b ipyramidal c r y s t a l s -6 Cleaved and etched (001) faces of c r y s t a l s grown at 1.15 x 10 - 2 - 1 - 6 - 2 - 1 g.cm" .s~ and 44.51 x 10" g.cm" .s~ were viewed under a d i f f e r e n t i a l i n t e r f e r e n c e c on t r a s t microscope. The d i s l o c a t i o n etch p i t s are shown in - 143 -C/3 to PC H 2 0 O 1 5 0 l O O 50 i I I I 1 ° 3 0 6 0 9 0 S U P E R S A T U R A T I O N ( C - G s ) 2 g hexahydrate/g solvent xlO F i g . 30. P l o t of growth r a t e , measured as the r a t e of movement of the (001) face of NiS04 a 6H 2 0, versus supe r sa tu ra t i on at 3 7° . L ine f i t t e d by l i n e a r reg re s s i on a n a l y s i s . - 144 -5 0 r CM E o d) 101 X H i P C a 0 5 0 1 I 1 1 0 3 0 6 0 9 0 S U P E R S A T U R A T I O N C C ^ C s ) g hexahydrate/g solvent xlO2 F i g . 31. P l o t of growth r a t e , measured as the o v e r a l l r a te of i nc rease i n weight of a NiSC^ a 6H2O s i n g l e c r y s t a l , versus s upe r sa tu ra t i on a t 3 7 ° . L ine f i t t e d by l i n e a r r eg re s s i on a n a l y s i s . - 145 -Table XV Growth data f o r N i S 0 4 a 6H 20 i n water a t 37° and a f low r a t e of 3.02 cm.s " 1 Measurement K n Weight i nc rease 1.51 x 1 0 " 3 g . c m " 2 . s _ 1 1.39 Movement (001) 3.53 x 1 0 " 4 cm.s " 1 1.21 face I - 146 -F i g . 32. Movement of the (001) c r y s t a l face o f NiS04 a 6H2O versus time to show su r face c o n t r o l l e d growth at 37° . Supe r sa tu ra t i on : 6.89 x 1 0 - 2 g hexahydrate/g s o l v e n t , • 2.36 cm.s -1, • 6.01 cm.s -1; 8.21 x 10~2 g hexahydrate/g s o l v e n t , O 2.64 c m . s - 1 , • 8.49 cm.s-1. Arrows i n d i c a t e change o f f l ow r a t e . - 147 -F i g . 33. There was a q u a l i t a t i v e c o r r e l a t i o n between the growth r a te and d i s l o c a t i o n etch p i t d e n s i t y , the c r y s t a l s a t the lower growth r a te having a lower d i s l o c a t i o n d e n s i t y . However, on l y a q u a l i t a t i v e determinat ion cou ld be made as even at the lowest growth r a t e , the d i s l o c a t i o n den s i t y was very high and count ing was not p o s s i b l e . 4.2 Flow c e l l grown b ipyramida l c r y s t a l s Examination of the c r y s t a l s under a su r face i l l u m i n a t i o n microscope showed a pronounced growth " s p i r a l " or " p l a t e a u " p ro t rud ing from the cent re of the (001) face and extending over approx imately 90% of the su r face (see F i g . 33). The s i z e and height o f the s p i r a l appeared to be p ropo r t i ona l to the growth r a t e . 5. S i n g l e c r y s t a l d i s s o l u t i o n 5.1 F l u i d i z e d - b e d grown c r y s t a l s The s lopes of p l o t s of d i s t ance moved of the (001) face as a f u n c t i o n of time were c a l c u l a t e d and used as a measure of an observed apparent r a t e cons tant , K 0 b s , as d i scussed i n s e c t i o n A.2. D i s s o l u t i o n was c a r r i e d out at 37° and a high f low r a te of 5.43 c m . s - 1 such tha t d i s s o l u t i o n was e s s e n t i a l l y c o n t r o l l e d by the su r face r e a c t i o n . The r e s u l t s i n Table XVI show tha t there i s no s i g n i f i c a n t d i f f e r e n c e i n K 0 b s f o r the 2 sets of c r y s t a l s . I t seems l i k e l y t ha t the numbers of d i s l o c a t i o n s i n the N i S 0 4 a 6H2O c r y s t a l s were so great tha t any e f f e c t due to d i f f e r e n c e s i n the number of d i s l o c a t i o n s on subsequent d i s s o l u t i o n r a te s was obscured. The e f f e c t of the d i s s o l u t i o n i n h i b i t o r sodium t r i po l ypho spha te , on K o b s i s shown i n Table XVII. D i s s o l u t i o n was c a r r i e d out a t 30° and a f low r a t e of 5.43 cm.s ^. I n h i b i t o r s are s t r o n g l y adsorbed on the steps formed i n the i n i t i a l stages of d i s s o l u t i o n i . e . k i n k s , steps and the s i t e s of emergent d i s l o c a t i o n s and i t was a n t i c i p a t e d tha t d i f f e r e n c e s i n K 0 b S f o r the two sets - 148 -0.05mm 0.1mm F i g . 33. a) D i s l o c a t i o n etch p i t s on the c leaved and etched (001) plane of a NiS04 a 6H 20 c r y s t a l . b) Growth " s p i r a l " on the (001) face of N i S 0 4 a 6H 20. - 149 -Table XVI Growth and d i s s o l u t i o n rates of f l u i d i z e d - b e d grown NiSCL a 6H ?0 c r y s t a l s Growth M e a n K o b s a , Range o f K Q b s ra te x 10° (001) face x 1 0 s (001) face x 10 b -2 -1 (g.cm .s ) ( c m . s - 1 ) ( c m . s - 1 ) 1.15 1.03 0.98 - 1.09 44.51 0.98 0.80 - 1.09 a Mean of 3-5 de te rm ina t i on s . - 150 -Table XVII Growth and d i s s o l u t i o n rates o f f l u i d i z e d - b e d grown NiS04 a 6H2O c r y s t a l s i n the presence and absence of i n h i b i t o r Growth r a te x 10 6 7 1 (g.cm" .s " ) Contro l K obs x _ ] ° 5 (cm.s ) K o b s (001) face i n presence of d i s s o l u t i o n i n h i b i t o r Mean K o b s a x 10 5 ( c m . s - 1 ) Range Kobs * ">05 ( c m . s - 1 ) 1.15 0.79 0.54 0.46 - 0.59 44.51 0.72 0.57 0.55 - 0.59 a Mean of 3 determinat ions - 151 -of c r y s t a l s would be more r e a d i l y observed. Although K 0 k s was decreased i n the presence o f the i n h i b i t o r , there was no s i g n i f i c a n t d i f f e r e n c e i n KQ^S f o r the c r y s t a l s grown at d i f f e r e n t r a t e s . 