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Creep of compacts of colloidal boehmite (A100H) during dehydroxylation 1968

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CREEP OF COMPACTS OF COLLOIDAL BOEHMITE (A100H) DURING DEHYDROXYLATION by ROBERT GUSTAVE ST-JACQUES B.A. , B.A.Sc. (METALLURGY), University of Montreal A THESIS SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE i n the Department of METALLURGY We accept t h i s thesis as conforming to the standard required from candidates f o r the degree of Master of Applied Science Members of the Department of Metallurgy THE UNIVERSITY OF BRITISH COLUMBIA November, 1968 In p resen t i ng t h i s t hes i s in p a r t i a l f u l f i l m e n t of the requirements fo 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 fo r re ference and Study. I f u r t h e r agree that permiss ion fo r ex tens i ve copying of t h i s t hes 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 is r e p r e s e n t a t i v e s . It is understood that copying or p u b l i c a t i o n of t h i s thes i s fo r f i n a n c i a l gain s h a l l not be a l lowed wi thout my w r i t t e n pe rm i ss i on . The U n i v e r s i t y of B r i t i s h Columb Vancouver 8, Canada Department of ABSTPACT A compressive creep study of cold compacted c o l l o i d a l boehmite has been c a r r i e d out during t h 3 dehydroxylation reaction. The creep tests were made as a function of temperature, applied stress and the r e l a t i v e density of the cold compact. The a c t i v a t i o n energy for creep has been found to be 9.1 ± 1.5 Kcal/mole. The t o t a l creep rate was due to the stress associated with the neck formation at the points of contact and the applied s t r e s s . The creep rate i s proportional to the applied s t r e s s . The f i n a l form of *u ^ - i - • • rn i / / ,-9,100 ± 1,500. the t o t a l creep rate equation i s e =10.144 exp ( — 2 ••• ) R I + 2.2 x 10 ^ a ] sec \ Electron photomicrographs of fractured surfaces of deformed specimens revealed the presence of contact points i n the aligned f i b e r s , confirming the existence of the d r i v i n g force for shrinkage. Equations r e l a t i n g the change i n length and the strength of a compact with time have been tested with the experimental data, which indicated that the rate c o n t r o l l i n g mechanism may be volume d i f f u s i o n for the creep process. ACKNOWLEDGEMENTS The author wishes to acknowledge the help given by Dr. A. CD. Chaklader throughout this work. Thanks are also extended to the s t a f f of the Department of Metallurgy for t h e i r advice. F i n a n c i a l aid provided by the National Research Council and by the Quebec Mini s t r y of Education i s g r a t e f u l l y acknowledged. i i i TABLE OF CONTENTS PAGE I. INTRODUCTION 1 1.1 Reactive hot-pressing and i t s importance to the ceramic industry 1 1.2 Phenomenological explanation for enhanced compaction 3 1.3 Previous studies of deformation during phase transformations 3 1.4 Previous studies of reactive hot-pressing of Boehmite (A100H) . . . . . 5 1.5 Explanation for enhanced compaction of Boehmite . . . 9 1.6 Objective of this work 10 I I . EXPERIMENTAL TECHNIQUES AND RESULTS 11 I I . 1 Material 11 a) Description 11 b) Preparation of compacts 14 I I . 2 Equipment 16 I I . 3 Creep at a constant heating rate 16 11.4 Creep under isothermal conditions 18 11.5 Creep under d i f f e r e n t stresses 20 11.6 Density dependence of creep 26 11.7 Complementary experimental work 26 a) Creep tests with K a o l i n i t e 26 b) Electron microscopy study 26 c) Weight loss vs. shrinkage 26 d) Measurements of s p e c i f i c surface areas 27 e) Compressive strength of the compacts 27 i v TABLE OF CONTENTS (continued) PAGE I I I . DISCUSSION 3 6 I I I . l E f f e c t of the soaking time 36 I I I . 2 Creep due to surface tension 39 I I I . 3 Neck formation 40 I I I . 4 E f f e c t of the density on the creep rate 41 111.5 P a r t i c l e deformation 41 111.6 Phenomenological equation of the creep rate . . . 43 111.7 Equation r e l a t i n g the change of length of the compacts with time 50 111.8 Strength of the compacts as a function of time . 54 IV. SUMMARY AND CONCLUSIONS 60 V. SUGGESTIONS FOR FUTURE RESEARCH 61 VI. APPENDIX - Expansion correction 62 VII. REFERENCES 65 V LIST OF FIGURES NO. PAGE 1 Translucent Y _A12 u3 sheet made by reactive hot pressing 2 2 A schematic model of i n t e r p a r t i c l e bonding with deformation 4 3 Compaction curves of Boehmite . 8 4 Transmission electron micrographs of boehmite powder. 12 5 Structure of Boehmite showing atomic arrangement . . 13 6 Weight of powder and applied pressure vs. f r a c t i o n a l density of the compacts 15 7 Schematic diagram of furnace and loading assembly . . 17 8 E f f e c t of applied stress on creep at a constant heating rate, 27°C/minute during dehydroxylation . . 19 9 Creep at d i f f e r e n t temperatures under 265 p s i . . . . 21 10 Creep at 500°C, under 265 and zero p s i . . . . . . . 22 11 Stress dependence of creep at 350°C 23 12 Stress dependence of creep at 400°C 24 13 Stress dependence of creep at 550°C 25 14 F r a c t i o n a l density dependence of creep at 400°C . . . 28 15 F r a c t i o n a l density dependence of creep at 500°C . . . 29 16 Creep of K a o l i n i t e 30 17 Replica electron micrographs of fractured surface of boehmite compact a f t e r dehydroxylation 31 18 Creep at 500°C, under 265 p s i and a f t e r d i f f e r e n t soaking times 37 19 Creep, f r a c t i o n decomposed and s p e c i f i c surface area at 500°C, as a function of time 38 20 Creep rate as a function of f r a c t i o n a l density . . . 42 21 Creep rate as a function of stress at d i f f e r e n t temperatures 44 v i LIST OF FIGURES (continued) NO. PAGE 22 Log eg as a function of log a 45 23 Log of creep rates as a function of the r e c i p r o c a l of the absolute temperature 47 24 Log{^— [1 - (T -)^^]}as a function of log time 55 L o L o 25 Log strength as a function of log time 59 26 Net d i l a t a t i o n of the specimen holding frame 63 27 Net d i l a t a t i o n of specimen holding frame and corrected creep curves 64 v i i LIST OF TABLES NO. PAGE I Stress dependence of the creep rate 33 II F r a c t i o n a l density dependence of the creep rate . . . 33 III F r a c t i o n reacted as a function of time 34 IV S p e c i f i c surface area as a function of time 34 V Compressive strength of specimens a f t e r dehydroxy- l a t i o n 35 VI C o e f f i c i e n t s of the phenomenological equation of the creep rate 48 1 I. INTRODUCTION 1.1 REACTIVE HOT-PRESSING AND ITS IMPORTANCE TO THE CERAMIC INDUSTRY Reactive hot-pressing i s a process by which powdered materials can be d e n s i f i e d , at much lower temperatures and i n shorter periods than conventionally used. This process i s e s s e n t i a l l y a hot pressing technique which i s c a r r i e d out i n conjunction with either a polymorphic transformation or a decomposition reaction. The a p p l i c a t i o n of pressure during such a transformation or a decomposition reaction can produce considerable i n t e r p a r t i c l e bonding, r e s u l t i n g i n the formation of a strong and dense body. In order to obtain translucent alumina f o r example, i t i s normally necessary to hot-press alumina powder under 6000 p s i at 1500°C for a period of 2 to 5 hours. By pressing aluminum hydroxide during i t s dehydroxylation reaction (350°C - 550°C), however, a translucent alumina sheet can be produced a f t e r 10 minutes under 15,000 p s i at 500°C (Figure 1). The a p p l i c a t i o n of pressure during the polymorphic transformation o ( 2) of non-stabilized z i r c o n i a powder (1160 - 1205 C) has been found to be a very e f f e c t i v e method of f a b r i c a t i n g very dense and strong non- s t a b i l i z e d z i r c o n i a products instead of the normal hot-pressing process at 1800°C. When compared to the conventional hot-pressing technique, reactive hot pressing presents the advantages of shorter time, much lower temperatures 2 Figure 1 : Translucent Y-AI2O3 sheet produced by Reactive Hot-Pressing at 500°C/ 10 rains. Thickness : 0.04 inch. 3 and consequently the p o s s i b i l i t y of using higher pressures. 