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Creep of compacts of colloidal boehmite (A100H) during dehydroxylation St-Jacques, Robert Gustave 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), U n i v e r s i t y o f M o n t r e a l  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 t h e s i s as conforming t o the s t a n d a r d r e q u i r e d from candidates f o r the degree o f Master of A p p l i e d S c i e n c e  Members o f the Department of M e t a l l u r g y THE UNIVERSITY OF BRITISH COLUMBIA November, 1968  In p r e s e n t i n g t h i s t h e s i s  i n p a r t i a l f u l f i l m e n t of the requirements  for  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 r e f e r e n c e and Study. I f u r t h e r agree t h a t p e r m i s s i o n f o r e x t e n s i v e c o p y i n g of t h i s  thesis  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 t h a t c o p y i n g or p u b l i c a t i o n  of t h i s t h e s i s f o r f i n a n c i a l g a i n s h a l l not be a l l o w e d w i t h o u t my written permission.  Department of The U n i v e r s i t y of B r i t i s h Columb Vancouver 8, Canada  ABSTPACT  A compressive creep study of c o l d compacted boehmite has The  been c a r r i e d out  during  the r e l a t i v e d e n s i t y  a c t i v a t i o n energy f o r creep has t o t a l creep r a t e was  formation  due  of the  9.1  reaction. applied  c o l d compact.  been found to be  The ± 1.5  Kcal/mole.  to the s t r e s s a s s o c i a t e d w i t h the neck  at the p o i n t s of c o n t a c t  creep r a t e i s p r o p o r t i o n a l *u the  t h 3 dehydroxylation  creep t e s t s were made as a f u n c t i o n of temperature,  s t r e s s and  The  colloidal  and  the a p p l i e d s t r e s s .  to the a p p l i e d s t r e s s .  ^ - i • • rn i / / t o t a l creep r a t e e q u a t i o n i s e =10.144 exp  The  The  f i n a l form of  ,-9,100 ± 1,500. ( — ••• ) 2  RI  +  2.2  x 10  surfaces  ^ a  sec  \  E l e c t r o n photomicrographs of f r a c t u r e d  of deformed specimens r e v e a l e d  i n the a l i g n e d f o r shrinkage. strength  ]  fibers,  confirming  the presence of c o n t a c t  the e x i s t e n c e  Equations r e l a t i n g  of the d r i v i n g f o r c e  the change i n l e n g t h and  of a compact w i t h time have been t e s t e d w i t h the  process.  the  experimental  d a t a , which i n d i c a t e d t h a t the r a t e c o n t r o l l i n g mechanism may volume d i f f u s i o n f o r the creep  points  be  ACKNOWLEDGEMENTS  The  author wishes to acknowledge the h e l p g i v e n by  Dr. A. C D . Chaklader  throughout t h i s work.  Thanks a r e a l s o  extended to the s t a f f o f the Department o f M e t a l l u r g y advice.  for their  F i n a n c i a l a i d p r o v i d e d by the N a t i o n a l Research C o u n c i l  and by the Quebec M i n i s t r y of E d u c a t i o n  i s gratefully  acknowledged.  iii TABLE OF CONTENTS PAGE  I.  INTRODUCTION 1.1  1.2  1.3  1.4  1  R e a c t i v e h o t - p r e s s i n g and ceramic i n d u s t r y  i t s importance to the 1  Phenomenological e x p l a n a t i o n f o r enhanced compaction  3  P r e v i o u s s t u d i e s of deformation transformations  3  Previous  d u r i n g phase  s t u d i e s of r e a c t i v e h o t - p r e s s i n g  Boehmite (A100H)  II.  of . . . . .  1.5  E x p l a n a t i o n f o r enhanced compaction of Boehmite . . .  1.6  O b j e c t i v e of t h i s work  EXPERIMENTAL TECHNIQUES AND II. 1  5 9 10  RESULTS  11  Material  11  a) D e s c r i p t i o n  11  b) P r e p a r a t i o n of compacts  14  II. 2  Equipment  16  II. 3  Creep at a constant h e a t i n g r a t e  16  11.4  Creep under i s o t h e r m a l c o n d i t i o n s  18  11.5  Creep under d i f f e r e n t s t r e s s e s  20  11.6  D e n s i t y dependence of creep  26  11.7  Complementary e x p e r i m e n t a l  work  26  a) Creep t e s t s w i t h K a o l i n i t e  26  b) E l e c t r o n microscopy study  26  c) Weight l o s s v s . s h r i n k a g e  26  d) Measurements of s p e c i f i c s u r f a c e areas  27  e) Compressive s t r e n g t h of the compacts  27  iv TABLE OF CONTENTS  (continued)  PAGE III.  DISCUSSION  3  III.l  E f f e c t o f the s o a k i n g time  36  III. 2  Creep  39  III. 3  Neck f o r m a t i o n  40  III. 4  E f f e c t o f the d e n s i t y on the creep r a t e  41  111.5  P a r t i c l e deformation  41  111.6  Phenomenological  111.7  E q u a t i o n r e l a t i n g the change o f l e n g t h of the compacts w i t h time  111.8  IV.  V.  VI.  VII.  due to s u r f a c e t e n s i o n  e q u a t i o n o f the creep r a t e  . . .  S t r e n g t h o f the compacts as a f u n c t i o n of time  6  43  50 .  54  SUMMARY AND CONCLUSIONS  60  SUGGESTIONS FOR FUTURE RESEARCH  61  APPENDIX - Expansion  62  REFERENCES  correction  65  V  LIST OF FIGURES NO.  1  2  PAGE  Translucent Y A 1 2 3 pressing _  u  sheet made by r e a c t i v e hot 2  A s c h e m a t i c model of i n t e r p a r t i c l e bonding w i t h deformation  4  3  Compaction curves o f Boehmite  8  4  T r a n s m i s s i o n e l e c t r o n micrographs of boehmite powder.  12  5  S t r u c t u r e o f Boehmite showing atomic arrangement  13  6  Weight of powder and a p p l i e d p r e s s u r e v s . f r a c t i o n a l d e n s i t y of the compacts  15  7  Schematic diagram of f u r n a c e and l o a d i n g assembly  . .  17  8  E f f e c t of a p p l i e d s t r e s s on creep at a c o n s t a n t h e a t i n g r a t e , 27°C/minute d u r i n g d e h y d r o x y l a t i o n  . .  19  9  Creep at d i f f e r e n t  .  . .  temperatures under 265 p s i . . . .  10  Creep at 500°C, under 265 and zero p s i  11  S t r e s s dependence  of creep at 350°C  23  12  S t r e s s dependence  of creep a t 400°C  24  13  Stress  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 d e n s i t y dependence  of creep at 500°C  . . .  29  16  Creep o f K a o l i n i t e  30  17  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 s u r f a c e of boehmite compact a f t e r d e h y d r o x y l a t i o n  31  Creep a t 500°C, under 265 p s i and a f t e r s o a k i n g times  37  18  19  dependence  . . . . . . .  21 22  different  Creep, f r a c t i o n decomposed and s p e c i f i c s u r f a c e at 500°C, as a f u n c t i o n of time  area  20  Creep r a t e as a f u n c t i o n of f r a c t i o n a l d e n s i t y  . . .  21  Creep r a t e as a f u n c t i o n of s t r e s s at d i f f e r e n t temperatures  38 42  44  vi LIST OF FIGURES  (continued)  NO.  PAGE  22  Log eg as a f u n c t i o n of l o g a  45  23  Log of creep r a t e s as a f u n c t i o n of the r e c i p r o c a l of the a b s o l u t e temperature  47  25  Log{^— [1 ( T ) ^ ^ ] } a s a f u n c t i o n of l o g time o o Log s t r e n g t h as a f u n c t i o n o f l o g time  26  Net d i l a t a t i o n o f the specimen h o l d i n g  27  Net d i l a t a t i o n o f specimen h o l d i n g creep curves  24  -  L  -  55  L  frame  59 63  frame and c o r r e c t e d 64  vii  LIST OF  TABLES  NO.  I II  PAGE  Stress  dependence of the  F r a c t i o n a l density  creep r a t e  dependence of the creep r a t e  33 ...  33  III  F r a c t i o n reacted  as a f u n c t i o n of time  34  IV  S p e c i f i c surface  a r e a as a f u n c t i o n of time  34  V  VI  Compressive s t r e n g t h lation  of specimens a f t e r dehydroxy-  C o e f f i c i e n t s of the phenomenological e q u a t i o n of creep r a t e  35 the 48  1  I.  INTRODUCTION  1.1  REACTIVE HOT-PRESSING AND ITS IMPORTANCE TO THE CERAMIC INDUSTRY  R e a c t i v e h o t - p r e s s i n g i s a process  by which powdered m a t e r i a l s  can be d e n s i f i e d , a t much lower temperatures and i n s h o r t e r p e r i o d s than c o n v e n t i o n a l l y used.  This process is  i s e s s e n t i a l l y a h o t p r e s s i n g technique  c a r r i e d out i n c o n j u n c t i o n w i t h e i t h e r a polymorphic  or a decomposition  reaction.  transformation  The a p p l i c a t i o n o f p r e s s u r e  such a t r a n s f o r m a t i o n o r a decomposition  which  during  r e a c t i o n can produce  c o n s i d e r a b l e 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 f o r m a t i o n of a s t r o n g and dense body.  In o r d e r t o o b t a i n t r a n s l u c e n t alumina f o r example, i t i s normally  necessary  to hot-press  alumina powder under 6000 p s i a t  1500°C f o r a p e r i o d of 2 to 5 hours.  By p r e s s i n g aluminum  hydroxide  d u r i n g i t s d e h y d r o x y l a t i o n r e a c t i o n (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 a t 500°C ( F i g u r e 1 ) .  The  a p p l i c a t i o n o f p r e s s u r e d u r i n g the polymorphic  transformation  o  of n o n - s t a b i l i z e d z i r c o n i a powder (1160 - 1205 C) has been found  ( 2)  to  be a very e f f e c t i v e method o f f a b r i c a t i n g very dense and s t r o n g nons t a b i l i z e d z i r c o n i a products  i n s t e a d of the normal h o t - p r e s s i n g  process  at 1800°C.  When compared to the c o n v e n t i o n a l h o t - p r e s s i n g technique, r e a c t i v e hot p r e s s i n g p r e s e n t s  the advantages of s h o r t e r time, much lower temperatures  2  F i g u r e 1 : T r a n s l u c e n t Y-AI2O3 sheet produced by R e a c t i v e H o t - P r e s s i n g at 500°C/ 10 rains. Thickness  : 0.04  inch.  3  and  1.2  consequently  the p o s s i b i l i t y o f u s i n g h i g h e r  pressures.  