5.2 Flow c e l l grown c r y s t a l s ^obs f ° r t n e f l ° w c e ^ grown c r y s t a l s as a f unc t i on o f the growth r a te i s shown in F i g . 34. There i s an inc rease i n KQ^S w i t h growth r a t e . However t h i s c o r r e l a t i o n i s u n l i k e l y to be due to d i f f e r e n c e s i n d i s l o c a t i o n den s i t y of the c r y s t a l s as shown i n s e c t i o n D.5.1. The most l i k e l y exp lanat ion i s t ha t d i s s o l u t i o n was most r ap id at the growth " p l a t e a u " or " s p i r a l " on the (001) f a c e . The c r y s t a l s grown at the h igher growth ra te s had l a r g e r s p i r a l s and hence d i s s o l v ed at a f a s t e r r a t e . Fur ther q u a n t i t a -t i v e evidence would be needed to prove t h i s . E. CRYSTAL DEFECTS AND DISSOLUTION RATE 1. Choice of potassium perch!orate S i ng l e c r y s t a l s o f .KC lO^ are a more s u i t a b l e model than NiSO^ a 6H2O f o r s tudy ing c r y s t a l de fec t s and d i s s o l u t i o n r a t e , f o r the f o l l o w i n g reasons; a) KC10 4 can be grown i n gels as l a r g e , we l l - fo rmed c r y s t a l s w i th a s i g n i f i c a n t l y lower d i s l o c a t i o n den s i t y than NiSO^ a 6H2O. b) I t i s a n t i c i p a t e d t ha t by us ing a model, such as gel grown KCIO^ where there should be severa l orders of magnitude fewer d i s l o c a -t i o n s than NiSO^ a 6H2O, d i f f e r e n c e s i n d i s s o l u t i o n r a t e s , due to v a r i a t i o n i n the numbers of d i s l o c a t i o n s of c r y s t a l s grown at d i f f e r e n t growth r a t e s , may be more r e a d i l y observed. In a d d i t i o n , KC10 4 c r y s t a l s can be e a s i l y c leaved a l ong the (001) c leavage plane and a s u i t a b l e e tch ing s o l u t i o n has been r epo r ted . 5 0 1 -4 0 • E 152 s x 3 * 5 0 h I 1 5 0 G R O W T H R A T E x l O ° Ccm.s " 1 ) 4 0 3 0 O 1 5 3 5 5 5 G R O W T H R A T E x 1 0 5 ( g . c m r V ) F i g . 34. P l o t s of K 0bs a s a f u n c t i o n of the growth r a t e f o r s i n g l e c r y s t a l s of N i S 0 4 a 6H2O, at 30° and a f l ow r a te of 5.43 cm.s " ! . - 153 -2. C h a r a c t e r i z a t i o n The octahedra l c r y s t a l s from the th ree growth l a y e r s , 0 -1 , 2-3, 4-6 cm were c h a r a c t e r i z e d by the f o l l o w i n g methods to ensure tha t the c r y s t a l s were i d e n t i c a l i n t h e i r chemical and c r y s t a l l i n e c h a r a c t e r i s t i c s . 2.1 X-ray d i f f r a c t i o n X-ray d i f f r a c t i o n pat terns f o r the octahedra l c r y s t a l s grown at the 0 -1 , 2-3 and 4-6 cm growth l e v e l s were i d e n t i c a l w i th each o the r . A l l d va lues were c h a r a c t e r i s t i c o f KCIO^ (Se lec ted Powder D i f f r a c t i o n da t a , 1974) (Table XV I I I ) . 2.2 Thermal a n a l y s i s Thermal a na l y s i s r e s u l t s are g iven i n Table XIX. On heat ing the samples, on ly one endothermic peak was observed a t 311° or 306° depending on whether a c lo sed pan w i th p inho le or an open pan was used. KCIO^ does not form hydrates (Whaley, 1973) and t h i s was conf irmed expe r imenta l l y as no weight lo s s occurred on heat ing the samples to 500°. A l l samples showed i d e n t i c a l thermograms. The endothermic peak corresponds to an e n a n t i o t r o p i c , p o l y -morphic phase t r a n s i t i o n from the orthorhombic form to a c u b i c , high temperature form (Donnay and Ondik, 1973; Ba r i n and Knacke, 1973). Coo l ing the samples from 320° r e s u l t e d i n an exothermic peak between 281-286° depending on the c o o l i n g r a t e , demonstrat ing the r e v e r s i b i l i t y of the phase t r a n s i t i o n . 2.3 Impurity a n a l y s i s As d i scussed i n E.3.33 of the l i t e r a t u r e survey, i m p u r i t i e s i ncorporated i n t o the c r y s t a l dur ing growth can exe r t a profound i n f l u e n c e on the d i s s o -l u t i o n k i n e t i c s . Therefore the octahedra l c r y s t a l s were analyzed f o r po s s i b l e impur i t y content by X-ray energy a n a l y s i s . - 154 -Table XVIII X-ray data f o r KC10 4 c r y s t a l s grown at 0-1 cm, 2-3 cm and 4-6 cm growth l e v e l s Sample data Standard d a t a 9 d(A) R e l a t i v e d(A) R e l a t i v e I n t e n s i t y I n t e n s i t y 5.59 m 5.61 m 4.44 m 4.42 w 3.96 w 3.98 w 3.75 m 3.78 m 3.606 vs 3.629 m 3.478 vs 3.487 vs 3.328 s 3.359 s 3.123 vs 3.145 vs 2.859 vs 2.890 vs 2.796 m 2.831 m a X-ray powder d i f f r a c t i o n data f i l e : card #7-211 - 155 -Table XIX Thermal a na l y s i s o f KC1CL c r y s t a l s Hab i t Gel growth l e v e l (cm) Endothermic peak maximum °C (scanning r a t e °C/min) Exothermic peak maximum °C , (scanning r a te °C/min) Mixed P 0 - 1 311 (20) Cubic P 0 - 1 311 (20) Cubic 0 0 - 1 306 (20) Octahedral 0 0 - 1 306 (20) Octahedral 0 4 - 6 306 (20) Octahedral 0 4 - 6 306 (20) Octahedral 0 4 - 6 306 (20) 281 (20) Octahedral 0 4 - 6 306 (20) 284 (10) Octahedral 0 4 - 6 306 (20) . 