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Physico chemical studies of the reaction of strontium choride with fluorine Rantamaa, Anssi Kalervo 1969

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PHYSICO CHEMICAL STUDIES OF THE REACTION OF STRONTIUM CHLORIDE WITH FLUORINE hy ANSSI KALERVO RANTAMAA B.Sc, University of British Columbia, 1964 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF M.Sc. in the Department of Chemistry We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA September, 1969 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of Brit ish Columbia, I agree that the Library shall make it freely available for reference and Study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the Head of my Department or by his representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of The University of Brit ish Columbia Vancouver 8, Canada Date QyU£ - /£~ / 9 f i i ABSTRACT The kinetics of the reaction of solid strontium chloride with fluorine gas have been studied by gravimetric, thermometric, and microphotographic methods. ESR and X-ray crystallography were used to study the products. The reaction commenced after an induction period of 1 to 10 minutes. On single crystal specimens studied microscopically, formation and growth of nuclei of SrFg thereafter occupied several minutes before the nuclei coalesced to form a continuous SrF 2 layer. By thermometric studies on a polycrystalline boule of reactant on a thermocouple, the extent of reaction during the 4 nucleation period was found to be proportional to t , suggesting 2 nuclei formed proportional to t and subsequent two-dimensional growth at constant linear rate. On single crystal specimens, 2 microphotography showed a t law for number of nuclei only for one specimen with a rough surface. For smooth surfaces, number of nuclei was generally constant, but linear growth was confirmed in many cases. Two growth rates were measured, an i n i t i a l rate -4 - l of 6.4 x 10 mm sec and a less reproducible rate to which a _ 3 transition sometimes occurred in later stages of 1.7 x 10 J mm sec~*. The nucleation was found to be non-activated and the change in rate was ascribed, together with an increase in the number of nuclei late in the nucleation period, to effects of mechanical strain. The development of the main reaction after establishment of a continuous reaction interface was followed gravimetrlcally, and i l l found to obey the Ginstling-Brounshtein equation for diffusion through a spherical shell of solid reaction product, having a sharp interface with the reactant. A lower limit of 2 x 10"^ 2 -1 cm sec A was found for the diffusion coefficient, suggesting that the process i s gaseous diffusion in cracks in the product layer. The c r y s t a l l l n i t y of the product depended on the rate of reaction. For rapid, high-temperature reaction, the product gave a powder diffraction pattern, but for a sample reacted more slowly with a controlled supply of Fg, the product was found to be essentially a single crystal (diffuse diffraction spots indicating ranges of disorientation of no more than about 5°) with the same crystallographic orientation as the reactant. Attempts to locate the ESR signal found in earlier work were only partially successful, but suggest that the signal is largely in the product phase, and that i t represents a by-product rather than a reaction intermediate. iv TABLE OF CONTENTS Page TITLE PAGE i ABSTRACT . 1 1 TABLE OF CONTENTS iv LIST OF FIGURES v LIST OF GRAPHS v l ACKNOWLEDGMENT v i i INTRODUCTION 1 EXPERIMENTAL 1 0 Apparatus and Instruments . . . . . . 1 0 Materials 14 Procedure 1 5 RESULTS AND DISCUSSION 17 Reaction Vessels. 17 Typical Course of a Reaction 17 Products 2 0 Nucleation Period 2 7 Main Reaction Period 3 9 Location of ESR Signal 4 7 Reaction Mechanism 48 BIBLIOGRAPHY 5 1 APPENDIX 5 3 V LIST OF FIGURES Page Figure 1. ESR spectra obtained from F 2 treated S r C l 2 (previous work) 7 Figure 2. Computed spectrum of S r C l 2 defect (previous work) 8 Figure 3 . Quartz balance and gravimetric apparatus. . 11 Figure 4. Zone refiner 12 Figure 5. Illustration of reaction stages 18 Figure 6. Samples from mlcrophotographic run 19 Figure 7. Oscillation pictures of 22 (a) SrClg single crystal (partially hydrated) (b) SrFg product from slow reaction (c) SrF 2 product from fast reaction Figure 8. Bernal chart for interpretation of oscillation photographs 2 3 Figure 9. Oscillation photograph of block containing reactant and product layers 24 Figure 10. Mutually compatible angles between a line and four threefold axes (line perpendicular to one of the axes) 26 v i LIST OF GRAPHS Page Graph 1. Nuclear radii versus time , . . 28 Graph 2. Nuclear radii versus time (illustrating change in rate) 29 Graph 3. Nuclear radii versus time (illustrating similar growth rate for new nuclei) 30 Graph 4. Nuclear radius versus time for growth along scratch. . 3 2 Graph 5 . Second and third roots of number of nuclei versus time for smooth crystal face 3 5 Graph 6. Square root of number of nuclei versus time for badly scratched crystal face 3 6 Graph 7. Temperature versus time for thermometric experiment 38 Graph 8. Temperature versus time for nucleation period only (thermometric experiment) 40 Graph 9. Corrected temperature versus time for nucleation period 4 i Graph 10. Fraction reacted versus time for gravimetric reaction 43 Graph 11. Ginstllng-Brounshtein function versus time for gravimetric reaction 44 Graph 12. Mass" 2^ versus the Ginstllng-Brounshtein constant for gravimetric reaction 46 v l i ACKNOWLEDGMENT I would like to thank Professor L. G. Harrison, my research director, for his valuable advice and guidance throughout this work. I N T R O D U C T I O N INTRODUCTION Solid phase reactions have several features which sharply distinguish them from reactions in liquid or gas phase. The concept of concentration has less meaning since the reactant is completelyMestroyed, there being no continuous variation in the concentration of the reactant. Induction and nucleation periods are also more generally Important to the f i e l d of the solid state kinetics than in other phases. Diffusion plays an important part in solid state reactions since many reactions depend on mass transport. Diffusion in many solids i s only possible due to another peculiarity of solids, the presence of defects. The oxidation of a l k a l i halides by halogens has been extensively studied in this lab with an emphasis towards discovering the role in reaction mechanisms of electronic defects known as "colour centres". In the present work, however, studies relating to nuc-leation and diffusion processes have been more extensive than those concerned with defect structure. Studies of nucleation in solids have been concerned mainly with decomposition of metal azldes, oxalates and other f a i r l y 1 2 3 4 5 6 7 unstable species,' * J as well as dehydration of alums.