PHENOMENOLOGICAL EXPLANATION FOR ENHANCED COMPACTION  Enhanced compaction o f a powder compact d u r i n g e i t h e r a decomposition  r e a c t i o n o r a polymorphic phase t r a n s f o r m a t i o n has been (3)  r e p o r t e d by s e v e r a l workers utilizes  .  The process  of r e a c t i v e h o t - p r e s s i n g  the f a c t t h a t the r e a c t i v i t y o f a s o l i d i s c o n s i d e r a b l y  enhanced d u r i n g phase t r a n s f o r m a t i o n s , decomposition,  or d i s s o c i a t i o n  (4) reactions and  (the H e d v a l l e f f e c t )  u n s a t i s f i e d valence  .  I t i s suggested  that broken bonds  l i n k s may e x i s t both on the s u r f a c e and i n  the b u l k o f the p a r t i c l e s o f a s o l i d d u r i n g a decomposition  reaction;  these may be a v a i l a b l e f o r i n t e r f a c i a l r e a c t i o n l e a d i n g to i n t e r particle 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 d u r i n g a r e a c t i o n can produce a t r a n s i e n t p l a s t i c s t a t e which may be u t i l i z e d  fordensification  (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 a c r o s s  the i n t e r f a c e .  However to e x p l a i n the  e l i m i n a t i o n of pores o r v o i d s from the compact i t i s necessary to p o s t u l a t e a mechanism i n v o l v i n g m a t e r i a l t r a n s p o r t .  I f there i s  a p l a s t i c s t a t e . d u r i n g the r e a c t i o n , the m a t e r i a l can flow and 1.3  easily  t h i s may r e s u l t i n d e n s i f i c a t i o n . 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  d u r i n g phase t r a n s f o r m a t i o n s  of m e t a l l i c m a t e r i a l s  S i m i l a r e f f e c t s would a l s o be expected  i n other c r y s t a l l i n e s t r u c t u r e s  such as ceramic  on p l a s t i c behaviour  oxides.  Observations  i n quartz  4  t  NO  INTERPARTICLE  BONDING  INTERPARTICLE DEFORMATION.  INTERPARTICLE  WITHOUT  BONDING  F i g u r e 2 : A Schematic Model o f I n t e r p a r t i c l e Deformation.  BONDING  DEFORMATION.  WITH  Bonding w i t h  5 c r y s t a l s d u r i n g the a to 6 phase change have been r e p o r t e d by Chaklader^^, while H a r t ^ i n pure  i n an i n v e s t i g a t i o n of creep  deformation  z i r c o n i a , u s i n g a c r e e p - i n - b e n d i n g method w i t h programmed  temperature  i n c r e a s e , showed the occurrence of s u p e r p l a s t i c i t y  transformation p l a s t i c i t y  at temperatures  or  near the m o n o c l i n i c to 3 C)  t e t r a g o n a l phase t r a n s f o r m a t i o n .  A l s o , Morgan and S c a l a '  prepared h i g h d e n s i t y oxide ceramics from h y d r o x i d e s by  have  application  of p r e s s u r e d u r i n g the d e h y d r o x y l a t i o n r e a c t i o n and showed t h a t phase changes, accompanying chemical r e a c t i o n s , can a i d the s i n t e r i n g p r o c e s s , e s p e c i a l l y under a p p l i e d p r e s s u r e .  U t i l i z a t i o n of  phenomenon allowed them to f i r e a t temperatures  much lower  this  than  those used p r e v i o u s l y .  (9) A study by Sunderland  and Chaklader  of the neck growth  between t i p s 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 d e f o r m a t i o n  and  i n t e r a c t i o n a t the c o n t a c t p o i n t d u r i n g d e h y d r o x y l a t i o n r e a c t i o n . The k i n e t i c s of compaction  d u r i n g the d e h y d r o x y l a t i o n r e a c t i o n  of c h i n a c l a y , f i r e c l a y , magnesium hydroxide and aluminum hydroxide have been s t u d i e d by Cook and C h a k l a d e r .  They concluded that  the t r u e mechanism o r mechanisms of compaction  cannot be  determined  s o l e l y by k i n e t i c a n a l y s i s , although i t can be assumed that the enhanced compaction  i s dependent on the d e h y d r o x y l a t i o n r e a c t i o n  and  other phase changes o c c u r r i n g i n the m a t e r i a l .  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 s t r e n g t h o r b u l k d e n s i t y of a boehmite compact and, the e x t e n t o f the d e h y d r o x y l a t i o n r e a c t i o n o c c u r r i n g d u r i n g the d e n s i f i c a t i o n process  under r e a c t i v e h o t - p r e s s i n g c o n d i t i o n s .  The  r e s u l t s were a n a l y z e d u s i n g the e m p i r i c a l r e l a t i o n t h a t the s t r e n g t h i s p r o p o r t i o n a l to the e x t e n t o f r e a c t i o n . each h o t - p r e s s i n g c o n d i t i o n b o t h  I t was assumed t h a t a t  the r e a c t i o n and s t r e n g t h 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 f o r m a t i o n , reached  a pseudo-equilibrium  state.  The  temperature c o e f f i c i e n t o f the r e a c t i o n can be  determined  p r o v i d e d an e q u i l i b r i u m c o n d i t i o n i s a t t a i n e d and t h i s s h o u l d a v a l u e f o r the enthalpy o f the r e a c t i o n to be o b t a i n e d .  permit  The energy  v a l u e s o b t a i n e d from the a n a l y s i s o f the data were s m a l l e r than the e n t h a l p y v a l u e s r e p o r t e d by o t h e r workers f o r the r e a c t i o n  concerned.  However, i n view o f the f a c t t h a t the standard s t a t e o f t h i s r e a c t i o n was n o t known and the u n c e r t a i n t y o f the assumption t h a t the s t r e n g t h at any s t a g e was p r o p o r t i o n a l to the extent o f r e a c t i o n , t h i s disagreement was n o t unexpected.  Nevertheless,  t h a t d e n s i f i c a t i o n was d i r e c t l y r e l a t e d and  the r e s u l t s showed  to the r e a c t i o n i n v o l v e d  t h a t the compaction b e h a v i o r d u r i n g the d e h y d r o x y l a t i o n r e a c t i o n  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 b e h a v i o r  a f t e r the  reaction.  In o r d e r to s u b s t a n t i a t e t h i s f u r t h e r , attempts were made by Cook and C h a k l a d e r t o dehydroxylation process.  study  the k i n e t i c s of compaction d u r i n g the  I n i t i a l experiments under i s o t h e r m a l c o n d i t i o n s  d i d not permit u s e f u l c o n c l u s i o n s to be made f o r the f o l l o w i n g reasons: a)  A t h i g h temperatures,  the d e h y d r o x y l a t i o n r e a c t i o n took p l a c e w i t h i n  a few minutes and the creep r a t e was  too f a s t to be measured  accurately. b)  The compaction r a t e was  very s e n s i t i v e to the s i z e of the  specimen as t h i s c o n t r o l l e d  the volume of vapor phase formed  d u r i n g the r e a c t i o n . c)  The r a t e of vapor phase removal c o u l d be c o n t r o l l e d by v a r y i n g the a n n u l a r space between the d i e w a l l and the p l u n g e r s and  this  a l s o a f f e c t e d the r a t e o f compaction. d)  At h i g h e r temperatures, when a s i g n i f i c a n t p o r t i o n of the d e h y d r o x y l a t i o n r e a c t i o n was  completed d u r i n g the heating-up  p e r i o d , the study o f compaction r a t e produced erroneous and nonreproducible  results.  For these r e a s o n s , Cook and Chaklader e v a l u a t e d the compaction k i n e t i c s by s t u d y i n g the compaction b e h a v i o r over a range of c o n s t a n t heating  rates.  In the work of Cook and Chaklader, the powder was p r e s s e d under a c o n s t a n t p r e s s u r e of 5000 p s i i n a c y l i n d r i c a l d i e and the compaction was  recorded  as the temperature was  increased.  Figure 3  shows the compaction curves r e p l o t t e d from Cook's d a t a t o g e t h e r w i t h a t h e r m o g r a v i m e t r i c (TGA) p l o t of the same m a t e r i a l f o r comparison.  The s i m i l a r i t y between the compaction curves and the TGA i s q u i t e apparent. weight l o s s period.  Between 350°C and 550°C there was  (15%) and about 8%•compaction was  plot  a significant  obtained during  this  T h i s range of temperature corresponds to the d e h y d r o x y l a t i o n  of boehmite.  The temperature g r a d i e n t from the s u r f a c e to the core  of the compact caused the s u r f a c e to reach the d e h y d r o x y l a t i o n  temperature  10  Boehmite 5 0 0 0 psi constant pressure  30  8  J 25  AL  -J20  j o Heating rate — 2°C/min. _ J J  I O in 2  A •  400  —6°C/min. I  .»• -l2°C/min. _|, TGA l2°C/min. \  II  ~ 200  •I  II  600  800  TEMP. (°C)  -Figure _3 _:_ Compaction curves of Boehmite.  JL  ±  1000  j_  1200  o 0  range b e f o r e the c o r e .  With a slow h e a t i n g r a t e , there was  sufficient  d e h y d r o x y l a t i o n a t the s u r f a c e to produce a hard c y l i n d r i c a l s l e e v e w h i l e the c e n t e r was compaction  still  unreacted.  T h i s r i g i d m a t e r i a l slowed  the  a t low h e a t i n g r a t e s as shown i n F i g u r e 3.  