THE ROLE OF SURFACE DIFFUSION IN THE SINTERING OF MICROPOWDERS

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THE ROLE OF SURFACE DIFFUSION IN THE SINTERING OF MICROPOWDERS

J. Lis, R. Pampuch

To cite this version:

J. Lis, R. Pampuch. THE ROLE OF SURFACE DIFFUSION IN THE SINTERING OF MICROPOWDERS. Journal de Physique Colloques, 1986, 47 (C1), pp.C1-219-C1-223.

�10.1051/jphyscol:1986132�. �jpa-00225561�

JOURNAL D E PHYSIQUE

C o l l o q u e Cl, s u p p l 6 m e n t a u n02, Tome 47, f 6 v r i e r 1986 p a g e

THE ROLE OF SURFACE DIFFUSION IN THE SINTERING OF MICROPOWDERS

J. L I S and R. PAMPUCH

I n s t i t u t e o f M a t e r i a l s S c i e n c e AGH, A l . M i c k i e w i c z a , 3 0 , PL-30-059 Cracow, P o l a n d

R6sumg - En u t i l i s a n t d e s donnges d e d i f f u s i o n sQres, o n a P v a l u &

l e s m o d i f i c a t i o n s gEomBtriques p e n d a n t l e f r i t t a g e r g s u l t a n t d e l ' a c t i o n s i m u l t a n g e d e l a d i f f u s i o n e n volume, a u x j o i n t s d e g r a i n s , e n s u r f a c e , e n u t i l i s a n t s d e s mod6les 2 deux s p h B r e s p o u r M ~ O , ~ 1 2 0 ~ e t Uo2. I1 a 6 t 6 montr6 q u e d a n s l e s m i c r o p o u d r e s d ' o - x y d e s , c o n t r a i r e m e n t aux systBmes m g t a l l i q u e s , l ' a p p r o c h e d e s cen- t r e s d e g r a i n s r s s u l t e e s s e n t i e l l e m e n t d e l a d . i f f u s i o n e n s u r f a c e . D ' a u t r e s mgcanismes d o i v e n t e t r e c o n s i d S r 8 s p o u r e x p l i q u e r l e r e - t r a i t p e n d a n t l e f r i t t a g e e t e l i m i n a t i o n d e l a p o r o s i t e .

A b s t r a c t - Using r e l i a b l e d i f f u s i o n d a t a , t h e g e o m e t r i c c h a n g e s d u r i n g s i n t e r i n g o f t w o - s p h e r e s models due t o a p a r a l l e l o p e r a t - i o n o f volume, g r a i n boundary, and s u r f a c e d i f f u s i o n h a v e been e- v a l u a t e d f o r MgO,

A1~02* ^{and U02. I t} h a s been shown t h a t , i n con- trast t o m e t a l l i c s y t m s , s u c h o x i d e s y s t e m s ( i f composed o f v e r y s m a l l p a r t i c l e s a s i n m i c r o p o w d e r s ) s h o u l d show t h e predominance o f e f f e c t s due t o s u r f a c e d i f f u s i o n and a v e r y low e x t e n t o f t h e a p p r o a c h o f p a r t i c l e c e n t r e s by volume and boundary d i f f u s i o n . H e n - c e , phenomena o t h e r t h a n t h e s i m p l e a p p r o a c h o f p a r t i c l e c e n t r e s s h o u l d be c o n s i d e r e d a s t h e main c a u s e of s h r i n k a g e and p o r e e l i - m i n a t i o n d u r i n g s i n t e r i n g of t h e o x i d e micropowders.

I- lNTRODUCTION

The e f f e c t s o f s u r f a c e d i f f u s i o n 3n g e o m e t r i c c h a n g e s i n s i n t e r i n g of p a r t i c l e s y s t e m s , as compared w i t h t h e o n e s due t o volume and g r a i n boundary d i f f u s i o n , a r e n o t v e r y i m p o r t a n t w i t h l a r g e - p a r t i c l e s y s t e m s b u t a r e n o t n e g l i g i b l e w i t h micropowders which h a v e a l a r g e s u r f a c e a r e a . A c c o r d i n g t o / 1 / / 2 / , t h e p r i n c i p a l g e o m e t r i c c h a n g e s due t o s u r - f a c e d i f f u s i o n i n a s y s t e m o f two s p h e r i c a l p a r t i c l e s ( A i n ~ ' i g . 1 ) a r e

