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Deformation of compacts of magnesium hydroxide during dehydroxylation 1970

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DEFORMATION OF COMPACTS OF MAGNESIUM HYDROXIDE DURING DEHYDROXYLATION PHILIP WILLIAM SUNDERLAND, P. ENG. B. A. Sc. , UNIVERSITY OF BRITISH COLUMBIA 1965 A THESIS SUBMITTED IN P A R T I A L F U L F I L M E N T OF THE REQUIREMENTS OF THE DEGREE OF MASTER OF A P P L I E D SCIENCE in the Department of M E T A L L U R G Y We accept this thesis as conforming to the standard required from candidates for the degree of Master of Applied Science Members of the Department of Metallurgy THE UNIVERSITY O F BRITISH COLUMBIA August, 1970 In p r e s e n t i n g t h i s t h e s i s in p a r t i a l f u l f i l m e n t o f the r e q u i r e m e n t s f o r an advanced d e g r e e at t h e U n i v e r s i t y o f B r i t i s h C o l u m b i a , I a g r e e t h a t t h e 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 s t u d y . I f u r t h e r a g r e e 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 o f t h i s t h e s i s f o r s c h o l a r l y p u r p o s e s may be g r a n t e d by the Head o f my Depar tment o r by h i s r e p r e s e n t a t i v e s . I t i s u n d e r s t o o d t h a t c o p y i n g o r p u b l i c a t i o n o f t h i s t h e s i s f o r f i n a n c i a l 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 w r i t t e n p e r m i s s i o n . Depar tment o f tM£THU.Urt 6-V The U n i v e r s i t y o f B r i t i s h C o l u m b i a V a n c o u v e r 8, Canada Date SclPT Zl j H7P.. A B S T R A C T The deformation behaviour of p o l y c r y s t a l l i n e compacts of Mg(OH)2 during dehydroxylation has been studied i n an attempt to evaluate the nature of s t r a i n that can be int r o d u c e d into the compact during the reaction. A study of neck-growth between tips of single c r y s t a l s of Ca(OH)-, and between two h e m i s p h e r i c a l tips of Mg(OH),, compacts showed both deformation and i n t e r a c t i o n at the contact point during the dehydr oxylation reaction. Load-dependent deformation of the compacts gave a total s t r a i n p r o p o r t i o n a l to the on e - t h i r d power of the applied s t r e s s . The creep d e f o r m a t i o n of Mg(OH)2 compacts during dehydroxylation was a l s o studied under i s o t h e r m a l conditions. The o v e r a l l creep behaviour can be divided into three stages. The i n i t i a l stage is i n i t i a t e d by the dehydroxylation reaction. D u r i n g the second or steady state creep stage the highest creep rate was obtained. The steady state c r e e p rate was de t e r m i n e d as a function of temper- ature . p r e s s u r e , and r e l a t i v e density of the green compact. The re s u l t s are r e p r e s e n t e d by: A cr e_ + ( - 1 7 5 0 0 \ - 1 e x P \ R T J t ° ? P a r t i c l e s l i d i n g was c o n s i d e r e d to be the most probable m e c h a n i s m for creep during the second stage. i i A C K N O W L E D G E M E N T S The author wishes to acknowledge the a s s i s t a n c e and encouragement generously given by Dr. A. C. D. Ch a k l a d e r and others throughout this work. Thanks are a l s o extended to the faculty and staff of the Department of M e t a l l u r g y f o r t h e i r advice. F i n a n c i a l a s s i s t a n c e p r o v i d e d by C l a y b u r n - H a r b i s o n Co. Ltd. i n the f o r m of a F e l l o w s h i p is g r a t e f u l l y acknowledged. i i i T A B L E O F C O N T E N T S P a g e I I n t r o d u c t i o n 1 1. 1 R e a c t i v e H o t P r e s s i n g 1 1. 1. 1 H y p o t h e s e s f o r R e a c t i v e H o t P r e s s i n g 2 1. 1. 2 T h e o r i e s of H o t P r e s s i n g 4 1. 2 O b j e c t i v e s of t h i s I n v e s t i g a t i o n 6 1. 3 C h o i c e of E x p e r i m e n t a l S y s t e m 8 1. 4 P r o p e r t i e s of the E x p e r i m e n t a l S y s t e m 9 1. 4. 1 P h y s i c a l and C h e m i c a l P r o p e r t i e s 9 1. 4. 2 S t r u c t u r a l A s p e c t s of the D e c o m p o s i t i o n 11 1. 4. 3 K i n e t i c s of D e c o m p o s i t i o n 18 II E x p e r i m e n t a l 20 2. 1 A p p a r a t u s 20 2. 1. 1 F u r n a c e and L o a d F r a m e 20 2. 1. 2 V a c u u m S y s t e m 23 2. 1. 3 P h o t o g r a p h y 23 2. 1. 4 L o a d i n g and D i s p l a c e m e n t M e a s u r e m e n t 24 2. 1. 5 F u r n a c e T e m p e r a t u r e C o n t r o l and P o w e r S u p p l y 25 2. 2 E x p e r i m e n t a l T e c h n i q u e 26 2. 2. 1 G r o w t h of C a ( O H ) z ( P o r t l a n d i t e ) S i n g l e C r y s t a l s 26 Page iv 2. 2. 2 E x p e r i m e n t s on T i p to T i p Contact 28 A. Ca(OH)2 C r y s t a l s 28 2. 2. 3 P r e p a r a t i o n of Mg(OH);? Compacts 30 B. Mg(OH)2 Compacts 30 2. 2. 4 D e f o r m a t i o n of M g ( O H ) 2 C y l i n d r i c a l Compacts 33 2. 2. 5 T e m p e r a t u r e D i s t r i b u t i o n i n Specimens 37 III R e s u l t s 40 3. 1 C a l c i u m Hydroxide Single C r y s t a l s 40 3. 2 T i p to T i p Contact of M a g n e s i u m Hydroxide Compacts 40 3. 3 D e f o r m a t i o n of M a g n e s i u m Hydroxide Compacts 42 3. 3. 1 U n i f o r m Heating Rate 42 3. 3. 2 11 Isothermal" D e f o r m a t i o n (Creep) 47 (a) E f f e c t s of T e m p e r a t u r e on D e f o r m a t i o n 51 (b) E f f e c t of S t r e s s at Constant and T e m p e r a t u r e 51 (c) E f f e c t of G r e e n Density 51 IV D i s c u s s i o n 4.1 Shrinkage V e r s u s C r e e p 57 4. 2 Weight L o s s V e r s u s C r e e p 59 V Page 4. 3 Stages of C r e e p 59 4. 4 C r e e p Rate 66 4. 4. 1 E f f e c t of T e m p e r a t u r e 66 4. 4. 2 S t r e s s Dependence 69 4. 4. 3 De n s i t y Dependence 69 4. 5 T o t a l C r e e p S t r a i n 75 4. 5. 1 E f f e c t of T e m p e r a t u r e 75 4. 5. Z E f f e c t of S t r e s s 77 4. 5, 3 E f f e c t of Density 77 4. 5. 4 Phenomenological Behaviour 82 4. 6 Postulated M e c h a n i s m s of C r e e p 83 4. 6, 1 P h y s i c a l Changes A c c o m p a n y i n g D e h y d r o x y l a t i o n 83 4. 6. Z A c t i v a t i o n E n e r g i e s C o n c u r r e n t P r o c e s s e s 84 4. 6. 3 V i s c o u s F l o w and G r a i n Boundary Sl i d i n g 85 4 6. 4 P o s s i b l e M e c h a n i s m s of D e f o r m a t i o n 86 4. 6. 4. 1 Sl i p M e c h a n i s m s 87 4.6.4,2 Stacking R e a r r a n g e m e n t 88 V VI Summary and C o n c l u s i o n s Suggestions f o r F u t u r e Work 90 93 Page VII Appendices I Tempera ture D i s t r i bu t i on With in the C y l i n d r i c a l Spec imen 94 II Creep Data - I so the rmal Condit ions 97 III A c c u r a c y of the T h e r m a l Expans ion C o r r e c t i o n 115 VIII B ib l iography 118 Publ ica t ions : 1) P . W. Sunderland and A . C. D. Chaklader , Mat . R e s . B u l l . , 2, 1111-1118 (1967). 2) P . W. Sunderland and A . C. D. Chaklader , J . A m . C e r a m . S o c , 52_ , 410-414 (1969). v i i L I ST O F F I G U R E S NO. P A G E 1 Com p a c t i o n of Mg(OH)2 as function of temperature. (After C h a k l a d e r and C o o k ^ and M o r g a n and Sc a l a ( 2 ) 7 2 a) Structure of Mg(OH)2 - Schematic rep re sentation 12 b) Structure of MgO - Schematic r e p r e s e n t a t i o n ... 12 (13) 3 Goodman's v ' proposed m e c h a n i s m f o r the de- hydroxylation, showing collapse n o r m a l to the 0- planes i n the f o r m a t i o n of p e r i c l a s e 15 4 B a l l and T a y l o r ' s p r o p o s e d inhomogeneous m e c h a n i s m for the dehydroxylation, showing donor and acceptor regions, and the d i f f u s i o n of M g + + and H+ 17 5 Schematic r e p r e s e n t a t i o n of the e x p e r i m e n t a l apparatus 21 6 The loading f r a me, showing the thermocouples 22 7 The apparatus used for growing Ca(OH)2 c r y s t a l s . . . 27 8 T i m e - t e m p e r a t u r e p r o f i l e used for the decompo- si t i o n of Ca(OH)2 tips and for u n i f o r m heating rate experiments 29 9 E l e c t r o n m i c r o g r a p h of M g ( O H ) 2 powder . . . 31 10 R e l a t i v e density obtained i n green compacts of Mg(OH)2> v e r s u s p r e s s u r e . . 34 11 Specimen surface temperature as a function of time for the " i s o t h e r m a l " tests at four different temperatures . 36 12 Specimen surface and centre temperatures f o r two different " i s o t h e r m a l " conditions . . . .39 1 3 Growth of contact a r e a during decomposition of Ca(OH)2 tips under load : . 41 v i i i LIST. O F F I G U R E S - continued NO. P A G E 14 Growth of contact a r e a during decomposition of Mg(OH)2 compact tips under load 43 15 E v i d e n c e of bond f o r m a t i o n during the tip - to - tip contact shown i n F i g u r e 14 a) c r a t e r i n one tip b) m a t e r i a l r e m oved f r o m the c r a t e r adhereing to the other tip 44 16 F a m i l y of D e f o r m a t i o n - tim e curves f o r experiments under v a r i o u s loads at a u n i f o r m heating rate, showing the method of m e a s u r i n g the total d eformation (e T ) 45 17 Total: d e f o r m a t i o n as a function of load ( u n i f o r m heating rate) . . 48 18 L o g - L o g plot of total d e f o r m a t i o n as a function of load ( uniform heating rate). 49 19 T e m p e r a t u r e , deformation and s y s t e m p r e s s u r e s v e r s u s time f o r a t y p i c a l 11 i s o t h e r m a l " run 50 20 D e f o r m a t i o n v e r s u s time f o r specimens of 0. 50 r e l a t i o n density, at " i s o t h e r m a l " t e m p e r a t u r e s as shown. S t r e s s 6. 0 kg/cm^ 52 21 D e f o r m a t i o n v e r s u s time f o r specimens of 0. 50 re l a t i v e density, at " i s o t h e r m a l " temperatures as shown. S t r e s s 13. 6 kg/cm^ 53 22 D e f o r m a t i o n v e r s u s time f o r specimens of 0. 50 r e l a t i v e density, at 360°C, f o r s t r e s s e s as shown... 54 23 D e f o r m a t i o n v e r s u s time f o r specimens of v a r i o u s r e l a t i v e densities as shown, at 9. 25 kg/ cm^ 56 24 Creep, weight l o s s and shrinkage v e r s u s time 60 25 Stages of C r e e p 61 L I S T O F F I G U R E S - continued NO. P A G E 26 D e f o r m a t i o n and S y s t e m p r e s s u r e . v e r s u s time , 63 2 7 D e f o r m a t i o n and Sy s t e m p r e s s u r e v e r s u s time 64 28 A r r h e n i u s - type plot of creep rate v e r s u s temperature 67 29 S t r e s s dependence of m a x i m u m creep rate 70 30 Density dependence of m a x i m u m creep rate 73 31 T o t a l s t r a i n v e r s u s temperature 76 32 T o t a l s t r a i n v e r s u s s t r e s s 78 33 L o g - L o g plot of total s t r a i n v e r s u s s t r e s s 79 34 T o t a l s t r a i n v e r s u s density. ... 80 35 T o t a l s t r a i n v e r s u s l/c» 81 36 T h e o r e t i c a l temperature d i s t r i b u t i o n in the specimens for i s o t h e r m a l creep tests 96 3 7 Comparative values of the deformation m e a s u r e d by the n o r m a l apparatus and a t r a v e l l i n g m i c r o s c o p e 117 L I S T O F T A B L E S x N O . P A G E I P r o p e r t i e s of M g ( O H ) 2 and MgO 10 II Summary of M e c h a n i s m s and K i n e t i c s of Mg(OH)2 Deh y d r o x y l a t i o n 13 III D e f o r m a t i o n Data f or U n i f o r m Heating Rate. 46 IV T e m p e r a t u r e Dependence of I s o t h e r m a l C r e e p 68 V S t r e s s Dependence of I s o t h e r m a l C r e e p 71 VI D e n s i t y Dependence of I s o t h e r m a l C r e e p 74 -1- C H A P T E R I 1. Introduction 1. 1 Reactive Hot P r e s s i n g S e v e r a l w o r k e r s have recently (1 _4) shown that the hot p r e s s - ing of the decomposible compounds such as Mg(OH)2> etc. during the decomposition r e a c t i o n r e s u l t s i n high density products. The p r o c e s s u t i l i z e s a transient 11 r e a c t i v i t y " r e s u l t i n g f r o m either c h e m i - c a l decomposition (̂  ~4) or a p o l y m o r p h i c phase t r a n s f o r m a t i o n to obtain dense, high strength c e r a m i c bodies at c o m p a r a t i v e l y low temperatures and p r e s s u r e s , u s u a l l y beiow 1000°C and 10,000 p s i . The p r o c e s s has a l l the advantages of conventional hot p r e s s i n g : low p o r o s i t y and hence high strength i n the product, fine g r a i n size since r e c r y s t a l l i z a t i o n and g r a i n growth are m i n i m i z e d by the compara- t i v e l y low temperatures, and accurate dimensions of the product, as well as r e q u i r i n g lower t e m p e r a t u r e s and holding times than the conventional hot p r e s s i n g p r o c e s s . The p r o c e s s has been applied to many c e r a m i c systems. Chaklader and M c K e n z i e (4) p r e s s e d s e v e r a l natural clays as w e l l as synthetic hydroxides of a l uminum and magnesium. U n s t a b i l i z e d z i r c o n i a was d e n s i f i e d ^ ^ by c y c l i n g it through the m o n o c l i n i c i^====*»tetragonal phase t r a n s f o r m a t i o n , and up to 99. 8% of theo- 8 6 0 ° C r e t i c a l density was obtained. Another a p p l i c a t i o n ^ ) was to the production of c e r m e t s of alumina with i r o n , copper and chromium. The low temperature r e q u i r e d f o r the decomposition of boehemite (600°C) -2- r e s u i t e d i n a m i n i m a l f o r m a t i o n of i n t e r f a c i a l phases which could reduce the strength of the product. M o r g a n and Schaeffer have r e p o r t e d work on the f a b r i c a t i o n of magnesia by a p r o c e s s they c a l l " p r e s s u r e c a l c i n t e r i n g " , which i s e s s e n t i a l l y i d e n t i c a l to r e a c t i v e hot p r e s s i n g ; T h e y conducted a s e r i e s of i n v e s t i g a t i o n of the p r o c e s s , a n a l y s i n g such effects as the nature ( c h e m i c a l history) of the p r e c u r s o r and the effect of i m p u r i t y content on d e n s i f i c a t i o n . C h a klader and Cook have a l s o studied the hot p r e s s i n g c h a r a c t e r i s t i c s of the Mg(OH)2 *** MgO system, as w e l l as boehmite and two clays. 1. 1. 1 Hypotheses f o r R e a c t i v e Hot P r e s s i n g (8) In the e a r l i e r papers they suggested that the f o r m a t i o n of strong, dense compacts by r e a c t i v e hot p r e s s i n g might be a s s o c i a t e d with an "enhanced r e a c t i v i t y " during or just after a phase change, which is known as the "Hedvall E f f e c t " . ^) The p r e c i s e nature of this r e a c t i v i t y has not been established, although C haklader has made the following statements r e g a r d i n g the m e c h a n i s m s of r e a c t i v e hot pressing:^ 4 )• "The idea of using the high r e a c t i v i t y of a s o l i d during a decomposition r e a c t i o n or a p o l y m o r p h i c phase change (the H e d v a l l Effect) f o r d e n s i f i c a t i o n stems f r o m the following hypotheses and observations: -3- (a) B r o k e n bonds and u n s a t i s f i e d valence l i n k s exist both on the s u r f a c e and i n the bulk of p a r t i c l e s undergoing a decompo- siti o n r eaction; these b r o k e n bonds and links may be a v a i l a b l e f o r i n t e r - face r e a c t i o n l e a d i n g to i n t e r p a r t i c l e bonding. (b) V e r y t r a n s i e n t i n s t a b i l i t y of the atomic p o s i t i o n during 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 state which may be u t i l i z e d f o r d e n s i f i c a t i o n " . The f i r s t p r o p o s i t i o n i s e a s i l y accepted. It i s w e l l known that bonds of strength comparable to the bulk t e n s i l e strength of the m a t e r i a l are. f o r m e d by clean m e t a l s u r f a c e s i n f r i c t i o n a l contact i n high v a c u u m where surface contamination i s prevented. Contact a r e a s are obtained f r o m e l e c t r i c a l r e s i s t a n c e measurements. While the nature of c h e m i c a l bonding i n c e r a m i c s i s quite unlike the m e t a l l i c bond, it i s easy to understand the p o s s i b i l i t y of bond f o r m a t i o n where clean oxide s u r f a c e s are brought together i n t i m a t e l y on an atomic scale. It i s the n e c e s s i t y of producing suitable contact that p r e c l u d e s the p r o d u c t i o n of f r i c t i o n a l bonding i n c e r a m i c systems. P l a s t i c flow is r e q u i r e d to b r i n g finite a r e a s into contact, and under low temperature conditions sufficient flow is not p o s s i b l e . T h e r e f o r e it can be seen that the f o r m a t i o n of i n t e r p a r t i c l e bonds of fini t e strength depends upon some mass t r a n s f e r mechanism, such as p l a s t i c flow or diffusion. It i s to be expected that the l a r g e evolution of water vapour (or some other gas) would have a purging effect, reducing p o s s i b l e surface contaminants to such a low l e v e l that bonding can take place f r e e l y between contacting -4- a s p e r i t i e s . The second propostion, concerning a t r a n s i e n t t r a n s f o r - mation p l a s t i c i t y * , i s more important. T o see exactly how p l a s t i c flow enters the d e n s i f i c a t i o n p r o c e s s it is useful to c o n s i d e r the p o s s i b l e means of d e n s i f i c a t i o n of a powder compact subjected to p r e s s u r e at an elevated temperature (hot p r e s s i n g ) . 