In a d d i t i o n to compaction a d d i t i o n a l enhanced compaction  was  d u r i n g the decomposition  reaction,  a l s o o b t a i n e d d u r i n g the Y~alumina  to a-alumina phase change a t 1100°C.  1.5  EXPLANATION FOR  ENHANCED COMPACTION OF BOEHMITE (3 C)  Morgan and S c a l a to the decomposition  '  claimed t h a t on r a i s i n g  the  temperature  range, d e n s i f i c a t i o n occurs by a complex  super-  i m p o s i t i o n of c h e m i c a l l y induced f r a g m e n t a t i o n and mechanical ment of newly formed, very f i n e oxide g r a i n s (generated from hydroxide).  rearrangethe  They r e p o r t e d t h a t water vapor g i v e n o f f d u r i n g  this  f i r s t s t a g e p r o b a b l y c o n t i n u e s to a c t i v a t e f u r t h e r s i n t e r i n g of the oxide mass and a t the end of the r e a c t i o n escapes,  l e a d i n g to the  t h e o r e t i c a l d e n s i t y and t r a n s l u c e n c y . Cook and C h a k l a d e r s u g g e s t e d p r o c e s s , i n t e r a c t i o n between (OH)  i o n s to form ^ 0  subsequent d i f f u s i o n of these molecules s c a l e p a r t i c l e movement.  t h a t i n the d e h y d r o x y l a t i o n molecules  does not i n v o l v e any l a r g e  I n order to e x p l a i n 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 a p p l i e d s t r e s s , l a r g e  s c a l e p a r t i c l e rearrangement must e x i s t .  They concluded  f r a g m e n t a t i o n d u r i n g the d e h y d r o x y l a t i o n process may affect  the p a r t i c l e  flow.  and  also  that significantly  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 c y l i n d r i c a l specimens of f i b r i l l a r c o l l o i d a l boehmite was investigated by compression isothermal conditions.  creep tests under  11  II  EXPERIMENTAL TECHNIQUES AND RESULTS  II.1  a)  MATERIAL  Description  The m a t e r i a l used i n t h i s study was c o l l o i d a l boehmite s u p p l i e d 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 o f the powder a r e d e s c r i b e d by I l e r ^ " ^  as h a v i n g  A100H, 83.1%;  bound water, 3.3%; 1.7%.  a c e t a t e as a c e t i c a c i d , 9.8%;  p h y s i c a l l y adsorbed water, 1.8%;  sulphate  as SO^,  The true d e n s i t y of the m a t e r i a l i s 2.28 grams p e r c c .  particles  The  a r e f i b r i l l a r , b e i n g about 50 angstroms i n diameter and  1000 to 2000 angstroms l o n g .  F i g u r e s 4(a) and 4(b) show  e l e c t r o n photomicrographs o f the powder. microscope were prepared  transmission  Specimens f o r the e l e c t r o n  by d i s p e r s i n g 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 grid.  chemically  f i l m p l a c e d on a copper  The water was evaporated o f f and the copper g r i d was p l a c e d  i n t h e e l e c t r o n microscope. than F i g u r e 4 ( a ) .  F i g u r e 4(b) shows f i b e r s i n a more d i s p e r s e d  The powder c o n s i s t s o f d i s c r e t e f i b e r s i n the form  of l o o s e l y a s s o c i a t e d porous aggregates.  The  dehydroxylation  o f boehmite to gamma alumina i n v o l v e s  a minor change i n the o v e r - a l l c r y s t a l s t r u c t u r e .  only  The s t r u c t u r e of  (12) boehmite  c o n s i s t s of oxygen i o n l a y e r s that do not f i t w i t h  other b u t w i t h i n which the oxygen i o n s a r e i n c u b i c p a c k i n g . d i r e c t i o n s form z i g - z a g chains between the planes  each The OH  of the oxygen i o n s .  F i g u r e 5 shows the a-plane and the c-plane o f a model of boehmite. When the hydroxy1 ions a r e removed, the l a y e r s form a c u b i c arrangement o f oxygen i o n s w i t h  close-packed  the s m a l l e r aluminum ions remaining i n  state  (a)  X40,000  (b) X120,000  F i g u r e 4 : T r a n s m i s s i o n e l e c t r o n micrographs powder.  of boehmite  "a"  plane  it  j  "c" plane  Figure 5 :  S t r u c t u r e of boehmite atomic arrangement.  showing  Glossy b l a c k 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  The hydroxyl  formula  i o n s and  sites.  A100H g i v e s a p r o p o r t i o n of 2 to 1 between the  the aluminum atoms.  However the aluminum  ions  l y i n g a t the s u r f a c e of the boehmite f i b e r s would be s u b j e c t e d c a t i o n i c s c r e e n i n g and would p i c k up h y d r o x y l  groups i n o r d e r  to to  2 become s t a b l e . these h y d r o x y l  Because the s u r f a c e a r e a i s l a r g e (250 m /gram), groups are r e s p o n s i b l e f o r a measurable excess of  water over the formula distinct  A100H.  T h i s c h e m i c a l l y bound water i s  from the p h y s i c a l l y adsorbed water.  c h e m i c a l l y bound water p l u s  He  b)  the s u r f a c e w i t h OH  the  to  the  groups  and  r e p o r t e d a l s o t h a t when the powder i s heated up  300°C, the a c e t a t e and II.1  found t h a t  the a c e t a t e corresponded c l o s e l y  t h e o r e t i c a l amount r e q u i r e d to cover acetic acid.  Iler  to  adsorbed water are removed.  P r e p a r a t i o n of Compacts  The  powder was  compacts 0.190  cold-pressed  i n c h i n diameter and  weight of the powder and f a b r i c a t i o n was  density.  0.270 - 0.280 i n c h l o n g .  the l o a d a p p l i e d on the ram  during  The the  v a r i e d to o b t a i n compacts of d i f f e r e n t d e n s i t i e s but  of the same l e n g t h . the p r e s s u r e  i n a c y l i n d r i c a l d i e to form  F i g u r e 6 shows the weight of the powder  and  a p p l i e d to form the compacts as a f u n c t i o n of the  green  To ensure i d e n t i c a l compaction r a t e , the compacts were  cold-pressed  at 0.1  i n c h per minute i n an I n s t r o n machine.  batches of compacts, each of 50 p e l l e t s , . were prepared  The  Three  i n t h i s manner.  d e n s i t i e s of the compacts were c a l c u l a t e d from weight to  volume r a t i o .  I t was  observed t h a t the compacts having  f r a c t i o n a l d e n s i t y were too f r a g i l e  to handle and  less  than  0.50  that compacts of more  15  F i g u r e 6:  R e l a t i o n between p r e s s u r e on p i s t o n , w e i g h t of powder and f r a c t i o n a l d e n s i t y of p e l l e t s h a v i n g c o n s t a n t dimensions.  16 than 0.65  f r a c t i o n a l d e n s i t y were s t r o n g but very d i f f i c u l t  r e l e a s e i n t a c t from the d i e due  to f r i c t i o n .  experiments  w i t h compacts of 0.60  11.2  have been performed  to  Hence, most of the fractional density.  EQUIPMENT  The Sunderland  apparatus  (9)  used  i n the creep study has been b u i l t  and i s shown i n F i g u r e 7.  by  I t c o n s i s t e d of a h o r i z o n t a l -3  r e s i s t a n c e vacuum f u r n a c e i n which a p r e s s u r e of <5 x 10 maintained.  The vacuum chamber was  water c o o l e d and  l o a d i n g d e v i c e l a i d o u t s i d e the h e a t i n g zone. and  the ram were made of s t a i n l e s s s t e e l .  programmed f o r c o n s t a n t h e a t i n g r a t e s  chromel-alumel  thermocouple t o u c h i n g i t s s u r f a c e .  used  study.  The  (sensitivity  directly  ram 11.3  The same i n conjunction with occasionally  d i s t r i b u t i o n d u r i n g the  l i n e a r d i m e n s i o n a l change was : 0.0001 i n c h ) and was  creep  measured by a d i a l  displacement  indicator  p l o t t e d as a f u n c t i o n of the  A t r a n s d u c e r was  time  a l s o a v a i l a b l e to r e c o r d  the d i m e n s i o n a l change on a s t r i p - c h a r t r e c o r d e r ;  the n o n - l i n e a r i t y  a  of the i n t e r i o r of the specimen i n  the temperature  to g i v e the creep r a t e .  for isothermal  recorded by  An a d d i t i o n a l thermocouple was  to measure the temperature  o r d e r to determine  of the specimen was  to c o n t r o l the temperature  a Honeywell c o n t r o l l e r .  l o a d i n g frame  or c o u l d be used  The  used  the s p r i n g  The f u r n a c e c o u l d be  creep t e s t s .  thermocouple was  temperature  The  torr was  however,  of the t r a n s d u c e r v o l t a g e over a l a r g e range of prevented  i t s use.  CREEP AT A CONSTANT HEATING RATE  The frame and  c y l i n d r i c a l specimen was  the ram  and  the system was  p l a c e d l o o s e l y between the l o a d i n g pumped down to 5 x 10  -3  torr.  A  L o a d i n g Frame  18  s t r e s s o f 105 p s i was  then a p p l i e d and the specimen was  a r a t e of e i t h e r 27 or 2°C p e r minute.  heated a t  The creep data o b t a i n e d was  s u b s e q u e n t l y c o r r e c t e d f o r the expansion of the h o l d i n g frame  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 t e s t s were made under the same s t r e s s heating rates  (2 and 27°C per m i n u t e ) .  (105 p s i ) but a t d i f f e r e n t  However, both the creep r a t e  and the t o t a l creep i n c r e a s e d w i t h i n c r e a s e d s t r e s s i n Figure  II.4  (Appendix I ) .  (155 p s i ) as shown  8.  CREEP UNDER ISOTHERMAL CONDITIONS  The compact was obtainable  heated i n vacuum a t the maximum h e a t i n g  (200°C per minute) u n t i l  reached the t e s t  temperature.  the specimen, i t was  the s u r f a c e temperature had  By p l a c i n g a thermocouple  less  inside  found t h a t the i n s i d e of the specimen took an  e x t r a 30 seconds to r e a c h the t e s t temperature but that t h e r e was  rate  thereafter  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 l o a d 30 seconds a f t e r the thermocouple t o u c h i n g the s u r f a c e o f the compact had reached the t e s t temperature. t e s t s were c a r r i e d out a t f i v e temperatures: 550°C.  