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Studies relating to the structures of ionic surfaces Siddiqui, Rafiq Ahmad 1961

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STUDIES RELATING TO THE STRUCTURES OF IONIC SURFACES by RAFIQ AHMAD SIDDIQUI M.Sc, Aligarh Muslim University, 1952 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY in the Department of CHEMISTRY We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA Ap r i l , 1961 In presenting t h i s t h e s i s i n p a r t i a l f u l f i l m e n t of the requirements 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 permission 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. It 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 aUxwed without my written permission. Department of r.hrmi «f.ry The U n i v e r s i t y of B r i t i s h Columbia, Vancouver 8, Canada. Date 12. 4. 1961 W^z Pntuersitg of ^riitsh (Eolmnbta F A C U L T Y O F G R A D U A T E S T U D I E S P R O G R A M M E O F T H E FINAL ORAL EXAMINATION F O R T H E D E G R E E O F DOCTOR OF PHILOSOPHY of R. A . SIDDIQUI B.Sc, Aligarh Muslim University, 1950 M.Sc , Aligarh Muslim University, 1952 W E D N E S D A Y , M A Y 3rd, 1961, A T 2:30 P .M. I N R O O M 342, C H E M I S T R Y B U I L D I N G COMMITTEE IN CHARGE Chairman: G . M . S H R U M B. C B I N N I N G L. G . H A R R I S O N W . A . B R Y C E L . D . H A Y W A R D R. E. BURGESS S. A . J E N N I N G S F. A . F O R W A R D C. A . M c D O W E L L J. H A L P E R N R. S T E W A R T External Examiner: PROFESSOR F. C. T O M P K I N S , FJt.S. , Chemistry Department, Imperial College of Science & Technology London, England. STUDIES RELATING TO THE STRUCTURE OF IONIC SURFACES ABSTRACT This work is designed to 'give information on. the thermo-dynamic properties and chemical - reactivity of the surface of an ionic crystal. The principal studies concern halogen exchange be-tween hydrogen chloride gas'and the surface of sodium bromide. The most interesting feature of this investigation has been the measurement of the equilibrium constant for the reaction and the calculation therefrom of the changes in thermodynamic pro-perties attending the replacement of a bromide ion by a chloride ion in the surface. This appears to be the first reported measure-ment of an equilibrium constant for,a simple substitutional reaction involving concentrations in a solid surface. The work differs sharply from previous studies of isotopic exchange, which have been ex-clusively kinetic. The form of the equilibrium equation indicates the formation on the surface of a two-dimensional solid solution of NaCl and NaBr, which deviates from ideality to an appreciable extent, so that the equilibrium constant K is a function of the extent of ex-change. Since K is independent of temperature (20° - 9S°Q. / \ H = O and the equilibrium can be discussed entirely in terms of entropy. The entropy changes calculated from K are unexpectedly large. For the exchange of an isolated chloride ion with a bromide ion in the pure NaBr surface, A S = - 13 +'2 cal/mole deg.K. The variation of K with extent of exchange is used to arrive at a tentative subdivision of this quantity as follows: Effects of ex-changed ion on its neighbours = - 5 cal/mole deg.K. Entropy change of exchanged ion itself = - 8 cal-mole deg.K. Of the latter figure, about -2 cal/mole deg.K. may be a simple mass effect. These large entropy decreases are strictly surface effects. An earlier study of the same reaction at very high temperatures with a liquid alkali halide phase gives an entropy change of only -3 cal/ mole deg.K, which is almost entirely attributable to the mass effect. The changes observed in the present work are discussed in relation to the probable structure of the surface of sodium bromide. They are consistent with the "Verwey distortion" in which the anions are displaced outwards from the ideal surface, the distortion in-creasing with the size and polarizability of the anions. The kinetics of the reaction have been studied rather less ex-tensively. The most striking feature of the results, in comparison with previous studies, is that all reactions involving bromine are faster than those involving chlorine isotopes only. Adsorption of HC1 and HBr on Na Br has been studied to eliminate the possibility that adsorption has a significant effect on the exchange reaction. The exchange reaction has been used to study diffusion of chloride ions into sodium bromide at room temperature, and. ap-pears to afford a useful method of investigating very slow diffusion processes. The result suggest that diffusion takes place mainly along dislocations. The dehydration of high surface area sodium bromide has been studied, and evidence has been obtained for the formation of a "surface hydrate" overlying the lattice of anhydrous NaBr. This process may be regarded as adsorption with a discontinuous iso-therm, and implies that.the NaBr surface is energetically homo-geneous. It has been found that color centers can be produced easily in alkali halides by means of a Tesla Coil discharge. Centers thus produced in NaCl have been examined spectroscopically; the spectra suggest that the colored crystals contain a stoichiometric excess of sodium. G R A D U A T E STUDIES Field of Study: Physical Chemistry Topics in Physical Chemistry J . A . R. Coope C. A . McDowell '-}•'" R. F. Snider Topics in Inorganic Chemistry H . C. Clark H . Heal Radiochemistry D . R. Wiles Topics in Organic Chemistry G . G . S. Dutton L. D . Hayward A . Rosenthal R. Stewart -Related Studies: Atomic Physics M . Bloom Theory of Measurements A . M . Crooker Elementary Quantum Mechanics .' F. A . Kaempffer Physics of the Solid State ...-..„ G . Bate P U B L I C A T I O N S 1. G . Hahn and R. A . Siddiqui, "Standardization of Myrobalan Extracts for the Manufacture of Fountainpen Inks", Pakistan J . Sci. and Ind. Research, 1, 63, 1958. 2. S. Siddiqui, G . Hahn, and R. A . Siddiqui, "A Process for the Modification of Tannin Extracts for the Manufacture of Writing Inks", Pakistan Patent No. 108274 (1958). i i ABSTRACT The experimental work described in this thesis i s designed to give information on the thermodynamic properties and chemical reactivity of the surface of an ionic crystal. The principal studies concern halogen exchange between hydrogen chloride gas and the surface of sodium bromide. For this reaction, like any ordinary chemical reaction, both kinetics and equilibrium may be investigated. In the present study, the most Interesting feature has been the measurement of the equilibrium constant and the calculation therefrom of the changes in thermodynamic properties attending the replacement of a bromide ion by a chloride ion in the surface. This appears to be the f i r s t reported measurement of an equilibrium constant Involving concentrations in a solid surface. The work differs sharply from previous studies of isotopic exchange, which have been exclusively kinetic. The equilibrium i s best represented by the equation RlnK - A S° + _dS. (X) - Rln PHBr X where X and (1-X) are the fractions of the surface anion — — o sites occupied by Cl and Br respectively, A S refers to the entropy changes of the exchanged ions at X ° 0, and i i i Sj^X) describes the effect of any anion on the entropy of i t s neighbours in the surface* The equation indicates the formation of a two-dimensional solid solution of NaCl and NaBr, deviating from ideality through the term S^X), so that the equilibrium constant K i s a function of X, Since K i s independent of temperature (20°-95°C.)> AH - 0 and the equilibrium equation contains entropy terms only. - 3 From the value K - 6X10 at X - 0 i t i s estimated that SC1- " SBr" + - i ( X ^ - 0 " ~ 1 3 c a l/mole d eS- K dX o o where Sgj- and S^. refer to surface ions. The variation of K with X i s used to arrive at a tenta-tive estimate, based on some simplifying assumptions, of so that J S i ( X ) & -5 cal/mole deg. K, dX S° _ - S° r ~ -8 cal/mole deg, K. Cl Br Of this, about -2 cal/mole deg. K may be a simple mass effect. These large decreases in entropy are discussed in rel a -tion to the probable structure of the surface of sodium bromide; they are consistent with the "Verwey distortion" in which the anions are displaced outwards from the ideal surface, the distortion increasing, ceteris paribus, with the size and polarizability of the anions. iv The kinetics of the exchange reaction have been studied. It has not proved possible to analyze the rate curves in detail. The most striking feature, in comparison with previous studies, is that a l l reactions involving bromine (initially in either the gaseous or the solid phase) are faster than those involving chlorine isotopes only. The reason for this may be either the availability of d-orbitals of bromine for bonding in a transition complex, or the polarizability of the bromine atom. The exchange reaction has been used to study diffusion of chloride ions into sodium bromide at room temperature. It is possible to measure diffusion coefficients of about -22 2 -1 5 10 cm sec , smaller by a factor of about 10 than can be measured by most conventional methods. The results suggest that diffusion takes place principally along dislocations. The dehydration of high surface area sodium bromide has been studied, and is found to take place at a vapour pressure different from the equilibrium value for the system, NaBr.2H20; NaBr; Ry). This is attributed to the formation of a "surface hydrate" overlying the lattice of anhydrous NaBr. This process may be regarded as adsorption with a discontinuous isotherm, and implies that the NaBr surface is energetically homogeneous. It has been found that color centers may readily be produced in the a l k a l i halides by a Tesla Coil discharge. Centers thus produced in sodium chloride have been examined spetroscopically. The technique may be useful in experiments to establish the mechanism of exchange reactions such as that described i n this thesis. v i TABLE OF CONTENTS Page (a) T i t l e Page i (b) Abstract i i (c) Table of Contents v i (d) Acknowledgments xx INTRODUCTION 1-19 I. Probable Nature of Ionic Surfaces 2 II. Probable Distortion of Surfaces from the Ideal Geometry of the Substrate 4 A. The Verwey Type of Distortion 4 B. The Moliere and Stranski Type of Distortion 7 III. Surface Disordering or Melting 8 IV. Experimental Evidence on the Reactivity and Thermodynamic Properties of A l k a l i Halide and Metallic Oxide Surfaces 9 A. Heat Capacity of Small Particles 9 B. Infrared Absorption by Small Particles 10 C. Possible Influence of Adsorbed Layers on Surface Tension 14 D. Chemical Properties of Surfaces 14 E. Kinetic Properties of Surfaces 15 (i) Exchange Reactions 15 •i v i i Page ( i i ) Diffusion Processes 16 V. Objects of the Present Investigation 18 SECTION I GENERAL EXPERIMENTAL DETAILS 20-33 1. Vacuum System 20 2. Calibration of the Spiral Pressure Gauge 22 3. Preparation of Materials 23 SECTION II STUDIES ON ADSORPTION 34-64 1. Adsorption on Sodium Bromide Crystals 34 (i) Method for Irreversible Adsorption 34 - Results 37 ( i i ) Manometric Method 39 - Results and Discussion 41 - Possible Effect of Adsorption on the Entropy of the Surface 54 2. Adsorption on Parts of the Apparatus 57 - Adsorption of HCl and HBr on Blank Adsorption System 58 SECTION III KINETICS OF THE HCl/NaBr EXCHANGE REACTION 65-85 1. Apparatus 65 2» Procedure 68 v i i i Page (i) Calibration of the Spectrometer 68 (ii) Exchange Reaction 68 3* Results and Discussion 69 (i) General Features of the Rate Curves 69 (ii) Effect of Adsorption of Gases in the Reaction System 7 3 ( i i i ) Effect of Circulation Time 7 4 (iv) Effect of Pressure 76 (v) Effect of Temperature 77 (vi) Effect of X, the Fraction of Sodium Bromide Surface Covered by Chloride Ions, on the Reaction Curve 82 (vii) Comparison with Results of Other Exchange Reactions 82 SECTION IV CHEMICAL EQUILIBRIUM OF THE HCl/NaBr EXCHANGE REACTION 86-143 1. Mass-Spectral Analysis 86 (i) Pressure Effect 87 (ii) Memory Effect 90 ( i i i ) Effect of Composition 97 2. Procedure 99 I x Page (i) Calibration with Standard HCl-HBr Mixtures 99 (ii) Procedure for Exchange Reaction 100 3 0 Results 103 - Analysis of the Results 103 - Results 105 4. Discussion 117 (i) Enthalpy Change 118 (ii) Entropy Change 120 ( i i i ) The Entropy Change at X=0 122 (iv) Suggested Subdivision of the Entropy Change 123 (a) Mass Effect 123 (b) Effect of Ionic Size 126 (c) Possible Contribution of each Chloride Ion to Entropy of its Neighbours 127 (d) Check of Self-Consistency of Assumptions in (c) • 141 SECTION V DIFFUSION OF CHLORIDE ION INTO SODIUM BROMIDE CRYSTALS 144-163 1. Experimental 145 2• Procedure 146 3. Methods of Calculation 146 (i) Calculation of X after Diffusion 146 X Page (ii) Calculation of Diffusion Coefficient 150 4. Results 153 5. Discussion 158 SECTION VI THE HYDRATION AND DEHYDRATION OF SODIUM BROMIDE 164-181 1. Experimental 165 (i) Dehydration and Hydration Experiments ' 166 (ii) X-Ray Diffraction Photographs 167 ( i i i ) Particle Size and Surface Area 167 20 Results 168 (i) Dehydration and Hydration Experiments 168 (ii) X-Ray Diffraction Photographs 174 3. Discussion 176 SECTION VII PRODUCTION OF COLOR CENTERS IN ALKALI HALIDE CRYSTALS BY HIGH FREQUENCY DISCHARGE 182-192 1. Experimental 183 2. Results 184 (i) Analysis of the Spectroscopic Data for NaCl 184 (ii ) Effect of Aging on the Absorption Bands of NaCl 188 ( i i i ) Visual Observations on Coloring of Other Compounds 190 3. Discussion BIBLIOGRAPHY xi Page 191 193-202 x i i LIST OF TABLES Page INTRODUCTION Table 1 Wavelengths absorbed by a l k a l i halides as computed by Rosenstock (47). SECTION II Table 1 pH Values of the calibration standards(each containing 10.0 g». N a B r / U t e r g o l u t i o n > . Table 2 pH Values of the solution of the adsorbent, dissolved after the removal of reversibly adsorbed gases. Table 3 Temperature and pressure values of various HCl adsorption experiments. Table 4 Summary of experimental conditions of the HBr adsorption experiments. Table 5 Table 6 Table 7 Table 8 200 seconds o. for HCl Values of n f l, p Q and p 6 Q m i n u t e for HCl o adsorption isotherm at 22 C. Values of n , p and p a o adsorption isotherm at 22~C. Values of n , p and p„„ a o r60 minute o adsorption isotherm at 90 C. for HCl Values of n&t J>Q and p 6 Q for HBr o adsorption isotherm at 22 C. 12 38 39 44 46 50 50 51 51 x i i i Page Table 9 Values of n , p and p „ r n for HBr a* ro r i 5 0 seconds o adsorption isotherm at 22 C. 52 SECTION III o Table 1 I n i t i a l rates of reaction at 25 C. and various pressures. 76 Table 2 I n i t i a l rates at 5 cm. pressure and various temperatures. 80 Table 3 I n i t i a l rates of HCl/„ „ exchange reaction. 81 NaBr SECTION IV Table 1 The effect of total pressure on the reciprocal "peak ratio" of a standard mixture (5.4 mole % HBr). 88 Table 2 The effect of total pressure on the reciprocal "peak ratio" of standard mixture (5.4 mole % HBr). 90 Table 3 Peak ratios obtained on successive flushing of the machine with pure-HCl. 92 Table 4 Ratio of HBr content to that of the succeeding specimen(smoothed values from Figure 2). 95 Table 5 Peak ratios obtained on successive flushing of the mass-spectrometer with the fresh specimen of the sample containing some HBr. 96 Table 6 Peak ratios of the standard mixtures. 97 2 Table 7 Values of the peak ratio, and 10 r • 106 e xiv Table 8 Table 9 Table 10 Table 11 Table 12 Table 13 Table 14 Table 15 Table 16 Table 17 SECTION V Table 1 Table 2 Page 108 110 113 -2 -2 Values of 10 /r and 10 /r C obtained in e e e two experiments at different temperatures. Values of K and X for Run 5A and Run 6A. e 2 Experimental values of 10 xPeak 80. Peak 36 2 Values of 10 K obtained in a number of Runs and tabulated against the corresponding value of X . 116 e Standard entropies of alkali and silver halides (cal/mole deg.K). 125 Values of f(X) calculated for different values of X. 132 2 Values of In(10 K) and f(X) for Run 5A. 135 2 Values0 of In(10 K) and f (X) for Run 6A. 136 Values of _dS. (in cal/mole deg.) for d X 1 different values of X obtained in Runs 5A and 6A. 139 Entropies of random and separated configurations• 143 2 Values of 10 r obtained in Series A and Series B of Run 5. 148 Values of C from a l l the results of Run 5B. 149 z Table 3 Values of 10 r obtained in Run 6. Table 4 Summary of Run 6 diffusion experiments. Table 5 Summary of Runs 2-6 diffusion experiments. Table 6 Vibration frequencies calculated on various assumptions. SECTION VI Table 1 The dissociation pressure of NaBr.21^0. SECTION VII Table 1 Spectral location of the absorption bands. Table 2 Spectral location of the original and the developed peaks obtained with the NaCl specimen. Table 3 Visual observations on the development of color in ionic crystals on exposure to high frequency discharge. xvi LIST OF FIGURES Page SECTION I Figure 1 Vacuum system 21 Figure 2 Spiral pressure gauge calibration 24 Figure 3 Accessory apparatus for HCl preparation 27 Figure 4 Vacuum f i l t r a t i o n apparatus 28 SECTION II Figure 1 Calibration curves 36 Figure 2 Adsorption of HCl (22°C; 4.12 cm. Hg.) 43 Figure 3a o Adsorption of HCl (0 C ; 6.1 cm. Hg.) 45 Figure 3b Adsorption of HCl (25°C; various pressures) 45a Figure 3c o Adsorption of HCl (90 C ; various pressures) 45b Figure 4 Adsorption of HBr (22°C; various pressures) 47 Figure 5 Adsorption isotherms 49 A and A - HCl B and B - HBr Figure 6 Blank Adsorption of HCl (25°C; various pressures) 59 Figure 7 Correction curves for blank HCl adsorption (22°C. and various pressures) 60 Figure 8 Blank Adsorption of HBr (22°C; various pressures) 61 xv i i Figure 9 Correction curves for blank HBr adsorption o (22 C ; various pressures) Figure 10 Blank Adsorption Isotherms for HBr - A and HC1 - B (22°C.) SECTION III Figure 1 Absorption c e l l Figure 2 Typical rate curve Figure 3 I n i t i a l part of the typical rate curve (Figure 2.A) Figure 4 Reaction curves A - Tight packed crystals B - Loose packed crystals Figure 5 Reaction curves %(D-D Q) A - -20 C. B - 2S°C. C - 60°C. D - 90°C. %(D-DQ) Figure 6 Reaction curves (-78°C.) A - Original B - Additional subsequent reaction o Figure 7 Effect of X on reaction curves (60 C.) A - F i r s t exposure B - Second exposure Page 63 64 66 70 72 75 78 79 83 x v i i i Page SECTION IV Figure 1 Pressure effect on peak ratio 89 Figure 2 Peak ratio obtained with various specimens HC1 - A HBr - B 93 Figure 3 Effect of composition on peak ratio A - Normal scale divisions B - 10 x normal scale divisions 98 Figure 4 Calibration curve 101 Figure 5 Plot of 10" / r e vs. 10 / r e C e 107 Figure 6 Plot of K against X e 109 Figure 7 Plot of peak ratio against specimen number for Run 5A - 1; 6A - 2; 6E - 3 114 Figure 8 See Figure 10 Figure 9 Plot of f(X) against X 133 2 Figure 10 Plot of ln(10 K) against f(X) 137 Figure 11 Plot of X against _dS.(X) 140 dX SECTION VI Figure 1 A - region in which the humidity became sensitive to s t i r r i n g B - f i r s t occurrence of the phenomenon shown in Figure 2 169 Figure 2 The variation of humidity with time after leakage had been promoted for a few minutes 170 Figure 3. The onset of the hydration process of anhydrous sodium bromide. 0 - dry box p a r t l y open to atmosphere C - dry box closed (but leaking) Figure 4. A t y p i c a l cycle of p a r t i a l hydration and dehydration; zero of time-scale a r b i t r a r y . 0 - dry box p a r t l y open to atmosphere C - dry box closed (leaking) D - desiccant (P 0Cv) placed i n dry box Plate 1 X-ray d i f f r a c t i o n photographs of NaBr at various stages of hydration. XX ACKNOWLEDGMENTS I am deeply grateful to Dr. L. G. Harrison for guidance throughout the present work. I wish to thank Dr. D. C, Frost for assistance in the Mass-Spectral Analysis, Mr. I. H. Warren for the Surface Area determinations, and Mrs. M. Z e l l for assistance in the Infrared Spectroscopy. I am grateful to Professor C. A. McDowell for the f a c i l i t i e s available in the department. I wish to express thanks for a scholarship from C.S.I.R. (Pakistan) under the auspices of the Colombo Plan. RAFIQ A. SIDDIQUI 1 INTRODUCTION The main part of the work described in this thesis i s an investigation of several aspects of the sodium bromide -hydrogen chloride interface, most particularly the exchange of anions between the solid and the gas phase. The exchange reaction under consideration i s represented as HCl(gas)+Br"(NaBr surface) ^± HBr(gas)+Cl (NaBr surface). Information has been obtained on: (a) the adsorption of the gas on the solid, in order to show the effects of adsorption on the exchange reaction; (b) the kinetics of the reaction, to determine the reactivity of the surface anions and the time required for the system to reach equilibrium; (c) the equilibrium constant, to investigate the thermo-dynamic properties of the interfacej (d) the diffusion of anions in the so l i d phase in the region of room temperature. Two other phenomena have been studied less extensively:-(i) the behaviour of small particles of NaBr .2^0 during dehydration at room temperature; this process appears to involve the formation of an unusual type of "surface hydrate". 