1. 1. 2 T h e o r i e s of Hot P r e s s i n g The behaviour of a compact through a h i s t o r y of die f i l l i n g i n a g r a v i t a t i o n a l f i e l d , v i b r a t o r y compaction, applied p r e s s u r e , d e n s i f i c a t i o n up to the point of c l o s e d pore formation, and f i n a l l y m e c h a nisms of pore e l i m i n a t i o n can be followed. The f a c t o r s which cont r o l the compaction of a powder to a dense body are manifold: p a r t i c l e s i z e , p a r t i c l e size d i s t r i b u t i o n , p a r t i c l e shape, the mech- a n i c a l p r o p e r t i e s of the m a t e r i a l - i . e. its s u s c e p t i b i l i t y to f r a c t u r e or flow, or its work hardening rate if p l a s t i c flow o c c u r s , the a n i s o - t r o p y of m e c h a n i c a l p r o p e r t i e s , the m e l t i n g point, surface energy and f i n a l l y the rates of self d i f f u s i o n and of g r a i n growth. Some of these p r o p e r t i e s a r e obviously i n t e r r e l a t e d . * T r a n s f o r m a t i o n p l a s t i c i t y i s taken to denote an anomalous propensi t y f o r p l a s t i c flow, manifested by low flow s t r e s s and u s u a l l y by l a r g e " ductility 1', accompanying a s o l i d - s o l i d phase t r a n s f o r m a t i o n or decomposition reaction. -5- When a powder is p l a c e d in some container (say a die) the density obtained w i l l be quite low since i r r e g u l a r l y shaped p a r t i c l e s may f o r m b r i d g e s , or powder with a range of p a r t i c l e s i z e s may segregate , giving r i s e to l e s s e f f i c i e n t packing than if the s i z e s were thoroughly mixed. (This segregation w i l l not be a l t e r e d by sub- sequent operations and t h e r e f o r e w i l l not be c o n s i d e r e d further). If subjected to either v i b r a t i o n or p r e s s u r e , p a r t i c l e r e arrangement w i l l occur, f i l l i n g l a r g e voids. V i b r a t i o n w i l l quickly produce a pack- ing density c h a r a c t e r i s t i c of the p a r t i c l e shape and si z e d i s t r i b u t i o n . A p p l i c a t i o n of p r e s s u r e w i l l cause d e n s i f i c a t i o n by f r a c t u r e and flow of the p a r t i c l e s , depending on the strength and d u c t i l i t y of the p a r t i c l e s . Only a v e r y soft m a t e r i a l can densify completely by the flow mechanism, and no useful c e r a m i c m a t e r i a l can by f a b r i c a t e d to high density by flow alone on a c o m m e r c i a l b a s i s . The constraint offered by surrounding p a r t i c l e s p r o b a b l y prevents d e n s i f i c a t i o n beyond the point at which a line contact between three or more p a r t i c l e s is formed. F r o m this point mass t r a n s p o r t by bulk diffusion, s urface (i. e. g r a i n boundary) diffusion, or by e v a p o r a tion - condensation is probably a m o re important f a c t o r than p l a s t i c behaviour, i n most cases N a b a r r o - H e r r i n g (diffusional) creep m a y b e operative, although this m e c h a n i s m is not c o n s i d e r e d a l i k e l y o n e(^'. The e l i m i n a t i o n of trapped gas f r o m pores may be a p r o b l e m since the p r e s s u r e w i l l eventually counteract the a v a i l a b l e d r i v i n g f o r c e (reduction of surface -6- energy plus applied p r e s s u r e ) unless the gas is soluble and t h e r e - fore can diffuse through the structure. The d e n s i f i c a t i o n of MgO by p r e s s u r e c a l c i n t e r i n g of Mg(OH)2 has been shown to occur i n two stages. A p p r o x i m a t e l y half the o b s e r v e d d e n s i f i c a t i o n o c c u r s simultaneously with the dehydroxylation of the b r u c i t e . The r e m a i n d e r of the d e n s i f i c a t i o n takes place f r o m about 550°C un t i l the f i n a l density is reached, u s u a l l y at about 850° to 900°C. S i m i l a r be- haviour has been observed by Chaklader and C o o k ^ . T h i s is shown in F i g u r e 1. M o r g a n and Schaeffer ^ have suggested that the f i r s t stage of d e n s i f i c a t i o n is a r e s u l t of a s l i p m e c h a n i s m based on t h e i r o b s e r v ation of the f o r m a t i o n of a (111) texture i n magnesia r e s u l t i n g f r o m the f i r s t stage. T h i s departs f r o m the theory e a r l i e r propounded (2) by M o r g a n and S c a l a who suggested that c r u m b l i n g of the p r e c u r s o r b r u c i t e flakes into tiny p e r i c l a s e (MgO) cubelets was r e s p o n s i b l e f o r the i n i t i a l d e n sification. The second stage is p r o b a b l y due to d i f f u s i o n a l t r a n s p o r t or g r a i n growth p r o c e s s e s . T h i s is c o n f i r m e d by the fact that no additional t e x t u r a l development has been o b s e r v e d d u r i n g stage II. The p r e v i o u s l y d e t e r m i n e d p r o p e r t i e s of the e x p e r i m e n t a l s y s t e m are s u m m a r i z e d i n section 1. 4. 1. 2 O b j e c t i v e s of this Investigation The purpose of this i n v e s t i g a t i o n i s to study the flow c h a r a c t e r i s t i c s of powder compacts of Mg(OH)2 during the dehydroxy- lat i o n r e a c t i o n and thus to provide evidence of t r a n s f o r m a t i o n - 7 - F I G U R E I Compaction of M g ( O H ) 2 as a function of temperature. (After C h aklader and Cook, Q (8) and M o r g a n and Scala, /\ (2))- -8- p l a s t i c i t y . If a flow p r o c e s s is operating during the dehydroxylation, its p r e s e n c e should a i d i n understanding the enhanced d e n s i f i c a t i o n o b s e r v e d during the r e a c t i v e hot p r e s s i n g of a decomposible compound. A n attempt has a l s o been made to explore the p o s s i b i l i t y of bond f o r m a t i o n a c r o s s the i n t e r f a c e between two single c r y s t a l s while decomposing under load. 1. 3 Choice of E x p e r i m e n t a l S y s t e m When this study was f i r s t being c o n s i d e r e d it was felt that some m a t e r i a l available as natural or e a s i l y grown single c r y s t a l s would make a suitable p r e c u r s o r . C a l c i t e i s an obvious choice, as v e r y l a r g e and quite pure single c r y s t a l s are c o m m e r c i a l l y available. Unfortunately , however, the decomposition of c a l c i t e does not give a coherent CaO l a y e r on the c a l c i t e surface , as has been demon- stra t e d by s e v e r a l workers^ ^ T h u s , as expected, e a r l y experiments with this m a t e r i a l were u n s u c c e s s f u l . The second choice was the s y s t e m Ca(OH)2 (Portlandite) - CaO, as s m a l l c r y s t a l s of Ca(OH)2 are quite e a s i l y grown T h i s s y s t e m has the disadvantage that both the product and p r e c u r s o r t r a n s f o r m r e a d i l y to c a l c i u m carbonate upon exposure to m o i s t a i r containing CO2, i . e . the l a b o r a t o r y atmosphere, making handling di f f i c u l t if contamination is to be avoided. T h e r e f o r e , i n order to study quantitatively the nature of t r a n s f o r m a t i o n p l a s t i c i t y c o l d compacts of synthetic m a g n e s i u m -9- hydroxide powder were produced. These compacts were subjected to c o m p r e s s i v e creep d e f o r m a t i o n (at low s t r e s s e s ) during the dehydroxylation reaction, under v a r y i n g conditions. M a g n e s i u m hyd r o x i d e was chosen f o r these experiments as it has s e v e r a l advantages over other p o s s i b l e choices: the s t r u c t u r a l r e l a t i o n s h i p between p r e c u r s o r and product i s simple, the c r y s t a l s t r u c t u r e s themselves are simple,and the r e a c t i o n kin e t i c s and morphology are quite w e l l understood. The m a t e r i a l s are a l s o r e l a t i v e l y easy to handle (although magnesia with high surface a r e a rehydrates in m o i s t air) and f i n a l l y magnesia i s a useful r e f r a c t o r y . The relevant p r o p e r t i e s of this s y s t e m are c o n s i d e r e d i n the next section. 1. 4 P r o p e r t i e s of the E x p e r i m e n t a l S y s t e m The behaviour of the Mg(OH ) 2 - MgO s y s t e m has been the subject of c o n s i d e r a b l e investigation, m a i n l y because of the influence of the conditions of decomposition on the subsequent hot p r e s s i n g or s i n t e r i n g behaviour of the product phase. " A c t i v e " MgO is produced by the c a l c i n a t i o n of Mg(OH ) 2 at low temperatures, which produces high s p e c i f i c surface a r e a s , as w i l l be seen l a t e r . 1. 4. 1 P h y s i c a l and C h e m i c a l P r o p e r t i e s Table I s u m m a r i z e s some important p r o p e r t i e s of the p r e - cursor-product p a i r . The decomposition M g ( O H ) 2 ^-MgO + H 2 O o c c u r s at t e m p e r a t u r e s i n excess of 300°C, and i s e s s e n t i a l l y complete (except f o r the r e m o v a l of absorbed water) at about 400° C. - 10 - T A B L E I P R O P E R T I E S of Mg(OH)? and MgO F o r m u l a Weight Ratio S p e c i f i c G r a v i t y S t r u c t u r e T y p e L a t t i c e P a r a m e t e r s Bond Lengths B r u c i t e M g ( O H ) 2 58. 34 1 1. 449 2. 385 Hexagonal C d l 2 a Q = 3.147A c 0 = 4. 769A 0 - 0 3. 13, 2. 98A Mg - 6 0 2. 16A P e r i c l a s e MgO 40. 32 0. 691 1 3.58< 2 0> Cubic N a C l a Q = 4. 213A( 2 1) 0 - 0 2. 98A<22) Mg - 6 0 2. 10A + 19 K c a l / m o l at 600° K -11- D e c o m p o s i t i o n of single c r y s t a l s has shown (13-15) that a pseudo- morphous product i s obtained, with only a few p e r c e n t shrinkage f r o m the o r i g i n a l dimensions. The product c r y s t a l i s only 47 volume percent MgO, and i s composed of an aggregate of v e r y s m a l l (about 100 A, (1^)) c r y s t a l l i t e s having a definite c r y s t a l l o g r a p h i c r e l a t i o n s h i p to the b r u c i t e . 1. 4. 2 S t r u c t u r a l A s p e c t s of the D e c o m p o s i t i o n B r u c i t e (Mg(OH)2) has a C d l 2 type s t r u c t u r e , with the hydro- xy l ions a r r a n g e d in hexagonal (close packed l a y e r s ) i n hep stacking sequence. The Mg"*~̂  ions are i n octahedral sites between e v e r y second p a i r of O H l a y e r s . The arrangement is shown s c h e m a t i c a l l y in F i g u r e 2. T h i s stacking of OH l a y e r s r e s u l t s i n a pronounced b a s a l cleavage and i n the c h a r a c t e r i s t i c I'platy" shape of the hydroxide ( F i g u r e 9 ) . P e r i c l a s e (MgO) has a N a C l type (cubic) s t r u c t u r e , ( F i g u r e 2), c o n s i s t i n g of oxygen ions i n clos e packed l a y e r s , f o r m i n g the (111) planes, with Mg i n a l l the o c t a h e d r a l sites. A number of i n v e s t i g a t o r s (1^-15) have c o n s i d e r e d the s t r u c t u r a l r e l a t i o n s h i p s i n v o l v e d i n the dehydroxylation reaction. The most recent and a u t h o r i t a t i v e work is that of G o r d o n and K i n g e r y (15), which c o n s i s t s of e l e c t r o n and o p t i c a l m i c r o s c o p y , and a k i n e t i c study. The m e c h a n i s m s p r o p o s e d by v a r i o u s authors are s u m m a r i z e d in T a b l e II, which includes both m o r p h o l o g i c a l and k i n e t i c aspects. - 1 2 - -e— o - . o o Q Brucite a) e — e ^ o Q o (edge view of ( 0 0 0 1 ) planes, - e — e — e — e - - e -a ion g - <n2o> direction ) e e e e e Periclase b) A ' - M g O-O 9 - 0 H F I G U R E 2 a) Structure of M g ( O H ) 2 " Schematic r e p r e s e n t a t i o n b) St r u c t u r e of MgO - Schematic r e p r e s e n t a t i o n T A B L E II S U M M A R Y O F M E C H A N I S M S AND K I N E T I C S O F M g ( O H ) 2 D E H Y D R O X Y L A T I O N Authors M e c h a n i s m or Model Type of K i n e t i c s A c t i v a t i o n E n ergy, k c a l / m o l K i n g e r y and Gordon ( l 5 ) 1) Nucleation and growth pr o c e s s , with F i r s t o r d e r for coherentnucleation, resultant large s m a l l p a r t i c l e s , strains and f i s s u r i n g . t h ick single c r y s - 2) A s m a l l amount of decomposition causes tals m o r e complex, la r g e changes in the p h y s i c a l state of the c r y s t a l , having a considerable effect on the subsequent p r o c e s s and product. The model explains: a) the s t r u c t u r a l r e l a t i o n s h i p . b)the product c r y s t a l l i t e size, c) the c r a c k i n g p r o c e s s , and d) the d" spacing range. 38 ~ 43 A n d e r s o n and H o r l o c k ( l 4) A n i n t e r f a c e reaction, d e s c r i b e d in t e r m s of a contracting d i s c along the b a s a l plane. 1 9 - 2 7 w i G r e g g and D e s c r i b e d weight los s data s a t i s f a c t o r i l y i n Razouk t e r m s of the contracting sphere model. 12 - 27 Z h a b r o v a and G o r d e e v a ^ ' Showed that t h e i r data could be d e s c r i b e d equally well by the contracting sphere or u n i m o l e c u l a r decay law. -14- The l i s t i s not e x h a u s t i v e , but i n c l u d e s the m o s t r e c e n t and s i g n i f i c a n t w o r k i n t h i s f i e l d . V a r i o u s d e c o m p o s i t i o n s t u d i e s p e r f o r m e d i n the e l e c t r o n m i c r o s c o p e have shown the c r y s t a l l o g r a p h i c r e l a t i o n s h i p d eveloped between the p e r i c l a s e and the p a r e n t b r u c i t e (13-15)_ One set of the (111.) p l a n e s of the p e r i c l a s e a r e n o r m a l to the c - a x i s of the b r u c i t e . In a d d i t i o n , the^HO) d i r e c t i o n of the p e r i c l a s e i s p a r a l l e l to the (lio) d i r e c t i o n of the p a r e n t b r u c i t e . G o r d o n and K i n g e r y c o n c l u d e d that the d e c o m p o s i t i o n of b r u c i t e i s m o s t l i k e l y a n u c l e a t i o n and g r o w t h p r o c e s s i n w h i c h coherent n u c l e a t i o n of MgO r e s u l t s i n l a r g e c o h e r e n c y s t r a i n s and c r a c k i n g , i n the v e r y e a r l y stages of weight l o s s as shown i n F i g u r e 3 . T h i s c r a c k i n g i s a m a j o r change i n the p h y s i c a l state of the c r y s t a l , and has a p r o n o u n c e d e f f e c t on the subsequent p r o c e s s and p r o d u c t s . T h i s m o d e l e x p l a i n s : a) the o b s e r v e d s t r u c t u r a l r e - l a t i o n s h i p , b) the s m a l l c r y s t a l l i t e s i z e of the p r o d u c t , c) the o b s e r v e d c r a c k i n g p r o c e s s , and d) the o b s e r v a t i o n of a range of d - s p a c i n g s d u r i n g the d e c o m p o s i t i o n p r o c e s s . A n d e r s o n and H o r l o c k ^ found that the r e a c t i o n p r o c e e d e d f r o m the edges of the b r u c i t e p l a t e l e t s (for l a r g e s i n g l e c r y s t a l s a p p r o x i m a t e l y 1 by 3 mm), p r o d u c i n g a " p o l y c r y s t a l l i z a t i o n " s u b s e - quently a t t r i b u t e d to the c o h e r e n c y s t r a i n by G o r d o n and K i n g e r y . The f o r m e r a u t h o r s found that the m a j o r p a r t of the d e c o m p o s i t i o n Brucite OH Mg OH OH Mg OH OH Mg OH F I G U R E 3 Goodman's Mg- 0 + H 2 0 Mg 0 • H 2 0 Mg Periclase 0 Mg 0 Mg 0 Mg 0 ( 1 3 ) proposed m e c h a n i s m for the dehydroxylation, showing collapse n o r m a l to the closed~packed oxygen planes in the f o r m a t i o n of p e r i c l a s e . - 1 6 - originated at the "edge" of the platelets, an obs e r v a t i o n contradicted by Gordon and Ki n g e r y . Goodman w a s the f i r s t w o rker to use an e l e c t r o n m i c r o s c o p e to study this decomposition, but he did not observe the i n i t i a l c r a c k i n g r e p o r t e d by the others. He was the f i r s t to recognize that the 0~ l a y e r s r e m a i n e d sub s t a n t i a l l y undisturbed during the decomposition; T h i s r e q u i r e d d i f f u s i o n of water (or its i o n i c components) between the O - l a y e r s , as s c h e m a t i c a l l y r e p r e s e n t e d i n F i g u r e 3. Goodman proposed an a t o m i s t i c m e c h a n i s m that was e s s e n t i a l l y homogeneous. In this mechanism, he c o n s i d e r e d that H^O was u n i f o r m l y r e m oved f r o m a l l p a r t s of the decomposing c r y s t a l (though not n e c e s s a r i l y at the same time) by a two stage p r o c e s s . Water would f i r s t be f o r m e d by r e a c t i o n between h y d r o x y l ions, causing the f i r s t o b served shift i n la t t i c e p a rameter, and then even- tually escape between the oxygen l a y e r s of the p a r t i a l l y decomposed c r y s t a l , as shown i n the F i g u r e . Although Gordon and K i n g e r y did not make s p e c i f i c comment on the mass t r a n s p o r t n e c e s s a r y f o r decomposition, B a l l and T a y l o r (1^) point out that the movement of the product water would be e x t r e m e l y l i k e l y to cause d i s r u p t i o n of the m a t e r i a l . T h ey felt that the o b s e r v e d behaviour was d e s c r i b e d better by the concept of an inhomogenous s o l i d state reaction, operating as follows: The decomposing c r y s t a l would develop donor and acceptor regions ( F i g u r e 4) between which d i f f u s i o n of M g + + ( ionic F I G U R E 4 B a l l and T a y l o r ' s proposed inhomogenous m e c h a n i s m for the dehydroxylation, showing donor and acceptor regions, and the di f f u s i o n of Mg++ and H+. -18- radius = 0. 