* J % , f Nucleation has been found to obey a power law of the form N = kt^ where N i s the number of nuclei, k is a constant and t is the time and/S an integer. Commonly observed values of/5 are 1, 2 8 and 3 . The usual explanation given is that for a one step nucleation/^ = 1, and for a two step nucleation^ = 2, etc. Here, "two-step" may imply either the formation of an intermed-2 late (concentration proportional to time) which is then converted to a nucleus at a rate proportional to i t s concentration, or, as in Bagdassarlan's mechanism, the formation of two identical Intermediates which combine to form a nucleus. The linear growth rate of the nuclei has in most cases been found to be constant.' The overall rate law is thus a power law whose order depends on the number of nucleation steps and whether the nucleus is growing in two or three dimensions. For example, a two step nucleation followed by a two dimensional growth would give for the overall rate law* extent of reaction 4 proportional to t . An approximate diffusion law for transport through a reacting layer, where a sharp interface is formed, was derived by o Jander for a spherical particle. Consider a sphere, i n i t i a l radius b, reacting to give a sharp interface at radius a. The diffusing species has concentration at b and 0 at a. Then, i f M is the amount of diffusing species crossing the reacted zone by time t and V"m i t s molar volume in the product, by Pick's Law dM = 4TT a2D (dc) dt <3r>r=a where D « diffusion coefficient. From the geometry of the situation (1) 3 1 M » 4 77 (b -a-*) ( 2) 3 v m and 2 dM s -4TT a da V M Combining (l) and (3) (3) Jander used the quasi-stationary state approximation in the form C (r-a) b-a (5) so that (<9C) = C, ( 3 r ) « bTa Integrating gives ^ ( b - a ) d a = -j2DQlvmdt ^) -b 2 + ab - a 2 = - D C ^ t (8) and Introducing the fraction reacted 3 into (8) gives c* = l - a-2 D G 1V mt = ( i - ( l - o C ) l / 3 ) 2 b 2 (9) (10) which is the Jander equation. The flaw in the equation l i e s in the expression for C used to derive i t . The C used Is the same as that for a concentration gradient across a semi-infinite solid with a plane surface. Thus the Jander equation is only useful for small since i t neglects convergence of diffusion paths near the centre of the sphere. Glnstling and Brounshtein 1 0 used the correct quasi-stationary expression for G in a spherical shell C = ^ ( r - a ) r(b-a) so that (3C) = Cjb O r ) r = a aXbTa). <l2> 4-Substituting into (4) and integrating yields /a 2 D c l V M t = 7b ^ a / b~ a) d a a n d substituting a = b(l - c<)l/3 gives 1 - 2 < - (l-o<.)?/?,2DC1Vmt ( 1 3 ) This is the Ginstllng-Brounshtein equation. It holds for a l l values of <=>(. i f the quasi-stationary state approximation is valid, for which the required condition is c±Vm «' 1 1 1 . . Despite the fact that the Jander equation has been shown to be an approximation to the Ginstllng-Brounshtein, both continue 12 to be used as equivalent along with the Dunwald-Wagner equation oC = 1 - ( 6 ) 2 y (l ) exp (-Dn2tTT2/b2) (TT) £Sl( n2) which, as pointed out by Harrison^ refers to diffusion occurring without a sharp interface, as in the formation of a spinel. Diffusion cannot occur, at least at a reasonable rate, in a perfect ionic crystal because the activation energy for diffusion via a "change places" mechanism is too high. The need for some sort of la t t i c e defects to allow diffusion to occur at observed rates was realized in the 1930's by Frenkel, Schottky, Koch, Wagner and Smekal who proposed various different mechanisms for diffusion. The union of their theories s t i l l gives the best overall picture when mechanisms for diffusion in an ionic crystal are considered. Lattice defects are of two types, large-scale defects and point defects. The "Smekal crack", (later shown to correspond to a dislocation line) an example of the former, allowed for 5 diffusion along cracks in the crystal. Point defects often consist of, or are associated with vacancies in the anion or cation l a t t i c e combined either with vacancies in the complemen-tary la t t i c e or with i n t e r s t i t i a l s (to maintain electrical neutrality). The Prenkel defect is a cation vacancy combined with a cation i n t e r s t i t i a l . The Schottky defect is a cation vacancy balanced by an anion vacancy. Vacancies resulting from Frenkel or Schottky defects are often in equilibrium and their number thus temperature dependent. Lattice vacancies also result from impurity ions of different charge from the ions replaced. Their number is fixed by the impurity content. , Though a l l these effects play a part in diffusion processes in ionic crystals, often one type of temperature dependent defect is found to predominate in a given l a t t i c e . In alk a l i halides the Schottky defect predominates while in silver halides the Frenkel defect i s more important. In alkaline earth halides the antl-Frenkel defect i s most common (the Frenkel defect was post-ulated for cation lattice disorder, thus "anti" refers to the anion l a t t i c e ) . The treatment of ionic crystals with X-rays and UV radiation as well as by chemical means results In the formation of "colour centres". The subject of colour centres is a f i e l d 14 in i t s e l f and has been reviewed by Schulman and Compton. Briefly, colour centres are electronic defects which have absorption bands in the visible and UV regions. Despite exten-sive work in this f i e l d only one centre, the F-centre, an electron in an anion vacancy, was conclusively identified (although, many structures were proposed for various centres) 6 u n t i l the advent of electron spin resonance spectroscopy (ESR) in the early 1 9 5 0 , s . 