Creep  350, 400, 450, 500  and  The d u r a t i o n of the t e s t s v a r i e d from 10 to 20 minutes,  depending on the t e s t temperature.  However, s e v e r a l experiments  were c a r r i e d out f o r p e r i o d s up to one hour.  As p r e v i o u s l y noted the l o a d was t e s t temperature was  reached.  a p p l i e d 30 seconds a f t e r the  A c c o r d i n g l y at 350°C, the l o a d  a p p l i e d 3 minutes a f t e r the power was  was  turned on and a t 550°C i t was  19  Figure  8  :  E f f e c t of a p p l i e d s t r e s s on creep at a h e a t i n g r a t e of 27°C per minute.  constant  20  a p p l i e d a f t e r 4% minutes.  T h i s e x p l a i n s why  i n F i g u r e 9 the  of the d i f f e r e n t curves s h i f t e d to an i n c r e a s i n g time as the temperature i n c r e a s e d .  origin test  However, the f a c t t h a t the curves o r i g i n a t e  at a p o i n t where j^- i s d i f f e r e n t from-zero i n d i c a t e s t h a t the o L  shrank even w i t h o u t any 265  applied stress.  p s i , the creep r a t e i n c r e a s e d  48 x 1 0 ~  sec"  5  1  at 550°C.  at 550°C the creep r a t e s approached II.5  seconds a t 350°C or 800  seconds  zero.  155  changing the s p r i n g of the l o a d i n g d e v i c e ,  and  265  p s i c o u l d be  c a l i b r a t e d i n an I n s t r o n  To  applied.  the d i m e n s i o n a l change was  applied stress. under 265  C or 500  C over d i f f e r e n t p e r i o d s  Figure  11,  12 and  l i n e a r 10 - 15 seconds a f t e r the l o a d i s a p p l i e d . i s believed  The  any'  creep  creep curves become This  to be  an  t r a n s i e n t creep adjustment  f o r the d i s t r i b u t i o n of s t r e s s on the whole specimen.  p a r t of the creep has  It  from 21 ± 2 to 31 ± 2 x  13 show some t y p i c a l  550°C r e s p e c t i v e l y .  observed i n most experiments and  10.  i s creep w i t h o u t  At 500°C, the creep r a t e i n c r e a s e d psi.  and  determined.  from t h i s f i g u r e t h a t there  curves at 350°C, 400°C and  period  was  s h r i n k a g e when the compact undergoes  e f f e c t of the a p p l i e d s t r e s s i s shown i n F i g u r e  i s q u i t e evident  sec.  spring loading device  61,  ( i . e . f r e e of a p p l i e d s t r e s s ) a s e r i e s of specimens  were heated under vacuum at 350  The  The  s t r e s s e s of 31,  t e s t i n g machine to ±0.05 l b .  f i n d i f there i s any  dehydroxylation  was  at 350°C to  CREEP UNDER DIFFERENT STRESSES  By 105,  With an a p p l i e d s t r e s s of  from 11 x 10 ^ sec  A f t e r 1600  compacts  not been taken i n t o c o n s i d e r a t i o n i n the  This creep  10  T  1  1  r  0.02  0.04  AL 0.06  0.08  0 psi 0.10 500 °C reached  0.12 265 p s i 0.13  400  _1_ 1000  2000  3000 Time, seconds  •igure 10  :  Creep at 500°C,  under 265  and zero  DSI.  3600  Time (sec) F i g u r e 11 : S t r e s s dependence of Creep at 350°C  0  I  1  I  1  1  |  F r a c t i o n a l Density :  1  0.60  0.01  0.02:  -  1  ^  load  applied  0.03  -  0.04  -  0.05  \ 400 C reached  \  \ \ \  0.06  31 p s i \ \  105 p s i  \  -  265 p s i  1  0.07  -  1 0.08  1  1  1  100  200  300  l 400  l 500  Time (sec) F i g u r e 12 : S t r e s s Dependence of Creep at 400°C  i 600  25  26  data a n a l y s i s .  T a b l e I on page' 33., summarizes the creep r a t e s  o b t a i n e d over the temperature s t r e s s e s i n the range  11.6  range  350 - 550°C and under d i f f e r e n t  31 to 265 p s i .  DENSITY DEPENDENCE OF CREEP  The e f f e c t o f d e n s i t y on the creep b e h a v i o r o f the compacts was s t u d i e d by u s i n g specimens having v a r i o u s f r a c t i o n a l  densities  r a n g i n g from 0.42 to 0.68.  tests  F o r t h i s purpose,  the creep  were c a r r i e d out a t 400 and 500°C under a p r e s s u r e of 105 p s i . F i g u r e s 14 and 15 show some o f the creep curves of t e s t s made a t 400°C and 500°C. of specimens used  11.7  a)  T a b l e I I shows creep r a t e s f o r the complete t o study the d e n s i t y dependence of c r e e p .  COMPLEMENTARY EXPERIMENTAL WORK  Creep  tests with K a o l i n i t e  Creep  t e s t s were made a t 575 and 600°C under 105 p s i to study  the b e h a v i o r o f another h y d r o x i d e m i n e r a l under i d e n t i c a l conditions.  b)  series  testing  The r e s u l t s a r e shown i n F i g u r e 16.  E l e c t r o n microscopy  study  A few specimens, a f t e r the creep t e s t , were f r a c t u r e d p e r p e n d i c u l a r to t h e i r c y l i n d r i c a l a x i s .  D i r e c t r e p l i c a s were made by shadowing g o l d  on the f r a c t u r e d s u r f a c e and subsequently To detach the carbon f i l m , hydrochloric acid.  c)  e v a p o r a t i n g a l a y e r o f carbon.  the alumina specimens were d i s s o l v e d i n  E l e c t r o n micrographs  a r e shown i n F i g u r e 17.  Weight l o s s v s . s h r i n k a g e  A s e r i e s of specimens were heated f o r d i f f e r e n t p e r i o d s i n a i r  27 at 350°C and i n vacuum (5 t o r r s ) a t 500°C i n o r d e r to c o r r e l a t e the weight l o s s or f r a c t i o n r e a c t e d w i t h the creep.  The r e s u l t s ' a r e  included i n Table I I I .  d)  Measurements  o f s p e c i f i c s u r f a c e 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 f o r d i f f e r e n t p e r i o d s . T h e i r s p e c i f i c s u r f a c e was measured w i t h an Aminco Sor-BET machine. T a b l e IV shows the v a l u e s  e)  obtained.  Compressive s t r e n g t h of the compacts  In o r d e r to c o r r e l a t e the s t r e n g t h of a compact w i t h the e x t e n t o f the r e a c t i o n , a s e r i e s of specimens were deformed under 105 p s i at 400°C and 500°C f o r v a r i o u s p e r i o d s . compression  was  cross-heads  displacement was  are summarized  determined  i n T a b l e V.  Their strength i n  i n an I n s t r o n t e s t i n g machine. 0.05  i n c h per minute.  The  The results  28  i  — T  T  1  r  105 p s i 0.01  0002 \-  load  applied  0.03 AL L„  0C044  0.05  0.67 0.60  0.06  0.07  0.08  L  h  400°C reached  J  I  100  200  I  300  I  400  i  I  500  L 600  Time (sec) F i g u r e 14 : F r a c t i o n a l D e n s i t y Dependence, of creep at 400 C  29  (b) X75.000 F i g u r e 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 s u r f a c e of boehmite compact after dehydroxylation.  32  X200.000 F i g u r e 17(c) : R e p l i c a e l e c t r o n m i c r o g r a p h o f f r a c t u r e d s u r f a c e of boehmite compact a f t e r d e h y d r o x y l a t i o n .  33  TABLE I STRESS DEPENDENCE OF THE CREEP RATE* CREEP RATES 350°C 31 p s i 61 ' 105 155 265  400  5.7 ± 0.6 5.9 7.8 7.4 10.7  10  5  450  1 0 . 0 ± 1.0 1 8 . 2 ± 1.5 10.7 18.4 11.8 18.2 12.0 19.4 15.3 22.5  *  -1  sec 500  25 ± 2 25 29 30 31  550°C 43 ± 3 45 46 48 48  F r a c t i o n a l D e n s i t y o f 0.60  TABLE  II  FRACTIONAL DENSITY DEPENDENCE OF THE CREEP RATE* CREEP RATES  10  5  sec -1  400°C Density  Density 0.42 0.45 0.54 0.56 0.60 0.67  500°C  12.9 ± 1.0 11.5 12.6 12.0 12.0 8.7  0.43 0.45 0.47 0.48 0.63 0.68  * A p p l i e d S t r e s s : 105 p s i  35 ± 2 29 28 34 30 : 32  34  TABLE I I I  FRACTION REACTED AS A FUNCTION OF TIME  500°C i n vacuum 0  %  min.  1 2  5 60  350°C i n a i r 2 min. 6 15 30 60  0.30 0.60 0.70 0.93 0.96 1.00  *  0.30 0.13 0.21 0.23 0.37  Due to Heating P e r i o d  TABLE IV  SPECIFIC SURFACE AREA* AS A FUNCTION OF TIME  0  500 C i n vacuum  105 s e c . 170 330 1 hr. 2h h r .  2 301 m /gm 326 309 319 283  400°C i n a i r  500°C i n a i r 2  .105 s e c . 15  min.  18 h r s .  180 s e c .  2  255 m /gm 317  262 m /gm 12 h r s .  270 288 m /gm 2  * ± 10%  TABLE V COMPRESSIVE STRENGTH OF SPECIMENS AFTER DEHYDROXYLATION  400°C  50 s e c 80 100 150 200 300  500°C  990 p s i 1100 1400 1350 1700 1650  40 sec 50 70 80 120 150  1600 p s i 1750 2200 1950 2250 2900  36 III.  DISCUSSION  III.l  EFFECT OF THE  The  SOAKING TIME  compacts have been found  a p p l i c a t i o n of the l o a d extended  (Figure 9).  from 30 to 210 seconds  4 to 6.5%  to s h r i n k even b e f o r e the I f the soaking time i s  t h i s s h r i n k a g e i n c r e a s e s from  as shown by the t y p i c a l curves of F i g u r e 18.  t e s t i n g c o n d i t i o n s were i d e n t i c a l w i t h r e s p e c t to (500°C) and s t r e s s expected.  of  partially  the a p p l i e d s t r e s s  t o t a l creep was  the  temperature  (265 p s i ) , the creep curves are p a r a l l e l as  When the l o a d was  the r e a c t i o n was  As  a p p l i e d a f t e r a long s o a k i n g p e r i o d ,  completed,  so that the  to the o v e r a l l creep was  contribution  s h o r t and  the  c o r r e s p o n d i n g l y s m a l l e r than when the l o a d  was  a p p l i e d w i t h o u t any s o a k i n g p e r i o d .  In  o r d e r to e s t a b l i s h a r e l a t i o n between.the s h r i n k a g e  observed d u r i n g the d e h y d r o x y l a t i o n r e a c t i o n and  the creep  experiments  l o s s of the  specimen was  were c a r r i e d out i n which the weight determined  under the. same h e a t i n g c o n d i t i o n s as were  used f o r the creep study. of  itself,  The v a r i a t i o n o f s p e c i f i c s u r f a c e area  boehmite on c a l c i n a t i o n was  a l s o determined.  