2 (ii) the production of color centers in Ionic crystals by a new technique using a high-frequency electrical discharge (Tesla coil)• Because of the variety of measurements, each type of study is presented separately and the specific experimental details are given in appropriate sections. The results are discussed particularly in relation to the information which they give on the structure of the solid surface. It is therefore considered desirable to begin with a summary of the present state of knowledge on the nature of ionic surfaces. I. Probable Nature of Ionic Surfaces It is possible to imagine a number of ways in which a real surface may differ from an ideal surface, the latter being the surface which would be obtained by cutting a crystal along the appropriate plane, without subsequent distortion. From a rigorous thermodynamic point of view, Cabrera (30) has classified surfaces into three types: singular, vicinal and non-singular surfaces. These are defined in relation;to the behaviour of Wulff's plot of surface free energy, against an angular co-ordinate with its pole at the center of the crystal. From the point of view of physical models, these types of surfaces may be thought of as having the following 3 characteristics:-(a) Singular surfaces are atomically f l a t except for the presence at high temperatures of point defects• According to Cabrera i t i s not l i k e l y that point defects, at any rate, w i l l appear in the surface layer of any kind of singular interface at low temperatures. At high temperatures however, surface vacancies or i n t e r s t i t i a l (adsorbed) atoms or both w i l l appear as i s well known. Most probably the vacancies are the species present in the greatest concentration. The singular surfaces, although atomically f l a t , need not be ideal in the sense of closely resembling a layer of the same crystallographic orientation isolated out of the under-lying l a t t i c e . It i s quite probable that the ions in the surface layer are appreciably displaced from their "ideal" positions, as suggested, for example, by Verwey (2). Such displacements would affect the thermodynamic properties of the surface, and consequently the equilibrium in any reaction with a gas, to a significant extent. This type of distortion is therefore considered in more detail below, (b) Vicinal surfaces differ from the corresponding singular surfaces only in that they contain steps and kinks. These defects might considerably affect the rate of any process taking place at the surface, but are not present in so high a concentration that the overall thermodynamic properties of the 4 surface w i l l be altered significantly, (c) Non-singular surfaces are completely roughened or distorted surfaces, with the disturbance of the crystal l a t t i c e extending to a considerable thickness. Herring (32) has pointed out that non-singular surfaces w i l l not exist at very low temperatures. They may be thought of, for many purposes, as surfaces which have undergone something analogous to a melting phenomenon. It i s probable that such disordering takes place abruptly at a definite transition temperature analogous to a melting point. The question of whether most real surfaces are disordered in this way under ordinary conditions has by no means been resolved. The work which has been done on this i s reviewed in more detail below. II . Probable Distortion of Surfaces from the  Ideal Geometry of the Substrate A. The Verwey Type of Distortion Bom's la t t i c e theory has been applied to crystal surface phenomena by a number of authors. Many calculations (e.g. of the surface energy of the a l k a l i halides) have considered Bom repulsive forces and pure Coulomb forces between the ions (supposed to be unpolarizable), on the assumption that in the free surface the ions have the same spacing, and relative positions as in the interior of the 5 crystals. In r e a l i t y rather considerable distortions of the la t t i c e and an appreciable polarization of the surface ions as a consequence of their non-symmetrical surroundings must be expected. Braunbek (21) and Lennard-Jones and Dent (22) have tried to calculate the displacement of the surface ions; the latter authors take the polarization of these ions into account. In a l l these calculations however, the positive and negative surface ions were assumed to be in the same plane. Accordingly they must be considered to be rather poor approxi-mations to the actual state of affairs in the crystal surface, as i t may be expected - as was f i r s t pointed out by Madelung (23) - that the displacement of the ions in the surface w i l l be different for the positive and negative ions. Verwey (2) gives an improved theory and relevant calcula-tions of the l a t t i c e deformation at the surface of a l k a l i halide crystals. It was seen that the displacement of the positive ions in the surface layer i s completely different from that of the negative ion. The positive ions are shifted over an appreciable distance towards the crystal so that their distance to the underlying negative ions i s appreciably shorter than the normal distance. The displacement of the negative ions i s in a l l cases smaller than that of the positive ions and in most cases even has an opposite sign, 6 i.e., in a direction away from the crystal. Hence i t may be inferred that the cube face of the a l k a l i halide crystals undergoes a rather important l a t t i c e distortion leading to an ionic double layer of appreciable strength. In the case in which the size of the positive and nega-tive ions differ most the displacement of the positive ions i s largest. This i s mainly determined by the size of the negative ions. The Verwey model for the free surface structure of a l k a l i halide crystals at 0°K has been used by Patterson (3) to estimate the effect of surface distortion on the surface energy of these crystals. Several aspects of the Verwey model have been examined. These include the effect of various repulsive potentials and forms of distortion. It appears that the Verwey model leads to surface energies of the a l k a l i halides which are smaller than can be j u s t i f i e d by the few experimental data available or by extrapolation from the liquid state. Undoubtedly the picture of separate displacement of positive and negative surface ions i s a more r e a l i s t i c approach than used by previous workers. However, quantitative results for the distortion and associated energy change calculated by the classical Born-Mayer method with simple polarization corrections must be considered with some caution. It i s suggested by Patterson 7 that the difference is a fundamental one and requires a more detailed treatment of the polarization and repulsive terms* B. The Moliere and Stranski Type of Distortion Moliere and Stranski (25) examine the possibility that the surface ions may move laterally from the position directly above the ions of the underlying lattice* They find that the perfect simple lattice is in fact an unstable configura-tion for the surface ions, of almost half of the alkali halides* Instead a configuration is favoured in which the ions are grouped together, in pairs producing a polarization of each ion* The dipoles formed make up chains on the surface* After such a deformation of the surface layer, the distance between surface layer and substrate is found to be considerably less than that determined by Lennard-Jones and Dent, although i t varies from salt to salt* Moliere and Stranski have pointed out the importance of these surface structures for crystal growth and other phenomena* The assumptions made in their calculations have been examined by Patterson (4), who has cast doubt on the existence of these surface structures for the alkali halides* It seems that surface deformations should not be divided into displacements perpendicular to the plane, treated by Verwey and those within the plane, treated by Moliere and Stranski* 8 A fairly exact treatment of surface deformations as a single problem would, however, be a very arduous task* III. Surface Disordering or Melting The mobility of surface atoms of solids at temperatures well below the melting point is a well known phenomenon, and is made use of in the sintering of powders (1). An account of a number of effects associated with the mobility of atoms on surfaces of metals is given by Chalmers et al.(15)• Many of the effects may be explained by the presence of liquid films on the surfaces of crystals. Likewise the fact that crystals cannot be superheated above their melting points is readily understood i f , even below the melting point, the solid already has a thin film of liquid on i t . Some authors think that there is^a more fundamental thermodynamic reason for this, namely that the free energy of a solid has a dis-continuity at the melting point. Burton, Cabrera and Frank (29) have considered the possibility that T c, the c r i t i c a l temperature of surface disordering, may be thigh in vacuo, but much lower when a gas is interacting with.surface. Cabrera has considered the effect of adsorbed gas on lowering T c (118). From his theoretical calculations Cabrera (30) concludes that in kinetic processes surfaces become non-singular. 9 Robertson (119) has pointed out that substantial increases in the entropy and hence the mobility of surface atoms are required to give agreement between experiment and transition-state theory of the rate of surface-catalysed reactions. Nicolson (38) found that surface tension of crystals is changed by the presence of adsorbed layers. IV. .Experimental Evidence on the  Reactivity and Thermodynamic Properties  of Alkali Halide and Metallic Oxide Surfaces A. Heat Capacity of Small Particles Morrison (48) measured the heat capacity of sodium chloride in the form of small particles (average crystal size 0.04 micron and 0.07 micron) and of bulk crystals, in the temperature range 12° to 270° K. The effect of particle size on heat capacity of solids at low temperature has been predicted theoretically (49, 50, 51). It is shown experi-mentally (48) that the surface contribution to the heat capa-city at very low temperatures is quantitatively larger than that predicted by theory. It is suggested tentatively by , Morrison (48) that the discrepancy is due to the roughness of the crystal surface. -However, i t is important to understand the effects of free surfaces on the normal modes of vibration of crystal 10 lattices in the investigation of such subjects as the specific heats of very fine powders (14) and the infrared lattice vibration spectra described in the following pages* Some theoretical expressions have been developed for frequencies and displacements of the normal modes of vibration for two and three dimensional alternating diatomic lattices with free boundaries (Wallis, 14). Significant features of the results of these calcula-tions are:- (i) that the presence of the surface should: lead to the existence of vibration frequencies lower than those of the optical modes of an infinite crystal; (ii) that the frequencies calculated are not sufficiently low to be correlated with the, low-temperature heat capacity measure-: ments of Morrison (48). .The latter work required the presence in the surface of a vibration with Einstein characteristic temperature 43°K, frequency 9x10^  sec" 1, or wavelength 330 microns. B. Infrared Absorption by Small Particles Rosenstock (47) computed the frequencies of the vibra-tional motion of atoms in a crystal of the NaCl-type. - Four subsidiary frequencies are found in addition to the "limiting frequency*1 • The experimental absorption measurements made on thin evaporated films are fitted more closely by some of the subsidiary frequencies than by the limiting frequency. The measurement of the far infrared absorption by alkali halides 11 is not at a l l well described by one single frequency as classical theory would demand (Barnes 48). Absorption bands are obtained with definite structure which seems to depend on sample thickness. : In view of the fact that the samples used were evaporated films at most a few microns in thickness, i t should not be surprising that the absorption spectrum is different from the,case of infinite crystals. Results of the computation show that for a large crystal the so-called "limiting frequency11 - the only optically active frequency according to the old theory in which correct boundary conditions are not taken into account - would have the greatest intensity, compared to the subsidiary frequencies. For small crystals (roughly defined as crystals in which a substantial fraction of the atoms are close to one of the surfaces), these relative intensities may of course, be reversed or otherwise changed. The computed values of the limiting wavelengths A £ and the subsidiary wavelengths X ^ , ^4+> X.3- ^ A4. for NaCl and NaBr are reproduced below. 12 TABLE (1) Wavelengths absorbed by a l k a l i ha l ides as computed by Rosenstock (47) ( \^ in microns) A 2 x 4+ X 3 -NaCl 45.6 60.2 46.2 107.0 NaBr 54.6 69.1 49.8 162.6 I t i s to be noted that most of the observed "subsidiary" wavelengths (and i n the case o f NaCl a l l o f them) are l a r g e r than A.£• Comparison wi th experiment shows that i n every case the observed absorpt ion peak i s matched much bet ter by the one or more of the "subs id iary frequencies" i n most cases , than by the " l i m i t i n g frequency" X £ « In view o f the fac t that the samples used were evaporated f i l m s , the r e l a t i v e i n t e n s i t i e s pred ic ted for i n f i n i t e c r y s t a l s are reversed . I t w i l l be seen that . the c a l c u l a t e d frequencies are not s u f f i c i e n t l y low to account for the surface heat capaci ty of sodium c h l o r i d e . ' In any comparison o f t h e o r e t i c a l and . experimental work, i t would be wise to note that the wave-lengths c a l c u l a t e d by Rosenstock for A . o _ > A . A - ^ A A J . i a A 4 . 66.7 95.5 13 sodium chloride could also arise as harmonics of the 330 micron vibration suggested by the heat capacity measurements* It has been shown by Wallis (112) that a one-dimensional diatomic lattice with free ends and nearest neighbour Hooke's law interactions may possess one or possibly two "surface'1 modes of vibration, i.e* modes in which the displacement amplitudes are relatively large at one or both ends of the lattice and decrease roughly exponentially toward the interior of the lattice* In,a subsequent paper (14) Wallis has developed theoretical expressions for the frequencies and displacements of the normal modes of vibration of two? and three dimensional lattices of the sodium chloride, employing the free boundary conditions in which atoms on the surface,are assumed to interact only with their nearest neighbours on the interior of the,lattice and are otherwise free* The use of free boundary conditions leads to the existence of surface modes of vibration in which the displacement amplitude is relatively large for a light atom on a boundary and decreases roughly exponentially toward the interior of the lattice* A band of surface mode ofifrequencies lies in the "forbidden" gap between the acoustical and optical branches* 14 C . Poss ib le Influence of Adsorbed Layers on Surface Tension Surface tension i n c r y s t a l s of NaCl type , ca l cu la ted with reference to the (100) p lanes , i s found to be greater than the corresponding surface energy by a fac tor of about 5 (Nicolson, 38) . The experimental work confirms the existence of these surface forces . The basis of the method used, i s the measurement of the un i t c e l l dimensions of small c r y s t a l s compared with those of normal s i z e . As the p a r t i c l e s i ze i s diminished, surface forces of the order of those ca l cu la ted cause a gradual change i n the un i t c e l l dimensions which becomes measurable by standard X-ray powder technique before l i n e broadening masks the e f f e c t . Samples of small c r y s t a l s of sodium ch lor ide were found to show changes i n the un i t c e l l dimensions of the s ign and order of magnitude expected, provided that adsorbed gases were absent. The e f fec t of surface tension i s to reduce each s ide of the cube by an amount independent of i t s dimension (38)• D . Chemical Propert ies o f Surfaces In one or two cases, p a r t i c u l a r l y i n studies of m e t a l l i c oxides , i t has been not iced that the chemical nature of the surface i s not the same as that of the bu lk . This points to a d i f ference i n thermodynamic propert ies between surface and bulk s u f f i c i e n t l y great to lead to chemical change i n some instances . For example, Teichner and Morrison (39) found that 15 the surface of n i c k e l oxide would decompose to m e t a l l i c n i c k e l at 4 0 0 ° C , although the d i s s o c i a t i o n pressure of NiO at t h i s temperature has been reported to be of the order of -28 10 atm. The decomposition i n t h i s case involved cons ider-ably more than jus t the outermost atomic l a y e r . Zinc oxide appears to show s i m i l a r behaviour. I t s e l e c t r i c a l conduct i -v i t y appears to ind icate the separation of m e t a l l i c Zinc on the surface at oxygen pressures below about 10"^ mm. i n temperature ranges where the bulk l a t t i c e i s e n t i r e l y s table (115). E . K i n e t i c Propert ies of Surfaces  ( i ) Exchange Reactions 18 The i so top ic exchange of 0 between gaseous oxygen and s o l i d oxides (41, 42, 43) ind icates the h igh r e a c t i v i t y of surface oxygen atoms of the s o l i d oxides . The reac t ion consists of a r a p i d exchange followed by a slow process . Ind irec t evidence for the r e a c t i v i t y of s p e c i a l l y prepared oxides towards c e r t a i n gases can be c i t e d from the l i t e r a t u r e upon heterogeneous c a t a l y s i s (44). The i so top ic exchange of halogen between halogen gases and sodium c h l o r i d e c r y s t a l s (Harr ison , 10) shows s i m i l a r s u r p r i s i n g ease of r e a c t i o n . The react ions of ch lor ine with the evaporated f i lms are more r a p i d and more extensive; the extent of reac t ion often exceeds the equivalent of one surface l a y e r . The exchange 16 with bromine i s almost instantaneous but does not exceed the equivalent of one surface layer* Beyond the problem of e s t a b l i s h i n g the form of the k i n e t i c laws governing the exchange, there i s the more fundamental problem of understanding the d e t a i l e d reac t ion mechanism. Because of the lack of s u f f i c i e n t experimental data , the mechanisms of the exchange react ions are d i f f i c u l t to e s t a b l i s h . From the d e t a i l e d inves t iga t ion of the i so top ic exchange reac t ion between gaseous ch lor ine and s o l i d sodium c h l o r i d e Harrison et a l . (100) conclude that the mechanism of the react ion does not require the in troduct ion during preparat ion of metastable surface s tructure or of any s p e c i f i c s u p e r f i c i a l impuri ty , but involves the s o l i d surface i n thermal e q u i l i -brium. F u r t h e r , from energetic considerat ions o f the exchange react ion they conclude that some s t r u c t u r a l i r r e g u l a r i t y must be present to al low the surface to exchange at - 2 0 ° C . ( i i ) D i f f u s i o n Processes The theory of d i f f u s i o n i n i o n i c c r y s t a l s due to Frenkel and extended by J o s t , based on the concept of thermal e q u i l i -brium disorder i n the l a t t i c e , has provided a sound bas is for the d iscuss ion of many d i f f u s i o n phenomena i n i o n i c c r y s t a l s . However, i t i s obvious that d i f f u s i o n along the surface layer w i l l be somewhat d i f f e r e n t from d i f f u s i o n i n the b u l k . 17 Recently, much experimental evidence has been reported i n d i c a t i n g that layers subjacent to the surface and d i s -locat ions penetrat ing the whole c r y s t a l may behave anomalously i n d i f f u s i o n processes . (a) I t i s shown by Harrison (45) that r e s u l t s o f slow exchange experiments from 2 0 ° - 2 0 0 ° C . can be explained on the bas is that the a c t i v a t i o n energies for migrat ion i n subsurface layers are lower than i n b u l k . (b) The e f fect of gross imperfections on ch lor ide ion d i f f u s i o n i n c r y s t a l s of sodium c h l o r i d e and potassium ch lor ide has been inves t igated by Barr (8) . I t i s shown that the d i f f u s i o n of ch lor ide ion i n s ing l e c r y s t a l s of NaCl and KCl i s very s ens i t i ve to the concentrat ion of d i s l oca t ions i n the c r y s t a l s . The general e f fect of a decrease i n d i s l o c a t i o n density i s to increase the apparent a c t i v a t i o n energy. An important feature i s that the d i f f u s i o n follows the k i n e t i c s of simple bulk d i f f u s i o n i n a s e m i - i n f i n i t e s o l i d . (c) Extensive experimental work on ca t ion and anion d i f f u s i o n i n the a l k a l i ha l ides has been done by Laurent et a l . (89, 90, 96, 114). Th i s work has shown that the l a r g e -angle boundaries i n pressed compacts make a large contr ibut ion to the o v e r a l l d i f f u s i o n c o e f f i c i e n t for anions . The c o n t r i b u -t i o n i s propor t iona l to the concentrat ion of boundaries and, s u r p r i s i n g l y enough, takes the form of a change i n 18 pre-exponential factor with no change i n a c t i v a t i o n energy. V. Objects of the Present Investigation The main objects of the present i n v e s t i g a t i o n are to study:-(a) the various aspects ( k i n e t i c s and equilibrium) of the exchange reaction between sodium bromide and hydrogen chloride represented as HCl(gas)+Br"(NaBr surface) ^± HBr(gas)+Cl~(NaBr surface). (b) the subsequent d i f f u s i o n of C l ion to other parts of the c r y s t a l ; (c) the adsorption of hydrogen chloride and hydrogen bromide on the s o l i d , to determine what influence t h i s adsorption may have on the exchange reaction; (d) the hydration and dehydration of sodium bromide c r y s t a l s ; t h i s work arose i n c i d e n t a l l y to the main project, and appears to involve an i n t e r e s t i n g surface phenomenon. The most important s i n g l e feature of the work i s the study of the Chemical Equilibrium, which allows thermodynamic data, most p a r t i c u l a r l y entropy changes, to be obtained from experiments at and around room temperature. This gives information on the change i n thermodynamic properties when B r"(NaBr surface) i s « P ^ e d by Cl ( m B l 8 u r f a c e ) as functions 19 of the proportion of C l and Br on the surface of sodium bromide. I t i s expected that increase i n the proportion of C l ion would decrease surface d i s t o r t i o n of the Verwey type because of the lower p o l a r i z a b i l i t y and smaller si z e of C l • Since the change i n the d i s t o r t i o n of the surface w i l l be l o c a l i z e d and w i l l p r i n c i p a l l y a f f e c t the f i r s t and second nearest neighbours, the phenomena may be easier to interpret than many other processes involving i o n i c surfaces. 20 SECTION I  GENERAL EXPERIMENTAL DETAILS Th i s sect ion contains a d e s c r i p t i o n of the vacuum system and mater ia l s used i n most of the studies described i n t h i s t h e s i s . Methods relevant only to a p a r t i c u l a r sect ion of the work, e . g . the i n f r a r e d technique used for fo l lowing the k i n e t i c s of the HCl/NaBr exchange r e a c t i o n , are not given here , but are inc luded i n the complete d e s c r i p -t i o n of t h i s aspect of the work. 1. Vacuum System A schematic diagram of the vacuum system constructed for the present inves t iga t ion i s shown i n F igure 1. The impor-tant parts are represented by c a p i t a l l e t t e r s and the stop-cocks by numerals. Stopcocks and the g l a s s - j o i n t s were greased with Apiezon N . The parts exposed to vacuum were outgassed over a per iod of ten days. A d e s c r i p t i o n of the vacuum system i s given below. A i s a mercury d i f f u s i o n pump backed by a Duo-seal o i l pump (not shown i n the diagram). The c o l d trap B i s kept at l i q u i d nitrogen temperature and C i s a l i q u i d ni trogen Dewar f l a s k . D i s an i o n i z a t i o n gauge of "inverted e lectrode assembly" type , Westinghouse catalogue number WL5966, used i n 22 conjunction with the circuit of Alpert (120) and a Pye scalamp galvanometer. The maximum sensitivity (uncalibrated) —6 at 5 ma. grid current was 2 cm. deflection /10 mm. E and F are six l i t e r gas storage vessels. The one li t e r bulbs used for mixing gases are shown by G and H. I is a quartz spiral pressure gauge capable of measuring pressures up to one atmosphere. The U-tube J was used for condensing gaseous mixtures. The reaction vessel (Volume 224.4 ml.) is marked by K. A convection heater L was used to ensure complete mixing of the gas phase. A glass wool plug was provided at M to protect the system against accidental blowing over of the crystals during evacuation. Sample bulbs are marked by N and 0 (Volume — 15 ml.). An additional glass-joint cone P was provided for easy extension. Q is a capillary leak with a , loose-fit wire, used in the adjustment of the spiral gauge I. The volumes of the different parts of the system are conveniently indicated by giving the numbers of the stopcocks which are closed. 