15 16 17 18 Kanzlg et a l ' ' used ESR to characterize electron deficient defects produced by low temperature X-irradlatlon of a l k a l i halides. The possibility that electronic defects might play the role of intermediates In chemical reactions had been mentioned by in 20 2 1 Garner and Haycock, Thomas and Tompkins, Mitchell and 2 2 Harrison. 23 Harrison et a l J in the study of the reactions KC1/F2 and NaCl/F2, found electronic defects being formed. The electron spin resonance spectra were consistent xfith an electron deficient centre, the H-centre (a CI2 " molecule-Ion in a single anion s i t e ) . Although the analogy between a l k a l i halides and alkaline earth halides i s not a close one, (besides the difference between predominant defects, conductivity and transference experiments show the current in the former almost completely due to cations, and due to anions in the latter) a search of reactions of alkaline earth chlorides with fluorine, for ESR active defects, was carried out. An ESR signal was found in the course of the reaction SrCl2/F2 whose intensity increased as the reaction proceeded. 2k The spectrum was found (see figures 1 & 2 ) to be consistent with the model of a single chlorine atom occupying various positions along a fourfold axis of S r C l 2 , between two anion sites. The presence of orientation dependent spectra and the absence of an ESR signal in the unreacted S r C l 2 led to the conclusion that the defect was concentrated at the reaction 1 I I 1 1 1 — 3150 3200 3250 3300 3350 3400 H (gauss) interface and that oxidation of chloride ions in the S r C l 2 was occurring slightly ahead of the reaction interface. There were apparent inconsistencies in the previous work* -i f the signal were present only at the reaction interface i t should decrease in intensity (not increase) as the reaction continues; figure 1(C) is a single crystal spectrum, but shows "powder" lineshapes at A and D. These features as well as the lack of kinetic information on this type of reaction was the motivation for this work whose purpose is to study the kinetics and mechanism of the reaction S r C l 2 + P 2 —»• SrF 2 + C1F. E X P E R I.-MENTAL 10 EXPERIMENTAL GAS HANDLING SYSTEM The fluorine was handled in glass and s i l i c a systems using stopcocks greased with kel - F. Right angle stopcocks were used to counteract partially kel - F*s tendency to streak. The disposal system was a section of 2 5 mm glass tubing approximately 1 0 0 cm long, f i l l e d with 80 mesh soda lime and evacuated with a Welch Duo Seal mechanical pump. The high vacuum side consisted of a Balzer o i l diffusion pump using silicone o i l (Dow Corning 7 0 3 Fluid) which gives only gaseous products i f accidentally reacted with halogens, backed by a Welch mechanical pump. GRAVIMETRIC APPARATUS Because of lack of space near the fluorine supply a portable system was used to carry out experiments using the quartz spiral balance apparatus (figure 3 ) » The quartz balance was obtained from Microchemlcal Specialties, Berkeley, and had an extension of 1 0 cm/gm up to i t s capacity of 2 gms. Changes in weight could be observed by sighting on the fine index arm with a cathetometer. ZONE REFINER The zone refiner was a horizontal type constructed in this laboratory by R.W. Burton. The heating elements were two separate windings of Chromel A wire imbedded in asbestos surrounding the hollow core (see figure 4 ) . One element ran the length of the entire furnace while the other was close-sound near the centre. Each was individually controlled by a variac. The sample was contained in a graphite boat (made from 1 " diameter rod of graph-i-tite G obtained from Basic Carbon Corp., 11 F i g . 3 Quartz balance and gravimetric apparatus 1 3 Sanborn, N.Y.). The graphite was contained in s i l i c a tubing through which dry was passed. The furnace was chain-driven by an electric motor turning one third of a revolution per hour and geared to give a speed of approximately one inch per hour. After a zone pass, the furnace was returned to i t s original position by a lead weight attached to one end of the furnace via a pulley. The operating temperature was ^  890° at the centre and 830° at the ends. PHOTOGRAPHY Photographs of the crystals were taken by two different but roughly equivalent methods. The use of a bellows with a camera gave a magnification of about 8X, which when printed using an enlarger gave overall magnification between 3 0 X and 40X. The f i t t i n g of a macrolens to a Bausch and Lomb microscope allowed focussing inside the optical c e l l and a camera was attached directly to the microscope using an adapter. The overall magnification was the same as by the other method. Lighting from below was supplied by a lamp with a 100 watt bulb. Tri-X 3 5 mm film, shot at f 2 . 8 at 1 / 1 2 5 s e c , developed in mycrodol-X, and enlarged onto F - 4 kodabromide paper, was used. ELECTRON SPIN RESONANCE ESR signals were detected with a Varian E 3 spectrometer with a 4-inch magnet. THERMOCOUPLES Thermocouples, of Pt with Pt 10$ Rh, were read using a Honeywell dual range potentiometer. 1 4 X-RAY DIFFRACTION X-ray powder photographs were taken using a Debye-Scherrer camera of diameter 1 4 . 3 cm and nickel filtered copper radiation. A camera of 5 « 7 3 cm diameter was used to take oscillation pictures of the reactant and product. The crystallographic orientation of the cleavage plane of the crystal was checked using a precession camera. MATERIALS The fluorine was obtained from Matheson Co. (quoted 98$ pure) and used after passing through a sodium fluoride trap (to remove HF). The fluorine was stored up to two weeks in a 5 1 . glass bulb with no detectable change in the ensuing reactions. The strontium chloride used came from three different sources. Nominally pure S r C l 2 single crystals were supplied by Dr. J.A. Morrison (prepared by the Bridgman Stockbarger method). Crystals were prepared by melting S r C l 2 in a Pt crucible (start-ing material SrCl 2*6H 2 0 B&A reagent) using a Meker burner or an Induction furnace. These samples were cooled slowly in a i r to room temperature but were invariably cloudy and polycrystalline. The samples used were taken from near the centre of the poly-crystalline mass. SrClg crystals were also prepared by heating S r C l 2 » 6 H 2 0 (B&A reagent) at 1 1 0 ° u n t i l anhydrous, then mixing in 1% by weight of FbClg and zone refining in the apparatus already described. After three zone passes the samples were cooled to room temperature (a period of 8 to 1 2 hours) in a dry N 2 atmos-phere and