T h i s i s important  (13) as i t has been shown  t h a t f o r most h y d r o x i d e s , s u r f a c e a r e a  increases considerably after c a l c i n a t i o n . results  of t h r e e d i f f e r e n t experiments;  F i g u r e 19 shows the creep, f r a c t i o n decomposed  and s u r f a c e a r e a a t 500°C, as a f u n c t i o n of time. experiment was  made under 265 p s i .  The  creep  A s e r i e s of powder samples have  been heated  i n vacuum a t 500°C f o r d i f f e r e n t p e r i o d s .  r e a c t e d was  calculated  from the weight  The  l o s s measurements.  fraction The  curves  0.02  0.04  0.06  0.08  0.10  210 seconds soak 500°C reached  0.12 30 seconds soak  JL  JL  1000  400 F i g u r e 18:  Creep at 500°C  2000 )  Time, seconds  under 265 p s i and a f t e r d i f f e r e n t s o a k i n g  3000 times,  0.04 0.08 AL  Creep o .h L  0.16 Fraction  Reacted  1.0 a 0.5 0  _  300  S p e c i f i c Surface  gm 200 100 •-  JL  -L 100  300  500  1000  2000  3000 Time (sees)  F i g u r e 19 : Creep, f r a c t i o n decomposed and s u r f a c e a r e a .as a f u n c t i o n of time a t 500°C  f o r the s p e c i f i c s u r f a c e a r e a and  the f r a c t i o n r e a c t e d reached  steady v a l u e s i n a s h o r t e r time than the creep curve. d i f f e r e n c e can be e x p l a i n e d as b e i n g due  to the f a c t  This that  removal  of the vapour phase i s f a s t e r from a l o o s e powder such as used f o r the s u r f a c e a r e a and  the percentage  transformed t e s t than from  a compact as used f o r the creep measurements. water vapor p r e s s u r e i n the compact may  The presence of  a l s o have reduced  the r a t e  (14) of the r e a c t i o n  .  Hence, i t appears  r e a s o n a b l e to say  creep d e f o r m a t i o n ceases when the r e a c t i o n i s over.  that  the  The s m a l l  2 i n c r e a s e i n s u r f a c e a r e a (250 to 320 m /gm) Iler  as due  has been e x p l a i n e d by  to i n c r e a s e i n i n t e r n a l p o r o s i t y .  A d i s p e r s e d sample of the boehmite powder was carbon f i l m i n the h o t - s t a g e of the H i t a c h i e l e c t r o n The specimen was photographs  not exposed  at d i f f e r e n t  observed.  Up  to 800°C, no  CREEP DUE  significant  However, a t 50,000 m a g n i f i c a t i o n ,  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  III.2  microscope.  to the e l e c t r o n beam except to take  temperatures.  change of the specimen was  heated on a  very poor.  TO SURFACE TENSION  The creep b e h a v i o r of boehmite d u r i n g the d e h y d r o x y l a t i o n r e a c t i o n i s very d i f f e r e n t from the creep b e h a v i o r of k a o l i n i t e magnesium h y d r o x i d e .  With no a p p l i e d s t r e s s i t has been observed  t h a t a compact of k a o l i n i t e undergoes a change i n l i n e a r of  l e s s than 0.5%  i n c u r s a weight kaolinite. or 600°C  and  dimension  d u r i n g i t s d e h y d r o x y l a t i o n r e a c t i o n although i t  l o s s of 14%.  F i g u r e 16 shows two creep curves of  When the specimen was  ( b e f o r e the l o a d was  maintained f o r 30 seconds  at  a p p l i e d ) the d i m e n s i o n a l change of  575  the compact was n e g l i g i b l e .  In the case o f magnesium  hydroxide,  (13) Sunderland  reported  a t o t a l creep  0.5% s h r i n k a g e  under zero l o a d compared to  o f 8% a t 400°C and under 210 p s i .  T h i s shrinkage i n  the case of boehmite may be up to 10% ( F i g u r e 10). Before  any shrinkage  can take p l a c e i n t e r a c t i o n between  p o i n t s of c o n t a c t i s n e c e s s a r y . rise and  to s h r i n k a g e lowering  The f r e e energy change t h a t g i v e s  o f a powder compact i s the decrease i n s u r f a c e  area  o f the s u r f a c e f r e e energy by the e l i m i n a t i o n o f s o l i d -  vapor i n t e r f a c e .  The d r i v i n g f o r c e f o r neck-growth between two  particles  i s the e f f e c t i v e s t r e s s a s s o c i a t e d w i t h  curvature  a t the p o i n t s o f c o n t a c t .  the r a d i u s o f  This stress i s inversely  p r o p o r t i o n a l to the r a d i u s o f c u r v a t u r e .  The f i b e r s o f the boehmite  powder s t u d i e d have a diameter o f about 0.005y.  Using  the g e n e r a l  2Y  formula ——, where y i s the s u r f a c e energy and R i s the r a d i u s o f K curvature  2  and assuming a s u r f a c e energy as low as 100 ergs p e r cm , the  s t r e s s a t the p o i n t of c o n t a c t between two f i b e r s o f boehmite i s over 10,000 p s i . creep  study  T h i s s t r e s s i s much l a r g e r than those and i s expected to induce  between the p a r t i c l e s III.3  a p p l i e d i n the  the necks ( p o i n t s o f c o n t a c t )  to grow.  NECK FORMATION  In o r d e r  to see i f t h e r e was any evidence  of neck  formation,  compacts were f r a c t u r e d p e r p e n d i c u l a r l y to the c y l i n d r i c a l a x i s . D i r e c t r e p l i c a s were made on the f r a c t u r e d s u r f a c e s and examined i n the e l e c t r o n microscope.  F i g u r e 17(a)  shows that the t e x t u r e i s  composed o f bent but a l i g n e d f i b e r s .  I t appears that the f i b e r s  were a l i g n e d i n p a r a l l e l a r r a y s during  the c o l d compaction o f the  powder ( F i g u r e 4 ( a ) ) .  41 During  the d e h y d r o x y l a t i o n  were formed between a d j a c e n t associated with  r e a c t i o n , a g r e a t number o f necks  f i b e r s i n order  the s m a l l r a d i u s of c u r v a t u r e  F i g u r e s 17(b) and 17(c) higher magnifications. between two a d j a c e n t  a t the p o i n t s o f c o n t a c t .  show the f r a c t u r e d s u r f a c e a t The b l a c k spots which are a l i g n e d a r e v o i d s  f i b e r s , fused a t the p o i n t s o f c o n t a c t .  Between two p a r a l l e l rows of b l a c k spots The m a t e r i a l t r a n s p o r t a s s o c i a t e d w i t h  the f i b e r s a r e d i s c e r n a b l e .  the neck growth has c r e a t e d  these v o i d s and a l s o produced the shrinkage t u r n produced the creep  III.4  to lower the s t r e s s  observed d u r i n g  o f the compact, which i n  the experiments.  EFFECT OF THE DENSITY ON THE CREEP RATE  The  creep  i n F i g u r e 20.  r a t e as a f u n c t i o n o f the green d e n s i t y i s shown  I t i s apparent from the f i g u r e t h a t creep  independent o f the d e n s i t y , although  t h i s cannot be c o n c l u s i v e  because o f the s c a t t e r o f the data, p a r t i c u l a r l y w i t h specimens.  r a t e i s almost  the low-density  T h i s may be due to the f a c t t h a t the f i b e r s a r e a l i g n e d  ( F i g u r e 17(a)) and t h a t the t o t a l number o f p o i n t s o f c o n t a c t between them do not change very much by v a r y i n g the d e n s i t y .  III.5  PARTICLE DEFORMATION  The  neck f o r m a t i o n  observed i n the case o f the creep  compacts d u r i n g d e h y d r o x y l a t i o n it  cannot by i t s e l f  of boehmite  e x p l a i n the f a c t  that  i s p o s s i b l e to o b t a i n a body o f t h e o r e t i c a l d e n s i t y under r e a c t i v e  hot-pressing  conditions.  In e f f e c t , i f s u f f i c i e n t p r e s s u r e  i s applied  i n a c l o s e d d i e , the pores can e v e n t u a l l y be e l i m i n a t e d and specimens of the t h e o r e t i c a l d e n s i t y produced.  O •  500 C 400°C  a  = 105 p s i  40  L J  i -  - f  -  dt  x 10 • 20 -1 sec  10  .40  50  .60 Fractional  Densitv  F i g u r e 20 : Creep Rate as a F u n c t i o n of F r a c t i o n a l  Density.  .70  43 The  d r i v i n g f o r c e f o r the growth of the necks i s the s m a l l  radius of curvature theory  predicts  neck i n c r e a s e s  a s s o c i a t e d w i t h the neck.  that the d r i v i n g  At the same time, the  f o r c e decreases as the s i z e of the  and t h a t t h i s leads  d i f f e r e n t from the t r u e d e n s i t y .  to an end-point d e n s i t y which i s By a p p l y i n g  a s t r e s s as low as 265  p s i i n the creep experiments, the creep r a t e was i n c r e a s e d 50 % depending on the t e s t temperature, whereas the t o t a l was i n c r e a s e d  from 50 to 100 %.  Hence, i t i s b e l i e v e d  a p p l i e d s t r e s s caused some p a r t i c l e d e f o r m a t i o n d u r i n g  from 10 to creep  that the the  dehydroxylation  reaction.  III.6  PHENOMENOLOGICAL EQUATION OF THE CREEP RATE  The  creep r a t e s between 350 and 550°C under 31 to 265 p s i  w i t h compacts h a v i n g a f r a c t i o n a l d e n s i t y of 0.6 a r e shown i n Table I page 33.  These creep r a t e s  s t r e s s as shown i n F i g u r e  e^, a r e p l o t t e d as a f u n c t i o n of the a p p l i e d  21.  I t can be seen t h a t the creep r a t e i s  p r o p o r t i o n a l to the a p p l i e d s t r e s s a t a constant i n the range o f s t r e s s e s s t u d i e d . Figure  21 to zero  temperature a t l e a s t  By e x t r a p o l a t i n g  the curves on  s t r e s s a creep r a t e e^ i s found f o r each  temperature.  