, f i r s t , a n i n c r e a s e of t h e n e c k w i d t h ( B ) and , n e x t , g r a i n growth by c o a l e s c e n c e o f t h e two p a r t i c l e s due t o m i g r a t i o n o f t h e g r a i n boundary Out of t h e s y s t e m a f t e r a t t a i n m e n t o f c o n f i g u r a t i o n C. I n s y s t e m s o f ma- n y p a r t i c l e s a c o n c o m i t a n t growth of p o r e s a d j a c e n t t o t h e

p a r t i c l e s s h o u l d t a k e p l a c e . Both phenomena h a v e been found w i t h many s i n t e r i n g s y s t e m s a l r e a d y i n t h e f i r s t s t a g e s o f s i n t e r i n g / 3 / - / 6 / . These c h a n g e s d e c r e a s e t h e d r i v i n g f o r c e f o r t h e s i m p l e a p p r o a c h of p a r t i c l e c e n t r e s due t o volume and boundary d i f f u s i o n . Hence, i t i s of i n t e r e s t t o compare q u a n t i t a t i v e l y t h e i n t e r d e p e n d e n c e o f g e o m e t r i c a l c h a n g e s i n model s y s t e m s c a u s e d by volume, g r a i n boundary, and s u r f a c e d i f f u s i o n on t h e b a s i s of r e l i a b l e d i f f u s i o n d a t a . There i s , s u r p r i s i n g - l y , o n l y a s i n g l e s t u d y o f t h i s k i n d i n t h e l i t e r a t u r e /7/ which r e f e r s

,moreover, t o m e t a l l i c s y s t e m s . I n t h e p r e s e n t p a p e r s u c h a comparison

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986132

c l - 2 2 0 JOURNAL DE PHYSIQUE

h a s been made f o r l a r g e r and s m a l l - p a r t i c l e o x i d e s y s t e m s u s i n g a somewhat d i f f e r e n t a p p r o a c h as i n / 7 / .

I1 - GEOWTRIC CHAEGdS IIT MODELS W E TO PARALLZL DIFFUSIOIil MXCIIANISMS The r o l e o f e f f e c t s o f s u r f a c e d i f f u s i o n s h a l l be e v a l u a t e d w i t h r e g a r d

F i g . 1 - Geometric c h a n g e s due t o s u r f a c e d i f f u s i o n i n a s y s t e m o f two s p h e r i c a l p a r t i c l e s

t o a model of two s p h e r i c a l p a r t i c l e s . By u t i l i s i n g t h e n u m e r i c a l s o l u t i o n s d e v e l o p e d by N i c h o l s and M u l l i n s / 1 / / 2 / t h e g e o m e t r i c c h a n g e s of t h e model a n d , hence, A 1 c a n be c a l c u l a t e d f o r s u c c e s s i v e i n c - r e m e n t s o f t i m e o f i s o t h e r m a l h e a t i n g and compared w i t h s h r i n k a g e due t o a p p r o a c h o f p a r t i c l e c e n t r e s by volume and g r a i n boundary

d i f f u s i o n f o r t h e same model o f two s p h e r e s . The l a t t e r was c a l c u l a t e d by u s i n g t h e model p r o p o s e d by J o h n s o n /7/.

The c a l c u l a t i o n s were b a s e d on c a r e f u l l y s e l e c t e d v a l u e s o f s u r - f a c e - , g r a i n boundary-, and volume d i f f u s i o n c o e f f i c i e n t s ( t h e f i r s t f r - om mass t r a n s f e r m e t h o d s ) a t t e m p e r a t u r e s above 0.6 T, , ^{where Tm} i s t h e m e l t i n g p o i n t , u n d e r n e u t r a l and o x i d i s i n g a t m o s p h e r e s , r e s p e c t i - v e l y , i n c a s e o f m e t a l s and o x i d e s / 8 / - / 2 5 / . The d a t a f o r g r a i n boun- d a r y d i f f u s i o n c o e f f i c i e n t s were t a k e n from s o u r c e s where t h e p r o d u c t Dbbb w a s q u o t e d ('). Fig.2 shows t h e e x p e c t e d r e l a t i o n s f o r MgO o f two p a r t i c l e s i z e s . S i m i l a r r e l a t i o n s were o b t a i n e d a l s o f o r

4A1203 and UO?, t h e two o t h e r o x i d e s y s t e m s f o r which c o m p l e t e and r e l i a b l e d a t a a r e a v a i l a b l e . A t y p i c a l example o f t h e e x p e c t e d beha- v i o u r o f m e t a l l i c s y s t e m s c o n s i d e r e d ( e F e , A g , C u , N i ) i s shown i n F i g . 3 .