1.2 PHENOMENOLOGICAL EXPLANATION FOR ENHANCED COMPACTION Enhanced compaction of a powder compact during either a decomposition reaction or a polymorphic phase transformation has been (3) reported by several workers . The process of reactive hot-pressing u t i l i z e s the fac t that the r e a c t i v i t y of a s o l i d i s considerably enhanced during phase transformations, decomposition, or d i s s o c i a t i o n (4) reactions (the Hedvall e f f e c t ) . I t i s suggested that broken bonds and u n s a t i s f i e d valence l i n k s may e x i s t both on the surface and i n the bulk of the p a r t i c l e s of a s o l i d during a decomposition reaction; these may be a v a i l a b l e for i n t e r f a c i a l reaction leading to i n t e r - p a r t i c l e b o n d i n g M o r e o v e r , very transient i n s t a b i l i t y of the atomic p o s i t i o n during a reaction can produce a transient p l a s t i c state which may be u t i l i z e d for d e n s i f i c a t i o n (Figure 2). I n t e r p a r t i c l e bonding can be achieved by r e l i n k i n g the broken bonds across the i n t e r f a c e . However to explain the elimination of pores or voids from the compact i t i s necessary to postulate a mechanism inv o l v i n g material transport. If there i s a p l a s t i c state.during the reaction, the material can flow e a s i l y and this may r e s u l t i n d e n s i f i c a t i o n . 1.3 PREVIOUS STUDIES OF DEFORMATION DURING PHASE TRANSFORMATIONS Unusual d u c t i l i t y e f f e c t s have been observed i n studies of (6) mechanical deformation during phase transformations of m e t a l l i c materials Similar e f f e c t s would also be expected i n other c r y s t a l l i n e structures such as ceramic oxides. Observations on p l a s t i c behaviour i n quartz 4 t NO INTERPARTICLE BONDING INTERPARTICLE BONDING WITHOUT DEFORMATION. INTERPARTICLE BONDING WITH DEFORMATION. Figure 2 : A Schematic Model of I n t e r p a r t i c l e Bonding with Deformation. 5 c r y s t a l s during the a to 6 phase change have been reported by Chaklader^^, while H a r t ^ i n an i n v e s t i g a t i o n of creep deformation i n pure z i r c o n i a , using a creep-in-bending method with programmed temperature increase, showed the occurrence of s u p e r p l a s t i c i t y or transformation p l a s t i c i t y at temperatures near the monoclinic to 3 C) tetragonal phase transformation. Also, Morgan and Scala ' have prepared high density oxide ceramics from hydroxides by a p p l i c a t i o n of pressure during the dehydroxylation reaction and showed that phase changes, accompanying chemical reactions, can aid the s i n t e r i n g process, e s p e c i a l l y under applied pressure. U t i l i z a t i o n of this phenomenon allowed them to f i r e at temperatures much lower than those used previously. (9) A study by Sunderland and Chaklader of the neck growth between tips of s i n g l e c r y s t a l s of CaCOH)^ and between two hemis- p h e r i c a l t i p s of compacted Mg(0H)2 has shown both deformation and i n t e r a c t i o n at the contact point during dehydroxylation reaction. The k i n e t i c s of compaction during the dehydroxylation reaction of china clay, f i r e c l a y , magnesium hydroxide and aluminum hydroxide have been studied by Cook and C h a k l a d e r . They concluded that the true mechanism or mechanisms of compaction cannot be determined s o l e l y by k i n e t i c a nalysis, although i t can be assumed that the enhanced compaction i s dependent on the dehydroxylation reaction and other phase changes occurring i n the material. 1.4 PREVIOUS STUDIES OF REACTIVE HOT-PRESING OF BOEHMITE (A100H) McKenzie and C h a k l a d e r ^ made the f i r s t attemnt to e s t a b l i s h a r e l a t i o n between the strength or bulk density of a boehmite compact and, the extent of the dehydroxylation reaction occurring during the d e n s i f i c a t i o n process under reactive hot-pressing conditions. The res u l t s were analyzed using the empirical r e l a t i o n that the strength i s proportional to the extent of reaction. I t was assumed that at each hot-pressing condition both the reaction and strength r e s u l t i n g from the i n t e r p a r t i c l e bond formation, reached a pseudo-equilibrium state. The temperature c o e f f i c i e n t of the reaction can be determined provided an equilibrium condition i s attained and this should permit a value f o r the enthalpy of the reaction to be obtained. The energy values obtained from the analysis of the data were smaller than the enthalpy values reported by other workers f o r the reaction concerned. However, i n view of the fac t that the standard state of this reaction was not known and the uncertainty of the assumption that the strength at any stage was proportional to the extent of reaction, this disagreement was not unexpected. Nevertheless, the results showed that d e n s i f i c a t i o n was d i r e c t l y related to the reaction involved and that the compaction behavior during the dehydroxylation reaction was s i g n i f i c a n t l y d i f f e r e n t from the compaction behavior a f t e r the reaction. In order to substantiate this further, attempts were made by Cook and C h a k l a d e r t o study the k i n e t i c s of compaction during the dehydroxylation process. I n i t i a l experiments under isothermal conditions did not permit useful conclusions to be made for the following reasons: a) At high temperatures, the dehydroxylation reaction took place within a few minutes and the creep rate was too f a s t to be measured accurately. b) The compaction rate was very s e n s i t i v e to the s i z e of the specimen as this controlled the volume of vapor phase formed during the reaction. c) The rate of vapor phase removal could be controlled by varying the annular space between the die w a l l and the plungers and this also affected the rate of compaction. d) At higher temperatures, when a s i g n i f i c a n t portion of the dehydroxylation reaction was completed during the heating-up period, the study of compaction rate produced erroneous and nonreproducible r e s u l t s . For these reasons, Cook and Chaklader evaluated the compaction k i n e t i c s by studying the compaction behavior over a range of constant heating rates. In the work of Cook and Chaklader, the powder was pressed under a constant pressure of 5000 p s i i n a c y l i n d r i c a l die and the compaction was recorded as the temperature was increased. Figure 3 shows the compaction curves replotted from Cook's data together with a thermogravimetric (TGA) p l o t of the same material for comparison. The s i m i l a r i t y between the compaction curves and the TGA p l o t i s quite apparent. Between 350°C and 550°C there was a s i g n i f i c a n t weight loss (15%) and about 8%•compaction was obtained during this period. This range of temperature corresponds to the dehydroxylation of boehmite. The temperature gradient from the surface to the core of the compact caused the surface to reach the dehydroxylation temperature 10 8 A L IO 2 in Boehmite 5000 psi constant pressure 30 J 25 - J 2 0 j o o Heating rate — 2°C/min. _ J J 0 •I —6°C/min. I A II • II .»