286 (5) P c l o sed pan w i th p inho le 0 open pan a i n c r e a s i n g temperature k decreas ing temperature - 156 -2.31 X-ray energy a n a l y s i s X-ray energy spec t ra were obta ined f o r the KCIO^ c r y s t a l s from the 0-1 and 4-6 cm growth l e v e l s . Only the energy peaks c h a r a c t e r i s t i c of KC10 4 were observed ( F i g . 35). 3. D i s l o c a t i o n content of KCIO^ c r y s t a l s 3.1 D i s l o c a t i o n s and etch p i t s The d i f f e r e n t techniques f o r d e t e c t i n g d i s l o c a t i o n s have been b r i e f l y d i scussed i n s e c t i o n E.3.32 of the l i t e r a t u r e survey. Etch ing i s the s i m p l e s t , most r ap i d and most e x t e n s i v e l y employed method f o r determin ing d i s l o c a t i o n den s i t i e s i n n on -me ta l l i c c r y s t a l s . Etch p i t d e n s i t i e s i n the 8 -2 range of zero to about 10 cm" can be conven ien t l y measured w i th a m i c r o -scope (Johnston, 1962). Vogel e t a l . (1953) e s t ab l i s hed the v a l i d i t y of the etch p i t method f o r r e v e a l i n g the s i t e s o f emergent d i s l o c a t i o n s . They measured the spacings between etch p i t s i n a g ra i n boundary by an X-ray method. Good agreement was found between, the measured spacings and those c a l c u l a t e d from the d i s l o c a t i o n model of a g ra i n boundary. There are two.types of d i s l o c a -t i o n , the edge and screw d i s l o c a t i o n s (see s e c t i o n A.4.21 of the l i t e r a t u r e survey) but the e x i s t i n g evidence i s t ha t etch p i t s are formed rega rd le s s of the edge or screw cha rac te r or the o r i e n t a t i o n w i th re spect to the s u r f ace . 3.2 Etch ing of KCIO^ c r y s t a l s Low index, (001) c leavage planes of KC10 4 were etched w i th a mixture of concentrated s u l phu r i c a c i d and 0.25 M sodium s u l f i t e . Th is etchant was f i r s t used by Pate l and Rao (1979) f o r e tch ing KCIO^ c r y s t a l s . They demonstrated the r e l i a b i l i t y of the etchant f o r r e v e a l i n g d i s l o c a t i o n s i n the f o l l o w i n g ways. F i g . 35. X-ray energy a n a l y s i s of KC104 c r y s t a l s from a) 0-1 cm and b) 4-6 cm growth l e v e l s . - 158 -a) there was a one-to-one correspondence between the etch p i t s on the oppos i te halves o f a c leaved c r y s t a l , showing t ha t the etch p i t s corresponded to l i n e de fect s t ha t were present i n the c r y s t a l p r i o r to c leavage. b) the etch p i t s grew b igger and deeper on success i ve e tch ing imp ly ing tha t the e tch ing was proceeding along l i n e d e f e c t s . A f u r t h e r experiment was c a r r i e d out to v e r i f y the f i n d i n g s of Pa te l and Rao (1979). The etch p i t d i s t r i b u t i o n s on the c l e a ved , etched sur faces of KCIO^ c r y s t a l s were noted. The sur faces were then po l i s hed by exposure to water f o r 2-3 mins, to produce a smooth su r face f r e e of etch p i t s . A f t e r r e - e t c h i n g , the etch p i t d i s t r i b u t i o n on each c r y s t a l plane c l o s e l y resembled the d i s t r i b u t i o n p r e v i ou s l y noted f o r the p lane. The etch p i t s were t y p i c a l l y o f a hexagonal shape, and were po inted o r f l a t t e n e d a t the apex (see F i g . 36). 3.3 D i s l o c a t i o n d e n s i t y There are two ways of d e s c r i b i n g the d i s l o c a t i o n content of a c r y s t a l (Johnston, 1962). One way i s to s p e c i f y the t o t a l length of d i s l o c a t i o n i n 1 cm of the c r y s t a l . Another way, more commonly used (and the one used i n 2 t h i s s t udy ) , i s to count the number of d i s l o c a t i o n s that i n t e r s e c t 1 cm of a plane passed through the c r y s t a l . The two methods are p r a c t i c a l l y equ i va len t ( to w i t h i n a f a c t o r of 2 or 3) unless the d i s l o c a t i o n s are d i s t r i -buted i n a very a n i s o t r o p i c manner. I t i s p o s s i b l e to es t imate the maximum d i s l o c a t i o n den s i t y t ha t can be reso lved w i th the var ious d e t e c t i o n methods. For the e tch p i t method (us ing an o p t i c a l microscope) the maximum d i s l o c a t i o n den s i t y i s approx imately 8 -? 