If e  i s subtracted;  o  from e_, a v a l u e l e« — e_ — e  b  This value  e  S  r  e i s obtained, b r  o  i s the creep r a t e caused by the a p p l i e d s t r e s s .  i s p l o t t e d as a f u n c t i o n o f l o g a ( a p p l i e d s t r e s s ) i n F i g u r e s p i t e o f the e x p e r i m e n t a l s c a t t e r , the b e s t  line  Log e b 22.  In  t h a t can be drawn has a s l o p e  46  of one. and  This  stress.  i n d i c a t e s a d i r e c t p r o p o r t i o n a l i t y between the T h i s b e h a v i o r i s u s u a l l y a t t r i b u t e d to v i s c o u s  g r a i n boundary s l i d i n g  and  Nabarro-Herring creep.  sections  give further information  The  that  fact  scattered  the p o i n t s  The  values  e  to the  e x t e r n a l s t r e s s was  s t r e s s only  to d i f f e r e n t temperatures line,  i n d i c a t e s that  i s temperature  This  a t 500°C ( F i g u r e l O )  experimentally  which i s s l i g h t l y sec  corresponding  present.  flo\T,  following  was  lower than t h a t of the  the  no  creep or s h r i n k a g e has and  are  independent.  i n d i c a t e t h a t d e f o r m a t i o n occurred.: even when  Q  rate  about the p o s s i b l e mechanism.  randomly on b o t h s i d e s of the  creep r a t e due  The  creep  21 x 10 ~* ± 2  found to be  extrapolated  been v e r i f i e d  value  sec  of 25 x 10 ^  -1  Hence the p h e n o m e n l o g i c a l e q u a t i o n has Creep r a t e = e The  term e  creep.  i s the  Q  The  c o n t r i b u t i o n of  term "b"  Figure  i s the  The  i n the p l o t .  t h i s p l o t and equation  (1)  The  found to be therefore  r  the  l o g of  the  the v a l u e s  calculated from the  of  from the  (1) tension  of the  to the  creep r a t e as a f u n c t i o n of t e s t (an A r r h e n i u s  e x t r a p o l a t i o n at a = 0 a r e  ± 1.5  total  applied stress.  a c t i v a t i o n energy has  9.1  terms:  ^  surface  the  Kcal/mole.  .  .  also  been c a l c u l a t e d from The  phenomenological  the parameters A and extrapolated  creep d a t a a t 265 p s i .  values  , - 9 , 1 0 0 ± 1,500, ( —  — — RT  B given at a = 0,  the  plot).  becomes:  Creep r a t e = A exp  with  11  temperature of the  s h r i n k a g e r a t e s g i v e n by  included  + be  coefficient  23 shows the  r e c i p r o c a l of the a b s o l u t e  0  two  , _  ) +  Ba  i n T a b l e VI. "B"  "A"  is calculated  is  Fl'-Mire  23  : Log of creep r a t e s as a f u n c t i o n of the r e c i p r o c a l of the a b s o l u t e temperature.  48  TABLE VI  COEFFICIENTS OF THE EQUATION  Creep r a t e = A e ~  a t 60% D e n s i t y  Temperature  -1 A sec S u r f a c e Energy  B sec psx Applied Stress  x 10~l x 10 x 10 x 10 x 10  350°C 400 450 500 550  0.130 0.136 0.146 0.140 0.164  1.9 1.9 1.9 2.6 2.6  Average  0.144  2.2 x 1 0 ~  7  9 ,  ^ ° + Ba RI  49 The  f i n a l form o f the e q u a t i o n i s :  Creep  rate  : [ 0 . 1 4 4 exp ( ~  9 , 1 0  ° ~  +  D  2  . 2 x 10~ o  ]  7  sec"  The k i n e t i c study o f the decomposition o f boehmite (300 to  (14) 400p) by C a l l i s t e r e t a l  has produced  an a c t i v a t i o n energy o f  67 - 70 Kcal/mole which i s e s s e n t i a l l y independent  o f the water  vapor p a r t i a l p r e s s u r e r a n g i n g from 0 . 0 0 (dry n i t r o g e n ) to 0 . 5 0 atm. Eyraud and G o t o n ^ " ^ 1  c a l c u l a t e d an a c t i v a t i o n energy  a t a p r e s s u r e of 1 t o r r s i m i l a r experiments  to the p r e s s u r e a t which the  o f t h i s study were made.  discrepancies  o f 42 Kcal/mole  Callister  e x p l a i n e d the  (42 compared to 70 K c a l ) 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 b e i n g r e s p o n s i b l e f o r the r e a c t i o n i n a vacuum. Compared t o 42 Kcal/mole, found i n t h i s study  the a c t i v a t i o n energy  (10 Kcal/mole)  f o r creep  i s considerably smaller.  This  i s a l s o the case f o r magnesium h y d r o x i d e , where the a c t i v a t i o n f o r creep i s 17 K c a l / m o l e ^ " ^ 1  ation reaction.  compared to 2 9 - 4 3 ^ ^  I n the case o f k a o l i n i t e ,  i n F i g u r e 18 g i v e an a c t i v a t i o n energy  energy  f o r the d e h y d r o x y l -  the creep curves shown  of about  15 K c a l f o r the creep  (17) compared t o 3 8 - 6 5  f o r the d e h y d r o x y l a t i o n r e a c t i o n .  From  this  g e n e r a l o b s e r v a t i o n i t i s concluded t h a t the creep i s not c o n t r o l l e d by  the d e h y d r o x y l a t i o n r e a c t i o n .  However, as the m a t e r i a l does not  creep b e f o r e the s t a r t o f the d e h y d r o x y l a t i o n r e a c t i o n , i t i s r e a s o n a b l e to assume t h a t the creep p r o c e s s was i n i t i a t e d by the d e h y d r o x y l a t i o n reaction. It i s believed  t h a t the v e r y s m a l l s i z e of the f i b e r s may be  an important f a c t o r i n the k i n e t i c s o f creep.  The neck f o r m a t i o n  1  50  between the f i b e r s suggests t h a t 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 f o r neck growth between alumina  crystals. (>lu).  The only d a t a a v a i l a b l e a r e f o r l a r g e alumina spheres A t h i g h temperatures  (1600 - 1900°C) the a c t i v a t i o n  energy  (18} f o r neck growth i s 140 - 150 K c a l  .  The a c t i v a t i o n energy f o r  (19) s u r f a c e d i f f u s i o n o f A ^ O ^ has been r e p o r t e d However, the boehmite  to be 75 Kcal/mole.  f i b e r s used i n t h i s study can be compared  to p o l y m e r i c chains and i t i s i n t e r e s t i n g to note t h a t the a c t i v a t i o n energy f o r creep o f polymers  above the g l a s s t r a n s i t i o n temperature i s  c l o s e to the a c t i v a t i o n energy f o r p o l y m e r i s a t i o n . energy f o r d i f f u s i o n o f a s m a l l molecule i n a polymer  The a c t i v a t i o n l i e s between  5 and 15 Kcal/mole ° c ^ ^ and the a c t i v a t i o n energy f o r p o l y m e r i s a t i o n  (21) of b u t a d i e n e  i n the presence of c o b a l t i s 12.7 Kcal/mole.  This  suggests t h a t t h e r e may be s i m i l a r i t i e s between the creep o f f i b r i l l a r boehmite  and the flow b e h a v i o r o f o r g a n i c polymers.  S t u d i e s o f the  very e a r l y stages o f g r a i n growth o f alumina may w e l l h e l p to e l u c i d a t e the r a t e c o n t r o l l i n g mechanism o f the creep p r o c e s s observed i n t h i s investigation. 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 e q u a t i o n has been developed by Wadsworth and  (22) Chaklader reaction.  , f o r the d e n s i f i c a t i o n p r o c e s s d u r i n g a d e h y d r o x y l a t i o n The main c o n s i d e r a t i o n s i n t h i s  t h e o r e t i c a l development are  a)  t h a t the p a r t i c l e s a r e s p h e r i c a l i n shape,  b)  they deform a t the p o i n t s o f c o n t a c t under a x i a l p r e s s u r e i n a d i e and the c r o s s - s e c t i o n a l a r e a o f the specimen remains c o n s t a n t d u r i n g compaction.  In the p r e s e n t under creep  i n v e s t i g a t i o n , the specimens were t e s t e d  c o n d i t i o n s and not under h o t - p r e s s i n g c o n d i t i o n s as  p o s t u l a t e d i n the theory. experimentally r e a c t i o n was s t r e s s and  However, i t has been  t h a t the d i a m e t r a l s h r i n k a g e  almost compensated by  due  observed to the  the b u l g i n g due  dehydroxylation  to the  compressive  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  e q u i v a l e n t to the change of l i n e a r dimension i n a compacting d i e where there i s no  diametral  The t h i s has  shrinkage.  e s s e n t i a l s t e p s i n the d e r i v a t i o n are i n c l u d e d here,  not y e t been p u b l i s h e d .  c r o s s - s e c t i o n a l area A',  For a double a c t i n g d i e of  constant  a t 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 u n i t volume o o O f f L  q  i s the i n i t i a l  r  Av  specimen l e n g t h .  A f t e r deformation w i l l be nA'L  and  at time t , t h i s  where n i s the  t  t o t a l number of p a r t i c l e s u n i t volume a f t e r and L i s the new Area A' The  as  n  L  Q  D  A' = n L  deformation l e n g t h . Hence,  A'  (1)  number of p a r t i c l e s per u n i t volume (n or n ) Q  on the p a c k i n g  will  geometry which i n c l u d e s the c o - o r d i n a t i o n number  l o c a t i o n of the n e a r e s t neighbours.  Then n  Q  per  can be d e f i n e d  depend and  as  3 l/(4/3irr  0  )p > Q  where p  p a r t i c l e radius.  Q  i s the p a c k i n g  after  r i s the average  T h i s r e l a t i o n can be r e w r i t t e n as 1/3  and  f a c t o r , and  =  Kp  1 / 3  (2)  n  °  deformation n  1/3  Kp_  1/3  (3)  52  Assuming t h a t the same p a c k i n g  geometry i s being  r e a c t i o n proceeds, i . e . p - p  and i n t r o d u c i n g equations  into  ( 1 ) , we  Q  retained, while  the  (2) and (3)  obtain 3  r  3  r  w  o In the case o f f i b e r s  the m a t e r i a l can be assumed  A c r o s s - s e c t i o n of two p a r a l l e l  to behave  similarly  to s p h e r e s .  