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Electronic defects as reaction intermediates in sodium chloride films Adams, Richard James 1963

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ELECTRONIC DEFECTS AS REACTION INTERMEDIATES IN SODIUM CHLORIDE FILMS by RICHARD JAMES ADAMS M.Sc, London U n i v e r s i t y , 1958 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY i n the Department of CHEMISTRY We accept t h i s t h e s i s as conforming t o the re q u i r e d standard THE UNIVERSITY OF BRITISH COLUMBIA October 1963 I n p r e s e n t i n g t h i s t h e s i s i n p a r t i a l f u l f i l m e n t 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 that 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 reference and study- I f u r t h e r agree that per-m i s s i o n f o r extensive copying of t h i s t h e s i s f o r s c h o l a r l y purposes may be granted by the Head of my'Department or by h i s representatives,, I t i s understood that copying or p u b l i -c a t i o n of t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission* Department of The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada, The U n i v e r s i t y of B r i t i s h Columbia FACULTY OF GRADUATE STUDIES PROGRAMME OF THE FINAL ORAL EXAMINATION FOR THE DEGREE OF DOCTOR OF PHILOSOPHY of , RICHARD JAMES ADAMS B.Sc, The Un i v e r s i t y of London, 1953 M.Sc, The Un i v e r s i t y of London, 1958 THURSDAY, DECEMBER 5, 1963, AT 2:30 P.M. IN ROOM 261, CHEMISTRY BUILDING COMMITTEE IN CHARGE Chairman: F.H. Soward N. B a r t l e t t L.G. Harrison W.A. Bryce L.W.. Reeves R.E. Burgess " J.R. Sams' G.G.S. Dutton E. Teghtsoonian External Examiner: F.C. Tompkins, F.R.S. Imperial College of Science and Technology London ELECTRONIC DEFECTS AS REACTION INTERMEDIATES IN SODIUM-CHLORIDE FILMS A B S T R A C T Evaporated films of radioactive sodium chloride have been prepared by d i r e c t sublimation onto a water cooled quartz substrate at 10~5 mm of mercury. These possess s p e c i f i c surfaces of from 30-100 m^/g and show remarkably high exchange r e a c t i v i t y to chlorine. From k i n e t i c studies using ^ C l incorporated i n the s o l i d i t has been found that the extent of ex-change C follows a f r a c t i o n a l power of the time C = a t n and that the rate i s independent of surface area, so that the p o s s i b i l i t y of the rate c o n t r o l l i n g step involving d i f f u s i o n i s ruled out. These features had been reported i n an e a r l i e r study but required confirmation with a wider range of s p e c i f i c surface and a modified procedure to measure surface area before reaction. The major part of the work i s designed to e l u c i -date the role of e l e c t r o n i c defects i n the exchange mechanism from the pressure and temperature depen-dence of the exchange rate and from the e f f e c t of introducing e l e c t r o n i c defects by X - i r r a d i a t i o n or f l u o r i d a t i o n . These l a t t e r processes cause the ki n e t i c s of the reaction to change completely to a second-order law, and provide strong evidence to support an e a r l i e r tentative suggestion that e l e c t -ronic defects are involved i n the reaction, and that a process of adsorption of a chlorine molecule into a pair of defects i s important. Detailed mechanisms are proposed for both the power law and the second-order reactions, l a r g e l y on the basis of the pressure dependence'. Both mechanisms use two species of e l e c t r o n i c defect, corresponding to Seitz's models for V2 and V 4 centres, and the "power law" mechanism requires a t r a n s i t i o n complex between the two defects. Measurements by X-ray d i f f r a c t i o n on the p a r t i c l e s i z e i n the evaporated films has shown them to be i n the range 250-500 A, and an estimate of the s t r a i n :< from the same r e s u l t s suggests that roughly one d i s l o c a t i o n per p a r t i c l e i s present. GRADUATE STUDIES F i e l d of Study: Chemistry Topics i n Physical Chemistry Topics i n Organic Chemistry Topics i n Inorganic Chemistry Surface Chemistry R.F. Snider J.A.R. Coope A.V. Bree R.E. Pincock D.E. McGreer J.P. Kutney N. B a r t l e t t , W.R. Cullen L.G. Harrison PUBLICATIONS Device to prepare sodium chloride of high r e a c t i v i t y and surface area by vacuum sublimation. R.J. Adams and L. G. Harrison, The Rev. of S c i . Instrum. Dec. 1963 Oxidation of the anion band in a l k a l i h a l i d e s . L. G. Harrison, R. J . Adams, M. D. B a i j a l and D. H. Bir d , accepted for p r o v i s i o n a l programme, 5th International Conference on the Re a c t i v i t y of Sol i d s , Munich, August 1964. - i i -Abstract Evaporated f i l m s of r a d i o a c t i v e sodium c h l o r i d e have been prepared by d i r e c t s u b l i m a t i o n onto a water cooled quartz substrate at 10"^ mm of mercury. These possess s p e c i f i c surfaces of from 30-100 m^/g and show remarkably high exchange r e a c t i v i t y to c h l o r i n e . 36 From k i n e t i c s t u d i e s using CI incorporated i n the s o l i d i t has been found that the extent of exchange C f o l l o w s a f r a c t i o n a l power of the time C = a t n and that the r a t e i s independent of surface area, so that the p o s s i b i l i t y of the r a t e c o n t r o l l i n g step i n v o l v i n g d i f f u s i o n i s r u l e d out. These features had been reported i n an e a r l i e r study but r e q u i r e d c o n f i r m a t i o n w i t h a wider range of s p e c i f i c surface and a modified procedure to measure surface area before r e a c t i o n . The major part of the work i s designed t o e l u c i d a t e the r o l e of e l e c t r o n i c defects i n the exchange mechanism from the pressure and temperature dependence of the exchange r a t e and from the e f f e c t of i n t r o -ducing e l e c t r o n i c defects by X - i r r a d i a t i o n or f l u o r i n a t i o n . These l a t t e r processes cause the k i n e t i c s of the r e a c t i o n t o change completely t o a second-order law, and provide strong evidence to support an e a r l i e r t e n t a t i v e suggestion that e l e c t r o n i c defects are i n v o l v e d i n the r e a c t i o n , and that a process of adsorption of a c h l o r i n e molecule i n t o a p a i r of defects i s important. D e t a i l e d mechanisms are proposed f o r both the power law and the second-order r e a c t i o n s , l a r g e l y on the b a s i s of the pressure dependence. Both mechanisms use two species of e l e c t r o n i c d e f e c t , corresponding t o - i i i -S e i t z ' s models f o r V2 and c e n t r e s , and the "power law" mechanism r e q u i r e s a t r a n s i t i o n complex between the two d e f e c t s . Measurements by X-ray d i f f r a c t i o n on the p a r t i c l e s i z e i n the o evaporated f i l m s has shown them t o be i n the range 250-500 A, and an estimate of the s t r a i n from the same r e s u l t s suggests that roughly one d i s l o c a t i o n per p a r t i c l e i s present. L. W. Reeves - x i i i -Acknowledgement s I should l i k e t o express my s i n c e r e thanks t o Dr. L. 6. H a r r i s o n f o r h i s ready enthusiasm and indispensable guidance throughout t h i s work. I should a l s o l i k e t o thank Professor C. A. McDowell f o r p r o v i d i n g generous departmental f a c i l i t i e s and Dr. J . T r o t t e r who k i n d l y made a v a i l a b l e the X-ray equipment r e q u i r e d . F i n a l l y , I am indebted t o H. R. MacMillan Esq., C.B.E., D.Sc, LL.D., who donated the award of a Queen E l i z a b e t h Scholarship f o r the year 1962-63. - i v -TABLE OF CONTENTS (a) T i t l e page. Page i (b) A b s t r a c t . i i (c) Table of Contents. i v (d) Acknowledgements. x i i i INTRODUCTION A. Previous Work on Gas/Solid Exchange Reactions. 1 B. Exchange i n Evaporated Films of Sodium C h l o r i d e . 4 C. Non-stoicheiometry i n A l k a l i H a l i d e C r y s t a l s . 5 D. Models and No t a t i o n f o r F and V cen t r e s . 7 E. Production of F and V-centres by X - i r r a d i a t i o n i n A l k a l i H a l i d e s . 10 F. Production of V-centres by doping i n A l k a l i H a l i d e s . 10 G. Evidence f o r E l e c t r o n i c Defects i n the KI / C I 2 O x i d a t i o n . 11 H. Objects of the present work. 12 EXPERIMENTAL A « O u t l i n e of Procedure. 15 B. Exchange Apparatus. 16 Exchange procedure. 16 C. Radiochemical Counting Equipment. 18 D. Evaporated F i l m Apparatus. 20 Procedure f o r a s u b l i m a t i o n . 23 E. B.E.T. Surface Area Measurements. 24 Apparatus. 26 Determination of Isotherm. 28 - V -Page F. S i n t e r i n g Procedure. 30 G. Halogen Handling System. 31 Chl o r i n e d r y i n g system. 33 F l u o r i n e handling system. 34 H. X - i r r a d i a t i o n Procedure. 36 I . Bleaching of X - i r r a d i a t e d F i l m s . 37 J . C a l i b r a t i o n s of Apparatus. 40 McLeod Gauge. 40 Dead space of adso r p t i o n system. 41 Ra d i o a c t i v e c a l i b r a t i o n s of sodium c h l o r i d e . 41 K. Volumes of Various Apparatus. 44 McLeod dead space. 44 Exchange apparatus, f l u o r i n e and c h l o r i n e bulbs. 44 RESULTS A. The Form of the Rate Law. 46 B. Power Law Reactions. 53 Untreated f i l m s . 53 Sin t e r e d f i l m s . 59 X - i r r a d i a t e d and bleached f i l m s . 60 C. Second Order Reactions. 62 X - i r r a d i a t e d f i l m s . 62 F l u o r i n a t i o n r e a c t i o n s . 66 - v i -Page DISCUSSION A. Evidence f o r Time-dependent Defect Concentrations. 73 B. E s s e n t i a l Features of an Explanation of the Power Law. 75 C. E l e c t r o n i c Defects i n the Exchange Mechanism. 75 D. Power Law Mechanism. 78 The nature of D^  and l>2' 78 Pressure dependence of a. 81 Exchange step and t r a n s i t i o n complex. 84 E. Mechanism of Second-order Reactions 85 F. Summary of Conclusions and Suggestions f o r Further Work 90 APPENDIX A P a r t i c l e S i z e and I n t e r n a l S t r a i n by X-ray D i f f r a c t i o n A. I n t r o d u c t i o n . 92 R e l a t i o n of ^ t o p a r t i c l e s i z e . 93 The measurement of s t r a i n . 93 B. Experimental. 95 Pr e p a r a t i o n of quartz p a r t i c l e s . 95 Pr e p a r a t i o n of sample of evaporated f i l m of sodium 95 c h l o r i d e . Counting techniques. 95 S t a t i s t i c a l counting e r r o r s . 96 Scanning procedure,. 96 Li n e width c o r r e c t i o n s . 98 C. Res u l t s and D i s c u s s i o n ; 101 The instrumental l i n e width b. 101 Sodium c h l o r i d e f i l m l i n e widths. 103 Tabulated r e s u l t s . 105 - v i i -Page APPENDIX B. Summary of Experimental R e s u l t s . 109 Tables X I I I - XVI. 111-114 B i b l i o g r a p h y . 115 - v i i i -LIST OF TABLES EXPERIMENTAL Table 1. Table I I . Table I I I . RESULTS Table IV. Table V. Table VI. Table V I I . APPENDIX A Table V I I I . Table IX. Table X. Table XI. Table X I I . C a l i b r a t i o n of the McLeod gauge. S p e c i f i c a c t i v i t y of the sodium c h l o r i d e f i l m s . Volumes of exchange system, f l u o r i n e and c h l o r i n e bulbs. The exchange.of c h l o r i n e w i t h sodium c h l o r i d e f i l m s at room temperature. C a l c u l a t i o n of a c t i v a t i o n energies at -5°to 25° and 25° - 60°C. Re s u l t s of s i n t e r i n g experiments on f i l m s of sodium c h l o r i d e . R e s u l t s f o r second-order r e a c t i o n s on X - i r r a d i a t e d and f l u o r i n a t e d f i l m s . Page 40 43 45 56 59 61 65 Quartz l i n e widths f o r CuK^ and MoK^ r a d i a t i o n . 103 F i l m I ; measured l i n e widths and <K doublet 107 c o r r e c t i o n s . F i l m I ; Jones shape c o r r e c t i o n and c a l c u l a t i o n 107 of s i z e (6 ) . F i l m I I ; Jones shape c o r r e c t i o n and c a l c u l a t i o n 107 of s i z e ( 6 ) . C a l c u l a t i o n s t o determine the apparent s t r a i n 108 - i x -Page APPENDIX B Table X I I I . Summary of r e s u l t s f o r untreated f i l m s . m Table XIV. Summary of r e s u l t s f o r s i n t e r e d f i l m s . 112 Table XV. Summary of r e s u l t s f o r X - i r r a d i a t e d f i l m s . 113 Table XVI. Summary of r e s u l t s f o r f l u o r i n a t e d f i l m s . 114 - X -LIST OF FIGURES P a B e INTRODUCTION Figure 1. Anio n i c a d s o r p t i o n at a semiconductor s u r f a c e . 3 Figure 2. The formation of V-centres during the o x i d a t i o n of sodium c h l o r i d e by f l u o r i n e . 6 Figure 3. The nomenclature f o r e l e c t r o n i c d e f e c t s . 9 EXPERIMENTAL Figure 4. Radiochemical exchange apparatus. 17 Figure 5. A t y p i c a l Geiger counter plateau. 19 Figure 6. Evaporated f i l m apparatus and f i l m c o l l e c t o r 21 Figure 7. Deviations of B.E.T. p l o t s from l i n e a r i t y . 25 Figure 8. Gas adso r p t i o n apparatus f o r surface area determination. 27 Figure 9. F i l m s i n t e r i n g furnace. 32 Figure 10. C h l o r i n e p u r i f i c a t i o n system. 35 Figure 11. Bleaching f i l t e r s f o r F and F* absor p t i o n . 39 Figure 12. C a l i b r a t i o n apparatus f o r s p e c i f i c a c t i v i t y determination. 42 RESULTS Figure 13. Log-log p l o t s t o show the "power law" C = a t n f o r se v e r a l r e a c t i o n s at 25°C. 47 Figure 14. Second order p l o t f o r an X - i r r a d i a t e d f i l m . 48 Figure 15. Second order p l o t f o r a f l u o r i n a t e d f i l m . 49 Figure 16. N o n - l i n e a r i t y of the "power law" p l o t f o r an X - i r r a d i a t e d f i l m , and r e v e r s i o n t o the power law on b l e a c h i n g . 51 x i -Page Figure 17. D e v i a t i o n from the "power law" as e q u i l i b r i u m i s approached. 52 Figure 18. Successive exchange of a f i l m w i t h two gas samples. 54 Figure 19. L i n e a r p l o t showing extent of r e a c t i o n i n r e l a t i o n to surface area. 55 Figure 20.(a)Absence of f u n c t i o n a l r e l a t i o n of a w i t h s p e c i f i c s urface. 57 (b)Dependence of a on pressure. 57 Figure 21. Pressure dependence of a at -5°, 25° and 60°C. 58 Figure 22. ( a ) P l o t of second order r a t e constant (kj^) against c h l o r i n e pressure. 63 (b) & (c) F r a c t i o n exchanged /C e' p l o t t e d against the delay time. . 63 Figure 23. F l u o r i n a t i o n of sodium c h l o r i d e at d i f f e r e n t f l u o r i n e pressures. 67 Figure 24. P l o t of a f l u o r i n a t i o n showing e f f e c t of c i r c u l a t i o n time i n r e a c t i o n v e s s e l . 68 Figure 25. Ch l o r i n e exchange s t a r t e d 1 and 5 minutes a f t e r f l u o r i n a t i o n . 69 Figure 26. Exchange s t a r t i n g 5 minutes a f t e r f l u o r i n a t i o n : i n d u c t i o n p e r i o d . 71 Figure 27. Exchange s t a r t i n g f i v e minutes a f t e r f l u o r i n a t i o n : a c c e l e r a t i n g r e g i o n . 72 - x i i -DISCUSSION Figure 28. Figure 29. APPENDIX A. Page Pos t u l a t e d concentration-time behaviour of r e a c t i o n 80 intermediates. F i n a l stages i n the t r a n s f e r of a r a d i o a c t i v e c h l o r i n e 86 atom from bulk t o surface. Figure 30. C a l c u l a t i o n of h a l f - h e i g h t l i n e width from a. sodium 97 c h l o r i d e (222) l i n e p r o f i l e . Figure 31. Experimental sodium c h l o r i d e l i n e p r o f i l e compared 99 - ? 2 to the Gaussian f u n c t i o n exp(-k*x ). Figure 32. Comparison of the Instrumental p r o f i l e quartz (202) 100 l i n e w i t h a Cauchy p r o f i l e . F igure 3 3 . ( a ) V a r i a t i o n of instrumental l i n e width b w i t h Bragg 102 angle. ( b ) C a l c u l a t i o n of £ f o r f i l m I. 102 Figure 34. Sodium Ch l o r i d e f i l m I I and Quartz l i n e widths at 104 two d i f f e r e n t wave lengths. Figure 35. P l o t s to determine the apparent s t r a i n >\. 106 INTRODUCTION A. Previous Work on Gas/Solid Exchange Reactions The exchange of atoms of a common c o n s t i t u e n t between the gas phase and the s o l i d surface was b r i e f l y reviewed (1) by Roberts and Anderson i n 1952. However, both e a r l y observations (2, 3) and the d e t a i l e d work i n the e a r l y f i f t i e s by Winter (4, 5, 6) on the exchange of oxygen w i t h t r a n -s i t i o n metal oxides has provided much phenomenological i n f o r m a t i o n but no d e t a i l e d mechanism. His general conclusions were t h a t : -( i ) the exchange process could be analysed k i n e t i c a l l y i n t o an i n i t i a l r a p i d f i r s t order exchange process followed by a much slower exchange i n the b u l k , ( i i ) that the adso r p t i o n of oxygen at the surface destroys defects (but the type of defect concerned was not s p e c i f i e d ) . For the i n t r i n s i c semi-conductors stu d i e d one would expect a high a c t i v a t i o n energy of adsorption at room temperature s i n c e the process 2e + \ 0 2 -» 0 2" re q u i r e s the removal of e l e c t r o n s from the valence band t o a region out-side the s o l i d surface ( 7 ) . However, the process c o u l d occur at lower energies i f the adsorbed oxygen were incorporated i n t o the surface w i t h d e s t r u c t i o n of defects already present i n the s u r f a c e ^ s u c h as the chemi-s o r p t i o n of oxygen on cuprous oxide (8) and cobalt oxide (9)» I t i s a l s o p o s s i b l e that d i s l o c a t i o n s play an important part i n f a c i l i t a t i n g i n c o r p o r a t i o n by the a n n i h i l a t i o n of c a t i o n vacancies at the po i n t s of emergence of d i s l o c a t i o n s r e s u l t i n g i n a higher oxygen-containing phase i n these regions (10). I t has been pointed out that the ready transference of e l e c t r o n s i s p o s s i b l e i n the presence of a no n - s t o i c h i o m e t r i c phase c o n t a i n i n g donor - 2 -l e v e l s ( 1 ) ; the r a i s i n g of the Fermi l e v e l w i l l decrease the a c t i v a t i o n energy E a (see Figure 1 ) . Winter has suggested that defect dependent r e a c t i o n s i n t o the b u l k of the s o l i d are more l i k e l y t o occur i n compounds of v a r i a b l e valency where non-stoichiometry i s known to e x i s t , such as i n the t r a n s i t i o n metals. The r e l a t i v e s i m p l i c i t y of a l k a l i metal h a l i d e s from the view point of defect s t r u c t u r e (12) and the thermodynamic data a v a i l a b l e are obvious reasons f o r choosing them as the s o l i d phase i n any exchange process. As w i t h oxides i t i s t o be expected from surface e n e r g e t i c s that exchange would take place only at r a t h e r h i g h temperatures. However, experimental evidence (13) showed that l i k e the oxides, a r a p i d surface exchange at low temperatures occurred, followed by a slower extension of the process i n t o the b u l k , i n d i c a t i n g (14) that s t r u c t u r a l i r r e g u l a r i t i e s must be present at l e a s t i n the surface l a y e r i t s e l f and p o s s i b l y over a more extensive r e g i o n . The experimental r e s u l t s showed that the a c t i v a t i o n energy of the i n i t i a l exchange r e a c t i o n must be approximately zero, whereas the minimum exchange energy c a l c u l a t e d (15) f o r an i d e a l surface was 2.5 e.V.. Burton, Cabrera and Frank (16) showed by s t a t i s t i c a l thermo-dynamics that low index faces d i s o r d e r only at very h i g h temperatures; but Cabrera suggested (17) that d i s o r d e r i n g may occur at low temperatures i f there i s strong adsorption on the surface. The o r i g i n a l purpose of the work on f i l m s of sodium c h l o r i d e evaporated i n vacuo (18) was t o attempt to avoid surface d i s o r d e r i n g by adsorption of atmospheric gases. The r e s u l t s , discussed i n s e c t i o n B of t h i s i n t r o d u c t i o n were not what had been expected. - 3 -Figure 1. A n i o n i c Adsorption at a Semiconductor Surface. F i g . 