4 x 10 cm" . The d i s l o c a t i o n d e n s i t i e s of the gel-grown KC10 4 c r y s t a l s were severa l orders of magnitude below t h i s va l ue . - 159 -0.1mm Fig. 36. Dis location etch p i t s on the cleaved and etched (001) plane of KC10 d . - 160 -I t was observed on a l l c leaved and etched c r y s t a l s that a t the po in t a t which pressure from the s c a l pe l blade had been app l i ed dur ing c leavage, a small c l u s t e r of densely packed d i s l o c a t i o n etch p i t s was present . S ince these etch p i t s were l a r g e l y a r e s u l t of the c l e a v i n g process , they were not i nc luded i n the count of d i s l o c a t i o n den s i t y . 3.4 D i s l o c a t i o n den s i t y and growth r a t e F i g . 37 shows the number o f KCIO^ c r y s t a l s f a l l i n g w i t h i n a g iven d i s l o c a t i o n den s i t y range f o r the 0-1 cm, 2-3 cm and 4-6 cm growth l e v e l s . The average c r y s t a l growth r a t e i s g rea te s t near the top of the gel column where the concen t ra t i on g rad ient s are high (0-1 cm growth l e v e l ) and sma l l e s t near the bottom where the concen t ra t i on g rad ient s are low (4-6 cm growth l e v e l ) . The d i s l o c a t i o n d e n s i t i e s are approx imate ly normal ly d i s t r i b u t e d , the mean den s i t y being s h i f t e d to lower va l ue s , the lower the r a t e o f growth (see a l s o Table XX). The range o f the d i s t r i b u t i o n of d i s l o c a t i o n d e n s i t i e s a t each growth l e v e l a l s o decreases as the growth r a t e i s decreased. A l l c r y s t a l s had a d i s l o c a t i o n den s i t y 3 4 - 2 o f between 10 - 2 x 1 0 cm . Th is den s i t y range i s r e l a t i v e l y low, as the as-grown den s i t y f o r non -meta l l i c c r y s t a l s i s u s u a l l y i n the range of 4 6 — 2 10 - 10 cm" (Johnston, 1962). However, growth of c r y s t a l s i n ge l s enables a high degree of s t r u c t u r a l p e r f e c t i o n to be ach ieved, f o r the reasons o u t l i n e d i n s e c t i o n B.4.2 of the l i t e r a t u r e survey. Several workers have shown tha t the d i s l o c a t i o n den s i t y increases as the supe r sa tu ra t i on (and hence the growth r a te ) i s i n c r ea sed , f o r a v a r i e t y of c r y s t a l l i n e ma te r i a l s (see s e c t i o n B.3 of the l i t e r a t u r e su rvey ) . However, the v a l i d i t y of the conc lu s ions reached i n a number of these s tud ie s i s ques t i onab le . Pate l and Rao (1979) showed t ha t the d i s l o c a t i o n den s i t y of KC10 A c r y s t a l s grown i n s i l i c a ge l s decreased w i th the depth below - 161 -6h c) 1 Pi U S 0 1 OS w 81 6 2 0 b) _L a) 1 4 6 8 10 12 14 16 18 DISLOCATION DENSITY xlO" 3 (cm"2) 20 F i g . 37. Number of KCIO4 c r y s t a l s w i th a g iven d i s l o c a t i o n den s i t y range from the a) 0-1 cm b) 2-3 cm and c) 4-6 cm growth l e v e l s . - 162 -the g e l - s o l u t i o n i n t e r f a c e ( i . e . decreas ing growth r a t e ) . T h e i r obse rva t ion i s based on a s i n g l e den s i t y measurement a t depths i n the gel on ly 0.4 cm apa r t . Th is study shows there to be a cons ide rab le range i n d i s l o c a t i o n d e n s i t y , eg. between 5000-20,000 cm f o r c r y s t a l s grown a t a depth of 0-1 cm. The work by van Batche lder and Vaughan (1967) was a q u a l i t a t i v e e va l ua t i on of two c leaved and etched c r y s t a l s grown a t d i f f e r e n t r a t e s , f o r both NaCl and KC1. Henisch e t a l . (1965b)counted the number of etch p i t s on c r y s t a l faces o f ca l c i um t a r t r a t e . No d e t a i l s o f the etchant used were g iven and no experiments to e s t a b l i s h i t s r e l i a b i l i t y f o r r e v e a l i n g d i s l o c a -t i on s were c a r r i e d out. In a d d i t i o n , e tch ing techniques are u s u a l l y done on c l e a n , c leavage planes and not on c r y s t a l f a ce s . 4. D i s s o l u t i o n of KCIO^ c r y s t a l s The o v e r a l l bulk d i s s o l u t i o n r a te of the octahedra l c r y s t a l s may be descr ibed by Eqn. 44 (see s e c t i on B.3). D i s s o l u t i o n occurred under s ink cond i t i on s s i nce a t no time d i d the concen t ra t i on of KCIO^ exceed 3.9% of i t s s a t u r a t i o n s o l u b i l i t y . When C s . » C and S i s con s tan t , the o v e r a l l d i s s o l u t i o n r a t e i s p ropo r t i ona l to an observed r a t e cons tan t , K ' o b s -F i g . 38 shows t y p i c a l p l o t s of concen t ra t i on change/S w i th t ime f o r the -5 -1 octahedra l c r y s t a l s a t d i f f e r e n t growth l e v e l s . The s lopes (mg.cm .s ) were determined us ing l i n e a r reg re s s i on ana l y s i s and were used to c a l c u l a t e K"'obs ( c m . s - 1 ) from the r e l a t i o n s h i p : K ' o b s = ^ i (49) where V i s the volume of d i s s o l u t i o n medium. Values of C s and S f o r the c r y s t a l s grown a t three growth l e v e l s are given i n Table XX. Due to the s i z e d i f f e r e n c e s between c r y s t a l s , the t o t a l su r face area f o r d i f f e r e n t - 163 -M I N U T E S F i g . 