2. Calibration of the Spiral Pressure Gauge A mercury manometer was attached at P. Changes in the pressure of the system were recorded simultaneously by reading the manometer and the position of the light spot on the scale of the spiral gauge assembly. The pressure of the 23 gas was plotted against the deflection of the light spot (Figure 2), and the deflection was found to be exactly proportional to the, pressure up to 8 cm* Hg*, the sensitivity being 4.1 cm* deflection /cm* Hg* 3. Preparation of Materials Hydrogen chloride (anhydrous) An extension of the vacuum system used for the preparation of hydrogen chloride gas is shown diagramatically in Figure 3. Tube A contains concentrated sulfuric acid* Potassium chloride crystals are put in the tubes B and C. D is a glass-joint socket for connections with the vacuum system at P (Figure 1)* Stopcocks 1 and 2 open to the atmosphere. Potassium chloride (Analytical Reagent grade) was obtained from British Drug Houses* Bromide ion was not mentioned as impurity* Sulfuric acid (Reagent grade) was a Baker and Adamson product, claimed to be 96*5% ^SO^* Hydrogen chloride is produced by the reaction of sulfuric acid on potassium chloride* The apparatus is connected with the vacuum system and evacuated for about an hour to expel the dissolved .air* Part of the tube C containing KCl crystals is cooled to liquid nitrogen temperature* The vacuum system is cut out by closing stopcock No* H(Figure 1). A few drops of sulfuric acid are added gradually to the crystals in tube B, by ti l t i n g the tube A. The hydrogen 8 12 16 20 24 28 Deflection (cm.) Figure 2. Spiral pressure gauge calibration 25 c h l o r i d e produced i s condensed on the potassium c h l o r i d e c r y s t a l s i n tube C . The apparatus i s evacuated again and the condensed gas i s allowed to f i l l the apparatus, by warming the tube C up to room temperature. The apparatus i s evacuated aga in . T h i s process i s repeated to remove exchangeable gases adsorbed on the surfaces exposed to the vacuum. The tube C i s cooled,again and the r e a c t i o n i s allowed to proceed for an hour. Stopcock 3 (Figure 3) i s c losed and stopcock 1 i s opened to the atmosphere. The apparatus i s . evacuated for a short time to remove any uncondensable gas., Vacuum system i s cut out by c l o s i n g stopcock no . 11 (Figure 1). The condensed hydrogen c h l o r i d e i s allowed to evaporate at dry i c e temperature .and stored i n bulb E . Evaporation of the gas at dry i c e temperature e l iminates the moisture as w e l l as any s u l f u r i c a c i d vapor, from the gas. Some i n t e r a c t i o n o f the gas and the grease i s not iceable from the darkening of the.grease over a long per iod o f t ime. In order to determine the B^SO^ impurity a large specimen (about 2 l i t e r s at 5 cm. Hg.) was d i s so lved i n 2 m l . o f doubly d i s t i l l e d water and tes ted by barium c h l o r i d e s o l u t i o n , and from the absence of p r e c i p i t a t i o n i t was concluded that the gas specimen was free from s u l f u r i c a c i d . 26 Hydrogen bromide (anhydrous) Hydrogen bromide gas was obtained from the Matheson Company. The p u r i t y claimed for the gas i s 9 9 . 8 % HBr (anhydrous). Hydrogen bromide from the l e c t u r e b o t t l e i s condensed i n tube B (Figure 3) at l i q u i d n i trogen temperature. The apparatus i s evacuated for a short time and the gas evaporated at d r y - i c e temperature and recondensed i n tube C . Stopcock 3 (Figure 3) i s c losed and the apparatus evacuated again for a few minutes. The connecting tubes and the storage ves se l F (Figure 1) are f lushed wi th the gas. HBr i s evaporated at dry i c e temperature and s tored i n the ves se l F . • • Darkening of the.stopcock grease i s greater wi th HBr than i n the case of H C l . Small P a r t i c l e s o f Sodium Bromide Apparatus The arrangement used-for the vacuum f i l t r a t i o n i s shown i n F igure 4 . A i s a f i l t r a t i o n f l a s k ; B and C are Buchner funnels , whose edges are ground smooth for an a i r - t i g h t contact , to exclude atmospheric a i r during f i l t r a t i o n . A piece of cobaltous c h l o r i d e paper i s p laced at D , to i n d i c a t e the humidity o f the incoming a i r . The blue c o l o r appears at . .. about 5% r e l a t i v e humidity . E i s a heater used to warm up the dry a i r cooled to l i q u i d n i trogen temperature at F 28 Figure 4. Vacuum Filtration Apparatus 29 (Figure 4). G and H are calcium chloride tubes. The outlet I i s used to f i l l evacuated vessels with dry a i r . The outstanding feature of the arrangement i s the ease of operation. Although the joined Buchner funnels hold sufficiently good vacuum, they are separated easily by lateral sliding movement. Materials Sodium bromide (Reagent grade) was obtained from Baker and Adamson Chemical Company. Chloride ion impurity i s claimed to be less than 0.2% by weight. Acetone (Reagent grade) was supplied by Mallinckrodt Chemical Company. Doubly d i s t i l l e d water was used for the preparation of solu-tions. Method Sodium bromide crystals of small size and cubical shape, in the size range of 1 to 20 microns, are obtained by a modification of the method described by Marshall (53). The essential difference i s in the use of acetone instead of absolute ethyl alcohol. This i s necessitated because of the higher solubility of sodium bromide in ethyl alcohol (2.33% by weight (54) ) compared to that of sodium chloride (0.63% by weight (56) ) at room temperature. A 100-ml. portion of saturated sodium bromide solution i s frozen in a tube at dry-ice temperature (using acetone-30 d r y i c e bath) wi th constant s t i r r i n g to freeze the s o l u t i o n q u i c k l y . The tube i s cracked o f f and the frozen mass dropped i n t o two l i t e r s of acetone. Th i s mixture i s shaken v igorous ly u n t i l the frozen mass d i s in tegra tes i n t o smal l c r y s t a l s . Vacuum f i l t r a t i o n i s s t a r t e d immediately. During f i l t r a -t i o n the c r y s t a l s are kept covered wi th acetone. A f t e r the c r y s t a l s are t rans ferred to the Buchner funne l , the f i l t r a t i o n i s completed under dry a i r by j o i n i n g the two funnels as shown i n F igure 4. The powder so obtained cons i s t s o f NaBr. 21^0 c r y s t a l s w i th adsorbed water,and acetone. Acetone i s removed during vacuum des i cca t ion over a p e r i o d o f ten hours . The subsequent dehydration i s c a r r i e d out i n a dry box us ing F2O5 a s d e s i c -cant . The d e t a i l s of t h i s process form the subject o f Sect ion VI o f t h i s t h e s i s . The fo l lowing were found to be the important fac tors a f f e c t i n g the s i z e o f the p a r t i c l e s . (1) R e l a t i v e proport ion o f acetone and the s a l t s o l u t i o n . . Larger q u a n t i t i e s o f -acetone r e s u l t i n the p r e c i p i t a t i o n o f smaller c r y s t a l s . I t seems l i k e l y that increase o f the proport ion of acetone increases the removal o f adsorbed water, thereby decreasing the chances of growth of smal l p a r t i c l e s . T h i s view i s supported by the observation that acetone conta in ing smal l amounts o f water i s l e s s e f f i c i e n t and r e s u l t s 31 i n the precipitation of larger crystals. (2) Rates of precipitation of the salt solution. The rapidity with which the salt solution i s frozen affects the size of the crystals. In a quick freezing process the crystals are less l i k e l y to grow in size. (3) Thoroughness of shaking during precipitation. Size of the crystals and the uniformity of powders i s influenced by the degree and duration of agitation of the frozen mass and acetone during precipitation, uniform powders of smaller crystals are obtained on increasing the agitation and time of shaking. Both of these factors affect the removal of adsorbed water from the crystals. (4) Time. The average size of the crystals depends on the time elapsed between f i l t r a t i o n and desiccation. The wet crystals have a tendency to grow with time. Therefore smaller crystals are obtained on quick desiccation after f i l t r a t i o n . (5) Desiccation and dehydration. The efficiency^of desiccation and dehydration has a large effect on the crystal size. Large quantities (about 2 kg.) of P2°5 a r e u s e d a s desiccant to dehydrate one hundred grams of the precipitated crystals in a few days. Frequent s t i r r i n g of the crystals and the desiccant i s done to f a c i l i t a t e the process of dehydration. 32 Size and Shape of Crystals The crystals viewed tinder the microscope have well defined cubic shape. They have a tendency to group together in small clusters* The average size of the crystals is about 3 microns on an edge. Surface Area Assuming simple surfaces of cubic crystals, estimates of the specific surface areas from average particle size were made. For two batches the specific surface was estimated by applying the B.E.T. equation to adsorption isotherms of nitrogen at 77° K on NaBr surface. Values from microscopic examination and gas .adsorption are of the same order of magnitude, namely ^ 0,6 m /g. Properties Sodium bromide is hygroscopic and small crystals of the salt are extremely sensitive to moisture. The amount taken up by a microcrystal in a few minutes exposure to atmosphere is sufficient to dissolve i t . This necessitates drastic conditions for dehydration and storage of the powder. After a period of three months a slight brown tint was noticed to develop on crystals kept in a desiccator. This... batch of the crystals was not used in the experimental work. Similar behaviour was observed by Schamp and Katz (85). 33 The crystals are very easily colored pink by high frequency discharge, obtained from a Tesla c o i l . The bulk density of the powder is of the order of 0.3 gm/cc (less than one-tenth of their ultimate density). The powder can be stored in dry conditions for a few months without any significant change in the particle size. 34 SECTION II  STUDIES ON ADSORPTION 1. Adsorption on Sodium Bromide Crystals Adsorption of hydrogen chloride and hydrogen bromide gases on the surface of sodium bromide crystals was investi-gated by two different methods* The method based on pH measurements was designed to examine irreversible adsorption* The other method based on manometric measurements gives information about the rate of adsorption and determines both reversible and irreversible adsorption provided neither is very rapid* (i) Method for Irreversible Adsorption Assuming that one molecule of HCl or HBr occupies an area of the order of 10 A* ^  in the adsorbed layer* the amount of the adsorbed monolayer of the gas on 10*0 grams of the, sodium bromide crystals with specific surface of about n ~4 0*63 m /gm, is found to be of the order of 1x10 moles* A significant fraction of the irreversibly adsorbed layer can therefore be determined by pH measurements of the solution obtained on dissolving the sodium bromide crystals* The pH-meter used for the measurements was sensitive enough to detect a few percent of this amount as can be seen from the 35 calibration Table 1. Materials High surface area sodium bromide was prepared according to the method described in the previous section* Reagent grade Hydrochloric acid was obtained from Baker and Adamson Chemical Company* Doubly d i s t i l l e d water was used for a l l experimental work* Procedure The Beckman Zeromatic pH meter 9602 was used for pH determinations* Temperature*corrections were made manually* The instrument was standardized before and after each series of measurements* The accuracy of the instrument was of the order of 0*02 pH units* The pH meter was calibrated with standard solutions of hydrochloric acid containing 10*0 grams of sodium bromide crystals from the batch used-for adsorption studies. The calibration curve i s shown in Figure (1)* 10.0 gm. of the powder was taken in the adsorption tube and the system was evacuated for an hour* Hydrogen chloride gas was introduced i n the adsorption system. The gas was pumped o u t from the adsorption system after an exposure of two hours, for 10 minutes, since-this was themteianum pumping time in exchange reactions, between successive gas specimens* The powder was dissolved i n boiled d i s t i l l e d water to make F i g u r e 1. pH C a l i b r a t i o n Curves A - T h e o r e t i c a l B - Observed C - Observed w i t h 10 gms. of NaBr per l i t e r of s o l u t i o n 37 one l i t e r of so lu t ion and the pH of the so lu t ion was deter-mined v A ser ies of experiments i s done vary ing the exposure t imes. A blank was prepared by d i s s o l v i n g 10.0 gms. of the powder to make one l i t e r of s o l u t i o n . Results The r e s u l t s of the c a l i b r a t i o n of the instrument are given i n Table 1, and Figure (1) . The v a r i a t i o n of pH corresponding to the change i n hydroch lor ic a c i d concentrat ion i s r epro -d u c i b l e , making i t poss ib le to measure the a c i d concentration -6 down to 2.5x10 NHCl. In F igure (1) values of pH are p l o t t e d against concentration of the a c i d i n the three cases A , B and C . The case B re fer s to so lut ions containing no sodium bromide, C re fers to so lut ions containing 10.0 gm. of sodium bromide per l i t e r of so lu t ion and A re fer s to the c a l c u l a t e d pH values of the so lu t ion without sodium bromide. 38 TABLE 1 p values of the calibration standards, (each containing H 10.0 gm. NaBr/ l t t e r 6 o l u t i o n ) . Standard HCl Concentration pH of the Solution Solution in N 1 0.0N 5.3 -6 2 2.5x10 N 5.15 3 2.5xl0"5N 4.6 4 2.5xlO*4N 3.64 5 2.5xl0"3N 2.65 6 2.5xl0"2N 1.65 P„ values of the samples obtained from the adsorption H experiments are given in Table 2. It is apparent that the variations in pH values do not correspond to time of exposure. 39 TABLE 2 F„ values of the solution of the adsorbent, dissolved after ii the removal of reversibly adsorbed gases* Sample Time of Exposure pH Values in Minutes of the Solution 1 0.0 5.13 2 15.0 5;2 3 30.0 5.54 4 60.0 5.48 5 120.0 5.39 Since the observed change in the pH values is in the wrong direction i t does not indicate the presence of irre-versibly adsorbed layer. The expected pH value, calculated on the basis of a complete monolayer is about 4.1, and for a tenth of monolayer the expected value would be about 5.2. The observed values close to or higher than 5.3 definitely indicate that no significant amount of the surface is covered by irreversibly adsorbed gas. It is further concluded that nearly a l l of the adsorbed gas is pumped out within ten. minutes. (ii) Manometric Method The apparatus used in the pH method is employed for 40 manometric investigation. The changes in pressure are read from the deflection of the spiral gauge. The accuracy obtained in reading the pressure is of the order of 0.012 cm. 30.0 grams of the powder is placed in the adsorption tube and the system is evacuated for an hour. The gas is introduced into the adsorption system and the pressure of the gas recorded within the f i r s t ten seconds is taken as the i n i t i a l reading. The changes in the pressure are recorded at small intervals of time, and,the adsorption is allowed to proceed for an hour. The gas is pumped out for half an hour and the next adsorption experiment is performed on the same crystals. Corrections due to adsorption on the glass surface are determined in a blank run. Results and Discuss ion Experimental condit ions i n the study of adsorption were maintained as c lose as poss ib le to those of exchange e x p e r i -ments, i n order to obtain information regarding the e f fec t of adsorption on the exchange r e a c t i o n . The adsorption e x p e r i -ments described i n t h i s sec t ion are i n fac t complicated due to the simultaneous exchange r e a c t i o n . Pure HGl introduced i n the adsorption system, becomes a mixture of HGl and HBr gases. The composition of t h i s mixture v a r i e s wi th time u n t i l the e q u i l i b r i u m composition i s a t t a i n e d . The rates and the extent of adsorption being d i f f e r e n t for the two gases, i t i s d i f f i c u l t to sor t out t h e i r separate contr ibut ions to the o v e r a l l adsorpt ion . The objects o f t h i s i n v e s t i g a t i o n are t h r e e f o l d : -(a) To determine the extent o f any i r r e v e r s i b l y adsorbed l a y e r , i n order to e l iminate the p o s s i b i l i t y that the surface phase concerned i n the e q u i l i b r i u m studies o f Sect ion IV i s such an adsorbed layer and not the surface layer of the s o l i d i t s e l f . T h i s object i s s a t i s f a c t o r i l y met by the pH measure-ments. (b) To determine whether the r e v e r s i b l e adsorption has any important inf luence on the k i n e t i c s o f the exchange r e a c t i o n . 42 On comparing the r a t e curve for adsorpt ion (time for h a l f -complete process , t^ about f i v e minutes) to that of exchange r e a c t i o n (time f o r half-complete r e a c t i o n , t^ about t h i r t y seconds) at room temperature (Sect ion I I I ) , i t appears that observed adsorption process i s not s i g n i f i c a n t i n the exchange r e a c t i o n , unless the f i r s t few percent of the t o t a l adsorption has any s p e c i a l in f luence . (c) To determine the p o s s i b l e e f fec t o f the r e v e r s i b l y adsorbed layer on the thermodynamic proper t i e s o f the under-l y i n g sur face , and hence on the e q u i l i b r i u m studies o f Sect ion I V . C a l c u l a t i o n on t h i s i s given at the end o f t h i s s e c t i o n . The r e s u l t s o f HCl adsorption ( i n the sense discussed above) on 31.2 grams o f sodium bromide c r y s t a l s at 2 2 ° C . and 4.12 Cm. Hg. pressure are shown g r a p h i c a l l y i n F igure (2 ) . Curves A , B and C were obtained on repeat ing the adsorption experiment on the same c r y s t a l s , w i th f resh specimens o f HCl gas, under the same condi t ions o f temperature and pressure . Since the rates and extent o f adsorption i n the three cases are o f the same order o f magnitude, the p o s s i b i l i t y of any considerable i r r e v e r s i b l e adsorption i s r u l e d out . Th i s agrees wi th the conclusions a r r i v e d at from the pH determina-t i o n s , discussed above. The important fac t i s that the adsorbed gas i s completely removed from the surface o f the 44 crystals in a short evacuation time (about 10 minutes). Adsorption of HCl on the same crystals was investigated under different conditions of temperature and pressure. The experimental data are summarised in Table (3) and the results are shown graphically in Figures (3a, 3b and 3c). TABLE 3 Temperature and pressure values of various HCl adsorption experiments. Weight of Sodium Bromide = 31.2 grams. Run Pressure Temperature Cm.Hg. C. 1 5.97 0 2 0.77 25 3 1.59 25 4 3.53 25 5 4.12 25 6 4.65 25 7 5.16 25 8 6.90 25 9 1.99 90 10 2.83 90 11: 5.58 90 12 6.54 90 45 46 Results of HBr adsorption on the crystals are shown in Figure (4). The experimental conditions are given in Table (4). TABLE 4 Summary of experimental conditions of the HBr adsorption experiments. Weight of Sodium Bromide "31,2 grams. Run Pressure Temperature Cm.Hg. °C. 1 1.55 25 2 2.55 25 3 4.67 25 4 4.93 25 5 7.24 25 Adsorption of HBr on the crystals was also found to be reversible like the case of HCl discussed above. There i s ample jus t i f i c a t i o n for the assumption that no irreversibly adsorbed gases are involved in exchange experiments described in Section IV. Adsorption isotherms for the two gases, however, have different characteristics; whereas the HCl isotherm at room temperature shows multilayer adsorption, the isotherm for HBr indicates the formation of a monolayer only, at the temperature 48 and wi th in the pressure range of these experiments, as shown i n F igure (5)• The same behaviour i s exhib i ted by the i s o -therms drawn with adsorption values at 200 and 150 seconds for HCl and HBr r e s p e c t i v e l y i n the above experiments. These isotherms are given i n Figure (5) for comparison wi th 60 o minute isotherms. The adsorption isotherm for HCl at 90 C . shows s i m i l a r c h a r a c t e r i s t i c s o f m u l t i l a y e r adsorpt ion . The i n i t i a l and f i n a l pressures are here inaf ter denoted by p Q and p t r e s p e c t i v e l y , where the subscr ipt t denotes the time o f adsorption corresponding to the f i n a l pressure . The amount o f the gas adsorbed on sodium bromide i s ca l cu la ted from the corrected values obtained on tak ing in to cons iderat ion the adsorption of the gas on the parts o f the adsorption system. The values of p Q , p t and n&, the number o f moles of gas adsorbed on sodium bromide for HCl and HBr adsorption isotherms under var ious experimental condit ions are given i n Tables (5, 6, 7 , 8 and 9 ) . I t w i l l be seen tha t , although the i s o -therms suggest m u l t i l a y e r adsorpt ion , the amounts o f gas adsorbed are very much l ess than the estimated monolayer -4 capaci ty of about 3X10 mole for a 30 g . specimen. 48.0 50 TABLE 5 Values of n a, p Q and p$Q d n i 1 f . p for HCl adsorption isotherm at 22° C. Po n a p60 m. ,«+6 Cm.Hg. xlO Cm.Hg. 0,792 7.665 0.724 1.634 13.799 1.507 3.609 14.673 3.476 5.024 17.852 4.861 7.073 36.634 6.776 TABLE 6 Values of nfl, p Q and p 2 Q ( ) s e c o n d s for HCl adsorption isotherm at 22° C. po n a p200 s. +6 Cm.Hg. xlO Cm.Hg. 0.792 4.380 0.754 1.634 6.680 1.573 3.609 7.984 3.537 5.024 9.638 4.936 7.073 14.124 6.944 51 TABLE 7 Values of n &, p Q and p^g m f l n i l f r g f° r H G 1 adsorption isotherm at 90° C. po n a p60 m. Cm.Hg. xlO* 6 Cm.Hg 2.044 8.062 1.963 2.902 6.353 2.839 5.720 5.947 5.661 6.700 12.301 6.578 TABLE 8 Values of n . p and p.. . _ for HBr adsorption isotherm a' r o *b0 minute at 22° C. p n p o a, 60 m. +6 Cm.Hg. xlO Cm.Hg. 1.488 13.907 1.361 2.610 15.439 2.468 4.849 15.988 4.702 5.049 18.726 4.878 7.424 16.862 7.271 52 TABLE 9 Values of n , and p, _. , for HBr adsorption isotherm a ro r150 seconds at 22°C. Po n a p150 s. +6 Cm.Hg. xlO Cm.Hg. 1.488 6.680 1.425 2.610 8.323 2.532 4.849 8.323 4.769 5.049 9.854 4.955 7.424 8.323 7.342 The type of adsorption observed here is somewhat obscure. The shape of the HCl isotherm suggests multilayer formation, but only a small proportion of the surface is involved. In this respect, the process does not resemble a typical physical adsorption, but appears to require certain "active sites" on the surface. It is shown later in this thesis (Section VI) that adsorption of water vapour, by contrast, takes place over the whole surface in a manner indicating energetic homogeneity. Perhaps what we have here is heterogeneity in the original sense proposed by H. S. Taylor, in which most of the surface is homogeneous but the parts which are near to an edge (or possibly a growth step) are more active. 53 The apparently greater re luctance o f HBr to form m u l t i -layers i s a l so not i n accordance with a p h y s i c a l adsorption process which should occur more r e a d i l y wi th the more conden-s i b l e gas. The complicat ing feature i s probably the o r i e n t a -t i o n of the po lar molecules, r e l a t i v e to each other and to the under ly ing surface . The strong dipoles of HCl may have a greater tendency to or i en t themselves r e l a t i v e to each other and form a favourable array i n the f i r s t layer for adsorption o f subsequent l a y e r s . The weaker d ipoles of HBr may be more s trongly inf luenced by the underly ing surface . T h i s may lead to a tendency to p a r a l l e l o r i e n t a t i o n of the d i p o l e s , l eav ing the f i r s t l ayer with l i t t l e e l e c t r o -s t a t i c inf luence on subsequent l a y e r s . 