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Particle growth characteristics of MgO Aihara, Kunio 1973

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PARTICLE GROWTH CHARACTERISTICS OF ACTIVE MgO BY KUNIO AIHARA B.A.Sc., Tokyo Institute of Technology, 1966 M.A.Sc, Tokyo Institute of Technology, 1968 A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in the Department of METALLURGY We accept this thesis as conforming to the required standard Members of the Department of Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA January, 1973 In presenting t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f 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 t h a t permission f o r e x t e n s i v e copying o f 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 r e p r e s e n t a t i v e s . It i s understood that copying or p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l gain s h a l l not be allowed without my w r i t t e n permission. Department of Metallurgy  The U n i v e r s i t y of B r i t i s h Columbia Vancouver 8, Canada Date March 9, 1973 i ABSTRACT The particle growth characteristics of active MgO in the size range "JO-kOO A have been studied by the x-ray line broadening technique. The starting material was a synthetic magnesium hydroxide, which was decomposed and then heat treated under isothermal conditions in the temperature range ^00-900° C in vacuum and in H2O vapor. The particle •growth rate was very much higher in vapor than that in vacuum. The results were analysed by the conventional grain growth equation, Tp- =; Kt and newly developed models. In these models, surface diffusion, bulk diffusion and evaporation-condensation have been considered for mass transport mechanisms. The activation energy for the particle growth process of MgO in vapor was calculated to be about 31 Kcal/mole. i i ACKNOWLEDGEMENTS The author wishes to acknowledge the assistance and encouragement given by his research d i r e c t o r , Dr. A.CD. Chaklader. Thanks are also extended to other f a c u l t y members and fellow graduate students for th e i r h e l p f u l advice. Special thanks are extended to Dr. J. Nadeau for h i s generous help. F i n a n c i a l assistance provided by the National Research Council of Canada i s g r a t e f u l l y acknowledged. i i i TABLE OF CONTENTS Page 1. INTRODUCTION 1 1.1 Introduction to Subject ...; i 1.2 Review of Literature 1+ 1.2.1 Kinetics of Decomposition of MgCOH^ k 1.2.2 Crystallography and Morphology of Decomposi-tion 5 1.2.3 Characteristics of Active MgO 8 1.2.4 Effect of Atmosphere on Particle Growth .... 10 1.2.5 Particle Growth of Active MgO 15 1.2.6 Reactive Hot Pressing of MgO 15 1.2.7 Theory of Grain Growth 16 1.3 Objective of This Work 23 EXPERIMENTAL 25 2.1 Material 26 2.2 Furnace for Heat Treatment 27 2.3 Heat Treatment Procedure 29 2.3.1 Calcination and Heat Treatment in Air 29 2.3.2 Heat Treatment in H20 Vapor, Argon and Vacuum JO 2.4 Particle Size Measurement 30 2.4.1 General Methods of Size Measurement 30 2.4.2 X-Ray Line Broadening Technique 31 2.4.3 Separation of K and K Lines 55 a l a2 2.4.4 Procedures for Particle Size Measurement ... 35 iv Page 2.5 Electron Microscopic Studies 35 2.6 Other Studies 37 2.6.1 Infrared Spectroscopic Study 37 2.6.2 Thermo-Gravimetric Analysis 39 3. RESULTS 40 3.1 Particle Size Measurements 40 3-. 1.1 Particle Size of MgO Prepared in Air 41 3.1.2 Effect of the Atmosphere on the Growth of MgO Powder 47 3.1.3 Particle Growth of MgO in 1 Atmosphere of Water Vapor 47 3.1.4 Particle Growth of MgO in Vacuum , 50 3.2 Electron Microscopic Observations 50 3.2.1 Dehydroxylated Mg(0H>2 50 3.2.2 MgO Powder Formed by Combustion of Mg Metal 55 3.3 Thermo-Gravimetric Analysis 58 3.4 Infrared Spectroscopic Study 62 3.4.1 MgO Prepared in H^ O and in Vacuum 62 3.4.2 Vacuum Heat Treatment of the MgO Prepared in H20 Vapor 6 2 4. DISCUSSION 6 5 4.1 Particle Growth of MgO Powder in H2O Vapor and in Vacuum 65 V Page 4.2 E f f e c t of the Atmosphere on the P a r t i c l e Growth Rate 68 4.3 Models for the P a r t i c l e Growth of MgO 71 4.3.1 Evaporation and Condensation Mechanism 73 4.3.2 D i f f u s i o n Models 74 4.4 P a r t i c l e Growth Curves:Theory vs. Experiment 84 4.5 The A c t i v a t i o n Energy for.the P a r t i c l e Growth in H 20 Vapor 86 4.6 Possible Mechanisms f or the MgO P a r t i c l e Growth.... 87 4.7 D i f f u s i o n C o e f f i c i e n t s 89 5. SUMMARY AND CONCLUSIONS 93 6. SUGGESTIONS FOR FUTURE WORK 94 BIBLIOGRAPHY 95 APPENDICES 97 T i LIST OF FIGURES Figure Page 1-1 Translucent MgO made by reactive hot pressing 5 1-2 Decomposition rate of Mg(OH)o as a function Qf P 6 H^O 1-3 Heat of solution in 5.1 N HC1 against the tempera-ture of calcination , 9 1-4 Surface area and fraction decomposed after 2 hours calcination of MgCOH^ ? 9 1-5 Surface area of MgO powder against the temperature of calcination 12 1-6 Particle growth of MgO at 150°C, in vacuum and in 4.6 mm Hg water vapor 12 1-7 Grain-boundary diffusion coefficient as a function of V ' • • 15 1-8 Logarithmic plot of particle size change during heat treatment 1-9 Mass transport from particle 1 to particle 2 16 1-10 The power law for grain growth 19 1-11 Boundary migration accompanied with pores 20 1- 12 Back force due to interface 22 2- 1 Electron micrographs of MgCOH)^  powder 26 2-2 The furnace used for heat treatments 28 2-3 The tube for vacuum heat treatments 28 2-4 Hall plot for the separation of strain effect and crystallite size effect on the X-ray line broadening 3 3 2-5 The separation of I, . and I, ~)h 2-6 The schematic diagram of electron microscope 2-7 The sample holder for.the infrared spectroscopic study 38 v i i Figure Page 3-1 X-Ray line profile (220) of the MgO prepared in air at 1100°C for 9 hours 42 3-^2 X-Ray line profile (220) of the MgO prepared in air at 595°C for 3 minutes , . 43 3-3 Hall plot of the MgO prepared in air at 595°C for 3 minutes 44 3-3b Lattice strain versus temperature of calcination ... 45 3-4 The particle size of MgO decomposed in air, the starting material was Mg(0H)2 46 3-5 The particle size of MgO heat treated in various atmospheres 48 3-6 The particle size of MgO heat treated in 1 Torr water vapor, starting material was decomposed MgO (~75A).. 49 3-7 The particle size of MgO heat treated in vacuum, starting material was decomposed MgO (~75 A*) 49 3-8 MgO prepared in H20 at 435°C for 30 minutes ........ 51 3-9 MgO prepared in vacuum at 985°C for 120 minutes .... 52 3-10 MgO prepared in air at 660°C for 4.5 hours 53 3-11 MgO smoke 54 3-12 Refraction effect due to the sharp corner .......... 55 3-13 Streaks on the diffraction rings ,. 56 3-14 High resolution diffraction pattern of MgO smoke ... 57 3-15 Weight loss of MgO prepared in vacuum as a function of temperature 59 3-16 Weight loss of MgO prepared in H2O vapor as a function of temperature 60 3-17 The rate of weight loss of MgO prepared in vacuum and in H2O vapor 61 3-18 MgO powder prepared in vacuum at 780°C for 40 minutes 63 3 -r l9 MgO powder prepared in H20 vapor at 680°C for 45 minutes 63 v i i i Figure Page 3-20 MgO powder prepared in H20 vapor at 410°C for 70 minutes and the heat treated in vacuum 64 3- 21 Exposed in air after heat treatment in vacuum 64 4- 1 Logarithmic plot of particle size of MgO heat treated in water vapor 66 4-2 Logarithmic plot of particle size of MgO heat treated in vacuum 67 4-3 Residual adsorbed (OH) on, MgO surface after prolonged pumping in. vacuum 70 4-4 Electron microphotograph of MgO particle heat treated in H20 vapor at 785°C for 240 minutes 72 4-5 The two-sphere model 73 4-6 Diffusion area for each mechanism 76 4-7 The radii of particles as a function of time for the two-sphere model 77 4-8 The three-sphere model 79 4-9 The radii of particles as a function of time for the three-sphere model 82 4-10 The growth rate as a function of r-^/r2 4-11 Log K 1 / / n vs. 1/T for the growth of MgO particle in H20 vapor 87 4-12 Diffusion coefficients as a function of temperature 91 ix LIST OF TABLES Table Page 2-1 Semi-quantitative spectroscopic analysis of Mg(OH) 25 4-1 The values of n and K"^0 in the equation, Dn=Kt, for the MgO particle growth 68 t 4-2 Experimental values of particle growth rate of MgO.. 69 4-3 Diffusion coefficients estimated from the experimental values of the particle growth rate .... 90 1 I. INTRODUCTION 1.1 Introduction to Subject Conventional ceramic processes involve a prolonged sintering treatment at elevated temperatures in the final stage of fabrication. Although hot pressing techniques appear to be very promising, they have not been widely used commercially. This is primarily due to the fact that the die materials currently available are not stable enough for continuous and sustained operations at the high temperatures and high pressures needed for hot pressing. On the other hand, hot pressing at a temperature at which a phase change or a decomposition occurs, referred to as "Reactive Hot Pressing", shows considerable improvement over conventional sintering or hot pressing. Generally, reactive hot pressing of oxides is carried out below 600-700°C and only for a few minutes. Preliminary investigations of the applications of this technique on hydroxides and carbonates indicate that a significant improvement in sintering properties can be achieved by this process. For example, in order to produce trans-lucent magnesia i t is normally necessary to hot press MgO powder at 1500°C under 5000 psi. for a period of 6-12 hours. By pressing magnesium hydroxide powder during its dehydration reaction 2 vr / ™ N 350°C-400°C „ rt , „ Mg(OH) 2 >• MgO + H 20 however, a translucent magnesia can be produced a f t e r 10 minutes under 15,000 p s i . at 450-500 °C , ( Figure 1-1). Thus, rea c t i v e hot pressing presents the advantages of shorter time, much lower temperature and consequently the p o s s i b i l i t y of using higher pressure. Because of t h i s , the reactive hot pressing process has drawn the attention of s c i e n t i s t s and i n d u s t r i a l i s t s f or further studies and a p p l i c a t i o n s . The mechanisms involved during reactive hot pressing appear to be very complex as several concurrent phenomena occur. In addition to the e s s e n t i a l requirement of a phase change or a decomposition reaction mass transport must be involved i n order to achieve a high density i n the powder compact. Enhanced p l a s t i c i t y both during a decomposition 24 i c reaction and a polymorphic phase transformation X D have been encountered and reported previously. Furthermore, the formation of a f l u i d phase i n a p a r t i c u l a t e compact during a decomposition reaction may give r i s e to p s e u d o - p l a s t i c i t y . ^ A l l the previous investigations i n t h i s f i e l d have dealt only with the phenomological aspect of reactive hot pressing. No atomistic mechanism has so far been postulated to explain the enhanced d u c t i l i t y exhibited by a s o l i d during a phase change. It i s reasonable to expect that some mass transport (atom movement) must occur during the l a t e r stage of reactive hot pressing, as p a r t i c l e s l i d i n g alone cannot r e s u l t i n the formation of a f u l l y dense body. Recent studies on the c h a r a c t e r i s t i c s of MgO f r e s h l y formed from F i g u r e 1-1: T rans lucent MgO produced by R e a c t i v e Hot P r e s s i n g at 500°C^ 10 minutes under 15,000 p s i . T h i c k n e s s : 0.5 mm the decomposition of MgCQH^ crystals indicated that MgO crystallites continued to grow above the decomposition temperature. In the present work, the particle growth of MgO produced by calcining MgCOH^ was studied in order to evaluate the mechanism of mass transport, which operates in the later stages of reactive hot pressing. 