1(a) TJ Valence band 0 Conduction band F i g . K b ) // Fermi l e v e l Donor l e v e l \//x y/\ j Valence band F i g . 1(c) band The a c t i v a t i o n energy E a of a n i o n i c adsorption on a semiconductor of work f u n c t i o n 0: (a) Adsorption outside the surface of a pure i n t r i n s i c semiconductor: high E a > (b) Adsorption outside the surface of a n o n - s t o i c h i o m e t r i c phase w i t h donor l e v e l s : E a decreased by decrease of 0. (c) Adsorption i n , r a t h e r than o u t s i d e , the surface of the pure semiconductor: E a reduced because e l e c t r o n never leaves l a t t i c e completely. - 4 -B. Exchange i n Evaporated Films of Sodium C h l o r i d e I t had been expected that the avoidance of surface contamination by vacuum evaporation of sodium c h l o r i d e would g r e a t l y reduce the r a t e of the room temperature exchange or suppress i t a l t o g e t h e r . By c o n t r a s t , the r e s u l t s and conclusions of the f i r s t study on evaporated f i l m s (19) were as f o l l o w s : -( i ) the exchange at room temperature was much more r a p i d than i n any previous experiments. ( i i ) the exchange of surface and bulk were not k i n e t i c a l l y separate. ( i i i ) the exchange of the whole s o l i d obeyed an unusual k i n e t i c law of the form, C = a t n where C i s the amount exchanged and t i s the time. (Iv) the constant a c o r r e l a t e d w i t h mass and not w i t h the surface area of the s o l i d , (v.) i t was concluded that the rate-determining steps of the r e a c t i o n take place i n the bulk of the s o l i d phase; n e i t h e r the surface exchange nor d i f f u s i o n to the surface i s r a t e -c o n t r o l l i n g , s i n c e both of these would c o r r e l a t e w i t h surface area. ( v i ) the unusual r a t e law i m p l i e s (once d i f f u s i o n has been e l i m i n -ated) that the concentrations of defects i n the s o l i d are time dependent. More s p e c i f i c a l l y , the law appeared t o show that the r e a c t i o n i s s e l f i n h i b i t e d by the b l o c k i n g of vacancies by c h l o r i n e atoms or molecules taken up from the gas phase. - 5 -( v i i ) on t h i s b a s i s , a t e n t a t i v e mechanism was devised (20) which i n v o l v e d a s t o i c h i o m e t r i c excess of c h l o r i n e i n the s o l i d phase, i . e . , the type of e l e c t r o n i c defect known c o l l e c t i v e l y as V-centres. This mechanism served t o i l l u s -t r a t e i n general terms the type of r e a c t i o n steps which must be i n v o l v e d , but was very s p e c u l a t i v e i n d e t a i l . C. / Non-Stoichiometry on A l k a l i H a l i d e C r y s t a l s O p t i c a l a b s o r p t i o n bands i n d i c a t i n g the presence of e l e c t r o n i c de-f e c t s are observed when a l k a l i h a l i d e c r y s t a l s are heated i n e i t h e r a l k a l i metal or halogen vapour (21). The "F-centres" and "F'-centres" absorbing i n the v i s i b l e and a s s o c i a t e d w i t h a l k a l i metal excess, are of p r e c i s e l y known s t r u c t u r e . The nature of the "V-centres", absorbing i n the U.V. and a s s o c i a t e d w i t h halogen excess, i s much l e s s d e f i n i t e l y known (22). F-centres and V-centres can a l s o be produced simultaneously i n the same c r y s t a l by X - i r r a d i a t i o n (12). This i s the c h i e f way i n which V-centres have been produced i n a l k a l i c h l o r i d e s , i n which doping w i t h c h l o r i n e does'not produce o p t i c a l l y d etectable concentrations of V-centres ( i n marked co n t r a s t t o the behaviour of bromides and i o d i d e s ) . Recent work i n t h i s l a b o r a t o r y , concurrent w i t h the s t u d i e s reported on i n t h i s t h e s i s , has shown that V-centres can be produced i n o p t i c a l l y d e tectable concentrations by chemical o x i d a t i o n of s i n g l e c r y s t a l s of potassium i o d i d e and sodium c h l o r i d e at room temperature. The oxidants used are gaseous c h l o r i n e and f l u o r i n e r e s p e c t i v e l y (23). (See Figure 2.) 70 ft i8 ft 35 50 55 58 Figure 2. The Formation of V-centres during the Oxidation of Sodium C h l o r i d e by F l u o r i n e . (from unpublished work of Harrison and B i r d i n t h i s l a b o r a t o r y ) - 7 -D. Models and Notation f o r F- and V-centres. The F-centre; when a c r y s t a l i s heated i n the presence of a l k a l i metal vapour and quenched, a s i n g l e o p t i c a l a bsorption band, the F band, i s found (21). The excess of a l k a l i metal ions i s incorporated i n the c r y s t a l and causes the formation of anion vacancies i n which the excess e l e c t r o n s are trapped (22), and the F-centre i s a vacancy c o n t a i n i n g one e l e c t r o n . The s t r u c t u r e of the F-centre has been confirmed unequivocally and s t u d i e d i n d e t a i l by para-magnetic resonance (24). The F'-centre; i f the F band i s bleached by r a d i a t i o n of a some-what sho r t e r wavelength than the F band maxima then a new band designated F 1 i s formed on the low energy s i d e of the F band. The e f f e c t of i r r a -d i a t i o n appears t o be t o e j e c t one e l e c t r o n from i t s anion vacancy t r a p to be captured by another F-centre. The F*-centre i s thus two e l e c t r o n s (with p a i r e d spins) trapped at a s i n g l e anion vacancy (25). V-centres The F-centre may be thought of as a r i s i n g from e l e c t r o s t a t i c i n t e r -a c t i o n of an e l e c t r o n w i t h the f i e l d of an anion vacancy ;-r> s i m i l a r l y , e a r l y attempts t o e x p l a i n the s e v e r a l U.V. absorption bands observed on halogen doping or X - i r r a d i a t i o n p o s t u l a t e d e l e c t r o s t a t i c a t t r a c t i o n of a hole t o a c a t i o n vacancy (12). However, a hole thus l o c a l i s e d converts an i anion t o a i n e u t r a l halogen atom, w i t h power t o bond c o v a l e n t l y t o i t s neighbours; and more recent work (26) has focussed a t t e n t i o n on t h i s covalent bonding. I t has not yet proved p o s s i b l e t o e l u c i d a t e d e f i n i t e l y the s t r u c t u r e s of most of the V-centres producing important o p t i c a l absorption bands. S e i t z ' s s t r u c t u r e s may s t i l l be used w i t h the r e s e r -- 8 -v a t i o n that a hole may be a s s o c i a t e d w i t h two or more c o v a l e n t l y bonded halogen atoms, while two holes trapped together c o n s t i t u t e (as S e i t z recognised) a d i s s o l v e d halogen molecule. The n o t a t i o n used by S e i t z i s too cumbersome when i t becomes necessary t o w r i t e a chemical equation i n c l u d i n g V-centres as reagents or products. A new n o t a t i o n has t h e r e f o r e been proposed by H a r r i s o n (27) which w i l l be used throughout t h i s treatment. The two n o t a t i o n s are summarised i n Figure 3. In Harrison's n o t a t i o n , the customary i o n s i g n i s omitted f o r an i o n on i t s proper s i t e . I f these signs are replaced by the s u f f i c e s (a) and (c) f o r an i o n and c a t i o n r e s p e c t i v e l y , then V-centres acquire super-s c r i p t s which represent the number of trapped p o s i t i v e h o l e s . The untrapped hole i s designated X ( a ) \ where X(a) i s the h a l i d e i o n . Thus the s e l f - t r a p p i n g of two holes i n potassium i o d i d e t o form a t r i h a l i d e i o n could be w r i t t e n Anion and c a t i o n vacancies are shown as a and c w i t h ac f o r the vacancy p a i r ; e.g., f o r the t r a p p i n g of a p o s i t i v e hole in-~an a l k a l i c h l o r i d e t o give S e i t z ' s model (12) of a V. centre I t i s seen that the l e t t e r s i n the two brackets s p e c i f y the t o t a l s of anion and c a t i o n s i t e s occupied by the V-centre complex. In t h i s terminology, the F-centre must be shown as a and the F' centre as a", s i n c e the former i s a vacant anion s i t e w i t h no change. - 9 -Figure 3. Nomenclature f o r E l e c t r o n i c Defects. Defect F S e i t z ' s Models Harrison's Notation (a) <v2> o o -f-C l ( a ) 2 (C 2) * 6 C l ( a ) + ( c ) -(H) O CI(a) (ac) (v 3 ) C l ( a ) + ( c 2 ) = C l ( a ) + ( a O - 10 -E. Production of F- and V-centres by X - i r r a d i a t i o n In A l k a l i H a lides Free e l e c t r o n s and holes may be produced i n a l k a l i h a l i d e s by i r r a -d i a t i n g them w i t h X-rays. The d e n s i t y of the F-centres r i s e s monotoni-c a l l y w i t h i r r a d i a t i o n and e v e n t u a l l y reaches a s a t u r a t i o n value c h a r a c t e r i s -t i c of the temperature and i n t e n s i t y of the r a d i a t i o n (28). The presence of V bands a r i s i n g from X - i r r a d i a t i o n has confirmed (29, 30) the r e s u l t s obtained by doping w i t h excess halogen (21). I t was shown that at room temperature only the V 2 and Vg bands are s t a b l e . and bands obtained at l i q u i d n i t r o g e n temperature were shown (31) to disappear on warming t o -100°C. Thus the and bands are not present i n specimens i r r a d i a t e d at room temperatures (12). I t i s appropriate t o mention here that e l e c t r o n s f r e e d from F-centres at room temperature by the use of F l i g h t b leach V 2 centres w i t h h i g h e f f i c i e n c y (12), converting them t o V3 centres: C l ( a i ) 2 " H " ( c 2 ) = + a _ > a + + C l ( a ) + ( c 2 ) * + C l ( a ) (v 2 ) (v 3 ) However, Vg centres w i l l r e s i s t f u r t h e r r e d u c t i o n , presumably because they are n e g a t i v e l y charged. F. Production of V-centres by Doping i n A l k a l i Halides The presence of V-centres i n a l k a l i bromides (33) and iod i d e s (21, 34, 35) by a d d i t i v e c o l o u r a t i o n i s w e l l known. However, i t has not been p o s s i b l e t o form V-centres i n a l k a l i c h l o r i d e s and f l u o r i d e s i n t h i s manner (21) i n s i n g l e c r y s t a l s . Their presence i n f i l m s of sodium c h l o r i d e evaporated i n c h l o r i n e gas has been detected by o p t i c a l a b s o r p t i o n s t u d i e s (36). I t has been suggested that the p r i n c i p a l requirement i s a s u f f i c i e n t number of the appropriate vacant l a t t i c e s i t e s i n the f i l m s . Straumanis (37) 18 3 found a l a r g e c o n c e n t r a t i o n of vacancies (^3.10 /cm ) i n f i l m s of sodium c h l o r i d e prepared by evaporation: S e i t z estimated the number 18 3 of defects i n evaporated sodium c h l o r i d e l a y e r s as 10 /cm (32). G. Evidence f o r E l e c t r o n i c Defects i n the KI / C I 2 O x i d a t i o n The a n i o n i c o x i d a t i o n of potassium i o d i d e has been st u d i e d r e c e n t l y (38) i n t h i s l a b o r a t o r y and a mechanism proposed based on the formation of V-centres i n the bul k . The experimental approach was d i f f e r e n t from the f l u o r i n a t i o n s t u d i e s , the r e a c t i o n being followed c h i e f l y by measuring e l e c t r i c a l c o n d u c t i v i t y , and the a l k a l i h a l i d e samples being powders or pressed p e l l e t s ( u s u a l l y prepared from s o l u t i o n - p r e c i p i t a t e d p a r t i c l e s i n the s i z e range 3-19/-*.). The f o l l o w i n g are the p r i n c i p a l features of the r e s u l t s : -( i ) the c o n d u c t i v i t y of pressed p e l l e t s always increases at the s t a r t of the r e a c t i o n . This increase may be i o n i c or e l e c t r o n i c depending on the value of the i n i t i a l c o n d u c t i v i t y . P o s i t i v e hole conduction r e s u l t s from the i n i t i a t i o n of a n u c l e a t i o n process, w h i l e i o n i c conduction occurs without n u c l e a t i o n , above a c r i t i c a l i n i t i a l c o n d u c t i v i t y , ( i i ) o x i d a t i o n s of s i n g l e c r y s t a l s produces V bands which are b e l i e v e d (22) t o a r i s e from a l i n e a r t r i - i o d i d e i o n i n which two p o s i t i v e holes are trapped together. The accompanying changes i n c o n d u c t i v i t y are s i m i l a r to those observed f o r high r e s i s t a n c e p e l l e t s . To account f o r these phenomena i t i s supposed that o x i d a t i o n at - 12 -the surface produces p o s i t i v e holes i n the valence band and demands a supply of c a t i o n s , so that currents of both p o s i t i v e holes and c a t i o n vacancies are e s t a b l i s h e d from surface t o b u l k . The growth i n con-ductance and i t s subsequent second order decay i s accounted f o r by the formation of the l i n e a r t r i - i o d i d e i o n 1 ^ ) 3 (c) by the r e a c t i o n , 2 l ( a ) + + 1(a) + c- _>l|;a) "•"•"(<;)" I I a and i t s d e s t r u c t i o n t o form the species I ( a ) g ( c 2 ) thus, i C a ^ C c ) ' + c" _ > T ( a ) 3 + + ( c 2 ) = The r a t e s of these r e a c t i o n s are c o n t r o l l e d by the c a t i o n vacancy concentrations i n the b u l k . H. Objects of the Present Work The f i r s t object was the p r e p a r a t i o n of f i l m s of sodium c h l o r i d e of high s p e c i f i c s u r f a c e . P r e v i o u s l y , sodium c h l o r i d e f i l m s w i t h a h i g h s p e c i f i c surface of the order of 20 m /g have been prepared (39, 40) by s u b l i m a t i o n i n a current of dry n i t r o g e n at atmospheric pressure. How-ever, only the surface l a y e r was a c c e s s i b l e t o i s o t o p i c exchange w i t h a gaseous phase at room temperature (15). While f i l m s prepared at 10 ^ mm of mercury showed high bulk r e a c t i v i t y t o exchange (19), the measured surface areas were low, being of the order of 0.5-8 m /g. An unfortunate feature of these l a t t e r r e s u l t s was that the surface areas could be measured only a f t e r the exchange r e a c t i o n had been completed and that s i n t e r i n g might have occurred during the exchange r e a c t i o n or subsequent handling of the f i l m . Rudham (18) has r e c e n t l y shown that c h l o r i n e and HC1 do cause s i n t e r i n g of NaCl f i l m s at room temperature - 13 -although the e f f e c t w i t h Clg seems t o be r a t h e r s m a l l . I n the present work attempts t o prepare m a t e r i a l f r e e from gaseous contamination of the surface have been abandoned. The p r e p a r a t i o n of a hig h s p e c i f i c surface f i l m possessing bulk r e a c t i v i t y i n ordinary h i g h vacua of the order of 10"^ mm of mercury has been achieved and the apparatus so designed that the t o t a l surface area could be determined and the s p e c i f i c surface area approximately c a l c u l a t e d before the exchange r e a c t i o n was begun. Secondly, the l a c k of c o r r e l a t i o n of the parameter a i n the l o g -r i t h m i c r a t e equation w i t h the s p e c i f i c surface was t o be confirmed. High s p e c i f i c area f i l m s and the d i r e c t measurement of the surface area of the m a t e r i a l prepared and s t o r e d under vacuum c o n d i t i o n s made t h i s p o s s i b l e . T h i r d l y , a more d e t a i l e d i n v e s t i g a t i o n of the k i n e t i c s of the exchange process was r e q u i r e d . I t i s p o s s i b l e t o r e l a t e both a and n i n the r a t e equation to the various r a t e constants of the r e a c t i o n steps i n any proposed mechanism. In p a r t i c u l a r , the pressure dependence of a i s a most important f a c t o r , s i n c e , f o r example, d i r e c t pressure de-pendence would i n f e r molecular V-centres and square-root dependence atomic V-centres ( i n e q u i l i b r i u m w i t h the gas phase) as r e a c t i o n i n t e r -mediates. F i n a l l y , (and most important) the e f f e c t s of the d e l i b e r a t e i n t r o -d u c t i o n of e l e c t r o n i c defects i n t o the s o l i d by X - i r r a d i a t i o n and f l u o r i n a t i o n before the exchange was d e s i r a b l e i n order t o o b t a i n more d i r e c t i n f o r m a t i o n on the r o l e of these defects i n the process. - 14 -Although a considerable amount of i n f o r m a t i o n i s a v a i l a b l e on the X-ray method of making e l e c t r o n i c d e f e c t s , the value of t h i s approach f o r the present purpose i s somewhat v i t i a t e d by the f a c t that both e l e c t r o n excess and d e f i c i e n t centres are formed c o n c u r r e n t l y . This complicates the subsequent i n t e r p r e t a t i o n by a v a r i e t y of p o s s i b l e i n t e r a c t i o n s . O x idation of the anion band by f l u o r i n e however should r e s u l t only i n V-centres; t h i s i s supported by the r e l a t e d work on the o x i d a t i o n potassium i o d i d e by c h l o r i n e , described above and the spectro-scopic observations on the o x i d a t i o n of sodium c h l o r i d e by f l u o r i n e . The k i n e t i c s of the f l u o r i n e r e a c t i o n on f i l m s were, however, unknown and t h e r e f o r e r e q u i r e d considerable p r e l i m i n a r y i n v e s t i g a t i o n s before t h i s method proved a p p l i c a b l e . EXPERIMENTAL - 15 -A. O u t l i n e of Procedure The vacuum apparatus used f o r the study of c h l o r i n e exchange r e -a c t i o n s was developed from that reported i n the previous s t u d i e s on f i l m s (19). Novel features were, however, introduced i n order to a l l o w ( i ) the surface area of the f i l m to be measured before the exchange ( i i ) X - i r r a d i a t i o n , b l e a c h i n g and s i n t e r i n g to be a p p l i e d to the f i l m sealed under vacuum and ( i i i ) the f i l m t o be introduced a f t e r these treatments i n t o the exchange system under hig h vacuum. The procedure c o n s i s t e d of the f o l l o w i n g steps; ( i ) preparation of the evaporated f i l m which i s completed when the c o l l e c t o r i s flame sealed at E (Figure 6 ) . ( i i ) the determination of the'surface area by krypton adsorption ( 7 ) , the adsorbate being subsequently pumped o f f l e a v i n g the f i l m i n the c o l l e c t o r which i s then sealed o f f again at F (Figure 6 ) . ( i i i ) any f u r t h e r treatments of the f i l m p r i o r t o the exchange, i . e . X- i r r a d i a t i o n or s i n t e r i n g , ( i v ) i n t r o d u c t i o n of the f i l m i n t o the exchange apparatus at the ground glass j o i n t 3 (see Figure 4) before the f i n a l prepa-r a t i o n s f o r the exchange r e a c t i o n , (v) On completion of the exchange r e a c t i o n the halogens were c a r e f u l l y pumped o f f , the system opened at the ground g l a s s j o i n t 5 (Figure 4) and the r e s i d u a l f i l m washed out i n t o a 250 ml. standard f l a s k w i t h s e v e r a l washings of water. Depending on the r e a c t i o n s s t u d i e d t h i s i s analysed f o r f l u o r i d e as l e a d c h l o r o f l u o r i d e or g % a v l r a e t r i c a l l y as c h l o r i d e ( 4 1 ) - 16 -and the