54 Poss ib le E f f e c t o f Adsorpt ion on the  Entropy of the Surface I t i s evident that the observed adsorption can have l i t t l e e f fect on the whole surface . However, supposing that the adsorbed layer i s formed on only a small f r a c t i o n o f the surface , on which i t i s close-packed (coverage 0 • 1) at the o h o r i z o n t a l part o f the 22 C . HCl isotherm, we may make a rough order-of-magnitude estimate of the e f fec t of the adsorbed layer on that f r a c t i o n of the surface . Le t us assume that the data can be represented, up to the h o r i z o n t a l p o r t i o n of the isotherm, by a Langmuir expression 9 - k (1-6)P A F a d 8 . " - R T l n k k may be estimated as the r e c i p r o c a l of the pressure at hal f -coverage . (Half-coverage, Q - 0 .5 , w i l l be taken as the standard state of the adsorbed l a y e r ) . From the 2 2 ° and 9 0 ° isotherms, an i s o s t e r i c heat of adsorption may be est imated. 55 .dlnp, A Hada <"dT >0 * " " R T 2 " The standard entropy of adsorption may be written as A sads " A sad«orbate + 2 A Surface The factor two arises because, in the standard state of the adsorbed layer, assuming one adsorbed molecule per ion-pair for complete coverage, one mole adsorbate is attached to 2 moles surface. Whence 2 A s s u r f " A s a d s " A sadsorbate o o o " A Hads " A Fads " A sadsorbate o The mwniimim value of A S s u r f .may be estimated by assuming that the three-dimensional gas becomes a two-dimensional gas on adsorption (a "lattice gas", the configurational entropy of which is represented by the 8/(1-6) of the Langmuir equation), and that the molecules lose both rotations on adsorption. A sadsorbate " A s t r a n s + A s r o t A S° „ - 2R + Rln(2 TT mkpA  t r a n S Nh2 3 A s° - - a - Rln 8 *//re kr ~ ^ The numerical estimate of ^  S g u r ^ for HCl adsorption at 22° C. is as follows:-0 » 0,5 at p - 0.68 Cm.Hg. k » 112 atm * o -1 A F a d s " ~ 2 » 7 7 0 c a l 0 - 0.5, P ( 9 < f o ) „ 4 . 4 9 o -1 AH a d g • -4,700 cal mole 0 = 0.5, A = 2Nx(area per ion-pair) - 2x6.02xl02?x20xl0~16 cm2 3 -1 V » 24,200 cm mole o - 1 - 1 A S t r a n g • - 18.3 cal mole deg r - 1.30 X e o -I -1 A s r o t - -7.96 cal mole deg A Ssurf " %(- 4 » 7 0gt 2 » 7 7 0 + 18.3 + 7.96) m 9.9 cal mole deg * The significance of this calculation is that, when a 57 adsorption with such a low heat of adsorption occurs readily at low pressures at room temperature, not much entropy must be lost in the adsorption process. If the adsorbate loses a number of degrees of freedom of motion, the surface must be acquiring some motions to compensate. It i s most probable o thatAS „ i s substantially less than the maximum value surf. calculated above. No account has been taken of the out-of-plane vibrations of the adsorbate, and the assumption that a l l rotations are suppressed i s probably an exaggeration. This calculation indicates that an adsorbed layer covering the whole surface might have an important effect on i t s thermodynamic properties; but in the present case, only a small fraction of the surface could be seriously affected. 2. Adsorption on Parts of the Apparatus Adsorption of HCl and HBr gases on the parts of the adsorption system was investigated in sufficient detail to determine the correction factors to be applied to the adsorp-tion results discussed on the preceding pages, to the results of kinetic investigations, discussed in the following section, and to determine the experimental basis for the "memory effect", "pressure effect" and "composition effect" encountered in the mass-spectral analysis of the mixture of these two gases, described in detail in Section IV. Adsorption of these gases on the blank adsorption system, 58 may be due to two causes, namely, adsorption on the glass surface exposed to the gas phase, and adsorpt ion or reac t ion w i th the Apiezon N grease used i n stopcocks and the glass j o i n t s . However, s ince the reac t ion system f o r the exchange experiments, and the gas r e s e r v o i r of the mass-spectrometer had condit ions s i m i l a r to those of the adsorption system as regards the g lass surface and the grease, the r e s u l t s o f adsorption reported i n these .pages are q u a l i t a t i v e l y a p p l i -cable to these systems as w e l l . Separate experiments were done w i th an enlarged grease surface to determine i t s behaviour i n adsorpt ion . An important r e s u l t was obtained i n the study o f adsorption o f these gases on polyethylene tub ing , used as a par t o f the apparatus i n the k i n e t i c i n v e s t i g a t i o n . These r e s u l t s are used to expla in some of the behaviour observed i n the course of the k i n e t i c studies described i n the next s e c t i o n . Adsorpt ion of HCl and HBr on Blank Adsorpt ion System Experimental condit ions f o r these inves t iga t ions were the same as for the study o f adsorpt ion on the c r y s t a l s . T y p i c a l r e s u l t s o f HCl adsorption are shown i n F igure (6); from these the correc t ions f o r t h i s adsorption used i n the study o f adsorption on NaBr were estimated to be as shown i n F igure (7 ) . Resul ts o f HBr adsorption are given i n F igure (8) and the c o r r e c t i o n fac tors for t h i s are obtained from 62 Figure (9). The behaviour of the two gases in the blank adsorption differs from that observed in the case of adsorption on sodium bromide surface. This i s shown by the isotherms for the two gases obtained from the blank runs, given i n Figure (10). whereas the HCl isotherm seems to approach a limiting value within the experimental pressure range, the isotherm for HBr shows a continuous increase within the same pressure range, suggesting the occurrence of a solution process i n the bulk of the glass and/or grease, rather than monolayer or multilayer adsorption. Measurements using an adsorption tube with i t s entire inner surface covered with fresh Apiezon N grease, showed that, at f i r s t , gases are desorbed from the grease in f a i r l y large quantity, and that increasing amounts of HCl or HBr were taken up in the successive exposures of the same sample of grease to the gas. It appeared that a very large number of exposures of the grease to the gas would be required before the behaviour of the grease became reproducible and conse-quently i t was not found possible to carry out measurements which would establish the relative importance of glass and grease in the effects observed i n the mass spectrometer inlet train. 24 65 SECTION I I I KINETICS OF THE HCl/NaBr EXCHANGE REACTION The course of the r e a c t i o n was fol lowed by continuous recording o f the hydrogen bromide i n f r a r e d absorption peak at 2620 m i l l i m i c r o n . A double beam i n f r a r e d spectrometer was used to e l iminate the overlapping hydrogen c h l o r i d e absorp-t i o n peak at 2940 m i l l i m i c r o n . 1. Apparatus A Perkin-Elmer double beam i n f r a r e d spectrometer (model 21) was used. A s p e c i a l l y designed absorption c e l l was constructed as shown i n Figure (1 ) . Reaction c e l l A i s p r o -v i d e d wi th a f inger B and a jacket C for temperature c o n t r o l . A i s connected wi th the absorption c e l l E by two bridges D and F of wide-bore t u b i n g . A.convect ion heater i s provided at F . The windows G and H are made o f sodium c h l o r i d e . The balancing c e l l I i s connected wi th the absorption c e l l by a f l e x i b l e polyethylene tube J (supported by pieces o f g lass tube so that i t can be evacuated).. : I t was pos s ib l e to regulate the temperature of the a i r c i r c u l a t i n g i n the jacket w i t h i n Z 1 C . o f the des i red v a l u e . A F i g u r e 1. F I R e a c t i o n c e l l A b s o r p t i o n c e l l B a l a n c i n g c e l l 67 During the determination of the infrared absorption spectrum of HBr, i t was noticed that the peak height of pure HBr specimen diminished, whereas a peak corresponding to the HCl absorption maximum developed with time. It was found subsequently that the sodium chloride windows were attacked by HBr gas. The peak corresponding to the HCl absorption maximum was in fact the absorption peak of HCl obtained as a result of the exchange reaction. The extent of the exchange reaction calculated from the amount of HCl, (estimated from i t s peak height) indicated that the. reaction involves hundreds of layers of sodium chloride windows, and i s thus far more extensive than the exchange reaction reported in this thesis (probably due to the effect of moisture on the sodium chloride windows). This complication i s avoided by covering the internal surfaces of the windows with Kel-F grease (a polymer of C F C l ^ ) * To reduce the otherwise excessive background, the windows of the balancing c e l l are also covered with Kel-F grease to an approximately matching thickness of the grease layer with that on the windows of the absorption c e l l . The Kel-F grease does not interact with the gases of the reaction system. 68 2. Procedure ( i ) C a l i b r a t i o n of the Spectrometer The instrument was ca l ibra ted , w i th standard samples o f the pure gases HCl and HBr and mixtures o f known composit ions. The r e l a t i v e proport ions o f the gases, are ind ica ted f a i r l y accurate ly by the peak heights o f absorption spectrum; but due to the v a r i a t i o n s i n the s e n s i t i v i t y of the instrument from day to day i t was not f e a s i b l e to c a l i b r a t e the instrument for absolute amounts o f the gases over a long p e r i o d . ( i i ) Exchange React ion The sodium bromide powder (about 30 grams) i s p laced i n the r e a c t i o n c e l l and evacuated for h a l f an hour on the o i l -pump. The temperature of the; c r y s t a l s i s adjusted by running a i r through the jacket at the appropriate temperature during t h i s per iod of evacuation. The hydrogen c h l o r i d e gas i s p laced i n the balancing c e l l I. The two c e l l s are connected w i th the tube J . J i s evacuated for twenty minutes on the oi l-pump• The apparatus i s t rans ferred to the I.R. Spectrometer, which i s set at 2620 m i l l i m i c r o n s , corresponding to the HBr absorption maximum. The scanning arrangement i s disconnected, a l lowing the drum c a r r y i n g the recording chart to be ro ta ted manually a t a d e f i n i t e r a t e , so that the r e s u l t i s obtained 69 d i r e c t l y as a p l o t o f HBr concentrat ion against t ime. The convection heater i s allowed to warm up for f i v e minutes before s t a r t i n g the r e a c t i o n . Hydrogen c h l o r i d e i s introduced in to the r e a c t i o n v e s s e l by opening the stopcock provided i n the tube J . A few seconds are allowed for the gas to equal ize the pressure i n the two c e l l s , and the stopcock i s c l o s e d . The recorder i s adjusted to read an o p t i c a l densi ty o f zero w i th in the f i r s t two seconds. The reac t ion i s u s u a l l y allowed to proceed for h a l f an hour, the recorder chart being moved u s u a l l y 6 cm./min. 3 . Results and Discuss ion ( i ) General Features of the Rate Curves The most important r e s u l t o f the k i n e t i c i n v e s t i g a t i o n o f the HCl/NaBr exchange r e a c t i o n i s the r a p i d i t y o f the r e a c t i o n as ind ica ted by the approximate h a l f - l i f e and the time requ ired to reach e q u i l i b r i u m . A t y p i c a l r a t e curve obtained at room temperature i s shown i n F igure (2). D D , D and Doc are r e s p e c t i v e l y the o p t i c a l dens i t i e s i n i t i a l l y , at any time during the r e a c t i o n and at i n f i n i t e t ime. I t i s ev ident ly not pos s ib l e to represent the experimental curve by any- simple expression e s p e c i a l l y i n the par t beyond a few minutes of the r e a c t i o n t ime. Some random f luc tuat ions i n the curve were noted i n a l l the experiments. The reason for the 71 behaviour may be p a r t l y the slow mixing of the gases and p a r t l y adsorpt ion o f the gases i n the r e a c t i o n system. These fac tors are considered i n d e t a i l below. I t i s apparent that the r e a c t i o n i s not f i r s t o r d e r . Th i s r e s u l t i s i n accord wi th the e q u i l i b r i u m studies d i s -cussed i n the next s e c t i o n . These suggest that as a r e s u l t o f the exchange, the entropy o f Br ions neighboring any C l i on introduced i n the surface i s changed; hence the entropy of a c t i v a t i o n AS for any ac t iva ted complex depends on X , the f r a c t i o n of the surface covered by C l i o n s . Consequently, unless the dependence of the r a t e constant k on X i s deter -mined, an exact ana lys i s o f the r a t e curves i s not p o s s i b l e . However, there are some general features o f the curve which can be discussed to y i e l d information re levant to the main purpose of the present work, i . e . the i n v e s t i g a t i o n of the chemical e q u i l i b r i u m reported i n Sect ion I V . A t y p i c a l r a t e curve (Figure 2) shows a sharp bend at 1 - 2 minutes and thereaf ter i s roughly l i n e a r for some t ime, l e v e l l i n g o f f w i th in t h i r t y minutes. Therefore i n the studies of the chemical e q u i l i b r i u m , the c r y s t a l s are always exposed to the gas for t h i r t y minutes. The reac t ion i s u s u a l l y h a l f -complete i n about one minute. . The f i r s t few minutes o f a t y p i c a l r eac t ion are p l o t t e d i n F igure (3)• Th i s i n i t i a l part o f the r e a c t i o n appears to be f i r s t order wi th t i , the per iod 6 Figure 3. I n i t i a l part of the t y p i c a l rate curve (Figure 2 , a) . 73 for half-complete r e a c t i o n , equal to 17 seconds, and Doc equal to 5.5. As mentioned before , i n any d e t a i l e d ana lys i s the e f fec ts of temperature, pressure o f the gases, and surface coverage by C l i on have to be taken i n t o account. The poss ib le complica-t ions a r i s i n g from the adsorption o f gases and the c i r c u l a t i o n time l a g should be given due cons idera t ion . These e f fec t s are discussed i n d e t a i l below. ( i i ) E f f e c t o f Adsorpt ion o f Gases, i n the Reaction System The d i f ferences i n the rates and extents o f adsorption o f hydrogen c h l o r i d e and hydrogen bromide gases i n the r e a c t i o n system has been discussed i n Sect ion II, and i t has been pointed out that the r e l a t i v e contr ibut ion of the two gases to the o v e r a l l adsorpt ion of the gaseous mixture cannot r e a d i l y be determined on account of the occurrence o f the exchange r e a c t i o n . To determine the e f fec t s of adsorption on the , k i n e t i c s o f the r e a c t i o n s tudied by the present technique two fac tors should be considered, namely: (a) the e f fec t o f adsorpt ion i n changing the concentrat ion and composition o f the gaseous mixture , and (b) the e f fec t of the adsorbed layer on the r e a c t i o n mechanism. Both of these fac tors are extremely involved and at the moment not amenable to a quant i ta t ive i n v e s t i g a t i o n . Since the rates o f adsorption (Figure 2, Sect ion II) and the rates o f exchange reac t ion (Figures 2 and 3) 74 are both greatest w i th in the f i r s t few minutes, the f i r s t fac tor would be important at t h i s stage of the r e a c t i o n . However, as the adsorbed layer b u i l d s up during the course o f the r e a c t i o n the second fac tor would be dominant i n the l a t t e r par t o f the r e a c t i o n . I t was found that adsorption o f gases on the polyethylene tubing connecting the r e a c t i o n c e l l and reference c e l l could give a spurious r e a c t i o n curve , and i t was therefore necessary to keep the stopcocks between t h i s *tube and both c e l l s c losed during the r e a c t i o n . ( i i i ) E f f e c t o f C i r c u l a t i o n Time Although a convection heater i s used to mix the r e a c t i o n gases, the res i s tance for mixing o f the gases o f fered by the powdered mass introduces a complicat ion which may be reduced, to a considerable extent , by improved design o f the r e a c t i o n c e l l . However, w i th the present arrangement, the increased res i s tance to mixing o f the gases o f fered by a t i g h t l y packed mass of powdered c r y s t a l s inf luences the shape o f the r a t e curve , shown i n F i g u r e (4 ) . The slow mixing o f the gases explains the smaller slope of the par t o f the r a t e curve (A) beyond two minutes of the r e a c t i o n time compared wi th the slope of the curve (B) obtained wi th normally packed c r y s t a l s under s i m i l a r condit ions o f temperature and pressure . 4.0 F i g u r e 4. , Reaction Curves A - T i g h t packed c r y s t a l s B - Loose packed c r y s t a l s 76 ( iv ) E f f e c t o f Pressure The e f f ec t of pressure of the hydrogen c h l o r i d e gas on the r e a c t i o n curve was inves t igated by studying react ions at roughly one-hal f and twice the normal pressure used i n the exchange r e a c t i o n (about 5 Cm.Hg.) • The best way at present a v a i l a b l e for analyzing the r e s u l t s i s to d i v i d e the i n i t i a l r a t e ( d D / d t ) t ° o by the f i n a l o p t i c a l dens i ty D*, • Figures obtained i n t h i s way are shown i n Table (1 ) . TABLE 1 . . . o I n i t i a l rates of r e a c t i o n at 25 C . and var ious pressures* 2 -1 Approximate Pressure 10 /dtK (sec ) (Cm.Hg.) Doo „ d t . t ° o Number of Runs 10 1.67 2 5 1.98 5 2.5 5.0 1 These f igures appear to ind i ca te that the r a t e o f r e a c t i o n increases as the pressure decreases. A part of t h i s e f f ec t may be caused by the change i n the p o s i t i o n of e q u i l i -brium as the gas pressure i s reduced, but t h i s would be i n s u f f i c i e n t to account for the marked increase i n ra te at 2.5 cm. Hg . 77 (v-) Effect of Temperature Reaction curves were obtained at various temperatures in o o the range of -20 to 98 C. The behaviour of the rate curve remains essentially the same throughout the temperature range investigated. Slight variations are most probably due to the variations in the effects of adsorption and mixing time at different temperatures. The curves obtained at -20°, 25°, 60° and 98° C. are shown in Figure(5). At lower temperatures adsorption increases so much as to dominate a l l other effects. Thus, in reaction curves obtained at -78° C. (Figure 6), the 2 value of 10 (D-DQ) actually decreases with time on account of adsorption of the gases. Curve (B)= of Figure (6) shows the exchange reaction obtained on introducing additional hydrogen chloride to the reaction system after the adsorption had reached equilibrium. It i s , however, difficult to decide whether the additional hydrogen chloride introduced exchanges with the surface of sodium bromide or with the adsorbed layer. It is most likely to be a combined effect. Initial rates, composed in the same way as for the previous results on pressure dependence, are shown in Table (2). They indicate that the reaction is essentially indepen-o o dent of temperature in the range 25 C. to 98 C , so that its activation energy may be taken as zero in this range. 2 4 6 8 10 12 time ( minutes ) Figure 5. Reaction Curves. A - -20°C; %(D-D Q) x 10 E - 25°C. C - 60°C. D' - 98°C; %(D-D Q) x 10 oo 10 15 20 Figure 6. O r i g i n a l B time ( minutes ) Reaction Curve (-78°C.) - A d d i t i o n a l subsequent r e a c t i o n TABLE 2 I n i t i a l rates at 5 cm. pressure and various temperatures. o 2 -1 Temperature ( C . ) 10 /dtK (sec ) Number of Runs Doc dt t=o - 2 0 1.28 1 + 25 1.67 5 + 60 1.61 2 + 98 1.69 1 A summary o f the i n i t i a l r eac t ion rates obtained under var ious condit ions o f temperature and pressure i s given i n Table (3 ) . 81 TABLE 3 I n i t i a l ra tes of H C l / N a B r exchange react ion* Run Temperature ° C . Approximate Pressure (Cm. Hg.) (dD) W t = o Doc a 25 10 0.125 ~ 7.5 b 25 5 0.120 5.5 c 25 5 0.080 -4 d 25 5 0.0732 6.9 e -20 5 0.255 -2.0 f 98 5 0.220 13 8 25 5 0.190 h 25 10 0.0332 2 i 60 5 0.0420 3.2 J 60 5 0.0436 — 2.3 k 25 5 0.103 -4.5 1 25 2.5 0.05 1 Runs b and c: C r y s t a l s t i gh t ly -packed (b) and normally packed ( c ) . Runs i and j : Successive exposures ( i n chronolog ica l order) of the same c r y s t a l s to two gas specimens. Run k: A t h i r d exposure o f the c r y s t a l s from i and j to another gas specimen at a d i f f e r e n t tempera-t u r e . 82 (v i ) E f f e c t o f X . the F r a c t i o n o f Sodium Bromide Surface  Covered by C h l o r i d e Ions, on the Reaction Curve In order to determine the e f f ec t o f X on the reac t ion curve , a specimen o f sodium bromide c r y s t a l s was exposed to o hydrogen c h l o r i d e gas at 60 C . The r e a c t i o n curve (A) obtained i s shown i n F igure (7 ) . The gas phase was pumped out for about an hour and a f resh specimen o f HCl was introduced i n the r e a c t i o n system conta in ing the same sodium bromide c r y s t a l s w i th the surface p a r t l y covered by C l ions i n t r o -duced i n the o r i g i n a l exchange r e a c t i o n . The r e a c t i o n curve (B) obtained on the second exposure to hydrogen c h l o r i d e gas i s shown i n F igure (7) . The form o f the curve i s p r a c t i c a l l y unchanged. Therefore the shape o f the curve cannot be explained on the bas i s o f the e f fec t o f X on the ra te of the r e a c t i o n . The r e a c t i o n i s d e f i n i t e l y repeatable . However, the extent o f the reac t ion i s less<x i n the second exposure because of the condit ions of the chemical e q u i l i b r i u m . Hence the suggestion of Dunning (102), that the exchange might involve i r r e v e r s i b l e des truct ion of growth steps i s not app l i cab le i n the present case . ( v i i ) Comparison wi th Resul ts o f Other Exchange Reactions  (a) A c t i v a t i o n Energy In t h e i r i n v e s t i g a t i o n o f the C J ^ N a C l ^ system Harr i son 84 et a l . (100) observed that the exchange reaction is remarkably rapid even at temperatures as low as -20° C. Their results show an apparent activation energy of -5.2 kcal/mole. The system H C l / N a C l studied by Harrison et aU (113) showed a small positive apparent activation energy (4.1 kcal/mole at 25° to 71° C , decreasing to 0.2 kcal/mole at -40° to -65° C ) . The difference in the behaviour is ascribed to easier physical adsorption of C l 2 . If the rate of the reaction is proportional to the concentration of chlorine molecules in a physically adsorbed layer, the activation energy E of the exchange process is given by E - Q-5.2 where Q is the heat of adsorption. Since Q is unlikely to be much greater than 5.2 kcal/mole, E must be negligibly small. The present results resemble the H C l / N a C ^ results in that they do not show negative activation energy due to physical adsorption. It has already been noted that a large part of the reaction is complete before an appreciable amount of adsorption has taken place. (b) Rates The period required for half-complete reaction, t^ for the systems C l 2 / N a C i and H C l / N a C l is of the order of 60 min. (100, 113), but for the system B r 2 / N a C l the value is less than a minute, the exchange of one layer being complete within 85 one or two minutes. An estimate o f t^ from the curve (Figure 3) f o r the i n i t i a l part o f the r e a c t i o n i n the present case o f H C l / N a B r > i s about 17 seconds, which shows that the exchange r e a c t i o n In t h i s system i s fas t compared wi th those o f C ^ / f l a d H C l / N a C i systems. The d i f ference i n the rates of the exchange reac t ion i n these systems may be ascr ibed to the ease o f formation of the t r a n s i t i o n complex. I t i s seen above that systems i n which a bromide ion i s a const i tuent o f e i t h e r o f the phases show much fas ter r e a c t i o n compared to those i n which only c h l o r i d e ions are invo lved . T h i s suggests that some c h a r a c t e r i s t i c of the bromide ion i s favourable f o r the formation of whatever t r a n s i t i o n complex i s invo lved i n the r e a c t i o n . The c h a r a c t e r i s t i c concerned may be e i t h e r the a v a i l a b i l i t y o f d - o r b i t a l s o f bromine or the l arge p o l a r i z a -b i l i t y o f the bromide i o n . I t has been shown by Laurent and Benard (114) that the m o b i l i t y o f h a l i d e ions i n d i s l o c a t i o n s i n the a l k a l i ha l ides can be c o r r e l a t e d wi th the p o l a r i z a -b i l i t y o f the i o n s . 