• -l2°C/min. _|, ~ TGA l2°C/min. \ JL ± j _ 200 400 600 800 TEMP. (°C) 1000 1200 -Figure _3 _:_ Compaction curves of Boehmite. range before the core. With a slow heating rate, there was s u f f i c i e n t dehydroxylation at the surface to produce a hard c y l i n d r i c a l sleeve while the center was s t i l l unreacted. This r i g i d material slowed the compaction at low heating rates as shown i n Figure 3. In addition to compaction during the decomposition reaction, a d d i t i o n a l enhanced compaction was also obtained during the Y~alumina to a-alumina phase change at 1100°C. 1.5 EXPLANATION FOR ENHANCED COMPACTION OF BOEHMITE (3 C) Morgan and Scala ' claimed that on r a i s i n g the temperature to the decomposition range, d e n s i f i c a t i o n occurs by a complex super- imposition of chemically induced fragmentation and mechanical rearrange- ment of newly formed, very fin e oxide grains (generated from the hydroxide). They reported that water vapor given off during this f i r s t stage probably continues to activ a t e further s i n t e r i n g of the oxide mass and at the end of the reaction escapes, leading to the t h e o r e t i c a l density and translucency. Cook and C h a k l a d e r s u g g e s t e d that i n the dehydroxylation process, i n t e r a c t i o n between (OH) ions to form ^ 0 molecules and subsequent d i f f u s i o n of these molecules does not involve any large scale p a r t i c l e movement. In order to explain the d e n s i f i c a t i o n of p a r t i c u l a t e compacts i n the presence of an applied s t r e s s , large scale p a r t i c l e rearrangement must e x i s t . They concluded that fragmentation during the dehydroxylation process may also s i g n i f i c a n t l y a f f e c t the p a r t i c l e flow. 10 1.6 OBJECTIVE OF THIS WORK In order to understand the compaction mechanisms during reactive hot-pressing of hydroxides, a programme of research was undertaken to study the flow behavior of powder compacts during the dehydroxylation reaction. This work forms a part of that programme. The flow behavior of cold compacted cylindrical specimens of f i b r i l l a r colloidal boehmite was investigated by compression creep tests under isothermal conditions. 11 II EXPERIMENTAL TECHNIQUES AND RESULTS II.1 MATERIAL a) Description The material used i n this study was c o l l o i d a l boehmite supplied by E.I. du Pont de Nemours and Company under i t s trade-mark name of Baymal. The c h a r a c t e r i s t i c s of the powder are described by I l e r ^ " ^ as having A100H, 83.1%; acetate as acetic acid, 9.8%; chemically bound water, 3.3%; p h y s i c a l l y adsorbed water, 1.8%; sulphate as SO^, 1.7%. The true density of the material i s 2.28 grams per cc. The p a r t i c l e s are f i b r i l l a r , being about 50 angstroms i n diameter and 1000 to 2000 angstroms long. Figures 4(a) and 4(b) show transmission electron photomicrographs of the powder. Specimens for the electron microscope were prepared by dispersing A100H i n d i s t i l l e d water and then t r a n s f e r r i n g i t to a carbon support f i l m placed on a copper g r i d . The water was evaporated o f f and the copper g r i d was placed i n the electron microscope. Figure 4(b) shows fi b e r s i n a more dispersed state than Figure 4(a). The powder consists of discre t e f i b e r s i n the form of loosely associated porous aggregates. The dehydroxylation of boehmite to gamma alumina involves only a minor change i n the o v e r - a l l c r y s t a l structure. The structure of (12) boehmite consists of oxygen ion layers that do not f i t with each other but within which the oxygen ions are i n cubic packing. The OH direc t i o n s form zig-zag chains between the planes of the oxygen ions. Figure 5 shows the a-plane and the c-plane of a model of boehmite. When the hydroxy1 ions are removed, the layers form a cubic close-packed arrangement of oxygen ions with the smaller aluminum ions remaining i n (a) X40,000 (b) X120,000 Figure 4 : Transmission e l e c t r o n micrographs of boehmite powder. "a" plane j i t "c" plane Figure 5 : Structure of boehmite showing atomic arrangement. Glossy black b a l l s : Hydroxyl Ions. Large gray b a l l s : Oxygen Ions. Small b a l l s : Aluminum Ions. 14 a random arrangement i n the i n t e r s t i t i a l s i t e s . The formula A100H gives a proportion of 2 to 1 between the hydroxyl ions and the aluminum atoms. However the aluminum ions l y i n g at the surface of the boehmite f i b e r s would be subjected to c a t i o n i c screening and would pick up hydroxyl groups i n order to 2 become stable. Because the surface area i s large (250 m /gram), these hydroxyl groups are responsible for a measurable excess of water over the formula A100H. This chemically bound water i s d i s t i n c t from the p h y s i c a l l y adsorbed water. I l e r found that the chemically bound water plus the acetate corresponded cl o s e l y to the t h e o r e t i c a l amount required to cover the surface with OH groups and a c e t i c acid. He reported also that when the powder i s heated up to 300°C, the acetate and adsorbed water are removed. II.1 b) Preparation of Compacts The powder was cold-pressed i n a c y l i n d r i c a l die to form compacts 0.190 inch i n diameter and 0.270 - 0.280 inch long. The weight of the powder and the load applied on the ram during the f a b r i c a t i o n was varied to obtain compacts of d i f f e r e n t densities but of the same length. Figure 6 shows the weight of the powder and the pressure applied to form the compacts as a function of the green density. To ensure i d e n t i c a l compaction rate, the compacts were cold-pressed at 0.1 inch per minute i n an Instron machine. Three batches of compacts, each of 50 p e l l e t s , . were prepared i n this manner. The densities of the compacts were calculated from weight to volume r a t i o . I t was observed that the compacts having less than 0.50 f r a c t i o n a l density were too f r a g i l e to handle and that compacts of more 15 Figure 6: R e l a t i o n between pressure on p i s t o n , weight of powder and f r a c t i o n a l density of p e l l e t s having constant dimensions. 16 than 0.65 f r a c t i o n a l density were strong but very d i f f i c u l t to release i n t a c t from the die due to f r i c t i o n . Hence, most of the experiments have been performed with compacts of 0.60 f r a c t i o n a l density. 11.2 EQUIPMENT The apparatus used i n the creep study has been b u i l t by (9) Sunderland and i s shown i n Figure 7. I t consisted of a ho r i z o n t a l -3 resistance vacuum furnace i n which a pressure of <5 x 10 torr was maintained. The vacuum chamber was water cooled and the spring loading device l a i d outside the heating zone. The loading frame and the ram were made of s t a i n l e s s s t e e l . The furnace could be programmed for constant heating rates or could be used for isothermal creep t e s t s . The temperature of the specimen was recorded by a chromel-alumel thermocouple touching i t s surface. The same thermocouple was used to control the temperature i n conjunction with a Honeywell c o n t r o l l e r . An a d d i t i o n a l thermocouple was occasionally used to measure the temperature of the i n t e r i o r of the specimen i n order to determine the temperature d i s t r i b u t i o n during the creep study. The l i n e a r dimensional change was measured by a d i a l i n d i c a t o r ( s e n s i t i v i t y : 0.0001 inch) and was plotted as a function of the time to give the creep rate. A transducer was also available to record d i r e c t l y the dimensional change on a s t r i p - c h a r t recorder; however, the no n - l i n e a r i t y of the transducer voltage over a large range of ram displacement prevented i t s use. 11.3 CREEP AT A CONSTANT HEATING RATE The c y l i n d r i c a l specimen was placed loosely between the loading -3 frame and the ram and the system was pumped down to 5 x 10 t o r r . A Loading Frame 18 stress of 105 p s i was then applied and the specimen was heated at a rate of e i t h e r 27 or 2°C per minute. The creep data obtained was subsequently corrected f or the expansion of the holding frame (Appendix I ) . No s i g n i f i c a n t d i f f e r e n c e was observed between the t o t a l creep when tests were made under the same stress (105 psi) but at d i f f e r e n t heating rates (2 and 27°C per minute). However, both the creep rate and the t o t a l creep increased with increased stress (155 psi) as shown i n Figure 8. II.4 CREEP UNDER ISOTHERMAL CONDITIONS The compact was heated i n vacuum at the maximum heating rate obtainable (200°C per minute) u n t i l the surface temperature had reached the te s t temperature. By placing a thermocouple ins i d e the specimen, i t was found that the ins i d e of the specimen took an extra 30 seconds to reach the test temperature but that thereafter there was less than a 10°C temperature d i f f e r e n t i a l between the out- s i d e and the i n s i d e of the specimen. I t was accordingly decided to apply the load 30 seconds a f t e r the thermocouple touching the surface of the compact had reached the test temperature. Creep tests were c a r r i e d out at f i v e temperatures: 350, 400, 450, 500 and 550°C. The duration of the tests varied from 10 to 20 minutes, depending on the test temperature. However, several experiments were c a r r i e d out for periods up to one hour. As previously noted the load was applied 30 seconds a f t e r the test temperature was reached. Accordingly at 350°C, the load was applied 3 minutes a f t e r the power was turned on and at 550°C i t was 19 Figure 8 : E f f e c t of applied stress on creep at a constant heating rate of 27°C per minute. 