78A, compared to about 1. 75 f o r water) and H + would occur as shown. The donor regions (probably adjacent to free s u r - faces or cracks) would eventually be completely destroyed. The close packed O H - l a y e r s of the acceptor regions would become close packed O" l a y e r s , with the addition of sufficient M g + + to f o r m MgO. 1. 4. 3 K i n e t i c s of D e c o m p o s i t i o n The decomposition k i n e t i c s have been e x t e n s i v e l y investigated but no general agreement as to an exact m e c h a n i s m has been made. F a i l u r e to obtain agreement has been attributed to v a r i a t i o n s i n the m a t e r i a l , e x p e r i m e n t a l conditions, and i n the size of the sample used (15). G regg and Razouk v ' i n t e r p r e t e d t h e i r data by means of a contracting sphere model: 1/3 ^ (1 - * = 1 R obtaining a c t i v a t i o n e n e r g i e s of 12 to 27 k c a l / m o l e for M g ( O H ) 2 powders, and 27. 6 k c a l / m o l e for b r u c i t e . A n d e r s o n and H o r l o c k v ' used a contracting d i s c model: 1/2 ^ (1 - <A )U* = 1 -• R and obtained a c t i v a t i o n e n e r g i e s of 27.6 k c a l / m o l e for powder, and 23. 6 k c a l / m o l e f o r two types of b r u c i t e . -19- Z h a b r o v a and G o r d e e v a ( * ^ h a d e a r l i e r s h o w n that no s i n g l e m o d e l c o u l d u n e q u i v o c a b l y be u s e d : T h e y f i t t e d t h e i r da ta s u c c e s s f u l l y to a c o n t r a c t i n g s p h e r e r e l a t i o n s h i p and to a u n i - m o l e c u l a r ( f i r s t o r d e r ) d e c a y l a w of the f o r m In ( l - « ) = k i t + cons tan t i n w h i c h k j i s a n u c l e a t i o n r a t e cons tan t and o*> i s the f r a c t i o n a l we igh t l o s s . G o r d o n and K i n g e r y ( ^ ) c o n c l u d e d that t h e i r da ta c o u l d be s t be i n t e r p r e t e d u s i n g the u n i m o l e c u l a r m o d e l , b e c a u s e of the c o m p l e t e d i s r u p t i o n of the s t a r t i n g m a t e r i a l e a r l y i n the d e c o m p o s i t i o n . L a r g e c r y s t a l s p r o b a b l y show m i x e d c o n t r o l as the f r a g m e n t a t i o n m a y be i n c o m p l e t e , m a k i n g b o t h c o n t r a c t i n g d i s c and the f i r s t o r d e r m e c h a n i s m o p e r a t i v e . T h e y a l s o c o n c l u d e d that the effect of w a t e r v a p o u r b a c k p r e s s u r e w a s c o n s i d e r a b l e c a u s i n g d i s c e r n a b l e v a r i a t i o n of r a te w i t h s a m p l e s i z e , and f r o m w o r k e r to w o r k e r w i t h v a r i o u s c o n d i t i o n s . H o r l o c k , M o r g a n and A n d e r s o n (19) s t u d i e d the effect of w a t e r v a p o u r on the d e c o m p o s i t i o n , s h o w i n g that the ra te of we igh t i o s s i s m u c h h i g h e r i n v a c u u m than i n w a t e r vap ou r a t m o s p h e r e . -20- C H A P T E R II 2. Expe rimental 2. 1 Apparatus The apparatus, shown in a schematic view in Figure 5, was constructed to permit the decomposition of various systems in a con- trolled atmosphere, since it was felt that gaseous atmospheres .could produce considerable effects during and following decomposition. The design was intended to have fairly general applicability in the area of neck growth, sintering model studies, and for that reason incorporated some features not absolutely essential to the work forming the present study. 2.1. 1 Furnace and Load Frame The specimens themselves were mounted in a loading frame (Figure 6) which was removeable from the furnace for specimen mount- ing. The load frame was fabricated from Inconel X-750. The pushrod slid in boron nitride bushings, gave fairly low values of coefficient of static friction (about 0. 0 5 when clean), permitting the use of small loads for studies with single crystals. The various "grips" slid onto the pushrod and anvil, permitting ready change from one type of specimen to another. When in position in the furnace the load frame was enclosed by a resistant element consisting of 10 turns of No. 6 A. W. G. Chromel wire, operating at 10 volts. The furnace had a power rating of one F I G U R E 5 Schematic representation of the e x p e r i m e n t a l apparatus . r f X 1 1 6 i r- F I G U R E D The loading frame, - showing the thermocouples. kilowatt with this winding. The heater was i n s u l a t e d f r o m the water jacketted v acuum chamber by c o n c e n t r i c s i l i c a tubes separated by corru g a t e d s t a i n l e s s steel r a d i a t i o n s h i e l d s , which p r o v i d e d reasonably ef f i c i e n t i n s u l a t i o n with m i n i m u m surface area, p e r m i t t i n g easy pump- down to high vacuums. Z. 1. Z V a c u u m S y s t e m The furnace chamber was fitted with two Z i n c h diameter P y r e x windows, p e r m i t t i n g viewing of the s p e c i m e n when i n p o s i t i o n i n the furnace. The sight path was through 3/4 i n c h holes i n the furnace i n s u l a t i o n and between turns of the heating c o i l . The pumping s y s t e m c o n s i s t e d of a Z inch E d w a r d s E O Z oi l d i f f u s i o n pump with l i q u i d nitrogen trap and b u t t e r f l y i s o l a t i o n valve, backed by a B a l z e r s Duo 5 m e c h a n i c a l pump. C o a r s e and fine bleed valves p e r m i t t e d a d m i s s i o n of any d e s i r e d gas or vapour into the chambe and by balancing b l e e d rate against pumping rate any d e s i r e d p r e s s u r e _5 between 1 atmosphere and 1 x 10 T o r r could be obtained f a i r l y e a s i l y . V a c u u m gauging was by means of an E d w a r d s P i r a n n i - Penning gauge unit. Z. 1. 3 Photography Specimens i n the furnace were photographed with one of two different lens systems, depending on the m a g n i f i c a t i o n r e q u i r e d . A conventional 135 mm Telephoto lens with extension tubes p e r m i t t e d m a g n i f i c a t i o n s l i g h t l y i n excess of 1:1, and higher magnifications were pr o v i d e d by L e i t z Optics, having a m a g n i f i c a t i o n of about 4 x . The -24- specimens were photographed i n sihouette, being backlighted by a m i c r o s c o p e i l l u m i n a t o r . The c a m e r a was a 35 mm single lens reflex. 2. 1. 4 Loading and D i s p l a c e m e n t M easurement The p u s h r o d of the loading f r a m e was contacted by a s p r i n g loading device. Substitution of different s p r i n g s p e r m i t t e d loads f r o m 10 grams to about 3 k i l o g r a m s f o r the present experiments. T h i s s y s t e m had an inherent load v a r i a t i o n with displacement but for the s m a l l d i s p l a c e m e n t s i n v o l v e d i t was not felt that the v a r i a t i o n would be significant. The springs were s e l e c t e d to m i n i m i z e this effect. A piece of hardened 0. 030 diameter d r i l l r o d p a s s i n g through a s l i g h t l y u n d e r s i z e d hole i n a p i e c e of 1/8 i n c h thick neopren e rubber p r o v i d e d a means of t r a n s m i t t i n g the motion outside the vacuum system. The rod was s m e a r e d with v acuum grease and p r o v i d e d a v e r y low f r i c t i o n f o r c e which was alm o s t exactly balanced by the r a m f o r c e of the d i a l i n d i c a tor, about 20 grams, and was only used f o r loads i n excess of 100 grams and so did not provide a l a r g e source of e r r o r i n the load. The displacement was m e a s u r e d i n two ways; by an inductive displacement t r a n s d u c e r connected to a P h i l l i p s s t r a i n gauge bridge and Heathkit s t r i p chart r e c o r d e r , or d i r e c t l y by a S t a r r e t d i a l i n d i c a t o r (0. 0001 i n c h p e r divi s i o n ) , connected i n tandem with the t r a n s - ducer. Use of the t r a n s d u c e r - r e c o r d e r combination was t e r m i n a t e d after experience showed that c o r r e c t i o n f o r the d r i f t of the r e c o r d e r involved more d i f f i c u l t y than manual r e c o r d i n g of the d i a l i n d i c a t o r readings. - 25 - 2. 1. 5 F u r n a c e T e m p e r a t u r e C o n t r o l and Power Supply T e m p e r a t u r e measurement was by means of C h r o m e l - A l u m e l thermocouples. These were either connected d i r e c t l y to a compensated potentiometer c o n t r o l l e r (Honeywell S e r v o t r o n i k or V e r s a t r o n i k ) or connected to a Pye Potentiometer or Heathkit r e c o r d e r with an icewater (0°C) c o l d junction. M o s t of the e x p e r i m e n t a l work with m a g n e s i u m hydroxide was done using three t h e r m o c o u p l e s ( F i g u r e 6) of No. 32 A. W. G. wire. F o r the experiments two of the thermocouples were i n contact with the s p e c i m e n and g r i p (Nos. 1 & 2) while the t h i r d was f r e e to m e a s u r e radiant t e m perature within the furnace. T h e r m o c o u p l e s 1 and 2 were g e n e r a l l y i n agreement within 5 degrees Centigrade, while the t h i r d was as much as 20 and 30 degrees different, depending on the p a r t i c u l a r t h e r m a l conditions. F o r some of the e a r l y e xperiments temperature was m e a s u r e d by means of a 1/8 i n c h O. D. Inconel sheathed thermocouple, pl a c e d in s i d e the f i x e d grip. T h i s obviously was not r e p r e s e n t a t i v e of the s p e c i m e n temperature except under i s o t h e r m a l (steady state) con- ditions, but it was used for temperature c o n t r o l during l i n e a r l y i n - c r e a s i n g temperature runs. The power to the furnace windings was supplied by 2 K V A Powerstat. which was used i n conjunction with the c o n t r o l l e r s to provide optimum c o n t r o l at a p a r t i c u l a r t emperature setting. -26- 2. 2 E x p e r i m e n t a l Technique 2. 2. 1 Growth of Ca(OH)z (Portlandite) Single C r y s t a l s The Ca(OH ) 2 single c r y s t a l s used were grown by the i n t e r - d iffusion of solutions of p o t a s s i u m hydroxide and c a l c i u m c h l o r i d e by a technique due to Dave and C h o p r a (1^) > m o d i f i e d s l i g h t l y as follows: A 100 m l beaker was p l a c e d inside a 600 m l beaker, F i g u r e 7 , and the two were f i l l e d with C O 2 - f r e e d i s t i l l e d water (prepared by bubbling nitrogen through d i s t i l l e d water) just above the top of the 100 m l beaker. In this work the solutions were introduced through two stopped funnels through fine glass tubing extensions rather than by pipette as suggested i n the r e f e r e n c e i n o r d e r to prevent turbulence and p r e m a t u r e m i x i n g of the solutions. When the d i s t i l l e d water had been added and the funnels f i l l e d with saturated solutions of K O H and C a C l 2 molten p a r a f f i n wax was poured onto the d i s t i l l e d water to a depth of about 1/4 inch to prevent contamination by a t m o s p h e r i c gases. 50 m l of the K O H solution and 40 ml of C a C l 2 was admitted to the beakers. In two or three days c r y s t a l s s t a r t e d to appear on the outside of the s m a l l beaker and the inside of the l a r g e r one. In four days growth was e s s e n t i a l l y complete and the wax was l i f t e d out and the c r y s t a l s c a r e f u l l y r e m oved f r o m the walls of the beaker by s c r a p i n g them off with a s t i r r i n g r o d equipped with a rubber s c r a p e r . The c r y s t a l s were r i n s e d with d i s t i l l e d water and then s t o r e d i n tightly capped j a r s . E a c h run produced about 500 s m a l l c r y s t a l s . Only a s m a l l number of them were suitable f o r  -28- experiments as many were eit h e r v e r y s m a l l , quite i m p e r f e c t or broken fragments of l a r g e r c r y s t a l s . The c r y s t a l s had obvious hexagonal morphology and f r a c t u r e d v e r y e a s i l y on the b a s a l planes. T y p i c a l defects were pockets of trapped solution, or "pipe" extending some distance into the c r y s t a l s f r o m the root end. The c r y s t a l s were not analy s e d as p u r i t y was not fel t to be of great importance at this stage of the investigation, but Dave and Ch o p r a < 1 2) quote 99- 6 5 % Ca(OH) 2 and 99. 6% of the t h e o r e t i c a l c a l c i u m i n t h e i r c r y s t a l s . 2. 2. 2 E x p e r i m e n t s on T i p to T i p Contact A. Ca(OH)?, C r y s t a l s F o r these experiments the c a m e r a set-up with 4 X mag- ni f i c a t i o n was used to view and r e c o r d the behaviour of the c r y s t a l s . D u r i n g these e a r l y experiments the l i n e a r temperature p r o g r a m m e r was not ava i l a b l e so the heating rate was uncontrolled, giving a temp- er a t u r e - time p r o f i l e s i m i l a r to that shown i n F i g u r e 8. The p r o c e d u r e of s e l e c t i o n and mounting was tedious as the useful c r y s t a l s were t y p i c a l l y v e r y s m a l l ; l e s s than 1mm i n diameter and 2 to 3 mm long. C r y s t a l s of good size and shape were se l e c t e d f r o m t h e i r storage j a r , examined under a m i c r o s c o p e (50X) to ensure _4 suitable tip shape, then l i g h t l y etched i n 10 N H y d r o c h l o r i c a c i d s o l u t i o n ; followed by r i n s i n g i n d i s t i l l e d water to give a f r e s h surface, then mounted, loaded and evacuated as quickly as p o s s i b l e to m i n i m i z e surface t r a n s f o r m a t i o n to C a C 0 3 « Time, minutes F I G U R E 8 T i m e - t e m p e r a t u r e p r o f i l e used for the decomposition of Ca{OH) 2 tips and for u n i f o r m beating rate e x p e r i m e n t s . -30- Mounting the c r y s t a l s i n the load f r a m e was done with a c o m m e r c i a l furnace cement " S a i r s e t " as this p r o v i d e d a suitable mount- ing f o r the c r y s t a l s i n a s m u c h as it was quick setting, strong and yet e a s i l y r e m o v e d f r o m the grips after a run. A f t e r the s y s t e m had been evacuated to a v a c u u m of about 0. 02 Tor i ; the furnace power was switched on and the run commenced. Photographs were taken before, during and after the decomposition, which could be followed e a s i l y , as the p r e s s u r e in the furnace was to some extent p r o p o r t i o n e d to the decomposition rate. 2. 2. 3 P r e p a r a t i o n of Mg(OH)? Compacts B. Mg(OH)2 Compacts T o study qu a l i t a t i v e l y both flow and bond formation, p a i r s of h e m i s p h e r i c a l tipped p e l l e t s were p l a c e d i n the l o a d f r a m e and de- composed under v a r i o u s loads. D e t a i l s of s p e c i m e n p r e p a r a t i o n are given i n the following section. F o r deformation studies under c o m p r e s s i v e loading, Mg(OH)2 compacts were p r e p a r e d f r o m A l c a n magnesium hydroxide (Alcan Ltd. , M o n t r e a l , C h e m i c a l P r o d u c t s D i v i s i o n ) . T h i s m a t e r i a l contained i m p u r i t i e s as follows: M g O - 9 6 % - A l 2 G " 3 + F e 2 O 3 - 1. 