t o t a l weight of the o r i g i n a l f i l m thus c a l c u l a t e d , B. Exchange Apparatus The exchange apparatus i s shown i n Figure 4, This apparatus i s so designed as t o a l l o w f l u o r i n e and c h l o r i n e t o exchange w i t h the r a d i o a c t i v e sodium c h l o r i d e f i l m s being s t u d i e d , the r e a c t i o n being followed by the radiochemical d e t e c t i o n of ^ C l l i b e r a t e d i n t o the gas phase. The r e a c t i o n v e s s e l c o n s i s t s of the lower limb X, bounded by the two v e r t i c a l s i d e arms and the upper h o r i z o n t a l counting chamber Y. The l a t t e r contains a gas f i l l e d geiger counter (R.C.L. model 10312) spot welded t o the platinum leads I , and t o the tungsten-to-glass s e a l s B. The s o l i d t o be s t u d i e d l i e s i n the t h i n - w a l l e d glass bulb F introduced i n t o the lower limb by the B.19 ground g l a s s j o i n t connection 3. The con-v e c t i o n heater c o i l C of nichrome (10 watts) i s lagged w i t h asbestos t o c i r c u l a t e the r e a c t i o n products t o the counter; the c i r c u l a t i o n time measured i n a separate experiment was found to be approximately one minute (see Figure 24). The g l a s s storage bulbs G and H c o n t a i n c h l o r i n e and f l u o r i n e r e s p e c t i v e l y . A l l taps and j o i n t s are sealed w i t h e i t h e r s i l i c o n e (Dow Corning) or KEL-F No. 90 grease. The l a t t e r was found i n the presence of f l u o r i n e to r e q u i r e frequent i n s p e c t i o n and- replacement due t o i t s tendency t o 'streak' on l i q u e f y i n g . Exchange Procedure The bulbs G and H are f i l l e d w i t h dry c h l o r i n e and f l u o r i n e at the r e q u i r e d pressure, through the ground j o i n t M of the gas handling apparatus (Figure 10). The system i s then removed from the gas h a n d l i n g apparatus and the upper envelope c o n t a i n i n g the geiger tube i s placed i n a l e a d Y A Z B 0 5 10 15 cm. • 1 i i ( f o r n o t a t i o n key see t e x t ) Figure 4. Radiochemical Exchange Apparatus. - 18 -c a s t l e , the geiger leads are connected t o the decade s c a l e r (Nuclear i Chicago Model 151 A) and the background count determined u s u a l l y f o r 30 minutes. The apparatus i s evacuated f o r a f u r t h e r 30 minutes when stopcock 6 (Figure 4) i s c l o s e d . By t i l t i n g the whole system the t h i n g l a s s bulb F, h o l d i n g the f i l m i s broken by the s l i d i n g g l a s s plunger E; considerable care being taken t o keep the f i l m between the two v e r t i c a l sidearms, otherwise a h i g h background count i s obtained. I f the r e a c t i o n i s t o be performed i n the dark a l l l i g h t i s e l i m i n a t e d from the i n t e r i o r by covering the outside w i t h aluminium f o i l at l e a s t t o (boundary shown dotted i n Figure 4) stopcocks 1, 2 and 6. The apparatus i s f i n a l l y reassembled i n the lea d c a s t l e , connected to the s c a l e r and the convection heater switched on. To commence the exchange stopcock 1 ( f o r Cl£ admission) i s opened f o r a few seconds and then c l o s e d . The gas phase a c t i v i t y i s subsequently recorded, u s u a l l y at one minute i n t e r v a l s at f i r s t , then up t o periods of 60 minutes f o r the course of the r e a c t i o n which may l a s t s e v e r a l days. C. Radiochemical Counting Equipment The Nuclear Chicago model 151A. decade s c a l e r c o n s i s t s of a d i s -c r i m i n a t o r , two plug i n decade s c a l e r c i r c u i t s , a r e g i s t e r d r i v e r c i r c u i t , an electromechanical r e g i s t e r , an e l e c t r o n i c a l l y r e g u l a t e d h i g h voltage power supply and a low voltage power supply. The R.C.L. model 10312 geiger tube has a normal p l a t e a u range of 900-1100 v o l t s . These are i n d i v i d u a l l y checked; however aging occurs (42) and a l s o the E.H.T. v o l t -meter readings on a s c a l e r may be up t o 100 V. i n e r r o r . Therefore at p e r i o d i c i n t e r v a l s a short p l a t * a u check was performed to determine the - 20 -optimum operating v o l t a g e . This was achieved by ( i ) e s t a b l i s h i n g the s t a r t i n g p o t e n t i a l and ( i i ) r a i s i n g the E.H.T. voltage by 20 v o l t steps t a k i n g counts from some standard source u n t i l the counting r a t e s t a r t s t o increase r a p i d l y . The ope r a t i n g voltage i s then 50 v o l t s above the lower 'knee* of the p l a t e a u . A t y p i c a l curve f o r such a c a l i b r a t i o n i s shown i n Figure 5. A l l recorded counts have been c o r r e c t e d f o r background and f o r coincidence l o s s (42) at counting r a t e s exceeding 1 0 4 counts per minute (c.p.m.) The c o r r e c t i o n i s based on the assumption that the dead time equals (n.T) minutes during each minute; where n i s the recorded 60 count r a t e i n counts per minute and T i s the dead time (42) of 200 micro-seconds f o r such a s e l f quenching system, i . e . f o r 1 0 4 c.p.m. % of counts l o s t = n.T x 100 60 10 4.2.10" 4 .100 60 3*37. No. of counts l o s t 3J3. »10 4 = 330 c.p.m. 100 Corrected count r a t e = 10,330 cpm. D. Evaporated F i l m Apparatus D e t a i l s of t h i s apparatus are shown i n Figure 6. The sodium c h l o r i d e f o r s u b l i m a t i o n i s h e l d i n the si d e arm A of the main v e s s e l B which con-t a i n s the c y l i n d r i c a l water cooled condenser C. The pa r t s A, B and C are constructed of quart z . At D there i s a graded s e a l to the pyrex r e c e i v e r system, i n order that the two c o n s t r i c t i o n s E and F may be e a s i l y - 21 -Figure 6. Evaporated F i l m Apparatus and F i l m C o l l e c t o r evaporator at the B.10 j o i n t ) - 22 -sealed o f f i n the subsequent handling of the sublimate. The support 6 f o r the metal scraping arm H may be of pyrex or soda-glass. The arm H i s of m i l d s t e e l ; at the upper end I , a t h i n n i c k e l sleeve i s f i t t e d c l o s e l y over the arm H and spot welded t o i t , and the scraper blade of 0.008 i n c h t h i c k platinum f o i l i s attached t o the n i c k e l sleeve by wrapping i t round s e v e r a l times and spot welding. The blade should meet the quartz condenser surface at about 45°. At J , the g l a s s i s c o l l a p s e d onto the rod H t o give a c l o s e f i t which l o c a t e s the rod pre-c i s e l y but there i s no m e t a l - t o - g l a s s s e a l . I f G i s made of soda g l a s s , a n i c k e l sleeve over-wound w i t h platinum f o i l may be used at J to ensure c o m p a t i b i l i t y of metal and g l a s s i f any s e a l i n g happens to take p l a c e . A hole i s blown at K to ensure complete evacuation of G and avoid slow pumping out through J , but the apparatus i n i t i a l l y l a c k e d t h i s p r e c a u t i o n . The d e t a i l e d arrangement of heaters on the s i d e arm i s very important. The three heaters L, M and N are a l l of Chrome1 A: (20 s.w.g. 4<ft>/ft.). L i s operated at the minimum temperature which w i l l g i v e a reasonable r a t e of s u b l i m a t i o n : N needs t o be about the same temperature as L i n order t o prevent condensation on the outer w a l l of the v e s s e l B w h i l e m i n i m i s i n g the very h i g h temperature gradients i n B. Hence L and N are u s u a l l y connected together i n s e r i e s . M i s operated at a higher tempera-tur e t o prevent the formation- of a s o l i d plug of sublimed m a t e r i a l at the mouth of the s i d e arm. The operating c h a r a c t e r i s t i c s of the heaters are: L, 22-ft-, 88 watt; M, 9XL , 50 watt; N, 7-f3u, 28 watts. The B.29 and B.10 j o i n t s at the top and bottom of v e s s e l B are l u b r i c a t e d w i t h Apiezon T grease and cooled by a i r b l a s t s w h i l e the heaters are o p e r a t i n g . - 23 -Procedure f o r a Sublimation. The side arm A i s charged w i t h l - 2 g of r a d i o a c t i v e sodium c h l o r i d e . I n the f o l l o w i n g experiments t h i s i s u s u a l l y 0.4 g of r a d i o a c t i v e sodium 36 c h l o r i d e ( s p e c i f i c a c t i v i t y approximately lOO^c/g) c o n t a i n i n g CI d i l u t e d by f u s i o n i n a platinum c r u c i b l e w i t h about 4 g of reagent grade (May and Baker) m a t e r i a l . The fused mass i s broken up i n a mortar j u s t s u f f i c i e n t l y t o a l l o w i t t o be loaded i n t o the si d e arm. The r i g h t angle bend i n the sid e arm prevents the m a t e r i a l which d e c r e p i t a t e s from reaching the r e c e i v e r . The apparatus i s connected t o the vacuum system through stopcock 0. Before s u b l i m a t i o n , the apparatus i s evacuated t o b e t t e r than 10*"* mm of mercury. During the s u b l i m a t i o n , the pressure does not u s u a l l y r i s e above 10~^ mm, of mercury as measured on an i o n i s a t i o n gauge w i t h a c o l d t r a p between i t and the su b l i m a t i o n system. The apparatus i s connected t o the vacuum pumps, a mercury d i f f u s i o n backed by a r o t a r y o i l pump, throughout o p e r a t i o n . The three heaters are a l l switched on simultaneously and kept on f o r approximately 10 minutes. Heating i s dis c o n t i n u e d w h i l e the accumu-l a t e d product i s scraped o f f by r o t a t i n g i t through a h a l f - c i r c l e . Some of the p a r t i c l e s acquire an e l e c t r o s t a t i c charge and have t o be tapped down i n t o the r e c e i v e r which i s removed and t i l t e d t o f a c i l i t a t e t h i s o p e r a t i o n . The whole procedure, a ten minute s u b l i m a t i o n p e r i o d followed by s c r a p i n g , i s u s u a l l y repeated twice t o y i e l d 1-200 mgm., or order of 5 m of product. The scraper sometimes leaves a t h i n l a y e r of sample adhering t o the condenser. To ensure easy removal of each successive sample as i t i s formed i t i s best t o r o t a t e the condenser back t o i t s - 24 -o r i g i n a l p o s i t i o n each time and thus form each new sample on top of the o r i g i n a l s u r f a c e . However, i f i t i s important t o get the highest a t t a i n -able surface areas, i t would probably be best to use a f r e s h part of the condenser surface each time, and t o remove the f i l m even more f r e q u e n t l y . The product f a l l s p a r t l y i n t o the r e c e i v e r P and p a r t l y i n t o the annular space Q. At the end of the process, stopcock 0 i s c l o s e d and the whole device i s removed from the vacuum system and t i l t e d t o get a l l the product i n t o P. The apparatus i s then reconnected t o the pumping system, the pressure checked and the evaporator removed by s e a l i n g o f f at E. The r e c e i v e r i s f i n a l l y re-evacuated t o 5.10"^ mm. of mercury p r i o r t o c l o s i n g tap 0. The pressures are measured throughout the evaporation w i t h an " i n v e r t e d e l e c t r o d e assembly" type i o n i s a t i o n gauge (not shown) Veeco type R.G. 75P w i t h a l i q u i d n i t r o g e n t r a p between i t and the evaporator, i n c o n j u n c t i o n w i t h the c i r c u i t of A l p e r t (43) and a Pye scalamp galvanometer. The maximum s e n s i t i v i t y ( u n c a l i b r a t e d ) at 5 m.A* g r i d current was 2 cm d e f l e c t i o n / 1 0 " ^ ;#m. of mercury. E. B.E.T. Surface Area Measurements The use of krypton as the adsorbate f o r surface area measurements i s w e l l known. The main advantage of i t s use compared t o n i t r o g e n i s the r e d u c t i o n of the dead space c o r r e c t i o n due t o the lower pressure of monolayer a d s o r p t i o n . This may be seen as f o l l o w s ; s i n c e the t o t a l moles of gas n are given by where i s the volume of the a d s o r p t i o n v e s s e l ( l e s s the volume of - 25 -the absorbent) at a temperature T 2 and i s the volume of the gas bur e t t e from which the adsorbate i s d e l i v e r e d . I t f o l l o w s that a r e -d u c t i o n i n ?2 w i l l reduce the e r r o r i n c a l c u l a t i n g the number of moles adsorbed n** caused by e r r o r s i n the c a l i b r a t i o n of V^ and V 2 # For measurements up to l a r g e f r a c t i o n s of an atmosphere (e.g. w i t h n i t r o g e n as adsorbate), V 2 must be known to about 0.1 ml.; but when krypton i s used at pressures about 1000 times smaller the corresponding t o l e r a n c e i n volume i s about 100 ml. The vapour pressure of krypton at 77°A has been c a l c u l a t e d by i n t e r -p o l a t i o n from t a b l e s (44)• Although no d i r e c t experimental check on the vapour pressure was c a r r i e d out, the d e v i a t i o n s of the B.E.T. p l o t s from l i n e a r i t y (see Figure 7) agree w e l l w i t h those normally found i n most B.E.T. work (45) and i n d i r e c t l y c o n f i r m the c a l c u l a t i o n . The plateaus i n the isotherms are too i l l - d e f i n e d t o permit a rough check on Vm by the "point B" method, since the value of the constant C i s u s u a l l y very low (6-12); but the shape of the isotherm compares w e l l w i t h a c a l c u l a t e d B.E.T. isotherm f o r the same C, and the c a l c u l a t e d Vm l i e s at the c o r r e c t r e l a t i v e pressure. Apparatus The vacuum apparatus used f o r the surface area measurements i s shown i n Figure 8. The c h i e f p a r t s of the system are i n d i c a t e d by c a p i t a l l e t t e r s and the stopcocks by numerals. A l l stopcocks and j o i n t s were greased w i t h Apiezon M or T grease. A i s a s i n g l e stage mercury d i f f u s i o n pump backed by a Duo s e a l r o t a r y o i l pump (not shown i n the diagram). The c o l d t r a ps B, F and G are -2 10 ; I I l l i 1 ! 1 1 1 1 1 ' 1 J 0 2 4 6 8 10 12 x 10-2 io 20 30 40 50 60 x 10"2 P/Po Figure 7. Deviations of B.E.T. P l o t s from L i n e a r i t y - 28 -kept at l i q u i d n i t r o g e n temperature during the adsorption run. The krypton supply C ( A i r c o Co., s p e c i f i e d mass s p e c t r o m e t r i c a l l y pure) was s u p p l i e d i n a 1 l i t r e b u l b . This was attached v i a stopcock 4 to the b u r e t t e D whose c a p a c i t y of about 1 c c , ( e s s e n t i a l l y the volume of the bulb E ) allowed pressures of up t o 20 cm. of mercury t o be manipulated. The McLeod gauge H was designed t o read krypton pressures of up to 1 mm of mercury by a t t a c h i n g a 0.5 cc bulb I t o the c a p i l l a r y above H. D e t a i l s of these c a l i b r a t i o n s are given at the end of t h i s s e c t i o n . The adsorbent i n the c o l l e c t o r i s attached by a B.14 j o i n t t o stopcock 11. The c o l l e c t o r i s maintained at -197°C by immersion i n a l i q u i d n i t r o g e n f i l l e d dewar J . , the l e v e l of which i s maintained constant t o + 0.5 cm. throughout the determination of the adsorption isotherm. Determination of Isotherm By a d j u s t i n g stopcock 9 the manometer D i s f i l l e d w i t h mercury to a constant height (see * i n Figure 8 ) . Taps 2, 3, 7 and 12 are opened and traps B, F, G and J f i l l e d w i t h l i q u i d n i t r o g e n . When the pressure i n the system f a l l s t o l e s s than 10"^ mm of mercury, the stopcocks 3 and 7 are c l o s e d and 6 i s opened to the krypton supply. By c a r e f u l l y opening stopcock 4, 10-20 cm. of gas are admitted to the b u r e t t e ; then 4 and 6 are c l o s e d . The b u r e t t e bulb E now being f i l l e d w i t h gas t o a l e v e l X , say, the pressure d i f f e r e n c e ( X j - X p i s c a l c u l a t e d from the reading Xg on the adjacent s i d e arm. On subsequent admission of krypton t o the system, the mercury r i s e s t o the reference height (*) thus a l l o w i n g the volume a l s o t o be c a l c u l a t e d . An a l t e r n a t i v e procedure which was found simpler and adopted commonly i s t o c a l i b r a t e the 'dead volume* of the adsorption - 29 -system which includes; the McLeod bulb and i s bounded by stopcocks 6, 7 and 11; on a d m i t t i n g krypton t o t h i s volume v i a stopcock 6 t o measure i t s pressure d i r e c t l y using the McLeod. Krypton i s then admitted to the f i l m (immersed i n l i q u i d nitrogen) by opening stopcock 13, and adsorption i s allowed t o proceed u n t i l the pressure remains constant (10-15 minutes). This f i n a l pressure i s again recorded on the McLeod, stopcock 13 i s c l o s e d and a f u r t h e r a l i q u o t of krypton admitted. As i s w e l l known (51) r i n c e the B.E.T. p l o t i s only v a l i d i n the r e l a t i v e pressure range 0.05 < p/po < 0.35 some p r e l i m i n a r y knowledge of the a d s o r p t i o n c a p a c i t y i s t h e r e f o r e r e q u i r e d i n order t o o b t a i n s u i t -able a l i q u o t s of gas over t h i s r e g i o n . For most of the d i r e c t l y pre-pared f i l m s whose surface areas were of the order of 50 m2/g i t was found that an a l i q u o t of approximately 17yu.moles of krypton was s u i t a b l e . For measurements on s i n t e r e d f i l m s , however, t h i s f i g u r e i s f a r too high and the gas b u r e t t e c o u l d not be used; thus the 'dead volume' method was always used i n these cases. The calculation o f the surface area i s a standard procedure (7) and r e l i e s on the v a l i d i t y of the B.E.T. equation v - V m. c.p./( P o-p) [ l + (c-1) (p/Po)] (2) where V m i s the volume of krypton adsorbed at N.T.P. f o r complete mono-l a y e r a d s o r p t i o n . C i s exp (E^-EjVR.T.) where i s the heat of adsorp-t i o n i n the f i r s t l a y e r , E^ the heat of l i q u e f a c t i o n of the krypton on the surface (and i s assumed t o be the heat of a d s o r p t i o n i n a l l l a y e r s except the f i r s t ) , p i s the e q u i l i b r i u m pressure a f t e r a dsorption of Vcc - 30 -and p Q the vapour pressure of krypton at the temperature of the experiment i . e . , -197°C. Then from equation (2) i t f o l l o w s that p l " + C - l " v(p 0-p) l m J A p l o t of p / v ( p Q -p) versus (p/p 0) gives a s t r a i g h t l i n e i f the theory i s obeyed. The i n t e r c e p t i s ( l / V m > C ) and the slope (C-l/V m.C) thus V m and C can be found. Assuming an atomic r a d i u s of 1.87A* f o r the c l o s e packed krypton atoms, by m u l t i p l y i n g V m by 2.24 one obtains 2 -1 the t o t a l area of the adsorbent i n metres gram . A summary of the data f o r a l l the surface area measurements i s given i n Appendix B. A f t e r the area has been determined, the dewar at J ' i s removed, stopcocks 13 and 11 are c l o s e d , and the sample removed t o a second vacuum l i n e c o n t a i n i n g an i o n gauge where i t i s outgassed f o r about 30 minutes t o below 10"^ m/m of mercury. With the vacuum s t i l l a p p l i e d i t i s flame sealed at F (Figure 6) and weighed t o o b t a i n the approximate f i l m weight, before i n s e r t i n g i t i n t o the exchange apparatus at the ground glass j o i n t ( 3 ) . F. S i n t e r i n g Procedure Some e f f e c t s of s i n t e r i n g of evaporated f i l m s of sodium c h l o r i d e on the exchange k i n e t i c s have been report e d (38). The a c t u a l l o s s i n surface area on s i n t e r i n g however was open to doubt. In a d d i t i o n f u r t h e r s t u d i e s might be expected to give some i n d i c a t i o n of the excess con c e n t r a t i o n