1.2 Review of Literature To study the particle growth of active MgO formed by dehydration of MgCQH^, i t is important to consider a l l factors which affect the decomposition and subsequent processes. 1.2.1 Kinetics of Decomposition of Mg(OH)2 The kinetics of the decomposition of brucite, Mg(OH)2 MgO + R^ O, have been studied by measuring the weight loss as a function of time under isothermal conditions. The decomposition in vacuum has been interpreted as an interfacial process by several workers. Gregg and Razouk interpreted their data by means of a contracting sphere model: n a/3 _ , Kt Cl - a) = 1 - — , in which a is the fraction decomposed, t is the time, R is the i n i t i a l crystal radius and K is the growth constant. This equation is based on the assumptions that nucleation on the surface of a spherical particle is rapid and that the reaction is controlled by the movement of the spherical interface. They obtained the activation energy of 12-27 Kcal/mple for the precipitated Mg(OH>2, and 27.0 Kcal/mole for the tabular brucite. 5 Anderson and Harlock interpreted their data by a contracting disc model: (1 -a) 1/2 and obtained activation energy of 27.6 Kcal/mole for the precipitated Mg(OH)2 and 23.6 Kcal/mole for the tabular brucite and 19.3 Kcal/mole for the in i t i a l stage of dehydroxylation of single crystals. 3 The latest study in this field was by Gordon and Kingery-They have shown that the weight loss data of well ground (-325 mesh) Mg(OH)2 can be treated with an equation of first order kinetics and the activation energy for decomposition was 29 Kcal/mole, for a large single crystal, the contracting disc model could be used for interpreting data and the activation energy for this was 30-32 Kcal/mole. As expected, the decomposition rate is significantly affected by 4 water vapor pressure. Anderson and Horlock have shown that any barrier to escaping water vapor through the bed of hydroxide powder influences not only the rate of decomposition but also the nature of the product - MgO. The effect of P u on decomposition rate is shown in Figure 1-2. It can be seen from the figure that in vacuum, the rate of weight loss is much higher than that in H^ O atmosphere. 1.2,2 Crystallography and Morphology of Decomposition The crystal structure of Mg(0H)2 is Cdl2~type, namely (OH) groups exist in pseudo-hexagonal close packed positions and Mg atoms occupy the octahedral sites of (OH) groups at every second layer. Brucite 6 Figure 1-2: Decomposi t ion r a te as a f u n c t i o n o f P R o . [ a f t e r Anderson and H o r l o c k ] 7 [Mg ( 0 1 1 ) 2 ] i s hexagonal, and because of weak bonding between the la y e r s , i s e a s i l y cleaved along basal planes. Magnesia (MgO) has the NaCl structure, namely two interpenetrating face centered cubic c e l l s . This i s equivalent to a face centered cubic +2 l a t t i c e of oxygen ions with every octahedral s i t e occupied by a Mg ion. The crystallography of decomposition was studied by J . Garrido^ employing X-ray techniques and the following o r i e n t a t i o n r e l a t i o n s h i p between the Mg(OH) 2 and MgO was found: [111]MgO // [0001]Mg(OH)2 and [110]MgO // [0110]Mg(OH) 6 7 This r e l a t i o n s h i p was l a t e r confirmed by several workers ' using the electron d i f f r a c t i o n technique. In both cases the electron beam was used as the heat source while observing images and d i f f r a c t i o n patterns. Gordon and 'Kingery ^ observed, by o p t i c a l microscopy that (1) the reaction began i n i t i a l l y as an i n t e r f a c i a l process, which proceeded away from cracks, cleavage steps and external surfaces,and progressed two-dimensionally along the basal plane of the b r u c i t e c r y s t a l s , (2) short l y a f t e r the decomposition started, massive cracking occurred over the e n t i r e c r y s t a l , (3) the c r y s t a l i n the i n i t i a l stage of t h i s cracking process was o p t i c a l l y transparent, (4) a f t e r the cracking process was completed, the c r y s t a l became les s transparent throughout (not j u s t i n the area adjacent to the o r i g i n a l cleavage cracks) i n d i c a t i n g that decomposition was proceeding through the crystal. The in i t i a l interface reaction accounted for only a small portion of the total reaction. These results indicate that the kinetics of the decomposition reaction of MgCOH^ are not simple. g The decomposition product is MgO of very small particle size o (a, 80 A) and the small crystals formed from each parent single crystal remain agglomerated in roughly the shape of the parent hexagonal plate. The spongy appearance of these particles indicates that they are made up of a network of small crystallites. The shape of these small particles has not been determined because of the limitation of the resolving power of electron microscopes. 1.2.3 Characteristics of Active MgO 9 Eubank was the first to point out that MgO particles produced from the decomposition of MgCOH)^  in the temperature range 300-500°C o had very small particle size of about 50-100 A. He determined the particle size using the X-ray line broadening technique. MgO powder prepared by thermal decomposition at low temperatures has a higher heat of solution and a higher rate of dissolution in acid, indicating that the oxide prepared at a low temperature is "active" and of higher energy.content than the bulk material"^ (Figure 1-3). Because of these, this MgO is called "active MgO". This higher energy content may arise from the very high surface area of the material or to the existence of strain in the lattice, or to both. Gregg and Pacher^ ""'" studied the change of surface area as a 9 300 700 MOO 1500 TEMPERATURE ( *C) Figure 1-3: P l c t of the heat of s o l u t i o n i n 5.1N-HC1 aga ins t the temperature o f c a l c i n a t i o n f o r MgO powder. [ a f t e r L i v e y ] 0 200 400 600 TEMPERATURE (°C) Figure 1-k-. Surface area and f r a c t i o n o f decomposed a f t e r 2 hours c a l c i n a t i o n o f MgfOHJg. [ a f t e r Greeg and Packer] 10 function of calcination temperature by the BET method. Their result i s shown in Figure 1-4. It is apparent that there is a large increase in surface area just after the decomposition and as the calcination temperature increases surface area decreases. The i n i t i a l increase in surface area corresponds to the formation of very small crystals of MgO, and the reduction of surface area at higher temperature correspond to sintering (or coalescence) of fine MgO particles. 1.2.4 Effect of Atmosphere on Particle Growth The effect of atmosphere during the decomposition of Mg(0H)2 on the particle size of the MgO produced, has been studied by Livey et a l . They reported that the particle size of MgO varied with calcination environments. The variation, of surface area with calcination tempera-ture in air and in vacuum is shown in Figure 1-5. The rate of surface area decreased more slowly in vacuum than in a i r . The effect of water vapor on the growth of MgO particles was also 12 studied by Anderson and Morgan. They observed that the presence of water vapor accelerated the particle growth tremendously, as can be seen in Figure 1-6. It was suggested that this accelerated growth might be due to an effect of r^O vapor on the surface diffusion of the rate controlling species. 13 Eastman and Cutler, while studying the effect of R^ O vapor on the initjLal sintering of MgO, considered the following defect reaction. Mg 2 + + 0 2" + H20 y Mg 2 + + 2(OH)" + V M 2+ (1-1) 11 where the equilibrium constant K is given by [<OH)"] 2[V ] K = 5 ^ ~ (1 -2) 2+ The result of this reaction is the production of Mg vacancies [V^2+] • Assuming that the vacancy concentration is equal to one-half the (OH) concentration to maintain electrical neutrality, we have the equation 4 [ v ] 3 K = p M g (1-3) H £0 This indicates that the concentration of magnesium ion vacancies in 1/3 MgO is proportional to P . On this basis, D (diffusion coefficient) r i „ U 1/3 should be dependent on P . On the other hand, at high P u the - 2+ association of 2(OH) ions and Mg vacancies should be considered. If complete association is assumed, K 2 may be written as K = S6- (1 -4 ) H 20 and the concentration of magnesium vacancies is directly proportional to P The data were interpreted in terms of the grain-boundary rl_U AL ( o .31 diffusion model ( -— /A(t) " = constant), and from the dependence of o rate on P (Figure 1-7) i t was concluded that for partial pressures H 20 up to about 5 mm Hg, the cation vacancy model was applicable and above 5 mm Hg P , the associated cation vacancy model was applicable. The activation energies under these two conditions were 80 Kcal/mole and 48 Kcal/mole, respectively. 12 Figure 1-5: Surface area o f MgO powder aga in s t temperature o f c a l i n a t i o n . [ a f t e r L i v e y ] n P H 2 0 4.6 mm Mg in vacuum 50 10 0 TIME Ik) Figure 1-6: P a r t i c l e growth o f MgO at 1050 ° C , i n Vacuum and i n P-H 2 0 h .6mm. [ a f t e r Anderson. 13 o 3 o 5 2 e> o 1 1 1 1 1 1 1 " - •mm - / / I 0 5 0 -/ / I 0 0 0 / / 9 5 0 " — -1 1 f i i i i -3 -2 -1 0 1 2 3 L 0 G ( P H j 0 ) Figure 1-7: Grain-boundary d i f f u s i o n c o e f f i c i e n t , D G , as a f u n c t i o n o f P n n . d [ a f t e r C u t l e r ] 1.2.5 Particle Growth of Active MgO The only systematic study of particle growth of active MgO has 14 been done by Kotera et a l . They calcined both natural and synthetic magnesium hydroxide in air and then kept the active MgO in air at a constant temperature, and measured the particle size by the X-ray line broadening technique. Some of their results are shown in Figure 1-8, where the average particle diameter is plotted as a function of time on a log-log scale. They obtained a constant slope (~ = ^  = 0.13) in the log-log plot for synthetic MgCOH^ and concluded from this that a single mass-transport mechanism was operative for the particle growth. Ik UJ N 50 100 50 100 TIME 500 (mirO 500 (min.) f o r pure s y n t h e t i c Mg [ 0 H ] 2 f o r b r u c i t e from Nevada Figure 1-8: Logarithmic p l o t of p a r t i c l e s i z e d u r i n g heat treatment of MgO prepared from two kinds of B r u c i t e . [ a f t e r Kotera] 15 The activation energy for the process was found to be 17 Kcal/mole. On the other hand, they observed a gradual increase in the slope = from 0.15 to 0.33) with increasing temperature for natural brucite, which had impurities [such as CaO (0.82%), Fe 20 (0.79%), A120 (0.23%), and Si0 2 (0.14%)]. This is indicative of a change of mechanism of mass-transport with temperature. They suggested the surface diffusion mechanism for MgO prepared from synthetic Mg(0H)2 for the following reasons: (1) low activation energy (17 Kcal/mole), (2) the temperature i s very much lower than the melting point, 0.34-0.39 Tm, [the melting point (Tm) of MgO is 3100°K]. It is generally accepted that above 1/2 Tm bulk diffusion is operative and between l/2Tm and l/3Tm surface diffusion becomes predominant. For natural brucite, because of impurities, larger number of lattice defect (vacancy) can be induced and this can enhance the bulk diffusion even at lower temperatures. As discussed previously, although the particle growth rate is greatly affected by P u Kotera et a l . did not study the growth under controlled E^O partial pressures. 