20 applied a f t e r 4% minutes. This explains why i n Figure 9 the o r i g i n of the d i f f e r e n t curves s h i f t e d to an increasing time as the test temperature increased. However, the f a c t that the curves o r i g i n a t e at a point where j^- i s d i f f e r e n t from-zero indicates that the compacts L o shrank even without any applied s t r e s s . With an applied stress of 265 p s i , the creep rate increased from 11 x 10 ^ sec at 350°C to 48 x 10~ 5 s e c " 1 at 550°C. Af t e r 1600 seconds at 350°C or 800 seconds at 550°C the creep rates approached zero. II.5 CREEP UNDER DIFFERENT STRESSES By changing the spring of the loading device, stresses of 31, 61, 105, 155 and 265 p s i could be applied. The spring loading device was c a l i b r a t e d i n an Instron testing machine to ±0.05 l b . To f i n d i f there i s any shrinkage when the compact undergoes dehydroxylation ( i . e . free of applied stress) a s e r i e s of specimens were heated under vacuum at 350 C or 500 C over d i f f e r e n t periods and the dimensional change was determined. The e f f e c t of the applied stress i s shown i n Figure 10. I t i s quite evident from this figure that there i s creep without any' applied s t r e s s . At 500°C, the creep rate increased from 21 ± 2 to 31 ± 2 x 10 sec. under 265 p s i . Figure 11, 12 and 13 show some t y p i c a l creep curves at 350°C, 400°C and 550°C re s p e c t i v e l y . The creep curves become l i n e a r 10 - 15 seconds a f t e r the load i s applied. This transient creep was observed i n most experiments and i s believed to be an adjustment period for the d i s t r i b u t i o n of stress on the whole specimen. This part of the creep has not been taken into consideration i n the creep  T 1 1 r 0.02 0.04 AL 0.06 0.08 0.10 500 °C reached 0.12 0.13 _1_ 0 p s i 265 p s i 400 1000 2000 Time, seconds •igure 10 : Creep at 500°C, under 265 and zero D S I . 3000 3600 Time (sec) Figure 11 : Stress dependence of Creep at 350°C 0 0.01 I I 1 1 1 | F r a c t i o n a l Density 1 : 0.60 0.02: 1 - 0.03 ^ load applied - 0.04 - 0.05 \ \ 31 p s i 400 C reached \ \ \ - 0.06 \ \ 105 p s i \ 265 p s i - 0.07 1 1 - 0.08 1 1 1 l l i 100 200 300 400 500 600 Figure Time (sec) 12 : Stress Dependence of Creep at 400°C 25 26 data a n a l y s i s . Table I on page' 33., summarizes the creep rates obtained over the temperature range 350 - 550°C and under d i f f e r e n t stresses i n the range 31 to 265 p s i . 11.6 DENSITY DEPENDENCE OF CREEP The e f f e c t of density on the creep behavior of the compacts was studied by using specimens having various f r a c t i o n a l densities ranging from 0.42 to 0.68. For th i s purpose, the creep tests were c a r r i e d out at 400 and 500°C under a pressure of 105 p s i . Figures 14 and 15 show some of the creep curves of tests made at 400°C and 500°C. Table II shows creep rates for the complete series of specimens used to study the density dependence of creep. 11.7 COMPLEMENTARY EXPERIMENTAL WORK a) Creep tests with K a o l i n i t e Creep tests were made at 575 and 600°C under 105 p s i to study the behavior of another hydroxide mineral under i d e n t i c a l t e s t i n g conditions. The r e s u l t s are shown i n Figure 16. b) Electron microscopy study A few specimens, a f t e r the creep t e s t , were fractured perpendicular to t h e i r c y l i n d r i c a l axis. Direct r e p l i c a s were made by shadowing gold on the fractured surface and subsequently evaporating a layer of carbon. To detach the carbon f i l m , the alumina specimens were dissolved i n hydrochloric acid. Electron micrographs are shown i n Figure 17. c) Weight loss vs. shrinkage A seri e s of specimens were heated for d i f f e r e n t periods i n a i r 27 at 350°C and i n vacuum (5 torrs) at 500°C i n order to correlate the weight loss or f r a c t i o n reacted with the creep. The results' are included i n Table I I I . d) Measurements of s p e c i f i c surface areas Samples of 1 gram of boehmite powder were heated i n vacuum (5 t o r r s ) a t 500°C and i n a i r at 400°C and 500°C for d i f f e r e n t periods. Their s p e c i f i c surface was measured with an Aminco Sor-BET machine. Table IV shows the values obtained. e) Compressive strength of the compacts In order to cor r e l a t e the strength of a compact with the extent of the reaction, a seri e s of specimens were deformed under 105 p s i at 400°C and 500°C for various periods. Their strength i n compression was determined i n an Instron testing machine. The cross-heads displacement was 0.05 inch per minute. The r e s u l t s are summarized i n Table V. 28 AL L „ 0.01 0002 \- 0.03 0C044 0.05 0.06 0.07 L 0.08 h i — T T 1 r 105 p s i load applied 400°C reached 0.67 0.60 J I I I i I L 100 200 300 400 500 600 Time (sec) Figure 14 : F r a c t i o n a l Density Dependence, of creep at 400 C 29  (b) X75.000 Figure 17(a) and (b) : R e p l i c a e l e c t r o n micrographs of f r a c t u r e d surface of boehmite compact a f t e r dehydroxylation. 32 X200.000 Figure 17(c) : R e p l i c a e l e c t r o n micrograph of f r a c t u r e d surface of boehmite compact a f t e r dehydroxylation. 33 TABLE I STRESS DEPENDENCE OF THE CREEP RATE* CREEP RATES 1 0 5 -1 sec 350°C 400 450 500 550°C 31 p s i 5.7 ± 0.6 10.0 ± 1.0 18.2 ± 1.5 25 ± 2 43 ± 3 61 ' 5.9 10.7 18.4 25 45 105 7.8 11.8 18 .2 29 46 155 7.4 12.0 19.4 30 48 265 10.7 15.3 22.5 31 48 * F r a c t i o n a l Dens i ty of 0.60 TABLE I I FRACTIONAL DENSITY DEPENDENCE OF THE CREEP RATE* CREEP RATES 10 5 sec -1 400°C 500°C Dens i t y Dens i ty 0.42 12.9 ± 1.0 0.43 35 ± 2 0.45 11.5 0.45 29 0.54 12.6 0.47 28 0.56 12.0 0.48 34 0.60 12.0 0.63 30 0.67 8.7 0.68 : 32 * A p p l i e d S t ress : 105 p s i 34 TABLE III FRACTION REACTED AS A FUNCTION OF TIME 500°C i n vacuum 350°C i n a i r 0 min. 0.30 2 min. 0.30 % 0.60 6 0.13 1 0.70 15 0.21 2 0.93 30 0.23 5 0.96 60 0.37 60 1.00 * Due to Heating Period TABLE IV SPECIFIC SURFACE AREA* AS A FUNCTION OF TIME 0 500 C i n vacuum 500°C i n a i r 400°C i n a i r 105 sec. 170 330 1 hr. 2h hr. 2 301 m /gm 326 309 319 283 .105 sec. 15 min. 18 hrs. 2 255 m /gm 317 270 180 sec. 12 hrs. 2 262 m /gm 288 m2/gm * ± 10% TABLE V COMPRESSIVE STRENGTH OF SPECIMENS AFTER DEHYDROXYLATION 400°C 500°C 50 sec 990 p s i 40 sec 1600 p s i 80 1100 50 1750 100 1400 70 2200 150 1350 80 1950 200 1700 120 2250 300 1650 150 2900 36 II I . DISCUSSION I I I . l EFFECT OF THE SOAKING TIME The compacts have been found to shrink even before the a p p l i c a t i o n of the load (Figure 9). I f the soaking time i s extended from 30 to 210 seconds this shrinkage increases from 4 to 6.5% as shown by the t y p i c a l curves of Figure 18. As the t e s t i n g conditions were i d e n t i c a l with respect to temperature (500°C) and stress (265 p s i ) , the creep curves are p a r a l l e l as expected. When the load was applied a f t e r a long soaking period, the reaction was p a r t i a l l y completed, so that the contribution of the applied