of defects present i n the evaporated f i l m s over that expected f o r thermal e q u i l i b r i u m ( 7 ) • - 31 -The s i n t e r i n g apparatus i s shown i n Figure 9. The f i l m i n the c o l l e c t o r i s placed i n the c y l i n d r i c a l quartz furnace tube H shown cut-away and plugged at both ends B, t o reduce the temperature gradients i n the tube. The platinum h e a t i n g c o i l G i s embedded i n a sodium-s i l i c a t e - a l u m i n a cement i n s u l a t i n g j a c k e t D, the outside of which i s covered by aluminium f o i l C. The a i r temperature at the bulb E i s measured by a chromel-alumel thermocouple F. Previous c a l i b r a t i o n s showed that an o v e r a l l v a r i a t i o n of + 5° could be expected over the 14 hours s i n t e r i n g process. The experimental s i n t e r i n g procedure c o n s i s t e d of the f o l l o w i n g steps:-( i ) The surface area of the prepared f i l m i n the c o l l e c t o r i s determined on the B.E.T. apparatus, ( i i ) The f i l m i s s i n t e r e d i n the furnace at a steady temperature f o r 1 4 + 1 hours, ( i i i ) The surface area i s redetermined on the B.E.T. apparatus, ( i v ) The c o l l e c t o r i s then sealed o f f at F and the f i l m stored p r i o r t o i n s e r t i o n i n the exchange system. G. Halogen Handling System I t has been found q u i t e u n s a t i s f a c t o r y t o handle c h l o r i n e i n any system c o n t a i n i n g mercury d i f f u s i o n pumps; the s l i g h t e s t a c c i d e n t a l contamination leads t o c l o g g i n g of the pumps. Hence a l l operations w i t h halogen gases i n t h i s l a b o r a t o r y have been confined to a s i n g l e vacuum system (of considerable extent, s i n c e i t i s shared by a l l members of the l a b o r a t o r y ) which i s evacuated by a 3 -stage B a l z e r d i f f u s i o n pump - 32 -Figure 9. F i l m S i n t e r i n g Furnace. - 33 -c o n t a i n i n g Dow Corning No, 703 S i l i c o n e F l u i d , A c c i d e n t a l passing of halogens through the d i f f u s i o n pump gives only v o l a t i l e products. A l l stopcocks i n the apparatus are greased w i t h Kel-F No. 90 grease. An important fea t u r e i s the use of r i g h t angled stopcocks throughout i n order to reduce the tendency of t h i s grease t o produce l e a k s . Sulphuric a c i d manometers are used throughout, (see Figure 10) operating non-l i n e a r l y w i t h some a i r i n the c l o s e d limb, and c a l i b r a t e d against mercury manometers, A d i s p o s a l l i n e f o r c h l o r i n e and f l u o r i n e i s connected t o a l l p a r t s of the system. I t i s separate from the main vacuum l i n e but i s served by the same pumps. C h l o r i n e i s u s u a l l y trapped i n l i q u i d n i t r o g e n , w h i l e f l u o r i n e i s absorbed i n soda-lime. The vacuum i n the system has u s u a l l y been checked by a Veeco RG.75P ' i o n i s a t i o n ' gauge w i t h a "non-burnout" i r i d i u m f i l a m e n t ; but the emission from these f i l a m e n t s i s immediately destroyed by the s l i g h t e s t a c c i d e n t a l contamination w i t h c h l o r i n e . Attempts are c u r r e n t l y being made t o r e -place the i o n i s a t i o n gauge by an o i l McLeod gauge, but d i f f i c u l t i e s of outgassing the o i l have not yet been overcome. The s u l p h u r i c a c i d used as a manometric f l u i d has a vapour pressure of about 7.10"^ mm of mercury as measured by the i o n i s a t i o n gauge. Ch l o r i n e Drying System The most important contaminant i n c h l o r i n e i s water vapour, which i s known t o cause r a p i d s i n t e r i n g of the f i l m s ; however, some non-condensable gases which were a l s o present i n the stock c y l i n d e r of c h l o r i n e r e q u i r e d removal. - 34 -The p u r i f i c a t i o n system i s shown i n Figure 10. The d i s p o s a l l i n e (not shown) i s connected t o stopcock 4. F and G are s u l p h u r i c a c i d manometers and D and E are s u l p h u r i c a c i d d r y i n g t r a p s . P u r i f i c a t i o n was e f f e c t e d as f o l l o w s ; c h l o r i n e from the stock supply was admitted t o the 2 - l i t r e bulb A, stopcocks 2, 4 and 5 being c l o s e d . Approximately 1 atmosphere was admitted, the pressure being read on manometer F. Non-condensable gases were f i r s t removed by opening stopcock 4 t o the c h l o r i n e d i s p o s a l system (not shown) c o n s i s t i n g of two U-tubes i n l i q u i d n i t r o g e n and passing the mixture of impure gases through them; the c h l o r i n e condenses i n the f i r s t tube, the second tube serves as a guard t r a p , w h i l e the non-condensable gases are removed t o the pump. The dewars around the c h l o r i n e are then removed, and the c h l o r i n e r e -condensed i n K; f i n a l l y stopcock 4 i s c l o s e d . The second step i s the removal of water vapour: the s u l p h u r i c a c i d wash b o t t l e s D and E as w e l l as the r e c e i v e r bulb B having been evacuated, stopcocks 6, 7, 8, 9 and 12 were cl o s e d and 10, 11, 13 and 14 were l e f t open. On opening stopcock 5 s l o w l y , c h l o r i n e passes through the dr y i n g traps D and E v i a C t o the storage bulb B. When h a l f the gas has been d r i e d , the remainder i s brought across by p l a c i n g the condensing f i n g e r L i n a dewar of l i q u i d n i t r o g e n . Stopcock 14 i s f i n a l l y c l o s e d and the dewar removed. To dispense the c h l o r i n e t o the exchange apparatus the l a t t e r i s attached at M. F l u o r i n e Handling System The use of f l u o r i n e gas i n pyrex and s i l i c a apparatus c o n t a i n i n g Figure 10. Chlorine P u r i f i c a t i o n System. - 36 -platinum leads appears to be q u i t e s a t i s f a c t o r y so long as the gas i s dry. Since any water present w i l l be converted t o HF, i t i s only necessary t o remove t h i s by passing over sodium f l u o r i d e to ensure s a t i s f a c t o r y behaviour. F l u o r i n e gas at 300 p . s . i . s u p p l i e d by the Matheson Chemical Company ( s p e c i f i c a t i o n 98% pure) i s dispensed by reducing the pressure i n three successive expansions at a s e r i e s of monel needle valves connected by a few feet of high pressure 3/8" copper t u b i n g , ; the exchange apparatus and the supply l i n e s having been evacuated t o 10"" mm of mercury by a r o t a r y o i l pump and checked w i t h a t e s l a c o i l d ischarge. The f l u o r i n e i s admitted e i t h e r d i r e c t l y t o the storage bulb H (see Figure 4) at pressures of the order of 1 atmosphere (measured on a h e l i c o i d t e s t gauge) or where low f l u o r i n e pressures ( l e s s than 50 mm , of mercury) are r e q u i r e d , from a small tapped bulb (approximately 30 cc.) at a s i m i l a r pressure connected i n t o the system f i r s t p r i o r to f l u o r i n a t i o n . I n e i t h e r event excess f l u o r i n e i s removed by a soda lime t r a p . The monel metal t o copper couplings are backed by t e f l o n sleeve r i n g s . L u b r i c a t i o n of the ground g l a s s j o i n t s and stopcocks by Kel-F No. 90 grease i s u n i v e r s a l ; however considerable d e t e r i o r a t i o n of the grease i s observed i n the presence of f l u o r i n e due t o d i s s o l u t i o n of the gas and subsequent l i q u e f a c t i o n . H. X - i r r a d i a t i o n Procedure The prepared f i l m i n i t s c o l l e c t o r i s attached to the X-ray source of an XRD-5 spectrometer assembly by means of a brass b l o c k , which i s d r i l l e d out so as to a l l o w a beam of 1 cm^ cross s e c t i o n a l area to s t r i k e the t h i n w a l l e d bulb at P (see Figure 6 ) . The i r r a d i a t e d s o l i d i s - 37 -kept i n the dark both during and a f t e r X - i r r a d i a t i o n . The storage times a f t e r i r r a d i a t i o n and before r e a c t i o n are kept as short as p o s s i b l e . The molybdenum r a d i a t i o n at an i n t e n s i t y of 20 mA g e n e r a l l y produced a d e f i n i t e orange c o l o u r a t i o n at about 3 hours although t h i s v a r i e d con-s i d e r a b l y from specimen t o specimen, probably due t o the v a r y i n g t h i c k -nesses of the g l a s s bulb w a l l s . An approximate c a l c u l a t i o n on the number of F centres produced by i r r a d i a t i o n f o r say 3 hours can be made. The energy t o form an F centre at room temperature (12) « 100 eV. = 1.6.10" 1 0 erg. Suppose the ads o r p t i o n i n g l a s s w a l l s i s ignored, then the i n t e n s i t y of X - i r r a d i a t i o n = 2 x 10"^ watt, cm" 2 <i - 1 - 2 = 2 x 103 erg.sec .cm No. of F centres formed =» 2 x 10°^ see"*.cm" 2 1.6.10-iO = 1.2.10" 1 3 s e c " 1 , cm"2 No. produced i n 3 hours = 1.3.10 1 7 cm'2 This agrees w i t h the order r e q u i r e d f o r v i s i b l e c o l o u r a t i o n (19). I . Bleaching of X - i r r a d i a t e d Films The e f f e c t s of ble a c h i n g X - i r r a d i a t e d f i l m s of a l k a l i h a l i d e s are both w e l l known and complicated (19). These f i l m s however when i r r a d i -ated bleached r a p i d l y i n d a y l i g h t , i n about one hour, u n l i k e s i n g l e c r y s t a l s whose colour remains constant f o r s e v e r a l days (44). - 38 -In order to study the e f f e c t s of b l e a c h i n g i n both the F and F' regions a double l i g h t f i l t e r was used whose t r a n s m i s s i o n c h a r a c t e r i s t i c s was such that both f i l t e r s r e s u l t e d i n only F l i g h t t r a n s m i s s i o n , while removal of the blue f i l t e r F and F' b l e a c h i n g would occur, (see Figure 11). These f i l t e r s were mounted over the end window of a l i g h t t i g h t box con-t a i n i n g the f i l m which was i r r a d i a t e d by a 6V 18A tungsten ribbon lamp v i a a 3 i n c h f o c a l length condenser and a water bath heat f i l t e r a l l mounted on an o p t i c a l bench. A l l l o a d i n g and unloading of the f i l m was e f f e c t e d i n a few seconds i n h e a v i l y subdued l i g h t . A B C - Corning F i l t e r No. 5030 G H - Corning F i l t e r No. 3480 - 40 -J. C a l i b r a t i o n s of Apparatus McLeod Gauge The constants of the instrument were determined as f o l l o w s : -P r i o r to s e a l i n g the bulb I (see Figure 8) to the main bulb H, the l a t t e r was f i l l e d w i t h water at 24°C and weighed; the c a p i l l a r y stem was s i m i l a r l y f i l l e d w i t h mercury and the u n i f o r m i t y of the bore having been e s t a b l i s h e d the weight of mercury per u n i t length e s t a b l i s h e d . From de n s i t y t a b l e s (44) the volume per u n i t length i s thus r e a d i l y c a l c u l a t e d . For most measurements the recorded pressures l i e i n the range 5.10" 2 - 1mm of mercury. By r a i s i n g the mercury l e v e l t o the f i d u c i a l mark * (see Figure 8) and reading the pressure d i f f e r e n c e L i n mm i n the r i g h t hand c a p i l l a r y , i f the volume of the bulb plus c a p i l l a r y (volume t o * i n Table 1) i s v and the main bulb volume i s V then, p = v L mm Hg (4) V thus f o r runs 21-80 p - 4.39 2.10" 2 mm Hg (5) A summary of the McLeod constants i s given i n Table 1 below. TABLE 1. C a l i b r a t i o n of the McLeod Gauge I C a l i b r a t i o n Run No. C a p i l l a r y Radius Volume t o * Volume H (m/x) (cc) (cc) 1 1-7 511.4 0.5776 339.5 2 8-10 546.5 0.7326 294 3 11-20 380.7 1.491 339.5 4 21-83 380.7 1.487 339,5 - 41 -Dead Space of Adsorption System In the present r e s u l t s using krypton adsorption i t i s estimated that the whole of the dead space c o r r e c t i o n a r i s i n g from the volume of the f i l m c o l l e c t o r of 1 6 + 2 cc. i s i n s i g n i f i c a n t and has been ignored. This can be shown as f o l l o w s ; since the average f i l m adsorbs between 1-10 cc. of krypton at N.T.P. f o r monolayer adsorption t h i s corresponds to at l e a s t 9 l i t r e s of krypton at p/po = 0.05 and 1.3 l i t r e s at p/po = 0.35. Thus even the greatest e r r o r represents an a d d i t i o n a l volume of only 1% and f o r most of the data i t i s very much l e s s . Thermomolecular pressure c o r r e c t i o n s as a p p l i e d by Kington and Holmes (46) have been ignored s i m i l a r l y , due to the wide bore of the c o l l e c t o r tube. R a d i o a c t i v e C a l i b r a t i o n s of Sodium C h l o r i d e The s p e c i f i c a c t i v i t y of the r a d i o a c t i v e sodium c h l o r i d e provided by the Atomic Energy D i v i s i o n of Canada was about 0.1 mC/g. This i s d i l u t e d by a f a c t o r of about ten i n preparing the f i l m . The s p e c i f i c a c t i v i t y c a l i b r a t i o n i n v o l v e s converting a known weight of t h i s f i l m i n t o HC1 gas and determining i t s counting r a t e i n the exchange system. 36 From the s p e c i f i c a c t i v i t y thus found the molar concentration of CI i n the gas phase during the exchange r e a c t i o n can be c a l c u l a t e d . The apparatus used i s shown i n Figure 12. Approximately 100 mgm . of the prepared f i l m i s a c c u r a t e l y weighed and about 2 g of non-active sodium c h l o r i d e added and placed at B, and 10 c c . of anhydrous s u l p h u r i c a c i d i s placed i n A. The whole i s reassembled, j o i n t s 1, 2 and 3 being greased w i t h KEL-F and evacuated f o r at l e a s t one hour i n order to outgas Figure 12. C a l i b r a t i o n Apparatus f o r S p e c i f i c A c t i v i t y Determination. - 43 -the a c i d . Stopcocks 1 and 2 on the exchange apparatus are c l o s e d , and as the apparatus i s v e r t i c a l the condensing f i n g e r L (see Figure 4) i s placed i n a dewar of l i q u i d n i t r o g e n . Stopcock 5 i s now closed and the s u l p h u r i c a c i d c a r e f u l l y added t o the s o l i d by r o t a t i n g the bent side arm; e s p e c i a l care being taken at the commencement when the ten-dency t o f r o t h i s at a maximum. A f t e r complete d i s s o l u t i o n of the s o l i d , s t o p c o c k 6 on the exchange apparatus i s closed and the dewar at L removed. The apparatus i s f i n a l l y removed to the lead c a s t l e support and the a c t i v i t y determined. By then opening stopcocks 1 or 2 and re-determining the a c t i v i t y the r e l a t i v e volumes of the exchange system can be found. Since the volumes of the bulbs G and H may be found d i r e c t l y by f i l l i n g w i t h water, the absolute volume of the exchange system i s thus c a l c u l a b l e . In the f o l l o w i n g t a b l e the s p e c i f i c a c t i v i t i e s thus determined f o r the f i v e separate batches of r a d i o a c t i v e sodium c h l o r i d e are shown i n column I I I and the corresponding volume of the exchange system at the time of the c a l i b r a t i o n i n column IV. TABLE I I . S p e c i f i c A c t i v i t y of the Sodium C h l o r i d e Films C a l i b r a t i o n Run S p e c i f i c A c t i v i t y V o l . of Exch. App. No. App. c.p.m./G. (cc) 1 18-20 190,500 366 1 2 21-26 29,225 366 1 3 27-33 38,540 366 1 4 34-50 86,600 317 2 5 51 85,700 352 1 6 60-80 88,450 341 3 7 81-83 96,100 336 3 - 44 -Volumes of Various Apparatus (a) McLeod Dead Space In the c a l c u l a t i o n of surface areas by the B.E.T. method i t was found more convenient and accurate t o expand the krypton a l i q u o t i n t o the McLeod gauge and determine i t s pressure the r e . This volume was bounded by stopcocks 6, 7 and 13 and the mercury surface of the McLeod. I t was determined by a t t a c h i n g a known volume to the B.14 cone at stop-cock 13 and determining the pressure r a t i o f o r s e v e r a l pressure increments. Since t h i s volume was 460 c c , the pressure r a t i o P 2 / P 1 = 0.520, then the McLeod dead space X was given by X/(X + 1053) = 0.520 X = 503 c c . (b) Exchange Apparatus, F l u o r i n e and C h l o r i n e Bulbs Three d i f f e r e n t pieces of exchange apparatus have been used i n t h i s work designated 1, 2 and 3. The f i r s t two were f o r c h l o r i n e exchange only whereas the t h i r d , shown i n Figure 4, had both a f l u o r i n e and a c h l o r i n e bulb. I n a d d i t i o n the a c t u a l volumes of the exchange system were o f t e n changed s l i g h t l y by the a d d i t i o n s of m o d i f i c a t i o n s so that runs i n the same s p e c i f i c a c t i v i t y batch s e r i e s are not n e c e s s a r i l y ex-changing i n the same volumes. In the t a b l e below are l i s t e d these three volumes f o r each run from the f i r s t r a d i o a c t i v e exchange at run 20. - 45 -Table I I I Volumes of Exchange systems, F l u o r i n e and C h l o r i n e bulbs Run Apparatus Exchange CI2 bulb volume F£ bulb volume number volume (cc) (cc) (cc) 20-21 1 366 302 22-23 2 266 247 24-27 2 269 247 28-33 1 366 302 34-39 2 304 246 40-41 2 304 246 42 1 365 302 43 2 304 246 44-46 1 352 302 48-51 1 352 302 60-71, 47 3 341 292 300 72-80 3 341 292 81-83 3 336 292 RESULTS - 46 -In a l l equations i n t h i s s e c t i o n , C represents the counting r a t e the gas phase, c o r r e c t e d f o r background. i s the observed i n f i n i t y reading f o r any r e a c t i o n which was followed to completion, and C e i s the c a l c u l a t e d counting r a t e corresponding to e q u i l i b r i u m d i s t r i b u t i o n of 36 CI between s o l i d and gas. Thus = A.m. n n n g + n s (6) where A = s p e c i f i c a c t i v i t y of f i l m , mQ = f i l m mass, and n and n are the t o t a l numbers of CI atoms i n gas and s o l i d phases. C e' i s the a c t i v i t y corresponding t o exchange w i t h an i n f i n i t e amount of gas : C e' = A.m. A. The Form of the Rate Law Two c l e a r l y - d i s t i n g u i s h e d types of r a t e law have been observed:-(1) For f i l m s which have not been subjected to any treatment designed to produce e l e c t r o n i c d e f e c t s , as In the e a r l i e r work, the unusual "power law" i s obeyed: C - a . t n Figure 13 shows l o g - l o g p l o t s f o r a number of such r e a c t i o n s at room temperature. (2) For f i l m s which have been exposed t o X-rays or t o gaseous f l u o r i n e before exchange, simple second-order k i n e t i c s are found. = k c t (7) iPeo Figures 14 and 15 show t y p i c a l second-order p l o t s f o r X - i r r a d i a t e d and f l u o r i n a t e d f i l m s . Figure 14. Second Order P l o t f o r an X - i r r a d i a t e d f i l m . - 49 -Figure 15. Second Order P l o t f o r a F l u o r i n a t e d F i l m . (a-x) x 10 8 Time (mins.) - 50 -The data were analyzed c a r e f u l l y to ensure that the d i s t i n c t i o n between the r a t e laws was unequivocal. In most cases, one of the r a t e laws gave a good p l o t w h i l e the p l o t f o r the other was markedly n o n - l i n e a r (Figure 16). A few r e a c t i o n s appeared to agree f a i r l y w e l l w i t h both laws; but c l o s e r i n v e s t i g a t i o n showed i n a l l such cases that roughly h a l f the r e a c t i o n d i d not f i t the second-order p l o t , although i t occupied only a small p r o p o r t i o n of the graph on account of the r e c i p r o c a l con-c e n t r a t i o n s c a l e . These cases were mostly X - i r r a d i a t e d f i l m s i n which the e l e c t r o n i c damage had been l a r g e l y removed by b l e a c h i n g . I t was t h