86 SECTION IV CHEMICAL EQUILIBRIUM OF THE HCl/NaBr  EXCHANGE REACTION . Mass-spectra l ana lys i s was employed for the i n v e s t i g a t i o n of the chemical e q u i l i b r i u m o f the exchange r e a c t i o n . The method i s complicated by a "memory e f fec t" , a "pressure effect" and a "composition e f fec t" . From the pre l iminary work on the a n a l y t i c a l technique, i t was found that the d i f f i c u l t i e s can be removed and quant i ta t ive r e s u l t s obtained wi th c a r e f u l a t t en t ion to procedure e s p e c i a l l y as regards the order o f ana lys i s o f the samples w i th d i f f e r e n t hydrogen bromide content. 1. Mass-spectra l Ana lys i s The ana lys i s o f the gaseous mixture was c a r r i e d out i n 79 a l l cases by measuring the r a t i o of the height of the HBr 35 peak (ma88 80) to that of the HCl peak (mass 36) , here inaf ter r e f e r r e d to as "peak r a t i o " and represented by Peak 8 0 / p e a k 3 5 . In pre l iminary inves t igat ions i t was found that the peak r a t i o for any p a r t i c u l a r sample was s e r i o u s l y a f fec ted by the previous sample o f d i f f e r e n t peak r a t i o . D e t a i l e d study of t h i s "memory effect" l e d to a standard procedure f o r ana lys i s o f a ser ies of samples i n which the inaccuracy r e s u l t i n g from 87 this effect was completely eliminated, so that the calibration curve of HBr/HC^ ratio against Peak 80/p e a k 3 5 became a straight line passing through the origin (up to about 25 mole percent of HBr). The mole ratio of the gaseous mixture is represented by HBr/RC^ or the symbol r and henceforth referred to as "mole ratio". In addition a small pressure effect was observed and a very large change of relative sensitivity for HBr and HCl on using mixtures containing more than 25 mole per cent of HBr. The latter effect is of interest in its e l f , but of no prac-ti c a l importance for the present analyses, since i t occurs outside the range of HBr/gQ^ ratios found in the exchange experiments• (O Pressure Effect The analysis of a sample at different pressures yields different values of the peak ratio. The experimental values are given in Table (1). The increase in total pressure is 35 + indicated by the increasing (HCl ) peak (volts). 88 TABLE 1 The effect of total pressure on the reciprocal "peak ratio" of a standard mixture (5*4 mole % HBr). (HC1 3 5) + peak Peak 36 (volts) Peak 80 8.15 76.2 13.41 74.4 17.81 75.0 20.31 72.9 21.86 72.9 28.85 65.4 Similar variations (increasing reciprocal peak ratio) are observed with decreasing total pressure of the standard mixture shown graphically in Figure (1) and Table (2). The lack of reproducibility at 8 - 9 volts after a cycle of Increasing and decreasing pressure appeared to be caused by a change in composition of the gas in the storage bulb. This does not affect the normal analytical procedure, where the pressure was held constant. 84 Figure 1. Pressure effect on peak ratio. 90 TABLE 2 The effect of total pressure on the reciprocal "peak ratio" of standard mixture (5.4 mole % HBr). (HC1 3 5) + peak Peak 36 (volts) peak 80 28.0 64.8 25.45 76.8 20.2 76.9 15.2 82.7 12.5 86.5 9.45 86.0 Use of restricted range of pressures (7.5 - 9.5 volts) eliminates the complication arising from this effect. The pressure of the samples is adjusted with respect to the 35 + (HCl ) peak between these limits. ( i i ) Memory Effect Measurements on samples of pure HCl after the analysis of a sample containing HBr. A sample of pure HCl analysed after the sample containing some HBr shows the presence of HBr. On repeating the analysis with fresh portions of HCl, gradually decreasing amounts of HBr are indicated. The source of this contamination is the 91 HBr adsorbed on parts of the instrument. I t was found that the contamination r e s u l t s c h i e f l y from the gases adsorbed i n the i n l e t t r a i n and the large storage bulb o f the mass-spectrometer. The f l u s h i n g of these part s wi th samples of pure HCl decreases the peak r a t i o (Peak 8 0 / p e a k 35) of the sample. In one of the experiments the machine was saturated wi th pure HBr and then pumped out for a long t ime, and then repeatedly f lushed wi th a sample of pure H C l . The v a r i a t i o n s i n the peak r a t i o of each successive f lush ing specimen o f HCl are given i n Table (3) and shown g r a p h i c a l l y i n F igure (2) by curve ( A ) . 92 TABLE 3 Peak r a t i o s obtained on successive f lush ing o f the machine w i th pure H C l . Peak 80 X 1 Q 2 Specimen Time P . M . Peak 36 1 1.25 0.710 2 2.20 0.592 3 2.55 0.491 4 3.29 0.449 5 4.00 0.414 6 4.30 0.391 7 5.00 0.355 8 5.30 0.349 9 6.30 0.322 10 7.0 0.324 11 7.30 0.297 12 8.00 0.284 13 8.30 0.263 14 9.00 0.251 15 9.30 0.238 These r e s u l t s appear to i n d i c a t e a normal "washing-out" e f fec t corresponding to a constant p a r t i t i o n c o e f f i c i e n t for 0.8 94 HBr between the gas phase and some other phase, e . g . an adsorbed layer on the wa l l s o f the i n l e t t r a i n o f the mass-spectrometer or a s o l u t i o n of HBr i n the grease used i n the j o i n t s o f t h i s system. As would be expected for such a process the r a t i o o f HBr contents i n two successive "washings" i s approximately constant . I f "smoothed" values of HBr content are taken from curve ( A ) , F igure (2) , the r a t i o becomes constant from specimen number 5 onwards as shown i n Table (4), 95 TABLE 4 Rat io o f HBr content to that o f the succeeding specimen (smoothed values from Figure (2) ) . Specimens Rat io 4/5 1.083 5/6 1.064 6/7 1.057 7/8 1.060 8/9 1.059 9/10 1.053 10/11 1.053 11/12 1.053 12/13 1.061 13/14 1.048 14/15 1.050 The t o t a l amount o f HBr washed out i n the course o f these washings wi th HCl i s much greater than could be accounted for by a monolayer o f adsorbed HBr on the wal l s o f the apparatus. A l s o the phenomenon i s not r e v e r s i b l e i n the manner which would be expected for a simple p a r t i t i o n process . I f a specimen conta ining some HBr i s introduced to the system, very few washings are requ ired to b r i n g the HBr reading up to a steady value (see Table 5; curve B , F igure 2) and the amount o f HBr which can have red i s so lved or been readsorbed i n the apparatus i n the course o f these washings i s much smaller than that p r e v i o u s l y removed by pure H C l . TABLE 5 Peak r a t i o s obtained on successive f lush ing o f the mass-spectrometer w i th the f resh specimen of the sample conta in ing some HBr. Peak 80 x l Q 2 Specimen Time P . M . Peak 36 1 0.30 0.276 2 1.15 0.449 3 1.45 0.524 4 2.00 0.576 5 2.30 0.593 The sample was analysed a f t er f l u s h i n g the machine severa l times w i th HCl to b r i n g down the peak r a t i o to a smal l value of the order of 0.217. In a subsequent ana lys i s o f the same sample, the peak r a t i o was found to be about 0.593. T h i s value i s therefore takeni;to be the true peak r a t i o o f the sample. The samples were therefore analysed i n the order o f increas ing HBr content . A p o r t i o n o f the sample was used to 97 f l u s h the machine and pumped out a f t er ten minutes, . A fresh p o r t i o n was used for q u a n t i t a t i v e r e s u l t s , ( i i i ) E f f e c t of Composition Standard mixtures w i th HBr content above 25 mole percent show anomalous r e s u l t s . The s e n s i t i v i t y for HCl increases enormously. Table (6) and Figure (3) show the peak r a t i o s obtained w i th standard mixtures covering a wide range of compositions• TABLE 6 Peak r a t i o s o f the standard mixtures . Peak 80 Peak 36 0,0208 0,00487 0.0554 0.0127 0.0708 0.0192 0.123 0.0301 0.248 0.0623 0.961 0.215 2.83 0.446 5.44 0.625 16.66 0.755 Thi s e f fec t was not inves t igated i n s u f f i c i e n t d e t a i l to determine whether i t occurs i n the i n l e t t r a i n of the mass 2 4 6 8 10 12 14 16 18 Mole Ratio Figure 3. Effect of composition on peak ratio. A - Normal scale divisions B - 10 x normal scale divisions 99 spectrometer or inside the instrument its e l f . Two possibilities may be put forward:-It is possible that a large proportion of each gas specimen dissolves in the inlet train, and the gas on which measurements are made represents a vapour phase in equilibrium with the adsorbed phase. The observed behaviour represents a solution obeying Henry* 8 Law over a limited range of concentra-tions only. Such an explanation does not f i t in very well, however, with the striking irreversibility of the memory effect, which suggests that solution and vapour phase are by no means in equilibrium. The alternative, which seems more probable, is that electron transfer from HCl to,HBr takes place to a significant extent, leading to a great increase in the ionization efficiency for HCl at high HBr content. This possibility would be worth more detailed study. The appearance of pressure-dependent peaks attributed to collision processes is quite common in organic systems (116), although nothing precisely analogous to this proposed simple electron transfer process giving a large shift in sensitivity seems to have been reported. 2. Procedure (i) Calibration with Standard HCl-HBr Mixtures The calibration of the mass-spectrometer was repeated three times over a period of eighteen months. No change in 100 the behaviour o f the machine was observed. The c a l i b r a t i o n was done i n accordance wi th the normal procedure set for the ana lys i s as regards the order and pressure of the standard mixtures , w i th mixtures i n the range 1.1% - 25% o f HBr by volume. The graph o f H B r / H C l v s . Peak 8 0 / p e a k 3 6 (Figure 4) i s a s t r a i g h t l i n e pass ing through the o r i g i n and wi th a slope o f 4 .00 . Conclusion - f o r a l l samples g i v i n g Peak 8 0 / p e a l c 3 5 -2 r a t i o above the previous memory e f fec t and l e s s than 6x10 , the H B r / H C l r a t i o i s found by, m u l t i p l y i n g the peak r a t i o by 4 .00. Above t h i s HBr content , the r e l a t i v e s e n s i t i v i t i e s of the mass-spectrometer for HBr. and HCl change r a p i d l y as shown i n F igure (3) . ( i i ) Procedure f o r Exchange Reaction Apparatus The r e a c t i o n v e s s e l K (Volume 224.4 m l . ) , was a par t of the vacuum system shown i n F igure 1, Sect ion I . P r o v i s i o n was made for c i r c u l a t i o n o f the gas*by convect ion. The main part o f the r e a c t i o n ves se l was kept at a d e f i n i t e tempera-t u r e . The furnace used f o r higher temperature cons is ted o f an o e l e c t r i c a l l y heated copper c y l i n d e r . Temperatures up to 100 C . + o could be success fu l ly c o n t r o l l e d w i t h i n . 2 C . over very long periods (about a month). A known quant i ty o f the dry powder (about 30 grams) was dropped in to the reac t ion ves se l K and the system was 101 Figure 4 . Calibration Curve 102 evacuated immediately for at l e a s t ten hours (usual ly for considerably longer p e r i o d s ) , Gare was taken to open the stopcock slowly to avoid the blowing over of the c r y s t a l s . T h i s was to a large extent checked by the glass-wool p lug provided at M (Figure 1; Sect ion I ) , The system was eva-cuated down to 10 mm, pressure . The convection heater was switched on , and hydrogen c h l o r i d e was introduced in to the r e a c t i o n system, u s u a l l y to about 5 cm, Hg, pressure . The sample bulbs were evacuated, t h e i r surface being cleaned from adsorbed gases by T e s l a c o i l d i scharge . The reac t ion was allowed to proceed for 30,0 minutes and the e n t i r e gas phase was condensed i n sample bulbs at l i q u i d n i trogen temperature. The system was eva-cuated for h a l f an hour, the vacuum being tes ted wi th T e s l a c o i l d i scharge . Ten samples were obtained i n t h i s way, us ing f resh specimens o f HCl and the same ^crystals , and a l l the samples were analysed mass-spectrometr ica l ly . Summary o f A n a l y t i c a l Procedure (1) Pure HCl was allowed to run through the machine repeatedly and the peak r a t i o was observed each t ime, u n t i l i t reached a -2 very small value (usual ly of the order o f 0,2$10 ) . (2) The samples were analysed i n the order of increas ing HBr content• 103 (3) The machine was flushed once with the sample for ten minutes before quantitative measurements were done. (4) The pressure of the samples was adjusted by fixing the HCl peak within 7.5 - 9.5 volts. (5) H^/flcl r a t l ° w a s obtained from the calibration curve. 3. Results A number of experiments were performed to determine the equilibrium constant of the exchange reaction. In each experi-ment several samples of HCl gas, always at the same pressure of 5 cm. and occupying a volume of about 214 ml., were exposed successively to the same sample of NaBr (about 30 grams, total 2 surface area about 18 m ). In most of the experiments, the time of contact of each gas sample with the solid was 30 minutes. In two of the earlier experiments, the fi r s t few gas samples were left in contact with the solid for only one or two minutes; from these data, some rough figures on the kinetics of the reaction were .obtained for comparison with the results of the detailed studies described in the preceding section. Analysis of the Results : The decrease in the HBr content of successive gas samples suggests that an equilibrium equation of the form (l.IV) HBr X o HCl 1-X (l.IV) 104 may be obeyed, where HBr i s the mole ratio obtained on multi-HC1 plying the peak ratio by 4.0, and hereinafter represented by r . X i s the fraction of the sodium bromide surface covered by chloride ions, and therefore, (1-X) represents the fraction of the surface covered by bromide ions. Provided that there i s a reasonable range of X for which K i s constant, the total exchangeable surface and hence the value of X and (1-X) may be found as follows:-Writing n C • ]> r , 1 for a l l gas specimens of a series up to and including the one with which we are concerned, and the total exchangeable material oc C = > r m 1 for an i n f i n i t e number of gas specimens, then with subscript e to indicate the equilibrium conditions ( r e , 6 e), the e q u i l i -brium equation (l.IV) becomes: r e °e " K (l.IV.a) c f f i - c e or 1 — + J L (l.IV.b) r C r C KC e e em m This type of equilibrium expression implies that Cl and Br occupy random positions on the partly exchanged surface, as 105 a two-dimensional s o l i d s o l u t i o n . I f they were separated out as two 2-dimensional phases, X and (1-X) would not appear i n the e q u i l i b r i u m expression ( l . I V ) , and successive gas samples would show constant HBr content u n t i l the exchange of surface was complete. A p l o t o f I I v s . should be l i n e a r g i v i n g C M as the **e^ e ^e r e c i p r o c a l o f i t s s lope . When CJQ has been found i n t h i s way (which i s c l o s e l y analogous to the method o f f i n d i n g the monolayer capaci ty for an adsorption process which obeys the Langmuir i sotherm), K can i n p r i n c i p l e be found from S l o p e / ^ n t ; e r c e p t o f the same graph; hut s ince i t i s d i f f i c u l t to estimate the in tercept accura te ly , and s ince t h i s method does not al low for any v a r i a t i o n of K , i . e . the c a l c u l a t i o n o f K for any po ints which do not l i e on the l i n e , i t i s be t ter to use the value of C M i n equation ( l . I V . a ) to evaluate K for a l l po ints i n d i v i d u a l l y . The assumption that K i s independent of X i s not c o r r e c t . K i s a funct ion of X , and passes through a ra ther f l a t maximum at X ^ 0 . 6 ; the p l o t o f equation ( l . I V . b ) therefore has a l i n e a r p o r t i o n frOm which C can be estimated and K thereafter c a i -rn cu lated from points for a l l values o f X . Resul ts T y p i c a l r e s u l t s o f mass-spectral ana lys i s o f the gas specimens obtained i n two experiments, namely Run 5A ( 2 1 ° C.) 106 and Run 6A ( 7 0 ° C . ) are given i n Table (7) TABLE 7 2 Values o f the peak r a t i o , and 10 r p . Run 5A ( 2 1 ° C . ) Run 6A ( 7 0 ° C . ) 10 2Peak 80 0 !Q 2 Peak 80 Specimen Peak 36 10 r e Peak 36 10 r e 1 1.141 4.564 1.321 5.284 2 0.767 3.068 0.914 3.656 3 0.563 2.252 0.715 2.860 4 0.465 1.860 0.572 2.288 5 0.414 1.656 0.429 1.716 6 0.327 1.308 0.359 1.436 7 0.247 0.988 0.318 1.272 8 0.188 0.752 0.270 1.080 9 0.182 0.728 0.212 0.848 10 0.174 0.696 0.171 0.684 -2 -2 Values o f 10 / r A and 10 / r C c a l c u l a t e d from these data are e e e plettesa i n Figure (5) and given i n Table (8) . 107 0.5 0.9 1.3 10" 2/r e Figure 5. Run 6A 108 TABLE 8 -2 -2 Values o f 10 / r e and 10 / r C obtained i n two experiments at d i f f e r e n t temperature. Run 5A ( 2 1 ° G . ) Run 6A ( 7 0 ° C . ) scimen 1 0 " 2 / r e 1 0 " 2 / r e C e 1 0 " 2 / r e 1 0 ' 2 / r e ( 1 0.219 4.80 0.189 3.58 2 0.326 4.27 0.274 3.07 3 0.445 4.50 0.350 2.96 4 0.538 4.58 0.437 3.10 5 0.605 4.51 0.584 3.69 6 0.765 5.20 0.696 4.04 7 1.012 6.45 0.785 4.24 8 1.330 8.10 0.925 4.72 9 1.372 8.00 1.178 5.75 10 1.433 8.05 1.485 7.05 Values o f K and X^ c a l c u l a t e d for the two experiments mentioned above are tabulated below and shown g r a p h i c a l l y i n F igure (6 ) . The curves of Figure (6) represent a t h e o r e t i c a l f i t according to the funct ion f(X) discussed below and also shown i n Figure (10). 109 O < 3 00 o e/ e; I e • \ e e \ e e / o o o o o o o O o * o o CM O CM CM O CM 00 vO CM a _ 0 T c 110 TABLE 9 Values of K and X e for Run 5A and Run 6A. Run 5A (21°C.) Run 6A (70°C.) >cimen 102K xe 10 R x e 1 1.01 0.181 1.22 0.181 2 1.33 0.302 1.61 0.306 3 1.45 0.391 1.94 0.405 4 1.62 0.466 2.14 0.483 5 1.83 0.532 2.02 0.541 6 1.83 0.584 2.07 0.590 7 1.63 0.624 2.20 0.635 8 1.40 0.653 2.20 0.671 9 1.56 0.681 1.98 0.700 10 1.70 0.709 1.76 0.724 The plot of 10 K vs. X e passes through a max inn mi in each case at X e of the order of 0.6. The mean value of R obtained from the values of Run 5A -2 is 1.65x10 , (X e - 0.466 - 0.709) and from the values of -2 Run 6A is 2.13x10 , (X e - 0.483 - 0.671). The values of C m for Run 5A and 6A, obtained graphically, are 0.252 and 0.292 oc respectively. Since (L^ - ]> r, where r - HBr/ H C l, these values I l l of are proportional to the total exchangeable surface in each case. Assuming the observed interionic distance (2.98 X) in sodium bromide crystals as the interionic distance in sodium bromide surface, the surface area may be calculated from the value of as follows:-Each Br" in the surface may be taken to represent a square on the surface, having the nearest neighbour sodium ions at the four corners. The total surface is therefore given by N B r" x area of the square - Nggj. x 17.76 X 2 where Nfir- is the total number of Br in the original exchange-able sodium bromide surface, and % g r represents the corres-ponding number of HBr molecules in the gas phase which would be obtained on exchanging the entire surface bromide ions by chloride ions. Hence -NHBr * 8 proportional to C^. On transforming the value of into number of moles and hence into number of molecules we obtain nmx - 0.885 x 10 2 0 2 Therefore the surface area (in m ) is given by 20 -20 2 0.885x10 xl7.76x10 - 15.72m 112 Thi s estimate of surface area i s i n good agreement w i th the surface area determined by the a p p l i c a t i o n of B . E . T . equation 2 g i v i n g a value o f the order of 18 m ( s p e c i f i c surface of the 2 order o f 0.6 m ; the weight of the Sodium bromide c r y s t a l s about 30 grams). The above agreement between the two values o f the surface area and the general c h a r a c t e r i s t i c s o f the r e a c t i o n suggest very s trongly that i n the present exchange reac t ion i t i s only the outer surface that i s involved i n the r e a c t i o n . A f t e r some of the C l " had d i f fused away from the surface the sodium bromide c r y s t a l s o f Run 6A were used i n Run 6E o (described i n d e t a i l i n Sect ion V) at 95 C , i n order to determine the e f fect o f temperature on the exchange r e a c t i o n , and to examine the p o s s i b i l i t y of the growth steps being involved i n the exchange r e a c t i o n as suggested by Dunning 2 (102)• Values o f 10 xPeak 80 obtained i n Run 6A and 6E are Peak 36 2 tabulated below (Table 10) and corresponding values of 10 r are shown g r a p h i c a l l y i n F igure (7 ) . 113 TABLE 10 2 Experimental values of 10 x Peak 80. Peak 36 Run 6E (95°C.) Run 6A (70°C.) 2 2 10 Peak 80 10 Peak 80 Specimen Peak 36 Specimen Peak 36 X 1 0.550 4 0.572 0.483 2 0.440 5 0.429 0.541 3 0.360 6 0.359 0.590 4 0.305 7 0.318 0.635 5 0.280 8 0.270 0.671 6 0.224 9 0.212 0.700 The surface of the crystals used in Run 6E had previously undergone several sequences of exchange reaction, followed by diffusion of chloride ions, and was already partly covered by chloride ions in runs 6A, B, C and D (see Section V). The 2 values of 10 xPeak 80 obtained in Run 6E were found to Peak 36 correspond very closely with the values of Run 6A from speci-men number 4 onwards. Since the peak ratio of specimen number 1 in Run 6E corresponds closely with that of specimen number 4 in Run 6A, i t is concluded that the surfaces in these corresponding stages of the two Runs 6A and 6E have comparable surface coverage by chloride ions. F i g u r e 7. Run 5A - 1; bA - 2; 6E - 3. 115 This explains the correspondence in the values of succeeding specimens* Whence i t is concluded that the -2 equilibrium constant K (K - 2*13x10 ) calculated from the two sets of values is independent of temperature (Run 6A, 70° C. and Run 6E, 95° C*) i.e. dlnK - AH - 0 . dT RT The above result also establishes the fact that no irreversible change in the structure of the surface takes place in the exchange reaction. Hence the possibility suggested by Dunning (102) that the growth steps might be involved in the exchange reaction is not applicable in the present case. Since the mechanism involving growth steps requires that the exchange reaction be unrepeatable on account of the destruction of most of the length of the growth steps. Values of the equilibrium constant obtained from a number of Runs under various conditions of temperature and surface composition are summarised in Table (11). 