stress to the o v e r a l l creep was short and the t o t a l creep was correspondingly smaller than when the load was applied without any soaking period. In order to e s t a b l i s h a r e l a t i o n between.the shrinkage observed during the dehydroxylation reaction and the creep i t s e l f , experiments were carried out i n which the weight loss of the specimen was determined under the. same heating conditions as were used for the creep study. The v a r i a t i o n of s p e c i f i c surface area of boehmite on c a l c i n a t i o n was also determined. This i s important (13) as i t has been shown that for most hydroxides, surface area increases considerably a f t e r c a l c i n a t i o n . Figure 19 shows the res u l t s of three d i f f e r e n t experiments; creep, f r a c t i o n decomposed and surface area at 500°C, as a function of time. The creep experiment was made under 265 p s i . A series of powder samples have been heated i n vacuum at 500°C for d i f f e r e n t periods. The f r a c t i o n reacted was calculated from the weight loss measurements. The curves 0.02 0.04 0.06 0.08 0.10 0.12 210 seconds soak 500°C reached 30 seconds soak 400 JL 1000 J L 2000 3000 Figure 18: Time, seconds Creep at 500°C) under 265 p s i and a f t e r d i f f e r e n t soaking times, 0.04 0.08 AL o L . h 0.16 1.0 a 0.5 0 _ 300 gm 200 100 •- -L JL Creep F r a c t i o n Reacted S p e c i f i c Surface 100 300 500 1000 2000 Time (sees) Figure 19 : Creep, f r a c t i o n decomposed and surface area .as a f u n c t i o n of time at 500°C 3000 for the s p e c i f i c surface area and the f r a c t i o n reacted reached steady values i n a shorter time than the creep curve. This difference can be explained as being due to the fact that removal of the vapour phase i s fa s t e r from a loose powder such as used for the surface area and the percentage transformed test than from a compact as used for the creep measurements. The presence of water vapor pressure i n the compact may also have reduced the rate (14) of the reaction . Hence, i t appears reasonable to say that the creep deformation ceases when the reaction i s over. The small 2 increase i n surface area (250 to 320 m /gm) has been explained by I l e r as due to increase i n i n t e r n a l porosity. A dispersed sample of the boehmite powder was heated on a carbon f i l m i n the hot-stage of the Hitachi electron microscope. The specimen was not exposed to the electron beam except to take photographs at d i f f e r e n t temperatures. Up to 800°C, no s i g n i f i c a n t change of the specimen was observed. However, at 50,000 magnification, the r e s o l u t i o n of the t h i n ceramic f i b e r s was very poor. III.2 CREEP DUE TO SURFACE TENSION The creep behavior of boehmite during the dehydroxylation reaction i s very d i f f e r e n t from the creep behavior of k a o l i n i t e and magnesium hydroxide. With no applied stress i t has been observed that a compact of k a o l i n i t e undergoes a change i n l i n e a r dimension of less than 0.5% during i t s dehydroxylation reaction although i t incurs a weight loss of 14%. Figure 16 shows two creep curves of k a o l i n i t e . When the specimen was maintained for 30 seconds at 575 or 600°C (before the load was applied) the dimensional change of the compact was n e g l i g i b l e . In the case of magnesium hydroxide, (13) Sunderland reported 0.5% shrinkage under zero load compared to a t o t a l creep of 8% at 400°C and under 210 p s i . This shrinkage i n the case of boehmite may be up to 10% (Figure 10). Before any shrinkage can take place i n t e r a c t i o n between points of contact i s necessary. The free energy change that gives r i s e to shrinkage of a powder compact i s the decrease i n surface area and lowering of the surface free energy by the elimination of s o l i d - vapor i n t e r f a c e . The dr i v i n g force for neck-growth between two p a r t i c l e s i s the e f f e c t i v e stress associated with the radius of curvature at the points of contact. This stress i s inversely proportional to the radius of curvature. The f i b e r s of the boehmite powder studied have a diameter of about 0.005y. Using the general 2Y formula ——, where y i s the surface energy and R i s the radius of K 2 curvature and assuming a surface energy as low as 100 ergs per cm , the stress at the point of contact between two f i b e r s of boehmite i s over 10,000 p s i . This stress i s much larger than those applied i n the creep study and i s expected to induce the necks (points of contact) between the p a r t i c l e s to grow. III.3 NECK FORMATION In order to see i f there was any evidence of neck formation, compacts were fractured perpendicularly to the c y l i n d r i c a l axis. Direct r e p l i c a s were made on the fractured surfaces and examined i n the electron microscope. Figure 17(a) shows that the texture i s composed of bent but aligned f i b e r s . I t appears that the fib e r s were aligned i n p a r a l l e l arrays during the cold compaction of the powder (Figure 4(a)). 41 During the dehydroxylation reaction, a great number of necks were formed between adjacent f i b e r s i n order to lower the stress associated with the small radius of curvature at the points of contact. Figures 17(b) and 17(c) show the fractured surface at higher magnifications. The black spots which are aligned are voids between two adjacent f i b e r s , fused at the points of contact. Between two p a r a l l e l rows of black spots the f i b e r s are discernable. The material transport associated with the neck growth has created these voids and also produced the shrinkage of the compact, which i n turn produced the creep observed during the experiments. III.4 EFFECT OF THE DENSITY ON THE CREEP RATE The creep rate as a function of the green density i s shown i n Figure 20. I t i s apparent from the figure that creep rate i s almost independent of the density, although this cannot be conclusive because of the scatte r of the data, p a r t i c u l a r l y with the low-density specimens. This may be due to the fac t that the f i b e r s are aligned (Figure 17(a)) and that the t o t a l number of points of contact between them do not change very much by varying the density. III.5 PARTICLE DEFORMATION The neck formation observed i n the case of the creep of boehmite compacts during dehydroxylation cannot by i t s e l f explain the fact that i t i s possible to obtain a body of t h e o r e t i c a l density under reactive hot-pressing conditions. In e f f e c t , i f s u f f i c i e n t pressure i s applied i n a closed die, the pores can eventually be eliminated and specimens of the t h e o r e t i c a l density produced. 40 dt O 500 C • 400°C L J a = 105 psi i - - f - x 10 • -1 sec 20 10 .40 50 .60 Fr a c t i o n a l Densitv .70 Figure 20 : Creep Rate as a Function of Fr a c t i o n a l Density. 