38. P l o t of concen t ra t i on i n the bu lk/ su r face area versus time f o r K C I O 4 c r y s t a l s a t 10.5° and a r o t a t i o n speed of 500 rpm. Growth l e v e l s : • , 0-1 cm; • , 4 - 6 cm. L ines f i t t e d by l i n e a r r eg re s s i on a n a l y s i s . Table XX D i s l o c a t i o n d e n s i t i e s , s o l u b i l i t y , sur face areas and d i s s o l u t i o n ra te constants f o r KC10/, c r y s t a l s Growth l e v e l (cm) D i s l o c a t i o n dens i t y (cm ) Mean a ± one s tandard d e v i a t i o n C s (10.5°) (mg.crrf 3) S b (cm 2) K ' o b s x 1 0 3 ( cm. s T l ) Mean 0 - 1 12,371 ± 3,785 0.203 1.4 - 1.7 2.77 2.66 2.50 2.64 2 - 3 6,633 ± 1,476 0.203 1.0 - 1.6 2.62 2.44 2.34 2.47 4 - 6 3,668 ± 902 0.203 1.4 - 1.6 2.41 2.21 2.11 2.04 2.19 a Mean of 12-17 determinat ions b Between 8-11 c r y s t a l s f o r each experiment - 165 -d i s s o l u t i o n experiments v a r i e d between the ranges g iven i n Table XX. A sample c a l c u l a t i o n of the su r face area i s g iven i n Appendix I. Values of K ' q ^ determined a t the three growth l e v e l s , 0-1 cm, 2-3 cm and 4-6 cm are g iven i n Table XX. F i g . 39 shows a p l o t of the mean and the range of K o b s as a f u n c t i o n of the mean d i s l o c a t i o n den s i t y ± one standard d e v i a t i o n . K Q b s i ncreases w i t h i n c r ea s i n g d i s l o c a t i o n d e n s i t y , such tha t an approx imate ly 4 - f o l d d i f f e r e n c e i n mean d i s l o c a t i o n den s i t y produces a 17% d i f f e r e n c e i n K ^ , between c r y s t a l s grown at the lowest and h ighest growth r a t e s . An a n a l y s i s of va r i ance of the data i s shown i n Table XXI. The two sources of v a r i a t i o n are between K o b s a t each growth i l e v e l and between K ^ s a t d i f f e r e n t growth l e v e l s . S ince there are th ree i values of K ^ a t the 0-1 cm and 2-3 cm growth l e v e l s and fou r a t the 4-6 cm growth l e v e l , one observat ion was dropped from the l a t t e r group f o r the a n a l y s i s of v a r i ance . The e x c l u s i on o f the K 1 ^ va lue of 2.21 x 10~ cm.s " 1 d id not change the mean and the range of the K 1 ^ data a t the 4-6 cm growth l e v e l . The r a t i o of the two v a r i a n ce s , F, equal to 5.99, was te s ted aga in s t the F 2,6(P = 0.05) d i s t r i b u t i o n . Th is gave a s i g n i f i c a n t r e s u l t a t P = 0.05 i . e . the mean K' ^ f o r the d i f f e r e n t growth l e v e l s are d i f f e r e n t . The l e a s t s i g n i f i c a n t d i f f e r e n c e (LSD) a t a 5% l e v e l of s i g n i -f i c a n c e was obta ined t o determine where these d i f f e r e n c e s l i e . Two means are s i g n i f i c a n t l y d i f f e r e n t i f the abso lute d i f f e r e n c e between the two means i s g rea te r than the LSD. The c a l c u l a t e d LSD (0.05) was 3.25 x 10~^ and the f o l l o w i n g conc lu s ions may be drawn a) there i s no s i g n i f i c a n t d i f f e r e n c e between mean K ' o b s a t the 0-1 cm and 2-3 cm growth l e v e l s . b) there i s no s i g n i f i c a n t d i f f e r e n c e between mean K ^ a t the 2-3 cm and 4-6 cm growth l e v e l s . - 166 -8 10 12 14 16 DISLOCATION DENSITY xio^Ccm"2) F i g . 39. P l o t of the mean K'pbs a s a f u n c t i o n of the mean d i s l o c a t i o n den s i t y f o r KC10 4 c r y s t a l s . Ho r i z on ta l bars i n d i c a t e ± one standard d e v i a t i o n of d i s l o c a t i o n d e n s i t i e s . V e r t i c a l bars i n d i c a t e the range of K 0 b s . - 167 -Table XXI Ana l y s i s of va r i ance of K ' o b s data f o r KC10 4 c r y s t a l s grown' at d i f f e r e n t growth l e v e l s Source of v a r i a t i o n Sums of squares Degrees of freedom Mean Square ( va r iance) Between growth l e v e l s 3.2 x 10" 7 2 1.6 x 1 0 " 7 Between K ' o b s 1.6 x 10" 7 6 2.67 x 1 0 " 8 Tota l 4.8 x 10" 7 8 -- 168 -c) the mean K o b s a t the 0-1 cm and 4-6 cm growth l e v e l s are s i g n i -f i c a n t l y d i f f e r e n t (P = 0.05). The complex i n t e r r e l a t i o n s h i p s between growth r a t e * i m p u r i t i e s , d i s l o -c a t i o n den s i t y and d i s s o l u t i o n r a t e have been reviewed i n s e c t i o n E.3.33 of the l i t e r a t u r e survey. The pronounced e f f e c t s t ha t i m p u r i t i e s ( po in t de fec t s ) and d i f f e r e n c e s i n the c r y s t a l l i n e nature of c r y s t a l s may exer t on t h e i r d i s s o l u t i o n k i n e t i c s have been d i s cu s sed . X-ray d i f f r a c t i o n and thermal a n a l y s i s showed t ha t the c r y s t a l s from the d i f f e r e n t growth l e v e l s were i d e n t i c a l i n t