116 TABLE 11 2 Values of 10 K obtained in a number of Runs and tabulated against the corresponding value of X,. x e Run 1A (R.T.) Run 3A (R.T.) Run 4A (R.T.) Run 5A (R.T.) Run & (70°C. 0.05 0.10 0.30 0.43 . . . . . . . . 0.15 0.36 0.58 0.20 0.37 0.65 1.01 1.82 0.25 0.35 0.68 0.30 0,36 0.76 1.33 1.61 0.35 0.42 0.70 mm « mm mm 0.40 1.07 0.47 0.65 1.45 1.94 0.45 1.07 0.52 0.66 1.62 0.50 1.07 0.75 2.14 0.55 1.07 ^ mm mm wm 1.83 2.02 0.60 1.37 . . . . 1.83 2.07 0.65 1.51 1.63-1.40 2.20 0.70 1.66 1.56-1.70 2.20 0.75 1.94 1.76 0.80 ~ . . . . . . . . • V M M . . . . The value of K was not very reproducible from one batch of salt to another, the maximum variation in K being roughly a 117 -3 factor of 3 at any X. At X B 0, K varied from 2 to 6x10 , the latter value being the most reliable• Reactions at different temperatures on the same batch (Runs 6A and 6E) indicate that K is independent of temperature, i.e. AH " 0 for the exchange reaction. The maximum possible value of AH may be calculated from the change in K between Run 5A (21°C.) and Run 6A (70°C.) as i & f e . i l A - l ) Kj R T5 V Where K5, T^ and Kg, Tg are equilibrium constant and tempera-ture of Run 5A and Run 6A respectively. The numerical value of A Emax is +819 cal/mole. 4. Discussion The most significant feature of this investigation is the possibility of obtaining some thermodynamic properties for a process Involving changes in a solid surface at room temperature. Data of this kind are conspicuously lacking in the literature, largely because the calorimetric determination of the thermodynamic properties of surface is very difficult. The difficulties are greatest for entropy measurements, which require low temperature heat capacity data. The present study does not lead to the calculation of the surface energy or entropy of NaBr, but gives the changes in 118 these quantities when a Br ion i s replaced by Cl ion i n the surface layer. This appears to be the f i r s t case in which such changes have been measured for a process involving atoms in the solid surface i t s e l f , rather than an adsorbed layer. The results are therefore important as an i l l u s t r a t i o n of how such quantities may be obtained from essentially simple experiments at room temperature. It has been shown above that the equilibrium constant K i s independent of T at a l l X for the temperature range 20° - 95° C. Hence AH - 0 at a l l X for the overall reaction, and the reaction can be discussed mainly in terms of entropy changes. Hence, after a brief discussion of AH, this account w i l l be concerned chiefly with the values of AS as a function of X, and how one may attempt to resolve the overall value of AS into: (a) a mass effect for the exchanged ion; (b) other effects for the same ion;, and (c) effects of a l l the anions on their neighbours in the surface. (i) Enthalpy Change The overall reaction i s represented as HCl(g)+Br"(NaBr surface) ^ ± HBr(g)+Cl"(NaBr surface)• I t may be represented by a series of reaction steps as follows-119 AH(Kcal /mole) HCl(g) —> H(g)+Cl(g) +102.7 Cl(g)+e~ Cl"(g) - 87.3 Cl~(g)+Br"(surface) —> Br"(g)+Cl"(surface) Y Br"(g) —> Br(g)+e" +82.0 B*(g)+H(g) - > HBr(g) - 87.3 HCl(g)+Br"(surface) — * HBr(g)+Cl"(surface) 10.1+Y K i s independent o f T (20° - 9 5 ° C ) . Therefore A H - 0 or 10.1+Y - 0 or Y » -10.1 Kca l /mole . Therefore for the reac t ion s tep , c l ' ( g a s ) + B r (NaBr surface) — » B r ( g a s ) 4 ^ 1 (NaBr surface) A H ^ B -10.1 Kfcal/mole, where subscr ipt 1 ind icates A H for the s i n g l e s tep. The maximum value of A H for the o v e r a l l r eac t ion c a l -cu lated from Run 5A and Run 6A i s +8,19 ca l /mole . The e f fec t of t h i s value on A H^ can r e a d i l y be evaluated by equating 10.1+Y to 0.819 Rfcal/mole. 10.1+Y =0.819 120 Hence Y = -9.281.Kcal/mole or A H ^ » -9.281 Kcal/mole. The value of AHj_ between these two Halting values, namely -10.1 and -9.281, may be written as A nt « -9.691^0.409. kcal/mole. ( i i ) Entropy Change Since AH 8 0, we may write the condition for equilibrium in terms of entropy only as dS „ Q dX * where S = NHBr< SSBr" R l n pHBr> + W S H V R 1 , 1 PH C 1 > + *Cl- SC1" + N B r " SBr" + Sconfiguration- <2-IV> In this expression, N i s the number of moles of each species present, the subscripts Cl and Br refer to ions in the surface layer, and S c o ^ £ i g u r a t i o n » hereinafter repre-sented by S c, refers to the surface layer. Pmjr a n d P H C I refer to the corresponding pressure of the gases. The configuration of Cl and Br ions on the partly exchanged surface can be either as two separate two-dimensional phases of Cl and Br or a single two-dimensional phase of •» mm the randomly mixed Cl and Br ions. In the former case S c = 0 and the equilibrium expression reduces to the form 121 K - PHB r/P H C l» This i s evidently not the type of behaviour occurring in the system. In the case of a random mixture of Cl and Br ions we may write S R, - k l n ( N C l " + N B r " ) l + S± (X) N G l - i N B r"» where the term takes into account the fact that the vibrational entropy of any ion in the l a t t i c e may depend on whether i t s nearest anion neighbours are Cl or Br . The nature of this term i s discussed in detail below. SRt i s equal to the sum of S c and S^. Using Stirling's approximation and writing X • "cl-'O'cl- + NBr"> and (1-X) -N ? r-/(H c l. + H B r-). we have S R, - -N c l- klnX-N B r- kln(l-X) + S t(X). On substituting in equation (2.IV) and applying the condition for equilibrium, R l n ( ~ ^ 1 ! x ) - ( SHBr^ SHC1) + ( SC1" " SBr-) + d__S.(X) (3.IV) The standard states of Cl and Br to which the values of o S refer are best defined in the same manner as for the constituents of a solution, with Cl as solute (activity = concentration at X 8 8 0) and Br as solvent (activity = 1 at 122 X = 0). It w i l l be convenient, however, to keep separate terms throughout for the entropy of the exchanged chloride ion itself, and for the change in entropy which each chloride ion induces in the surrounding.ions. It wi l l be considered throughout this discussion that this latter effect extends to f i r s t and second nearest neighbours only. Thus d__S • (X) dX w i l l not vanish at X B 0, but: will have a value representing the effect of an exchanged chloride ion on its four Na nearest neighbours and four Br second nearest neighbours. ( i i i ) The Entropy Change at X 8 3 0 The entropy change on replacing one Br ion by a Cl" ion in a pure NaBr surface may now be calculated i f K is known at X » 0. This value may be obtained roughly by extrapolation of the curves of Figure (6) to X ° 0. In the detailed dis-cussion of below, i t is shown that these curves can be converted to straight lines (Figure 10), from which a somewhat better extrapolation can be made. The best value from this method is Kx=0 " 6 x l 0 " 3 • Then sSi- + iJSLOO - S° r- - RlnK - <S^ r-S° c ]) dX - Rln(6xl(f 3) - (47.44-44.62) • -13.0 cial/mol.deg. 123 The ra ther large decrease i n entropy (13 e .u . ) po ints to a large excess entropy o f the bromide ion i n the surface . The object o f the remainder of t h i s d i scuss ion i s to attempt to d i v i d e up the observed entropy decrease i n t o the separate contr ibut ions of var ious e f f e c t s , and to assess what the r e s u l t i n g f igures mean i n r e l a t i o n to surface s t r u c t u r e , ( iv ) Suggested Subdiv i s ion Of the Entropy Change (a) Mass E f f e c t The d i f ference i n the masses of c h l o r i d e ion and bromide ion can have an e f fec t on the v i b r a t i o n a l entropy. Maximum Mass E f f e c t , At temperature T (T/6 E ^>1, where 0 £ i s the E i n s t e i n c h a r a c t e r i s t i c Temperature) the v i b r a t i o n a l entropy per degree of freedom, S v ^ r a t ^ o n a ^ , here inaf ter represented by S y » i s given by the fo l lowing expression: S v - R ( l + l n T / 6 E ) . Therefore , for three degrees o f freedom S - 3R(l+lnT/e). v E Thus for two assemblies of v i b r a t i o n s of d i f f e r e n t G £ at the same temperature we have (SyVtVl " 3 R l n ( 0 E ) l » 124 and i f the v i b r a t i o n s concerned are of two ions of d i f f e r e n t masses, then assuming that the force constant o f the v i b r a -t ions i s the same for both ions and the d i f ference i n 0 £ i s s o l e l y caused by the d i f f erence i n mass where M . and M r e f e r to the masses of the two i o n s . Thus the maximum numerical value of the mass e f fec t for the r e p l a c e -ment of Br ion by C l ion i s % As - 3 R l n f C l x - -2 .4 cal /mole deg. K In comparison, the d i f ference i n entropy between an a l k a l i (or s i l v e r ) bromide and the corresponding c h l o r i d e i s u s u a l l y about -2.8 cal /mole deg. K . (see Table 12) . 125 TABLE 12 Standard Entropies of A l k a l i and Silver Halides (cal/mole deg.K) A S v Br Cl (Br - Cl) Na 20.1 17.3 -2.8 K 22.6 19.8 -2.8 Ag 25.6 23.0 -2.6 Hence the mass effect may be given as -2 .4 cal/mole deg.K. In this connection, i t i s interesting to compare the present results with those of Wlodarski and Arczynski (103) for the reaction Nad/-,. . .-y+HBr. ^ NaBr,-. . ..+HC1, v (liquid) (gas) (liquid) (gas) where the l i q u i d phase i s a solution of the two halides (NaCl and NaBr). At temperatures of the order of 900° C. these results give the entropy change for the exchange reaction as only about -2.89 e.u. decrease. Almost the entire decrease can be attributed to the mass-effect (which has the same numerical value for both vibrational and translational motions, so that the precise structure of the liquid phase i s not important for an order-of-magnitude estimate). 126 (b) Effect of Ionic Size and Related Properties If one f i r s t supposes that the equilibrium positions for ions in the surface represent an undistorted continuation of the bulk lattice, then i t would appear that the replacement of a bromide ion by a chloride ion should lead to an increase in entropy (apart from the mass effect). The overlap repul-sions between the exchanged ion and its neighbours would be diminished, so that the force constant for vibration would decrease, and the vibrations would acquire lower frequencies and correspondingly higher entropies. The observed entropy change, which is in the opposite direction (and very large) must thus be regarded as evidence for some sort of distortion of the surface. This is very likely to be the Verwey type of distortion, in which the anions, on account of their size and polarizability, move outwards from the ideal positions, while the cations move inwards. It seems probable that the anions in such an arrange-ment would have low-frequency out-of-plane vibrations which could account for considerable excess entropy (especially for bromide and iodide ions)• When a.bromide ion is replaced by the smaller and less polarizable•chloride ion, the distortion of the surface may collapse locally to a considerable extent, leading to a large entropy decrease both for the exchanged ion itself and for its neighbours in the surface. In the 127 fo l lowing pages, a t en ta t ive attempt i s made to separate the changes i n the exchanged ion and i t s neighbours. (c) Poss ib l e Contr ibut ion o f Each Chlor ide Ion to Entropy  o f i t s Neighbours Each Na ion i n the surface has four anions , i n a square arrangement, as i t s nearest neighbours. S i m i l a r l y each anions ( C l " or Br") has a square arrangement o f four anions as i t s second nearest neighbours. An attempt i s made here to assess the e f fec ts of the nature of the ions ( C l or Br ) i n each such square on the entropy of the ion at the center of the square. I t i s assumed that the observed v a r i a t i o n of the e q u i l i b r i u m constant K wi th X i s to be explained e n t i r e l y i n terms of t h i s e f f e c t . . . Assuming a random d i s t r i b u t i o n of C l " and Br (which i s obviously only an approximation, s ince we are going to say that the entropy depends on the r e l a t i v e arrangements of an ions) , the p r o b a b i l i t i e s o f the four-anion s i t e s at the corners of a square being occupied by var ious pos s ib l e numbers of C l and Br" ions are as fo l lows . 128 Conf igurat ion P r o b a b i l i t i e s 4Br" P o - ( 1 - X ) 4 l C l " , 3Br" p x - 4X ( 1 - X ) 3 2C1~, 2Br" p* - 6 X 2 ( 1 - X ) 2 3 C l " , l B r " p = 4X 3 (1-X) 4C1 p 4 - X * p^ includes both geometrical arrangements. Le t the change i n the entropy per mole o f ions of the c e n t r a l ion i n the conf igurat ions with one, two, three and four neighbouring C l ions be denoted by S^, S^, and S A r e s p e c t i v e l y , wi th a superscr ipt i n d i c a t i n g the c e n t r a l i o n , **1 ' S l o r S l * T * i e n u m b e r ° f n^oles o f conf igurat ions wi th a given c e n t r a l ion per mole of surface i o n - p a i r s can be e a s i l y obtained from the values of the p r o b a b i l i t i e s by m u l t i p l y i n g the values of p by the appropriate surface + coverage, i . e . , X for C l , (1-X) for Br , and 1 for Na . Contr ibut ions to the d i f f e r e n t i a l entropy may be c a l -cu lated as f o l l o w s : -129 C e n t r a l Ion Contr ibut ion to D i f f e r e n t i a l Entropy m Br : ..dCl - X ^ + s i m i l a r terms i n p 2 , p^, p^. dX C l c l : s i dXP^ + s i m i l a r terms i n p^, p^, p^. dX Br C l Br T o t a l anions: S" __djp +(S -S , )_dXP- + s i m i l a r terms i n 1 dX 1 1 dX 1 P 2 , p 3 and p^. N a 1 Si dp + s i m i l a r terms In p , p and p , . 1 dX 1 Z J * C l Br Assuming the d i f ference (S^ rS^ ) to be n e g l i g i b l y s m a l l , C l ft i . e . S^ i s o f the order of S^ , the t o t a l d i f f e r e n t i a l entropy i s given by Br Na T o t a l : (s£ +S^ ) dp^ + s i m i l a r terms i n p 2 > p 3 » and p^. - dX where S^, S 2 , S^ and are changes i n entropy per mole of ion p a i r s i n the respect ive conf igurat ions . To evaluate d S . , an assumption i s made that dX 1 S, - a S l f 2 53 ™ & 1 a 54 " *V where a i s a constant which i s assumed to have the same value 130 for anions and cations, so that the expression can be written for ion pairs 2 3 __dS, - _dS (Pl+ap2+a p3+a p A). dX 1 dX 1 a is evaluated from the experimental observation that K, the equilibrium constant, passes .through a maximum at X • 0.6. 2 In order to maximise dS. at X ° 0.6, we write _<LS. = 0, dX dX2 1 and evaluate i t for X ° 0.6 as follows J . _d? P l - - 2 + 6X - 4X2 = 0.16 12 dX _JL i d 12 dX J . _ d 12 dX J d 2 P 2 1 - 6X + 6X2 - -0.44 _l- ^ 2 p 3 " + 2X - 4X2 - -0.24 JL _d?pA - • X 2 0.36 12 dX* * Therefore _d?S, - S- (0.16-0.44a-0.24a2+0.36a3) Since S^  f 0 2 3 0.16-0.44a-0.24a +0.36a - 0. The required solution is a - 4/3. 131 i s c a l c u l a t e d as fo l l ows : -Le t f(X) = _1 _dS. Sx dX 1 2 3 8 3 _d(Pi+ap2 + a P3 + a P4) dX - 4-8X+28X 2-80X 3 3 27 The values o f f(X) for d i f f e r e n t values of X are given i n Table (13), and a p l o t of f(X) against X i s shown g r a p h i c a l l y i n F igure (9 ) . TABLE 13 Values o f f(X) c a l c u l a t e d for d i f f e r e n t values o f X . X f(X) 0.0 4.00 0.1 3.290 0.2 2.750 0.3 2.360 0.4 2.103 0.5 1.963 0.6 o 1.920 0.7 1.957 0.8 2.055 0.9 2.198 1.0 2.370 Now r e f e r r i n g to the equation ( 3 . I V ) , we have RlnK = dS + ( S ° , - - S ° -+2.82) dX i 0 1 B r or s u b s t i t u t i n g we get InK - 1 _dS + 1 ( S ° - - S ° -+2.82) R dX R C 1 B r S x f (X) for _dS -dX 1 133 134 InK - S 1 f ( X ) + l ( S ° « - S ° „ + 2 . 8 2 ) . (4.IV) — TJ CX Br R R i s then ca l cu la ted from the slope of the p l o t of InK 2 against f ( X ) . Values of In(10 K) and f ( X ) , f or Run 5A and 6A are given i n Table (14) and (15) r e s p e c t i v e l y and the 2 p l o t s o f ln(10 K) against f(X) are shown i n Figure (10) for the two cases. TABLE 14 Values of ln(10 2 K) and f(X) for Run 5A. 10 2 K X ln(10 2 K) f(X) 1.01 0.181 0.010 2.815 1.33 0.302 0.286 2.355 1.-45 0.391 0.372 2.125 1.62 0.466 0.484 2.011 1.83 0.532 0.605 1.937 1.83 0.584 0.605 1.920 1.63 0.624 0.489 1.921 1.40 0.653 0.338 1.929 1.56 0.681 0.445 1.941 1.70 0.709 0.531 1.951 Slope = -0.66 Therefore S, - -0.66R -1.31 e .u per mole of ion p a i r s . 136 TABLE 15 Values of ln(10 2K);and f(X) for Run 6A. 102K X ln(10 2K) f(X) 1,22 0.181 0.199 2.815 1.61 0.306 0.476 2.350 1.94 0.405 0.664 2.109 2.14 0.483 0.760 1.982 2.02 0.541 0.704 1.930 2.07 0.590 0.728 1.920 2.20 0.635 0.788 1.925 2.20 0.671 0.788 1.936 1.98 0.700 0.684 1.956 1.76 0.724 0.566 1.970 Slope •= -0.66 Therefore S L - r0.66R = -1.31 e.u. per mole of ion p a i r s . R e c a l l i n g that £ ± ' S l ^ P l + a P 2 + a 2 p 3 + a 3 p 4 ) " S, (4-8X+28X2-80X3) 1 ~3- 27 137 138 with a - 4/3 (__dS.) = -5.2 cal /mole deg. dX x=o Values o f dS for d i f f e r e n t values of X are given i n dX 1 Table (16) and p l o t t e d against X i n Figure (11). 139 TABLE 16 Values o f dS. ( i n cal /mole deg.) for d i f f e r e n t values o f dX -X obtained i n Runs 5A and 6A. Run 5A Run 6A X dX 1 2 10 K X dX 10 2 K 0.181 -3.688 1.01 0.181 -3.688 1.22 0.302 -3.085 1.33 0.306 -3.078 1.61 0.391 -2.783 1.45 0.405 -2.76 1.94 0.466 -2.634 1.62 0.483 -2.596 2.14 0.532 -2.537 1.83 0.541 -2.528 2.02 0.584 -2.515 1.83 0.590 2.515 2.07 0.624 -2.516 1.63 0.635 -2.522 2.20 0.653 -2.526 1.40 0.671 -2.536 2.20 0.681 -2.543 1.56 0.700 -2,562 1.98 0.709 -2.556 1.70 0.724 -2.581 1.76 I t w i l l be noted that the experimental values o f K decrease more r a p i d l y for X greater than 0.6 than can be accounted f o r by the funct ion f ( X ) . This ind icates that the region beyond the maximum provides a s ens i t i ve tes t of any funct ion used to represent the v a r i a t i o n of K wi th X . Unfortunate ly , i n the present work i t i s a l so a region of 140 rather large experimental e r r o r . The value o f K i s ca l cu la ted from K - r C / ( C - C ) and at large X , and hence large C the 6 6 i l l 6 £ measured value of K i s very s ens i t i ve to the value used for C m * The l a t t e r was estimated from the slope of a l i n e (see Figure 5) and i n most experiments i t would have been p o s s i b l e to draw the l i n e i n such a way that the values of K for X greater than 0.6 would a l l have been increased cons iderably . The quant i ta t ive form of the curve for X greater than 0.6 therefore cannot be regarded as having been es tab l i shed very d e f i n i t e l y i n the present case. (d) Check of the Se l f -cons i s tency o f the Assumptions  i n Sect ion ( c ) . The above c a l c u l a t i o n s were based on the assumption that the C l and Br ions i n the surface l ayer are randomly mixed at a l l values of X . The c a l c u l a t i o n s have ind ica ted that each C l acts so as to decrease considerably the entropy of i t s neighbours. This decrease would obviously be minimized mm i f the C l ions c lus tered together, i . e . i f a two-dimensional phase separation took p l a c e . I t i s therefore necessary to examine the numerical r e s u l t s o f the above c a l c u l a t i o n s to ensure that they are s e l f - c o n s i s t e n t , i . e . that the conf lgura-t i o n a l entropy of the random mixture i s at a l l X great enough to overcome t h i s tendency towards phase separat ion . What w i l l be done i s to c a l c u l a t e the t o t a l entropy per mole of surface for the random conf igurat ion (S_) and the K. "separated" conf igurat ion (S_) and show that the d i f ference between them i s p o s i t i v e at a l l X . We have: -s R = xs° l C + (i-x)s°r. + S ; a + + s c o n f l g + [ s i ( x ) ] o s s - x s ° r + <i-x)s°r- + s ° a + + x [stm)l X 1 R S conf ig L f ' J o L i N / J o - -R { XlnX + (1-X) In (1-X)} 2 3 +S 1 (P 1 +aP 2 +a p 3 +a p 4 ) 143 TABLE 17 Entropies of Random and Separated Conf igurat ions . A l l entropies -1 -1 given i n c a l mole degK • X Sconfig 3 S 1 ( P 1 + . . . + a p 4 ) 3 - a SjX V 8 ! 0 0 0 0 0 0.1 0.646 -0.476 0.31 +0.480 0.2 0.989 -0.866 0.62 +0.743 0.3 1.219 -1.200 0.93 +0.949 0.4 1.340 -1.492 1.24 +1.088 0.5 1.372 -1.760 1.55 +1.162 0.6 1.340 -2.010 1.86 +1.190 0.7 1.219 -2.260 2.17 +1.129 0.8 0.989 -2.520 2.48 +0.949 0.9 0.646 -2.800 2.79 +0.636 1.0 0 -3.100 3.10 0 The tendency of the system to separate out in to C l and Br" "phases" i s represented by the smaller numerical 3 3 values of - a S^X r e l a t i v e to those of S^(Pj+. • .+a. ,p 4 ) . The d i f ference i s , however, small i n comparison wi th S c o n £ ^ g , and the l a s t column shows, as r e q u i r e d , that the random conf igurat ion has the higher entropy at a l l X . This j u s t i f i e s the c a l c u l a t i o n s of sec t ion ( c ) . 144 SECTION V DIFFUSION OF CHLORIDE ION INTO SODIUM BROMIDE CRYSTALS I t has been w e l l es tabl i shed by t h e o r e t i c a l and e x p e r i -mental arguments that Schottky defects are responsible for i o n i c m o b i l i t y i n a l k a l i h a l i d e c r y s t a l s . The migrat ion of these vacancies , as neighbouring ions jump in to them, provides a mechanism for i o n i c s e l f - d i f f u s i o n and, i n the presence of an e l e c t r i c f i e l d , for e l e c t r o l y t i c conduction (86). Increas ing emphasis i s being given to the measurement of d i f f u s i o n c o e f f i c i e n t s wi th .the use o f r a d i o a c t i v e t racers (89, 85) . The most extensive work of t h i s k i n d on the a l k a l i ha l ides has been done by Laurent et a l . (89, 90, 96, 114). Schamp and Katz (85) have c a r r i e d out t r a c e r measurements o f the d i f f u s i o n of bromide ion i n sodium bromide i n the temperature range 3 6 0 - 6 8 8 ° C . and the i o n i c conduct iv i ty i n the range 3 4 0 - 6 0 0 ° C . Morrison et a l . (45) have extended the range of measure-o . ment of C l " ion d i f f u s i o n c o e f f i c i e n t s i n NaCl and K C l down o low temperatures (300 C. ) us ing an exchange technique. A new experimental technique was employed i n the present 145 work. The underly ing p r i n c i p l e i s as fol lows: the Br ions of sodium bromide surface are exchanged with C l ions i n a ser ies o f exposures of the c r y s t a l s to the gaseous hydrogen c h l o r i d e . The reac t ion v e s s e l i s evacuated for a long p e r i o d , during which the anions on the surface d i f fuse away from the exchanged reg ions . The amount., o f Br which w i l l re-exchange i s determined at the end of t h i s p e r i o d . In t h i s way the p r i n c i p a l advantage of the exchange technique i s r e ta ined , i n that a very small d i f f u s i o n dis tance can be measured; but the c h i e f disadvantage o f the exchange method, the continuous presence of a gas phase, which may a f fec t the s o l i d , i s e l iminated . The present work was designed to inves t igate the behaviour o f surface ions at very low temperatures ( i n the region of room temperature). The technique employed i s described i n d e t a i l below. 1. Experimental Experiments on the d i f f u s i o n of c h l o r i d e ions i n NaBr c r y s t a l s , are c a r r i e d out wi th the same mater ia l and apparatus as used for the i n v e s t i g a t i o n o f chemical e q u i l i b r i u m i n the preceding s e c t i o n . 