fibers  indicates  t h a t 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 s p h e r e s :  I n the t h i r d dimension, i f p o i n t s of c o n t a c t  a r e assumed,  then the geometry of neck growth between f i b e r s w i l l a l s o be s i m i l a r to the neck growth between spheres a t the p o i n t s of c o n t a c t .  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 f o l l o w i n g f i g u r e :  /  \  points of contact  Considering  a s i n g l e p a r t i c l e where  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 V  g  =  4/3iTr  3  2 AVg = 4nr Ar  i s the volume o f the volume  53  So Vg  r  o  o  °  can a l s o be expressed by Z V„ = — Vn where Z i s the c o - o r d i n a t i o n number S 2  volume of a neck. surface  and V  n  F o r most o f the mass t r a n s p o r t mechanisms  i s the (volume,  . . .)  4 7TX  Vn =  where x i s the neck r a d i u s .  0  4  2 r  (6)  AV = (6) and (5) S  Combining equations  ^ 1 V  =  3  | _ 2 r ^  (  )  So  r  (  o  a  r  )  Z,x  =  o  4 ( ? )  4r[4/3Trr ] J  0  ( f " ) ( l " f " ) = -^4 o o i6  (8)  3  r  r  r  In  sintering  following  4  o  t h e o r y , the neck r a d i u s i s r e l a t e d  to time by the  relationship x = Kt  1  /  (9)  n  where "n" i s an i n t e g e r whose v a l u e depends on the mechanism o f mass transport:  2 - v i s c o u s flow 3 - evaporation  condensation  5 - volume d i f f u s i o n 6 - g r a i n boundary d i f f u s i o n 7 - surface d i f f u s i o n Equation  (8) becomes ( ^ ) ( 1 " f-> = — o o 3  r  Using e q u a t i o n  k  t  4  /  n  (10)  o  (4) the f i n a l form o f the e q u a t i o n f o r s h r i n k a g e becomes  k_ L  o  U  _ (k.jl/3]L  o  =  K"  t  Vn  (ID  T y p i c a l creep d a t a o b t a i n e d i n t h i s i n v e s t i g a t i o n have been used  to v e r i f y e q u a t i o n  model, l o g {j— o L  The  [1  -  (11).  In o r d e r to determine  the o p e r a t i n g  dp—)"^^]} has been p l o t t e d a g a i n s t l o g time. L  o  l i n e a r p o r t i o n of the creep curves have been e x t r a p o l a t e d to j^o  = 0  L  i n o r d e r to f i n d a time, t = 0, c o r r e s p o n d i n g neck f o r m a t i o n a t the t e s t  to the b e g i n n i n g of the  temperature.  F i g u r e 24 shows the p l o t of the s h r i n k a g e d a t a o b t a i n e d a t different  temperatures  (350,  and w i t h compacts of 0.60  400,  500  and 550°C) under 265 p s i  f r a c t i o n a l density.  I t appears  t h a t over  a c e r t a i n p e r i o d the t h e o r e t i c a l l y p r e d i c t e d r e l a t i o n s h i p between the s h r i n k a g e and  time i s obeyed.  A f t e r a l o n g e r p e r i o d , however, the  d a t a tend to d e v i a t e from the p r e d i c t i o n . l i n e a r r e g i o n v a r i e s between 0.80 is  approximately  e q u a l to 5.  and 0.90  The  s l o p e (4/n)  which i n d i c a t e s  A c c o r d i n g to Kuczynski's  i n the t h a t "n"  derivation,  when n i s e q u a l to 5 the neck growth and s h r i n k a g e i s c o n t r o l l e d volume d i f f u s i o n .  by  However, i t s h o u l d be p o i n t e d out t h a t although  from t h i s a n a l y s i s an i n d i c a t i o n about the nature of the mechanism i n v o l v e d i n the creep p r o c e s s  can be o b t a i n e d , no c o n c l u s i o n should  be drawn w i t h o u t much e x t e n s i v e work.  III.8  STRENGTH OF THE  COMPACTS AS A FUNCTION OF TIME  From the d i s c u s s i o n of the p r e c e e d i n g s e c t i o n expected  (III.7) i t i s  t h a t w i t h the f o r m a t i o n of necks a t the p o i n t s of c o n t a c t ,  the compacts w i l l  a c q u i r e some s t r e n g t h , which w i l l  the growth of the neck.  With these assumptions,  increase with  an e q u a t i o n  the s t r e n g t h as a f u n c t i o n of time has been d e r i v e d  (22)  relating  and g i v e n below  55  T" • 0.04  Slope 0.86  550°C  O 500  a = 250 p s i Fract. density  0.90  ©  400  0.84  O  350  0.80  0.60  0.03  o  0.02 G  o  0.011 100  200 Figure  24  Log \  300  400 Time,  [1 - (T-)''] v s . l o g t 1  3  (sees)  500  The s t r e n g t h of  S of a compact  i s proportional  to the s t r e n g t h  the necks formed between p a r t i c l e s l o c a t e d on the plane where the  maximum s t r e s s i s a c t i n g . neck i s p r o p o r t i o n a l  I f we  assume t h a t  the s t r e n g t h  of a  to i t s c r o s s - s e c t i o n , then the s t r e n g t h  of the  compact i s S = KCn)  2 7 3  (1)  ^  where n i s the number of p a r t i c l e s per u n i t volume c r o s s - s e c t i o n per p a r t i c l e . transport  (shrinkage  u n i t volume  Due  and c r e e p ) ,  i s assumed.  and a  D  i s the neck  to the complexity of the mass a constant  number of p a r t i c l e s p e r  Moreover, i t i s assumed  that the second  s t a g e 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 c r o s s - s e c t i o n p e r p a r t i c l e a  2  =  ?  (2)  n  a  where Z i s the c o - o r d i n a t i o n number and a  n  i s the i n d i v i d u a l neck  section  2 a where x i s the neck r a d i u s . volume i s g i v e n  n  = TTX  (3)  I n most s i n t e r i n g models, the neck  by  4 V where r i s the p a r t i c l e r a d i u s .  V From  n  n  = ^ From e q u a t i o n ( 3 ) a 2  (4)  = -r^—  (5)  (III.7) n =  the p r e c e e d i n g s e c t i o n  (6)  1 / 3  where p i s a p a c k i n g f a c t o r .  Hence e q u a t i o n ( 5 ) becomes  ^ a_  V  n  1/3 (n)  = ~^~~ZZ  (7)  cross-  The 1 3  u n i t v a r i a t i o n of the volume of a compact due 2 a  A V  r,  1/3 n  - tf l  A V  n  £.  Tip  7  Combining equations  (8) and  n  4  /  3  2  a  n  2  (2)  . _JL 4/3  A V  2  n  TTZp  Equation  to neck f o r m a t i o n  (  9  )  p  (1) becomes,after  i n t r o d u c i n g equation _ 1/2 1/2 S = K (^E.) (AV)  (9) (10)  I t i s assumed t h a t the mass t r a n s p o r t mechanism i s volume d i f f u s i o n as has been observed From K u c z y n s k i ' s  i n the p r e c e e d i n g s e c t i o n  volume d i f f u s i o n model f o r s i n t e r i n g  (23)  (III.7). , i t is  simple to d e r i v e an e q u a t i o n of — • as a f u n c t i o n of time f o r a g i v e n o temperature. L  &. o where y i s the s u r f a c e  . % o  - K'  J v  t ' 4  energy.  For h o t - p r e s s i n g ,  2Y  2Y  i s r e p l a c e d by  (-^- + a) , a b e i n g  a p p l i e d s t r e s s d u r i n g the d e h y d r o x y l a t i o n . (10) and  (11)  5  r  the  S u b s t i t u t i n g AV i n e q u a t i o n  r e g r o u p i n g the c o n s t a n t terms, g i v e s S = K"  (-^ + a )  In o r d e r to v e r i f y e q u a t i o n was  used  i n creep experiments  The  compressive  a t 400  2 7 5  t  2  /  (12)  5  (12) a constant s t r e s s of 105 p s i and  500°C f o r v a r i o u s  s t r e n g t h of the c y l i n d r i c a l specimens was  periods. determined  i n an I n s t r o n machine.  I t has been noted  t h a t hydroxide  compacts  (magnesium h y d r o x i d e ,  and k a o l i n i t e , boehmite),  left  f o r a long p e r i o d a t a temperature  immediately  below the d e h y d r o x y l a t i o n range have almost no s t r e n g t h at a l l .  This  drop i n s t r e n g t h may be caused by the removal of p h y s i c a l l y  adsorbed  water and o t h e r v o l a t i l e m a t e r i a l s which were r e s p o n s i b l e f o r bonding i n the green  compact.  From t h i s o b s e r v a t i o n i t i s assumed t h a t the  s t r e n g t h of the compacts a f t e r the necks.  the d e h y d r o x y l a t i o n i s caused  The l o g of the s t r e n g t h o b t a i n e d i n the  only by  compression  t e s t i s p l o t t e d as a f u n c t i o n of l o g time i n F i g u r e 25.  Log  S = K'" + n l o g t  The v a l u e s of n o b t a i n e d  (0.35 and 0.40) are i n good  agreement w i t h the exponent of t (2/5) i n e q u a t i o n  (12).  i n d i c a t e s a g a i n t h a t the mechanism i n v o l v e d i n the creep  This 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 o r creep has been c a l c u l a t e d to be o n l y 10 Kcal/mole.  T h i s d i s c r e p a n c y between the u s u a l l y l a r g e  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 s m a l l v a l u e found f o r the a c t i v a t i o n energy o f the creep may be r e s o l v e d by c o n s i d e r i n g the n a t u r e of s o l i d s a f t e r the d e h y d r o x y l a t i o n r e a c t i o n . the decomposition  In t h i s  r e a c t i o n produced both very f i n e p a r t i c l e s  c a l c u l a t e d on the b a s i s of the s u r f a c e area v a l u e s ) and very s t r u c t u r e because of the presence postulated before. low  although  (41 A ° imperfect  of l a r g e i n t e r n a l p o r o s i t y as  The combination  a c t i v a t i o n energy necessary  case,  o f these two may  f o r the creep process  r e s u l t i n the as  observed  the r a t e 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 c o n c l u s i o n s h o u l d be drawn however from t h i s a n a l y s i s at present.  59  60  IV.  1.  SUMMARY AND  Compressive  CONCLUSIONS  creep t e s t i n g s of c o l d compacted c o l l o i d a l  have bet-n c a r r i e d out as a f u n c t i o n of temperature lation  temperature  boehmite  ( i n the dehydroxy-  r a n g e ) , a p p l i a d s t r e s s and r e l a t i v e d e n s i t y .  compacts have been found  to s h r i n k even w i t h o u t any  applied  The  stress  d u r i n g the d e h y d r o x y l a t i o n r e a c t i o n . 