transferred to a dry box. The central section of the samples was transparent although the ends were cloudy. One 15 cleavage plane, identified by X-ray crystallography as the (111) face, could easily be found in the transparent material. PROCEDURE Gravimetric The sample was introduced onto the quartz pan and the system evacuated without delay. After achieving a vacuum of 10~5 mm Hg, fluorine was introduced at a pressure of 29.3 cm and room temperature ( 2 3 ° ) . Most of the samples were cut from the slowly cooled melt. For comparison, reactions were also performed using SrClg crystals prepared by the Bridgman Stockbarger method, and crystals prepared in the zone refiner. Sample sizes ranged from 100 mg to 900 mg. Thermometrie Several layers of S r C l 2 were placed on a Pt/Pt 10% Rh thermocouple by dipping into molten S r C l 2 . Using the same i n i t i a l conditions as for gravimetric runs (23 .9 cm F 2 and 23°C) the temperature inside the reactant was determined during i t s reaction with fluorine in a 2 1. bulb. In most cases, this technique was successful, but in one or two experiments, the temperature rose sufficiently to trigger reaction of the thermo-25 couple wires with F 2 (probably above 650°C). Mi crophotographlc A sample of zone refined S r C l 2 was cleaved in the dry box and placed in a quartz c e l l with optical windows while s t i l l in the dry box. The c e l l was attached to main vacuum system and evacuated to 10"^ mm Hg. After introduction of 29.3 cm F ? at RT (23°C) the formation of nuclei on the (111) face was observed through the camera and pictures were taken at appropriate intervals. For comparison one reaction was done using SrClg prepared by the Bridgman Stockbarger method. The reactions were followed to the end of the nucleation period at which time the sample became completely opaque. Electron Spin Resonance Zone refined SrClg single crystals were exposed to 29 .3 cm of F 2 at RT (23°C) in the quartz optical c e l l for varying periods up to 3 minutes after which the Fg was pumped out, the sample transferred in a i r and the ESR spectra were taken. An attempt was made to determine quantitatively the distribution of the ESR signal in a partly reacted crystal by f i r s t s l i c i n g i t in half, and gripping the unreacted portion, shaving off portions of the reacted sample and measuring the intensity of the ESR signal. The amount shaved off was determined by focussing on the surface with a microscope with a very small focal range. The surface was shaved off by gently rubbing on a sheet of ground glass. Unfortunately the reacted sample crumbled even under these circumstances. ESR spectra of zone refined crystals, reacted to completion in the 2 1. bulb and the optical c e l l , were also taken. R E S U L T S A N D , D I S C U S S I O N 17 RESULTS AND DISCUSSION REACTION VESSELS Reactions were carried out in two different vessels» (a) a two l i t r e bulb (see figure 3 ) . which contained sufficient F 2 for 100$ reaction, (b) an optical c e l l in which, though i t was connected to an ample supply of F 2 through 12 mm glass tubing, the rate of reaction would be governed by gaseous diffusion during the main part of the reaction. The optical c e l l was used mainly to study early stages of the reaction, which probably proceed at similar rates in (a) and (b). TYPICAL COURSE OF A REACTION The course of the reaction can be s p l i t into four main stages* (see figure 5) (a) An induction period - no change observed by any method used. (1 - 10 min.) (b) A nucleation period - ( 5 - 1 0 min. from the end of the induction period) u n t i l the surface of the sample was completely covered by a layer of SrF 2. This period has been studied by photographic observation of growing nuclei (see figures 5 & 6), and by thermometry in separate experiments which necessarily used differently prepared S r C l 2 , so that no precise correlation i s possible. It is f a i r l y clear, however, that the period in which separate visible nuclei begin to grow and coalesce into a continuous layer of SrF 2 corresponds roughly to the period in which a temperature rise from room 18 F i g . 5 I l l u s t r a t i o n of reaction stages TIME -19 F i g . 6 Samples from microphotographlc run 2 0 temperature to ^ 60°C i s observed. In gravimetric experiments, no weight decrease;is detected during this period, (ie - less than 1% total reaction takes place. (c) A period of rapid reaction occurs at the end of the nucleation period and i s marked by a rapid rise in temperature to ^  600°C. This period was followed quantitatively in the gravimetric experiments, and was found to obey a kineticllaw for a diffusion-controlled reaction up to at least 90$ completion. In thermometric experiments, the temperature could be measured up to 600°C but no attempt was made to derive kinetic results from these high temperatures. (d) A cooling period - (lasting approx. 1 0 min. after the highest temperature recorded) followed thermomet-r l c a l l y to confirm Newton's Law of Cooling for the temperature range corresponding to (b) and thus correct for heat loss In stage (b). PRODUCTS The fu l l y reacted product from the 2 1 . bulb was white and coherent though i t crumbled upon handling. Fully reacted samples from the optical c e l l were similar except for a yellowish t i n t . Samples not allowed to react to completion showed a sharp inter-face between reactant and product. The loss in weight corres-ponded to the difference in formula weights of SrClg and SrFg. X-ray powder photography also indicated that SrF 2 was the product. A simple oscillation photograph of a piece of reacted 21 material showed the reacted material to have some single crystal character, to an extent apparently dependent on the rate of reaction. Material reacted in the 2 1. bulb was almost a powder, while samples reacted in the optical c e l l showed no powder lines although the single crystal spots were quite diffuse (see figure 7 ) . The relative orientations of the S r C l 2 and SrF 2 lattices were found by the following method. A partly-reacted sample was cut so that i t consisted of a single roughly rectangular block of SrF 2 attached to a similar block of SrClg. The reaction interface was parallel to a cleavage plane of the original S r C l 2 crystal. The sample was mounted so that the axis of a cylin-d r i c a l camera lay in the plane of the reaction interface. A