1.2.6 Reactive Hot Pressing of MgO The study of reactive hot pressing of MgO was done by Chaklader and Cook^ measuring compaction as the function of pressing temperature at constant heating ratesand a large compaction was found near the decomposi 2 4 tion temperature. Further study was done by Chaklader and Sunderland under isothermal conditions, The creep deformation of cold compacts of 16 Mg(0H)2 during the dehydroxylation reaction occurs in three stages. The first stage was initiated and probably was controlled by the dehydroxy-lation reaction. This stage was followed by a steady state. At this state the creep rate e can be represented by the equation: A r 17,500 . e = A a e f f exp(- — f c - ). During the last stage the creep rate asymptotically approaches zero. 1.2.7 Theory of Grain Growth The driving force for grain growth and crystalline growth is the 18 same, namely decrease of surface energy and strain energy. In the case of MgO powder as the strain energy term is small (see Appendix 2) only the change of surface energy with respect to grain growth will be considered here. The driving force for grain growth due to surface energy is the change in surface free energy. Consider the case, where a volume 'AV' is transferred from the particle 1 of radius r^ to the particle 2 of radius r^, as shown in Figure 1-9. AV F i g u r e 1-9: M a s s t r a n s p o r t f r o m p a r t i c l e 1 to p a r t i c l e 2 17 As a result of this, the radius of particle 1 becomes (r^-Air^) and the radius of particle 2 becomes (r 2+Ar 2) , where Ar^ = — ^ 2 a n ^ Ar,> = AV 2 • Hence, total surface free energy change AF can be described as, 4irr2 AF =y [ 4 i T r 1 2 + 4 T T r 2 2 - { 4 T r ( r 1 - A r 1 ) 2 + 4 T T ( r 2 - A r 2 ) 2 } ] = y( 8'Tr 1Ar 1-8'irr 2Ar 2) r ( 2 f - 2 f ) r l 2 2YAV (1- - -A ) (i_5) 1 2 where y is the surface energy. In the case of grain boundary, r 1 = - r 2 (1-6) therefore = ^ (1-7) AF r l The rate of grain growth, ^ , can be expressed as the rate constant, K', times the driving force AF (1-8) 18 where D is grain diameter K' varies with temperature as K1 = K exp(- {1-9) o RI Equation (i~8) can be integrated under the following conditions: (a) D, grain diameter - 2r^ (b) y is independent of r^ dD = 8K'YAV dt D D t / D dD = / 8K'yAV dt D o o D2 - D q 2 = 16K'yAV t (1-10) where D q is the grain size at t = 0, If D « D, o D2 = (16K'YAV t ) 1 / 2 D = ( K t ) 1 / 2 (1-11) jin D = l/21nK + 1/2 In t (1-12) Equation (1-12) predicts that i f the logarithum of the grain diameter D, is plotted as a function of the logarithum of time, a straight line with slope of 1/2 should be obtained. Experimentally however, a slope of 19 less than 1/2 has been frequently obtained. Beck et al. proposed a 19 more generalized equation as follows: = (Kt) n (1-13) However, this is a rather empirical equation. It is generally found that n(< 1/2) increases with increasing temperature of heat treatment as shown in Figure 1-10. The physical meaning of n has not been very clear. LOG D ^ higher \ temperature LOG t Figure 1-10: Power exponent n. However, attempts to derive equations with explicit values of n have 20 21 been made by Kingery and Francois and by Nichols. 20 Kingery and Francois considered that the growth rate could be controlled by the migration of pores , as shown in Figure 1-11, and this means dt V s ; (1-14) where D is pore size. P ' 20 Figure 1-11, [b]: Paths of m a t e r i a l t r a n s p o r t d u r i n g combined pore-boundary-m i g r a t i o n . Double arrows show d i r e c t i o n o f boundary movement. [ a f t e r K i n g l y e t a l ] 21 K' — originates from the diffusion path, and assuming D <* D P P 4£ = K"' \ (1-15) D D3 - D 3 = 3K"'t o or i f D » D o D -(3K"'t) 1 / 3 (1-16) 21 Nichols derived a growth law under the condition that the boundary movement could be affected by dragging of pores on the boundary. He got a set of grain growth equations, in which different mass-transport mechanisms may be operative. The force, F g, on the pore can be expressed as F - -rrrv sin20 2 2 (1-17) s ' where 0 is the angle of the cone defined by the boundary with its apex at the pore center (Figure 1-12). Under the assumption that sin20 <= A\F « i F s = K § - f (1-18) The rate of grain boundary movement, can be expressed as 22 boundary line of contact 2*trcos9 F s ysin9'2*r.cos0 = 7t ) f r sin20 F i g u r e 1-12: The hack f o r c e , F , due t o i n t e r f a c e , [ a f t e r R. E. R e e d - H i l l ] 23 = B x F dt s = B x K (1-19) where B is the mobility of pores. 23 Shewman has derived equations for the mobility of spherical pores with different mass-transport mechanisms. These are B B B From equation (1-19) and (1-20) Nichols obtained (assuming D >> D q and can be neglected), volume diffusion surface diffusion (1-21) vapor transport A _ Qb —5- exp( ) volume diffusion J Rl r —7- exp(——-) surface diffusion (1-20) r D l " Q r — exp(-^-) vapor transport r 4 D = K t D 5 = K 2t 3 D = K t 1.3 Objective of This Work The similarity of the activation energy of the creep deformation (17.5 Kcal/mole) during the dehydroxylation reaction obtained by 24 Sunderland and Chaklader, and the activation energy for particle 14 growth (17 Kcal/mole) obtained by Kotera et al. indicate that the rate determining mechanism may be the, same for both processes. 2k Thus, a more precise understanding of the p a r t i c l e growth w i l l help i n our understanding of the p l a s t i c i t y during decomposition, and ultimately r e a c t i v e hot pressing process. For t h i s purpose, a study of p a r t i c l e growth of ac t i v e MgO, produced from the same MgCOH^ as used by Sunderland and Chaklader for t h e i r creep study has been ca r r i e d out with s p e c i a l emphasis on the following f a c t o r s : (1) the power law, D n = Kt, for p a r t i c l e growth, and k i n e t i c s of p a r t i c l e growth, (2) the e f f e c t of atmosphere (P ) on the p a r t i c l e growth, (3) the c h a r a c t e r i s t i c s of the MgO p a r t i c l e s ; i . e . the shape, the s t r a i n and the surface condition, C4) a t h e o r e t i c a l model f o r p a r t i c l e growth. 25 2. EXPERIMENTAL 2.1 Material The material used in this study was a synthetic magnesium hydroxide supplied by the Aluminum Company of Canada Ltd., Montreal. The major impurities contained in this material were as follows; ^e2^3: ± m®% a n ^ CaO : 2.0% after ignition. Minor constituents determined by a spectroscopic analysis are listed in Table 3-1. Table ^-1. Semi-quantitative Spectroscopic Analysis Al 0.02 wt. % and Sb, As, Ba, Be, Bi, B, Cu 0.01 Cd, Cr, Co, Ga, Au, Mo, Pb trace Nb, Ni, Ag, Sr, Ta, Sn, Mn 0.03 W, V and Zn were non-Si 0.07 detectable. Ti 0.005 This material has also been 24 used previously by Sunderland for his study on creep deformation i of MgCOH)^  during dehydroxylation. The surface area of the material was determined by an AMINCO Figure 2- I Mg(OH) 2 27 2 2 A "Sor-BET" unit and was approximately 15 m /g. Transmission electron microscopic studies of Mg(OH)2 powder revealed that the particles were essentially hexagonal flakes as shown in Figure 2-1. Particles of Mg(OH)2 easily cleave along the basal plane and, in the figure C axis is parallel to the electron beam. 2.2 Furnace for Heat Treatment Magnesium hydroxide powder was calcined and subsequently heat treated in a furnace, the schematic diagram of which is shown in Figure 2-2. This was essentially a horizontal zirconia tube furnace about 20 inches long and 1.5 inches in diameter. It was heated by four globar elements. The temperature was controlled by a Wheelco temperature controller. One Pt-Pt 10% Rh thermocouple, placed in the zirconia tube near the sample holder, was connected with the temperature controller. Another Chromel-Alumel thermocouple was attached to the sample holder for accurately determining the temperature of the specimen. The temperature of the specimen was determined using the later thermo-couple and a potentiometer. In order to quickly obtain uniform tempera-ture throughout the whole specimen during calcination and for subsequent heat treatment, a thin metal sample holder (either a nickel boat or a nickel plate) was used. Preliminary tests indicated that the temperature distribution along 3 inches of the middle-section of the furnace was within 2°C, and the temperature was controlled within +5°C. In the case of calcination and heat treatment of Mg(0H)2 in the air atmosphere, the nickel boat was placed in the zirconia tube. For 28 Figure 2 - 3 : The tube for vacuume heat treatment 29 calcination and heat treatment in vacuum, a separate quartz tube with one end closed, was inserted into the furnace and was connected with a mechanical vacuum pump. The nickel specimen holder, attached to a Chromel-Alumel thermocouple, was inserted inside the quartz tube. A schematic diagram of this arrangement is also shown in Figure 2-3. 2.3 Heat Treatment Procedure 2.3.1 Calcination and Heat Treatment in Air The synthetic magnesium hydroxide was calcined in air in the temperature range of 395° -815°C, and over a period of 30 minutes. For these experiments, a weighed amount of MgCOH^ (40 mg) was placed on a nickel sample holder. To avoid the effect of water vapor produced by decomposition, the powder was spread uniformly and thinly on the nickel plate and was always less than 2 mm thick. This is particularly important in view of the fact that the rate of decomposition has been found to be affected by the thickness of the powder in a bed. The sample in the specimen holder was put in the furnace for a certain period and after heat treatment the specimen was air quenched. Initially a few tests were carried out in which the temperature of the specimen was measured as a function of time after inserting the specimen into the furnace. This was done to determine the time necessary for the specimen to reach the furnace temperature. This experiment showed that in less than one minute the nickel plate reached the furnace temperature. After calcination and heat treatment, the particle size of MgO was determined by the X-ray line broadening technique. 30 3.3.2 Heat Treatment iii H?0 Vapor, Argon and Vacuum For these experiments, a very fine crystallite MgO was chosen as the starting material. This is to avoid the effect of P^O a r i s i n 8 from the decomposition reaction, Mg(0H)2 MgO + H20 t. The fine crystallite MgO was made by calcining Mg(0H)2 in vacuum at 385°C for 2 hours. As at this temperature the growth rate of MgO particles is very slow, the size of MgO particles obtained was 70-80 &. These small MgO particles were sub-sequently heat treated either in 1 atmosphere of H20 or in 1 atmosphere of argon or in vacuum. The flow rate of H20 vapor was estimated to be 3 liters per minute and that of argon* was 80 cc. per minute. The degree of vacuum achieved by mechanical pump would be about 10 Torr. If air was leaking into the system, i t was apparent by the sound of the mechanical pump (this sound indicates vacuum is less than IO-"*" Torr). When this occurred the experi-ment was stopped and repeated again. 