e r e f o r e r e q u i r e d as a c r i t e r i o n of second-order behaviour that not more than the f i r s t 5% of the r e a c t i o n should deviate s i g n i f i c a n t l y from the second-order p l o t (see Figure 15). The r e a c t i o n was u s u a l l y f o llowed only up to about 20% of the c a l -c u l a t e d counting r a t e C g corresponding to e q u i l i b r i u m d i s t r i b u t i o n of r a d i o a c t i v e atoms between s o l i d and gas; the of the second-order p l o t s was u s u a l l y about t h i s f r a c t i o n of C e. Thus no account need be taken of the approach t o e q u i l i b r i u m i n c o n s i d e r i n g the s i g n i f i c a n c e of the r a t e laws. Figure 17 shows the d e v i a t i o n from l i n e a r i t y caused by the approach t o e q u i l i b r i u m i n a "power law" r e a c t i o n followed beyond the usual 20%. Two features of the r e s u l t s are p a r t i c u l a r l y s i g n i f i c a n t i n r e l a t i o n t o the question of what i s happening t o the defect concentrations as the r e a c t i o n s proceed. F i r s t l y , as mentioned above, the second-order r e a c t i o n s u s u a l l y stop completely at a much l e s s than C e. Secondly, f o r a "power law" r e a c t i o n , i f the gas phase i s removed i n the course 2 10 100 Time (mins.) Figure 16. Graph showing n o n - l i r i f e r i t y of the "Power Law" P l o t f o r an X - i r r a d i a t e d f i l m , and r e v e r s i o n to power law on bleaching. - 53 -of the r e a c t i o n and replaced by f r e s h c h l o r i n e , the approach t o the r e c a l c u l a t e d C e i s much slower than f o r the f i r s t gas phase (Figure 18). B. Power Law Reactions In the present work both the r a t e and the extent of exchange was greater than that found e a r l i e r (19). Thus, w i t h s i m i l a r values f o r the constant a, the slope n of the l o g - l o g p l o t has an average value of 0.39 + .07. The l i m i t i n d i c a t e s the t o t a l range of a l l r e s u l t s ; i n d i v i d u a l r e s u l t s being a s c e r t a i n a b l e more a c c u r a t e l y t o 5% of the mean value. Cur-vature of the l o g - l o g p l o t s f o r the h i g h temperature runs commenced a f t e r about 15 minutes i n most cases due to the exchange being more r a p i d than at 25° (see Figure 17). In these circumstances the exponent n i n the power law was obtained from the f i r s t 10 minutes of the r e a c t i o n curve. Some runs d i d deviate from t h i s l i n e a r i t y more than could be accounted f o r by the approach t o e q u i l i b r i u m but i n almost a l l those cases i t could be shown that a i r had leaked i n t o the apparatus by condensing the c h l o r i n e from the system at the end of the run and determining i f any r e s i d u a l a i r was present. The extent of the exchange r e a c t i o n i n r e l a t i o n t o the surface area of the f i l m s f o l l o w s d i r e c t l y from a c a l c u l a t i o n of the number of c h l o r i n e atoms i n the surface and the s p e c i f i c a c t i v i t y constant A. The r e s u l t of a t y p i c a l c a l c u l a t i o n i s shown i n Figure 19, f o r exchange at room temperature on an untreated f i l m . c (Arrows i n d i c a t e number of surface l a y e r s exchanged) 6th I ! 1 ' I I i I i | J 0 20 40 60 Time (mins.) Figure 19. L i n e a r P l o t showing extent of Reaction i n r e l a t i o n t o Surface Area. - 56 -Table IV The Exchange of C h l o r i n e w i t h Sodium Chl o r i d e f i l m s at room temperature. Run Wt. f i l m pel. o- a. 10"2.a/m. a/o-(mgm.) (atm.) (mVg) (c.p.m.) (c.p.m.g - 1) (c .p.m.g.i 21 478 ' :718 49.5 622 13.0 12.5 20 195 .487 83.6 273 14.0 3.26 22 247 .210 20.5 720 29.2 35.1 32 124 .072 48.6 452 36.5 9.30 33 42 .0195 54.5 179 42.7 3.29 The p r o g r e s s i v e l y i n c r e a s i n g times t o exchange each l a y e r r e f l e c t the decreasing c o n c e n t r a t i o n of the r a t e determining s p e c i e s , due t o s e l f -i n h i b i t i o n . This i s not t o be thought of as i n most g a s - s o l i d r e a c t i o n s as a r e f l e c t i o n of increased d i f f u s i o n time at i n c r e a s i n g depth i n t o the bulk. An i n t e r p r e t a t i o n based on d i f f u s i o n must r e s u l t i n the r e a c t i o n r a t e being dependent on the s p e c i f i c surface of the s o l i d . I t must be emphatically r e s t a t e d here that t h i s i s not what i s observed. As Figure 20(a) and Table IV show the r a t e s of r e a c t i o n (assuming a constant slope n i n the l o g - l o g p l o t s ) i s q u i t e independent of the s p e c i f i c surface area and t h i s f a c t alone n e c e s s a r i l y i n v a l i d a t e s any argument based on the r a t e c o n t r o l l i n g step i n v o l v i n g d i f f u s i o n . However; a was dependent on the f i l m mass as had been i n d i c a t e d e a r l i e r (see F i g u r e 20(b)). The pressure dependence of a had not however been i n v e s t i g a t e d p r e v i o u s l y . A c c o r d i n g l y , the exchange was s t u d i e d over a pressure range of 0.01 -1.0 atmospheres of c h l o r i n e at temperatures of -5°, 25° and 60°C (see Figure 21). I n a l l cases an i n v e r s e dependence on the square root of the pressure was observed at h i g h pressures, w h i l e at low pressures the r a t e appeared t o reach a maximum at 25° and 60°C. At t h i s highest - 58 -Figure 21. Pressure Dependence of a. 2.10-2 10-1 Chlorine Pressure (atm.) - 59 -temperature and at low pressures a d i r e c t dependence on the square root of the pressure was found. I t i s apparent that the r e s u l t s at 60°C show considerably more v a r i a t i o n than those at lower temperatures. This was almost c e r t a i n l y due t o the d i f f i c u l t y of c o n t r o l l i n g the tempera-tu r e i n the jacketed r e a c t i o n system by means of a hot a i r b l a s t . At pressures above 0.4 atm. the slopes of the a versus pressure p l o t s are p a r a l l e l and a l l o w the c a l c u l a t i o n of the a c t i v a t i o n energies over the two temperature ranges s t u d i e d . From the data i n Table V below the a c t i v a t i o n energies of 0.29 e.V. and -0.069 e.V are found f o r the exchanges i n the ranges 25-60°C and -5-25°C r e s p e c t i v e l y . Table V. -5- 25° and 25-60°C. T°C. 103/T°K l n ( 1 0 " 3 60 3.00 4.22 25 3.36 2.994 -5 3.73 3.58 3 6.8.10^ DU J UU H  .j. Q*29 2.0.10* 5 - o!o69 The former value of 6.8 k cal/mole i s considerably smaller than that found i n previous work on f i l m s (19). The l a t t e r value of -li6 k cal/mole over the lower temperature range i s probably accounted f o r by the p h y s i c a l a d s o r p t i o n of c h l o r i n e onto the surface. S i n t e r e d Films Exchange f o l l o w e d a power law curve when the f i l m s were s i n t e r e d at temperatures of 250-400°C f o r about 14 h r s . The values of a were a l l much l e s s than the value f o r u n s i n t e r e d f i l m s at comparable c h l o r i n e pressure, even when the surface remained as high as 33 nrg a f t e r s i n t e r i n g . - 60 -I t i s thus evident that the s i n t e r i n g process e n t a i l s important changes i n defect c o n c e n t r a t i o n s , q u i t e apart from the change i n surface area. M o d i f i c a t i o n of the surface s t r u c t u r e i s i n d i c a t e d a l s o by the B.E.T. p l o t s of the krypton adsorption isotherms. The ends of the l i n e a r r e g i o n occur at higher r e l a t i v e pressures than u s u a l , and the C value i s a l s o increased. The r e s u l t s are i n s u f f i c i e n t t o a l l o w any f u n c t i o n a l r e l a t i o n s h i p s t o be e s t a b l i s h e d d e f i n i t e l y . There was some i n d i c a t i o n of a c o r r e l a t i o n between O"and a 2 (Table VI, second column from r i g h t ) but the c o r r e -l a t i o n i s not good and seems p h y s i c a l l y u n l i k e l y . This appears to be f o r t u i t o u s , s i n c e a number of other v a r i a b l e s may r e a d i l y change mono-t o n i c a l l y w i t h O" . A b e t t e r c o r r e l a t i o n , f o r example, i s the apparent l i n e a r r e l a t i o n s h i p between.a and 1/T i n d i c a t e d by the l a s t column of Table VI. This i s not yet explained; i t seems that i t may be accounted f o r by defect e q u i l i b r i a i n c l u d i n g a "space-charge" e f f e c t s i m i l a r t o that discussed by Lehovec (50). T h e o r e t i c a l work on t h i s i s i n progress. X - i r r a d i a t e d and Heavily Bleached Films I t i s t o be expected that i f the colour centres introduced by X-i r r a d i a t i o n are h e a v i l y bleached, the f i l m would behave as an untreated one. Such behaviour was observed f o r one such f i l m that had been ex-posed to F + F' l i g h t f o r s i x hours. However, since b l e a c h i n g occurs more r e a d i l y at the surface of the powdered sample w h i l e the X - i r r a d i a t i o n products are more uniformly d i s t r i b u t e d through i t , the b l e a c h i n g process i s o f t e n I n e f f i c i e n t (unless the powder i s shaken w e l l during b l e a c h i n g ) . Thus i n a s e r i e s of runs (Nos. 48-51) where bleaching was attempted, p l o t s intermediate between l o g - l o g and second order were observed. The curves Table VI. Results of S i n t e r i n g Experiments on Sodium C h l o r i d e F i l m s . S i n t e r i n g No. m PC1 2 Temp. (mgm) (atm) (m2/g) (m2/g) (°C) 73 127 0.44 66.5 33.4 250 72 153 0.44 21.7 12.6 295 74 287 0.40 18.8 1.22 350 75 189 0.58 48.7 1.06 400 * - 0.40 - - -103/T°K a/m 1 0 4 <rf /(a/m) 2 10 7 A(a/m)/ A ( l/T) 1.91 524 1.21 1.76 295 1.45 1.60 197 0.32 1.49 71 2.10 - 1660 -' (•Interpolated from F i g . 21) - 62 -becoming p r o g r e s s i v e l y more l o g - l o g as the b l e a c h i n g time and wavelength approached that of F + F* l i g h t (see Figure 11). C. Second Order Reactions The k i n e t i c s of exchange of an X - i r r a d i a t e d f i l m w i t h c h l o r i n e are always second-order (Figure 14), provided that precautions are taken to exclude l i g h t and thus prevent blea c h i n g of the X-ray damage. The second order r a t e constants are c a l c u l a t e d according t o the method i n d i c a t e d by equations (25) t o (28) of the D i s c u s s i o n s e c t i o n below, from which i t appears that the most s i g n i f i c a n t r a t e constant i s k n = C g' k c, where k c i s defined by equation (7) and C e' i s the a c t i v i t y corresponding to exchange of the s o l i d w i t h an i n f i n i t e amount of gas. I n v e s t i g a t i o n of the dependence of k n on the v a r i a b l e s of the system was hampered by the large number of p o s s i b l e parameters, i n c l u d i n g time of i r r a d i a t i o n , delay time between i r r a d i a t i o n and exchange, bleac h i n g procedures, e t c . The l a r g e s t experimental d i f f i c u l t y i s t o o b t a i n uniform i r r a d i a t i o n c o n d i t i o n s , since each f i l m i s i r r a d i a t e d i n a t h i n glass bulb which i s subsequently broken, and the w a l l t h i c k n e s s of the bulb, and the geometry of the sample i n the i r r a d i a t i n g beam can c l e a r l y be important. However, the k i n e t i c s of the exchange appear t o be independent of i r r a d i a t i o n time at l e a s t f o r times greater than 30 minutes. For X - i r r a d i a t e d f i l m s , two s i g n i f i c a n t c o r r e l a t i o n s were e s t a b l i s h e d : the r a t e constant k n was d i r e c t l y p r o p o r t i o n a l to c h l o r i n e pressure (Figure 22a) w h i l e the f r a c t i o n of the s o l i d exchanged ( C ^ /C e') diminished l i n e a r l y w i t h i n c r e a s i n g delay time. The r e s u l t s f o r the l a t t e r v a r i a t i o n are somewhat e q u i v o c a l , since the short delay times happen t o correspond to Figure 22. (a) Dependence of Second-order Rate Constant (k ) on Pressure. The F r a c t i o n exchanged (C^/C e') versus delay time: (b) X - i r r a d i a t e d Films (c) F l u o r i n a t e d F i l m s . - 64 -low pressures. Thus there i s a l s o an apparent l i n e a r r e l a t i o n s h i p between ^oo /Ce' and P, but t h i s i s by no means so good as the c o r r e l a t i o n w i t h de-l a y time, which i s a l s o supported by the r e s u l t s f o r f l u o r i n a t e d f i l m s (Figure 22c). (The curve i n d i c a t e s that no r e a c t i o n at a l l should be observed f o r delay times greater than 6 minutes i n the case of f l u o r i n a t e d f i l m s ; t h i s has been confirmed at 20 minutes delay time.) The dependence of k f l and C w /C e' on surface area was not so c l e a r l y e s t a b l i s h e d . Table V I I i n c l u d e s a r e s u l t f o r a f i l m s i n t e r e d at 350°C to about 1/10 of i t s o r i g i n a l s u r f ace. For t h i s f i l m , k R was higher by a f a c t of about three than f o r an u n s i n t e r e d f i l m , and C ^ / C g 1 was 0.178 where a value of zero would have been expected. In the power law experiments, a was a f f e c t e d by s i n t e r i n g i n a manner not f u n c t i o n a l l y r e l a t e d to the change i n the surface area. This probably represents a change i n defect c o n c e n t r a t i o n s . For an X - i r r a d i a t e d f i l m , the defects produced during i r r a d i a t i o n are v a s t l y i n excess of anything present p r e v i o u s l y and the s i g n i f i c a n t e f f e c t of s i n t e r i n g should be on the surface area only. Further work would be u s e f u l t o r e s o l v e the e f f e c t of surface area and t o e s t a b l i s h more c o n c l u s i v e l y the dependence of C w /C e' on delay time. The l a t t e r r e q u i r e s m o d i f i c a t i o n s i n technique t o f a c i l i t a t e measurements at short delay times. In the i n i t i a l experiments on X - i r r a d i a t e d exchange, the r e a c t i o n was allowed t o proceed i n d a y l i g h t and was subject t o a v a r i a b l e i n d i r e c t l i g h t i n t e n s i t y . I t was found that n e i t h e r second-order nor l o g - l o g p l o t s r e s u l t e d f o r the whole r e a c t i o n . Regular l o g - l o g behaviour was observed i n i t i a l l y f o r about 15 minutes but the slopes of the p l o t there-a f t e r decreased, the exponent n f a l l i n g t o 0.10 + .03 over s e v e r a l hours. Table VII Results f o r Second Order Reactions on X - i r r a d i a t e d and F l u o r i n a t e d Films Delay c r Run Time P c i 2 lO^k Coo / c (min.) (atm) (m2/g) n 81 20 .0933 51.7 .334 6.60 .138 83 18 .188 60.0 .189 8.14 .166 44 14 .290 70.8 .309 15.2 .273 46 10 .429 67.3 .383 33.2 .332 45 7.5 .434 70.5 .425 23.3 .386 82* 30 .440 7.24 .212 81.9 .178 47 1 .184 7.15 .508 5.5 .380 61 2 .250 35.4 .373 222 .284 76 5 .220 57.0 .078 990 .055 u § (*sintered f i l m ) - 66 -The percentage exchange could be c a l c u l a t e d and I t was apparent that I t was s i g n i f i c a n t l y lower over the e n t i r e r e a c t i o n . This i s due presum-ably t o the l o s s of V-centres by r e d u c t i o n by the e l e c t r o n s l i b e r a t e d i n the F centre b l e a c h i n g . F l u o r i n a t i o n Reactions The f l u o r i n a t i o n of f i l m s of sodium c h l o r i d e i s extremely r a p i d at normal temperatures and pressures; (see Figure 23). Indeed, at pressures above 100 mm most f i l m s are completely f l u o r i n a t e d i n 2 minutes w h i l e at 760 mm the r e a c t i o n takes l e s s than 1 minute. Thus i t was not p o s s i b l e , w i t h the present apparatus, t o study the k i n e t i c s of the f l u o r i n a t i o n r e -a c t i o n f o r i t s own sake, but only t o use i t as a means of producing e l e c -t r o n i c damage t o the f i l m s before exchange. The r e s u l t s of such an attempt i s shown i n Figure 24, where f l u o r i n a t i o n at 258 mm of an X-i r r a d i a t e d f i l m o c c u r r i n g i n l e s s than 1 minute gives the p e r i o d i c v a r i a t i o n s i n a c t i v i t y shown, which a r i s e from the c i r c u l a t i o n time of the exchange v e s s e l . From the p e r i o d i c i t y Of the maxima, the average c i r c u l a t i o n time which puts a lower l i m i t on the response of the system, i s seen t o be 54 seconds. P a r t i a l f l u o r i n a t i o n i s best e f f e c t e d at pressures of about 50 mm of mercury for. periods of 30-60 seconds. The delay time between f l u o r i n -a t i o n and exchange apparently determines the extent of the ensuing second-order r e a c t i o n , as shown by the C ^ /C e values i n Figure 22 ( c ) . The ra t e constant a l s o appears t o increase r a p i d l y w i t h delay time, but these r e s u l t s are not as r e l i a b l e q u a n t i t a t i v e l y as those f o r X - i r r a d i a t e d f i l m s . 