2.  The  be 9.1  a c t i v a t i o n energy ± 1.5  f o r the creep p r o c e s s has been determined  Kcal/mole, which i s c o n s i d e r a b l y s m a l l e r than  a c t i v a t i o n energy  f o r the d e h y d r o x y l a t i o n r e a c t i o n  to  the  (42 K c a l / m o l e ) , i n -  d i c a t i n g t h a t the r a t e c o n t r o l l i n g mechanisms f o r these two  processes  are not the same.  that  creep was 3.  The  However, i t was  i n i t i a t e d by  the  the r e a c t i o n .  creep r a t e i s p r o p o r t i o n a l to the a p p l i e d s t r e s s , a l t h o u g h  t o t a l creep r a t e was stress  e x p e r i m e n t a l l y observed  caused by two  factors:  ( a ) , where y i s the s u r f a c e energy  2y/r and  the  the  applied  and r the r a d i u s of  c u r v a t u r e a t the p o i n t of c o n t a c t . 4.  The  stress  t o t a l creep r a t e  The presence  the d r i v i n g f o r c e w i t h o u t any  C ' *' 9  100  1  500  )  i n the e l e c t r o n microscope,  (2y/r) f o r the s h i r n k a g e , observed  applied  x 10~  7  a ]'•.  s-  thus c o n f i r m i n g i n compacts.  stress.  E q u a t i o n s p r e v i o u s l y developed,  the s t r e n g t h of a compact  (due  relating  although i n c o n c l u s i v e l y ,  the change i n l e n g t h and  to neck growth) w i t h time, have been  t e s t e d w i t h the p r e s e n t e x p e r i m e n t a l d a t a .  creep p r o c e s s may  + 2.2  o f necks a t t h e - p o i n t s of c o n t a c t between the a l i g n e d  f i b e r s has been observed  6.  ( w i t h i n the a p p l i e d  limit):  . creep r a t e =[0.144 exp 5.  (e) can be r e p r e s e n t e d by  This analysis  indicated  t h a t the r a t e d e t e r m i n i n g mechanism f o r the  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 r a t e of  boehmite compacts may creep d u r i n g 2.  help i n e l u c i d a t i n g  the mechanisms i n v o l v e d i n  dehydroxylation.  S t u d i e s of neck growth between two h e m i s p h e r i c a l t i p s of boehmite  single  c r y s t a l s would p r o v i d e i n f o r m a t i o n about the nature  and  mechanism of mass t r a n s p o r t d u r i n g d e h y d r o x y l a t i o n . 3.  In the p r e s e n t work, the dimensions of the specimens were kept  approximately  constant.  The  effect  of s c a l i n g may  affect  the  because of l o c a l i z e d p r e s s u r e of the vapor phase formed d u r i n g  creep, the  reaction. A.  A l l the creep experiments of t h i s study have been done i n vacuum.  The  e f f e c t of the p a r t i a l p r e s s u r e s on the k i n e t i c s  reaction  of the  dehydroxylation  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 p r e s s u r e s  on the creep b e h a v i o r d u r i n g d e h y d r o x y l a t i o n would help the r e a c t i o n  and  the creep  process.  to  correlate  62  VI.  APPENDIX  THERMAL  EXPANSION OF THE HOLDING FRAME  Due to the f a c t t h a t the d e h y d r o x y l a t i o n r e a c t i o n o f boehmite takes p l a c e over a wide range bf temperatures at  550°C,  test  (350 - 550), and t h a t  f o r example, the r e a c t i o n i s over a f t e r 4 minutes  temperature  (once the  i s r e a c h e d ) , the f u r n a c e has to be heated as f a s t as  possible.  With 9.2 amperes, the h e a t i n g r a t e i s about 200°C p e r minute. S i n c e the l o a d i n g frame i s c l o s e to the r e s i s t a n c e h e a t e r , i t expands f a s t e r than the ram and the d i a l i n d i c a t e s a c o n t r a c t i o n as shown i n Figure 26(b).  A f t e r 1500 seconds  the expansion o f each p a r t 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  l o a d i n g frame i s f i x e d to the w a t e r - c o o l e d chamber and i t seems t h a t it  does not c o n t i n u e t o expand as much as the ram.  apparent  expansion.  Figure  27 shows the r e l a t i v e p r o p o r t i o n s o f the expansion  curves compared t o the c o r r e c t e d creep c u r v e s . of  The r e s u l t i s an  the c o r r e c t i o n ,  Due to the importance  the creep r a t e s o b t a i n e d from the c o r r e c t e d  curves may be i n e r r o r by 10%. v a l u e has been found r e a s o n a b l e .  By r e p e a t i n g many experiments,  this  63  I 1000  I 2000  L_ 3000 Time, (sec)  F i g u r e 26(b) : Net d i l a t a t i o n o f h o l d i n g frame d u r i n g h e a t i n g (200°C/min.) and i s o t h e r m a l experiment a t d i f f e r e n t temperatures.  +0.005  T  T  A00  800  ~  Time, Figure  27(a) : Net d i l a t a t i o n o f h o l d i n g frame compared to c o r r e c t e d creep curve of the compact d u r i n g h e a t i n g r a t e of 27 C per minute.  T  (b)  12 (sees.)  : Net d i l a t a t i o n of h o l d i n g frame and c o r r e c t e d creep curve a t 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 I n c . p. 215 (1965).  2.  A . C D . Chaklader and V.T. Baker, " R e a c t i v e H o t - P r e s s i n g ; 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 N o n - s t a b i l i z e d ZrO ", Am. Soc. B u l l . , 44 [3] 258-59 (1965).  3.  Ceram.  (a)  A . C D . Chaklader and L.G. McKenzie, " R e a c t i v e H o t - P r e s s i n g of C l a y s , " Am. Ceram. Soc. B u l l . , 43 [12] 892-93 (1964).  (b)  T.G. C a r r u t h e r s and T.A. Wheat, " H o t - P r e s s i n g o f K a o l i n and of M i x t u r e s o f Alumina and S i l i c a , " P r o c . B r i t . Ceram. Soc., 3,259-73 (1965).  (c)  P.E.D. Morgan and E. S c a l a , "High-Density Oxides by Decomposition P r e s s u r e S i n t e r i n g of H y d r o x i d e s , " p r e s e n t e d a t the S i x t y - S e v e n t h Annual Meeting, The Am. Ceram. Soc., P h i l a d e l p h i a , Pa., May 3, 1965 ( B a s i c S c i e n c e D i v i s i o n , No. 13-B-65); f o r a b s t r a c t see Am. Ceram. Soc. B u l l . , 44 [4] 301 (1965).  4.  J.A. H e d v a l l , R e a k t i o n s f a e h i g k e i t f e s t e r S t o f f e ( R e a c t i v i t y o f S o l i d s ) , V e r l a g Johann Ambrosius B a r t h , L e i p z i g , (1938), 243 pp. R e p r i n t e d by Edwars I n c . , Ann A r b o r , Mich., 1943; Ceram. A b s t r . , 17 [4] 164 (1938).  5.  A. C D . Chaklader and L.G. McKenzie, " R e a c t i v e H o t - P r e s s i n g o f C l a y s and Alumina," J . Am. Ceram. Soc. 49 [9] 477-83 (1966).  6.  Xa) M. de Long and G.W. Rathenau, A c t a Met. ]_ 246 (1959). (b) M. de Long and G.W. Rathenau, A c t a Met. 9^ 714 (1961). (c) G.W. Greenwood and R.H. Johnson, P r o c . Roy. Soc. A283 403 (1965). (d) D. O e l s c h l a g e l and V. Weiss, T r a n s . Q u a r t e r l y A.S.M. 59 143 (1966).  7.  A. C D . Chaklader, "Deformation o f Quartz C r y s t a l s a t the T r a n s f o r m a t i o n Temperature," Nature, 197 791-92 (1963).  8.  J . L . H a r t and A . C D . 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 . C D . Chaklader, "Deformation d u r i n g D e h y d r o x y l a t i o n of H y d r o x i d e s , " Mat. Res. B u l l . , 2 1111 (1967).  10.  A . C D . Chaklader and R.C. Cook, " K i n e t i c s of R e a c t i v e H o t - P r e s s i n g of C l a y s and H y d r o x i d e s , " 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; P r o g r e s s i v e C o n v e r s i o n to Gamma, Theta and A l p h a Alumina," J . Am. Ceram. Soc. 44 [12] 618-624 (1961).  12.  "Alumina P r o p e r t i e s , " A l c o a Research L a b o r a t o r y , T e c h n i c a l Paper No. 10, p. 63, P i t t s b u r g , U.S.A. (1960).  13.  P.W. Sunderland and A . C D . Chaklader, "Creep d u r i n g D e h y d r o x y l a t i o n o f Magnesium Hydroxide," p r e s e n t e d a t the S e v e n t i e t h Annual Meeting,  66 REFERENCES (continued)  Am. Ceram. S o c , Chicago, 111., A p r i l 23, 1968 D i v i s i o n , No. 41-B-68). 14.  (Basic Science  W.D. C a l l i s t e r J r . , I.B. C u t l e r and R.S. Gordon, "Thermal Decomposition K i n e t i c s of Boehmite," J . Am. Ceram. Soc. 419-22 (1966).  [8]  15.  C. Eyraud and R. G o t o n , " K i n e t i c s of the Thermal D i s s o c i a t i o n of the Hydrates o f Alumina," J . Chim. Phys., ,51 430-33 (1954).  16.  R.S. Gordon and W.D. K i n g e r y , "Thermal Decomposition o f B r u c i t e , " J . Am. Ceram. S o c , 50 [1] 8 - 1 4 (1967).  17.  G.W. B r i n d l e y and M. N a k a h i r a , " K i n e t i c s of the Thermal D e h y d r o x y l a t i o n 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 f o r g r a i n growth i n Alumina," Mater. S c i . Res., _3 345-53 (1966).  19.  W.M. Robertson and R. Chang, "The K i n e t i c s of grain-boundary groove growth on alumina s u r f a c e s , " Mater. S c i . Res. _3 49-60 (1966).  20.  F. Bueche, " P h y s i c a l P r o p e r t i e s P u b l i s h e r s p. 90 (1962).  21.  Vene, Harvo; Makivo, I t s u r o , " K i n e t i c s of Butadienne Polymerization i n the p r e s e n c e o f c o b a l t c a t a l y s t sytems," Kogyo Kagaku Z a s s h i _71 [3] 418-21 (1968).  22.  M.E.  23.  G.C. K u c z y n s k i , " S e l f - D i f f u s i o n i n S i 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 . M e t a l s 1 ( 2 ) , T r a n s . AIME 185 [2] 169-78 (1949).  Wadsworth and A.CD.  of High Polymers,"  Interscience  C h a k l a d e r , p r i v a t e communication  (1968).  

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