h e i r chemical and c r y s t a l l i n e c h a r a c t e r i s t i c s . No impur i t y peaks were observed from X-ray energy a n a l y s i s , a l though t h i s technique would not de tec t t r a ce amounts of i m p u r i t i e s . Never the le s s , i t i s u n l i k e l y tha t i m p u r i t i e s were r e spon s i b l e f o r the observed d i f f e r e n c e s i n K ' Q b s f o r c r y s t a l s grown a t d i f f e r e n t l e v e l s . S ince c r y s t a l s grown a t f a s t e r r a te s i n co rpo ra te more impur i t y atoms than c r y s t a l s grown a t slower r a t e s , c r y s t a l s from the 0-1 cm l e v e l might be expected to con ta i n a higher concen t ra t i on of i m p u r i t i e s than c r y s t a l s from the 4-6 cm l e v e l (Ma l ic sko and Szomor, 1971; I z r a e l e t a l . , 1972; Brooks et a l . , 1968). Th i s would r e s u l t i n i n h i b i t i o n of the d i s s o l u t i o n r a t e f o r the c r y s t a l s from the 0-1 cm growth l e v e l , K ' o b s f o r the 0-1 cm l e v e l c r y s t a l s would be lower than K ' o b s f o r the c r y s t a l s from the 4-6 cm growth l e v e l . The r e s u l t s i n d i c a t e that t h i s i s not the case. C r y s t a l s w i th a higher d i s l o c a t i o n den s i t y w i l l have a higher thermo-dynamic a c t i v i t y r e l a t i v e to c r y s t a l s w i th a lower d i s l o c a t i o n d e n s i t y , due to the l o c a l i z e d energy a s soc i a ted wi th d i s l o c a t i o n s . Th is r e s u l t s i n a g reate r o v e r a l l d i s s o l u t i o n r a t e as shown by the data i n Table XX and F i g . 39. Although no attempt was made to determine the r a t e c o n t r o l l i n g step i n the d i s s o l u t i o n r e a c t i o n , the very low s o l u b i l i t y of the K C I O ^ - 169 -c r y s t a l s i n the d i s s o l u t i o n medium and the high r o t a t i o n speed would i n d i c a t e a su r face c o n t r o l l e d process. I t i s u n l i k e l y tha t d i f f e r e n c e s i n K'.Qjjg would be observed where d i s s o l u t i o n was t r an spo r t c o n t r o l l e d . Many s tud ie s have shown c o r r e l a t i o n s between d i s l o c a t i o n content of c r y s t a l s and p r ope r t i e s such as dehyd ra t i on , decompos i t ion, c a t a l y t i c a c t i v i t y e t c . (see Table I I ) but the o v e r a l l or bulk d i s s o l u t i o n o f c r y s t a l s has not been reported p r e v i o u s l y . Although the observed d i f f e r e n c e s i n K ' o b s f o r 9 e 1 " 9 r o w n KC10 4 c r y s t a l s were not l a r g e , i t may be p red i c t ed tha t the d i s s o l u t i o n of c r y s t a l s w i th d i s l o c a t i o n d e n s i t i e s d i f f e r i n g by severa l orders of magnitude would show very pronounced d i f f e r e n c e s i n the d i s s o l u -t i o n r a t e s . - 170 -SUMMARY AND CONCLUSIONS 1. The d i s s o l u t i o n an i so t ropy of we l l - fo rmed c r y s t a l s of NiSO^ a 6 ^ 0 grown under c o n t r o l l e d cond i t i on s was s tud ied us ing a s i n g l e c r y s t a l d i s s o l u t i o n method. K Q ^ f o r the (112) face was g rea te r than f o r the (111) face a t a l l f l ow r a te s s t ud i ed but an i so t ropy was l e s s pronounced a t the lower f l ow r a t e s . The apparent r a te constants f o r the t r an spo r t and sur face c o n t r o l l e d r e a c t i o n s , and K R , were of the same order of magnitude suggest ing t ha t the o v e r a l l d i s s o l u t i o n r e a c t i o n was under mixed con t r o l a t the lower f low r a t e s . A c t i v a t i o n energ ies were s l i g h t l y h igher than the normal range f o r t r an spo r t processes. K R (112) > K R (111) i n d i c a t i n g tha t an i so t ropy was due main ly to d i f f e r e n c e s i n the r a te of the su r face r e a c t i o n . At high f l ow ra te s there was a change to a predominantly su r face c o n t r o l l e d r e a c t i o n and a c t i v a t i o n energ ies were w i t h i n the accepted l i m i t s f o r these r e a c t i o n s . I t i s l i k e l y t ha t d i s s o l u t i o n an i so t ropy i s due to the d i f f e r e n c e s i n a c t i v a t i o n energy f o r the two faces . 