diffraction photograph was taken for a rotation of about 300° about this axis (the available apparatus did not permit a comp-lete 360° rotation). In such a photograph, a l l points corresponding to planes at the same angle to the axis of rotation must l i e along a figure-of-eight shaped curve. These curves are shown in figure 8, reproduced from Buerger, X-ray Crystallography, P. 152. The angle marked on each curve is the angle between the axis of rotation and the normal to the plane of reflection. In the present work, the prominent reflections which display the relative orientations of the lattices are a l l from ( i l l ) or (222) planes, and the normals to these are the three-fold symmetry axes of the crystal, and are in four directions at the tetrahedral angle (109°28' or i t s supplement 70°32 ' ) to each other. A diffraction photograph i s shown in figure 9 . On the 22 Fig. 7 Oscillation pictures of (a) S r C l 2 single crystal (partially hydrated) (b) SrF 2 product from slow reaction (c) StF0 product from fast reaction 23 F i g . 8 B e r n a l c h a r t f o r i n t e r p r e t a t i o n of o s c i l l a t i o n photographs F i g . 9 2k O s c i l l a t i o n photograph of block containing reactant and product layers 25 horizontal line corresponding to /s?= 90° (compare figure 8 ) , there appears an intense spot from S r C l 2 and more diffuse spot from SrF 2 (marked on figure 8 as a small cross and short curve). The diffraction angles for these spots correspond to the separ-ation of ( i l l ) planes in the respective la t t i c e s . These data confirm that the cleavage plane which i s the reaction interface in this sample is a ( i l l ) plane of both la t t i c e s . (There appears to be an error of about 5° in the mounting of the crystal. The features appear at 85° rather than 9 0 ° ) . The other prominent correlations occur for diffraction angles corresponding to the (222) separation, and indicating values of about 23° and 55° (again, for both l a t t i c e s ) . These together with f = 90° already mentioned, are mutually compatible values for the angles between a fixed axis and a set of four three-fold axes (see Appendix and figure 1 0 ) . The photograph shows, however, some much fainter features associated with reflections from (111) and (222) planes at angles which are not mutually compatible to the set already mentioned. In particular, both S r C l 2 and SrF 2 show a (111) reflection at 1 5 ° . This i s s t i l l compatible with f~ 85° , hut not with the other values mentioned above ( 1 5 ° and 25° are obviously incompat-ible when the angle between any two of the three-fold axes i s 7 0 ° 3 2 ' ) . This suggests that the original S r C l 2 crystal may have a small portion separated from the rest by a large angle (10 -1 5 ° ) t i l t boundary, the two portions having, however, a cleavage plane in common (the reaction interface). It is concluded that the SrF 2 in the sample i s oriented in the same sense as the S r C l 9 crystal from which i t grew. Topotaxy 26 Fig. 10 Mutually compatible angles between a line and four threefold axes (line perpendicular to one of the axes) 2? (the phenomenon in which a single crystal product is formed from the reaction of a single crystal) has been previously observed 26 by Borom and Pabst in the pyrohydrolysis of MgFg. NUCLEATION PERIOD Photographic Studies The kinetics of the nucleation period were followed by measuring the 8 " x 10" prints of pictures taken of the reacting crystal face. Overall enlargement was found by measuring the reacted crystal and comparing with the prints. Magnification varied from 26X to 42X since the size of the original crystal determined the degree of enlargement possible on 8 " x 10" prints. After an induction period, which ranged from 1 to 10 minutes, several irregular nuclei became visible on the surface of the crystal. The nuclei were found on the edge of the crystal or at a prominent scratch on the face of the crystal. The growth of these nuclei constituted the main part of the nucleation period. Near the end of the nucleation period, however, new nuclei were formed, mostly near the existing large nuclei. These small nuclei were mostly circular although some had hexagonal features (to be expected on a ( i l l ) face). In some of the runs a uniform and rapid darkening of the crystal was observed during the induction period. No explanation has been devised for this. Nuclear radius was measured as a function of time for individual nuclei in the different runs. Typical runs are shown in graphs 1, 2 and 3 . In any one run, the growth rate of a l l 28 Graph 1 Nuclear r a d i i versus time TIME (min.) 29 Graph 2 Nuclear radii versus time (illustrating change in rate) 8 9 TIME (min.) 30 Graph 3 Nuclear radii versus time (illustrating similar growth rate for new nuclei) J TIME (min.) 31 nuclei was approximately the same at the same time. The rate of growth Increases near the end of the runs. Two types of behaviour were found in different runs? in one the rate increases steadily throughout the run (graph 1), and in the other the rate changes sharply and two linear rates are apparent (graphs 2 and 3). In graph 3» points at 4.8 and 5»6 minutes are shown dotted because the photographs from which they were measured were slightly out of focus. These curves, however, give one of the best available illustrations of formation of new nuclei after the change in growth rate of the original nuclei. The new and old nuclei evidently grow at the same rate. In some cases the experimental points would allow the drawing of either a curve or two straight lines. With some individual exceptions, the i n i t i a l rate of nuclear growth was found to be 6.4 + 1 x 10"^ mm sec""1 (the i n i t i a l curvature is very slight). Where a sharp transition to a higher linear growth rate was observed, i t s value was less reproducible than the I n i t i a l rate and equal to 1.7 + 0.5 x 10"^ mm sec"**. One nucleus was observed to grow at an accelerated rate along a crack u n t i l the leading edge of the nucleus became rounded (see graph 4). A l l runs but one were made using zone refined SrClgj the exception was a run made using SrClg prepared by the Brldgman Stockbarger method. The rate of growth of most of the nuclei was found to be comparable to the rates found in other samples. One nucleus, however, was found to be growing at a very slow rate. More runs would be needed to confirm the occurrence of 32 Graph 4 Nuclear radius versus time for growth along scratch 33 this different behaviour. —4 —i The i n i t i a l rate of nuclear growth, 6.4 x 10 mm sec , which translates to ^ 2 x 10^ atomic spaclngs per second which is 10~9lJ (where O is the vibration frequency, ^ 10 1 2 s e c - 1 ) . The factor 10"*9 i s too small to be accounted for reasonably by an entropy of activation effect, and must be accounted for by one or both of the following!