5 % , CaO+Si02~2. 5 % , (after ignition). The p a r t i c l e size and shape was d e t e r m i n e d i n an e l e c t r o n m i c r o s c o p e by suspending a s m a l l amount of the powder i n a dilute HC1 solution, then p l a c i n g a drop of this suspension on a g r i d with a carbon support f i l m and allowing the water to evaporate. The powder is shown 31 - a) B e f o r e dehydroxylation b) A f t e r dehydroxylation at 450°C F I G U R E 9 E l e c t r o n m i c r o g r a p h s of the M g ( O H ) 2 powder. -32- i n F i g u r e 9- The mean p a r t i c l e d i m e n s i o n i n the b a s a l plane was estimated to be 150oA and the average thickness was about 250 A. Surface a r e a was a p p r o x i m a t e l y 15m^/gm. The powder was p r e s s e d into compacts i n a 0. 190 i n c h diameter die made f r o m A t l a s Keewatin steel, with plungers of d r i l l rod. B oth die and plungers were hardened and t e m p e r e d , the die to R.^60 and the plungers to R t55. The die was used s u c c e s s f u l l y to 100,000 p s i with Mg(OH)2, although g a l l i n g o c c u r e d at much lower p r e s s u r e s with MgO i n a s i m i l a r die. The bore had a v e r y slight taper i (about 0.0005 i n c h e s / inch), which f a c i l i t a t e d r e m o v a l of the compacts. It was fe l t that experiments with the tip to tip contact of decomposing bodies might demonstrate both flow and bond f o r m a t i o n with this m a t e r i a l and to this end a number of compacts were p r e s s e d f r o m Mg(OH)2 using a r a m shaped to give a h e m i s p h e r i c a l end on the pellet, (shown l a t e r i n F i g u r e 13). The compacts were produced using a f l o o r model Instron Machine which was c a l i b r a t e d so that the chart r e a d d i r e c t l y i n pounds per square inch. B y using the load c y c l e c o n t r o l it was p o s s i b l e to obtain v e r y r e p r o d u c i b l e s p e c i m e n density. The p r e s s i n g p r o c e d u r e was as follows: 1) The die was loaded (with pre-weighed charge). 2) The die was p l a c e d i n the machine and p r e l o a d e d to about 100 p s i by means of the manual c r o s s h e a d t r a v e r s e . -33- 3) The s p e c i m e n was p r e s s e d under a constant c r o s s h e a d speed of 0. 0 5 inches/min. 4) The c r o s s h e a d motion was stopped at a p r e d e t e r m i n e d load. 5) The load was allowed to r e l a x with constant c r o s s h e a d p o s i - tion f o r 5 minutes. 6) The load was r e l e a s e d at 0. 05 inches/minute, and the s p e c i m e n p r e s s e d out at 5 inches/minute. The specimens were then weighed, m e a s u r e d f o r length and diameter and stored i n stoppered v i a l s until needed f o r experiments. P r a c t i c a l considerations l i m i t e d the densities available f o r study. It was found that below a r e l a t i v e density of 0. 40 the specimens were too f r a g i l e to be handled e a s i l y , while above 0. 70 they tended to develop c i r c u m f e r e n t i a l c r a c k s upon r e m o v a l f r o m the die. The completed specimens were 0. 190 5 to 0. 191 inches (4. 839 to 4. 851 mm) diameter, and a p p r o x i m a t e l y 0. 32 inches (8. 13 mm) long. F i g u r e 10 shows the r e l a t i o n s h i p between f r a c t i o n a l density and the p r e s s u r e used i n compacting the specimens. The c o n s i s t e n c y of density was excellent; the' range of densities o b s e r v e d was about + 0. 4% at 5.0% r e l a t i v e density. 2. 2. 4 D e f o r m a t i o n of Mg(OH)p C y l i n d r i c a l Compacts S e v e r a l different approaches were taken to the p r o b l e m of c h a r a c t e r i z i n g the creep behaviour of the m agnesium hydroxide compacts. In a l l cases the specimens were p l a c e d between the flat s u r f a c e s of the anvils or grips and the f u l l load applied at r o o m temperature.  -35- The types of experiments undertaken were as follows: i) Q u a s i - u n i f o r m Heating Rate The f i r s t s e r i e s of runs were made to explore the r e p r o d u c e - ab i l i t y of the experiments, and to determine the effect of lo a d on the creep behaviour under these conditions. The heating rate was obtained by using a fi x e d setting of the powerstat, giving the heating rate shown in F i g u r e 8. ii) "Isothermal 1 1 , Runs In o r d e r to f a c i l i t a t e the det e r m i n a t i o n of an act i v a t i o n energy f o r the deformation, most of the experiments r e p o r t e d here were done under i s o t h e r m a l conditions. The m a x i m u m heating rate available was used to b r i n g the sp e c i m e n and load f r a m e to the test temperature, and this was done within 10 to 12 minutes of the start of heating. The average heating rate was 40°C/minute, with an almost l i n e a r rate of 26°C/minute f r o m 320°C to 405°C (the m a x i m u m temper- ature used i n these experiments), as shown i n a time-temperature p r o f i l e , F i g u r e 11. T e m p e r a t u r e was r e c o r d e d continuously during a l l e x p e r i m e n t a l runs. P e r i o d i c checks of the r e c o r d e r c a l i b r a t i o n was made during the runs. T h e r m a l expansion c o r r e c t i o n was nec e s s i t a t e d by the rather r a p i d r i s e i n temperature, which caused uneven t h e r m a l s t r a i n s i n the different p a r t s of the loading frame. Two t h e r m a l expansion runs were p e r f o r m e d f or each r u n or p a i r of i d e n t i c a l runs f or given temperature and load conditions, using a dummy quartz specimen. The expansion o o o o o o co o o CM - - 84 - S9 101 - 86 - f 1 m i i i a 0 5 10 15 20 Time, minutes 25 30 35 F I G U R E 11 Specimen surface temperature as a function tests at four different temperatures. of t i m e for the " i s o t h e r m a l " -37- data were subsequently used f o r c o r r e c t i n g the def o r m a t i o n data. The t h e r m a l expansion c o r r e c t i o n was a l s o v e r i f i e d using a t r a v e l l i n g m i c r o s c o p e (Appendix III). The v a r i a b l e s c o n s i d e r e d i n this s e r i e s of experiments were temperature, load ( c o m p r e s s i v e stress) and s p e c i m e n bulk density. Other f a c t o r s which could c o n c e i v a b l y be e x p e r i m e n t a l v a r i a b l e s , such as p a r t i c l e s i z e , shape and c h e m i c a l p u r i t y were held constant. The specimens were loaded into the load f r a m e , then into the furnace, and the s y s t e m way se a l e d and pumped down to about 10 T o r r . The run was u s u a l l y commenced as soon as pumpdown was complete, but extended holding p e r i o d s at low p r e s s u r e s (as long as 46 hours) had no d i s c e r n a b l e effect on the creep curve. T e m p e r a t u r e measurements during this group of runs were made using the thermocouples d e s c r i b e d e a r l i e r , but s e v e r a l additional runs were made with a thermocouple i n s e r t e d along the s p e c i m e n axis to measure temperature at the centre of the specimerij as d e s c r i b e d i n the following section. 2. 2. 5 T e m p e r a t u r e D i s t r i b u t i o n i n Specimens The c r e e p tests were p e r f o r m e d " i s o t h e r m a l l y " . However, since the s p e c i m e n was taken to the temperature f o r creep study as fast as p r a c t i c a l l y p o s s i b l e , there was a p e r i o d at the beginning of each experiment during which l a r g e t h e r m a l gradients existed. T h e r e are two ways of d e t e r m i n i n g the temperature d i s t r i b u t i o n i n the speciment -38- during the experiments: by t h e o r e t i c a l c o n s i d e r a t i o n of t h e r m a l di f f u s i v i t y , or by e x p e r i m e n t a l determination of the temperature of the center and on the surface of the specimen. A p r e c i s e t h e o r e t i c a l a n a l y s i s was not p o s s i b l e because of the l a c k of data n e c e s s a r y f o r such calculations. However, a p r e - l i m i n a r y o r d e r of magnitude calculation, was made using the method of C a r s l a w and J a e g e r (22). This, c a l c u l a t i o n , which indicates that an i n t e r i o r temperature of a p p r o x i m a t e l y 0. 97 of the surface t e m p e r a - ture w i l l be r e a c h e d i n 8 to 10 minutes is p r e s e n t e d i n Appendix I. The temperature d i s t r i b u t i o n during the creep study was a l s o d e t e r m i n e d experimentally. A thermocouple (No. 3) was i n s e r t e d at the center of the s p e c i m e n f r o m one end, as shown by the dotted line in F i g u r e 5. The temperature was m e a s u r e d continuously on the surface (using thermocouples 1 and 2) and at the centre. E x p e r i m e n t a l l y d e t e r m i n e d temperature p r o f i l e s f o r two surface t e m p e r a t u r es, 345° and 408° C are shown i n F i g u r e 12. A f t e r a v e r y l a r g e temperature gradient i n the i n i t i a l stages, a steady state, having a d i f f e r e n t i a l of f r o m 10° to 12°C between the surface and the centre temperature was reached, within 10 to 12 minutes of the start of heating. Thus, f o r kin e t i c a n a l y s i s , it was p o s s i b l e to assume the specimen to be at some ''steady state" temperature c h a r a c t e r i s e d by'the mean temperature . TIME (MIN.) 8 10 12 14 I ' I ' I 1 16 18 20 ' I ' l 4 6 8 TIME (MIN.) F I G U R E 12 Specimen surface and centre temperatures for two different " i s o t h e r m a l ' conditions. -40- C H A P T E R III 3 R e s u l t s 3. 1 C a l c i u m Hydroxide Single C r y s t a l s As d i s c u s s e d e a r l i e r only a v e r y few specimens of i single c r y s t a l c a l c i u m hydroxide were obtained with suitable p r o p e r t i e s for deformation study i n tip to tip contact. E x p e r i m e n t s were p e r f o r m e d with single c r y s t a l s 3 to 4 mm long, about 1 mm i n diameter, and of hexagonal c r o s s section. The s p e c i m e n p a i r was p l a c e d under a load of 10 g rams and decomposed. T h i s l o a d c o r r e s p o n d s to a contact p r e s s u r e of about 0. 5 kg/mm 2, based on the f i n a l contact area. F i g u r e 13 shows a s e r i e s of photographs of a p a r t i c u l a r p a i r of c r y s t a l s before, during, and after decomposition. Due to the i r r e g u l a r geometry of the contact and the v i r t u a l i m p o s s i b i l i t y of duplicating the curvature of the t i p s , no attempt was ma.de to analyse the neck growth data quantitatively. However, the phenomenon of neck growth during decomposition is c l e a r l y demonstrated i n this s e r i e s of photographs. M i c r o s c o p i c examination of the contact faces of the c r y s t a l after the neck growth experiments ind i c a t e d f u s i o n had taken place. T h i s was the f i r s t i n d i c a t i o n that d e f o r m a t i o n could take place i n the presence of a p p l i e d s t r e s s during the decomposition of hydroxide. 3. 2 T i p to T i p Contact of M a g n e s i u m Hydroxide Compacts F o l l o w i n g a s i m i l a r p r o c e d u r e , M g ( O H ) 2 compacts with h e m i s p h e r i c a l tips were decomposed while loaded into contact ( F i g u r e 14) D e f o r m a t i o n of the contact a r e a r e s u l t e d , as can be seen. C o n s i d e r a b l y - 41 - A f t e r decomposition F I G U R E 13 Growth of contact a r e a during the decomposition of C a ( O H ) ? tips under load. more i n t e r e s t i n g was the e x p l i c i t evidence of bond f o r m a t i o n which is pr o v i d e d i n the f o r m of a s m a l l piece of one tip left on the other, when the tips were brok e n apart following the decomposition ( F i g u r e 15). T h i s showed that the adhesion between the two tips was at least as great as the cohesion within them. 3. 3 D e f o r m a t i o n of M a g n e s i u m Hydroxide Compacts A f t e r the i n i t i a l e xperiment just d e s c r i b e d , attempts were made to study quantitatively the def o r m a t i o n behaviour of m a g n e s i u m hydroxide compacts during dehydroxylation, both at a u n i f o r m heating rate and under i s o t h e r m a l conditions. The experiments at u n i f o r m heating rate under different loads were c a r r i e d oat to determine the extent of def o r m a t i o n obtained, and to e s t a b l i s h l i m i t on loads, temperature, and density which could be used i n subsequent studies. T h e s e experiments a l s o showed the r e l a t i v e amount of shrinkage and load-dependent de- f o r m a t i o n which were produced under these conditions. 3. 3. 1 U n i f o r m Heating Rate The specimens used i n this s e r i e s of tests a l l had a nominal r e l a t i v e bulk density of 0. 50 (Table III):. A set of temperature-de- f o r m a t i o n curves f o r this s e r i e s of runs i s shown i n F i g u r e 16. The curves show a tendency to i n c r e a s i n g m a x i m u m slope and i n c r e a s i n g total d eformation with i n c r e a s i n g load. The total d e f o r m a t i o n obtained during decomposition was m e a s u r e d f r o m the i n i t i a l and f i n a l length at the end of the decomposition, - 43 - a) Before decomposition A£ti€i~ decomposition FlGfa'BE? M Gr^wtfa. &£ miii&ei area, during decomposition of Mg(©H)| Gô Mpâ et tips" under lead.- - 44 - b) M a t e r i a l removed f r o m the c r a t e r ad h e r i n g to the other tip. F I G U R E 15 E v i d e n c e of bond formation during the decomposition of Mg(OH)2 compact tips under load. - St - -46 - TABLE III DEFORMATION DATA FOR UNIFORM HEATING RATE LOAD, io/c\ p _gm SPECIMEN kg kg/err/ L 0 '°' c m 49 0.10 0.54 2.62 1.19 50 0.10 0.54 2.69 1-20 38 0.35 1.9 3.56 1.19 39 0.35 1.9 4.08 1.19 45 0.66 3.58 4.78 1.19 46 0.66 3.56 4.69 1.20 42 0.88 4.78 5.15 1.18 43 0.88 4.78 5.20 1.19 40 1.2 6.53 5.65 1.19 41 1.2 6.53 5.96 1.18 47 1.63 8.76 6.22 1.19 48 1.63 8.76 6.47 1.19 33 2.06 11.2 6.72 1.20 34 2.06 11.2 6.90 1.20 52 2.5 13.6 7.26 1.21 53 2.5 13.6 6.85 1.20 54 2.5 13.6 7.10 1.20 -47- as shown i n F i g u r e 16. T h i s total d e f o r m a t i o n was then converted to percent total s t r a i n and is plotted against load i n F i g u r e 17. A l o g - l o g plot of this data (Figixre 18) suggests a r e l a t i o n s h i p of the f o r m eT~ eo T+ K<T n where n i s approximately 1/3, and the extrapolated change of length under z e r o load was c a l c u l a t e d to be 0. 3%. 3. 3. 2 " I s o t h e r m a l " D e f o r m a t i o n (Creep) A s p r e v i o u s l y d i s c u s s e d , the optimum r e l a t i v e density that could be e a s i l y a c hieved by col d p r e s s i n g was 0. 50 of the density of m a gnesium hydroxide. F o r this r e a s o n most of the experiments under i s o t h e r m a l conditions were c a r r i e d out using compacts of 0. 50 r e l a t i v e density. A l l creep curves p r e s e n t e d have been c o r r e c t e d f o r t h e r m a l expansion of the loading f r a m e as outlined in Section 2. 2. 4, (ii). The c o m p r e s s i v e load was applied to the cold specimen, and maintained throughout the test. A t y p i c a l time deformation curve is shown i n F i g u r e 19, along with the s p e c i m e n surface temperature and p r e s s u r e i n the vacuum chamber. The apparent r e l a t i o n s h i p between the p r e s s u r e of the water vapour produced by the decomposition (as noted f r o m the vacuum gauge on the system) and the deformation is notable; the peak of the p r e s s u r e curve coincides i n time with the r e g i o n of m a x i m u m slope (maximum creep rate) of the d e f o r m a t i o n curve. The s i g n i f i c a n c e of this r e s u l t w i l l be d i s c u s s e d i n more detail l a t e r . F I G U R E 17 T o t a l d e f o r m a t i o n as a f u n c t i o n of l o a d ( u n i f o r m h e a t i n g r a t e ) . F I G U R E 18 L o g - L o g plot of t o t a l d e f o r m a t i o n as a f u n c t i o n of l o a d ( u n i f o r m h e a t i n g r a t e ) .  -51- (a) E f f e c t s of T e m p e r a t u r e on D e f o r m a t i o n The f i r s t s e r i e s of runs were p e r f o r m e d using a load 2. 50 kg (13. 