2. The e f f e c t of h ab i t m o d i f i c a t i o n on the d i s s o l u t i o n r a t e of NiSO^.a 6H2O i n 60% ethanol was s tud ied us ing a r o t a t i n g basket method. B ipyramidal c r y s t a l s were grown i n a f l u i d i z e d - b e d c r y s t a l l i z e r and p l a t y c r y s t a l s were r e c r y s t a l l i z e d from supersaturated s o l u t i o n s o f n i c k e l s u l f a t e con ta i n i n g small amounts of g e l a t i n . A c i c u l a r c r y s t a l s were prepared by the t o p o t a c t i c dehydrat ion of a c i c u l a r c r y s t a l s of N i S O ^ r ^ O , grown from s o l u t i o n a t room temperature. The th ree c r y s t a l hab i t s o f NiSO^ a 6H2O showed i d e n t i c a l X-ray d i f f r a c t i o n pat terns and t he re f o re had the same c r y s t a l s t r u c t u r e . DSC thermograms of p l a t y and a c i c u l a r - 171 -hab i t s were s i m i l a r but d i f f e r e d from the b ipyramida l h a b i t . The d i f f e r e n c e i n the DSC scans was a t t r i b u t e d to a d i f f e r e n c e i n water vapor pressure. K ' o b s f o r the b ipyramida l c r y s t a l s was g rea te r than f o r the p l a t y c r y s t a l s at both low and high r o t a t i o n ra te s but the d i f f e r e n c e was l e s s pronounced a t the lower r o t a t i o n r a t e . At the high r o t a t i o n speed, d i s s o l u t i o n was under mixed s u r f a c e - t r a n s p o r t c o n t r o l . K ' 0 ^ s f ° r the a c i c u l a r hab i t was s i m i l a r to the b ipyramidal hab i t a lthough i t s p repara t ion by means of dehydrat ion of N i S O ^ r ^ O might have been expected to a f f e c t the p rope r t i e s of the c r y s t a l sur face and the re f o re the d i s s o l u t i o n r e a c t i o n . 3. In t h i s s imple a n i s o t r o p i c , i no rgan i c model system, m o d i f i c a t i o n of c r y s t a l hab i t has an e f f e c t on bulk d i s s o l u t i o n ra te under cond i t i on s where the su r face r e a c t i o n c on t r i bu te s to the o v e r a l l d i s s o l u t i o n process. The d i f f e r e n c e i n K o b s must be due to d i f f e r e n t values of the o v e r a l l su r face energy of the c r y s t a l s . I n t r i n s i c d i s s o l u t i o n ra tes f o r the three hab i t s were s i m i l a r con f i rm ing tha t the d i f f e r e n c e s i n K ' o b s were due to hab i t m o d i f i c a t i o n . 4. The 6 polymorph of N i S0 4 . 6H 2 0 was r e c r y s t a l l i z e d a t 58° . These emerald green c r y s t a l s took about 5 days a t 58° to become e s t a b l i s h e d as the 66 form as c h a r a c t e r i z e d by X-ray and DSC but when once e s t a b l i s h e d underwent r ap i d t r a n s i t i o n to the blue-green 6a form at room temperature. 5. The emerald green c r y s t a l s s to red a t room temperature before the 66 form was e s t ab l i s hed r a p i d l y changed c o l o r to the blue-green of the 6a form. However, about 28 days elapsed before the thermogram corresponded to tha t of the 6a form even though the X-ray d i f f r a c t i o n pa t te rn corresponded to pure 6a w i t h i n a few days. - 172 -6. Two samples of NiSO^ a 6 ^ 0 c r y s t a l s grown i n a f l u i d i z e d - b e d c r y s t a l l i z e r w i th a 40 f o l d d i f f e r e n c e i n the growth r a t e , showed a q u a l i t a t i v e c o r r e l a t i o n between the growth r a te and d i s l o c a t i o n etch p i t den s i t y . However, no s i g n i f i c a n t d i f f e r e n c e was observed i n the s i n g l e c r y s t a l d i s s o l u t i o n ra te s of the [001) faces e i t h e r i n the presence or absence of a d i s s o l u t i o n i n h i b i t o r . I t seems l i k e l y that the numbers of d i s l o c a -t i on s i n the N i S 0 4 a 6H 20 c r y s t a l s were so great tha t any e f f e c t due to d i f f e r e n c e s i n the numbers of d i s l o c a t i o n s on subsequent d i s s o l u t i o n ra tes was obscured. 7. S i n g l e c r y s t a l s of N i S 0 4 a 6H 20 were grown at d i f f e r e n t ra tes i n a f low c e l l . Examination of the c r y s t a l s under a su r face i l l u m i n a t i o n m i c r o -scope showed a pronounced growth " s p i r a l " p ro t rud ing from the (001) f a c e , the s i z e and height of which appeared to be p ropo r t i ona l to the growth r a t e . The subsequent d i s s o l u t i o n of the c r y s t a l s i n the f low c e l l showed t ha t the d i s s o l u t i o n r a te of the (001) face increased as a f u n c t i o n o f growth r a t e . I t i s l i k e l y t ha t the h igher d i s s o l u t i o n ra te of c r y s t a l s grown at a f a s t e r r a te was due to a more r ap id d i s s o l u t i o n of the growth " s p i r a l " . 8. The e f f e c t of the de fec t content on the d i s s o l u t i o n r a t e of KCIO^ i n 95% ethanol was s tud ied us ing a r o t a t i n g basket method. Octahedral c r y s t a l s of KCIO^ were grown i n s i l i c a g e l s . C r y s t a l s from the 0-1 cm, 2-3 cm and 4-6 cm growth l e v e l s showed i d e n t i c a l X-ray d i f f r a c t i o n p a t t e r n , DSC thermograms and X-ray energy a n a l y s i s pa t t e rn s . 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S c i . , 54 (1965c) 169-175. \ 187 APPENDIX I CALCULATION OF SURFACE AREAS B ipyramidal NiSO^ a 6 ^ 0 c r y s t a l s C a l c u l a t i o n one - from su r face areas of faces a) (111) face 1.695 mm 2.02 mm Area of (111) trapezium = 1.695 + 2.02)0.47 = 0.873 mm2 b) (112) face 0.677 mm 1.695 mm c) (001) face 0.856 mm Area of (112) trapezium = Jg(0.677 + 1.695)0.856 2 = 1.015 mm 0.677 mm 0.677 mm Area o f (001) square = 0.677' 0.458 mm - 188 -Sur face area of one c r y s t a l = 8.