146 2. Procedure Br ions on the sodium bromide surface are replaced by repeated exposures to fresh specimens of HCl according to the method described i n the preceding section. The extent of exchange at the end of the experiment i s calculated as usual. The reaction system i s then pumped out continuously f o r a period of seven days, the c r y s t a l s being kept at the desired temperature. The exchange reaction i s repeated at the end of t h i s period i n the same manner as o r i g i n a l l y . The reaction system i s evacuated as before over a period of one week. These experiments are repeated a number of times, the exchangeable Br" ion being determined at the end of each evacuation period of seven days. 3. Methods of Calculation ( i ) C alculation of X a f t e r D i f f u s i o n In a normal exchange experiment as described i n the pre-ceding section, the peak r a t i o J of the successive specimens of the gas decreases gradually to a small value (Table 7, Section IV)• This decrease i n the peak ratio.. has been explained on the basis of the chemical equilibrium e x i s t i n g between the gas phase and the s o l i d surface (Section IV), the equilibrium constant K being given by 147 Some r e s u l t s of the experiments on the d i f f u s i o n of anions are given below. The r e s u l t s o f the o r i g i n a l exchange reac t ion ( ser ies A of Run 5) are a l so given for comparison. 148 TABLE 1 2 Values o f 10 r obtained i n Ser ies A and Ser ies B of Run 5. o Temperature = 21 C . D i f f u s i o n Time = 180.5 hours . Specimen Run 5A Run 5B 1 0 2 r 1 0 2 r 1 4.564 1.420 2 3.068 1.104 3 2.252 1.120 4 1.860 0.904 5 1.656 0.800 6 1.308 0.736 7 0.988 8 0.752 9 0.728 10 0.696 The value of C for any sample i n Run B i s c a l c u l a t e d as fo l lows , w i th the a i d o f the value of K found i n the o r i g i n a l exchange Run A . or C K = r e e C - C m e r e C e - K< Cnf Ce> 149 or C - K c m . r e +K L e t the amount of surface covered by C l ions a f t er the d i f f u s i o n time t , be denoted by C f c . I f the sum o f the r g values o f Run B up to any p a r t i c u l a r gas sample i s represented by C ^ , the value o f C f c i s given by C = C - C t e B r e +K C B The c a l c u l a t i o n o f C t for Run 5B i s shown i n Table (2) . TABLE 2 Values o f C f c from a l l the r e s u l t s of Run 5B. From Run 5A, 10 2 K = 1 . 6 5 2 and 10 Cm - 25.2 Specimen 1 0 2 r e io 2c f i 10 2 (r e +K) 102C e 2 10 c t 1 1.420 1.420 3.07 13.6 12.2 2 1.104 2.524 2.75 15.1 12.6 3 1.120 3.644 2.77 15.0 11.4 4 0.904 4.548 2.55 16.3 11.8 5 0.800 5.348 2.45 17.0 11.7 6 0.736 6.084 2.39 17.4 11.3 150 ( i i ) C a l c u l a t i o n of the D i f f u s i o n C o e f f i c i e n t L e t the amount o f d i f f u s i n g mater ia l o r i g i n a l l y i n u n i t area o f the surface layer be denoted by A ^ . Concentration c t at time t , at a dis tance x from the surface i n the d i r e c t i o n o f d i f f u s i o n i s given by 2 where D i s the d i f f u s i o n c o e f f i c i e n t . For time zero , the subscr ipt 1 ra ther than 0 i s used s ince we s h a l l l a t e r have to d i s t i n g u i s h the zero-time values for successive periods o f d i f f u s i o n represented by subscr ipts 1, 2, e t c . In the surface layer x i s equal to zero . Therefore , ct ° A l ( T t D t ) ^ The thickness of the surface layer i s equal to the spacing between planes i n the l a t t i c e , i . e . d ^ ^ . Le t the amount of d i f f u s i n g m a t e r i a l i n u n i t area o f surface layer at time t be denoted by A , . . Then the concentrat ion c i s given by t c t - f t . dlOO Therefore , A. - A l d 1 0 0 t r ( X Dt) Denoting the surface covered by C l ions i n i t i a l l y by X. and 151 at time t by X t as before (Sect ion IV) we have A t g X t „ c t ^ d^ QQ  A l X l C l (TVDt)^ Therefore D - d 100 X l 2 1 T V %> t The d i f f u s i o n c o e f f i c i e n t for success ive periods of d i f f u s i o n at the same temperature i s ca l cu la ted as fol lows: F i r s t per iod -D = d 100 X l 2 1 iv, 'x,/ t Second p e r i o d -Assuming that the time for a complete s er i e s of exchange react ions (about s ix hours for s ix specimens) i s n e g l i g i b l e compared to the d i f f u s i o n p e r i o d of seven days, the d i f f u s i n g m a t e r i a l o r i g i n a l l y present i n .the surface during the f i r s t d i f f u s i o n per iod i s considered to continue the d i f f u s i o n independently of the successive exchange react ions at the end of each d i f f u s i o n p e r i o d . S i m i l a r l y the d i f f u s i n g mater ia l added i n the exchange react ions at the end of each successive d i f f u s i o n per iod d i f fuses independently. Then the concentra-t i o n c t (t2 denotes the time of the second d i f f u s i o n period) i s given by 152 2 2 . x x A. c t o " r 6 4 D < t l + t 2 ) A- e " 5 b t where A^ i s the amount o f mater ia l added to the surface at the end of the f i r s t d i f f u s i o n per iod (usual ly measured as an mm increase X 2 i n surface coverage by C l ) . I f at the end of the second d i f f u s i o n per iod the amount of C l remaining on the surface i s A t 2 or X t 2 , at x *= o, A f c 2 - c t = A l + A 2 d 100 2 ft D(t x+t 2)} * ( 7 V D t 2 ) * or 1 » ^ 1 + A 2 ^ 0 0 A t 2 SxD(t l+t 2 ) ( % A t 2 ( 7 r D t 2 ) ^ " _ f l i , + i X t 2 D C t ^ ) } * X t 2 ( 7VDt 2 )* Therefore D - d10Q 1 + i i i , 2 * ( X ( t + t )% X 7i> 2 1 2 c 2 2 S i m i l a r l y for t h i r d per iod 2 D - d 100 , X l 1 + X 2 1 + J U 2 TT ^ X t ( t +t +t ) * X t ( t +t )^ X t t ^ " c 3 v - l 2 3 y c 3 v 2 3 ^ 3 Taking the general case of n successive periods of d i f f u s i o n at d i f f e r e n t temperatures, the d i f f u s i o n c o e f f i c i e n t s 153 being denoted by D^, I>2> D n . , the expression may be w r i t t e n as -1 - 1 1 + 1 d 100 ~& 1 \ < D l t l + - " - H ) n t n > ^ X t n (D2t2^...-H)ntn)% + . . . + J j a 1 ) X t (D t n n n The d i f f u s i o n c o e f f i c i e n t D Q for the n th d i f f u s i o n per iod can be ca l cu la ted by successive approximations from the values o f D , t , and X for a l l o f the previous d i f f u s i o n per iods . 4. Results Table 3 shows the r e s u l t s o f the most extensive ser ies o f experiments. 154 TABLE 3 2 Values of 10 r obtained i n Run 6. o Time (nr . ) Temperature ( C . ) From A to B 155.5 70 " B " C 163 70 " C " D 138.5 70 " D " E 162 95 2 Specimen Values of 10 r 6A 6S 6G 6D 6E 1 5.284 4.216 2.016 1.196 2.200 2 3.656 2.920 1.620 1.052 1.760 3 2.860 2.244 1.344 0.988 1.440 4 2.288 1.636 1.232 0.924 1.220 5 1.716 1.424 1.064 0.824 1.120 6 1.436 1.028 0.920 0.712 0.896 7 1.272 8 1.080 9 0.848 10 0.684 155 The significance of a comparison of Runs 6A and 6E has been discussed in Section IV, and these results were shown graphically in Figure (7), Section IV. The values of X at a l l stages in Run 6 are summarized in Table (4). TABLE 4 Summary of Run 6 Diffusion Experiments. o o Temperature (6B, 6C, 6D) m 70 C. Temperature (6E) ° 95 C. Time Y v Y X10"5 \ x f \ Run sec. (initial) (final) (added) 6B 5.6 0.724 0.171 0.461 6C 5.88 0.632 0.431 0.280 6D 4.98 0.711 0.600 0.195 6E 5.83 0.795 0.411 0.296 The calculation of D may be exemplified by the following for Run 6C:-X l " X i ° 0 , 7 2 4 X« a X - 0.461 JL a X. - X. - 0.431 c2 * D - (2.98) 2vl0" 1 6 :(0.724 1 ^ +0.461 2 -x 1 i  £j4bi :.: 1 •) iO.431 |(5.6+5.88)X105}^ ° « 4 3 1 {5.88X105}^ n , a ' -21 2 -1 2.48X10 cm sec 156 The most s i g n i f i c a n t feature of the r e s u l t s c a l c u l a t e d i n t h i s way i s that the values of D for successive d i f f u s i o n periods at the same temperature are not constant . Thus for the f i r s t two d i f f u s i o n experiments i n Run 6:-, r r . , , , r r n _ -21 2 -1 D i f f u s i o n per iod 6A to 6B, D B 9.05X10 cm sec -21 2 -1 D i f f u s i o n p e r i o d 6B to 6C, D = 2.48X10 cm sec • The l a t t e r c a l c u l a t i o n i s o f course i n v a l i d a t e d by i t s r e s u l t , s ince the c a l c u l a t i o n i s based on the assumption that D i s the same i n both p e r i o d s . To improve the c a l c u l a t i o n , D may be assumed constant w i th in each p e r i o d , but vary ing from one per iod to the next . Table (5) shows the r e s u l t s o f a l l d i f f u s i o n experiments, inc lud ing those for Run 6 r e c a l c u l a t e d i n t h i s way. 157 TABLE 5 Summary of Runs 2-6 D i f f u s i o n Experiments. Time D XlO 5 Temperature x o 9 i oi Run (sec) ( ° C ) *t (an sec )X10 2B 11.3 22 1.343 0.450 3B 18.2 22 2.17 0.730 4B 15.7 70 1.39 0.337 5B 6.5 22 1.46 0.925 6B 5.6 70 4.23 9.05 6C 5.88 70 1.37 6D 4.98 70 0.90 6E 5.83 95 . . . . 4.2 o The very low value of D at 70 C . i n Run 4B may be con-s idered u n r e l i a b l e ; the gas samples had been stored for about two months before a n a l y s i s , and had probably l o s t an appreciable f r a c t i o n o f t h e i r HBr content by reac t ion wi th the stopcock grease. Discounting t h i s r e s u l t , the a c t i v a t i o n energy E may be estimated as f o l l o w s : -At 2 2 ° C . (mean o f Runs 2B, 3B, 5B), D » 0.702X10* 2 1 cm 2 sec" 1 -21 2 -1 At 7 0 ° C . (Run 6B) D - 9.05X10 cm sec Whence E • 10.7 k c a l mole From the l a s t two parts of Run 6, assuming that D has reached 158 a steady value at 70 C . : -™21 2 —1 A t 7 0 ° C . (Run 6D), D - 0.90X10 cm sec" —21 2 -1 At 9 5 ° C . (Run 6E) , D - 4*2X10 cm sec Whence E • 15*5 k c a l mole \ 5* Discuss ion The r e s u l t s given above do not appear consistent wi th a simple bulk d i f f u s i o n process throughout the volume o f the s o l i d * In successive experiments wi th the same s o l i d specimen, such as the parts of Run 6 (6A, 6B, etc*) the d i f f u s i o n c o e f f i c i e n t always decreased from one experiment to the next* This type of behaviour would normally be expected only when the d i f f u s i o n distance i s s u f f i c i e n t l y large for the semi-i n f i n i t e s o l i d approximation to break down* Thi s i s c e r t a i n l y not the case here , provided that we are dea l ing wi th simple bulk d i f f u s i o n . The t o t a l amount o f the d i f f u s i n g mater ia l used i n Run 6 corresponds to only about 2 atomic l a y e r s , and d i f f u s i o n distances are of the order of magnitude of T o t « ( l 0 " 2 1 c m 2 s e c " : L X l 0 6 s e c . ) l / i There are three obvious mechanisms by which the observed decrease i n D as d i f f u s i o n proceeds, may ar i se* These a r e : -159 (a) Dependence of D on C l concentrat ion; (b) Dependence o f D on distance from surface of the c r y s t a l ; and (c) Occurrence of d i f f u s i o n i n d i s l o c a t i o n s o n l y , not i n the whole bulk o f the s o l i d . Each o f these p o s s i b i l i t i e s w i l l now be considered i n some d e t a i l . mm (a) Dependence of D on C l Concentration In the NaBr l a t t i c e , each Br ion i s surrounded at second nearest neighbour distance by 12 other anions . Overlap repu l s ion wi th these 12 ions makes a s i g n i f i c a n t contr ibut ion to the energy o f the c e n t r a l i o n . An ion for which some of the second nearest neighbours are C l w i l l there -fore be s t a b i l i z e d r e l a t i v e to a normal anion i n the l a t t i c e and w i l l be l e ss l i k e l y to jump in to an anion vacancy which approaches i t . Thus as the C l concentrat ion increases i n any r e g i o n , i t w i l l become more d i f f i c u l t for anion vacancy to approach that r e g i o n . On t h i s b a s i s , i t appears reasonable that D should f a l l as d i f f u s i o n of C l proceeds. (b) Dependence of D on Distance from the Surface o f the  C r y s t a l s The p o s s i b i l i t y a r i s e s . t h a t D decreases r a p i d l y w i th distance from the surface , so that the s o - c a l l e d d i f f u s i o n process i s i n fac t only an exchange wi th two or three 160 subsurface l ayers ; t h i s p o s s i b i l i t y has a lready been suggested i n the case o f C l ^ / N a C l i s o t o p i c exchange (Harrison et a l , (45) ) , In the present case , the e q u i l i b r i u m should l i e s trongly i n favour of the C l ion going to the subsurface l a y e r s , s ince the decrease i n entropy on exchanging Br for C l i s a c h a r a c t e r i s t i c o f the surface and most of the entropy should be regained i n the d i f f u s i o n process . However, t h i s process would give a h igh concentrat ion of C l i n the l ayer immediately subjacent to the surface , and should lead to an appreciable co l lapse o f Verwey d i s t o r t i o n i n the surface layer i t s e l f . In consequence the surface exchange r e a c t i o n should not be reproducib le i n successive experiments on the same s o l i d . The observed r e p r o d u c i b i l i t y of the exchange reac t ion i s evidence against t h i s mechanism. (c) D i f f u s i o n i n D i s loca t ions I t has been experimentally determined (96) that although + the d i f f u s i o n o f Na ion i n mono**, and p o l y - c r y s t a l l i n e sodium c h l o r i d e takes p lace wi th the same speed, the d i f f u s i o n of C l ion i s fas ter i n the case o f a p o l y c r y s t a l l i n e sample. In the l a t t e r case, the fac t that the energy o f a c t i v a t i o n remains unchanged appears to ind i ca te that the increase i n v e l o c i t y of d i f f u s i o n i s not due to a modi f i ca t ion of the height of the energy b a r r i e r . The e n t i r e l y d i f f e r e n t behaviour o f the i n t e r c r y s t a l l i n e surfaces wi th regard to the 161 d i f f u s i o n o f cat ions and anions seems to be r e l a t e d wi th the higher p o l a r i z a b i l i t y o f the l a t t e r (Laurent 96) . I t thus seems poss ib le that i n the present case d i f f u s i o n i s proceeding only down d i s l o c a t i o n s and not through the whole bulk o f the s o l i d * A 3-micron c r y s t a l may be expected to con-t a i n only a few d i s l o c a t i o n s , so that the " i n t e r n a l surface" a r i s i n g from t h e i r presence i s o f the same order o f magnitude as the external surface . In t h i s case , s e m i - i n f i n i t e s o l i d approximations may be expected to break down at the observed stage, and the equations used i n any case become i n c o r r e c t , because par t of the d i f f u s i o n path i s now along the sur face , not perpendicular to i t . D i f f u s i o n Distance i n Re la t ion to A c t i v a t i o n Energy. I t remains to decide which o f the mechanisms (a) and (c) above, both of them q u a l i t a t i v e l y p l a u s i b l e , i s the more l i k e l y . I f i t i s assumed that the a c t i v a t i o n energies reported above are reasonably c lose to the true value ( i t i s evident that the method of c a l c u l a t i n g E i s not s t r i c t l y correc t i n e i ther case) , then i t i s pos s ib l e to estimate the v i b r a t i o n frequencies o f the d i f f u s i n g ions as given by both mechanisms. The r e s u l t s , given below, show that much more reasonable values are obtained for mechanism ( c ) , d i f f u s i o n in to d i s l o c a t i o n s . Q u a l i t a t i v e l y , the argument i s that the observed temperature dependence i s unusual ly small f or a 162 d i f f u s i o n phenomenon i n a s o l i d . Correspondingly, the ions are moving rather r a p i d l y , and d i f f u s i o n distances of the order of 1 micron i n 5X10^ sec. as required i n (c) are more reasonable than the distances of the order of 2A* required for mechanism (a) • For both mechanisms, D - D e - E / R T o 2 v i b r a t i o n frequency )J ^ D Q / d where d i s the (100) spacing for (a) and i s o f the same order of magnitude for ( c ) . The a c t i v a t i o n energies given above are qui te l i k e l y to be lower than the true value; the r e s u l t s are therefore shown i n Table (6) , for assumed a c t i v a t i o n energies of 10, 15 and 20 k c a l mole \ 163 TABLE 6 V i b r a t i o n Frequencies Ca lcu la ted on Various Assumptions o —22 2 —1 (a) From Table (5) , mean D at 22 C ^ 7 X 1 0 cm sec ; -8 d & 3X10 cm. (c) D i s c a l c u l a t e d from the fo l lowing: D i f f u s i o n distance ~ Jfji ^ 1 micron at 22°C and t - 5 X l 0 5 s e c . -8 d ^ 3X10 cm. -1 2 - 1 -1 Mechanism E ( k c a l mole ) T>^0 c ( c m sec ) lo%^pQ V sec -22 a 10 7X10 -13.7 20 -22 5 a 15 7X10 -10.0 1X10 -22 8 20 7X10 - 6.3 6X10 a c c c 10 2 X 1 0 " U - 6.3 6X10 8 -14 12 15 2X10 - 2.6 3X10 -14 16 20 2X10 + 1.2 2X10 164 SECTION VI THE HYDRATION AND DEHYDRATION OF SODIUM BROMIDE The study reported In t h i s sec t ion i s o f the dehydration of a large mass of micron-s ized p a r t i c l e s o f sodium bromide, 2 having a t o t a l surface o f the order of 100 m • The process does not appear to involve break-up of the c r y s t a l s to any s i g n i f i c a n t extent , and the system can be taken through cycles of dehydration and p a r t i a l hydrat ion without apparent change i n the nature of the processes o c c u r r i n g . The important feature of the r e s u l t s i s that , , whi le hydrat ion o f the completely or p a r t i a l l y anhydrous m a t e r i a l w i l l take p lace only at or above the normal d i s s o c i a t i o n pressure o f the d ihydrate , dehydration takes p lace at a d i f f e r e n t pressure which has a l l the experimental c h a r a c t e r i s t i c s of an e q u i l i -brium pressure . There can, o f course, be no true e q u i l i b r i u m i n v o l v i n g a phase a d d i t i o n a l to the three already present; but i f each c r y s t a l dehydrates from the surface inwards, a s i t u a t i o n may a r i s e i n which the hydrated phase i s nowhere i n d i r e c t contact wi th the vapour. Loss of water would proceed by d i f f u s i o n through the outer anhydrous region of each c r y s t a l . Suppose now that the s o l i d surface i s p a r t l y covered wi th an adsorbed layer which may be considered as a 165 d e f i n i t e two-dimensional phase, or surface hydrate d i f f e r i n g i n s tructure and thermodynamic propert ies from the normal three dimensional d ihydrate . I f t h i s surface i s o f s u f f i c i e n t l y great extent , dehydration w i l l tend to proceed at a water vapour pressure corresponding to the equ i l ibr ium: water vapour - surface hydrate - anhydrous s a l t . I t w i l l be seen that the adsorption phenomenon postulated here , wherein the adsorbed layer has the thermodynamic c h a r a c t e r i s t i c s o f an ordinary condensed phase, d i f f e r s from the major i ty o f adsorption phenomena. The adsorption isotherm must have a d i s c o n t i n u i t y i n surface coverage at a p a r t i c u l a r pressure . The s ign i f i cance of t h i s i s discussed b r i e f l y , and i t i s shown to be normal behaviour for an adsorbate on an energe t i -c a l l y homogeneous surface . The phenomenon may be uncommon i n p r a c t i c e c h i e f l y because few surfaces are e n e r g e t i c a l l y homo-geneous i n respect o f adsorption processes . 1. Experimental Sodium bromide p a r t i c l e s used i n the present inves t iga t ion were prepared according to the method descr ibed i n Sect ion I . During the p e r i o d of vacuum des icca t ion o f four days, adsorbed acetone and a small proport ion of water were given up. As determined from the t o t a l loss of weight i n the subsequent dehydration experiments, the p a r t i c l e s were 72% hydrated 166 (ca lcu la ted from the formula NaBr.2H 2 0) at the s t a r t o f the experiments. ( i ) Dehydration and Hydration Experiments These experiments were c a r r i e d out i n the dry box (a c o l l a p s i b l e type, o f t h i n polyethylene sheet) on a t o t a l specimen o f about 200 g. ( i n i t i a l l y ) o f sodium bromide. 100.0 gm. o f the specimen was kept i n a p e t r i d i s h on the pan of a two-pan balance . A s i m i l a r blank p e t r i d i s h was p laced on the other pan to cancel out the e f fec t of the adsorption or desorption o f moisture on the surface of the p e t r i d i s h during the experiments. The remainder o f the specimen was spread as widely as poss ib le i n a large p o r c e l a i n d i s h . Both parts of the specimen were s t i r r e d at frequent i n t e r v a l s . Dehydration was ef fected by means o f several dishes of phosphorus pentoxide; for hydrat ion , i t was necessary only to remove the desiccant and al low the water vapour pressure i n the dry box to b u i l d up by leakage from the atmosphere. A l l o experiments were c a r r i e d out at a room temperature of 22 C . Re la t ive humidity was measured wi th an American Instrument Co . Aminco-Dunmore e l e c t r i c hygrometer, catalogue number 4-5111. The sensing element (catalogue number 4-4730) i n s t a l l e d i n the dry box was suppl ied wi th a c a l i b r a t i o n chart i n d i c a t i n g that the sca le of the measuring instrument was almost l i n e a r i n r e l a t i v e humidity , covering the f u l l range 167 0-100%. The scale could be read to 0.1%. ( i i ) X-rav D i f f r a c t i o n Photographs Debye-Scherrer powder photographs were taken o f var ious specimens o f sodium bromide, sealed in to 0.5 mm. diameter Pyrex c a p i l l a r y tubes, us ing n i c k e l f i l t e r e d copper r a d i a t i o n and a 14.3 cm. camera. Measurements were made only s u f f i c i e n t l y accurate ly to index roughly the f i r s t 30 r e f l e c t i o n s from the known monocl lnic l a t t i c e o f NaBr. 21^0 i n add i t i on to the w e l l -known NaBr p a t t e r n . ( i i i ) P a r t i c l e S i ze and Surface Area The s i z e o f the anhydrous sodium bromide c r y s t a l s e s t i -mated on microscopic examination i s of the order of 3 microns 2 on an edge, which would have a s p e c i f i c surface o f 0.63 m / g . The t o t a l surface of the weighed sample i n the present study (80 g . a f t er dehydration) may therefore be estimated as 2 of the order o f 50 m , and represents near ly h a l f the sodium bromide surface exposed i n the dry box. The area , o f course , changes during dehyration even i f there i s no break-up of the c r y s t a l s . I f dehydration i s supposed to take p lace without change of e i t h e r c r y s t a l habi t or number of c r y s t a l s present , then from the dens i t i e s o f NaBr.21^0 and NaBr i t may be c a l -culated that the surface area w i l l shr ink by 36.5% o f i t s i n i t i a l extent during a complete dehydrat ion. 168 2. Results (i) Dehydration and Hydration Experiments The partially hydrated crystals, from which a l l acetone had been removed, were i n i t i a l l y at constant weight (the desiccant being exhausted) at a relative humidity of about 40%. On renewing the desiccant, the humidity f e l l rapidly, reaching 21.5% after seven hours. For the ensuing 80 hours, the humidity was almost constant, declining gradually to 18.7%; in this period, the humidity was entirely insensitive to stirring of the crystals and renewal of the desiccant (renewed once at 43 hours). These phenomena are shown in Figure (1). In the final stages of dehydration (region marked A in Figure (1) ) the humidity became sensitive to stirring. Later observations indicated that the important feature of the stirring was the agitation of the walls of the dry box, which promoted leakage of water vapour from the external atmosphere. If this was done after complete dehydra-tion, when the humidity had fallen to zero, the humidity returned to about 19.7%, for one or two hours, and thereafter decreased to zero again as shown in Figure (2). The fi r s t occurrence of this phenomenon is shown in region B of Figure (1). Accompanying changes in weight were just measurable on the rough balance (detection limit 0.015 g.) and were estimated Time( hr ) Figure 1. A - region in which the humidity became se n s i t i v e to S t i r r i n g . B - f i r s t occurrence of the phenomenon shown ir\ Figure %, 0 1 0 0 2 0 0 3 0 0 Time (min ) Figure 2 . The var-iafc-jon of humiditry with time after leakage had been promoted for a few minutes., 171 as an Increase of 0.06-0.03 g. as the humidity r o s e , and a s i m i l a r decrease as the humidity f e l l . Hydration was ef fected by removing the desiccant and e i ther us ing the leakage o f the dry box (regions marked "closed" i n Figures (3) and (4) ) or hastening the admission of water vapour by p a r t l y opening the entrance of the box (regions marked "open")• The l a t t er .procedure i s not of much i n t e r e s t ; the humidity simply rose r a p i d l y to that of the room, u s u a l l y 50 to 55%. When the dry box was c l o s e d , however, a d d i t i o n of water to the c r y s t a l s took place at a r e l a t i v e humidity roughly twice that observed during dehydrat ion. F igure (3) shows the beginning o f the f i r s t hydrat ion , i n which the r e l a t i v e humidity i s arres ted for a time between 20 and 217., and the increase i n weight of the c r y s t a l s remains constant at about 0.05 g . F igure (4). shows a t y p i c a l hydra-t i o n , i n which the humidity f e l l from 37.7 to 36.9% i n 50 hours , whi le the c r y s t a l s s t e a d i l y gained weight. Subsequent replacement of the desiccant l e d to dehydrat ion, again at 19.7% humidity . In a number of cyc les of add i t i on and removal of water, t h i s hys teres i s e f fec t p e r s i s t e d . The humidity during hydrat ion was only moderately reproduc ib le . The two important humidit ies may be assigned the values 37.7-3% and 19.7*1%. 