1 2 Time (mins.) Figure 23. F l u o r i n a t i o n of Sodium Chloride at d i f f e r e n t F l u o r i n e Pressures. F i g u r e 24. P l o t o.f a F l u o r i n a t i o n showing e f f e c t of C i r c u l a t i o n Time i n Reaction V e s s e l . - 69 -The r e a c t i o n w i t h the l a r g e s t delay time showed a very unusual phenomenon, i n that the second-order r e a c t i o n (which was of small extent, see Figure 26) was succeeded by a r a p i d l y a c c e l e r a t i n g r e a c t i o n (see Figure 25, curve f o r run 76). This r e a c t i o n proved to be p a r a b o l i c i n time (Figure 27) and i s thus analogous i n form to many s o l i d - s t a t e r e a c t i o n s i n v o l v i n g n u c l e a t i o n of a new s o l i d phase. Presumably t h i s represents some delayed r e o r g a n i z a t i o n of the o x i d a t i o n products i n the s o l i d phase, but more wdrk i s i n progress on t h i s phenomenon. - 72 -Figure 2 7. Exchange S t a r t i n g F i v e Minutes a f t e r F l u o r i n a t i o n . A c c e l e r a t i n g Region Log-log P l o t t o show P a r a b o l i c Law. 10 100 Time (mins.) l o g a r i t h m i c s c a l e DISCUSSION I - 73 -A. Evidence f o r Time-dependent Defect Concentrations I s o t o p i c exchange r e a c t i o n s almost i n v a r i a b l y show f i r s t - o r d e r k i n e t i c s , and a t h e o r e t i c a l treatment has been published (48) i n d i c a t i n g that t h i s i s q u i t e i n e v i t a b l e . This treatment depends, however, on two r e s t r i c t i v e c o n d i t i o n s which are not e x p l i c i t l y s t a t e d i n i t ; f i r s t l y , that the con-c e n t r a t i o n s of a l l r e a c t i o n intermediates should be independent of time, and, secondly, that the phases i n which the r e a c t i o n takes place should be t r u l y homogeneous, i . e . , without co n c e n t r a t i o n g r a d i e n t s . Any r a t e law other than a f i r s t - o r d e r one i n d i c a t e s that one of these c o n d i t i o n s i s v i o l a t e d ; the commonest case i s , of course, s e l f - d i f f u s i o n of an i s o t o p i c a l l y l a b e l l e d con-s t i t u e n t . The r a t e law f o r such a d i f f u s i o n process i s commonly of the form of the "power law" observed i n the present experiments, but only w i t h n = 0.50. Values of n d i f f e r i n g from 0.50 are evidence against a mechanism i n which d i f f u s i o n i s r a t e - c o n t r o l l i n g , but are not i n themselves s u f f i c i e n t t o e l i m i n a t e such a mechanism u n e q u i v o c a l l y . D i f f u s i o n c o n t r o l i s r u l e d out completely, however, by the absence of any c o r r e l a t i o n between the "a" f a c t o r i n the power law and the surface area of the s o l i d phase. The c o n f i r m a t i o n of t h i s r e s u l t was made a major o b j e c t i v e of the present work because of i t s importance i n d i s t i n g u i s h i n g between the two general c l a s s e s of p o s s i b l e mechanisms. I t appears t h e r e f o r e that the exchange mechanism i n v o l v e s defect s t r u c t u r e s w i t h i n the s o l i d phase, the concentrations of which are changing as the r e a c t i o n proceeds. This c o n c l u s i o n a p p l i e s e q u a l l y to the "power law" and the second-order r e a c t i o n s ; and i n both cases, other features - 74 -of the evidence show c l e a r l y that a defect of primary importance i n the mechanism i s decaying i n the course of the r e a c t i o n . The second-order processes provide the c l e a r e s t evidence, namely, that t h e i r i n f i n i t y readings (Ce©) are always much l e s s than the c a l c u l a t e d values f o r equi-l i b r i u m d i s t r i b u t i o n (C e) of the r a d i o i s o t o p e between s o l i d and gas (see Table V I I ) . Thus the concentrations of r e a c t i o n intermediates have changed i n such a way that the r e a c t i o n r a t e has become n e g l i g i b l e , before e q u i l i b r i u m has been reached. For the "power law" r e a c t i o n s , the r a t e law i t s e l f i m p l i e s a marked slowing-down of the r e a c t i o n as i t proceeds; t h i s feature i s i l l u s t r a t e d i n a more obvious way by the r e s u l t s of exchanging the same f i l m w i t h two successive gas samples (see Figure 18). H a r r i s o n has p r e v i o u s l y suggested a very t e n t a t i v e mechanism t o account f o r the power law (20). This mechanism now appears u n n e c e s s a r i l y complicated and p h y s i c a l l y un-r e a l i s t i c i n some of i t s d e t a i l s . In t h i s d i s c u s s i o n , however, two general features of the e a r l i e r proposal s h a l l be r e t a i n e d ; f i r s t l y , that some of the r e a c t i o n intermediates are e l e c t r o n i c defects (V-centres), and secondly, that one species of defect i s being destroyed i n a second-order process. These were e s s e n t i a l features of the e a r l i e r mechanism, and were proposed e n t i r e l y from the i n d i r e c t evidence of the r a t e law i t s e l f , and before second-order k i n e t i c s had been observed f o r any exchange r e a c t i o n . - 75 -B. E s s e n t i a l Features of an E x p l a n a t i o n of the Power Law I t i s p o s t u l a t e d that two defects must have concentrations dependent on time: a defect (D2) which takes part i n the exchange step i s i n -a c t i v a t e d on c o l l i d i n g w i t h another species of defect (D^) which i s i t s e l f being destroyed i n a second-order process. The mathematical reasoning here i s that a second-order process introduces the r e c i p r o c a l of the time, and i n t e g r a t i o n of t h i s i n the expression f o r r e a c t i o n of w i t h D2 gives a l o g a r i t h m and leads t o the t n form. I f C i s the amount of exchange, and and are the concentrations of D^  and D2 then, i d C 1 / d t = - k ^ * (8) dC 2/dt = - k 2 C 1 C 2 ( 9 ) dC/dt = k e C 2 (10) The s o l u t i o n of these equations reduces t o the form C = a t n i f k^t^> ( C ^ ) " 1 . With the i n i t i a l c o n d i t i o n s Cj » ( C 1) 0> c 2 = ( C 2^o a n d C=0, the constants i n the power law are: n - 1 - ( k 2 / k ! ) ( 11) « - ( C 2>o ( C i ) 0 k 2 / k V i n ( 12) C. E l e c t r o n i c Defects i n the Exchange Mechanism Both atomic and molecular types of V-centre a r e ' r e q u i r e d f o r our postu-l a t e d mechanisms, f o r the f o l l o w i n g reasons: (1) A second-order decay of defects i s r e q u i r e d t o account f o r both the d i r e c t l y - o b s e r v e d second-order k i n e t i c s and the assumed f i r s t step i n the k i n e t i c scheme t o e x p l a i n the power law. The most obvious ways - 76 -i n which a second-order decay can a r i s e are: (a) the adsorption of a c h l o r i n e molecule i n t o two d e f e c t s , each of which provides one anion vacancy; t h i s gives r i s e t o a molecular V-centre. (b) The evaporation of a c h l o r i n e molecule on the encounter of two atomic V-centres; t h i s i s e s s e n t i a l l y the reverse of ( a ) . (a) w i l l be used i n the "power law" mechanism, t h i s being the case i n which e l e c t r o n i c defects are not i n i t i a l l y present i n the s o l i d but may be formed on i n t e r a c t i o n w i t h c h l o r i n e . For the second-order exchanges, which are observed when e l e c t r o n i c d efects are i n i t i a l l y present i n excess of e q u i l i b r i u m , both (a) and (b) are p o s s i b i l i t i e s , but i t i s again found that (a) i s i n d i c a t e d by the k i n e t i c evidence. (2) The dependence of the "a" f a c t o r i n the power law upon the square root of the c h l o r i n e pressure i s strong evidence f o r the p a r t i c i p a t i o n of an atomic form of adsorbed or d i s s o l v e d c h l o r i n e i n the r e a c t i o n . The changeover'from d i r e c t t o inv e r s e dependence on the same f u n c t i o n of the pressure (Figure 21) i s reminiscent of the Langmuir-Hinshelwood k i n e t i c s f o r heterogeneously-catalysed r e a c t i o n s , and i s r e a d i l y accounted f o r by p o s t u l a t i n g that the r e a c t i o n needs both the adsorbed c h l o r i n e atoms and the centres which are blocked by the a d s o r p t i o n , so that the r e a c t i o n r a t e i s a maximum when h a l f these centres are occupied by c h l o r i n e atoms. Assumptions regarding i o n i c d efects In the d e t a i l e d r e a c t i o n scheme suggested below, the f o l l o w i n g assump-t i o n s are made concerning the i o n i c d efects of the c r y s t a l s , t h e i r e q u i l i b r i a w i t h each other and w i t h the l a t t i c e , and t h e i r m o b i l i t y : -- 77 -(1) Vacancies used up i n i n t e r a c t i o n w i t h c h l o r i n e are not replaced by thermal c r e a t i o n of new vacancies. This needs l i t t l e d i s c u s s i o n . The assumption that thermal e q u i l i b r i a between i o n i c defects and the l a t t i c e are completely frozen at room temperature i s not i n any way i n c o n s i s t e n t w i t h the m o b i l i t y which i s r e q u i r e d f o r the vacancy p a i r . Motion of defects may occur r e a d i l y i n c o n d i t i o n s i n which the c r e a t i o n of new vacancies i s impossible f o r reasons of a c t i v a t i o n energy. (2) The vacancy p a i r , ac, can move r a p i d l y throughout the whole c r y s t a l , and i n t o or out of the surface l a y e r , at room temperature. I t i s found necessary t o p o s t u l a t e that some species of defect i s used up very r a p i d l y by a d s o r p t i o n of c h l o r i n e at the beginning ;of the r e a c t i o n . This de-f e c t must i n c l u d e an anion vacancy and, even though the s i z e of the o c r y s t a l s i s u s u a l l y l e s s than 1000 A, the r e q u i r e d r a t e of m i g r a t i o n seems too great f o r i s o l a t e d vacancies at room temperature. The vacancy p a i r has been invoked f o r s i m i l a r reasons i n mechanisms f o r low-temperature b l e a c h i n g of colour c e n t r e s . Tharmalingam and L i d i a r d (49) have r e c e n t l y suggested, on the b a s i s of a t h e o r e t i c a l l y estimated a c t i v a t i o n energy, that the m o b i l i t y of the vacancy p a i r may be l e s s than has u s u a l l y been supposed. However, i t i s considered that the r e s u l t s add f u r t h e r weight t o the e a r l i e r k i n e t i c evidence and cast doubt on the new value of the m o b i l i t y . (3) The d i s t r i b u t i o n of i s o l a t e d anion and c a t i o n vacancies i s completely dominated by the "space-charge" e f f e c t p r e d i c t e d t h e o r e t i c a l l y by Lehovec (50), which leads t o an excess of c a t i o n vacancies i n the bulk , balanced by a very h i g h c o n c e n t r a t i o n of anion vacancies i n the surface l a y e r i t s e l f . The c a l c u l a t e d extent of the space charge i s s t r o n g l y - 78 -temperature dependent, and becomes l a r g e r than the c r y s t a l s at any temperature below about 300°C. (The e q u i l i b r i u m extent of the space-charge at room temperature would be about 1 mm, but the e q u i l i b r i u m presumably becomes frozen at a higher temperature.) The theory of the space charge needs to be amended f o r the case which the f i n i t e s i z e of the c r y s t a l i s important, and work on t h i s t o p i c i s i n progress i n t h i s l a b o r a t o r y . In the meantime, i t i s supposed that e s s e n t i a l l y a l l the anion vacancies are i n the surface l a y e r , w h i l e the c a t i o n vacancies are i n the b u l k . Charged species cannot t r a v e l from surface t o b u l k , or v i c e v e r s a , but each type of vacancy i s f a i r l y mobile w i t h i n i t s own r e g i o n . Cation vacancies can approach s u f f i c i e n t l y c l o s e t o the surface t h a t , w i t h the a s s i s t a n c e of an e l e c t r o n i c defect which may spread over more than one s i t e by covalent bonding, they may take p a r t , w i t h anion vacancies, i n defect s t r u c t u r e s such as C l ( a ) + ( a c 2 ) ~ . In consequence of these assumption, one might consider that processes i n v o l v i n g anion vacancies are q u i t e independent of those i n v o l v i n g vacancy p a i r s : the e q u i l i b r i u m a + c £ ac i s not e s t a b l i s h e d at room temperature. A l s o , the three species which s h a l l be r e q u i r e d t o move between surface and b u l k are a l l e l e c t r i c a l l y n e u t r a l . They are: ac; C l ( a ) 2 + + ( c 2 ) = ; C l ( a ) + ( a c 2 ) " . D. The Power Law Mechanism The nature of Pi and D7 The defect provides an a d s o r p t i o n s i t e f o r h a l f a c h l o r i n e molecule and t h e r e f o r e contains an anion vacancy. To account f o r the e a r l y establishment of the power law, most of the defect must be destroyed - 79 -w i t h i n the f i r s t minute of r e a c t i o n . I t i s t h e r e f o r e proposed that D} i s the vacancy p a i r , ac, and i s destroyed at the surface by adsorption of c h l o r i n e : C l 2 (g) + 2 ac — > C l ( a ) 2 + + ( c 2 ) - - (13) I f a l l the ac i n the b u l k are destroyed at the surface by t h i s r e a c t i o n , the surface c o n c e n t r a t i o n of the product depends i n v e r s e l y on the s p e c i f i c I | surface ( s ) . The product C l ( a ) 2 ( c 2 ) i s now i d e n t i f i e d w i t h D2. One now has a s i t u a t i o n i n which the c o n c e n t r a t i o n of D 2 i n i t i a l l y r i s e s r a p i d l y , but soon reaches an e s s e n t i a l l y constant value ( C 2 ) Q . However, the reactant D j , or ac, from which D 2 i s produced, now has a c o n c e n t r a t i o n depending i n v e r s e l y on the time. These v a r i a t i o n s are i l l u s t r a t e d i n Figure 28. The r e a c t i o n scheme r e q u i r e s D 2 t o be i n a c t i v a t e d f o r exchange by some f u r t h e r i n t e r a c t i o n w i t h the vacancy p a i r D j . Obviously, the important property of Dj here i s that i t contains an anion vacancy and thus enables the c h l o r i n e atoms of D 2 t o move to new s i t e s . This at once suggests two ways i n which D 2 could be i n a c t i v a t e d : f i r s t l y , i t could d i s s o c i a t e i n t o atomic c e n t r e s , C K a ^ ^ ^ r + ac — > C l ( a ) + ( c ) " + C l ( a ) + ( a c 2 ) " (14) secondly, i f the f u n c t i o n of D 2 i s t o provide a path f o r exchanging atoms between s o l i d and gas, D 2 must be i n the s u r f a c e , and i t s d i f f u s i o n i n t o the b u l k i s s u f f i c i e n t t o i n a c t i v a t e i t . This l a t t e r mechanism i s con-s i d e r e d t o be much the more probable, p a r t i c u l a r l y because the pressure dependence of the exchange r a t e i s d i f f i c u l t t o e x p l a i n without p o s t u l a t i n g e q u i l i b r i u m between atomic centres and the gas phase, and equation (14) - 81 -Implies a formation of atomic centres which has not yet reached e q u i l i b r i u m . Since ( G 2 ) Q r e s u l t s from the almost complete r e a c t i o n of i n i t i a l l y i n the co n c e n t r a t i o n ( C ^ ) D , there i s a d i r e c t r e l a t i o n between these two i n i t i a l c o n c e n t r a t i o n s : ( C 2 ) 0 - ( C ! ) 0 (N Dd 2/Ms) (15) i n which ( C ^ ) Q i s a mole f r a c t i o n i n the bulk , ( C 2 ) 0 i s a mole f r a c t i o n i n the surface l a y e r , N Q i s Avogadro's number, d the nearest neighbour spacing and M the molecular weight of NaCl. Equation (12) f o r the a f a c t o r of the power law, becomes: a = ( C l ) ; (N od 2/Ms) k-k n ( 1 6 ) n The pressure dependence • To account f o r the dependence of the a - f a c t o r on the square root of the c h l o r i n e pressure, the formation of atomic V-centres i n e q u i l i b r i u m w i t h the gas i s p o s t u l a t e d , the c h l o r i n e atoms being accommodated i n anion vacancies. The e q u i l i b r i u m set up i n the surface probably i n v o l v e s h o l e s , CI ( a ) * which are untrapped i n the sense that they are not a s s o c i a t e d w i t h c a t i o n vacancies, although they may be l o c a l i z e d by covalent bonding. The e q u i l i b r i u m may be w r i t t e n C l 2 ( g ) + 2 a+ 2 C l ( a ) + (17) and r e q u i r e s m o b i l i t y of a + across the s u r f a c e , s i n c e a C l 2 must be adsorbed i n a s i n g l e a c t . The e q u i l i b r i u m expressions are as f o l l o w s , i f Cg i s the c o n c e n t r a t i o n of p o s i t i v e holes and Cfl that of anion vacancies:-c 3 = ( c a ) 0 KJPVU + V * ) (18) - 82 -c a = ^ a V * 1 + K 1 P > <19> The p o s i t i v e holes can move by e l e c t r o n i c conduction, but can play no part i n the m i g r a t i o n of ions unless they are attached t o anion vacancies. The r a t e of anion m i g r a t i o n thus depends both on C3 and Cfl, which imme-d i a t e l y accounts f o r the observed "Langmuir-Hinshelwood" behaviour. On account of the e l e c t r o s t a t i c r e p u l s i o n between a hole and an anion vacancy, these species cannot long remain i n c l o s e p r o x i m i t y t o each other unless counterbalancing negative charges are present. Thus the mobile complex i s most probably s t a b i l i z e d by p i c k i n g up two c a t i o n vacancies as i t enters the b u l k . The r e s u l t i n g species C I ( a ) * ( a c 2 ) ~ corresponds t o S e i t z * s model of a V4 c e n t r e ; i t s c o n c e n t r a t i o n i s C^. I t has a l l the i n g r e d i e n t s which would be expected t o c o n t r i b u t e to a h i g h m o b i l i t y ; i t i s supposed that i t s c o n c e n t r a t i o n , on the other hand, i s very low, only a small p r o p o r t i o n of the a v a i l a b l e holes and vacancies being used up i n forming t h i s s p e c i e s . C l ( a ) + + a + + 2 c" «-* C l ( a ) + ( a c 2 ) " (20) C 4 = K 2 C 3 C a = K 2 ( C a ) 2 K l P * / ( l + K ^ ) 2 (21) I t i s assumed that the number of anion vacancies i n the surface i s con-t r o l l e d by the space-charge e f f e c t , so that the t o t a l number of anion vacancies i n the system i s an extensive property of the b u l k and not of the s u r f a c e . S i m i l a r l y , C4 i s a t r u e b u l k c o n c e n t r a t i o n and not a f u n c t i o n of s. I t should be noted that the pressure dependence of the a - f a c t o r i s the only experimental evidence i n the present work which r e q u i r e s the space-charge e f f e c t t o e x p l a i n - i t (except f o r the r e s u l t s on s i n t e r i n g - 83 -which cannot yet be i n t e r p r e t e d i n d e t a i l ) . I f the pressure dependence were d i f f e r e n t , i t might not be necessary to p o s t u l a t e complete i n -dependence of e q u i l i b r i a i n v o l v i n g a and ac, or to invoke the space-charge i n any way, although the general r o l e s of V-centres i n the r e a c t i o n might s t i l l be much as suggested. In t h i s connection, i t i s important t o note that the and P"^ dependences are e s t a b l i s h e d at d i f f e r e n t temperatures and the e x i s t e n c e of a maximum i n the a-P curve has been shown c l e a r l y at 60°C only, although the room temperature r e s u l t s appear _ o t o i n d i c a t e a maximum at 10 atm. Accepting t h i s l a t t e r f i g u r e , some rough c a l c u l a t i o n s can be made on the thermodynamics of the a d s o r p t i o n process of equation (17), s i n c e K l = 1 / pmax« F r o m pmax = 0 , 3 7 a t m a t 6 0 ° C a n d Pmax " 1 , 0 x 1 0 ~ 2 a t m at 25°C, i t i s c a l c u l a t e d , f o r the adsorption of 1 g-atm of CI, A H = -10.2 kcal/g-atom CI, AG298 =» 500 cal/g-atom, and AS298 = -39 cal/g-atom deg. The value of AH i s most e a s i l y discussed i n the t i g h t - b i n d i n g approximation, by c o n s i d e r i n g the p o s s i b l e energy of b i n d i n g of an adsorbed CI atom t o i t s neighbours i n a l o c a l i z e d covalent s t r u c t u r e (which very probably corresponds t o the a c t u a l s i t u a t i o n ) . W r i t i n g the simplest p o s s i b l e covalent s t r u c t u r e as Cl(a>2 +, which i s analogous t o the Cl2~ i o n i n s o l u t i o n , the heat of a d s o r p t i o n i s given t o a f i r s t approximation by A H » %D(C1 2) - D ( C l ( a ) 2 ) , whence D ( C l ( a ) 2 ) = 39 kcal/mole. In comparison, the V-centre which i s known t o have the s t r u c t u r e C l ( a ) 2 + i n KC1 has an o p t i c a l a b s o r p t i o n band at 7500 %\ the spectrum has not been analysed i n d e t a i l , but t h i s peak may perhaps be taken a s . g i v i n g a rough i n d i c a t i o n of the d i s s o c i a t i o n energy, and i t corresponds t o - 84 -38 kcal/mole (51). A s i m i l a r V-centre was found by Teegarden (36) i n a l k a l i c h l o r i d e s evaporated i n the presence of C l ^ , and Rudham (18) has r e c e n t l y suggested that t h i s species may be important i n s i n t e r i n g and exchange. The entropy change may be shown t o be reasonable without any very d e t a i l e d model of the adsorbed c h l o r i n e . Mott and Gurney have pointed out that the entropy of c r e a t i o n of a vacancy w i l l be determined l a r g e l y by the change i n the v i b r a t i o n frequencies of the nearest neighbours of the vacancy, which may amount t o a f a c t o r of 2 f o r 6 v i b r a t i o n s , g i v i n g exp( AS/R) = 2 = 64, whence A S = 8.4 cal/g-atom deg. I f i t i s assumed that the adsorbed atom loses a l l the entropy of gaseous c h l o r i n e , %S298(Cl2) = 26.7 cal/g-atom deg, and a l s o r e s t o r e s the normal l a t t i c e v i b r a t i o n frequencies of the s i x neighbouring atoms, g i v i n g a decrease of about 8.4 cal/g-atom deg, then the o v e r a l l entropy change on a d s o r p t i o n i s AS^gg = -35 cal/g-atom deg, i n reasonable agreement w i t h the observed v a l u e . The i n t e r p r e t a t i o n of the s i g n i f i c a n c e of P ^ , and of the pressure