(111) faces + 8 (112) faces + 2 (001) faces = (8.x 0.873) + (8 x 1.015) + ( 2 x 0 . 4 5 8 ) mm2 = 16.02 mm2 C a l c u l a t i o n two - us ing shape f a c t o r 2 The su r f ace area of a p a r t i c l e = f s . L where f s i s the su r face area shape f a c t o r and L i s a length parameter. f s f o r c r y s t a l s i n the 1.7 - 2.0 mm s i z e range i s 3.922 ( P h i l l i p s , 1973) and L i s 2.02 mm. Sur face area o f one c r y s t a l = 3.922 x 2 .02 2 = 16.003 mm2 2 Hence, the average su r f ace area o f 15 c r y s t a l s = 240.3 mm = 2.40 cm 2 P l a t y NiSO^ a 6H 90 c r y s t a l s — i Area of one c r y s t a l = (l.b) + ( i V ) + 2 [ ^ ( 1 + T ) p ] + 2[>2(b + b')p] - 189 -C r y s t a l # 1. (mm) b (mm) 1" (mm) b' (mm) P (mm) Area of c r y s t a l (mm2) 1 3.25 2.76 3.13 2.97. 0.7 26.75 2 4.69 4.15 3.56 3.05 1.37 51.48 3 2.82 2.81 2.82 2.81 0.97 26.76 4 2.32 2.05 2.32 2.05 0.79 16.43 5 2.82 2.56 2.37 2.29 1.08 23.50 6 2.53 2.30 1.95 1.93 0.73 15.94 7 2.20 2.12 2.08 1.78 1.13 17.61 8 2.1.6 2.10 2.48 2.21 0.98 18.79 9 . 2.40 2.21 1.87 1.76 1.02 17.00 10 2.53 2.12 2.02 1.66 0.96 16.71 11 2.25 1 . 8 3 . 2.25 1.83 0.91 15.67 To ta l su r face area of 11 c r y s t a l s = 246.64 mm' = 2.47 cm 2 - 190 -A c i c u l a r NiSOy, a 6H o0 c r y s t a l s Area of one c r y s ta l = 2 (1 ..b) + 2(1 .b ' ) + 2 (b .b ' ) C r y s t a l # 1 (mm) b (mm) b' (mm) Area o f c r y s t a l (mm2) 1 9.76 2.26 1.80 87.40 2 7.73 2.03 1.72 64.95 3 6.26 1.05 0.98 27.48 - 191 -Octahedral KClP, c r y s t a l s a Area of one c r y s t a l = 4pg(a + b ) c ] + 4 [%.d.e ] C r y s t a l # a (mm) b (mm) c (mm) d (mm) e (mm) Area of one c r y s t a l (mm?) 1 1.57 2.50 1.11. 1.59 0.76 11.452. 2 1.78 2.88 1.26 1.75 0.85 14.718 3 2.44 3.56 1.28 1.93 0.97 19.104 4 1.94 2.77 1.09 1.56 0.78 12.702 5 2.14 3.34 1.45. 2.03. 1.00 19.952 6 1.77 2.49 0.90 1.25 0.57 9.093 7 2.30 3.48 1.42 2.15 1.08 " 21.059 8 2.43 3.35 1.17 1.73 0.83. 16.397 9 1.84 2.71 1.03 1.56 0.78 11.807 TO 1.58 2.22 1.08 1.39 0.70 10.154 Tota l su r face area of 10 c r y s t a l s = 146.44 mm' = 1.464 cm 2 - 192 -APPENDIX II The a c t i v a t i o n e n e r g i e s . f o r su r face (E p ) and t r an spo r t (E^) c o n t r o l l e d d i s s o l u t i o n , c a l c u l a t e d from the separated r a t e constants K p ( i n t e r c e p t va lues ) and K t ( c a l c u l a t e d at a g iven f low ra te ) g iven i n Table IV were determined from Eqn. 50: Kg rr Tg - T-| 1 0 9 l<7 = -27303R ( nrpLT } ( 5 0 ) where Kg and K-| are the r a te constants a t temperatures Tg and T-| and E i s the a c t i v a t i o n energy. K^ f o r the (111) and (112) faces a t the two tempera-tures were taken at u =1 .7 c m . s - 1 . At 4 1 ° , K t f o r the two faces a t u = 1.7 c m . s - 1 was c a l c u l a t e d (see s e c t i o n A.5 o f the r e s u l t s and d i s c u s s i o n ) . E r and E t f o r the (111) and (112) faces are g iven i n Table XXI I . The l a rge d i f f e r e n c e i n E r f o r the (111) and (112) faces conf i rms tha t the observed d i s s o l u t i o n an i so t ropy i s due to the d i f f e r e n c e i n magnitude between E p f o r the two faces . Values o f E t are s i m i l a r and s l i g h t l y h igher than the range u s u a l l y accepted f o r t r an spo r t processes. However, the p r e d i c t i o n o f the r a te c o n t r o l l i n g step of a r e a c t i o n from i t s a c t i v a t i o n energy i s not always r e l i a b l e (see s e c t i o n B.4 of the r e s u l t s and d i s c u s s i o n ) . E r va lues f o r the (111) and (112) faces are h igher than the corresponding E a va lues a t the high f low r a t e (see Table V ) . E t i s lower than E a a t the low f l ow r a t e (see Table V) w i th the except ion of E^ f o r the (112) f a c e . E a a t the low f low r a t e was c a l c u l a t e d us ing Eqn. 50 and gave va lues of 15.0 and 10.4 k c a l . m o l " 1 f o r the (111) and (112) faces r e s p e c t i v e l y . Comparison of these E a va lues w i t h E^ shows t ha t E t i s lower than E a f o r both the (111) and (112) f ace s . - 193 -Table XXII A c t i v a t i o n energ ies f o r t r an spo r t and su r face c o n t r o l l e d d i s s o l u t i o n f o r the (111) and (112) c r y s t a l faces of N i S 0 4 a 6 H 2 0 C r y s t a l face 1 _ i (kca l .mol ) ^ -i ( k c a l . m o l " ) (111) (112) 31.7 13.9 8.50 9.90 - 194 APPENDIX I I I De r i v a t i on of growth ra te Eqns. 5 and 6 Rearranging Eqns. 3 and 4, r t , „ * „ * 'k* S = (C* - C j ) (3) kjr V ( C i * " C s ) «> At steady s t a t e , r t = r g = r and, ( C - C . ) + ( c i - c s ) = ( C - c s ) Therefore , •j ~~c" + T^-c = (C* " C J k. S k S v s ' r = K S (C* - C s ) (5) where K i s the o v e r a l l growth r a t e constant and i s g iven by 

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