2.4 Particle Size Measurement 2.4.1 General Methods of Size Measurement Particle sizes in the range 50 to 500 X are difficult to measure. The two most widely used conventional techniques are (a) X-ray line broadening and (b) electron microscopy. Both techniques have limitations, especially with respect to the shape of the particle, which may significantly introduce error in the particle size calculation. However, the X-ray line broadening technique has been preferred over electron microscopy for the following reasons: * Argon supplied by Canadian Liquid Air Co., 99.995% Ar (5 ppm 02, 33 ppm N2, 2 ppm H2, <10 ppm others) was used after being passed through Silica gel. 31 (1) The X-ray line broadening technique gives a value for the average particle size, as the intensity of reflected X-ray beam is pro-portional to the volume of the particles. (2) The X-ray line broadening technique is very sensitive to the o particle size change in the range of 50-500 A, for example, in this study o 5 A change in average particle size was easily detected for the specimen o whose average particle size was 100 A. (3) Electron microscopy has not enough resolution for the size of o 50 A under the normal operating conditions. In addition, during sampling, there is a general tendency for the carbon support film to pick up specific shapes (for example, flake or needle shape) or specific sizes from the powder. To determine an average size, a large number of observations and statistical treatment of the data are required. Moreover, the X-ray line broadening technique has been extensively used previously^'-'-0j39) to determine the particle size of colloidal mater-ials, colloidal suspensions, sol and very fine ceramic powders. For these reasons, the X-ray line broadening technique was mainly used for particle size determination for crystallite growth study. However, electron micro-scopy was also used for studying the morphology of powder and the shape of powder and other characteristics of Mg(0H)2 both before and after heat treatment. 2.4.2 X-Ray Line Broadening Technique The theoretical aspects of X-ray line broadening due to crystallite size and lattice strain have been adequately dealt with in several books on X-ray diffraction and their applications. A theoretical relationship predicting the effect of crystallite size on X-ray line broadening is shown in Appendix 1. The final equation due to the effect of the crystallite size on line broadening can be expressed as 32 A X P D cos e where 3- is the intensity half width, X is the wavelength of the X-ray beam, 6 is the Bragg angle and D is the average particle diameter. A is a constant and has a value of about unity. Because of strain in the l a t t i c e , the d changes and therefore the diffraction angle 0 also changes. The change i n 6 with respect to d can also be calculated using the Bragg equation as shown in Appendix 1. The half width $ of the diffraction line due to strain broadening i s given by where n is the strain. No simple relationship exists to allow separation of particle size effect 8 » and strain effect 3 , on the total line broadening 3. p S o >-In practice, however, the following assumption has generally been made; that i f the X-ray intensity distributions due to strain and cr y s t a l l i t e 2 2 size are in the Cauchy form i.e. a/(a + ire ) where a i s constant and 9 25 is the diffraction angle, the breadths are additive. Thus, 3 s = 2n tan9 3 = 3 + 3 p s (2-16) X + 2ntan6 D cos6 3 cos6 X 2nsine X (2-17) 33 The crystalline size D, and the strain n» can be graphically obtained c i ^ c B cos6 2 sine , , from a plot of — vs. — , as shown schematically in A A Figure 2-4. From the intercept with ® c o s Q — axis and the slope of this A plot and n can be obtained,respectively. C D (0 o u < 2 sin 9 X Figure 2-h: H a l l p l o t f o r the s e p a r a t i o n o f the s t r a i n e f f e c t and the c r y s t a l l i t e s i z e e f f e c t on the X - r a y l i n e broadening 2.4.3 Separation of K and K Lines • a± a2  To obtain a true width of a diffraction line, i t is necessary to separate the diffraction lines due to K and K . The separation of a, a„ 26 K and K was done by the Rachinger's graphical method. The a l a2 intensity ratio of K and K is known to be 2:1 and the difference in wavelength is also known. Therefore, the X-ray line profile of K 3h has the same shape as that produced by but the intensity is half and is shfited by A(29), (= 2 ^  tan9 ). Therefore, A I ( K }[29] = 1/2I ( K }[20 - A(29)] a2 al (2-18) and the observed profile I^ q^^[29] can be expressed as, W 2 6 1 = I ( K ) f 2 9 ] + I ( K ) [ 2 9 ] a 1 a 2 I ( K }[20] + \ I ( K }[29 - A(26)] a l a l (2-19) \K ) [ 2 9 ] = 1ob[2Q] ~ 2 X(K ) [ 2 9 " A ( 2 8 ) ]  a l a l (2-20) Thus I, -.[26] can be obtained graphically by substracting V 4 I, .[29 - A(29)] from I. , .[26] starting from the position where " l effect of K is zero, as shown in Figure 2-5. a2 I 2 9 <• Figure 2-5: The separation of I r k ] a n d I [k 35 2.4.4 Procedures for Particle Size Measurement A Philips diffTactometer, employing Ni fil t e r e d Cu-K^ radiation was used to get diffraction line profiles. To get smooth curves, a long time constant 30-45 second, and a slow driving speed 0.25 or 0.125 degree/minute (depending on the width of profiles) were choosen. One degree s l i t was used in this measurement. The profiles of (200), (220) and (420) were chosen for this study, because these lines have f a i r l y strong intensities and are reasonably separated in their diffraction angles, 6. After these profiles were recorded on a chart paper, the following procedures were adopted for the analysis. 1. Substract the background scattering. This was done graphically by choosing the intensity at a position f a i r l y away from the peak as a standard. 2. Separate reflection from reflection by the Rachinger's method. 3. Measure the half intensity width. 2 2 2 4. Subtract the instrumental width employing £ = ^ Qb ~ ^ 1' where 3 is the real intensity half width (true broadening due to particle size and strain) , 8 ^ is the observed half intensity width and 8^ . is the instrumental half intensity width (obtained from diffraction lines of well annealed MgO powder). _ _,, „ 6 cos6 2 sine 5. PlOt r V S . T . 2.5 Electron Microscopic Studies MgO particles were observed i n an electron microscope (Hitachi HU-11A> Images and diffraction patterns were taken to observe the morphology 36 v. j wm electron g u n c o n d e n s e r l e n s s a m p l e f o r u s u a l u s a g e o b j e c t i v e l e n s i n t e r m e d i a t e l e n s s a m p l e f o r h i g h resolution d i f f r a c t i o n u s a g e p r o j e c t e r l e n s p l a t e Figure 2-6: The schematic diagram of e l e c t r o n microscope f o r h i g h r e s o l u t i o n d i f f r a c t i o n 37 of the powder. Particles were mounted on carbon support film directly without using any liquid to suspend the powder. In some cases high resolution diffraction patterns were taken to get wide electron beam exposure area on the specimen. This was done to obtain continuous diffraction rings. This method is called the high resolution diffraction technique, because there is only one lens (projector) below the sample as compared with two lenses (objective and intermediate) in the conventional technique. By this procedure the- aberration caused by the objective and intermediate lenses can be avoided. A schematic diagram of the electron microscope for high resolution diffraction is shown in Figure 2-6. 2.6 Other Studies In order to study the effect of R^ O vapor on the mass transport during the crystallite growth process, attempts were made to detect the extent of surface absorption. For this an Infrared spectrophotometer and thermo-gravimetric analyser were used. 2.6.1 Infrared Spectroscopic Study A Perkin-Elmer infrared spectrophotometer (Model 621) was used for the surface study. MgO powder produced by calcining MgCOH^ in 4 vacuum or R^ O vapor was pressed in a disc under a pressure of 1.3 x 10 2 Kg/cm in a vacuum die. The size of disc was 10 mm diameter and 0.5-1 mm thick. A special sample holder was built for further heat treatment (for desorption) and subsequent study in IR spectrophotometer without exposure to air (Figure 2-7). The sample could be heat treated 58 pyex flask ^ vacuum tungsten heater thermocouple MgO disk ^ N a C I single crystal window Figure 2 -7: The schematic diagram of sample h o l d e r f o r IR study 39 _3 up to 350°C in vacuum (10 Torr.) and immediately a spectrograph was taken under vacuum through NaCl single crystal windows, as shown in Figure 2-7. 2.6.2 Thermo-Gravimetric Analysis Thermo-gravimetric analyses were carried out with a Du Pont 950 TGA unit. About 30-40 mg of powder was used on each run, Pt container was used. The weight was recorded at a constant heating rate at 15°C/ minute, while in vacuum, this vacuum was obtained by a mechanical _3 pump (^  10 Torr.). 40 3. RESULTS 3.1 Particle Size Measurements In the determination of particle size of MgO, the following proced-ure was employed. Initially, Mg(0H)2 was calcined in air for 9 hours at 1100°C in order to measure the instrumental intensity half width 0 of the X-ray diffractometer. Figure 3-1 shows the diffraction profile of the (220) reflection for this specimen. This profile is typical of the X-ray diffraction profiles for a sample having about 5-50y particle diameter, and the separation of the lines of Ka^ and Ka^ is evident. Figure 3-2, which was taken from the MgO prepared by calcining Mg(0H)2 in air for 10 minutes at 595°C, shows a broader (220) reflection and the height of the peak is also lower than the height of the peak in Figure 3-1. The separation of the lines of Ka^ and Ka^ in the latter case is not dis-cernible. The line broadening was caused by the small particle size and the strain in the powder. A plot of 2 sin6/X vs. £ cosQ/X (the Hall plot) for this specimen is shown in Figure 3-3. The intercept on the g cos6/X axis corresponds to the reciprocal of the particle size and the slope . indicates the strain in the particle. For this specimen, the particle o size was calculated from the intercept and was 113 A and the strain obtained from the slope was 0.44%. A large scatter of data in a l l Hall plots was encountered. For this reason, the least square method was applied to obtain the strain, at each temperature and time of heat treatment. When the calculated values of strain were plotted as a function of temperature, no apparent relationship was observed. This can be seen In Figure 3-3b. This large scatter in the data arose primarily from the determination of g, for the (420) plane, which was at 109.7 degrees. At this large angle, 41 the small broad peak overlaps the background scatter of the X-ray beam. This introduced large error in the determination of the angle and the half-width of the diffracted peak for the (420) plane. However, applica-tion of the least square method to this data produced a value for the mean strain as 0.44%, with a standard deviation of ± 0.11%. This value of the lattice strain for freshly formed MgO agrees well with the reported (38) value of 0.37 ± .07% for the same material No apparent systematic change in strain in MgO was observed with the heat treatment. For this reason and because of the inherent error in the determination of B for the (420) plane, a l l straight lines were drawn in the Hall plots with a constant slope (i.e. a constant strain of 0.44%) using only the data of the (200) and (220) reflections. These are shown in the appendix. The particle sizes were accordingly calculated from the intercepts of these plots. 