-(a) activation energy for the growth process (b) growth occurring only at sites which are present in very low concentration (ie - surface vacancies or kinks in growth steps). A decision between the two is not allowed for by present evidence. As an activation energy factor close to room temperature, -9 the factor 10 7 indicates 12.3 k cal/mole. If the growth curves are interpreted as continuous curves with slope governed entirely by temperature, then a similar value can be obtained on the assumption that the rise in temperature is about 15°t which is the average temperature rise observed in thermometric experiments during the nucleation period. Temperature dependence, however, does not explain the obser-vance of two distinct rates of growth as evident in graph 3» The transition from the I n i t i a l growth rate could readily be due to a sudden production of vacancies or kinks as a means of relieving mechanical stresses which build up in the remaining unreacted surface as the SrClg lattice is converted to the more closely spaced SrFg l a t t i c e . Such a process would be quite l i k e l y to produce new nucleation sites. In fact, the acceleration of growth of the original nuclei was invariably accompanied by the 3^ appearance of numerous new nuclei. Local regions of differing strain are also somewhat more plausible than local temperature variations (particularly since thermometric experiments could be interpreted well on the basis of essentially uniform temperature rise throughout the crystal). Also, whereas local temperature variations might be expected to be more or less random within certain limits, giving growth curves with many different slopes, the f i n a l rate of reaction of nuclei did not (as indicated earlier) vary within very wide limits. The hypothesis of a breakdown caused by mechanical stress is consistent with this, since i t would occur at a definite c r i t i c a l stress in a l l cases and probably lead to a similar concentration of newly-created defects in a l l cases. The fact that some growth plots were definitely curved and others consisted of two straight lines, although a l l had similar i n i t i a l and f i n a l slopes suggests that defects were not produced equally sharply by r e l i e f of stress in a l l cases. The difference cannot however be correlated with any other experimental variable in this work and the reason for i t is thus unknown. In 8 out of 9 experiments performed the number of nuclei remained constant from the beginning of the nucleation period u n t i l the rate of nuclear growth Increased (in every case the main reaction began no more than thirty seconds after the increase in rate). Where enough observations could be made the rate of Increase of the number of nuclei at this point was very rapid (graph 5)» In the other experiment the number of nuclei 2 increased throughout the nucleation at a rate proportional to t (see graph 6), suggesting that formation of nuclei i s a two step 35 Graph 5 Second and t h i r d roots of number of nuclei versus time f o r smooth c r y s t a l face 1 I I I I I I L 12.0 12.1 12.2 12.3 12.4 12.5 12.6 TIME (min.) 36 Graph 6 Square root of number of nuclei versus time for badly scratched crystal face TIME (min.) 3 7 process. This exception involved a crystal the surface of which was notably scratched. It would appear that nucleation on a smooth surface is very unlikely and occurs only at imperfections in the surface such as scratches, impurities and regions of stress or local high temperature. A dislocation line by i t s e l f seems not to be a l i k e l y nucleation site since i t i s very li k e l y that a considerable number of dislocation lines cut a given surface. Thermometrlc Studies By dipping the junction of a Pt/Pt 10% Rh thermocouple into molten S r C l 2 , i t was possible to coat the thermocouple with varying amounts of S r C l 2 . The SrClg was then reacted in the 2 1. bulb while the temperature was measured with a potentiometer. A typical temperature versus time plot is shown in graph 7 . Despite the difference in types of S r C l 2 used, the course of the reaction as followed thermometrically is very similar to the course of the reaction as followed photographically. In both, a nonreproducible induction period of the same order of magnitude is present, followed by a nucleation period which can also be visually observed during the thermometrlc runs. During the nucleation period the temperature increases slowly to a widely variable f i n a l value ( 3 6 - 80°C). The rise in temperature was so rapid at the end of the nucleation period (when the sample was completely covered with a layer of SrF 2), that the actual value of the last temperature observed varied a great deal. Once the surface was covered the temperature rose rapidly to 5 5 0 -650°C. The cooling curve was followed down to room temperature. 38 39 Since the cooling curve from approximately 60°C to room temper-ature was found to obey Newton's Law of Cooling the temperature readings during the nucleation period could be corrected for heat loss due to convection to give a "corrected adiabatic temperature" which should be linearly related to the extent of reaction. A "corrected adiabatic temperature" versus time plot is shown in graph 8. This plot can be linearized by taking the fourth or f i f t h root of the temperature (see graph 9)• Some of the thermometric runs did not obey the power law. These runs were in every case faster than those obeying the power law. It seems lik e l y that in these cases the thermocouple located at the centre of the sample does not register a true average temperature for the whole reacting phase of these fast reactions. The observation that the temperature rise is proportional to t^ can be explained as number of nuclei being formed proportional 2 to t and subsequent two-dimensional growth of these nuclei. This interpretation is consistent with the photographic