6 kg/cm 2) at different t e m p e r a t u r e s i n the range of 340° to 405° C. A t least two runs were made f o r a given set of e x p e r i m e n t a l conditions , to test r e p r o d u c i b i l i t y . F o u r p a i r s of r e p r e s e n t a t i v e t i m e - deformation curves are shown i n F i g u r e 20, and time-temperature de- f o r m a t i o n data are tabulated i n Appendix II (a). The second s e r i e s of runs were p e r f o r m e d with a load of 1. 1 kg, (6. 0 kg/cm^), and the same temperature was used in the previous s e r i e s . F o u r p a i r s of curves for this s e r i e s are shown i n F i g u r e 21, and data are p r e s e n t e d i n Appendix II (b). (b) E f f e c t of S t r e s s at Constant T e m p e r a t u r e F o l l o w i n g the same procedu r e outlined above, i s o t h e r m a l creep tests were p e r f o r m e d to determine the effect of load on deformation, using specimens of 0. 50 r e l a t i v e density. A temperature of 360°C was chosen f o r this study as it allowed a m a x i m u m range of loads to be used without f r a c t u r e of the compact. F i v e s t r e s s e s between 0. 55 and 13. 6 kg/cm^ were used f o r these experiments. The r e s u l t s are plotted i n F i g u r e 22 and r e c o r d e d i n tabular f o r m i n Appendix II (c). (c) E f f e c t of G r e e n Density P r e v i o u s creep studies of porous c e r a m i c bodies have shown that the creep rate v a r i e s with the r e l a t i v e density of the c o m p a c t ' ^ ). In o r d e r to determine the effect of the green density of CN h to CO 340 °C 4 0 5 ° C ^ 7 7 7 3 8 5 o c T 3 ^ ^ 360 °C 0 10 20 30 Time, min. 40 50 F I G U R E 20 Deformation v e r s u s time for specimens of 0. 50 r e l a t i v e density, at " i s o t h e r m a l " temp- eratures as shown. St r e s s 6. 0 kg/cm . Ul F I G U R E 21 Deformation v e r s u s time for specimens of 0. 50 r e l a t i v e density, at " i s o t h e r m a l " temp- erature s as shown. S t r e s s 6 . 0 kg/cm^.  - 55 - the compact on the deformation behaviour, a s e r i e s of experiments were c a r r i e d out under i s o t h e r m a l conditions. F o r this s e r i e s a tern 2 perature of 360°C and a load of 9. 25kg/cm was used. A s the specimens could be produced with r e l a t i v e densities i n the range 0. 4 to 0. 7, compacts having densities i n this range were used. A s expected, the v a r i a t i o n in green density s i g n i f i g a n t l y affected the creep behaviour as can be seen i n F i g u r e 23. The creep data are a l s o presented i n tabular f o r m in Appendix II (d).  -57- C H A P T E R IV 4 D i s c u s s i o n 4. 1 Shrinkage V e r s u s C r e e p The f i r s t c o n s i d e r a t i o n r e q u i r i n g c l a r i f i c a t i o n i s that of the nature of the d e f o r m a t i o n observed. It must f i r s t be e s t a b l i s h e d that the deformation produced during the decomposition of m a g n e s i u m hy- droxide compacts under load, either with a u n i f o r m heating rate or under i s o t h e r m a l conditions, is not due s i m p l y to mass l o s s a s s o c i a t e d with the decomposition. The r e a c t i o n i n v o l v e d i n decomposition i s - M g ( O H ) 2 - MgO + H 2 0 and this r e s u l t s i n a t h e o r e t i c a l weight l o s s of 30. 9% of the i n i t i a l specimen. It can e a s i l y be shown that a f u l l y dense specimen of b r u c i t e would if f u l l y t r a n s f o r m e d to p e r i c l a s e occupy only 4 7 % of its o r i g i n a l volume. Thus, there is a net volume reduction of 5 3 % a s s o c i a t e d with this decomposition. However, it i s w e l l e s t a b l i s h e d ( ̂  ) that the de- composition of b r u c i t e produces pseudomorphous r e l i c s with only slight d i m e n s i o n a l change. It was t h e r e f o r e n e c e s s a r y to e x p e r i m e n t a l l y determine the extent of shrinkage d i r e c t l y a s s o c i a t e d with mass l o s s so that this could be differentiated f r o m the creep deformation r e s u l t i n g f r o m the e x t e r - nally a pplied s t r e s s (during dehydroxylation). However, with the apparatus used, a finite load on the s p e c imen was r e q u i r e d to ensure -58- the function of the m e a s u r i n g system, so d i r e c t m easurement of s h r i n k - age without load i n the e x p e r i m e n t a l setup was not p o s s i b l e . T h e r e f o r e , s e v e r a l specimens were decomposed under the same conditions of temp- erature and vacuum i n the furnace of the creep apparatus. The c y l i n d r i c a l specimens were set v e r t i c a l l y on a f o i l pan to ensure that u n r e s t r i c t e d shrinkage could occur during decomposition. The d i m e n s i o n a l changes of the specimens, heated at t e m p e r a t u r e s i n the range of 300° to 500° C, were determined with a conventional m i c r o m e t e r ( s e n s i t i v i t y 0. 0001 in. ). A s the specimens were quite f r a g i l e after decomposition, p r e c i s e shrinkage measurement was d i f f i c u l t . However, the r e s u l t s indicated that the shrinkage was l e s s then 0. 4%. The r e s u l t s p resented in Section 3. 3. 1, f o r the deformation of m agnesium hydroxide compacts subjected to v a r y i n g loads and de- composed under a u n i f o r m heating rate a l s o support this estimate of the shrinkage. The extrapolated value of total s t r a i n at z e r o load was calculated to be 0. 3% on the b a s i s of the e x p e r i m e n t a l data. T h i s value compares f a v o u r a b l y with that obtained by d i r e c t shrinkage m e a s u r e - me nt s. Thus this shrinkage, due to the mass loss only, can be c o n s i d e r e d i n s i g n i f i c a n t i n c o m p a r i s o n with the 6 to 8% l i n e a r dimen- sional change obs e r v e d during the creep study. No attempt has been made to c o r r e c t the creep curves for the shrinkage, which is s m a l l e r than other potential e x p e r i m e n t a l s o u r c e s of e r r o r . T h i s o b s e r v a t i o n f i r m l y establishes f or the f i r s t time_that the m a t e r i a l can be deformed p l a s t i - c a l l y during a decomposition reaction. . -59- 4. 2 Weight L o s s V e r s u s C r e e p The shape of the creep curve (as opposed to the shrinkage curve) i s s i m i l a r to that of the weight l o s s curve determined thermo- grap h i c a l l y . T h i s i s shown c l e a r l y i n F i g u r e 24, where a creep curve and a weight l o s s curve p r e p a r e d under i d e n t i c a l heating conditions are compared. A load of 6. Qkg/cm^ and a l i n e a r heating rate of 2 5 ° C / m i n were used, on compacts having the same re l a t i v e density (0. 50). A shrinkage curve i s a l s o included for c o m p a r i s o n with the ob- s e r v e d deformation. The conditions of decomposition d i f f e r e d s l i g h t l y in that the t h e r m o g r a v i m e t r i c a n a l y s i s was c a r r i e d out i n a nitrogen atmosphere. T h i s may explain the non-coincidence of the creep and weight los s curves i n F i g u r e 24. 4. 3 Stages of C r e e p The creep curve is of s i g m o i d a l f o r m ( F i g u r e 25 and F i g u r e s 20 - 23), with three apparent stages. These can be termed: Stage I The i n i t i a t i o n p e riod, where a r a p i d i n c r e a s e of creep rate occurs. Stage II A p e r i o d of rapid, creep, which in s e v e r a l cases appears to approach l i n e a r i t y . Stage III A decay region, during which the rate d e c r e a s e s r a p i d l y and appears to approach z e r o asymptotically. F I G U R E 24 C r eep, weight l o s s and shrinkage v e r s u s time. - 6 1 - F I G U R E 25 Stages of Creep -62- The f i r s t stage appears to be i n i t i a t e d by the dehydroxylation reaction. T h i s i s shown i n F i g u r e 19, where the beginning of Stage I coincides with the r i s e of p r e s s u r e i n the vacuum system. T h i s stage appears to l a s t f o r the f i r s t 10 to 20% of the total creep. In the second stage, the creep rate is highest. D u r i n g this stage the temperature of the surface and the inside of the s p e cimen reached a steady state t h e r m a l condition, with a d i f f e r e n t i a l of 10° to 12°C throughout the decomposition, as d i s c u s s e d in Section 2. 2. 5, and shown i n F i g u r e 12. T h i s stage of the d e f o r m a t i o n coincides with the most r a p i d evolution of water vapour from, the specimen, and hence the highest s y s t e m p r e s s u r e s . The tendency of the s y s t e m p r e s s u r e to f o r m a sharp peak, as shown in F i g u r e 19, depends upon the temperature of the run, (specimen surface temperature). At 385° and 405°C the peak is quite pronounced; temp e r a t u r e s of 340° and 360° produced a b r o a d e r and fl a t t e r p r e s s u r e curve, as is expected, if the creep i s d i r e c t l y r e l a t e d to the decomposition. S e v e r a l more t i m e - d e f o r m a t i o n - p r e s s u r e r e - lationships are shown i n F i g u r e s 26 and 27 • These demonstrate c l e a r l y the r e l a t i o n s h i p between the s y s t e m p r e s s u r e and deformation. The r e l a t i o n s h i p between the s y s t e m p r e s s u r e and the rate of mass l o s s accompanying dehydroxylation is i n p r i n c i p l e a simple one. The pumping rate i s probably a function of the absolute s y s t e m p r e s s u r e , and if the exact pumping rate i s known it should be po s s i b l e to determine reasonably a c c u r a t e l y the rate of mass l o s s during F I G U R E 26 Deformation and s y s t e m p r e s s u r e v e r s u s time. F I G U R E 27 Def o r m a t i o n and s y s t e m p r e s s u r e v e r s u s time -65- the d e h y d r o x y l a t i o n . F r o m t h i s , the m a s s l o s s v e r s u s t i m e c u r v e c o u l d be obtained by i n t e g r a t i o n . T h i s a p p r o a c h i s c o m p l i c a t e d , u n f o r t u n a t e l y , by the v a r i a t i o n of su c h p a r a m e t e r s as the pumping r a t e , w h i c h depends to some extent on the m e c h a n i c a l c o n d i t i o n of the b a c k i n g pump » the type of gas p r e v i o u s l y pumped, the s y s t e m t e m p e r a t u r e , and other f a c t o r s . T h e s e f a c t o r s a r e p r o b a b l y c o n t r o l l a b l e , however, and the m e a s u r e m e n t of s y s t e m p r e s s u r e r e p r e s e n t s a p o t e n t i a l l y u s e f u l technique f o r c o r r e l a t i n g m a s s l o s s w i t h m e c h a n i c a l d e f o r m a t i o n d u r i n g d e h y d r o x y l a t i o n i n t h i s type of e x p e r i m e n t . In o r d e r to c h a r a c t e r i z e the o b s e r v e d c r e e p q u a n t i t a t i v e l y , d i f f e r e n t a s p e c t s of the t i m e - d e f o r m a t i o n c u r v e s h o u l d be c o n s i d e r e d . The b e g i n n i n g of Stage I seems to be r e l a t e d d i r e c t l y to the onset of d e h y d r o x y l a t i o n , and the extent of t h i s stage v a r i e s w i t h the t e m p e r a - t u r e , l o a d and d e n s i t y of the s p e c i m e n as can be seen i n F i g u r e s 20 - 23. L o w e r t e m p e r a t u r e s , and cons e q u e n t l y l o w e r r a t e s of d e h y d r o x y l a t i o n produce a m o r e p r o l o n g e d i n i t i a t i o n p e r i o d . The d u r a t i o n of Stage II v a r i e s w i t h the t e m p e r a t u r e and a p p l i e d load. A t h i g h e r t e m p e r a t u r e s and l o a d s , and l o w e r d e n s i t i e s , a l o n g e r and n e a r l y l i n e a r Stage II i s observed. A t l o w e r t e m p e r a t u r e s , h i g h e r d e n s i t i e s and l o w e r s t r e s s e s , the Stage III decay r e g i o n seems to f o r m a l a r g e r p o r t i o n of the curve. In a l l c a s e s , however, the slope of the c u r v e ( m a x i m u m c r e e p rate) i s s t r o n g l y i n f l u e n c e d by v a r i a t i o n s i -66- i n s t r e s s , density and temperature . The p a r a m e t e r s selected to c h a r a c t e r i z e the creep phenomenon are, t h e r e f o r e , the total creep s t r a i n developed under i s o t h e r m a l conditions and the m a x i m u m rate of creep. The total d eformation was m e a s u r e d following the p r o c e d u r e shown i n F i g u r e . 16, and the m a x i m u m creep rate was determined f r o m the slope of a line drawn tangent to the steepest part of the creep curve. The cr e e p rate is e x p r e s s e d as inches/inch/minute (or minute " •*•)• T h e s e two p a r a m e t e r s are somewhat a r b i t r a r i l y defined, but as i s shown i n the following sections, they provide a b a s i s f o r analyzing quantitatively the creep behaviour. In the following sections, the effects of temperature, s t r e s s and r e l a t i v e density on the m a x i m u m creep rate and the total o b s e r v e d s t r a i n are considered. 4. 4 C r e e p Rate 4. 4. 1 E f f e c t of T e m p e r a t u r e T o determine the act i v a t i o n energy f o r the creep p r o c e s s , the m a x i m u m creep rates have been plotted against r e c i p r o c a l absolute temperature i n F i g u r e 28. The A r r h e n i u s plot of both sets of creep rates, d e t e r m i n e d using specimens of r e l a t i v e bulk density 0. 50 and s t r e s s e s of 6. 0 and 13. 6 k g / c m 2 produced an ac t i v a t i o n energy of 17. 5 k c a l / m o l . The specimen p r o p e r t i e s , temperatures, s t r e s s e s and creep rate are s u m m a r i z e d in T a b l e IV. 2 - I 1™ _ L _ _ I 145 1-50 1-55 1-60 1-65 1000/T °K"' F I G U R E ZH A r r h e n i u s - type plot of c r e e p r a t e v e r s u t e m p e r a t u r e . - 68 - T A B L E IV T E M P E R A T U R E D E P E N D E N C E O F I S O T H E R M A L C R E E P N o m i n a l R e l a t i v e B u l k D e n s i t y = 0. 50 C- 13. 6 k g / c m 2 e e T S P E C I M E N T ° C m i n _ 1 X 1 0 4 % 81 340 24. 6 7. 55 1. 206 83 340 22. 9 7. 48 1. 206 76 360 43 4 7. 25 1. 208 75 360 42. 9 7. 25 1. 203 82 360 39. 0 6. 86 1. 196 79 385 66. 6 6. 95 1. 202 80 385 70. 6 6. 94 1. 206 77 405 90. 3 7. 26 1 204 78 405 100. 8 7. 52 1. 199 <T= 6. 0 kg/ cm^ 85 340 16 35 5. 97 1. 204 86 340 17. 9 5. 40 1. 203 96 340 20. 8 5. 43 1.217 97 340 20. 0 5. 08 1. 216 101 360 27. 6 5. 39 1. 208 102 360 30. 0 5. 38 1. 214 99 385 41. 3 5. 40 1. 217 100 385 40. 2 5. 36 1. 209 84 405 70. 0 5. 68 1. 210 98 405 60. 2 5. 42 1. 219 -69- 4. 4. 2 St r e s s Dependence The o b s e r v e d m a x i m u m creep rate i s plotted as a function of s t r e s s i n F i g u r e 29. The s t r e s s dependence i s e s s e n t i a l l y l i n e a r , showing pseudo-Newtonian behaviour, with an apparent inte r c e p t on the rate axis, i . e. finite rate at z e r o s t r e s s . A d i r e c t p r o p o r t i o n a l i t y between creep rate and s t r e s s i s g e n e r a l l y attributed to v i s c o u s flow, g r a i n boundary s l i d i n g or N a b a r r o - H e r r i n g creep. D e t a i l s of p o s s i b l e m e chanisms of cr e e p during dehydroxylation w i l l be d i s c u s s e d l a t e r . The data is s u m m a r i z e d i n T a b l e V. 4. 4. 3 Den s i t y Dependence The m a x i m u m creep rate v a r i e d strongly with the g r een density of the specimen. A s i m i l a r density dependence was al s o o b s e r v e d by (24 ) Coble f o r the creep of alumina at elevated temperatures. T o e x p l a i n the density dependence of creep rate, the effective s t r e s s acting within the s p e c i m e n must be considered. In a pa r t i c u l a t e compact, the effective s t r e s s acting on contact a r e a A, (on a c r o s s section of the compact), and the s t r e s s are r e l a t e d by - . CT eff = CTapplied A Any i n c r e a s e i n the r e l a t i v e density i n c r e a s e s the contact a r e a ( a s s u m i n g constant packing geometry) and thus reduces the effective s t r e s s , The contact a r e a i n a powder compact of spheres after ( 25 ) deformation and the r e l a t i v e density of the compact are r e l a t e d by v ' o LO F I G U R E 29 S t r e s s dependence of m a x i m u m creep rate - 71 - T A B L E V S T R E S S D E P E N D E N C E O F I S O T H E R M A L C R E E P Is o t h e r m a l C r e e p T = 360°C S t r e s s Dependence N o m i n a l r e l a t i v e bulk density = 0. S T R E S S S P E C I M E N k g / c m 2 m i n _ 1 X 1 0 4 % 103 104 105 0, 54 0. 54 0. 54 20. 9 19. 9 17. 7 3. 16 3. 48 2. 53 1. 214 1. 214 1. 212 101 102 6. 0 6. 0 27. 6 30. 0 39 38 1. 