dependence i n g e n e r a l , i s s t r o n g l y supported by t h i s order-of-magnitude agreement between thermodynamic q u a n t i t i e s estimated f o r a d s o r p t i o n as atomic V-centres and those c a l c u l a t e d from P ^ . The exchange step and the t r a n s i t i o n complex The exchange between bulk and surface must take place on the en-counter of V 2 ( s u r f ) w i t h V ^ ( b u l k ) , at a r a t e p r o p o r t i o n a l t o the two concentrations and t o the s p e c i f i c surface s. dC/dt • k 3 s C 2 C 4 (22) - 85 -Comparison w i t h equation (10) g i v e s . k e = kgSC^, and on combining t h i s w i t h equations (16) and (21) the f i n a l expression f o r the a - f a c t o r becomes a = K ( C I ) " (C a)2 K^/U + K P*) (23) where K = (N Qd 2/M) K 2 k 3 k n (24) n In these expressions, the d i r e c t and inverse dependences on s shown i n equations (16) and (22) have c a n c e l l e d t o leave the a - f a c t o r independent of s, as r e q u i r e d . In e f f e c t , although there i s non-uniform d i s t r i b u -t i o n of both V 2 - c e n t r e s and anion vacancies between surface and b u l k , a l l the concentrations that are concerned are r e a l l y b u l k concentrations. The f i n a l step i n the transference of a 3^C1 atom from bulk t o surface i s thus considered t o take place by way of a t r a n s i t i o n complex of V 2 ( s u r f ) w i t h a centre immediately beneath the s u r f a c e . This com-pl e x has an i n t e r e s t i n g geometry (see Figure 29); c h l o r i n e atoms (trapped holes) occupy three corners of a tetrahedron, the f o u r t h corner being vacant. Movement of t h i s vacancy along two sides of the tetrahedron b r i n g s about exchange. The complex i s surrounded by four unoccupied c a t i o n s i t e s t o complete a c u b i c a l v o i d i n the l a t t i c e i n which three uncharged c h l o r i n e atoms are the only occupants of eight s i t e s . These atoms may of course be g r e a t l y d i s p l a c e d from t h e i r normal l a t t i c e s i t e s . E. Mechanism of Second-order Reactions For second-order k i n e t i c s t o be observed i n the i s o t o p i c exchange r e a c t i o n i t i s necessary that the r a t e of d e s t r u c t i o n of a p a r t i c u l a r r e a c t i o n intermediate and the r a t e of exchange should both depend on the square of the c o n c e n t r a t i o n of the intermediate. I t i s considered that Figure 29. - 87 -the most probable intermediate i s the "V, centre " , CI (a) (ac,,)", since 4 * • ' i t i s l i k e l y t o be mobile and si n c e i t contains an anion vacancy which i s a p o t e n t i a l a d s o r p t i o n s i t e f o r a CI atom; t h i s centre i s thus assigned a s i m i l a r r o l e i n the proposed mechanism t o that of the vacancy p a i r i n the power law mechanism. W r i t i n g C 4 f o r the co n c e n t r a t i o n of V"4 and Ng f o r the number of moles of CI exchanged per mole of s o l i d at any time, we r e q u i r e the k i n e t i c equations t o reduce t o the form: dC 4/dt = - k 4 c | (25) dN g/dt = k 5 c | (26) S o l u t i o n of these equations w i t h the i n i t i a l and f i n a l c o n d i t i o n s ft = 0, c 4 = < c4) 0» N g = °» and t =oo , C 4 = 0 y i e l d s d ( C 0 0 -C)/dt = - ( k l / k s C g ' M C o o - C ) 2 (27) where C ^ = ^ ' ( N ^ ^ = < W < C 4 > o C e ' ( 2 8 ) The r a t e constant i n equation (27) i s k c; and si n c e k f l i s defined by k n = kc Ce'» t h e n k n = k 4 / k 5 (29) Now the r e s u l t s f o r X - i r r a d i a t e d f i l m s i n d i c a t e d that k was n d i r e c t l y p r o p o r t i o n a l t o the pressure P, w h i l e CQO/C^ was independent of P. Equations (28) and (29) then i n d i c a t e that both k 4 and k^ are d i r e c t l y p r o p o r t i o n a l t o P. ( I t may be noted that a p o s s i b l e d i r e c t r e l a t i o n s h i p of C w /CE* t o P was not q u i t e c o n c l u s i v e l y e l i m i n a t e d by the r e s u l t s ; but such a r e l a t i o n s h i p seems p h y s i c a l l y unreasonable 2 3 since i t leads t o k^ p r o p o r t i o n a l to P and k^ p r o p o r t i o n a l t o P , and these v a r i a t i o n s are almost impossible t o e x p l a i n on any reasonable mechanism.) - 88 -The requirements which the r e a c t i o n scheme must f u l f i l are now by no means so unusual and r e s t r i c t i v e as f o r the power law mechanism, and i t i s q u i t e p o s s i b l e that s e v e r a l r e a c t i o n schemes might be devised t o e x p l a i n a l l the k i n e t i c r e s u l t s . The f o l l o w i n g 'schemeiis.proposed* Two "V^" centres may react w i t h a molecule of c h l o r i n e at the surface t o form a p a i r of " V 2 " centres l y i n g adjacent t o each other; these are not very mobile and w i l l not separate f o r some time. The combined defect s h a l l be c a l l e d D5 and i t s c o n c e n t r a t i o n C^ _. I t i s supposed that an e q u i l i b r i u m i s e s t a b l i s h e d : 2 C l ( a ) + ( a c 2 ) " + C l 2 ^==* lei ( a ) 2 + + ( c 2 ) ^ l 2 (30) V 4 D 5 C 5 = ( k 5 ' / k 5 " ) C ^ P (31) This i s the p r i n c i p a l r e a c t i o n i n v o l v i n g adsorption and d e s o r p t i o n of c h l o r i n e and governs the r a t e of exchange: dN g/dt - k 5c|p (32) Some means i s a l s o r e q u i r e d whereby the e l e c t r o n i c defects can be i r r e v e r s i b l y destroyed. They are present i n great excess of e q u i l i b r i u m , and i f they are converted i n t o i o n i c d e f e c t s , such as ac, by desorption of C l 2 , then the i o n i c defects should be a n n i h i l a t e d by i n t e r a c t i o n w i t h the l a t t i c e . I t i s proposed that a small p r o p o r t i o n of i s destroyed as f o l l o w s : | c i ( a ) 2 " H ' ( c 2 ) = ] 2 2 ac + C l 2 + C l ( a ) 2 + + ( c 2 ) = (33) T h i s , through the e q u i l i b r i u m (30), becomes the r e a c t i o n which destroys V^, and we have: -(dC 4/dt) = k 6 C 5 = k 6 ( k 5 ' / k 5 " ) C 2 P (34) - 89 -Equations (32) and (34) show the r e q u i r e d dependence of both decay r a t e and exchange r a t e on P, and are the same as equations (25) and (26), w i t h K5 =» k^'P and k^ = k ^ k ^ ' / k ^ " ) ? . The mechanism allows the amount of c h l o r i n e adsorbed and desorbed i n the exchange r e a c t i o n t o be much greater than that desorbed d i r e c t l y i n the decay of e l e c t r o n i c d e f e c t s . This i s an e s s e n t i a l f e a t u r e , s i n c e the p r o p o r t i o n of the s o l i d exchanged i s of the order of 20 per cent, w h i l e the e l e c t r o n i c defects are u n l i k e l y t o exceed about one quarter of one per cent of the s o l i d . The present experimental evidence i s i n s u f f i c i e n t t o permit a d e t a i l e d d i s c u s s i o n of the decay of e l e c t r o n i c defects which i s going on during the delay time (and which i s not accompanied by any measurable e v o l u t i o n of c h l o r i n e , as was determined i n a blank run) or of the i n t e r e s t i n g d i f f e r e n c e s between X - i r r a d i a t e d and f l u o r i n a t e d samples. The l a t t e r , i n p a r t i c u l a r deserve extensive f u r t h e r study. - 90 -F. Summary of Conclusions and Suggestions f o r Further Work 1. Both the power law and the second-order law occur p r i n c i p a l l y because two defects are i n v o l v e d i n the a d s o r p t i o n or desorption of a molecule of c h l o r i n e . 2. Both types of r e a c t i o n i n v o l v e e l e c t r o n i c d e f e c t s , a r i s i n g e i t h e r from a d s o r p t i o n of c h l o r i n e or from the pretreatment ( X - i r r a d i a t i o n or vigorous o x i d a t i o n ) . 3. Both "molecular" and "atomic" defects are i n v o l v e d , these terms being used t o i n d i c a t e the number of trapped holes i n the d e f e c t , r a t h e r than t o imply the presence or absence of covalent bonding, which i s probably present i n both types of d e f e c t . 4. The power law r e a c t i o n s probably i n v o l v e a t r a n s i t i o n complex between an "atomic" defect and a "molecular" one. 5. The mechanism of the power law r e a c t i o n s seems t o r e q u i r e the e x i s -tence of a s t r o n g l y developed "space-charge" i n the c r y s t a l s , causing the anion vacancies t o be concentrated i n the surface l a y e r , and i n h i b i t i n g the movement of charged species between surface and bulk. A t h e o r e t i c a l study of the space-charge e f f e c t t o be expected i n very small c r y s t a l s would be u s e f u l . 6. The d e t a i l e d mechanisms proposed are based e n t i r e l y on i n d i r e c t k i n e t i c evidence, and lean p a r t i c u l a r l y h e a v i l y on the pressure dependence. Further work by more d i r e c t methods would be d e s i r a b l e , e s p e c i a l l y e l e c t r o n s p i n resonance s t u d i e s , i n view of the extensive use of atomic defects i n the mechanisms. - 91 -7. There i s evidence f o r a decay of e l e c t r o n i c defects i n these evaporated f i l m s which i s much more r a p i d than the bleac h i n g of colour centres i n la r g e s i n g l e c r y s t a l s . The decay i s more r a p i d f o r f l u o r i n a t e d than f o r X - i r r a d i a t e d samples. These processes need extensive f u r t h e r i n v e s t i g a t i o n . APPENDIX A Measurement of P a r t i c l e Size and I n t e r n a l S t r a i n by X-ray D i f f r a c t i o n - 92 -I n t r o d u c t i o n The measurement of p a r t i c l e s i z e from X-ray powder d i f f r a c t i o n measurements was e s t a b l i s h e d by Jones (52) as a p r a c t i c a l method, based on the t h e o r e t i c a l treatment of Laue (53). I f the i n t e n s i t y d i s t r i b u t i o n of the d i f f r a c t e d l i n e s can be a c c u r a t e l y found as a f u n c t i o n of angle then i t i s t h e o r e t i c a l l y p o s s i b l e to determine s i z e , shape and s t r a i n i n very small c r y s t a l l i t e s ( 5 4 ) . The experimental procedures are by no means easy however and r e q u i r e the use of many c o r r e c t i o n s which have been reviewed by Klug (55) i f the r e s u l t s are t o be r e l i a b l e . For t h i s purpose the parameter g e n e r a l l y measured i s the breadth of the l i n e , although t h i s does not completely s p e c i f y the p r o f i l e . Two d e f i n i t i o n s of breadth are c u r r e n t l y i n use; the h a l f breadth or width of the l i n e i n radians measured at h a l f , the height of the peak, and the i n t e g r a l breadth ( i n t e g r a t e d i n t e n s i t y d i v i d e d by the peak i n t e n s i t y ) . The breadth of a l i n e has two components i n p r a c t i c e . These are the i n t r i n s i c breadth (3 which i s r e l a t e d to the c r y s t a l t e x t u r e and the instrumental breadth b which depends on the experimental arrangement. To determine the i n t r i n s i c breadth ^ from the measured breadth B i t i s necessary to subtract the instrumental breadth b. Since l i n e broadening i s n e g l i g i b l e f o r p a r t i c l e s whose s i z e exceeds 1/*, these ( i f they are s t r a i n f r e e ) w i l l give the instrumental broadening b although care must be taken not t o exceed about lOOyu- or an i r r e g u l a r 'spotty' l i n e w i l l r e s u l t . In order t o place both specimens under p r e c i s e l y the same instrumental v a r i a b l e s Jones (52) has combined them i n the same c a p i l l a r y . U n f o r t u n a t e l y , the procedure could not be adopted here as the p a r t i c l e s are prepared and loaded under vacuum and i t was not - 93 -p r a c t i c a b l e t o load the quartz p a r t i c l e s w i t h them. I t i s r a r e that the i n t r i n s i c breadth can be obtained from the simple expression f = B - b. (35) used by von Laue, since the l i n e shapes of the pure d i f f r a c t i o n and instrumental broadening are r a r e l y i d e n t i c a l and c o r r e c t i o n s are necessary (52). R e l a t i o n of ^ t o p a r t i c l e s i z e In the absence of s t r a i n , the thickness £ of a c r y s t a l of uniform t h i c k n e s s i s r e l a t e d t o the i n t r i n s i c breadth ^ of a r e f l e c t i o n by € = ty^cosG (36) then the determination of the absolute c r y s t a l s i z e i s p o s s i b l e . In p r a c t i c e however, a c r y s t a l l i t e isCseldom of uniform t h i c k n e s s ; a c c o r d i n g l y the accuracy i s measured by i n t r o d u c i n g a shape f a c t o r K 6 = K-X/^ cose (37) where the numerical value of K can vary from 0.7-1.7 depending on the i n d i c e s ( h , k , l ) of the r e f l e c t i n g planes, the d e f i n i t i o n of breadth, and of s i z e as w e l l as on t h e i r u n i f o r m i t y of s i z e and shape. Even a f t e r t a k i n g such p o i n t s i n t o c o n s i d e r a t i o n the absolute accuracy w i l l be only 20-40% ( 5 5 ) . The Measurement of S t r a i n The i n t r i n s i c breadth ^ of a r e f l e c t i o n i s , i n a d d i t i o n , r e l a t e d to the i n t e r n a l apparent s t r a i n >J of a c r y s t a l l i t e by the expression ^ - "H tanG (38) where "rj i s given b y " ^ = 2^hkl^°^' where ^ h k l ^ e ^ d e * 8 t n e f r a c t i ° n °f - 94 -the c r y s t a l f o r which the t e n s i l e s t r a i n i n the h.k,!1 d i r e c t i o n l i e s between e and e + de. I t must be remembered that i t i s the v a r i a t i o n i n the u n i t c e l l s i z e which causes broadening. A uniformly expanded or contracted l a t t i c e causes a displacement of the r e f l e c t i o n s . I t should be p o s s i b l e to d i f f e r e n t i a t e between s i z e and s t r a i n forms of broadening because they depend d i f f e r e n t l y on 0, as discussed below (54). Wood (59) suggests that the two forms are a d d i t i v e provided both s i z e and s t r a i n l i n e p r o f i l e s corresponds t o a Cauchy d i s t r i b u t i o n f u n c t i o n ; as the s t r a i n broadening d i s t r i b u t i o n f u n c t i o n i s unknown since i t i s i n t i m a t e l y bound up w i t h the d i s l o c a t i o n p a t t e r n i n the c r y s t a l any p r e c i s e s e p a r a t i o n of these parameters i s at present impossible (60). However, a semi-empirical approach i s p o s s i b l e , f o r i f these forms are a d d i t i v e then ft cos© = I + -»i.sin0 (39) * x e a Such an approach has been undertaken by H a l l (61) f o r a s e r i e s of metals based on t h i s r e l a t i o n . By p l o t t i n g ^ c o t 0 / X against 2sin0/X a l i n e a r p l o t should r e s u l t , the slope g i v i n g the mean absolute s t r a i n and the r e c i p r o c a l of the i n t e r c e p t on the ^ c o s 0 / \ a x i s g i v i n g the c r y s t a l l i t e s i z e . Thus when broadening i s caused by s i z e alone the l i n e i s h o r i z o n t a l and when by s t r a i n alone the l i n e passes through the o r i g i n . He was thus able t o c o r r e l a t e the slope w i t h i n c r e a s i n g hardness of h i s metals, (see Figure 35). A f u r t h e r check on the v a l i d i t y of equation (39) i s t o determine the t r u e breadths of at two or more wavelengths and check that the r e s u l t i n g p l o t s are superlmposable. - 95 -Experimental P r e p a r a t i o n of Standard Quartz P a r t i c l e s Apart from the s i z e of the standard p a r t i c l e s being 10-lOOytc., i t i s important that they are s t r a i n f r e e . Often annealed metal f i l i n g s are used. Quartz p a r t i c l e s are a l s o i n common use (52,55) although they have l e s s d e f i n i t e h i s t o r y of p r e p a r a t i o n . A sample of quartz powder whose h i s t o r y was unknown was f r a c t i o n a t e d i n a s e t t l i n g column. Successive f r a c t i o n a l e l u t i o n s of the suspension a f t e r 5 minutes of settlement l e f t a residue of > 20ycc p a r t i c l e s that were loaded i n t o a 0.5 mm c a p i l l a r y f o r use as a r e f e r e n c e . C a l c u l a t i o n s based on a determination of the surface area of these p a r t i c l e s and micro f i l t r a t i o n u s i n g m i l l i p o r e f i l t e r s confirmed that l e s s than 10% of the p a r t i c l e s present were l e s s than lym.. P r e p a r a t i o n of Sample of Evaporated F i l m of NaCl The evaporated f i l m was prepared by the standard method and c o l l e c t e d under vacuum i n a 0.5 mm. Lindemann c a p i l l a r y i n s e r t e d o b l i q u e l y i n t o the side arm of the b a s i c c o l l e c t o r system (at the point * i n Figure 6). Counting Techniques The measurements of l i n e width were performed on a General E l e c t r i c XRD-5 d i f f r a c t o m e t e r coupled t o an i o n i s a t i o n chamber scanner and s c a l e r system (No. 2SPG) which allowed both h a l f - h e i g h t and i n t e g r a t e d i n t e n s i t i e s to be measured. The a n a l y s i s of the r e s u l t s followed the treatment of Jones (52). For measurements of p a r t i c l e s i z e CuK^ r a d i a t i o n was used w i t h a n i c k e l f i l t e r t o improve monochromacity. A detector s l i t width of 0.20° gave the maximum s e n s i t i v i t y without r e s u l t i n g i n any detectable l o s s of r e s o l u t i o n . - 96 -Experimentally i t was found that i n t e g r a l breadths appeared l e s s r e p r o d u c i b l e than h a l f height l i n e widths and were not used i n t h i s study. S t a t i s t i c a l Counting E r r o r s To measure a l i n e i n t e n s i t y w i t h some d e s i r e d degree of accuracy, a d e f i n i t e number of pulses must be counted. And since the background counting r a t e can be appreciable the p r o b a b i l i t y of e r r o r of the net peak height w i l l a l s o depend on the r a t i o of the t o t a l t o the background counting rates,/R. I f N t are the t o t a l counts recorded at the top of the peak ( i n c l u d i n g background) then the per cent probable e r r o r i n the net peak height i s given by (55) U„ - 0.675 4/ R(R + .1)/N t (40) (R-D Thus from a predetermined run over the l i n e the r a t i o R was found and the minimum number of counts r e q u i r e d f o r a maximum probable e r r o r of 1% was estimated g r a p h i c a l l y from a p l o t of equation (40) f o r d i f f e r e n t values of R. This background i s represented by the angular ranges on e i t h e r s i d e of the l i n e which always equal l e d the angular range of the l i n e . The t o t a l counts i n these regions were g e n e r a l l y greater than 10.K. ^ Scanning Procedure Having determined the minimum t o t a l counts necessary to define the l i n e the mounted specimen was f i r s t scanned t o l o c a t e the p r e c i s e peak p o s i t i o n and peak l i n e i n t e n s i t y and the goniometer set 1° below t h i s v alue. Line i n t e n s i t i e s were then measured at 6 second i n t e r v a l s over a 2° scan so that 10 p o i n t s were obtained f o r the base l i n e and 10 f o r the l i n e i t s e l f . The measurement of i n t e n s i t y was determined - 97 -Figure 30. C a l c u l a t i o n of Half-Height L i n e Width from a Sodium Ch l o r i d e (222) Line P r o f i l e . 