3.1.1 Particle Size of MgO Prepared in Air Following the procedure detailed above, the particle size of MgO was determined as a function of time, over the temperature range 395 - 815°C and this i s shown in Figure 3-5. The calcination was done in air using Mg(0H)2 as the starting material. A rapid increase in particle size was observed during the early stage of heat treatment. Figure 3-1: X-ray l i n e profile(220) of the MgO prepared i n a i r at 1100^ f o r 9 hours 0 J » 1 1 I L 64° 63° 62° 61° 60° 59° 2 9 (DEGREE) < LO F i g u r e 3-2: X - r a y l i n e p r o f i l e ( 2 2 0 ) o f the MgO prepared i n a i r a t 595°C f o r 3 minutes 44 Figure 3-3: H a l l p l o t of the MgO prepared i n a i r at 595°C f o r 3 min. 4 5 0.8 o — |n Air A — In Water Vapor • — |n Vacuum 0.6 OA A> • 2 0.4 < or h-U A A AO — " t r 0& A A TT" A -A -• • 0.2 0 I 1 1 1 1 4 0 0 600 800 1000 TEMPERATURE (°C) FIGURE 3 - 3 b LATTICE STRAIN VERSUS 'TEMPERATURE OF CALCINATION 46 300-2 N A I R 10 20 TIME (MIN.) 8I5°C 695T 585 °C 4 9 5 1 -— 3951 30 F i g u r e 3-4; P a r t i c l e s i z e o f MgO p r e p a r e d i n a i r , t h e s t a r t i n g m a t e r i a l w a s M g ( 0 H ) 2 -47 3.1.2 Effect of the Atmosphere on the Growth of MgO Powder The effect of the atmosphere during heat treatment on the growth of MgO particles is shown in Figure 3-5. The heat treatments were _3 carried out in (a) H^ O vapor at one atmosphere, (b) in vacuum ( 10 Torr.), and (c) in 1 atmosphere of dried argon, using small particles o of MgO (70-80 A) as the starting material. This material was prepared by calcining Mg(0H)2 at 380°C for 90 minutes in vacuum. The particle growth data of a sample prepared in air are also included in this Figure for comparison. The particle growth was slower in vacuum than in water vapor. For example, the average particle size of MgO prepared in vacuum was smaller than that of MgO prepared in H^ O vapor at 685°C. The particle size of MgO prepared in air or in argon was intermediate between the size of MgO prepared in H^ O and in vacuum. This indicates that the growth of MgO powders was affected by water vapor pressure. 3.1.3 Particle Growth of MgO in 1 Atmosphere of Water Vapor As can be seen from the previous section the effect of water vapor on the growth of MgO particle was significant. To study this effect further, a series of heat treatments of MgO was carried out for different periods in one atmosphere of E^O vapor in the temperature range 375°-790°C. The particle sizes determined by the X-ray line broadening technique are tabulated in appendix 3, and the data are plotted as a function of time for different temperatures in Figure 3-6. * at 885"C 300-1 1 685°C in I atom HgO 885*C in vacuum 5°C in I atom, argon 680°C in v acuum ± ± 0 50 100 150 200 TIME (MIN.) Figure 3-5: P a r t i c l e size of MgO heat treated i n various kind of atmospheres 4> 0 0 49 400 o < 111 N U J - J o < 200 o -435°C 375 °C IN P 50 100 150 200 250 TIME (MIN.) Figure 3-6: Particle size of MgO heat treated in H20 vapor, starting material was decomposed MgOf~75A) 0 1 7~ 985 °C V — 885 °C ° - 7 8 5 °C — • — 680°C IN VACUUM 1 x X 50 100 150 TIME ( M I N . ) 200 Figure 3 - 7 : Particle size of MgO heat treated in vacuum, starting material was decomposed M g O 7 5 A) 50 3.1.4 Particle Growth of MgO in Vacuum The particle growth of MgO in vacuum was found to be the slowest as can be seen in Figure 3-5. For this reason, the growth character-istics of MgO particles in vacuum were also studied. MgO was heat _3 treated in vacuum ( 10 Torr.) for different periods in the temperature range 680°-985°C. The particle sizes of these specimens were tabulated in Appendix 3 and also shown in Figure 3-7, in which the particle size is plotted as a function of time for different temperatures of heat treatment. 3.2 Electron Microscopic Observations 3.2.1 Dehydroxylated Mg(0H)2 Figure 3-8 shows the image and diffraction pattern of MgO prepared in R^ O vapor at 435°C for 30 minutes. This specimen has an average o particle size of 102 A as determined by the X-ray line broadening technique. This image shows that the small particles of MgO aggregate in a spongy relic on the parent hydroxide platelets. It is difficult to determine the shape of the particles from this electron micro-photograph. From the nature of the diffraction patterns however, an approximate shape of the particles can be deduced. The details of the study of the shape of particles will be discussed later (page53 ). The MgO particles heat treated in vacuum at 985°C for 120 minutes showed similar aggregation as can be seen in Figure 3-9. The diffraction pattern is also included in this figure. Figure 3-10 represents an electron microphotograph of the MgO prepared in air at 660°C for 4.5 hours. Very small round MgO particles formed by the disintegration of the original Mg(0H)9 are discernible in this electron microphotograph. Fiqure 3-8 MgO prepared in h^O vapor at 435°C for 30 minutes Figur-e 3-9 MgO prepared in vacuum at 985° C for 120 minutes . F i g u r e 3-11 M g O s m o k e 55 o The particle size measured from this figure (100-350 A) agrees with the results obtained by the X-ray line broadening technique (which o was average 263 A). As discussed later this diffraction pattern indicates that each particle may be spherical in shape. 3.2.2 Electron Microscopic Observation of MgO Formed by Combustion  of Mg It has been known that cube shaped MgO particles can be produced by burning Mg in air. The image and diffraction pattern of MgO smoke, are shown in Figure 3-11. This image shows cube shaped particles and straight equal thickness fringes, indicating that the surfaces are flat. The diffraction pattern shows lines of the face centered cubic structure, but streaks on the (111), (220), (420) and (422) reflections can be observed. These streaks are caused by refraction of the 29 electron beam, as MgO has an inner potential of -16 V. If an electron beam enters at an edge of the cube as shown in Figure 3-12, because of the negative innter potential in the crystal, the electron Figure 3-12. Refraction effect due to the edge shape corner. 56 beam w i l l refract as indicated in the figure. Because of tte, dynamical 27 effect two refraction spots w i l l be observed, as shown in Figure 3-13. index reflecting plane diffraction spots ( 2 0 0 ) q q q ( 22 0) ( M l ) and(2 2 2) p ^ q Figure 3-13. Streaks on CHI), (220), (220) reflections (after Mihama et al.) In the case of (200) reflection, as the streaks are parallel to the (.200) diffraction ring, the streak cannot be realized. A high resolution diffraction pattern of MgO smoke is shown in Figure 3-14. The (200) line i s sharp compared with (111) or (220) lines. This is because of 4he refraction effect o f the electron beam, and t h i s indicates that the shape of the c r y s t a l s i s cubic. ' In contrast to these diffraction patterns the diffraction patterns Figure 3-14 High resolution diffraction pattern of MgO smoke. 58 of MgO produced from the dehydroxylation of Mg(OH)2 [shown in Figures 3-8, 3-9, and 3-10] showed no streaks on the (111) and (220) lines and the sharpness of the (220) line is similar to the others. It can be concluded from this, that the shape of the particle is not cubic and may be spherical in shape. 3.3 Thermo-Gravimetric Analysis Thermo-gravimetric analyses (TGA) were carried out to determine the amount of absorbate present on the surface of MgO particle. For o this experiment MgO having a particle size of about 80 A was used. As shown in Appendix 4 one monolayer of R^ O chemisorbed on particles of o 40 A radius in the form of Mg(0H)2 would correspond to ^ 7% weight gain. The weight loss, when this water is removed, can be easily detected. Figure 3-15 and 3-16 show the weight loss as a function of temperature for MgO prepared in vacuum, and for MgO prepared in H^ O vapor after exposed in air, respectively. The time of storage in the desiccater after dehydroxylation had no significant effect as shown in these Figures. The total weight loss for the MgO prepared in vacuum was ^ 8% and that of the MgO prepared in H^ O vapor was 5.2%. Considering size s o e of these MgO particles 8° A for MgO prepared in H^ O vapor and 78 A for MgO prepared in vacuum, the weight loss per unit area is 44% bigger for MgO prepared in vacuum. In these figures the gradients of weight loss curves [d(AW/WQ)/dT] were also shown. Two weight loss curves, one of the MgO prepared in vacuum and the other of the MgO prepared in R^ O are compared in Figure 3-17. It is apparent that the MgO prepared in vacuum showed a greater weight loss around 500°C than the MgO prepared in H_0 vapor. 59 0 200 400 600 800 (°C) 0 200 400 600 800 (°C) 0 .01%/ c * t F i g u r e 3-15: Weight l o s s curves o f the MgO prepared i n vacuum as a f u n c t i o n o f temperature( h e a t i n g r a t e : 15 °C/min. } a f t e r exposure to a i r 6Q (°C) 0 hrs later 5 hrs later 8 hrs bter hrs later (°C) Weight l o s s curves o f the MgO prepared i n v a t e r vapor as a f u n c t i o n o f temperature)' h e a t i n g r a te :15 c / m i n , ) a f t e r exposure to a i r Figure3-1T: Rate o f weight l o s s o f MgO prepared i n vacuum and i n HgO v a p o r ( a f t e r exposure t o a i r ) 62 3.4 Infrared Spectroscopic Study 3.4.1 MgO Prepared i n H^ O and i n Vacuum Figure 3-18 and 3-19 show the i n f r a r e d transmission spectra of specimens prepared i n vacuum and i n R^O vapor, r e s p e c t i v e l y . Both IR traces were taken i n a i r atmosphere at room temperature. I t i s apparent that the MgO prepared i n vacuum has less transparency than the MgO prepared i n R^O vapor i n the range 1000-1300 cm and 1600-2600 cm \ These r e s u l t s i n d i c a t e some component i n a i r was adsorbed on the surface of the MgO prepared i n vacuum, however, the c h a r a c t e r i s t i c s of t h i s adsorbate cannot be discussed at the present time. 3.4.2 Vacuum Heat Treatment of the MgO Prepared i n H^ O Figure 3-20 shows three IR traces of (1) an MgO specimen prepared i n ^ 0 vapor at 410°C for 70 minutes (2) the same specimen as above but a f t e r a heat treatment i n vacuum at 280°C for 20 minutes and then cooled down to room temperature and an IR trace was taken i n vacuum, (3) the same specimen a f t e r a heat treatment at 345°C for 20 minutes. Lines (2) and (3) i n the figu r e show better transparency than l i n e (1), i n d i c a t i n g that the vacuum heat treatment p a r t i c a l l y removed the absorbed component from the surface of the p a r t i c l e s . The same specimen a f t e r a heat treatment i n vacuum [ l i n e (3)] was subsequently exposed to a i r , the IR traces were taken i n a i r . The e f f e c t of t h i s exposure to a i r i s shown i n Figure 3-21. A reduction of transparency was observed. I t can be infered from these r e s u l t s that the loss of IR transparency may be due to some adsorption on the surface of MgO p a r t i c l e s a f t e r the specimen was exposed to a i r . ){< i n vacuum befor heat treatment 3^5 C 20 min 280 C 20 min O < 3000 2000 1000 (cm"1) Figure 3-20: MgO powder prepared i n HgO at klO°C f o r 70 minutes and heat t r e a t e d i n vaeuum( taken i n vacuum) CO < or 1— t 3000 2000 FREQUENCY Figure 3-21: Exposed to a i r a f t e r heat t r e a t e d i n vacuum(figure 3-20) 1000 (cm*1) as 65 4. DISCUSSION 4.1 Particle Growth Data of MgO in H^ O Vapor . and In Vacuum As mentioned previously, one of the objectives was to determine the time exponent in the particle growth equation: D =('Kt^nFor this purpose the logarithm of the average particle size (D) was plotted as a function of logarithm of time as shown in Figurffi 4-1 and 4-2. Figure 4-1 represents the particle growth data in H^ O vapor and Figure 4-2 similarly represents the data obtained in vacuum. It is evident that in Figure 4-1 a l l straight lines drawn through the experimental data are nearly parallel, except the line of 375°C. It is considered that the reason why the line of 375°C was not parallel to the others is that D in equation Dn-D n = Kt could not be neglected o ^ o for a relatively small value of D. The experimental point at 790°C for 240 minutes was well above the straight line. This may have been 28 ^ due to discontinuous grain growth. From Figure 4-2, i t is apparent that the slopes ofthe straight lines drawn through the points are different and that the slope increases with increasing temperature. The lowest value of the slope was calculated to be 1/8.5 at 680°C and the highest value was 1/3.7 at 985°C. The values of n and K?