208 1. 214 108 109 9. 25 9. 25 30. 6 31.2 6. 58 6. 27 1. 212 1. 220 106 107 3. 53 3. 53 24. 9 24. 7 5. 02 4. 70 1. 205 1 212 75 76 82 13. 6 13. 6 13. 6 42. 9 43. 4 39. 0 7. 25 7. 25 6. 86 1. 203 1. 208 1 196 •72- 2 where >̂ and po are the r e l a t i v e densities at any face of radius a and a =0, r e s p e c t i v e l y , and R i s the radius of the d e f o r m e d sphere. T h i s means that <j> ct, a" or contact area, f o r a constant i n i t i a l packing density. Hence, T h i s r e l a t i o n may a l s o be obtained by c o n s i d e r i n g the s o l i d a r e a f r a c t i o n in a plane cut through the s p e c i m e n , the s t r e s s effective on this area, and the r e l a t i v e density of the specimen. A s i m i l a r c o n c l u s i o n was o-xov, m.«.w^ .̂y a. ,v.. .̂ F i n a l l y , since the s t r a i n rate is p r o p o r t i o n a l to the s t r e s s , The e x p e r i m e n t a l v a l i d i t y of the r e l a t i o n is shown i n F i g u r e 30, where the creep rate i s plotted as a function of 1/^ . The data of Coble and K i n g e r y ^ for the creep behaviour of A I 2 O 3 of v a r y i n g r e l a t i v e densities are a l s o plotted. It can be seen that this r e l a t i o n s a t i s f i e s both sets of data. T h i s r e s u l t i m p l i e s that the density dependence of the creep rate a r i s e s f r o m the s t r e s s concentration on the g r a i n bounda- r i e s or the contact a r e a between the p a r t i c l e s because of the p o r o s i t y i n the specimen. Up I G U R E 30 Density dependence of m a x i m u m creep rate. - 74 - T A B L E VI D E N S I T Y D E P E N D E N C E O F I S O T H E R M A L C R E E P S t r e s s 9. 25 k g / c m 2 T e m p e r a t u r e 360°C. N O M I N A L e e T R E L A T I V E S P E C I M E N Vo D E N S I T Y m i n ~ *X10' % ° _ 1 X 1 4 129 0. 963 0. 40 44. 9 c o l l a p s e d 130 0.972 0.40 51.3 c o l l a p s e d 124 1.072 0.45 41.2 7.62 125 1. 073 0. 45 40. 7 7. 05 108 1. 212 0. 50 30. 6 6. 58 109 1.220 0.50 31.2 6.27 120 121 1. 313 1. 317 0. 55 0. 55 31.4 29. 2 5. 96 6. 04 116 117 1. 425 1. 430 0. 60 0. 60 25. 5 24. 3 5. 42 5. 59 132 133 1. 537 1. 535 0. 65 0. 65 21.3 20. 2 5. 02 4. 87 136 137 1. 702 1. 700 0. 70 0. 70 19. 1 20. 1 4. 28 4. 21 -75- It s h o u l d be p o i n t e d out that the a c t u a l d e n s i t y of the compact at the i n s t a n t of m a x i m u m c r e e p r a t e i s not the same as the g r e e n d e n s i t y , s i n c e a c e r t a i n amount of d e c o m p o s i t i o n (and hence m a s s l o s s ) has t a k e n p l a c e at the t i m e the m a x i m u m c r e e p rate i s m e a s u r e d . The fact that the d e n s i t y dependence m a y be d e s c r i b e d by as s i m p l e a r e l a t i o n s h i p as e ^ _L_ shows that: 1) e i s independent of weight ?~ l o s s d u r i n g Stage I l ^ o r 2) the m a x i m u m rate o c c u r s at a c e r t a i n f r a c t i o n of the t o t a l weight l o s s i n a l l c a ses. The c r e e p r a t e d u r i n g Stage II a p p e a r s to be r e l a t i v e l y constant, e ven though the s y s t e m p r e s s u r e v a r i a t i o n shows that the r e a c t i o n r e a c h e s m a x i m u m r a t e and d i m i n i s h e s v e r y r a p i d l y , i n d i c a t i n g that the d e h y d r o x y l a t i o n rate has the same be h a v i o u r . T h i s suggests s t r o n g l y that the c r e e p r a t e m a y be independent of the extent of de- h y d r o x y l a t i o n as l o n g as the r e a c t i o n i s a c t u a l l y i n p r o g r e s s . 4. 5 T o t a l C r e e p S t r a i n The t o t a l p e r c e n t s t r a i n i s s u m m a r i z e d f o r a p a r t i c u l a r set of c o n d i t i o n s i n e a c h of the t a b l e s m e n t i o n e d i n the p r e c e d i n g s e c t i o n . ( T a b l e s I V - VI). The e f f e c t s of t e m p e r a t u r e , s t r e s s and g r e e n d e n s i t y upon the t o t a l s t r a i n w i l l now be c o n s i d e r e d . 4. 5. 1 E f f e c t of T e m p e r a t u r e The t o t a l s t r a i n i n p l o t t e d i n F i g u r e 31, f o r two d i f f e r e n t s t r e s s e s (6. 0 and 13. 6 k g / c m 2 ) and a range of t e m p e r a t u r e s . A l e a s t s q u a r e s f i t p e r f o r m e d on the data gave l i n e s t h r o u g h both sets of po i n t s having a z e r o slope. That i s , the t o t a l s t r a i n d e v e l o p e d i s independent -76- o 13.6 kg/cm 2 * 6.0 kg/cm2 340 360 380 400 T ,°C F I G U R E 31 T o t a l S t r a i n Ve r s u s T e m p e r a t u r e -77- of temperature. 4. 5. 2 E f f e c t of S t r e s s The total percentage s t r a i n under i s o t h e r m a l conditions is a l s o plotted as a function of s t r e s s i n F i g u r e 32. In o r d e r to f i n d the s t r e s s dependence of the total s t r a i n , a l o g - l o g plot of the data is made ( F i g u r e 33). The equation which adequately r e p r e s e n t s the data is found to be e T = e o T +k where the value of the power n i s a p p r o x i m a t e l y one t h i r d . e o T i s v e r y s m a l l , and so can not be d etermined f r o m this plot. T h i s behaviour is s t r i k i n g l y s i m i l a r to that o b s e r v e d e a r l i e r (Section 3. 3. 1) f o r total, s t r a i n at a u n i f o r m heating rate. 4. 5. 3 E f f e c t of D ensity The values of total s t r a i n o b s e r v e d following i s o t h e r m a l creep at 360°C, f o r a constant s t r e s s of 9. 2 kg/cm , are plotted against density in F i g u r e 34. The data have a l s o been tested on a l o g - l o g plot, on which a line drawn through the point gives a slope of a p p r o x i m a t e l y -1, suggesting a r e c i p r o c a l r e l a t i o n s h i p . The data are therefore plotted against ' a s shown i n F i g u r e 35. The e x p e r i m e n t a l scatter i n thesedata makes it i m p o s s i b l e to determine with ce r t a i n t y the f o r m of the r e l a t i o n s h i p . However, as the s t r a i n rate was shown to be i n v e r s e l y p r o p o r t i o n a l to the density, it i s l i k e l y that the density dependence of the total s t r a i n under i s o t h e r m a l conditions a l s o a r i s e s f r o m the effective s t r e s s acting on the compact, making the r e c i p r o c a l r e l a t i o n s h i p more probable. F I G U R E 32 T o t a l s t r a i n v e r s u s s t r e s s    -82- 4.5.4 P h e n o m e n o l o g i c a l Behaviour The r e l a t i o n s h i p o b s e r v e d between total s t r a i n and s t r e s s , i . e. e y (Tn ' w r i e r e n 1/3 is s i m i l a r to the dependence of the cold compacted density of the m a t e r i a l , which gave fo j ' = ^0 p - w i t h n a l s ° » i / 3 The s i m i l a r i t y of the s t r e s s dependence suggests some p o s s i b l e m e c h a n i s t i c r e l a t i o n s h i p , perhaps p a r t i c l e s l i d i n g , but no t h e o r e t i c a l argument can be advanced f o r this power law. A s i m i l a r power law dependence of density on s t r e s s has a l s o been r e p o r t e d by Smith a l s o on the basis of e x p e r i m e n t a l data. -83- 4. 6 P o s t u l a t e d M e c h a n i s m s of C r e e p 4. 6, 1 P h y s i c a l Changes Accompanying De h y d r o x y l a t i o n In o r d e r to postulate a m e c h a n i s m f o r the o b s e r v e d creep it i s n e c e s s a r y to c o n s i d e r the changes which accompany the de- composition. As d i s c u s s e d i n the Introduction, the dehydroxylation j of Mg(OH)2 f o r m s p a r t i c l e s of MgO, a p p r o x i m a t e l y 100 A diameter. C a l c i n a t i o n of the Mg(OH)2 used for this study ( s p e c i f i c surface a r e a I5m^/gm) i n the temperature range 3 50° to 400°C has produced surface areas of up to 250m /gm on the product MgO. T h i s c o r r e s p o n d s to f r e e cubes of average 66 A to a side. T h i s c a l c u l a t e d size i s i n good agreement with X - r a y line broadening experiments^ on the same m a t e r i a l , c a l c i n e d between 400° and 500°C, which produced a p a r t i c l e size range of 60 to 75 ?S 2 7 \ Samples of the Mg(OH)2 have been examined before and after dehydroxylation in the e l e c t r o n m i c r o s c o p e . The m a g n e s i u m hydroxide powder was p l a c e d on carbon support f i l m s on copper g r i d s , then c a l c i n e d i n a v a c u u m furnace (10~^ T o r r ) at temperatures f r o m 3 50° to 500°C. The samples were then examined to determine the extent of v i s i b l e change at v a r i o u s temperatures. At the t e m p e r a t u r e s used for this study (below 450°C) the hexagonal brucite platelets r e t a i n e d th e i r c h a r a c t e r i s t i c shape, although completely t r a n s f o r m e d to MgO. These experiments s e r v e d to c o n f i r m that the behaviour of this m a t e r i a l was qualitatively s i m i l a r to that o b s e r v e d by others (Section 1. 4) on m a t e r i a l s f r o m different sources. -84- 4. 6. Z A c t i v a t i o n E n e r g i e s of C o n c u r r e n t P r o c e s s e s It i s i n t e r e s t i n g to compare the a c t i v a t i o n energy obtained here for the creep p r o c e s s with the a c t i v a t i o n energies of other p r o c e s s e s which may occur c o n c u r r e n t l y during dehydroxylation. Although this approach may not r e v e a l the exact m e c h a n i s m s i n v o l v e d i n the de- f o r m a t i o n p r o c e s s , it is a b a s i s f o r comparing quite different pheno- mena. Such c o m p a r i s o n may lead to a hypothetical m e c h a n i s m for the deformation o b s e r v e d i n this investigation. The dehydroxylation i t s e l f i s the most important p r o c e s s a s s o c i a t e d with the creep, as the creep p r o c e s s o b s e r v e d is activated by the decomposition reaction. The most authoritative work on the de- {15} hydroxylation k i n e t i c s is that of Gordon and K i n g e r y v who have shown that the a c t i v a t i o n energy of the p r o c e s s v a r i e s with the s p e c i m e n geometry, p r i m a r i l y due to the back p r e s s u r e of the water vapor c r e a t e d by the dehydroxylation. The a c t i v a t i o n energy f o r the dehydroxylation, when c o r r e c t e d f o r the s p e c i m e n geometry appears to be i n the range of 38 to 40 k c a l / m o l . T h i s a c t i v a t i o n energy is more than double that determined for the creep p r o c e s s , which indicates that although the decomposition r e a c t i o n i n i t i a t e s the deformation, the rate c o n t r o l l i n g m e c h a n i s m f o r the creep is probably different f r o m that of the de- hydroxylation. The o b s e r v a t i o n that the creep rate during the second stage is independent of the rate of dehydroxylation lends support to this argument. (Section 4. 4. 3). - 85 - Studies of the r e h y d r a t i o n of MgO p r e p a r e d by the c a l c i n a t i o n of M g C 0 3 at 1000°C were c a r r i e d out by La y d e n and B r i n d l e y These studies i n d i c a t e d that the temperature dependence of the re a c t i o n rate constant may be d e s c r i b e d by an A r r h e n i u s - type re l a t i o n s h i p with an activ a t i o n energy of about 16 k c a l / m o l . The exact m e c h a n i s m was not determined, but it was f e l t most l i k e l y that the o v e r a l l rate was governed by the rate of an i n t e r f a c i a l reaction. T h i s could p r e s u m a b l y i t s e l f be dif f u s i o n controlled. A g r a i n growth study of MgO p r e p a r e d by the c a l c i n a t i o n of MgfOH)^ has been p e r f o r m e d by K o t e r a , Saito and Terada^ . Working i n a i r i n the temperature range 500° to 900° C they found an activa t i o n energy of 1 7 k c a l / m o l f o r the g r a i n growth, using m a t e r i a l p r e p a r e d f r o m p r e c i p i t a t e d Mg(OH)2- On the basis of the low ac t i v a t i o n energy of the p r o c e s s and the time exponent of g r a i n growth ( t n , n = 1/6), K o t e r a et a l suggested that the rate may be c o n t r o l l e d by surface d i f - fusion. The good agreement between the a c t i v a t i o n energy of the gr a i n growth p r o c e s s as determined by K o t e r a et a l , and that of the creep p r o c e s s investigated here suggests that the rate c o n t r o l l i n g m echanisms f o r these two p r o c e s s e s may be the same. 4. 6. 3 V i s c o u s F l o w and G r a i n Boundary S l i d i n g The s t r e s s dependence of the m a x i m u m creep rate i s l i n e a r , suggesting that the m e c h a n i s m of the deformation may be either v i s c o u s flow or g r a i n boundary s l i d i n g ( i n t e r p a r t i c l e sliding). - 86 - G r a i n b o u n d a r i e s i n the p r o p e r sense do not e x i s t i n a p a r t i c u l a t e c ompact of the type used, so p a r t i c l e ( e q u i valent to g r a i n s ) s l i d i n g i s c o n s i d e r e d to be synonymous here. G r a i n b o u n d a r y c r e e p i s g e n e r a l l y i m p o r t a n t only at t e m p e r a t u r e s above 0. 5 T m . T h i s suggests that some f o r m of i n c r e a s e d a t o m i c m o b i l i t y m u s t be p r e s e n t f o r t h i s m e c h a n i s m to be o p e r a b l e at the t e m p e r a t u r e s u s e d i n t h i s study. 4. 6. 4 P o s s i b l e M e c h a n i s m s of D e f o r m a t i o n F r o m the f o r e g o i n g i t a p p e a r s that the c r e e p d e f o r m a t i o n o b s e r v e d d u r i n g the d e c o m p o s i t i o n of M g ( O H ) 2 may be d i f f u s i o n con- t r o l l e d , as the a c t i v a t i o n e n e r g y of the c r e e p p r o c e s s i s s i m i l a r to those of g r a i n g r o w t h and r e h y d r a t i o n . On the other hand, i t i s p o s - s i b l e that the d e f o r m a t i o n o c c u r s by some other means. F o r e x a m p l e , (33) i t has been d e m o n s t r a t e d r e c e n t l y that a l o o s e p a r t i c u l a t e c ompact of a m i x t u r e of t u n g s t e n and o x a l i c a c i d can be d e n s i f i e d d u r i n g the d e c o m p o s i t i o n of the o x a l i c a c i d , a p p a r e n t l y without any c h e m i c a l r e a c t i o n between the two m a t e r i a l s . In t h i s case the enhanced d e n s i - f i c a t i o n of the t u n g s t e n powder was a t t r i b u t e d to the e f f e c t of gas phase l u b r i c a t i o n . A t p r e s e n t i t i s d i f f i c u l t to choose between these two m e c h a n i s m s : a) D e f o r m a t i o n c o n t r o l l e d by d i f f u s i o n , and b) D e f o r m a t i o n c o n t r o l l e d by gas phase l u b r i c a t i o n . T h i s s y s t e m i s f u r t h e r c o m p l i c a t e d by the f a c t that the M g ( O H ) 2 d i s i n t e g r a t e s into v e r y fine c r y s t a l l i t e s of MgO ( about 70 A ), thus cre a t i n g a l a r g e number of new i n t e r p a r t i c l e contact a r e a s f o r sliding. In addition, the p o s s i b l e contribution of s l i p to the o b s e r v e d d e f o r m a t i o n must be considered. 4. 6. 4. 1 S l i p M e c h a n i s m s A s near t h e o r e t i c a l l y dense bodies have been produced just above the decomposition temperature, the d e f o r m a t i o n of i n d i - v i d u a l c r y s t a l l i t e s must occur during the hot p r e s s i n g p r o c e s s at higher s t r e s s e s , indicating that the f r e s h l y f o r m e d MgO i s p l a s t i c . T h i s p l a s t i c i t y may be manifested even at low s t r e s s e s , giving r i s e to some or a l l of the c r e e p d e f o r m a t i o n o b s e r v e d i n this (31) study. Hulse, C o p l e y and P a s k showed that f u l l y dense p o l y c r y s - ta l l i n e MgO ( of a c e r t a i n and g r a i n size ) can y i e l d p l a s t i c a l l y at as low as 400°C. (at 35, 000 p s i ). T hey a l s o showed that the y i e l d s t r e s s on the J l O O j ^ l l O ^ s l i p s y s t e m of single c r y s t a l MgO is approx- i m a t e l y 10, 000 p s i at 400°C. In the present i n v e s t i g a t i o n the p a r t i c l e s are not c o n s t r a i n e d in the same manner as grai n s i n a s o l i d body, and the i n d i v i d u a l contact a r e a s may be v e r y s m a l l , giving r i s e to v e r y high s t r e s s concentrations. A l s o , the f r e s h l y f o r m e d MgO p a r t i c l e s may be highly defective as a r e s u l t of the type of s t r u c t u r a l r e a r r a n g e m e n t i n v o l v e d in the decomposition. A combination of a l l these effects may contribute to the c r e e p d e f o r m a t i o n observed. - 88 - 4, 6. 