24.20 25.00 25.80 Bragg Angle (2 9)° - 98 -by f i n d i n g the time f o r a preset count, c a l c u l a t e d from equation (40) (see Figure 30). Line Width C o r r e c t i o n s Two sets of c o r r e c t i o n s are g e n e r a l l y necessary. These are the c o r r e c t i o n s due t o the s p l i t t i n g of the 0( doublet and that a r i s i n g from the d i f f e r e n t l i n e shapes of the unknown and reference specimen (52). From a curve showing the sep a r a t i o n of the c< doublet d i n radians as a f u n c t i o n of © ( h a l f the Bragg angle) f o r the r a d i a t i o n used; i f B Q i s the observed breadth of the sodium c h l o r i d e specimen at some angle 0 and b Q the i n t e r p o l a t e d breadth of the reference specimen at the same angle then the r a t i o s d/B e and d/b e can be found and the appropriate g r a p h i c a l c o r r e c t i o n f o r the o< doublet a p p l i e d . B and b are then the breadths a f t e r the c o r r e c t i o n has been made (see Tables V I I - I X ) . The l i n e shape c o r r e c t i o n must now be a p p l i e d to the derived breadths b and B, which a r i s e s from d i f f e r e n t l i n e p r o f i l e s f o r the instrumental broadening f u n c t i o n f ( x ) d x and the true d i f f r a c t i o n broadening of the specimen F(kx)dx (55). Jones has provided a very u s e f u l g r a p h i c a l s o l u t i o n to t h i s problem f o r c e r t a i n d e f i n i t e p r o f i l e shapes. He has shown that i f the instrumental broadening p r o f i l e i s a Cauchy type f u n c t i o n (see Figure 32) and the pure d i f f r a c t i o n broadening i s Gaussian; as i s found i n these experiments, then h i s c o r r e c t i o n curve (a) may be a p p l i e d t o the r a t i o b/B t o give ^/B and hence . Unfo r t u n a t e l y , b/B i s q u i t e large i n these experiments ( ~ 0.85) so that the s i z e may be considerably underestimated by up to 257» i f these simple fun c t i o n s are only approximately c o r r e c t d e s c r i p t i o n s of the true l i n e shapes. - 99 -Figure 31. Experimental Sodium C h l o r i d e Line P r o f i l e compared to Gaussian Function exp(-k 2x ) 0.40 0.20 0 0.20 0.40 Angle (degrees) - 100 -Figure 32. Comparison of the Instrumental P r o f i l e Quartz (202) Line w i t h Gaussian and Cauchy P r o f i l e s . I n t e n s i t y c.p.s. Bragg Angle (2 0)° - 101 -In the author's opinion t h i s c o n s t i t u t e s the greatest s i n g l e source of e r r o r i n the determination of the absolute s i z e by t h i s method. Warren's c o r r e c t i o n (62) was found t o over-correct f o r (2 presumably due t o the instrumental broadening being more Cauchy than Gaussian i n form. Re s u l t s and Discuss i o n The Instrumental l i n e width b These were measured at 0.711 A* and 1.54 X using CuK^ and MoK^ r a d i a t i o n on the quartz p a r t i c l e s p r e v i o u s l y described and mounted i n a 0.5 mm Lindemann c a p i l l a r y . The r e s u l t s of the h a l f height l i n e widths are summarised i n Figure 3 3 ( a ) , the measurements and t h e i r o< doublet c o r r e c t i o n s are given i n Table VIII(a) and (b) below. Table V I I I (a) Molybdenum R a d i a t i o n Breadths i n degrees Quartz Line Widths Indices e b o d d/b 0 b/b o b 100 6.2 .290 .067 .231 .938 .272 101 12.4 .314 .138 .440 .793 .249 121 14.4 .367 .161 .439 .792 ,290 I n t e r p o l a t e d Values 0 b o d d/bQ b/bQ b 7.5 .298 .083 .277 .912 .272 10.0 .312 .109 .350 .859 .268 15.0 .347 .172 .496 .751 .260 Since the r e s u l t s f o r the s h o r t e r wavelength were more s c a t t e r e d and the corresponding b^ i s r e q u i r e d as a f u n c t i o n of the Bragg angle a set of i n t e r p o l a t e d values was taken i n t h i s case. 0 20 40 60 80 0 10 20 30 Bragg A n g l e 0 Figure 33. (a) V a r i a t i o n of Instrumental Line-Width I (b) C a l c u l a t i o n of ^ f o r F i l m I . b Q w i t h Bragg A n g l e s at two Wavelengths. | - 103 -Table V I I I (b) Copper R a d i a t i o n Breadths i n degrees Quartz L i n e Widths Indices 0 b o d d/b D b/b Q b 100, 10.2 .320 .051 .160 , .972 .311 101 13.2 .322 .068 .211 .950 .306 102 30.0 .346 .154 .445 .784 .271 NaCl f i l m l i n e widths The r e s u l t s f o r two NaCl f i l m s , designated f i l m I and f i l m I I , are shown i n Tables IX - XI and Figures 33 and 34. F i l m I was s t u d i e d w i t h molybdenum r a d i a t i o n only, but a B.E.T. measurement of surface area i s a v a i l a b l e f o r comparison w i t h the p a r t i c l e s i z e from X-ray d i f f r a c -t i o n . F i l m I I was s t u d i e d w i t h both molybdenum and copper K«t r a d i a t i o n s , but there i s no B.E.T. measurement. The l a s t column of Tables X and XI shows the p a r t i c l e s i z e £ c a l c u l a t e d assuming that there i s no s t r a i n and that the p a r t i c l e s are 100 o r i e n t e d cubes, so that K = 1.07 and 6 i s the cube root of the volume. For F i l m I , the mean value € = 250 A compares w i t h € = 553 A* c a l c u l a t e d from the B.E.T. s p e c i f i c surface of 50.0 m2/g. This s p e c i f i c surface assumes that the adsorbed Kr atoms are packed as i n s o l i d K r. The l i q u i d d e n s i t y of Kr gives values i n much b e t t e r agreement w i t h the X-ray measurements, v i z . , s p e c i f i c surface =» 71.6 m2/g, whence £ = 386 ft. However, i n view of the wide l i m i t s of e r r o r of both methods, l i t t l e s i g n i f i c a n c e has been attached t o t h i s agreement, and the close-packing ( s o l i d ) model f o r adsorbed Kr has been considered p h y s i c a l l y more reasonable and used f o r a l l other surface areas quoted i n t h i s t h e s i s . - 105 -The constancy of the values of £ c a l c u l a t e d f o r v a r y i n g 0 (Tables x and XI) suggests that the broadening i s indeed p r i m a r i l y caused by p a r t i c l e s i z e r a t h e r than s t r a i n . To t r y t o put t h i s on a more q u a n t i t a t i v e b a s i s , ^ cos 0/K has been p l o t t e d against 2 s i n 0/\ f o r both f i l m s (Table X I I and Figure 35). The r e s u l t s are not very s a t i s f a c t o r y , since the two l i n e s f o r the same f i l m at d i f f e r e n t X (Figure 35, 11(a) and 11(b)) should c o i n c i d e . The discrepancy between the two l i n e s probably represents a breakdown of the a d d i t i v i t y of B and b (equation 35), since the o v e r a l l l i n e shape i s c l o s e r t o Gaussian than Cauchy. However, some rough q u a n t i t a t i v e estimates can be made from the r e s u l t s . The highest p o s s i b l e value of the s t r a i n i n d i c a t e d by the slopes of the l i n e s i n Figure 35 i s ft*10~3, and the most probable value i s considerably l e s s . To make an order-of-magnitude estimate of the c o n c e n t r a t i o n of d i s -l o c a t i o n s , l e t us assume a square arra y of d i s l o c a t i o n s , w i t h separation 1. 2 Thus there i s one d i s l o c a t i o n per area 1 i n a plane perpendicular t o the d i s l o c a t i o n l i n e s . The s t r a i n a s s o c i a t e d w i t h a d i s l o c a t i o n of -15 2 u n i t s t r e n g t h should be roughly on atomic area, or about 10 J car. Thus *\ - 10° 1 5/1 2, so that 1 - (10" 1 5/y| cm. Then "V^* - 10~ 3 o corresponds t o l m ^ n " 100 A. The most probable value of 1 i s thus o s e v e r a l hundred A, which suggests that each c r y s t a l i n the evaporated f i l m i s constructed upon a s i n g l e d i s l o c a t i o n . Tabulated R e s u l t s Table V I I : F i l m I ; measured l i n e widths and oC-doublet c o r r e c t i o n s . Table V I I I : F i l m I ; Jones shape c o r r e c t i o n and c a l c u l a t i o n of<E.. Table IX: R e s u l t s f o r f i l m I I . Table X: C a l c u l a t i o n s t o determine s t r a i n . - 106 -Figure 35. The Determination of S t r a i n . s i n Q/K I . NaCl f i l m I , MoK^ (Thesis) I l a . b . NaCl f i l m I I , MoK^ and CuK^ (Thesis) I I I . A l f i l i n g s , CuK^ H a l l and Williamson (unpublished measurements) IV. M a r t e n s i t e rod, FeK^ , Wheeler and Jaswon (1947) -107 -Table IX Measured l i n e widths and c< -doublet c o r r e c t i o n s Molybdenum r a d i a t i o n Breadths i n degrees Sodium C h l o r i d e ( F i l m I ) Indices e B o d/B o B/B 0 B 200 7.2 .333 .231 .961 .320 220 10.2 .367 .305 .928 .340 222 12.6 .375 .366 .896 .336 420 16.3 .405 .460 .822 .333 Table X F i l m I ; Jones shape c o r r e c t i o n and c a l c u l a t i o n of 6 Ind i c e s 9 B b e b e/B S/B €&) 200 7.2 .320 .272 .850 .472 .151 292 220 10.2 .340 .267 .785 .561 .191 232 222 12.6 .336 .264 .764 .583 .196 228 420 16.3 .333 .258 .775 .570 .190 239 Table XI(a) Re s u l t s f o r F i l m I I u s i n g CuK^ and MoK^ R a d i a t i o n Copper R a d i a t i o n Breadths i n degrees In d i c e s e B o d/B o B b/B ** € ( X ) 200 16.0 .366 .232 .352 .300 .852 .169 584 220 22.7 .375 .304 .348 .286 .821 .181 566 222 28.2 .380 .377 .340 .275 .807 .181 594 420 37.7 .395 .542 .291 .255 .876 .128 934 Table XI (b) Molybdenum r a d i a t i o n Breadths i n degrees In d i c e s e V d/B o B b/B r €(A) 200 7.2 .308 .250 .294 .272 .925 .103 427 220 10.2 .330 .306 .306 .268 .875 .136 327 222 12.6 .353 .388 .312 .264 .846 .149 301 420 16.3 .382 .487 .304 .258 .850 .145 314 - 108 -Table X I I C a l c u l a t i o n s t o determine s t r a i n Breadths i n radians l i c e s cos9 ^cosO/X s i n 9 2sin6/X X x l O 3 x l O " 5 x l O " 8 200 2.95 .961 1.84 .276 .359 1.54 220 3.15 .922 1.88 .386 .502 1.54 222 3.21 .881,, 1.85 .473 .615 1.54 420 2.23 .791 1.15 .611 .794 1.54 200 1.79 .992 2.50 .125 .352 .711 220 2.37 .983 3.25 .177 .498 .711 222 2.60 .975 3.57 .216 .609 .711 420 2.53 .960 3.42 .281 .790 .711 APPENDIX B - 109 -Summary of Experiments The exchange st u d i e s commencing at run 20 and f i n i s h i n g at run 83 have been sub-divided i n t o four s e c t i o n s . The untreated f i l m s (see Table X I I I ) s i n t e r i n g experiments (see Table XIV), X - i r r a d i a t e d and bleached f i l m s (see Table XV), and f l u o r i n a t e d f i l m s (see Table XVI). The r e s u l t s are represented as f o l l o w s ( i ) A l l a and C e values have been c o r r e c t e d f o r a s p e c i f i c a c t i v i t y of 1 0 4 c.p.m./g; the values of s p e c i f i c a c t i v i t y are summarised i n Table I I of the Experimental S e c t i o n . ( i i ) Where no f i g u r e s are given f o r the r a t e laws, these are deemed too u n c e r t a i n to f a l l i n t o e i t h e r the second order or power law cate-gory (see p. 50 i n the R e s u l t s S e c t i o n ) . ( i i i ) The pre-treatment s e c t i o n has the f o l l o w i n g a b b r e v i a t i o n s ; - ... none X ... x - i r r a d i a t e d B ... bleached F ... f l u o r i n a t e d S ... s i n t e r e d where two treatments are a p p l i e d , i . e . , X - i r r a d i a t i o n followed by b l e a c h i n g the symbols are presented thus, X/B. t j ... i s the time of treatment (hours) t 2 ... i s the delay time between treatment and r e a c t i o n (mins.) tjj ... i s the b l e a c h i n g time (mins.) o~i and ... are the i n i t i a l and f i n a l s p e c i f i c surface areas on s i n t e r i n g . S u f f i x e s L and D t o the run numbers, s i g n i f y whether the r e a c t i o n s took place i n the presence or absence of l i g h t . ( i v ) F i n a l l y , In the r e s u l t s s e c t i o n the f i r s t column gives the a/m values i n c.p.m. sec . ~ n . g " ^ f o r power law behaviour, and k n i n I - 110 -min. f o r second order r e a c t i o n s . The second column gives the exponent n f o r the power law and C^, f o r the second order r e a c t i o n s . A l l r a d i o a c t i v e a c t i v i t i e s are given i n counts per minute. - I l l -Table X I I I Untreated Films at -5, 25 and 60°C. Exchange Re s u l t s Power Law Run Weight (m2/g) T°C P c i 2 a/m n C e gram. o~ (Ats) 2 0 L .1952 83.6 25 .487 1,400 .43 74,300 21L 2 2 L .478 49.5 25 .718 1,300 .39 19,120 .247 20.5 25 .210 2,920 .34 6,640 2 4 D .103 18.6 -5 .119 660 .45 2,093 2 8 L .201 28.7 58 .97 3,430 .35 3,550 3 0 L .115 55.3 60 .432 9,480 .37 3,345 3 1 L .0945 52.4 60 .145 4,540 .45 2,680 3 2 L .124 43.6 25 .072 3,650 .44 2,445 33^ .042 54.5 25 .0195 4,270 .43 731 3 4 L .132 65.4 60 .056 2,650 .36 4,390 .165 65.7 60 .698 6,220 .31 12,370 3 6 L .065 50.6 60 .0195 2,045 .45 4,595 3 ? L .055 59.3 60 .280 5,550 .31 4,225 3 8 D .0472 52.5 -5 .304 4,890 .36 3,705 3 9 D .126 91.6 -5 .492 3,580 .38 9,360 Table XIV Sintered F i l m s . Run Pre-treatment Type S i n t e r i n g Temp. ^ " i O-'f (OC) (m2/g) (m2/g) 7 3 D S 250 66.5 33.4 7 2 D S 295 21.7 12.6 7 4 D S 350 18.8 1.22 7 5 n S 400 48.7 1.06 Exchange R e s u l t s Power Law: Weight Temp. PC12 (g.) °C (atm.) a/m n C e .1273 25 .442 523 .54 9640 .1529 25 .442 296 .55 1120 .2870 25 .399 196 .53 18950 .1895 25 .579 72 .36 14020 Table XV X - i r r a d i a t e d Films Pre-treatment Exchange R e s u l t s Second Order Type fcl t2 tB Weight 9~ T P C I 2 10 2k C <hr) (min) (min) (g) (m2/g) (ec) (atm) X 3.0 60 _ .0996 46.5 25 .244 - -X 4.5 15 - .0888 86.4 25 .109 - - -X 40 100 - .0805 100.0 25 .360 - - -X .5 + .5 30 - .0621 44.8 25 .526 21.5 1,050 5,370 X 37 14 - .069 70.8 25 .290 15.2 1,415 5,190 X .5 7.5 - .081 70.5 25 .429 23.3 2,350 6,080 X 3.0 10 - .117 67.1 25 .434 33.2 3,360 10,130 X 3.0 20 - .226 51.8 25 .093 6.60 3,000 21,700 X 3.0 20 - .0471 60.1 25 .188 8.14 750 4,510 X 3.0 30 - .097 - 25 0 No r e a c t i o n X/B .5 40 5 .1091 61.1 25 .204 _ -X/B 3.0 55 1,400 .0569 52.3 25 .349 - - -X/B 3.0 20 120 .0402 49.9 25 .316 - - -S i n t e r i n g Temp. (°C) S/X 3.5 30 350 .147 7.24 25 .440 81.9 2,500 14,100 Power Law fcB a/m n C a (min) X/B 3.0 110 1,080 .1147 57.5 25 .395 2,010 .39 8,940 Table XVI F l u o r i n a t e d Films Pre-treatment Exehang R e s u l t s Second Order: Run Type t l t 2 tB P F 2 Weight T PC1 2 l o 2 k n C (sec) (sec) (min) (atm) (g) (m2/g) (°C) (atm) 6 0 D F 1200 480 - .50 .1701 39.1 25 .394 - - -4 7 D F 60 60 .072 .1040 7.11 25 .184 5.5 3 S500 9,200 6 1 D F 10 120 - .50 .263 35.4 25 .250 222 3,180 11,210 7 6 D F 60 300 - .066 .1121 57.0 25 .220 990 550 9,900 fcl (min) (min) 6 3 D X 690 20 _ ..' . .242 38.8 25 - No c h l o r i n e exchange F - - .375 - - ' -r e a c t i o n ; f o r k i n e t i c s 6 4 D X/B 960 30 120 .298 35.6 25 -u F - - .340 - - •• - of f l u o r i n a t i o n see 6 9 D F _ .560 .087 50.5 25 Figure 22. 7 0S F - - .954 .1281 47.6 25 -BIBLIOGRAPHY - 115 -BIBLIOGRAPHY (1) Roberts, L. E. J . , and Anderson, J . S., Rev. pure a p p l . Chem., 2, 1, (1952). (2) M o r i t a , N., and T i t a n i , 'T., B u l l . Japan Chem. S o c , 14, 9, (1940), 15, 47, (1940). (3) Urey, J . , J . Chem. Phys., 13, 351, (1945). (4) Winter, E. R. S., Nature, 164, 1130, (1949). (5) Winter, E. R. S., J . Chem. S o c , 1170, 1175, (1950); 1509, 1517, 1522, (1954); 2726, 3824, (1955).' (6) Winter, E. R. S., Discussions Faraday S o c i e t y , No. 8, 231, (1950). (7) Garner, W. E., "Chemistry of the S o l i d S t a t e " , Butterworths S c i . Pubs., (1955). (8) Garner, W. E., Stone, F. S., and T i l e y , P. F., Proc. Roy. Soc. A211, 472, (1952). (9) Rudham, R., and Stone, F. S., (Unpub. B r i s t o l Univ. Thesis.) (10) Derry, R., Garner, W. E., and Gray, T. J . , J . Chim. phys., 5_1, 670, (1954). (11) Dunlap, W. C., "An I n t r o d u c t i o n t o Semiconductors" Pub. Wiley (1960). (12) S e i t z , F., Revs. Mod. Phys., 26, 7, (1954). (13) M o r r i s o n , J . A., and Patt e r s o n , D., Trans. Faraday S o c , 52, 764, (1956). (14) H a r r i s o n , L. G., Morrison, J . A., and Rudham, R., J . Phys. Chem., 61, 1314 (1957). (15) H a r r i s o n , L. G., Morrison, J . A., and Rose, G. S., Proc. of 2nd I n t . Conference of Surface A c t i v i t y , 287, (1957). - 116 -(16) Burton, W. K., Cabrera, N., and Frank, F. C , P h i l . Trans., A243, 299, (1951). (17) Cabrera, N., Z. Elektrochem., 56, 294, (1952). (18) Rudham, R., Trans. Faraday S o c , 59, 1853, (1963). (19) H a r r i s o n , L. G., Hoodless, I . M., and Morrison, J . A., Di s c , of Faraday S o c , No. 28, Pt. I , 103, (1958). (20) H a r r i s o n , L. G., Hoodless, I . M., and Morrison, J . A., D i s c , of Faraday S o c , No. 28, P t . I I , 122, (1958). (21) Mollwo, E., Ann. physik. 29, 394, (1937). (22) Symons, M. C. R., and Doyle, W. T., Quart. Revs. 14, 62, (1960). (23) H a r r i s o n , L. G., and B i r d , D., (Unpublished work from t h i s l a b o r a t o r y . ) (24) Hutchinson, C. A., Phys. Revs., 75, 1769, (1949). (25) P i c k , H., Ann. Physik., 31, 365, (1938). (26) Kanzig, W., Phys. Revs., 99, 1890, (1955). (27) H a r r i s o n , L. G., J . Chem. Phys., 38, 3039, (1963). (28) Harten, H. U.„ Z. Physik., 126, 619, (1949). Nachr. Acad. Wiss. Gottingen, 15, 1950, (1950). (29) C a s l e r , R., Pringsheim, P., and Yuster, P., J . Chem. Phys., _18, 887, 1564, (1950). (30) Dorendorf, H., Z. Physik., 129, 317, (1951). (31) Alexander, J . , and Sneider, E. E., Nature, 164, 653, (1949). (32) S e i t z , F., Rev. Mod. Phys., 18, 384, (1946); 23, 328, 335, 336, (1951). (33) Teegarden, K. J . , J . Chem. Phys., 24, 161, (1956). (34) Uchida, Y., and Nakai, Y., J . Phys. Soc. Japan, 9, 928, (1954). - 117 -(35) Hersch, H. N., Phys. Rev., 105, 1410, (1957). (36) Teegarden, K. J . , B u l l . Amer. Physic. S o c , 1, Ser. I I , 113, (1956). (37) Straumanis, M. E., Amer. Min., 38, 662, (1953). (38) H a r r i s o n , L. G. , B a i j a l , M., and B i r d , D., Trans. Faraday S o c , (In course of p u b l i c a t i o n . ) (39) Young, D. M., and Mor r i s o n , J . A., J . S c i . Instrum., 31, 90, (1954). (40) Thompson, F. W., Rose, G. S., and Morrison, J . A., J . S c i . Instrum., 32, 325, (1955). (41) Vogel, A. I . , "Textbook of Q u a n t i t a t i v e Inorganic A n a l y s i s " , Longmans, p.324, 526, (1948). (42) Curran, S. C., and Craggs, J . D., "Counting Tubes" Butterworths S c i . Pubs., (1949). (43) A l p e r t , D. J . , App. Phys., 24, 875, (1953). (44) S i d d i q u i , R. A., Ph.D. Th e s i s , U.B.C., A p r i l (1961). (45) Handbook of Chemistry and Phy s i c s , 40th Edn., Chem. Rubber Pub. Co. (1958-59). (46) H i l l , T. L., " I n t r o d u c t i o n t o S t a t i s t i c a l Thermodynamics" Addison-Wesley Pub. Co. Inc., p.134, (1960). (47) Kington, G. L., and Holmes, J . M., Trans. Faraday S o c , 49, 431, (1953). (48) McKay, H. A. C., Nature, 142, 997, (1938). (49) Tharmalingham, K., and L i d i a r d , A. B., P h i l . Mag., 6, 1157, (1961). (50) Lehovec, K., J . Chem. P h y s i c s , 21, 1123, (1953). (51) Delbecq, C. J . , Smaller, B., and Yuster, P. H., Phys. Rev. I l l , 1235, (1958). - 118 -(52) Jones, F. W., Proc. Roy. S o c , A166, 16, (1938). (53) von Laue, M., Z. K r i s t . , 64, 115, (1926), a l s o Scherrer, P., f ? ; . Gottinger N a c h t r i c h t e n , 2, 98, (1918). (54) D'Eye, R. W. M., and Wait, E., "X-Ray Powder Photography", Butterworths S c i . Pubs., p. 216, (1960). (55) Klug, H. P., and Alexander, L. E., "X-Ray D i f f r a c t i o n Procedures", J . Wiley, N.Y., (1954). ($6) Wilson, A. J . C., Research 2, 246, 541, (1949). (57) Stokes, A. R., and Wilson, A. J . C., Proc. Camb. P h i l . S o c , 38, 313, (1942). (58) Stokes, A. R., and Wilson, A. J . C., P r o c Phys., S o c , 56, 174, (1944). (59) Wood, W. A., and Rachinger, W. A., J . I n s t . Metals, 75, 571, (1949). (60) van Bueren, H. G., "Imperfections i n C r y s t a l s " , North H o l l a n d Pub. Co., p. 329, (1960). (61) H a l l , W. H., P r o c Phys. S o c , 62, 741, (1949). (62) Warren, B. E., J . App. Phys., 12, 375, (1941). (63) Wheeler, J . A., and Jaswon, M. A., J . Iron and S t e e l I n s t . , 157, 161, (1947). 

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