40 30 20 1 I 10 «-0 Humidity Water Uptake L 1 0-3 0-2 o CL 15 a> -•— o - 0-1 0 2 Time ( hr) 4 6 Figure 3. The onset of the hydration process of. anhydrous sodium bromide a f t e r removal, of the desiccant. 5 - dry box partly open to atmosphere C - dry box closed (but leaking) . -si ro 5 0 4 0 - r , 30 20 >» •v ' i 3 I I 0 >\<-Weighty . Humidity | ^ y i \ 85 84 83 8 2 _ 8 I | v 0 20 4 0 6 0 Time ( hr) Figure A. A typical cycle of partial hydration and dehydration; zero of time-scale 0 - dry bo* partly open to atmosphere c - dry box closed (leaking) D - desiccant (P^Oj) placed in dry box 80 arbi trary 174 (i i ) X-ray Diffraction Photographs Plate (1) shows photographs for the following:-A: Anhydrous Sodium Bromide. B: 2.1% Hydrated Sodium Bromide. C: 10.9% Hydrated Sodium Bromide. D: Completely Hydrated Sodium Bromide. E: Blank (normally mounted capillary only)• F: Anhydrous NaBr, heated at 400°C. for 160 hours. In a l l cases, the lines present could a l l be assigned to the lattices of NaBr or NaBr.2^0. The lines shown in (E Flate 1) were obtained with a blank capillary mounted in the usual way. It was found that the lines originated because of the wax used as a support for the capillary. The presence of these lines in the other photographs may .therefore be ignored. Completely hydrated sodium bromide gave "spotty" photographs (D flate 1) indicating that recrystallization to larger particle sizes was taking place in the capillary tube which contained the specimen. In contrast, partly hydrated material gave sharp lines (B and C, plate 1) and appeared to be the most suitable type of sample for accurate measurements on the NaBr .2^0 lattice. As judged visually,; the relative intensities of the reflections from the two lattices correspond roughly to the degree of hydration of the sample (compare B and C plate 1). The sample which had been dehydrated until the humidity f e l l 175 ) ) I I D iini ) ) ) I 8 I (( )) 176 to zero showed, as expected, the anhydrous la t t i c e only. There was no evidence for any distortion of the la t t i c e s , or lack of cr y s t a l l i n i t y at any stage. 3. Discussion The most important feature of the results i s that, for a partly hydrated sample of high surface area sodium bromide, two different relative humidities can appear, experimentally, o to be the equilibrium value at 22 C : 37.7% during hydration and 19.7% during dehydration. Of these values, the former i s the one established when no addition or removal of water i s taking place (at the beginning of the whole series of experi-ments) and therefore appears to be the true equilibrium value for the system NaBr-NaBr^H^O-H^O. The same conclusion i s reached by comparison with previously reported values for this system (Table 1) which are not very consistent with each other, but a l l give relative humidities markedly higher than the value observed during dehydration in the present experiments. 177 TABLE 1 The D i s s o c i a t i o n Pressure o f NaBr. 2 ^ 0 0 D i s s o c i a t i o n Pressure Reference T C . mm, Hg. Re la t ive Humidity (%) 129 10 3.9 42.4 129 20 7.65 43.7 129 30 15.5 48.7 130 20 5.48 31.2 131 20 10.2 58 132 20 4.9 28.0 132 25 7.5 31.5 132 30 11.3 35.5 T h i s work 22 7.46 37.7-3 The dihydrate i s the only hydrate of sodium bromide known to e x i s t , and the X - r a y d i f f r a c t i o n photographs reported here show no evidence for the occurrence o f any other hydrated l a t t i c e . I t therefore seems most reasonable to ascr ibe the humidity of 19.7% observed i n dehydration to a surface e f f e c t . The observed increases i n weight, o f the order of 50 mg. , at the onset of hydrat ion (processes at 19% humidity i n Figures (2) and (3) ) support t h i s conc lus ion . I f one water molecule 178 o2 occupies about 10 A on tbe surface , a complete layer o f water 2 on about 50 m • of surface would represent about 1 m i l l i m o l e or about 18 mg. , of the same order of magnitude as the observed changes• I t i s concluded t h a t , when anhydrous sodium bromide i s o exposed to an increas ing pressure of water vapour at 22 C , an amount of water equivalent to no more than a few atomic layers of the c r y s t a l s i s taken up suddenly at 19.7% humidity or 3.90 mm. Hg. This water may be adsorbed on the surface , i n the sense that i t l i e s outside t h e . l a s t l ayer o f sodium bromide, or may be incorporated in to the outermost layers of the c r y s t a l s forming e i t h e r a d i s t o r t e d NaBr . 2 ^ 0 l a t t i c e or some completely d i f f e r e n t geometrical arrangement. On dehydration o f c r y s t a l s s u f f i c i e n t l y small that they do not break up i n the process , a s i m i l a r surface layer p e r -s i s t s throughout. Each c r y s t a l may then be envisaged as having a hydrated surface o v e r l y i n g an anhydrous sodium bromide l a t t i c e through which water i s d i f f u s i n g from the hydrated (NaBr. 2^0) i n t e r i o r . The e f fect o f c r y s t a l s i z e has not yet been determined; most probably , the required condi t ion i s that each c r y s t a l should contain only one or two d i s l o c a t i o n s ; i . e . i t should not be more than a few microns i n s i z e . Wooster (128) has shown that dehydration of large c r y s t a l s o f NaBr. 2 ^ 0 proceeds by a nuc leat ion mechanism. 179 The r e l a t i o n s h i p between the type o f uptake here observed, depending discont inuously on pressure , and the more common type of behaviour i n adsorption i n which surface coverage v a r i e s continuously wi th pressure , may be shown as f o l l o w s : -The p a r t i a l molar free energy of the adsorbate may be wr i t t en i n general as Fads " * l i e + fW where 0 i s the concentrat ion o f the adsorbed species r e p r e -sented as a surface coverage. I f the standard s tate o f the adsorbate i s to be defined so that i t s a c t i v i t y c o e f f i c i e n t i s u n i t y i n an i n f i n i t e l y d i l u t e adsorbed l a y e r , then f(9) must be w r i t t e n i n such a form that f ( 0 ) 0 ^ • Ojcons ider ing the gas phase of the adsorbate to be i d e a l , we may w r i t e for the adsorption process A F = F ads< e >- F gas ( p > - A F ° + f (0)-RTlnp and at e q u i l i b r i u m , RTlnp A F ° + f(9). Two l i m i t i n g types of behaviour may then a r i s e : -(a) I f f(0) increases monotonical ly wi th 6, "normal adsorp-t i o n behaviour" w i l l be observed, i . e . 9 w i l l increase mono-t o n i c a l l y wi th p . For an e n e r g e t i c a l l y homogeneous surface , t h i s requires that the adsorbed layer should not be a "condensed" 180 l a y e r , s ince the p a r t i a l molar free energy o f the l a t t e r should be independent o f concentrat ion or c o n f i g u r a t i o n , and therefore of 6. Thermodynamic and s t a t i s t i c a l treatments leading to con-tinuous adsorption isotherms have general ly regarded the adsor-bate as e i t h e r a two-dimensional imperfect gas or a " l a t t i c e gas" wi th a conf igura t iona l entrppy l i k e that of a s o l i d s o l u -t i o n (133, 134, 135). In the l a t t e r case, f ( 0 ) ° l n 6 and the 1-9 Langmuir isotherm i s obtained. (b) I f the adsorbed layer i s "condensed" on an e n e r g e t i c a l l y homogeneous surface , i t may be thought o f as a two-dimensional analogue of a pure s o l i d or l i q u i d , so that F - P ° r a d s c a d s at a l l 0, i . e . f(0)=0 at a l l 0. The surface coverage 0 w i l l then increase d iscont inuously from 0 to 1 at a pressure given by RTlnp 8 3 A F ° . Th i s i s the s i t u a t i o n envisaged to expla in the present r e s u l t s . I t c l o s e l y resembles the "two-dimensional condensation" phenomenon which has been treated t h e o r e t i c a l l y (133, 135) and observed experimentally (136, 137, 138) i n a few cases o f adsorption at very low temperatures and pressures . For p h y s i c a l adsorpt ion , i t i s e a s i l y shown (133) that such extreme condit ions are always necessary for the observation of t h i s phenomenon. For other types of adsorpt ion , the only fac tor which may prevent the occurrence of t h i s behaviour i n much more access ib le condit ions i s that most surfaces are 181 probably e n e r g e t i c a l l y heterogeneous. In t h i s connection, i t has already been suggested (139) that the a l k a l i ha l ides may be unusual i n having homogeneous surfaces . The present r e s u l t s appear to support t h i s conc lus ion . 182 SECTION VII PRODUCTION OF COLOR CENTERS IN ALKALI HALIDE CRYSTALS  BY HIGH FREQUENCY DISCHARGE Color centers may be produced i n a l k a l i h a l i d e c r y s t a l s , e i ther by the addi t ion o f s to ich iometr ic excess o f halogen or a l k a l i metal or by the use of i o n i z i n g r a d i a t i o n s ( e l ec trons , protons , X - r a y s , u l t r a v i o l e t rays or gamma r a y s ) . The subject has been reviewed extens ive ly by S e i t z (80 and 84)• The s t a b i l i t y o f the c o l o r centers has been shown by Markham (72) to depend on t h e i r mode o f formation. Improvements i n e x p e r i -mental technique have continued to y i e l d va luable information concerning the photochemical react ions involved i n the c o l o r i n g process . The present sect ion i s p r i m a r i l y concerned wi th a new experimental technique for the production o f c o l o r centers i n i o n i c c r y s t a l s by the h igh frequency discharge of a T e s l a c o i l . An attempt i s made to .explain the phenomena. In the case of NaCl v i s i b l e absorption spectra of the centers were obtained and the bands were i d e n t i f i e d . The s t a b i l i t y of the co lor centers over a per iod o f a few days was s tud ied . Th i s technique provides a r a p i d and convenient means of producing defects i n the a l k a l i h a l i d e s , and might be use fu l i n further work on the mechanism of C ^ / N a C l i s o t o p i c exchange. 183 For t h i s process , Harr i son (105) has suggested a mechanism i n which the ra te of reac t ion should be s ens i t i ve to the i n i t i a l concentrat ion of defects i n the s o l i d . 1. Experimental (1) Apparatus High frequency (1,000,000 cyc les / sec ) discharge i s obtained us ing a T e s l a C o i l leak t e s t er operat ing on 110 v o l t s , 60-cycles A - C power. A vacuum pump capable of] producing vacuum s u f f i c i e n t to obta in T e s l a C o i l discharge was used, ( i i ) Method C r y s t a l s are p laced i n a tube and evacuated for a few minutes wi th the oil-pump u n t i l discharge i s produced by the T e s l a C o i l , The c o i l i s brought c loser to the c r y s t a l s and the discharge continued for a few minutes, u n t i l the des ired development of the c o l o r i s obtained. ( i i i ) Specimens A l l o f the specimens of i o n i c c r y s t a l s used i n these experiments were p o l y c r y s t a l l i n e reagent grade chemicals , without any further treatment, except the sodium ch lor ide specimen which was cleaved from a large c r y s t a l ( I . R . c e l l window) obtained from the Harshaw Chemical Company. The weight of the samples was a r b i t r a r i l y f i xed at 184 about two grams. The sample o f NaCl used for measurements of o p t i c a l absorption was 15x5x2 mm. 2. Results ( i ) A n a l y s i s o f the Spectroscopic Data for NaCl A d e t a i l e d examination was made only i n the case of sodium c h l o r i d e . No o p t i c a l measurements were made on the other specimens. V i s u a l observations of the development of c o l o r and t h e i r s t a b i l i t y are given i n Table (3 ) . The sodium c h l o r i d e specimen was exposed to the T e s l a C o i l discharge i n l i v e vacuum obtained by an o i l -pump. Although the development o f co lor was not iceable w i t h i n an exposure time of f i v e minutes, an a d d i t i o n a l exposure of f i v e minutes was considered necessary for the o p t i c a l measurements. The measurements of o p t i c a l densi ty were done by Cary (model 11) spectrometer. The observed bands are i d e n t i f i e d by comparison wi th the publ ished work. Table (1) shows two sets o f values comparing the r e s u l t s o f the present work wi th those o f Yag i (75). TABLE 1 Spec tra l Locat ion o f the Absorpt ion Bands A - Absorpt ion Peaks (Reference 75) B - Absorpt ion Peaks (Present work) A (X-ray i r r a d i a t e d NaCl) B (NaCl exposed to T e s l a C o i l (Yagi) Discharge) Absorpt ion Peaks m//. Absorpt ion Peaks ny/. N 830 M 750 M 730 660 R, 620 R r 596 * R or c o l l o i d band 600 572 R, 552 R ? 526 F 465 F 450 K 292 * K 360 K* 258 The band, appearing between 550 and 660 m i l l i m i c r o n s may p o s s i b l y be an unresolved group o f the R peaks of Y a g i . On the other hand, t h i s band may be a c o l l o i d a l sodium band, resembling that reported by a number of workers, Siedentopf 186 G y u l a i , Savostianova, Mollwc and others (84). Siedentopf found that a d d i t i v e l y co lored NaCl conta in ing a tomica l ly dispersed F centers , which i s yel low i n c o l o r , turns o blue a f t e r being annealed at 400 C • , and reveals the presence of small c o l l o i d a l p a r t i c l e s o f sodium. Savostianova (109) has c a l c u l a t e d the e x t i n c t i o n c o e f f i -c i ent as a funct ion of wavelength, for c o l l o i d s o f various 6 s izes i n a specimen of N a C l , possessing one par t i n 10 by volume of m e t a l l i c Na . The peak of the e x t i n c t i o n curve for zero p a r t i c l e s i z e , which has a maximum at 550 m i l l i m i c r o n s , corresponds to the l i m i t i n which the p a r t i c l e s are much smaller than the wavelength of l i g h t . The peak of the e x t i n c -t i o n curve s h i f t s to longer wavelengths as p a r t i c l e s i ze increases . M o l l w (110) has observed these s h i f t s from 570 to 620 m i l l i m i c r o n s i n a d d i t i v e l y co lored c r y s t a l s of sodium bromide. Therefore the peak can be i d e n t i f i e d by i t s subsequent behaviour on aging, which may r e s u l t i n the coagulat ion of the c o l l o i d a l p a r t i c l e s , hence increas ing the p a r t i c l e s i ze and causing a s h i f t o f the peak towards the longer wavelength. No detectable bands were observed i n the U . V . range, wi th the specimen. On comparing the r e s u l t s of Table (1) a d i f ference of about 20 m i l l i m i c r o n s i n the l o c a t i o n of M and F bands of A and B i s observed. However, t h i s d i f f erence i s 187 w i t h i n the l i m i t s o f the v a r i a t i o n i n the l o c a t i o n o f a band observed. An estimate of t h i s v a r i a t i o n may be obtained by comparing the experimental values reported by various authors of the l o c a t i o n of absorption bands, tabulated by Ivey (106). Excepting the case of F band i n K I , where the maximum v a r i a t i o n i n two experimental values i s 31 m i l l i m i c r o n s , the maximum v a r i a t i o n i n the l o c a t i o n of, any band for any a l k a l i h a l i d e i s l e s s than 25 m i l l i m i c r o n s . The experimental values of the present work for M and F band are i n agreement wi th the general ly observed values for these bands (see 106)• But the band observed at 360 m i l l i m i c r o n s , located between K* and F bandsof Y a g i , corresponding to the K band at 292 m i l l i m i c r o n s , appears to be d i f f i c u l t to expla in on the bas i s of the l i m i t s o f v a r i a t i o n i n the l o c a t i o n of the absorption bands. The v a r i a t i o n of 25 m i l l i m i c r o n s ( i n an extreme case of 31 m i l l i -microns, for F band i n KT) i s most probably due to the s h i f t s i n the absorption maximum, r e s u l t i n g from d i f f e r e n t r e l a t i v e i n t e n s i t i e s o f the overlapping bands, obtained by var ious workers, depending upon the method of product ion . The d i f ference of 68 m i l l i m i c r o n s between the c loses t values of A and B , corresponding to K band i s rather large to be accounted for by t h i s s h i f t . Values of absorption peak for K band reported by other workers, Kle inschord (111), Duerig and Markham ((84), p r i v a t e communication to S e i t z ) f o r the case 188 of K C l (data on NaCl i s not ava i lab le ) correspond to 420 m i l l i -microns; the band appearing as a shoulder of F band on the short wavelength s i d e . Y a g i , however, reports the presence o f K and K r band i n N a C l , but i t i s d i f f i c u l t to i d e n t i f y the peak at 360 m i l l i -microns observed i n the present work wi th e i ther of these K The specimen was subsequently kept i n the dark i n a o des iccator at room temperature (22 C. ) for three days i n order to determine the behaviour of the band system as regards the v a r i a t i o n i n the peak heights and the l o c a t i o n of the maxima. A s i g n i f i c a n t s h i f t towards longer wavelengths was observed i n the l o c a t i o n of the R peak. The l o c a t i o n of the o r i g i n a l and the developed peaks are given i n Table (2) for comparison. Spec tra l Locat ion of the O r i g i n a l and the Developed Peaks or peaks. ( i i ) E f f e c t o f Aging on the Absorption Bands of NaCl TABLE 2 Obtained wi th the NaCl Specimen. Absorpt ion Peaks O r i g i n a l (mi l l imicron) Developed i n 3 Days (mi l l imicron) M R F * 730 600 450 360 450 360 730 612 189 I f the R band Is In fac t a group of unresolved peaks corresponding to those of A , then the s h i f t i n the l oca t ion of the maximum should be exp l i cab le on the bas i s o f the behaviour of group ACR^, R^, K(. peaks), and group B ( R g , Ry, R^ peaks) at room temperature. According to Y a g i , group B enhances at low temperatures. T h i s would cause a s h i f t i n the maximmof the * R band towards shorter wavelengths. However, s ince the e f fec t observed i s i n the opposite d i r e c t i o n , i t i s concluded that the R band i n A i s most probably a band corresponding to c o l l o i d a l sodium band. The s h i f t i n the l o c a t i o n o f the R peak may be caused by the increas ing c o l l o i d a l s i ze of the dispersed sodium meta l , on coagulat ion . On prolonged exposure to the h igh frequency d ischarge , par t o f a p o l y c r y s t a l l i n e sodium c h l o r i d e sample developed a deep v i o l e t c o l o r , whereas the other par t remained yel low as be fore . These c r y s t a l s were separated in to two groups according to t h e i r c o l o r and the time required for b leaching of these co lors at room temperature was found v i s u a l l y to be about three weeks, the v i o l e t c o l o r being more pers i s t en t than the ye l low. During the t r a n s i t i o n from yel low to v i o l e t c o l o r , the c r y s t a l s appeared to pass through a c o l o r l e s s s t a t e . No attempt has yet been made to f i n d any absorption band which may be present during t h i s stage. 190 ( i i i ) V i s u a l Observations on C o l o r i n g of Other Compounds The behaviour of other i o n i c compounds on exposure to the h igh frequency discharge , as observed v i s u a l l y , i s given i n Table (3) . TABLE 3 V i s u a l observations on the development of c o l o r i n i o n i c c r y s t a l s on exposure to h igh frequency discharge . N - Normal exposure - 5 minutes. L - Long exposure - more than 5 minutes. S - Short exposure - l e s s than 5 minutes. Specimen Exposure Developed Color S t a b i l i t y L i C l KF KC1 KBr NaF S or N L N L N L N L N L Green Powder White Pink •*? V i o l e t then B l u i s h Green L i g h t Blue C o l o r l e s s L i g h t Green Co lor l e s s Orange Pink Green Yellow T r a n s i t o r y More than a month -More than a few days About f i v e minutes About f i v e minutes A few minutes More than a few days • . . c o n t i n u e d TABLE 3 (Continued) 191 Specimen Exposure Developed Color S t a b i l i t y NaCl N L L i g h t Yellow-Brown A few weeks Deep V i o l e t More than three weeks NaBr N L L i g h t Blue Pink Orange A few seconds A few days N i t r a t e , s u l f a t e , carbonate, acetate , oxalate o f sodium, and potassium d i d not show any v i s u a l changes except a very t r a n s i -The mechanism of the formation of c o l o r centers i n i o n i c c r y s t a l s on exposure to h igh frequency discharge i s very l i k e l y to be a complicated one, s ince there are severa l pos s ib l e fac tors involved i n the product ion o f these centers . Some o f these are discussed below. High energy p a r t i c l e s , c o n s t i t u t i n g the discharge glow, bombard the c r y s t a l s , and during i n e l a s t i c c o l l i s i o n s t rans fer s u f f i c i e n t energy to the c r y s t a l ions to produce c o l o r centers . 6 The a l t e r n a t i n g f i e l d of (~20,000 v o l t s and 10 c y c l e s / = sec . frequency) may ag i ta te the c r y s t a l ions down to a cons ider-able depth, thereby increas ing the chances of evaporation from the surface . I f one of the i o n i c species i s evaporated tory green co lor i n the case of l ^ C O ^ . 3. Discuss ion 192 p r e f e r e n t i a l l y and pumped out , l eav ing a s to ich iometr ic excess of the other i o n , i t may r e s u l t i n the formation of c o l o r centers . The o s c i l l a t i n g f i e l d may introduce defects i n excess o f t h e i r e q u i l i b r i u m number at room temperature. 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