results If the behaviour of the exceptionally scratched crystal (as previously mentioned) i s the common behaviour for thermometric 2 runs. The t law is thus considered to arise only when many nucleation sites are available, which i s not the case for most photographic runs where observations are made on a single cleavage face with few scratches. The thermometric runs, on the other hand, involve almost spherical surfaces with many discon-tinuities between different crystal faces. MAIN REACTION PERIOD After the induction and nucleation periods the main part of the reaction could be observed gravimetrlcally. A typical run Is 40 Graph 8 Temperature versus time for nucleation period only (thermometric experiment) TIME (min.) 41 42 shown in graph 10. A run interrupted during this period was found to continue immediately upon reintroductlon of F 2 at approximately the same rate. Since the 2 1. bulb contained ample F 2 for completion of the reaction i t was quite li k e l y that the rate limiting process was diffusion through the solid. For spherical particles, with a constant diffusion coefficient D throughout the reaction, the appropriate rate law is the Ginstling-Brounshtein equation (equation 13. Introduction). This may be written where f G B = K Q B t (14) 1 - 2/3 oC - ( l - o C ) 2 / 3 = f ^ 2 D C l V m = KGB b 2 In these circumstances plots of f G B versus t should be linear. In the present work, some care was taken to choose particles which were close as possible to spherical} but i t is evident that there must be large temperature changes across the reaction zone in the course of the reaction, so that D might not be constant. Nevertheless plots of f G B against t were linear from 0.1 to = 0.9 (see graph 1 1 ) . K Q B can be related to the mass and density of the sample as followsi-4 Tfb = m 3 r , 2 _ .2/3 b = (3m) (4rrf ) thus 2/3 *GB = 2 D C l V m = 2 D C l V m (15) 43 44 Graph 11 Ginstllng-Brounshtein function versus time for gravimetric reaction 1 2 3 4 5 TIME (min.) ^5 - 2 / 3 and a plot of KGfi versus m should be linear. A reasonable linear relationship (see graph 12) i s obtained, with a fairly-wide scatter probably arising from the fact that many of the crystals were not very close to a spherical shape. (This plot is a moreftsensitive test of i n i t i a l shape than the plot of f _ , „ versus t in graph 11, since the greater part of the length of the line refers to quite late stages of the reaction, by which time the reaction interface may be smoother than the original outline of the crystal; note the values of << on the scale on the right of graph 1 1 ) . From the slope of the line in graph 12 and withp = 3«052 g o _ c 2 -1 cm -?, a value for DC^ Vm of 2 .0 x 10 J cm sec is found. Since the validity of the approximation by which the Ginstllng-Brounshtein equation i s derived implies that « 1, a lower limit for D is obtained (ie D » 2 .0 x 10"^ cm2 sec" 1). This is a very high value for the dlff u s i v i t y of any species in a solid. The rate-limiting diffusion step may involve transport of gases (F 2 inwards and C1F outwards) through pores in the polycrystalline SrF 2 layer or, i f the electron transfer takes place at the outer surface of the product layer, transport of F" in regions of rapid diffusion along intercrys-talllne boundaries. The latter possibility would also require the transport of electrons across the SrF 2 layer; there is no 2k evidence for such a process from the ESR studies, but absence of an ESB signal does not rule out the mechanism. In the case of gaseous diffusion, the dl f f u s i v i t y of C1F or F 2 is probably 2 1 about 0 . 3 cm sec x at the temperatures concerned, and is of course very sensitive to temperature. Channels for gas transport k7 across the reacting phase therefore need occupy no more than about 10"2$ of the cross-sectional area of the product layer to account for the observed rates of diffusion. If the process involves transport of ions, a maximum diff u s i v i t y (for zero activation energy) may be estimated as follows»- jump frequency of mobile species W -i^ e " E / k T where is 12 -1 a vibration frequency of order 10 sec . If a l l anions are mobile at a l l times, D = 1 ZW12 where Z is the number of nearest "E neighbours in the anion la t t i c e (Z = 6) and 1 is the nearest o neighbour spacing in the anion lattice (1 = 3-5 A ). Then D -3 2 _ i becomes approximately 10 cm sec , which is above the limit _ < p « of 2 x 10 J cm sec 1 . A mechanism involving ionic transport is thus just possible, but i t is evidently necessary that at least 1% of the ions can move with zero activation energy. This seems much less l i k e l y than the suggested mechanism in which gas-phase diffusion is the principal means of halogen transport across the reacted layer. LOCATION OF ESR SIGNAL Brief but repeated exposures of Fg to samples of SrClg single crystal did not result in ESR signals during the induction period. Weak broad signals were found once macroscopic nuclei had developed. Thus, either no radicals are produced during the induction period or their number is too small to detect. Four attempts to determine quantitatively the distribution of the ESR signal In a crystal reacted in the optical c e l l were unsuccessful because the reactant crumbled when being sectioned. Qualitatively, i t was observed that part of the ESR signal was 48 in the outer layers of the reacted region i f the reaction had been performed in the optical c e l l . In a separate experiment, a small crystal reacted to completion in the 2 1. bulb using an excess of Fg, showed no ESR signal. A similar crystal, exposed for several days to excess F 2 in the optical c e l l , (where the rate of reaction is limited by gaseous diffusion) displayed an orientation dependent ESR signal (with some powder-like features). 