43 The d r i v i n g force for the growth of the necks i s the small radius of curvature associated with the neck. At the same time, the theory predicts that the d r i v i n g force decreases as the s i z e of the neck increases and that this leads to an end-point density which i s d i f f e r e n t from the true density. By applying a stress as low as 265 p s i i n the creep experiments, the creep rate was increased from 10 to 50 % depending on the test temperature, whereas the t o t a l creep was increased from 50 to 100 %. Hence, i t i s believed that the applied stress caused some p a r t i c l e deformation during the dehydroxylation reaction. III.6 PHENOMENOLOGICAL EQUATION OF THE CREEP RATE The creep rates between 350 and 550°C under 31 to 265 p s i with compacts having a f r a c t i o n a l density of 0.6 are shown i n Table I page 33. These creep rates ê , are plotted as a function of the applied stress as shown i n Figure 21. I t can be seen that the creep rate i s proportional to the applied stress at a constant temperature at le a s t i n the range of stresses studied. By extrapolating the curves on Figure 21 to zero stress a creep rate e^ i s found for each temperature. If e i s subtracted; from e_, a value er i s obtained, o l b e« — e_ — e b r o This value e i s the creep rate caused by the applied s t r e s s . Log e S b i s p l o t t e d as a function of log a (applied stress) i n Figure 22. In s p i t e of the experimental s c a t t e r , the best l i n e that can be drawn has a slope   46 of one. This indicates a d i r e c t p r o p o r t i o n a l i t y between the creep rate and s t r e s s . This behavior i s usually a t t r i b u t e d to viscous flo\T, grain boundary s l i d i n g and Nabarro-Herring creep. The following sections give further information about the possible mechanism. The f a c t that the points corresponding to d i f f e r e n t temperatures are scattered randomly on both sides of the l i n e , i ndicates that the creep rate due to the stress only i s temperature independent. The values e Q i n d i c a t e that deformation occurred.: even when no external stress was present. This creep or shrinkage has been v e r i f i e d experimentally at 500°C (FigurelO) and was found to be 21 x 10 ~* ± 2 sec which i s s l i g h t l y lower than that of the extrapolated value of 25 x 10 ^ -1 sec Hence the phenomenlogical equation has two terms: Creep rate = e 0 + be 1 1 ^ (1) The term e Q i s the c o n t r i b u t i o n of the surface tension to the t o t a l creep. The term "b" i s the c o e f f i c i e n t of the applied s t r e s s . Figure 23 shows the log of the creep rate as a function of the r e c i p r o c a l of the absolute temperature of the test (an Arrhenius p l o t ) . The shrinkage rates given by the extrapolation at a = 0 are also included i n the p l o t . The a c t i v a t i o n energy has been calculated from th i s p l o t and found to be 9.1 ± 1.5 Kcal/mole. The phenomenological equation (1) therefore becomes: r . . ,-9 ,100 ± 1,500, , _ Creep rate = A exp ( — — — ) + Ba RT with the values of the parameters A and B given i n Table VI. "A" i s c a l c u l a t e d from the extrapolated values at a = 0, "B" i s calculated from the creep data at 265 p s i . Fl'-Mire 23 : Log of creep rates as a function of the r e c i p r o c a l of the absolute temperature. 48 TABLE VI COEFFICIENTS OF THE EQUATION Creep rate = A e ~ 9 , ^ ° + Ba RI at 60% Density Temperature -1 A sec Surface Energy B sec psx Applied Stress 350°C 0.130 1.9 x 10~l 400 0.136 1.9 x 10 450 0.146 1.9 x 10 500 0.140 2.6 x 10 550 0.164 2.6 x 10 Average 0.144 2.2 x 10~ 7 49 The f i n a l form of the equation i s : Creep rate : [0.144 exp ( ~ 9 , 1 0 ° D ~ + 2 . 2 x 10~ 7 o ] s e c " 1 The k i n e t i c study of the decomposition of boehmite (300 to (14) 400p) by C a l l i s t e r et a l has produced an a c t i v a t i o n energy of 67 - 70 Kcal/mole which i s e s s e n t i a l l y independent of the water vapor p a r t i a l pressure ranging from 0.00 (dry nitrogen) to 0.50 atm. Eyraud and Goton^ 1"^ calculated an a c t i v a t i o n energy of 42 Kcal/mole at a pressure of 1 t o r r s i m i l a r to the pressure at which the experiments of th i s study were made. C a l l i s t e r explained the discrepancies (42 compared to 70 Kcal) by the p o s s i b i l i t y of a d i f f e r e n t mechanism being responsible for the reaction i n a vacuum. Compared to 42 Kcal/mole, the a c t i v a t i o n energy for creep found i n th i s study (10 Kcal/mole) i s considerably smaller. This i s also the case for magnesium hydroxide, where the a c t i v a t i o n energy for creep i s 17 Kcal/mole^ 1"^ compared to 2 9 - 4 3 ^ ^ for the dehydroxyl- a t i o n r e a c t i o n . In the case of k a o l i n i t e , the creep curves shown i n Figure 18 give an a c t i v a t i o n energy of about 15 Kcal for the creep (17) compared to 3 8 - 6 5 for the dehydroxylation reaction. From this general observation i t i s concluded that the creep i s not con t r o l l e d by the dehydroxylation reaction. However, as the material does not creep before the s t a r t of the dehydroxylation reaction, i t i s reasonable to assume that the creep process was i n i t i a t e d by the dehydroxylation reaction. It i s believed that the very small s i z e of the f i b e r s may be an important factor i n the k i n e t i c s of creep. The neck formation 50 between the fi b e r s suggests that the creep a c t i v a t i o n energy may be related to the a c t i v a t i o n energy for neck growth between alumina c r y s t a l s . The only data a v a i l a b l e are for large alumina spheres (>lu). At high temperatures (1600 - 1900°C) the a c t i v a t i o n energy (18} for neck growth i s 140 - 150 Kcal . The a c t i v a t i o n energy for (19) surface d i f f u s i o n of A^O^ has been reported to be 75 Kcal/mole. However, the boehmite f i b e r s used i n this study can be compared to polymeric chains and i t i s i n t e r e s t i n g to note that the a c t i v a t i o n energy f o r creep of polymers above the glass t r a n s i t i o n temperature i s close to the a c t i v a t i o n energy for polymerisation. The a c t i v a t i o n energy for d i f f u s i o n of a small molecule i n a polymer l i e s between 5 and 15 Kcal/mole ° c ^ ^ and the a c t i v a t i o n energy for polymerisation (21) of butadiene i n the presence of cobalt i s 12.7 Kcal/mole. This suggests that there may be s i m i l a r i t i e s between the creep of f i b r i l l a r boehmite and the flow behavior of organic polymers. Studies of the very early stages of grain growth of alumina may we l l help to elucidate the rate c o n t r o l l i n g mechanism of the creep process observed i n this i n v e s t i g a t i o n . III.7 EQUATION RELATING THE CHANGE OF LENGTH OF THE COMPACTS WITH TIME A t h e o r e t i c a l equation has been developed by Wadsworth and (22) Chaklader , for the d e n s i f i c a t i o n process during a dehydroxylation reaction. The main considerations i n this t h e o r e t i c a l development are a) that the p a r t i c l e s are sp h e r i c a l i n shape, b) they deform at the points of contact under a x i a l pressure i n a die and the cros s - s e c t i o n a l area of the specimen remains constant during compaction. In the present i n v e s t i g a t i o n , the specimens were tested under creep conditions and not under hot-pressing conditions as postulated i n the theory. However, i t has been observed experimentally that the diametral shrinkage due to the dehydroxylation reaction was almost compensated by the bulging due to the compressive stress and as a consequence the change i n the diameter of the compact a f t e r the creep was less than 0.5%. This behavior may be considered equivalent to the change of l i n e a r dimension i n a compacting die where there i s no diametral shrinkage. The e s s e n t i a l steps i n the d e r i v a t i o n are included here, as this has not yet been published. For a double acting die of constant c r o s s - s e c t i o n a l area A', at time t = 0 the t o t a l number of p a r t i c l e s i s n A'L , where n i s the number of p a r t i c l e s per unit volume and o o O f f L q i s the i n i t i a l specimen length. A f t e r deformation at time t, this r A v t w i l l be nA'L where n i s the t o t a l number of p a r t i c l e s per unit volume a f t e r deformation and L i s the new length. Hence, (1) n Q L D A' = n L A' Area A' The number of p a r t i c l e s per unit volume (n or n Q) w i l l depend on the packing geometry which includes the co-ordination number and l o c a t i o n of the nearest neighbours. Then n Q can be defined as 3 l / ( 4 / 3 i r r 0 )p Q> where p Q i s the packing f a c t o r , and r i s the average p a r t i c l e radius. This r e l a t i o n can be rewritten as 1/3 = K p n 1 / 3 ° and a f t e r deformation (2) n 1/3 Kp_ 1/3 (3) 52 Assuming that the same packing geometry i s being retained, while the reaction proceeds, i . e . p - p Q and introducing equations (2) and (3) int o (1), we obtain 3 3 w r r o In the case of f i b e r s the material can be assumed to behave s i m i l a r l y to spheres. A cross-section of two p a r a l l e l f i b e r s i ndicates that i n two dimensions the s i t u a t i o n i s i d e n t i c a l to the case of spheres: In the t h i r d dimension, i f points of contact are assumed, then the geometry of neck growth between f i b e r s w i l l also be s i m i l a r to the neck growth between spheres at the points of contact. This (22) has been shown by Kuckzynski and i s i l l u s t r a t e d schematically i n the following f i g u r e : / \ points of contact Considering a si n g l e p a r t i c l e where i s the volume of the s p h e r i c a l p a r t i c l e and V S o i s the o r i g i n a l volume V g = 4 / 3 i T r 3 2 AVg = 4nr Ar 53 So r o ° o Vg can also be expressed by Z V„ = — Vn where Z i s the co-ordination number and V i s the S 2 n volume of a neck. For most of the mass transport mechanisms (volume, surface . . .) 