~^n, the rate constant in the particle growt1, equation, obtained from these plots are summarized in Table 4-1. In H_0 vapor, the fact that the particle growth exponent (n) has a constant o o a> to O CD p to «o 10 ii Q CD (0 « O O O o O o <D O 40 1 1—i i l i i I I T — r j i i i i i I I 985 C n = 3.7 885 °C n = 3.9 78 5 °C n = 70 680°C n = 85 I N V A C U U M I I I 1 0 2 0 4 0 1 0 0 T I M E ( M I N J 3 0 0 Figure k-2: Log D v s . Log t p l o t f o r the MgO p a r t i c l e growth i n vacuum as 68 1 Table 4-1. The values of n and Kn in the equation of Dn = Kt, for the MgO particle growth Atm. Temp. n K l / n 680°C 8.5 ft4- (A /sec) 785 8.0 95 in vac 885 3.9 85 985 3.7 84 375°C 10.8 55 435 7.0 63 in Ho0 ' 515 7.0 95 575 7.0 111 vapor 685 8.5 150* 790 6.5 200* These values were calculated from the line of n = 7.0 value of about 7, may indicate that the rate controlling mechanism for particle growth of MgO in R^ O vapor remains the same in the temperature range 435-790°C. In vacuum the value of the exponent (n) changed from 8.5 at 680°C to 3.7 at 985°C, which may be indicative of a gradual change in the mechanism of mass transport involved in the particle growth process. It is generally believed that at low temperatures surface diffusion is the predominant mechanism and at higher temperature (> 1/2 Tm) bulk diffusion may control particle growth. 4.2 Effect of the Atmosphere on the Particle Growth Rate The particle size as a function of time (as shown in Figure 2-3) under isothermal conditions indicates ? that the effect of R^ O vapor 69 on the growth rate i s significant. Because of a power law relationship (D n = Kt) betweeen the particle size and time, i t i s not possible to calculate the growth rate (dD/dt) for the whole period of heat treatment. However, to compare the growth rates under different environments, two approaches can be made, (a) to measure the growth rate at a constant particle size, and (b) to measure the growth rate at a fixed time. It is more informative to measure the growth rate at a constant particle size as the driving force i s inversely proportional to the radius of curvature of the particle (as discussed in 1.2.7). o o For this reason the growth rates (dD/dt) were measured at 100 A, 150 A o and 200 A particle size, using the values of K and n in Table 4-1. The growth rate data are summarized in Table 4-2. It is apparent from the table that the growth rate at a constant temperature decreased -9 with increasing particle size. For example, (dr/dt) 2.8 x 10 cm/sec ° -11 0 at 435°C at 100 A was decreased to 4.4 x 10 cm/sec at 200 A at the same temperature. Table 4-2. Experimental values of particle growth rate of MgO in ^ 0 vapor and in vacuum (calculated from the values of Table 4-1). Atm. Temp. dr/dt (= 1/2 dD/dt)[cm/sec] at D = 100 A at D = 150 A at D = 200 A in Ho0 435°C 2.8 X IO"9 2.5 X i o " 1 0 4.4 X i o " 1 1 z 515 4.9 X IO - 8 4.3 X 10-9 7.7 X io- i° vapor 575 1.5 X 10-7 1.3 X IO - 8 2.3 X IO"9 685 1.2 X 10-6 1.1 X 10-7 1.9 X i o - 8 790 2.8 X 10-6 2.5 X 10-7 4.4 X IO"8 Ih Vacuum 680°C 3.2 X 10-9 1.5 X 10-10 1.8 X l o - n 785 4.1 x IO" 8 2.4 x 10~9 3.2 x 10"10 885 7.0 x IO" 8 2.1 x IO - 8 9.1 x 10"9 985 7.0 x IO" 8 2.4 x 10" 8 1.1 x IO - 8 The enhanced particle growth in R^ O can be explained by considering enhanced surface diffusion through this surface hydroxyl compound. However, no direct experimental evidence of the presence of adsorbed compounds during heat treatment in ^ 0 vapor could be obtained, and dat on the diffusion coefficients in MgCOH^ are not available. 4.3 Models for Particle Growth of MgO The results have been analysed so far, on the basis of the available grain growth equation, i.e. Dn = Kt. This equation is generally applicable to a system which is theoretically dense or with small pores on the grain boundaries. Each grain is surrounded by a large number of grains and grain growth occurs by the migration of the grain boundaries. Pores and inclusions generally impede the boundary motion and thus affect the grain growth process. In the case of particle growth however, as studied in this investigation, the microstructural detail is not similar to that of the system just described above. As shown in Figures3-10 and 4-4, the particles are very loosely packed and are only linked to a few particle The particle growth during heating occurred by mass transport from one particle to another, resulting in the disappearance of some particles and growth of others. The particle growth characteristics of such a system are significantly different from the grain growth models ordinarily used for systems of nearly theoretical density. 72 X 60,000 Figure K-k; Electron micro-photograph of MgO p a r t i c l e s prepared at 785 C f o r 2h0 minutes i n H 2 0 vapor A l i t e r a t u r e survey reveals no work i n which a model has been proposed to explain the growth of one p a r t i c l e at the expense of another. For this reason, the following models concerning p a r t i c l e growth have been developed. In these models, mass transport by evaporation-condensation, bulk d i f f u s i o n and surface d i f f u s i o n have been considered only, as viscous flow and p l a s t i c flow i n the absence of an applied stress was not considered to be a l i k e l y mechanism for mass transport during p a r t i c l e growth. In t h i s model, a l l p a r t i c l e s were considered to be s p h e r i c a l and t h i s was consistent with electron microscopic studies. 73 4.3.1 Evaporation and Condensation Mechanism The Kelvin equation relating the equilibrium vapor pressure and the radius of curvature of a crystal is where PQ,P^: equilibrium vapor pressure of a flat surface and a surface of curvature r^, respectively. y = surface energy 6 = volume of atom K = BoltzmarP constant T = temperature in*K For a two-sphere model, as shown in Figure 4-5. Figure k-5: Schematic diagram of the two-sphere models 74 f d r2\ Growth rate of particle 21-^ —1, is proportional to the pressure difference around particle 1 and particle 2 dr d F = e<pi"V (4"2) where G is a function of temperature only. Then considering the Kelvin equation, ^ = G[P0 exp(|g-) - P Q exp(M-)] 2yi_ _ 2 ^ 2o^ < < c OkKTr1 KTr 2 ; KTr^ G P 2^ 6 A _ 1_} ( 4_ 3 ) 0 KT ^ r 2 ; v J On the other hand from the mass balance r.^ + r 2 3 = C (4-4) where C is constant. 4.3.2 Diffusion Models The vacancy concentration under a surface is inversely proportional to the partial pressure of the system. So, the Kelvin equation can be modified to obtain the vacancy concentration with respect to the radius of curvature as follows: 7 5 l n5> . 1x6. C 1 KTr^ where C q i s the equilibrium vacancy concentration under a f l a t surface. Hence the vacancy concentration difference between two spheres of radius r ^ and i s 2y<5C 4 C - ^ % - ^ > ( 4 - 6 ) For p a r t i c l e growth to occur, mass i s being transported through the neck region from the p a r t i c l e having radius r ^ to the p a r t i c l e of radius x^. This mass transport from one p a r t i c l e to another w i l l r e s u l t i n the reduction of volume of one p a r t i c l e . The rate of change of volume (dV/dt) of a p a r t i c l e having a radius r , corresponds to the change 2 of radius by 4n-r dr/dt. This must be equated t o the mass transported by d i f f u s i o n , which i s DS6 dc/dx 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 ; dc/dx the vacancy concentration gradient; S the d i f f u s i o n area and <5 the vacancy volume. 4Trr2 dr/dt = DS 6 dc/dx ( 4 - 7 ) dc For the two-sphere model, the vacancy concentration gradient can be approximated by Ac/r. andthe d i f f u s i o n area g , can be expressed as 76 A = B 2irr 1h for surface diffusion 2 2 ( 4 " 8 ) A = B^  irr, for bulk diffusion where h is the thickness of the surface layer B is proportionality constant and = 1 as shown in Figure 4-6. surface diffusion bulk diffusion Figure 4-6. Diffusion area for each mechanism. Introducing a l l of these values in equation 4-7; the f i n a l equations for the rate of change of radius of both particles are, for the surface diffusion model: 4-rrr 2 ^ 1 1 dt 47rr 2 ^ 2 2 dt 4Trr 1hD 6 BYC . , I s 1 o ,1 1 . . KT (r1 r ; / r l 4irr hD 6 B Y C O ± kr ( ^ " ^ ) / r i (4-9) and for the bulk diffusion model, 7 7 2 dr x Z ^ D ^ B J C , I i 4 * r l d T = KT ^ - ^ ^ l 2 d r 2 2Trr 1 2D b6 2B?C o  4 7 F r2 dt~ = KT ( r " - ^ > / r l (4-10) The integral forms of these equations are obtained from equation 4-3 and 4-4 for the evaporation condensation mechanism, and for the diffusion models these are obtained from the equation*4-9 and 4-10 introducing a integral constant C, in this case C corresponds to the total volume of 3 3 2 spheres, 4/3 ir (r^ + )• (a) for the evaporation and condensation mechanism 2y6 - dt , ( u , i _ j ,„ f G V i and (b) for the surface diffusion mechanism f ^ / ( f - - A = > dr , - - f J 1 r l 3 / C - ^ 3 1 J and (c) for the bulk diffusion mechanism f r / ( f - - 1 ) dr = - / j 1 r i 1 J D 62BhYC s o KT d t ' D,_62BYC b o 2KT d t -These integrals cannot be solved analytically so solutions were obtained with numerical calculation by a computer, under the boundary conditions, 3 3 r1 = 0.96 at t = 0 with C = 2 = [r^ + r 2 ). The programs for the computer are shown in Appendix 5. 78 The theoretical plots for the growth of the particle and the disappearance of the particle r^ as a function of time are shown in Figure 4-7 (a to c). Three different plots correspond to three different mechanisms of mass transport, viz. (a) surface diffusion, (b) bulk diffusion and (c) evaporation-condensation. These theoretical plots show the following characteristics. 1. Larger particles grow at the expense of the smaller ones. 2. The rate of growth of the larger particle (d^/dt) increases with increasing time (as can be seen from equations (4-9) and (4-10), d^/dt •> 0 0 , as r^ -*• 0 for surface diffusion mechanism and dr^/dt -»• constant as r^ -*• 0 for bulk diffusion mechanisms). 3. Comparing the growth rates at the final stage between the different mechanisms of mass transport, i t is apparent that the relative growth rate at the final stage for the surface diffusion mechanism is higher than that of the bulk diffusion mechanism. For the evaporation-condensa-tion mechanism, the relative growth rate at this stage (final) is the smallest. In the latter case, the growth rate decreases during the final stage. 4. For the smaller particle, the relative rate of disappearance (-dr^/dt) is the largest for the surface diffusion mechanism, after r^ reaches ^0.7 r^. This indicates that the probability of finding relatively smaller particles in a system is less i f the growth process is controlled by the surface diffusion mechanism, than n system,where the bulk diffusion mechanism or the evaporation-condensation mechanism is operative. 