4. 2 Stacking R e a r r a n g e m e n t Another p o s s i b l e s t r e s s dependent m e c h a n i s m of de- f o r m a t i o n of the p a r t i c l e s may stem f r o m the effect of s t r e s s on the r e a r r a n g e m e n t of the stacking sequence n e c e s s a r y f o r the t r a n s f o r m a t i o n f r o m the hexagonal to the cubic lattice configuration. In c o n s i d e r i n g the t r a n s f o r m a t i o n of MgCOH)^ to MgO , none of the p r e v i o u s i n v e s t i g a t o r s have studied in d e t a i l the r e q u i r e d change of stacking sequence. Two b a s i c models have, however, been proposed f o r the r e m o v a l of water vapor f r o m the m a t e r i a l during the r e a c t i o n . The model suggested by Goodman^ ^ f o r the t r a n s f o r - mation, as shown in F i g u r e 3, n e c e s s i t a t e s a s t r u c t u r a l collapse n o r m a l to the b a s a l oxygen planes due to the r e m o v a l of whole l a y e r s of oxygen (hydroxyl) ions. Because of e x p e r i m e n t a l d i f - f i c u l t i e s none of the investigators, have been able to determine the extent of the d i m e n s i o n a l change n o r m a l to the b a s a l planes. How- ever, if such a collapse o c c u r s , it i s p o s s i b l e that the p r e s e n c e of an e x t e r n a l s t r e s s having a component p a r a l l e l to the oxygen planes can cause de f o r m a t i o n during the dehydroxylation. A l t e r n a t i v e l y , if the decomposition p r o c e e d s by the i n - homogeneous m e c h a n i s m of B a l l and T a y l o r t F i g u r e 4, a stackin - 8 9 - sequence r e a r r a n g e m e n t i s n e c e s s a r y at some time during the reaction. It can be shown that the n e c e s s a r y r e a r r a n g e m e n t can occur by the passage of a p a r t i a l d i s l o c a t i o n of the f o r m 1/6 |^21lJ between e v e r y second oxygen l a y e r . T o provi d e the n e c e s s a r y stacking r e a r r a n g e m e n t without gross shape change of the c r y s t a l l i t e the s u c c e s s i o n of shifts would be i n the sequence 1/6 ^ 2 1 1 ^ 1/6 <,12l) ("b") and 1/6 < 112) ("c") on s u c c e s s i v e planes. A n a r b i t r a r i l y chosen plane r e q u i r i n g shift f r o m A B A B to A B C A could make the r e q u i r e d change with a, b or c. In the presence of an applied s t r e s s the shift would be in the d i r e c t i o n of that s t r e s s . One p r o p e r t y of the defo r m a t i o n could be r e l a t e d to this rearrangement. The obs e r v e d dependence of s t r a i n rate on s t r e s s ; e = e 0 + AO" where e 0 is the inter c e p t with the rate axis, and A i s a constant, could r e s u l t f r o m the fact that a s m a l l external s t r e s s could cause the sequence of p a r t i a l d i s l o c a t i o n s to change f r o m abc etc. to another sequence causing gross s t r a i n . T h i s hypothesis has not been developed in detail, as there is no d i r e c t i n d i c a t i o n i n this study that deformation of the p a r t i c l e s themselves is ac t u a l l y o c c u r r i n g . - 90 - V. Summary and C o n c l u s i o n s 5. 1 Contact deformation and bond f o r m a t i o n have been de- monstrated i n experiments i n which tips of single c r y s t a l Ca(OH>2 and cold-compacted Mg(OH)2 powder were decomposed while loaded in contact. 5. 2 Compacts of Mg(OH)2, of 0. 50 r e l a t i v e density have sheen decomposed under v a r y i n g c o m p r e s s i v e loads. The shrinkage accompa- nying dehydroxylation i n the absence of load was l e s s than 0. 4%. A load-dependent deformation of up to 7% at 13. 6 k g / c m 2 (the m a x i m u m st r e s s used) has been observed. The dependence of total s t r a i n on s t r e s s , at u n i f o r m heating rate takes the f o r m : e T = e # T + k <T n where e O T . is l e s s than 0. 4% and n is a p p r o x i m a t e l y 1/3. These observations f i r m l y e s t a b l i s h f o r the f i r s t time that this m a t e r i a l can be deformed p l a s t i c a l l y during a decomposition reaction. 5. 3 The creep behaviour of the compacts was explored, f o r different i s o t h e r m a l temperatures, s t r e s s e s and r e l a t i v e densities. The c o m p r e s s i v e c r e e p curve i s of s i g m o i d a l f o r m , s i m i l a r to the t h e r m o g r a v i m e t r i c curve f o r the same m a t e r i a l . The creep curve has three stages; Stage I - an i n i t i a t i o n p e riod, with r a p i d i n c r e a s e of creep rate. - 91 - Stage II - a p e r i o d of n e a r l y l i n e a r r a p i d creep. Stage III - a decay region, with r a p i d l y d e c r e a s i n g rate, apparently approaching z e r o asymptotically. 5. 4 The m a x i m u m creep rate (slope of the creep curve) has been measured, and its dependence on temperature, s t r e s s and density determined. The c r e e p rate shows a temperature dependence of the A r r h e n i u s f o r m , with an a c t i v a t i o n energy of 17. 5kcal/mo.l. T h i s i s a p p r o x i m a t e l y one-half the beet published value for the a c t i v a t i o n energy of dehydroxylation, so the mechanisms of the two p r o c e s s e s are thought to be different. C o m p a r i s o n of the acti v a t i o n energy with those of g r a i n growth and r e h y d r a t i o n (17 and lb. 1 k c a l / m o l , re s p e c t i v e l y ) suggest that the creep p r o c e s s may be di f f u s i o n c o n t r o l l e d . The creep rate has a l i n e a r r e l a t i o n s h i p with applied s t r e s s , in the s t r e s s range examined ( . 54 to 13. 6 kg/cm ), and an apparent fini t e creep rate at z;ero s t r e s s : e = e 0 + ACT A f u l l explanation of this behaviour has -not been developed, but it may relate to stacking sequence r e a r r a n g e m e n t during de- hydroxylation. - 92 - The c r e e p rate has been shown to be of the f o r m e * 1 / j T h i s has been explained i n t e r m s of an effective s t r e s s acting on i n t e r p a r t i c l e contacts. The i n t e r p a r t i c l e contact a r e a i s p r o p o r t i o n a l to density, giving the above result. The f i n a l f o r m of the creep rate equation i s : e 0 + A f f exp j - ILi.00) t -1 R T 5. 5 The total creep s t r a i n developed under i s o t h e r m a l conditions has a l s o been determined. The total s t r a i n has been found to be independent of temperature. Its v a r i a t i o n v e r s u s s t r e s s is of the f o r m n e_ = e__ + e cr where n is again a p p r o x i m a t e l y 1/3 and e o T l e s s than 0. 5%. The density dependence appears to be of the f o r m e T * 1/<J 5. 6 The creep m e c h a n i s m i s postulated to be i n t e r p a r t i c l e s l i d i n g , p robably s i m i l a r to g r a i n boundary s l i d i n g i n s o l i d m a t e r i a l s . However, it i s p o s s i b l e that deformation of the p a r t i c l e s o c c urs, p r o - bably by a m e c h a n i s m a s s o c i a t e d with stacking sequence rearrangement, although this work does not p e r m i t the-formulation of a r i g o r o u s hypo- thesis. It has, however, shown that load -dependent deformation can occur during dehydroxylation of MgfOH)^. - 93 - V I S u g g e s t i o n s f o r F u t u r e W o r k 6. 1 In o r d e r to e s t a b l i s h m o r e d e f i n i t i v e l y the r e l a t i o n s h i p b e t w e e n w e i g h t l o s s and c r e e p , e x p e r i m e n t s s h o u l d be d e v i s e d to m e a s u r e s i m u l t a n e o u s l y , and a c c u r a t e l y , the w e i g h t l o s s and d i m e n - s i o n a l change . 6. 2 The effect of s p e c i m e n s i z e has not b e e n s t u d i e d , and e x p e r i m e n t s w i t h v a r y i n g d i a m e t e r s m i g h t p e r m i t e x t r a p o l a t i o n to i z e r o d i a m e t e r , and hence e l i m i n a t i o n of any b a c k w a t e r v a p o u r p r e s - s u r e effect due to the c o m p a c t s i z e . 6. 3 A s the M g ( O H ) 2 p a r t i c l e s i n the c o m p a c t s undoub ted ly show a s t r o n g t e x t u r e , due to t h e i r p l a t y shape and the u n i a x i a l p r e s - s i n g , i t w o u l d be i n t e r e s t i n g to e x p l o r e the effect of t e x t u r a l o r i e n - t a t i o n on the d e f o r m a t i o n . T h i s c o u l d be done b y u s i n g s p e c i m e n s p r e s s e d s i d e w a y s . 6. 4 T h e effect of w a t e r v a p o u r p r e s s u r e on the d e f o r m a t i o n c o u l d a l s o be s t u d i e d . T h i s m i g h t s e r v e to c l a r i f y the m e c h a n i s m . 6. 5 T h e r ange of s t r e s s e s u s e d c o u l d be e x p a n d e d , p a r t i c u - l a r l y to l o w e r s t r e s s e s , so that the t r u e f o r m of the s t r e s s dependence at v e r y s m a l l s t r e s s e s c o u l d be d e t e r m i n e d . T h i s w o u l d p r o b a b l y r e q u i r e o p t i c a l m e a s u r e m e n t of d i m e n s i o n a l changes . 6. 6 The a c t i v a t i o n e n e r g y f o r the c r e e p p r o c e s s s h o u l d be c o m p a r e d w i t h one a c c u r a t e l y d e t e r m i n e d f o r the d e h y d r o x y l a t i o n of the s a m e m a t e r i a l . A P P E N D I C E S r 94 - A P P E N D I X I i T E M P E R A T U R E D I S T R I B U T I O N WITHIN T H E C Y L I N D R I C A L S P E C I M E N In o r d e r to a s s e s s the p o s s i b l e time lag between the specimen's surface and its centre, an approximate c a l c u l a t i o n was p e r - f o r m e d using a method due to C a r s l a w and J a e g e r ( 23)_ Values for the t h e r m a l conductibity and s p e c i f i c heat were f i r s t estimated, as e x p e r i m e n t a l values f o r Mg(OH)2 were not available i n the l i t e r a t u r e . The s p e c i f i c heat may be obtained i n s e v e r a l ways. One estimate, based on c o m p a r i s o n with values ( 20) f o r CaO, Ca(OH)2, and MgO i s 0. 30 cal/gm°C. V a l u e s f o r the s p e c i f i c heat of MgO f r o m (32) Wicks indicate a value between 0. 30 to 0. 40 for Mg(OH)2> based on 0. 265 c a l / g m ° C f o r MgO. A value of 0. 35 c a l / g m ° C was s e l e c t e d f o r the calculations. The t h e r m a l conductivity was e s t i m a t e d on the basis of the published values for MgO, which range f r o m about 0. 08 ( c a l / s e c / c m / C / c m ) f or pure, dense MgO, to 1 0 f o r powdered MgO. The r e l a t i v e bulk densities used i n the experiments were somewhat greater than expected f o r loose powders, but it was felt that the reduced p r e s s u r e ( 1 0 ~ 2 T o r r ) would compensate, and a value of K=10"^ was selected. The method used p e r m i t s the c a l c u l a t i o n of temperature as a function of time, the t h e r m a l d i f f u s i v i t y (K/^>) and a reduced radius for an infinite c y l i n d e r subjected to a step i n c r e a s e i n its surface temperature. The step i n c r e a s e is ind i c a t e d by V on F i g u r e 36 • - 95 - and the l o c a l temperature at any time t by v. A t y p i c a l steady state temperature of 400° is plotted on the left hand margin. It can be seen that a temperature i n excess of 390°F is reached at the s p e c i m e n centre (v/R=0) i n 8 to 10 minutes. T h i s was felt to j u s t i f y conducting the experiment and obtaining e x p e r i m e n t a l v e r i - f i c a t i o n of the s p e c i m e n temperature during the tests. It should be noted that the heat of r e a c t i o n (endothermic) has not been taken into account i n this calculation. Since it was found i n the e a r l y tests that the m a x i m u m r e a c t i o n rate did not develop un t i l a p p r o x i m a t e l y 5 minutes after test t emperature (405°C) had been reached (about 12 minutes f r o m the start of the run), it was fe l t that the m a j o r endothermic r e a c t i o n took place after the q u a s i - u n i f o r m temperature d i s t r i b u t i o n has been achieved. T e m p e r a t u r e measurements i n the centre of the s p e c i m e n during the test eventually c o n f i r m e d the p r e - dicted temperature d i s t r i b u t i o n . TIME, Minutes FIGURE 36 Theoretical temperature distribution in the specimens for the isothermal creep tests. »• 97 - A P P E N D I X II C R E E P D A T A - " I S O T H E R M A L " CONDITIONS The data i s p r e s e n t e d i n tabular (columnar) f o r m as time f r o m the star t of the run (minutes), s p e c i m e n surface temperature ( T ° C ) , and shrinkage f r o m the i n i t i a l length i n inches X10~5 (hundred thousandths). Duplicate runs a r e p r e s e n t e d i n the same table f o r comparison. The s p e c i m e n p a r t i c u l a r s and r u n load a r e a l s o presented. I n i t i a l length is given i n inches and s p e c i m e n density i n gm/cm . The s p e c i m e n numbers are in c l u d e d on the F i g u r e s i n Section 3, so that d i r e c t c o m p a r i s o n s may be made. A l l the data pr e s e n t e d have been c o r r e c t e d f o r t h e r m a l expansion by the method shown in Appendix III. The runs are grouped i n the manner i n which they were p r e s e n t e d i n Section 3. One set of four duplicate runs has been included (Nos. 8 5 , 8 6 , 9 6 , 97). A l l runs were st a r t e d with a s y s t e m p r e s s u r e of f r o m 10 to 50yn Hg, depending on the rate of r e a c t i o n (temperature). - 98 - A P P E N D I X II (a) Specimen 81 83 0. 3174 1. 206 0. 321 1. 206 T e m p e r a t u r e 340°C S t r e s s 13.6 k g / c m 2 N o m i n a l r e l a t i v e density 0. 50 11 me Min. T ° C Specimen No. T i m e Min. T ° C Specimen No. 81 83 81 83 0 40 0 0 31 340 1504 1 . 4 0 L 0 32 1564 1438 :': 5 5 0 -2 33 1620 1506 3 125 29 -74 34 1674 1565 4 194 44 -1 35 340 1727 1626 5 240 64 18 36 1783 1691 6 280 70 32 37 1835 1749 7 308 85 44 38 1884 1809 8 336 106 70 39 1932 1860 9 340 125 98 40 340 1976 1909 10 340 152 127 41 2017 1951 11 179 155 42 2058 1996 12 207 174 43 2092 2036 13 242 199 44 2125 2072 14 282 224 45 340 2160 2105 15 340 334 265 46 2189 2136 16 385 312 47 2216 2165 17 458 376 48 2239 2188 18 526 433 49 2264 2211 19 608 497 50 340 2296 2243 20 340 686 558 51 2315 2248 21 763 629 52 2259 22 840 703 53 2348 2279 23 918 785 54 2364 2283 24 999 863 55 340 2386 2294 25 340 1070 934 56 2393 26 1148 1003 27 1220 1069 28 1297 1144 29 1371 1211 30 340 1438 1292 < - 99 - A P P E N D I X II (a) Specimen 75 76 1 o 0. 318 1. 208 0. 3178 1. 203 Tempera tu re 360°C S t ress 13.6 k g / c m 2 N o m i n a l re la t ive density 0. 50 T i m e T ° C Specimen No. T i m e T ° C Specimen No. M i n . M i n . 75 76 75 76 0 40 0 0 31 360 2164 2095 1 4P 0 0 32 2204 2152 2 75 -7 7 33 2243 2210 3 145 13 0 34 2264 4 200 28 -12 35 360 2284 2278 5 244 31 -13 36 2296 2291 6 283 27 -12 37 2310 2305 7 312 14 -2 38 2316 2321 8 344 16 -2 39 2346 2339 9 362 70 40 360 2364 2355 10 360 113 41 2378 2369 11 360 190 -130 42 2385 2376 12 360 302 192 43 2392 13 360 416 275 44 2399 2386 14 360 539 361 45 360 2397 15 360 459 46 2423 2410 16 816 580 47 2435 2419 17 708 48 2439 2423 18 1050 850 49 2426 19 1163 998 50 360 20 360 1270 1099 21 1374 1246 22 1493 1459 23 1590 24 1669 1546 25 360 1755 1631 26 1845 1726 27 1913 1793 28 1986 1880 29 2067 1968 30 360 2116 2032 -100 - A P P E N D I X I I ( a ) S p e c i m e n 79 80 77 78 l 0 0. 3165 0. 317 0. 3166 0. 3195 1.202 1.206 1.204 1.199 AneOr* < ^ i o L !__./ 2 T e m p e r a t u r e 385 C, 405°C S t r e s s 13. 6 k g / c m N o m i n a l r e l a t i v e d e n s i t y 0. 50 o o T i m e T C S p e c i m e n N o . T i m e T C S p e c i m e n N o . M i n . M i n . 79 80 77 78 0 40 0 0 1 -40 4 0 2 60 3 - 1 3 125 7 -3 4 205 5 20 5 . 255 2 32 6 292 -3 25 7 320 -16 33 8 350 -21 39 9 369 0 58 10 382 50 118 11 386 155 229 12 385 299 390 13 385 460 566 14 385 640 758 15 385 831 956 16 1011 1120 17 1199 1296 18 1265 1448 19 1517 1588 20 385 1643 1717 21 1767 1845 22 1858 1946 23 19 50 203 6 24 2073 2100 25 385 2104 2152 26 2156 2181 2 7 2187 2200 28 2214 2224 29 2234 2244 30 385 2262 2272 0 40 0 0 1 45 0 0 2 102 0 0 3 191 23 -5 4 255 45 17 5 300 58 22 6 334 60 32 7 360 37 8 3 84 74 47 9 400 117 62 10 407 187 94 11 405 301 174 12 405 404 347 13 405 770 620 14 405 1045 928 15 405 1310 1223 16 1573 17 1798 1723 18 1991 1911 19 2128 2077 20 405 2202 2204 21 2258 2277 22 2282 2306 23 2400 2333 24 2360 - 101 * A P P E N D I X II (b) Specimen 85 86 96 97 1 Q 0.3182 0.3150 0.3135 0.3148 1.204 1.211 1.217 1.216 T e m p e r a t u r e 340°C S t r e s s 6. 