24 Gatton and Harrison had assumed that the defect must l i e in the S r C l 2 lattice since they expected the product of the highly exothermic reaction to be a powder. Simple oscillation photographs of S r C l 2 single crystal, SrF 2 from a sample reacted in the gravimetric apparatus (2 1. bulb), and SrF 2 from a sample reacted in the optical c e l l are shown in figure 7. Clearly, the rate of reaction is important in determining the nature of the product; the rapidly reacted sample being a randomly-oriented powder, while the slowly reacted sample has some single crystal character. The necessity for the defect to be in the S r C l 2 l a t t i c e is thus obviated. The lack of an ESR signal in the sample from the gravimetric apparatus is due either to high temperatures attained during the reaction, or the resultant powderlike product (as opposed to the sample reacted slowly, which was shown by X-ray analysis to have single crystal properties) which possibly has more channels for the escape of the defect. REACTION MECHANISM The overall reaction requires electron abstraction from Cl~ 49 (lattice) by F g with the formation of F" (lattice) and C1F. At suitable surface sites, this process might occur either in one step or in two steps with a C1F2"" Ion as an intermediate. The latter possibility i s one way of explaining the experimental behaviour which suggested a two-step nucleation process (graph 6 ) . On the other hand, nucleation may require the presence of two F~ ions on adjacent sites. In any case, i t is evident from the existence of an induction period, that suitable sites for nucleation are very sparsely distributed on the surface of the unreacted crystal. Evidence suggesting that such sites are produced in large numbers at a later stage by mechanical stress has already been discussed. For an electron transfer process occurring at room temperature, and therefore with an activation energy less than or approximately 0 . 5 eV, a position such as a kink site i s usually necessary to avoid the temporary removal of an electron from an anion site to a site which would be unfavourable by several eV. The main part of the reaction occurs in two sets of circumstances but the differences are probably in detail only. The reaction i n the 2 1. bulb was found to be diffusion _ c 2 -1 controlled with D greater than 2 x 10 J cm sec . This indicates a very low activation energy for diffusion through a solid (less than 0 . 3 eV) even at the temperatures attained (around 600°C). It seems more l i k e l y , in fact, that the diffusion is gaseous through pores in the product since the pores need comprise only 0.01$ of the cross-sectional area (assuming D for gas approximately 0 . 3 cm sec" A) to account for the high d l f f u s i v i t y . The mechanism is thus probably diffusion of F0 in 50 and C1F out. The reaction in the optical c e l l , like the work done by Catton, has a rate determined by gaseous diffusion in the glass tubing between the fluorine supply and the reaction. Unfortun-ately no thermometrlc runs were made in the optical c e l l , but i t seems reasonable to presume that these reactions must occur at lower temperatures than those in the 2 1. bulb. The structure of products from the optical c e l l was shown by X-ray studies to be much more ordered than the product from the 2 1. bulb, which was powderlike. The indications from ESR studies of the presence of CI atoms suggest an electron transfer process occurring over several atomic spacings, so that the CI i s not in an environment where i t can immediately react to form C1F. Such CI atoms are evidently not involved in a rate-determining step, since gaseous diffusion has been shown to be rate-determining, but i t is s t i l l not clear whether CI is a by-product of the reaction or an important intermediate. Evidence that CI is present throughout the reacted material suggests that i t i s a by-product. Another worker in this laboratory has recently obtained evidence suggesting that the ESR-actlve centre is actually C10 2, arising from OH" present as an impurity. 51 BIBLIOGRAPHY A. Wischin, Proc. Royal Soc, A172, 3 l 4 (1939). E.G. Prout and F.C. Tompkins, Trans. Far. Soc, 4 j i l48 (1947). W.E. Garner and H.R. Halles, Proc Royal Soc, A139, 576 (1933). W.E. Garner and W.E. Southon, J. Chem. Soc, 1705 (1935) . J.A. Cooper and W.E. Garner, Trans. Far. Soc, ^ 2, 1739 (1936). N.F.H. Bright and W.E. Garner, J . Chem. Soc, 1872 (1934). G.P. Acock, W.E. Garner, J . Milsted and H.J. Willavoys, Proc Royal Soc, Al89» 509 (19^7). W.E. Garner, P.W.M. Jacobs and F.C. Tompkins, Chemistry of the Solid State, edited W.E. Garner, Butterworths, London W. Jander, 2. anorg. allgem. Chem., 163. 1 (1927). A.M. Ginstling and B.O. Brounshtein, J. Appl. Chem., U.S.S.R., 2£, 1327 (1950). P.V. Danckwerts, Trans. Far. Soc, 46, 701 (1950). E.A. Giess, J. Am. Ceram. Soc, 46, 374 (1963). L.G. Harrison, Theory of Solid Phase Kinetics, from Comprehensive Chemical Kinetics, Vol. 2, edited C.H. Bamford and C.F.H. Tupper, Elsevier, Amsterdam, ( 1968) . J.H. Schulman and W.D. Compton, Color Centers In Solids, Pergamon, Oxford, (1963). W. Kanzig and J.0. Woodruff, J. Phys. Chem. Solids, <?. 70 (1958). J.G. Castner and W. Kanzig, J. Phys. Chem. Solids, 2, 178 (1957). M.H. Cohen, W. Kanzig and J.0. Woodruff, J. Phys. Chem. Solids, 11, 120 (1959). W. Kanzig, J. Phys. Chem. Solids, 12, 80 ( i 9 6 0 ) . W.E. Garner and E.W. Haycock, Proc Royal Soc, A2ll, 335 (1952). 52 J.G.N. Thomas and F.C. Tompkins, Proc. Royal S o c , A209. 550 (1951). J.W. M i t c h e l l , Fundamental Mechanisms of Photographic S e n s i t i v i t y , Butterworths, London, 242 (1951). L.G. Harrison, M.D. B a i j a l and D.J. Bird, Trans. Far. S o c , 60, 1099 (1964). L.G. Harrison, R.J. Adams and R.C. Catton, J . Chem. Phys., 4£, 4023 (1966). R.C. Catton and L.G. Harrison, J . Chem. Phys., 4£, 3810 (196?). N.V. Sldgwick, Chemical Elements and t h e i r Compounds, Vol. 2, Oxford ( 1950) . M.P. Borom and A. Pabst, P r o c of the 6 t h Int. Symp. on the Reactivity of Solids, 4 5 , ( 1 9 6 8 ) . 53 APPENDIX CALCULATION OF MUTUALLY COMPATIBLE ANGLES BETWEEN A LINE AND A SET OF FOUR THREE-FOLD AXES Let the four three-fold axes be expressed as unit vectors I1 ( I + 1 + k) a 2 = 1 (-1 - j . + k) Y3 £3 = 1 ( i - i - k) VJ V3 and the given line as a unit vector 1 = xi + yj. + zk then the cosines of the angles between 1 and the axes are given by cos 6- = l'a = 1 (x + y + z) 1 W cos © 0 * l ' a , = 1 (-x -y + z) w cos @~ = l * a 0 = 1 (x - y - z) 3 "" 3 V3 cos 6,, = I'&j, = i (-x + y -z) V3 If 1 is fixed perpendicular to &^ , then cos © = 0 and x + y + z = 0. Eliminating x from the other expressions, cos Q0 * 2 z i s cos 6~ = -2 (y + z) 3 ¥3 54 cos ©. = 2 y Since 1 is a unit vector, 2 2 2 and eliminating x y 2 + yz + z 2 - § = 0 For any t r i a l value of z, this quadratic may be solved for y, and hence © 2» ®3 a n d e 4 m a y D e computed. The results are shown In figure 10. 


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