80 Three-Sphere Model The particle growth characteristics involving only two spheres have been considered so far. In practice, however, particles are in contact with more than one particle. In such systems, more complicated growth characteristics can be expected. At present i t is not possible to develop such a complicated mathematical model. For simplicity, a three-sphere model has been considered. A schematic representation of this model is 'shown in Figure 4-8. Using the same procedure as employed previously for the two-sphere model, the following differential equations for the growth and the disappearance of the particles are obtained, Figure 4-8. Three-sphere model. for the bulk diffusion model; (4-11) and for the surface diffusion model 81 2 (4-12) where K' = s 1 o KT Applying a fourth-order Runge-Kutta's integral procedure, these equations were numerically solved (refer to Appendix V). The changes in the radii r^, r^ and r^ as a function of time, for the i n i t i a l relative sizes as 0.9, 1.0 and 1.1, are shown graphically in Figure 4-9, (a) and (b) for the surface diffusion and the bulk diffusion mechanisms, respectively. An attempt was also made to evaluate the effect of i n i t i a l particle size on the growth characteristics. This was done by choosing r^, and r^ as 0.9, 1.0 and 1.05, respectively (instead of 0.9, 1.0 and 1.1 as used previously). The values of r^, and r^ as a function of time for the bulk diffusion mechanism are plotted in Figure 4-9(c). Case (a) (for surface diffusion mechanism, r^ = 0.9, - 1-0 and r^ = 1.1). The particle 1 disappears leaving particles 2 and 3. At the stage when particle 1 disappears, particle 2 is bigger than particle 3. It can be predicted from the two-sphere model that particle 3 will eventually disappear leaving only particle 2 at the end. 38 PARTICLE SIZE ( a r b i t r a r y u n i t ) £8 84 Case (b) (for bulk diffusion mechanisms, r^ = 0.9, = 1.0 and r^ = 1.1). In this case particle 2 disappears finally leaving particle 3. Case (c) (for bulk diffusion mechanism, r^ = 0.9, - 1.0 and r^ = 1.05). Particle 2 finally remains, [similar to the ease (a)]. These results indicate that the governing criteria which determine the particle to survive are both the i n i t i a l particle size and the mass transport mechanism operative during the growth process. 4.4 Particle Growth Curves: Theory vs. Experiment If the growth curves theoretically predicted by the models are compared with the particle growth curves obtained experimentally, i t can be seen that the shape of the curves is quite different. Experimentally the growth rate was the fastest in the i n i t i a l stage, tappered off drastically in the final stage, the theoretical growth rate for the two-sphere model is slow in the i n i t i a l stage and gradually increases during the final stage. This anomaly may be resolved by considering the effect of the relative particle size on the growth of one and the disappearance of theother particle. The theoretically predicted effect of the relative particle size (v^/r^) on the growth rate of the larger one (dr2/dt) is shown in Figure 4-10. [This was obtained graphically from Figure 4-9(a)]. It is apparent that there is a drastic effect of the relative particle size on the growth rate especially where r^/x^ is less than 0.6. It is possible that the change of the ratio of particle size (r^/r^) with respect to time may account for the nature of the experimental growth curve. 85 OA 0.5 0,6 0,7 0.8 03 I.© > V > z Figure 4-10. The growth rate as a function of r-^/r2 (obtained from Figure 4-9(a)). 34 Alternatively, Oel found experimentally while working w i t h MgO that the distribution of particle size as a function of time at high temperature (1800°C) was narrow at an early stage, and at later stage the distribution curve was broad, but the ratio r^/v^ did not change very much with respect to time. If i t is considered that the ratio of particle sizes remained constant in this study, then the decrease in growth rate with increasing time can also be explained by the dependence of the growth rate (dr~/dt) on the particle size (r„). 86 From equation 4-9 . 2 d r2 „,1 1 , 4 l T r2 d T =K(r7 " ^ under conditions of x^jx^ ~ C, d r2 1 1 d T = K ( £ ' 1 } \ ( 4 " 1 3 ) _3 This equation shows that the rate d^/dt is proportional to r^ Because experimentally x^ increases with time, dr^/dt will correspondingly decrease with increasing time. The exact shape of growth curve cannot be predicted with such a simple model at the present time. 4.5 The Activation Energy for the Particle Growth in H^ O Vapor The activation energy for the particle growth was calculated from the empirical equation Dn = Kt, where K = K exp ( —Q ). In this O R l case only the particle growth of MgO powder in H^ O vapor was considered, as the particle growth exponent n had a constant value of about 7. An Arrhenius plot of the growth constant K"^n in H^ O vapor is shown in Figure 4-11. From the slope of this plot, the activation energy was calculated to be 31 i 3 Kcal/mole. 87 ( K ) n I.I 1.3 1.5 ( l/T'K) ( X l 0 3 a e g " ' ) ,1/n Figure 4-11. Log K vs. 1/T for the particle growth of MgO in water vapor. 4.6 Possible Mechanisms for the MgO Particle Growth The possible operative mechanisms in the particle growth process are discussed below. The following facts are considered for the discussion of the mechanisms. (a) Evaporation condensation mechanism is considered not to be applicable in the case of particle growth in MgO because the decomposite pressure of MgO at 900°K is as follows, -22 for Mg-0 system, 2Mg + 0 2 -» 2MgO > P 0 2 ^  1 0 T ° r r for Mg-H20 system, Mg + H20 ' _» MgO + H2 J * H 0 / 10 -18 88 (b) The particle growth rate i s higher in H20 vapor than that in vacuum, (c) The value of n In equation D n = Kt was constant (.« 7) for the growth in R^ O vapor -in the temperature range 435 — 79Q°C; for the growth in vacuum, n varied from 8.5 to 3.7 with increasing temperature from 680° to 985°C. This indicates that controlling mechanism is the same in vapor, but is changed in vacuum with increasing temperature. It is generally accepted that at lower temperatures, surface diffusion i s predominant, and at higher temperatures, bulk diffusion i s operative. 13 (d) A model was proposed by Cutler et. a l . based on the solubility of the hydroxide ion in MgO related the increase in the sintering rate to the increase in the cation vacancy concentration at higher temperatures. This i s an unlikely process because the value of n was different in vacuum and i n H^ O vapor. (e) The study indicated that in H^ O vapor the particles of MgO were convered with some unknown material. (f) The activation energy for the particle growth in H2O vapor 29 31 (31 Kcal/mole) was lower than that of bulk diffusion ' (79 Kcal/mole +2 _2 31 for Mg in MgO and 62.4 Kcal/mole for 0" in MgO) or surface diffusion of MgO (90 Kcal/mole). Considering the facts described above, following mechanisms may be proposed. 1. In H20 vapor, enhanced surface diffusion through species on MgO particle may be operative. 89 2. In vacuum at high temperatures (885°-985°C) bulk diffusion may be operative and at low temperatures (680° and 785°C) surface diffusion may be operative. At present, final conclusions concerning mechanisms of the growth process cannot be drawn because the physical meaning of the particle growth equation, D° = Kt has not been clarified. 4.7 Diffusion Coefficients With these considerations, attempts were made to calculate the diffusion coefficients using the theoretical models, equation 4-9 for surface diffusion and equation 4-10 for bulk diffusion, and using the experimental rate of particle growth (dr^/dt), from Table 4-2. For the calculations, the following values were chosen: o r 2 = 50, 75 and 100 A ^ = 0.8 r 2 2 33 Y = 1200 ergs/cm 6 - a /N = 1.86 x 10 cm o o h = 4 A (assumed to be the thickness of unit cell of MgO) K = 1.38 x IO - 1 6 ergs/deg. -2 where a is the lattice constant of MgO,N is the number of 0 atoms per unit cell. 90 Table 4-3. Diffusion Coefficients Estimated from the Experimental Values of Particle Growth Rates Atmos.Temp. Diffusion coefficient [cmg~7sec] at D=100 A at D=150 A at D=200 1 in HgO 515 575 685 72.0 .-. 1.5 x'lO"^ 2.9 x IO" 1 2 9.5 x 10-12 8.6 x 1 0 - 1 1 7,_2 x 10-1° in 680 2.3 x 10-15 vacuum 785 3^2 x 1 0 - i 2 3.1 x i o 3 1 ^ " 6.1 x 10" 1 5 1.9 x IO - 1 2 1.9 x 10" 1 1  1.5 x 10-10 885 6.2 x 10-J-5 985 6.8 x 10-15 2.5 x 10--^ 4.5 x 10-15 1.8 x l O " 1 ^ 3.6 x 1 0 - 1 5 1.2 x 10-12 1.1 x 10-U 1.0 x IO7** 1.8 x 10-15 for surface diffusion 3.2 x 10-13" h.O x 1 0 " 1 5 3.2 x 10-13 for bulk k.2 x 10-15 diffision Table 4-3 shows the surface diffusion coefficients in H^ O and 680° and 785°C in vacuum, and bulk diffusion coefficients for higher tempera-tures in vacuum. In Figure 4-12 the calculated diffusion coefficients for each mechanism were compared with the diffusion data obtained from literatures. The diffusion coefficient values obtained for the MgO prepared in vacuum at 680° and 785°C were close to the extrapolated values of the surface diffusion coefficient in MgO, which were obtained in air at higher temperature. However the diffusion coefficient obtained for the MgO prepared in ^ 0 vapor were several order of magnitude higher than the values extrapolated from the surface diffusion data. The larger diffusion coefficient can be explained by enhanced diffusion through the surface layer formed on MgO during heating in ^ 0 vapor. The larger bulk diffusion coefficients were obtained for the MgO prepared in vacuum at 885° and 985°C. The reason of this is not 91 U 10 UJ o u. LU O O CO 3 o 10 -11 10 15* is* surfoce diff. A O X Dz r l o o A 150 A Mg in MgO -2 0 in Mg0\ Kcal / mole vacuum-^)" 1 H2°. ' vapor OA 0,6 0.8 1.0 1.2 1.4- 1.6 Figure -12: D i f f u s i o n c o e f f i c i e n t s as a function of temperature clear, but may be due to (1) the effect of surface diffusion can not be neglected in this temperature range, or (2) the effect of impurities on the diffusion coefficients. From Figure 4-12, the activation energy for surface diffusion was also calculated, which was found to be 36 + 3 Kcal/mole. This corresponds to the activation energy for the particle growth in H^ O vapor, which is in good agreement with the value obtained when the particle growth data were analysed by the conventional growth equation Dn = Kt. This agreement may support the validity of the theoretical models proposed in this study. 5. SUMMARY AND CONCLUSION The particle growth of active MgO in the particle size range 70-U00 A has been studied by the x-ray line broadening technique. The active MgO was produced by calcining a synthetic magnesium hydroxide. The growth characteristics were studied as a function of time under isothermal conditions in the temperature range 400-900° C and in different environments. The results were analysed by the conventional grain growth equation, D n = jet. The value of the exponent n, has been found to be constant and about 7> when the particle growth was carried out in one atmosphere H20 vapor. In vacuum, however, the particle growth rate .-ms very much slower than in H2O vapor, and exponent n, changed from 8.5 to 3.7 with increasing heat treatment temperature from 680° C to 985° C. The activation energy for the particle growth process was 31 ± 3 Kcal/mole in H2O vapor. The amount of adsorption on the MgO particles in air after heat treatment in RVjO vapor was less than that after heat treatment in vacuum and exposure to air. It was proposed that the enhanced particle growth in HgO vapor may be due to the enhanced diffusion through the species on the surface of Mgo. Models for the particle growth based on several mechanisms of mass transport have been developed. The diffusion coefficients of MgO have been calculated from these models. The activation energy for the surface diffusion was similar to the value obtained by the conventional analysis. 94 6. SUGGESTIONS FOR FUTURE WORK 1. To e s t a b l i s h the exponent of the grain growth equation, D = 1/n (Kt) , precise experiments should be done considering, (a) the e f f e c t of impurities (b) the e f f e c t of H^ O p a r t i a l pressure (c) the e f f e c t of other environments, including CO^ gas . 2. For determining the mechanism of p a r t i c l e growth process, a more precise study of MgO surface should be done. 3. The e f f e c t of environments on the bulk d i f f u s i o n c h a r a c g e r i s t i c s of MgO has not been known, th i s may be another f r u i t f u l f i e l d of study. 