4 7TX Vn = 0 where x i s the neck radius. 2 r 4 AVS = (6) Combining equations (6) and (5) ^ 1 = 3 ( | _ ) 2 ( r a ^ ) = Z,x 4 ( ? ) VSo ro ro 4 r [ 4 / 3 T r r 0 J ] ( f " ) 3 ( l " f") = -̂ 4 (8) ro r o i 6 r 4 o In s i n t e r i n g theory, the neck radius i s related to time by the following r e l a t i o n s h i p x = K t 1 / n (9) where "n" i s an integer whose value depends on the mechanism of mass transport: 2 - viscous flow 3 - evaporation condensation 5 - volume d i f f u s i o n 6 - grain boundary d i f f u s i o n 7 - surface d i f f u s i o n Equation (8) becomes ( ^ ) 3 ( 1 " f-> = — k t 4 / n (10) o o r o Using equation (4) the f i n a l form of the equation for shrinkage becomes k _ U _ (k.jl/3]- = K" t V n (ID L o L o T y p i c a l creep data obtained i n this i n v e s t i g a t i o n have been used to v e r i f y equation (11). In order to determine the operating model, log {j— [1 - dp—)"^^]} has been plotted against log time. L o L o The l i n e a r p ortion of the creep curves have been extrapolated to j^- = 0 L o i n order to f i n d a time, t = 0, corresponding to the beginning of the neck formation at the test temperature. Figure 24 shows the p l o t of the shrinkage data obtained at d i f f e r e n t temperatures (350, 400, 500 and 550°C) under 265 p s i and with compacts of 0.60 f r a c t i o n a l density. I t appears that over a c e r t a i n period the t h e o r e t i c a l l y predicted r e l a t i o n s h i p between the shrinkage and time i s obeyed. A f t e r a longer period, however, the data tend to deviate from the p r e d i c t i o n . The slope (4/n) i n the l i n e a r region varies between 0.80 and 0.90 which indicates that "n" i s approximately equal to 5. According to Kuczynski's deri v a t i o n , when n i s equal to 5 the neck growth and shrinkage i s controlled by volume d i f f u s i o n . However, i t should be pointed out that although from this analysis an i n d i c a t i o n about the nature of the mechanism involved i n the creep process can be obtained, no conclusion should be drawn without much extensive work. III.8 STRENGTH OF THE COMPACTS AS A FUNCTION OF TIME From the discussion of the preceeding section (III.7) i t i s expected that with the formation of necks at the points of contact, the compacts w i l l acquire some strength, which w i l l increase with the growth of the neck. With these assumptions, an equation r e l a t i n g (22) the strength as a function of time has been derived and given below 55 T" 0.04 Slope • 550°C 0.86 O 500 0.90 © 400 O 350 0.03 0.84 0.80 a = 250 p s i Fract. density 0.60 o 0.02 o 0.011 100 200 300 G 400 500 Figure 24 Log \ [1 - (T-)1''3] vs. log t Time, (sees) The strength S of a compact i s proportional to the strength of the necks formed between p a r t i c l e s located on the plane where the maximum stress i s acting. I f we assume that the strength of a neck i s proportional to i t s cross-section, then the strength of the compact i s S = K C n ) 2 7 3 ^ (1) where n i s the number of p a r t i c l e s per unit volume and a D i s the neck cross-section per p a r t i c l e . Due to the complexity of the mass transport (shrinkage and creep), a constant number of p a r t i c l e s per unit volume i s assumed. Moreover, i t i s assumed that the second stage of s i n t e r i n g i s not reached, i . e . the number of necks i s constant. The neck cross-section per p a r t i c l e a ? = 2 a n (2) where Z i s the co-ordination number and a n i s the i n d i v i d u a l neck cross- section 2 a n = TTX ( 3 ) where x i s the neck radius. In most s i n t e r i n g models, the neck volume i s given by 4 V n = ^ (4) where r i s the p a r t i c l e radius. From equation ( 3 ) a 2 V n = -r^— (5) From the preceeding section (III.7) n 1 / 3 = (6) where p i s a packing f a c t o r . Hence equation(5) becomes ^ 1 / 3 a_ (n) V n = ~^~~ZZ (7) The unit v a r i a t i o n of the volume of a compact due to neck formation 1 3 A V 2 1/3 r, a n A V - tf n l £. Tip 7 n 4 / 3 2 a n 2 Combining equations (8) and (2) A V . _JL n4/3 2 ( 9 ) TTZp p Equation (1) becomes,after introducing equation (9) _ 1/2 1/2 S = K (̂ E.) (AV) (10) I t i s assumed that the mass transport mechanism i s volume d i f f u s i o n as has been observed i n the preceeding section (III.7). (23) From Kuczynski's volume d i f f u s i o n model for s i n t e r i n g , i t i s simple to derive an equation of — • as a function of time for a given L o temperature. &. . % - - K' t 4 ' 5 (11) o J v o r where y i s the surface energy. 2Y 2Y For hot-pressing, i s replaced by (-̂ - + a) , a being the applied stress during the dehydroxylation. Substituting AV i n equation (10) and regrouping the constant terms, gives S = K" (-^ + a ) 2 7 5 t 2 / 5 (12) In order to v e r i f y equation (12) a constant stress of 105 p s i was used i n creep experiments at 400 and 500°C for various periods. The compressive strength of the c y l i n d r i c a l specimens was determined i n an Instron machine. It has been noted that hydroxide compacts (magnesium hydroxide, and k a o l i n i t e , boehmite), l e f t f o r a long period at a temperature immediately below the dehydroxylation range have almost no strength at a l l . This drop i n strength may be caused by the removal of p h y s i c a l l y adsorbed water and other v o l a t i l e materials which were responsible for bonding i n the green compact. From t h i s observation i t i s assumed that the strength of the compacts a f t e r the dehydroxylation i s caused only by the necks. The log of the strength obtained i n the compression test i s plotted as a function of log time i n Figure 25. Log S = K'" + n log t The values of n obtained (0.35 and 0.40) are i n good agreement with the exponent of t (2/5) i n equation (12). This indicates again that the mechanism involved i n the creep process may be volume d i f f u s i o n . However, the a c t i v a t i o n energy f or creep has been calculated to be only 10 Kcal/mole. This discrepancy between the usually large a c t i v a t i o n energy f o r volume d i f f u s i o n and the small value found for the a c t i v a t i o n energy of the creep may be resolved by considering the nature of s o l i d s a f t e r the dehydroxylation reaction. In this case, the decomposition reaction produced both very f i n e p a r t i c l e s (41 A° calculated on the basis of the surface area values) and very imperfect structure because of the presence of large i n t e r n a l porosity as postulated before. The combination of these two may r e s u l t i n the low a c t i v a t i o n energy necessary for the creep process as observed although the rate c o n t r o l l i n g mechanism may be volume d i f f u s i o n . No d e f i n i t e conclusion should be drawn however from this analysis at present. 59 60 IV. SUMMARY AND CONCLUSIONS 1. Compressive creep testings of cold compacted c o l l o i d a l boehmite have bet-n c a r r i e d out as a function of temperature ( i n the dehydroxy- l a t i o n temperature range), appliad stress and r e l a t i v e density. The compacts have been found to shrink even without any applied stress during the dehydroxylation reaction. 