0 k g / c m 2 N o m i n a l r e l a t i v e density 0. 50 T i m e T ° C Specimen No. T i m e T C Specimen No. Min. Min. 85 86 96 97 o 0 40 0 0 0 40 0 0 1 40 3 0 1 40 -2 1 2 . 84 -3 -2 2 84 1 -2 3 165 -3 -16 3 165 - 1 -19 4 228 -5 -14 4 228 -11 -42 5 285 -4 -17 5 285 - 18 -52 6 320 -4 -32 6 320 -15 -62 7 340 -1 -42 7 340 -4 -68 8 340 18 -41 8 340 31 -61 9 340 32 -25 9 340 58 -35 10 340 61 -7 10 340 78 -14 11 88 2 5 11 96 11 12 114 32 12 111 29 13 155 45 13 120 66 14 200 55 14 132 78 15 340 149 81 15 340 157 104 1 6 292 1 1 6 16 179 136 17 342 152 17 2 1 6 1 9 6 18 402 191 18 256 237 19 452 234 19 300 296 20 340 509 283 20 340 349 352 2 1 556 333 21 387 413 22 605 384 22 437 483 23 654 441 23 494 547 24 704 499 24 550 611 25 340 756 549 25 340 608 678 26 819 605 26 659 . 741 27 858 659 27 715 799 28 921 720 28 774 857 29 974 773 29 840 907 30 340 1030 829 30 340 904 976 - 102 - A P P E N D I X II (b) cont. Specimen 85 86 96 97 T i m e T ° C Specimen No. T i m e T ° C Specimen No. Min. Min. 85 86 96 97 31 340 1080 883 31 340 970 1040 32 1119 929 32 1030 1091 33 1168 974 33 1087 1140 34 1216 1024 34 1 144 1182 35 340 1266 1073 35 340 1192 1220 36 1317 1117 36 1243 1257 37 1360 1160 37 1304 1295 38 1415 1200 38 1334 1328 39 1459 1235 39 1379 1363 40 340 1497 1277 40 340 1422 1398 41 1531 1317 41 1456 1423 42 1564 1361 42 1493 1453 43 1594 1395 43 1528 1474 44 1636 1431 44 1558 1494 45 340 1680 1461 45 340 1589 1507 46 1699 1492 46 1610 1518 47 1728 1525 47 1636 48 17 53 1542 48 1659 1537 49 1776 1565 49 1680 1545 50 340 1821 1592 50 340 1703 1560 - 103 - A P P E N D I X II (b) Specimen 84 98 99 100 I 0.3169 0.3140 0.3145 0.316 o ° I. 210 I. 219 I. 217 I. 209 T e m p e r a t u r e 385°C S t r e s s 6. 0 kg/cm N o m i n a l r e l a t i v e density 0. 50 ° n T i m e T C Specimen No. T i m e T C Specimen No. Min. Min. 84 98 99 100 0 40; 0 0 1 40 1 0 2 (5 1 0 3 153 10 -11 4 217 28 -12 5 270 44 -12 6 300 55 -14 7 3 31 59 -27 8 355 64 -19 9 375 80 -9 10 390 105 23 11 405 164 86 12 405 291 197 13 405 462 348 14 405 667 543 15 405 877 733 16 1087 921 17 1305 1091 18 1430 1250 19 1553 1389 20 40 5 1653 1499 21 1717 1545 22 1747 1599 23 1773 1625 24 1803 1655 25 405 1821 1675 26 1825 1697 27 1837 1708 28 1852 1729 29 1867 1741 30 40 5 1877 1747 0 40 0 0 1 40 0 1 2 62 -5 0 3 144 -24 -9 4 714 -29 -3 5 263 -31 -3 6 297 -40 -6 7 329 -48 -4 8 354 -49 11 9 371 -39 37 10 388 - 11 82 11 385 30 142 12 385 85 225 13 385 169 321 14 385 283 43 7 15 385 411 563 16 521 687 17 664 814 18 931 19 895 1045 20 385 1011 1152 21 1115 1259 22 1206 1348 23 1304 1423 24 1380 1490 25 385 1441 1546 26 . 1490 1599 27 1531 1624 28 1573 1651 29 1592 1671 30 385 1617 1702 - 104 - A P P E N D I X II (c) Specimen 103 104 105 I 0.316 0.316 0.3167 p 1.214 1.214 1.212 T e m p e r a t u r e 360°C S t r e s s 0. 54 k g / c m 2 N o m i n a l r e l a t i v e density 0. 50 o o T i m e T C Specimen No. T i m e T C Specimen No. Min. Min. 103 104 105 0 40 0 0 0 40 0 1 40 0 0 1 40 0 2 78 -5 -5 2 78 -5 3 148 -9 -11 3 148 -17 4 214 -5 -18 4 214 -14 5 267 -23 -19" 5 267 -30 6 302 -37 -43 6 302 -48 7 322 -52 -63 7 322 -65 8 354 -57 -63 8 354 -65 9 360 -50 -58 9 360 -61 10 360 -47 -50 10 360 -60 11 -40 -43 11 -60 12 -25 -25 12 -59 13 -9 12 13 -47 14 4 47 14 -34 15 360 26 96 15 360 -17 16 44 143 16 -4 17 91 196 17 32 18 135 256 18 74 19 191 305 19 119 20 360 245 365 20 360 164 21 306 428 21 211 22 3 74 493 22 272 23 440 558 23 341 24 502 617 24 384 25 360 570 676 25 360 443 26 636 740 26 500 27 705 800 27 562 28 768 856 28 608 29 818 918 29 659 30 360 862 964 30 360 698 - 105 - A P P E N D I X II (c) cont. Specimen 103 1 0 4 105 T i m e T U C Min. Specimen No. T i m e T C Min. Specimen No. 103 104 105 31 360 407 1006 31 360 732 32 940 1042 32 759 33 966 1076 33 786 34 984 1099 34 804 35 360 1004 1119 35 360 824 - 106 - A P P E N D I X II (c) Specimen 101 102 106 107. l Q 0.3176 0.316 0.3194 0.3165 1.208 1.214 1.205 1.212 T e m p e r a t u r e 360°C S t r e s s 6.0, 3. 5 k g / c m 2 N o m i n a l r e l a t i v e density 0. 50 T i m e T ° C Specimen No. T i m e T ° C Specimen No. Min. Min. 101 102 106 107 0 40 0 0 1 40 0 7 2 95 -3 1 3 172 -28 -20 4 218 -24 -33 5 267 -41 -46 • 6 ' 307 ' -57 -79 7 335 -84 -110 8 360 -99 -129 9 360 -91 -138 10 360 -86 -134 11 -70 -129 12 -43 -105 13 -4 -74 14 50 -33 15 360 107 16 16 195 94 17 263 152 18 345 231 19 33 316 20 360 525 414 21 617 508 22 703 602 23 783 696 24 869 795 25 360 953 884 26 1028 975 27 1098 1055 28 1176 1145 29 1247 1224 30 360 1308 1294 0 40 0 0 1 40 0 0 2 75 -4 -4 3 145 -29 -29 4 200 -51 -49 5 244 -70 -72 6 283 -88 -87 7 312 -102 -94 8 344 -80 -100 9 362 -75 -88 10 360 -67 -85 11 360 -50 -66 12 360 -24 -39 13 360 6 -5 14 360 49 46 15 360 98 102 16 159 168 17 220 242 18 294 319 19 371 397 20 360 460 479 21 543 553 22 614 627 23 686 699 24 • 766 782 25 360 835 853 26 898' 916 27 954 978 28 1036 1047 29 1096 1104 30 360 1143 1152 - 1 0 7 - A P P E N D I X II (c) cont. S pecimen 101 102 106 107 T i m e T ° C Min. Specimen No. T i m e Min. T ° C Specimen No. 101 102 106 107 31 360 1359 1359 31 360 1194 1199 32 1410 1419 32 1248 1248 33 1458 1473 33 1290 1283 34 1500 1523 34 1327 1329 35 360 1538 1564 35 360 1359 1349 36 1568 1592 36 1405 1391 37 1598 1616 37 1434 1411 38 1644 1636 38 1463 1430 39 1771 39 1481 1447 40 360 1793 40 360 1498 1464 - 108 - A P P E N D I X II (d) Specimen 136 137 lo So 0. 3045 1. 702 0. 3035 1. 700 T e m p e r a t u r e 360°C S t r e s s 9. 2 kg/cm/ N o m i n a l r e l a t i v e density 0. 70 T i m e M i n . T ° C Specimen No. T i m e T ° C Specimen No. Min. 136 137 136 137 0 40 0 0 31 360 417 523 1 40 2 1 32 477 582 2 62 -6 -7 33 533 638 3 132 -22 -29 34 590 698 4 192 -33 -51 35 360 643 755 5 240 -43 -71 36 717 820 6 277 -56 -94 37 765 873 7 307 -82 -129 38 821 928 8 336 -111 -162 39 871 966 9 360 -134 -194 40 360 924 1014 10 360 -152 -122 41 • 976 1055 11 -163 -232 42 1020 1090 12 -164 -235 43 1061 1124 13 -165 -232 44 1097 1157 14 -159 -226 45 360 1133 1185 15 360 -148 -213 46 1166 1211 16 -135 -197 4 7 1198 123 7 17 -122 -176 48 1223 1256 18 -107 -152 49 1244 1274 19 -84 -119 50 360 1263 1287 20 360 -64 -87 21 -39 -50 22 -13 .-7 23 19 45 24 56 98 25 360 93 146 26 139 207 27 : 194 271 28 248 331 29 303 392 30 360 361 458 - 109 - A P P E N D I X II (d) Specimen 132 133 1 o 0. 309 1. 537 0. 3108 1. 535 T e m p e r a t u r e 360°C S t r e s s 9- 2 kg/cm^ N o m i n a l r e l a t i v e density 0. 65 T i m e T ° C Min. S p e c i m e n No. T i m e T C Spe c i m e n No. Min. 132 133 132 133 0 40 0 0 31 360 736 727 1 42 0 3 32 797 791 2 . '86 -7 -5 33 854 850 3 156 -25 -17 34 920 908 4 218 -39 -24 35 360 978 964 5 262 -54 -31 36 1048 1031 6 298 -74 -57 37 1103 1080 7 335 -97 -87 38 1150 1127 8 360 -120 -110 39 1200 1177 9 360 -135 -132 40 360 1248 1221 10 360 -150 -144 41 . 1291 1264 11 -154 -155 42 1326 1301 12 -152 -155 43 1364 1336 13 -146 -153 44 1391 1363 14 -138 -145 45 360 1418 1389 15 360 -122 -132 46 1442 1418 16 -105 -107 47 1467 1446 17 -80 -75 48 1481 1475 18 -65 . -34 49 1495 1484 19 0 15 50 360 1506 1501 20 360 42 63 21 93 117 22 145 175 23 209 235 24 270 294 25 360 331 351 26 398 411 27 468 477 28 536 539 29 601 596 30 360 670 662 - 1 1 0 - A P P E N D I X II (d) Specimen 120 121 1 Q 0. 3189 0. 3148 $o 1. 313 I. 317 T e m p e r a t u r e 360°C S t r e s s 9. 2 k g / c m 2 N o m i n a l r e l a t i v e density 0. 55 T i m e T ° C Specimen No. T i m e T ° C Spe c i m e n No. Min. Min. 120 121 120 121 0 40 0 0 31 360 1536 1329 1 40 0 0 32 1589 1390 2 80 -8 -6 33 1632 1445 3 155 -26 -10 34 1676 1499 4 210 -37 -17 35 360 1712 1550 5 • 246 -59 -26 36 1758 1608 6 276 -76 -46 37 1784 1648 7 300 -95 -72 38 1802 1691 8 326 -177 -98 39 1824 1713 9 3 54 -125 -109 40 360 1843 1740 10 ;363 -114 -114 11 360 -99 -108 12 360 -67 -91 13 360 -22 -63 14 360 40 -19 15 360 111 36 16 200 97 17 290 166 18 391 258 19 495 336 20 360 597 434 21 692 518 22 793 618 23 890 712 24 995 801 25 360 1068 883 26 1161 964 27 1252 1047 28 1322 1121 29 1404 1191 30 360 1472 .1258 - I l l - A P P E N D I X I I (d) S p e c i m e n 129 130 108 109 1 o 0.3142 0. 963 0. 3104 0. 972 0. 3165 1. 212 0. 3132 1. 220 T e m p e r a t u r e 360°C S t r e s s 9. 2 k g / c m 2 N o m i n a l r e l a t i v e d e n s i t y 0. 40, 0. 51 T i m e M i n . T ° C S p e c i m e n N o . T i m e T C M i n . S p e c i m e n N o . 129 130 108 109 0 40 0 0 0 40 0 0 1 40 0 0 1 40 0 0 2 , 86 -8 -8 2 80 -11 -10 3 160 6 -7 3 157 -13 -11 4 215 14 -3 4 219 -7 -13 5 254 6 -1 5 262 3 -18 6 292 -2 -8 6 300 -17 -24 7 320 -12 -13 7 334 -25 -36 8 :348 5 10 8 360 -33 -39 9 ' 360 45 38 9 360 -15 -36 10 360 101 79 10 ; 360 -1 -21 11 360 185 171 11 33 4 12 360 290 246 12 87 47 13 360 414 394 13 160 102 14 360 545 541 14 237 171 15 360 682 697 15' 360 315 262 16 822 865 16 443 350 17 967 1019 17 498 451 18 1110 1174 18 603 555 19 • 1251 1325 19 704 659 20 360 1381 1464 20 360 802 751 21 1510 1594 21 908 848 22 1639 1718 22 1008 945 23 1763 1832 23 1110 1039 24 . 1872 1967 24 1199 1122 2 5 . 360 1976 2120 25 360 1280 1200 26 ' 2067 26 1362 1275 27 1445 1352 28 1524 1419 29 1593 1479 30 360 1660 1535 - 1 1 2 - A P P E N D I X II (d) cont. S p e c i m e n 108 109 T i m e Min. 31 32 33 34 35 36 37 38 39 40 T ° C 360 360 Spec i m e n No. 108 109 360 1725 1783 1833 1881 1915 1948 1980 2005 2030 2050 1590 1643 1688 1732 1766 1798 1826 1852 1874 1889 - 113 - A P P E N D I X II (d) Specimen 124 125 1 0 0. 3275 0.3120 o0 1.072 .073 T e m p e r a t u r e 360°C S t r e s s 9.2 k g / c m 2 N o m i n a l r e l a t i v e density 0. 45 T i m e T ° C Specimen No. T i m e T ° C Specimen No. Min. Min. 124 125 124 125 0 40 0 0 1 40 0 1 2 86 -8 -6 3 160 0 -1 4 214 4 5 5 254 -2 7 6 293 -9 -2 7 320 -19 -8 8 347 -8 -7 9 360 10 8 10 360 52 20 11 117 52 12 216 111 13 320 180 14 446 271 15 360 587 369 16 718 600 17 854 601 18 986 728 19 1103 861 20 360 1213 985 21 1325 1105 22 1439 1218 23 1548 1332 24 1642 1438 25 360 1734 1532 26 1810 1631 27 1892 1725 28 1950 1799 29 2021 1858 30 360 2088 1924 31 360 2137 1989 32 2186 2031 33 2223 2068 34 2260 2099 35 360 2292 2120 36 2334 37 2357 38 2374 39 2395 - 114 - A P P E N D I X II (d) Specimen 116 117 1 o 0. 3142 1. 425 0. 3130 1. 430 T e m p e r a t u r e 360 PC S t r e s s 9-2 kg/cm^ N o m i n a l r e l a t i v e density 0. 60 T i m e T ° C Specimen No. T i m e T ° C S p e c i m e n No. Min. Min. 116 117 116 117 0 40 0 0 31 360 1074 1002 1 40 0 0 32 1136 1062 2 78 -8 -8 33 1195 1119 3 150 -19 -15 34 1249 1178 4 208 -33 -14 35 360 1302 1235 5 256 -32 -16 36 1380 1304 6 294 -42 -29 37 1413 1360 7 326 -75 -51 38 1456 1410 8 350 -98 -67 39 1501 1464 9 362 -69 40 360 1540 1512 10 360 121 -73 41 1579 1557 11 360 122 -66 42 1600 1590 12 360 114 -53 43 1725 1623 13 360 101 -40 44 1641 1647 14 360 -77 -24 45 360 1657 1674 15 360 -46 -3 16 -2 28 17 65 65 18 106 111 19 173 164 20 360 241 216 21 313 279 22 389 346 23 472 416 24 552 491 25 360 624 558 26 . 705 637 27 787 713 28 863 786 29 935 853 30 360 1005 926 - 115 - A P P E N D I X III A c c u r a c y of the T h e r m a l E x p a n s i o n C o r r e c t i o n The data f r o m the e x p e r i m e n t a l runs were c o r r e c t e d f o r the t h e r m a l expansion of the loading f r a m e by the subtraction of a c o r r e c t i o n obtained f r o m runs made using a dummy quartz s p e c i m e n to obtain the expansion curve f o r the f r a m e alone. The c o r r e c t i o n s were averaged and subtracted f r o m the i n d i c a t e d c r e e p d e f o r m a t i o n values, i . e . : L (t) = L' (t) - c (t) where L (t) = the ac t u a l length at time t, L ' (t) = the indicated length and c (t) = the average change i n length developed during the t h e r m a l expansion runs. The c o r r e c t i o n has been v e r i f i e d by two methods: 1) C o m p a r i s o n of the tota l s t r a i n , (with a M i c r o m e t e r ) as d e t e r m i n e d by d i r e c t m e asurements of the specimens before and after dehydroxylation. 2) D i r e c t measurement i n the furnace using a t r a v e l l i n g m i c r o s c o p e . (Cathetometer). The f i r s t method gave an apparent a c c u r a c y of about 0. 001 inches f o r deformations of f r o m 0. 010 to 0. 020 inches, i n d i c - ating that the measurements are c o r r e c t to one part i n ten or twenty. - 116 - F i g u r e 3 7 compares the def o r m a t i o n curve, as c o r r e c t e d by the n o r m a l p r o c e d u r e with lengths m e a s u r e d with the t r a v e l l i n g m i c r o - scope. The two are i n agreement to within 10%, which i s felt to be sa t i s f a c t o r y .  - 118 - B I B L I O G R A P H Y A. C. D. Chaklader, Nature, 206, 392 (1965) P. E . D. M o r g a n and E . Scala, " H i g h Density- Oxides by D e c o m p o s i t i o n P r e s s u r e S i n t e r i n g of Hydr o x i d e s " , presented at the Sixty-Seventh Annual Meeting, The A m e r i c a n C e r a m i c Society, P h i l a d e l p h i a , Pa. , May 3rd, 1965. T. G. C a r r u t h e r s and T. A. Wheat, P r o c . B r i t i s h C e r a m i c Society, 3_, 259 (1965). a) A. C. D. Chaklader and L. G. M c K e n z i e , J. Am. Ceram. S o c , 49,47(1966). b) A. C. D. Chaklader and L. G. M c K e n z i e , Am. Ceram. Soc. B u l l . , 43, 892 (1964). A. C. D. Chaklader and V. T. Baker, B u l l . Am. C e r a m . Soc. , 44, 258 (1965). A. C. D. Chaklader and M. N. Shetty, T r a n s . Met. Soc. A. I. M. E . , 233, 1441 (1965). P. E. D. Morgan and N. C. Schaeffer, T e c h . Rep. A F M L - T R - 6 6 - 3 5 6 , Nov. 1966. A. ' C. D. Ch a k l a d e r and R. C. Cook, J. Am. Ceram. Soc. 47, 712 (1968). J. A. H e d v a l l i n Reaktionsfaehigheit f e s t e r Stoffe . , V . J . A. Barth, ( L e i p z i g ) , 1938. R e p r i n t e d by E d w a r d s B r o t h e r s , Inc. , A nn A r b o r , Mich. (1943). R. L. Coble and J. S. E l l i s , J. Am. Ceram. Soc. , 46, 438-41(1963). I. B. C u t l e r i n " K i n e t i c s of High T e m p e r a t u r e P r o c e s s e s " , ppi 294-301, ed. W. D. Kingery, M. I. T. P r e s s , and John Wiley & Sons, 1959. - 1 1 9 - N. G. Dave and S. K. Chopra, J. Am. C e ram. Soc. , 49_, 575 (1966). J. F. Goodman, Proc.; R o y a l Soc. (London), A_247, 346 - 52 (1958). P. J. A n d e r s o n and R. F. H o r l o c k , T r a n s . F a r a d a y Soc. , 5_8, 1993 - 2004 (1962). : a) R. S. Gordon and W. D. K i n g e r y , J. Am. Ceram. Soc. , 49, 654 - 660 (1966). b) R. S. Gordon and W. D. K i n g e r y , tbid. , 50, 8 -14 (1967). M. C. B a l l and H. F. W. T a y l o r , M i n e r a l Mag. , 32, 754 - 66 (1961). S. J. Gregg and R. I. Razouk, J. Chem. Soc. , (London), 1949, pp. S36 - 44. G. M. Z h a b r o v a and V. A. Gordeeva, K i n e t i k a i K a t a l i s , Akad. Nauk. SSSR, Sb. Statei, 1_9_6_0 pp. 31 - 42. R. F. H o r l o c k , P. L. M o r g a n and P. J. Anderson, T r a n s . F a r a d a y Soc. , 59, 721 - 28 (1963). Handbook of C h e m i s t r y and P h y s i c s , 44th ed. , pp. 2532, 2365. E d i t e d by C. D. Hodgman, R. C. Weast and S. M. Selby. C h e m i c a l Rubber P u b l i s h i n Co. , Cleveland, (1962 - 1963). X -Ray Powder Data F i l e , E d i t e d by Joseph V. Smith, A S T M , P h i l a d e l p h i a (I960). A. F e r r a r i and C. C o l l a , International C r i t i c a l T a b l e s , IV, 63, M c G r a w H i l l (1933). H. S. C a r s l a w and J. C. Jaeger, Conduction of Heat i n Sol i d s , 2nd ed;, p. 200. O x f o r d U n i v e r s i t y P r e s s , London (1959). R. L. Coble and W. D. K i n g e r y , J. Am. C eram. Soc. , 39_, 377 - 85 (1956). A. K. K a k a r and A. C. D. Chaklader, J. Appl. Phys. , 3_8, 3223 - 30 (1967). - 120 - G. M. F r y e r , T r a n s . B r i t . C eram. Soc. , 3 9 , 377 - 85 (1956). K. A i h a r a , Graduate Student, Department of M e t a l l u r g y , U. B. C. P r i v a t e Communication. G. K. L a y d e n and G. W. B r i n d l e y , J. Am. C e r a m . Soc. , 46, 518 - 22 (1963). Y. K o t e r a , T. Saito and M. T e r a d a , J. Jap. C eram. S o c , 36, 195 - 199 (1963). G. B. Smith, M e t a l &. Ind. (London), 72, 427 (1948). C. O. Hulse, S. M. Copley and J. A. Pask, J. Am. C eram. Soc. , 46, 317 - 323 (1963). C. E. Wicks and F. E . Block, " T h e r m o d y n a m i c P r o p e r t i e s of 65 E l e m e n t s - T h e i r Oxides, H a l i d e s , C a r b i d e s and N i t r i d e s , B u l l . 605, US B u r e a u of Mines, Washington (1963)." A. C D . Chaklader and G. Beynon, J. Am. Ceram. S o c , Oct. 1970, (To be published).

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