4. The theory of p a r t i c l e growth developed here, was too simple (two-, or three-sphere model). For better understanding of p a r t i c l e growth, t h i s theory should be extended further i n v o l v i n g multi-spheres. 95 7. BIBLIOGRAPHY 1. S. J. Gregg and R. I. Rayouk, J. Chem. Soc. (London), 36; 1946. 2. P. J. Anderson and R. F. Horlock, Trans. Fara. Soc, 58, 1993, 1962. 3. R. S. Gordon and W. D. Kingery, J. Am. Cer. Soc. 50, 8, 1967. 4. R. F. Horlock, P. L. Morgan and P. J. Anderson, Trans. Fara. Soc, 59, 721, 1963. 5. M. J. Garrido, Academie des science, 203, 94, 1936. 6. J. F. Goodman, Proc Poy. Soc. Ser. A, 247, 346, 1958. 7. R. S. Gordon and W» D. Kingery, J. Am. Cer. Soc, 49, 654, 1966. 8. P. J. Anderson and D. T. Livey, Powder Met., 7, 189, 1961. 9. W. R. Eubank, J. Am. Cer. Soc, 34, 225, 1951. 10. D. T. Livey, B. M. Wanklyn, M. Hewitt and P. Murray, Trans. Brit. Cer. Soc, 56, 217, 1957. 11. S. J. Gress and R. K. Packer, J. Chem. Soc, 51, 51, 1955. 12. P. J. Anderson and P. L. Morgan, Trans. Fara. Soc, 60, 930, 1964. 13. P. F. Eastman and I. B. Cutler, J. Am. Cer. Soc, 49, 526, 1966. 14. Y. Kotera, T. Saito and M. Terada, Bull. Chem. Soc. Japan, 36, 195, 1962. 15. A. C. D. Chaklader and V. T. Baker, Bull. Am. Cer. Soc, 44, 258, 1965. 16. A. C. D. Chaklader and G. Beynon, J. Am. Cer. Soc, 53, 577, 1970. 17. A. C. D. Chaklader and R. C. Cook, Bull. Am. Cer. Soc, 47, 712, 1968. 18. J. E. Burke and D. Turnbull, Progress i n Metal Phys., Pergamon Press 220, 1959. 19. P. A. Beck, J. C. Kermer, L. J. Demer and M. L. Holzworth, Trans. Am. Inst. Min. Eng., 175, 372, 1948. 20. W. D. Kingery and B. Francois, J. Am. Cer. Soc, 48, 546, 1965. 21. F. A. Nichols, J. Appl. Phys, 37, 4599, 1966. 22. R. E. Reed-Hill, Phys. Met. Princ., D. Van Nostrand Co., 208, 1964. 23. P. G. Shewmon, Trans. Met. Soc. AIME, 230, 1134, 1964. 24. P. W. Sunderland and A. C. D. Chaklader, J. Am. Cer. Soc, 52, 410, 1 9 6 9 . 96 25. W.J. Hall, J. Inst, of Met., 75, 1127, 1949. 26. W.A. Rachinger, J. Sci. Inst., 25, 254, 1948. 27. G. Honjo and K. Mihama, J. Phys. Soc. Japan, 9, 184, 1954. 28. J.E. Burke, Ceramics Microstructures, John Wiley & Sons, Inc., 681, 1966. 29. Y. Oishi and W.D. Kingery, J. Chem. Phys., 33, 905, 1960. 30. R. Lindner and G.D. Partitt, J. Chem. Phys., 26, 182, 1957. 31. W.M. Robertson, Sintering and Relative Phenomena, Gordon and Breach, Sci. Pub., 215, 1967. 32. P.T. Anderson, R.F. Horlock and J.F. Oliver, Trans. Faraday Soc, 61, 2754, 1965. 33. R.A. Swalin, Thermodynamics of Solid, John Wiley & Sons, Inc., 197, 1962. 34. H.J. Oel, Material Science Research, Vol. 4, Plenum Press, 249, 1969. 35. L.S. Darken and R.W. Gurry, Physical Chemistry of Metals, Mcgraw-Hill Book Company, 349, 1953. 36. C. Kittel, Introduction to Solid State Physics, John Wiley, 125, 1967. 37. A. Cimino, P. Porta and Mi Valini, J. Amer. Cer. Soc, 49, 152, 1966. 38. Z. Librant and R. Parapuch, J. Am. Ceram. Soc, 51, 109, 1968. 39. (a) D. Lewis and H. Pearson, "X-ray Line Broadening in Alkali Halides", Nature, 196, 162, 1962. (b) D. Lewis and H. Pearson, "X-ray Line Broadening in Calcium Fluoride", J. App. Phys., 35, 1939, 1964. (c) G.K. Williamson and W.H. Hall, X-ray Line Broadening from Filed Al and W., Acta. Met., 1, 22, 1953. 40. (a) B.D. Cullity, Elements of X-ray Diffraction, pp. 97-99 and 259-268, Addison - Wesley Pub. Company, Inc., Reading, Mass., U.S.A., 1956. (b) H.P. Klug and L.E. Alexander, "X-ray Diffraction Procedures", J. Wiley & Sons, N.Y., pp. 491-538, 1954. (c) B.E. Warren, "X-ray Diffraction", Addison - Wesley Pub. Co., 1969. (d) D. Lewis and M.W. Lindley, J. Am. Ceram. Soc, 47, 652, 1964. (e) CC. Murdock, The form of the X-ray diffraction bands for regular crystals of colloidal size, Phys. Rev., 35, 8, 1930. (f) A.E. Alexander and P. Johnson, "Colloidal Science", The Clarendon Press, Oxford, pp. 453, 1947. 97 APPENDIX I Theory of X-Ray Line Broadening l.X The Effect of Crystallite Size on X-ray Line Broadening The path difference for the X-ray reflected beams from two nearest planes separated by d, can be expressed as LI = 2d sin(6+e) where A2. • path difference G = Bragg angle e "= deviation from the Bragg angle 44 • 2d(sin6cose + cosesine) = 2d sine + 2dg cose (for small e) - , , « n\ + 2 ed cose ( 1 ) and the phase difference, <j>, i s expressed as 2TT . „ „ , Aired cosQ , „ x (ji = f - A £ => 2Tfn + - — . — ( 2) According to Frensnel's diaglam method, the amplitude of combined beam from n planes can be expressed as sin 4 2 where a = scattering power of a plane <J> = phase difference. The Frensnel's diagram is shown in the case of n = 5, 4> • 15° in Figure 1 98 Figure 1 : F r e s n e l s diagram i n the case of n=5, ^ =15* at e B 0 I = an, o and at e $ 0 I = a ,2iredn cos8 N  s l n ( X ) 2ired cos6 ( 4) To get the e where the i n t e n s i t y becomes {L/2^LJ^ , the following equation should be solved, — 0 = 1/2 I o . 2, ,2TTend cosG. ^2Trend cos8 ^ 2 ( 5) = 1/2 This gives 27rend cos0 = 1.40 ( 6) 99 The true intensity half width at an angle 8 is 2e. But experimentally it is convenient to measure with respect to 26 values, then the intensity half width 3p can be expressed as 3p = 4e ( 7) Then, , = A 1-40A , O S P 2Trnd cos6 v ' On the other hand, the size of crystal, D, can be expressed as D = nd ( 9) where d is lattice spacing n is number of plane 4 x 1.40 X JP 2TT x D C O S D cose 1.2 Effect of Strain Because of strain in the lattice, the spacing, d, changes, therefore the diffracting angle 6 also changes. The change in 6 with respect to d can be calculated by differentiating Bragg's equation, A = 2dsift B ( ID 100 as - Id = cose de ( 12) 2d from ( 11 ) and ( 12 ) id j sme - coseAe d J Ad de = - ~ tane for small 6 and d we can express as A6 = - 4^" tane ( -13) d where 2A6 can be represented by g , hal f width of the d i f f r a c t i o n l i n e due to s t r a i n broadening, and — can also be represented by a s t r a i n parameter n. F i n a l l y we get g = 2ritan6 where ft i s l i n e broadening due to s t r a i n . APPENDIX U 101 Strain Energy and Surface Energy of Active MgO Particles (a) Strain energy of the MgO particles Bulk-modulus for the cubic crystal can be expressed as: )respectively. Strain enrgy can be expressed as: TJ str.= 1/2 x B 5 2 where £> is strain , in this case o.l'/o was chosen from the data of the lattice constant expansion of crystallite MgO. Ustr. = 7-7 x 105 ergs/cm3 (b) Surface energy of the MgO particles The surface energy of the MgO particles can be expressed as: From the above calculation, i t can be considered that the strain energy is negligible compared to the surface energy. Usurf. = ^r2jf(l/2r)3 where r is the radius of the particles surf. for r = 50 A Jf = 1200 ergs/ cm' = 5.8 x lO^ ergs / cm^  APPENDIX X - r a y l i n e broadening data No. Temp. Time £ cose /TV £*»»*J from L -S method [200 J I220J [420 J s i z e s t r a i n s i z e + i n water vapor 100. A 95 435 'C 30 m i n . 1.201 1.228 1.529 113 A • 570 % 96 120 .988 1.008 1.248 136 .468 131 97 270 .890 .960 1.180 157 .505 147 9^  515 5 • 995 1.040 1.281 136 .506 125 92 11 • 9^9 1.002 1.181 13^ .405 133 90 20 .854 • 930 1.091 151 .406 149 89 - 30 .851 .890 I.050 149 .350 157 9i 60 .790 .828 I.050 182 .461 172 83 575 7-5 .840 .902 1.100 163 ^53 155 82 15 .750 .810 .928 165 .304 183 81 60 .673 .7^5 .910 210 .407 210 98 240 .576 .619 .835 294 .458 264 104 685 15 .645 .726 .920 24 0 A73 230 100 50 .585 .680 .846 264 .443 265 105 45 .590 .676 .898 305 • 532 265 106 150 . 5 ^ .627 .818 315 .471 296 101 150 .551 .646 .848 525 .509 • 296 84 790 10 .562 .605 .728 238 .288 274 85 30 .^73 .565 .707 342 • 395 333 88 60 .462 .508 .651 355 .329 385 99 24 0 • 356 • 379 .516 481 .284 102 575 30 1.490 1.489 1.712 79 .406 79 103 130 1.375 1.442 1.628 87 .441 87 i n a i r 59 595 5 2.05 54 58 30 I.708 67 73 495 1.5 1.5^0 1.424 1.64 892 .518 89 T4 3 1.505 1.424 1-55 89 .408 93 57 5 1.397 1.724 105 .719 91 56 30 1.249 1.353 1.595 105 .602 97 72 595 3 1.173 1.288 1.449 104 .463 103 60 10 1.09 1.20 1.35 113 .436 113 61 30 1.06 1.15 1.218 105 .256 118 53 695 5 .881 .924 1.160 157 .488 151 54 10 .829 .895 1.117 175 .503 163 T , 30 •777 .865 1.086 195 .555 176 64 815 2.5 .709 .756 .834 164 .210 210 63 5 .623 .729 .801 197 .287 238 62 30 - .583 .611 • 758 236 .310 286 i n argon 1231 705 30 .907 1.018 I.296 172 .670 152 124 j 120 .868 .950 I.198 171 • 57^ I65 + p a r t i c l e s i z e was determined g r a p h i c a l l y f o r the s t r a i n of 0.44$ X-ray line broadening data No. Temp. Time JSCOSS/JV feP'J IA"} from L-S method size + 1200 J [220J [1+20] size strain in vacuum 99 ^ 110 685 °C 16 min. 1.240 1.256 1.506 102 ft .480 % 111 56 1.063 1.190 130 .645 113 12v2 164 .987 1.699 i.20p 120 • 352 125 107 785 15 .935 I.053 1.195 135 A33 133 108 4 5 .882 .979 1.198 161 .5^3 145 109 150 .7^7 .865 • 930 158 .292 174 119 885 10 .926 .966 1.255 162 .587 14 0 117 30 .718 .7hQ .969 207 .449 200 118 120 .582 .650 .889 320 • 537 263 122 985 13 .855 .890 1.086 160 .410 160 120 4o .644 .750 .815 188 .274 217 121 120 .538 .606 .660 220 .198 294 + particle size was determined graphically for the strain of 0.44/o 105 H a l l p l o t In a i r 395°C 5 min. c 107 APPENDIX IF Weight Ga in due t o A d s o r p t i o n on the Surface o f MgO Powder C o n s i d e r i n g the c h e m i s o r p t i o n o f R"20 i n the form o f Mg +H 20=Mg(0H) 2 , one Mg atom combines w i t h one H 20 molecule. . The number o f Mg atoms N on the ( lOO)surface can be expressed a s : N=2/a2, © where a Q i s the l a t t i c e c o n s t a n t , 4.21 A The surface area S o f the MgO powder per u n i t weight can be expressed a s : S= 6 / T)f>, o where D i s the s i z e o f p a r t i c l e s , 80 A , p i s the d e n s i t y o f MgO, 3-58 g / cm5 . The weight g a i n W due t o the a d s o r p t i o n can be expressed a s : W = MH2O N S / NO Where N Q i s the Avogadro number, 6.03x 10^3 /mole % 2 0 ^ s the m o l e c u l a r weight o f RgO, 18 W = 7.08 x 10~2 7.08$> weight g a i n v i l l . b e observed i f mono-layer of H 2 0 i s adsorbed o on the surface o f MgO ( 80 A) p a r t i c l e s . & f. fl N P 11 F f o r two sphere model [bulk d i f f u s i o n front T-Q] 1 ed ] 1 DIMENSION T( 51) ,X(51) ,Y(51) , F J ( 5 1 ) 2 T « 1 ) = 0 . C 3 X(1)=0.0 4 DO 1 J=2,49 5 F J ( J ) = J A y [ . i i = r . . n ? « ( F . i ( . n - i . . i 7 T U ) = X< J )**2*<Z.C-X< J ) * * 3 ) * * l 1 I J ) ) * 0 . 0 2 + T ( J - ) ) .0/3.0) /< <2.0-XI J)*«3 I-** ( I .0/3.0 )-X ( P. Y C J ) = ( 2 . G - X ( J ) * * 3 1 * * 1 1 . 0 / 3 . 0 ) 9 1 CONTINUE 10 W R I T E < 6 , 1 0 ) ( T < J ) , X ( J ) , Y < J ) , J = l , 49) 11 10 FORMA T{ 3E16.7) *C0MP IL E f o r three sphere model [bulk d i f f u s i o n c o n trolled] 1 DIMENSION Y ( 4 ) , F ( 4 ) f Q ( 4 ) ? Y ( l t = 0 . 0 3 Y(2)=0.9 4 Y|3) = 1.0 5 Y(4) = l . l 6 H=0 .005  7 J=0 8 DO 10 [=1,20 9 CALL P K ( Y , F , Q , H , 4 t l 0 ) 10 J = J+1 11 10 WRITE16,?) J , Y < ? ) , Y { 3 ) , Y ( 4 ) 12 2 FORMAT ( IX, I4,3F15.6)  13 STOP 14 E NO 15 SUBROUTINE AU XRK(Y ,F) . 16 DIMENSION Y (4 ) , F ( 4 )  17 F ( 2 J = - ( 1 . 0 / Y ( 2 ) - 1 . 0 / Y ( 3 ) ) / Y ( 2 ) 18 F l 3 ) = Y ( ? ) * ( 1 . 0 / Y ( 2 l - 1 . 0 / Y ( 3 ) ) / ( Y ( 3 ) * Y ( 3 ) J - ( 1 . C / v ( 3 ) - 1 . 0 / Y i 4 ) ) / Y ( 3 ) 19 F (4 ) = Y(3 ) ; t ( 1 .0 /Y<3 ) - l .0 /Y (4 ) ) / (Y C4 ) »Y (4 ) ) 20 ^ETUPN APPENDIX VI The Effect of Curvature on the Equilibrium Pressure 109 The effect of curvature on the equilibrium pressure can be calculated with the Kelvin equation as: M?l /Po) = 2^/kTr - L r, =50 A T = 900*K t = 1200 ergs / cm S = 1.86 x 10 _p cm5 k =1.38 x 10~l6 ergs /deg. , ln(P-L /P0) = o.719 P X /P 0 =2.05. The order of magnitude i s same between the presure of f l a t surface and curved surface. 

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