2. The a c t i v a t i o n energy for the creep process has been determined to be 9.1 ± 1.5 Kcal/mole, which i s considerably smaller than the a c t i v a t i o n energy for the dehydroxylation reaction (42 Kcal/mole), i n - d i c a t i n g that the rate c o n t r o l l i n g mechanisms for these two processes are not the same. However, i t was experimentally observed that the creep was i n i t i a t e d by the reacti o n . 3. The creep rate i s proportional to the applied s t r e s s , although the t o t a l creep rate was caused by two f a c t o r s : 2y/r and the applied stress (a), where y i s the surface energy and r the radius of curvature at the point of contact. 4. The t o t a l creep rate (e) can be represented by (within the applied s t r e s s l i m i t ) : . creep rate =[0.144 exp C9'100* 1'500) + 2.2 x 10~ 7 a ]'•. s- 5. The presence of necks at the-points of contact between the aligned f i b e r s has been observed i n the e l e c t r o n microscope, thus confirming the d r i v i n g force (2y/r) for the shirnkage, observed i n compacts. without any applied s t r e s s . 6. Equations previously developed, r e l a t i n g the change i n length and the strength of a compact (due to neck growth) with time, have been tested with the present experimental data. This a n a l y s i s indicated although i n c o n c l u s i v e l y , that the rate determining mechanism for the creep process may be volume d i f f u s i o n . 61 V. SUGGESTIONS FOR FUTURE RESEARCH 1. A study of the e f f e c t of p a r t i c l e s i z e on the creep rate of boehmite compacts may help i n e l u c i d a t i n g the mechanisms involved i n creep during dehydroxylation. 2. Studies of neck growth between two hemispherical tips of boehmite singl e c r y s t a l s would provide information about the nature and mechanism of mass transport during dehydroxylation. 3. In the present work, the dimensions of the specimens were kept approximately constant. The e f f e c t of s c a l i n g may a f f e c t the creep, because of l o c a l i z e d pressure of the vapor phase formed during the reaction. A. A l l the creep experiments of this study have been done i n vacuum. The e f f e c t of the p a r t i a l pressures on the k i n e t i c s of the dehydroxylation reaction i s known and s i m i l a r l y a study of the e f f e c t of p a r t i a l pressures on the creep behavior during dehydroxylation would help to co r r e l a t e the reaction and the creep process. 62 VI. APPENDIX THERMAL EXPANSION OF THE HOLDING FRAME Due to the fac t that the dehydroxylation reaction of boehmite takes place over a wide range bf temperatures (350 - 550), and that at 550°C, f o r example, the reaction i s over a f t e r 4 minutes (once the test temperature i s reached), the furnace has to be heated as fast as pos s i b l e . With 9.2 amperes, the heating rate i s about 200°C per minute. Since the loading frame i s close to the resistance heater, i t expands fa s t e r than the ram and the d i a l indicates a contraction as shown i n Figure 26(b). A f t e r 1500 seconds the expansion of each part i s the same and the d i a l i n d i c a t o r i s back to i t s i n i t i a l p o s i t i o n . The loading frame i s f i x e d to the water-cooled chamber and i t seems that i t does not continue to expand as much as the ram. The r e s u l t i s an apparent expansion. Figure 27 shows the r e l a t i v e proportions of the expansion curves compared to the corrected creep curves. Due to the importance of the corr e c t i o n , the creep rates obtained from the corrected curves may be i n error by 10%. By repeating many experiments, this value has been found reasonable. 63 I I L_ 1000 2000 3000 Time, (sec) Figure 26(b) : Net d i l a t a t i o n of holding frame during heating (200°C/min.) and isothermal experiment at d i f f e r e n t temperatures. Figure 27(a) : Net d i l a t a t i o n of holding frame compared to corrected creep curve of the compact during heating rate of 27 C per minute. T T T +0.005 ~ A00 800 12 Time, (sees.) (b) : Net d i l a t a t i o n of holding frame and corrected creep curve at 500°C under 250 p s i . 65 IV. REFERENCES 1. J.E. Hove and W.C. R i l e y , "Modern Ceramics," John Wiley and Sons Inc. p. 215 (1965). 2. A.CD. Chaklader and V.T. Baker, "Reactive Hot-Pressing; F a b r i c a t i o n and D e n s i f i c a t i o n of Non-stabilized ZrO ", Am. Ceram. Soc. B u l l . , 44 [3] 258-59 (1965). 3. (a) A.CD. Chaklader and L.G. McKenzie, "Reactive Hot-Pressing of Clays," Am. Ceram. Soc. B u l l . , 43 [12] 892-93 (1964). (b) T.G. Carruthers and T.A. Wheat, "Hot-Pressing of Kaolin and of Mixtures of Alumina and S i l i c a , " Proc. B r i t . Ceram. Soc., 3,259-73 (1965). (c) P.E.D. Morgan and E. Scala, "High-Density Oxides by Decomposition Pressure S i n t e r i n g of Hydroxides," presented at the Sixty-Seventh Annual Meeting, The Am. Ceram. Soc., Philad e l p h i a , Pa., May 3, 1965 (Basic Science D i v i s i o n , No. 13-B-65); for abstract see Am. Ceram. Soc. B u l l . , 44 [4] 301 (1965). 4. J.A. Hedvall, Reaktionsfaehigkeit fester Stoffe (Reactivity of S o l i d s ) , Verlag Johann Ambrosius Barth, L e i p z i g , (1938), 243 pp. Reprinted by Edwars Inc., Ann Arbor, Mich., 1943; Ceram. Abstr., 17 [4] 164 (1938). 5. A. CD. Chaklader and L.G. McKenzie, "Reactive Hot-Pressing of Clays and Alumina," J . Am. Ceram. Soc. 49 [9] 477-83 (1966). 6. Xa) M. de Long and G.W. Rathenau, Acta Met. ]_ 246 (1959). (b) M. de Long and G.W. Rathenau, Acta Met. 9̂  714 (1961). (c) G.W. Greenwood and R.H. Johnson, Proc. Roy. Soc. A283 403 (1965). (d) D. Oelschlagel and V. Weiss, Trans. Quarterly A.S.M. 59 143 (1966). 7. A. CD. Chaklader, "Deformation of Quartz Crystals at the Transformation Temperature," Nature, 197 791-92 (1963). 8. J.L. Hart and A.CD. Chaklader, " S u p e r p l a s t i c i t y i n pure Zr0„," Mat. Res. B u l l . , 2 521-26 (1967). 9. P.W. Sunderland and A.CD. Chaklader, "Deformation during Dehydroxylation of Hydroxides," Mat. Res. B u l l . , 2 1111 (1967). 10. A.CD. Chaklader and R.C. Cook, "Kinetics of Reactive Hot-Pressing of Clays and Hydroxides," Am. Ceram. Soc. B u l l . , 47 [81 712-16 (1968). 11. R.K. I l e r , " F i b r i l l a r C o l l o i d a l Boehmite; Progressive Conversion to Gamma, Theta and Alpha Alumina," J . Am. Ceram. Soc. 44 [12] 618-624 (1961). 12. "Alumina Properties," Alcoa Research Laboratory, Technical Paper No. 10, p. 63, P i t t s b u r g , U.S.A. (1960). 13. P.W. Sunderland and A.CD. Chaklader, "Creep during Dehydroxylation of Magnesium Hydroxide," presented at the Seventieth Annual Meeting, 66 REFERENCES (continued) Am. Ceram. S o c , Chicago, 111., A p r i l 23, 1968 (Basic Science D i v i s i o n , No. 41-B-68). 14. W.D. C a l l i s t e r J r . , I.B. Cutler and R.S. Gordon, "Thermal Decomposition K i n e t i c s of Boehmite," J . Am. Ceram. Soc. [8] 419-22 (1966). 15. C. Eyraud and R. Goton,"Kinetics of the Thermal D i s s o c i a t i o n of the Hydrates of Alumina," J . Chim. Phys., ,51 430-33 (1954). 16. R.S. Gordon and W.D. Kingery, "Thermal Decomposition of Brucite," J . Am. Ceram. S o c , 50 [1] 8 - 1 4 (1967). 17. G.W. Brindley and M. Nakahira, "Kinetics of the Thermal Dehydroxylation of K a o l i n i t e and H a l l o y s i t e , " J . Am. Ceram. S o c , 40 [10] 346-50 (1957). 18. P.E. Evans "The a c t i v a t i o n energy for grain growth i n Alumina," Mater. S c i . Res., _3 345-53 (1966). 19. W.M. Robertson and R. Chang, "The Ki n e t i c s of grain-boundary groove growth on alumina surfaces," Mater. S c i . Res. _3 49-60 (1966). 20. F. Bueche, "Physical Properties of High Polymers," Interscience Publishers p. 90 (1962). 21. Vene, Harvo; Makivo, Itsuro, "Kinetics of Butadienne Polymerization i n the presence of cobalt c a t a l y s t sytems," Kogyo Kagaku Zasshi _71 [3] 418-21 (1968). 22. M.E. Wadsworth and A.CD. Chaklader, p r i v a t e communication (1968). 23. G.C. Kuczynski, " S e l f - D i f f u s i o n i n Si n t e r i n g of M e t a l l i c P a r t i c l e s , " J . Metals 1 (2), Trans. AIME 185 [2] 169-78 (1949).

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