I t may be s e e n t h a t w h i l e w i t h m e t a l l i c s y s t e m s and l a r g e r - p a r - t i c l e o x i d e s y s t e m s t h e change due t o c o a l e s c e n c e s h o u l d s t a x t & % e r

S t a g e a s compared w i t h t h e one b r o u g h t a b o u t by g r a i n - b o u n d a r y and volume d i f f u s i o n , t h i s i s n o t s o w i t h o x i d e s y s t e m s o f a p a r t i c l e s i z e (0.: urn. With o x i d e micropowders t h e t i m e dependence o f f o r m e r change i s slrnllar t o t h e one due t o g r a i n boundary d i f f u s i o n and s h o u l d s e t i n at a much e a r l i e r s t a g e t h a n t h e change due t o volume d i f f u s i o n . I n a d d i t i o n , a p p r e c i a b l e growth of t h e neck w i d t h by s u r f a c e d i f f u s i o n t o 0 . 7 r < x < r , where r i s t h e p a r t i c l e r a d i u s , s h o u l d o c c u r a l r e a d y i n t h e f i r s t s t a g e s o f s i n t e r i n g /compare tr and tz i n Fig.2/. Owing t o t h i s , t h e d r i v i n g f o r c e f o r g r a i n boundary d i f f u s i o n s h o u l d become n e g l i g i b l e a l r e a d y i n t h e i n i t i a l s t a g e s o f s i n t e r i n g , a t l e a s t w i t h m i c r o p o w d e r s . T h i s becomes e v i d e n t when one c o n s i d e r s t h e r e s u l t a n t ef-

( l ) ^{i s} t h e c o e f f i c i e n t o f g r a i n boundary d i f f u s i o n ; s b ^{i s t h e}

g r a i n boundary w i d t h .

TABLZ 1 CALCULATED &/ &' RATIOS FOR SOME OXIDES AND METALS

f, f,

E'ig.2 - E x p e c t e d r e l a t i v e s h r i n k a g e v s . t i m e o f i s o t h e r m a l h e a t i n g o f a s y s t e m o f two s p h e r e s o f MgO o f d i f f e r e n t p a r t i c l e s i z e b r o u g h t a b o u t by volume ( v ) , g r a i n b o u n d a r y ( b ) and s u r f a c e d i f f u s i o n ( S ) . t, and tz d e n o t e t h e t i m e a t which t h e neck w i d t h grows by s u r f a c e d i f f u s i o n t o x=O.7r and x = r , r e s p e c t i v e l y , where r i s t h e p a r t i c l e r a d i u s . With v and b t h e two l i m i t i n g c u r v e s c o r r e s p o n d t o s h r i n k a g e c o n t r o l l e d by c a t i o n . a n d a n i o n d i f f u s i o n , r e s p e c t i v e l y . l ) a t a f o r i n d i - v l d u a l l y o p e r a t i n g d l f f u s i o n mechanisms.

P i g . 5 - S x p e c t e d r e l a t i v e s h r i n k a g e v s . t i m e o f h e a t i n g of a s y s t e m o f two s p h e r e s o f *Fe of d i f f e r e n t p a r t i c l e s i z e . The symbols a r e t h e same a s i n E'ig.2.

Homologous t e m p e r a t u r e

T/Tm 0.65

0.90

N i

0 . 2 0 - 0.93 0.39 0.99 P a r t i c l e

s i z e

P m

0.1 100

0.1 1 0 0

Pig 0 0.04 0.11 2 . 1 . 1 0 - ~

5 . 1 0 ~ ~

Ag 0 1 .OO 0.84 0.99

J

A120j 1 . 3 . 1 0 - ~

0.11

..---

5 . 6 . 1 0 - ~ 7 . 3 . 1 0 - ~

u02 3.8.10-2

0.30

1 . 1 . 1 0 - ~

3 . 8 . 1 0 - ~

JOURNAL DE PHYSIQUE

f e c t of t h e t h r e e mechanisms a c t i n g s i m u l t a n e o u s l y .

If d i f f u s i o n a l mechanisms, which b r i n g a b o u t an a p p r o a c h of p a r t i c l e c e n t r e s , d y , a n d / o r g r o w t h o f neck w i d t h , d x , o p e r a t e s i m u l t a n e o u s l y

-

where: n s t a n d s f o r mechanisms c a u s i n g n e c k growth and m s t a n d s f o r t h e o n e s c a u s i n g a p p r o a c h of p a r t i c l e c e n t r e s . I f it i s f u r t h e r assumed t h a t t h e u n i q u e d r i v i n g f o r c e f o r mass t r a n s p o r t by d i f f u s i o n i s t h e c h e m i c a l p o t e n t i a l g r a d i e n t due t o n e c k c u r v a t u r e and t h a t t h e c o n t a c t a r e a between two s p h e r i c a l p a r t i c l e s h a s a s i m p l e g e o m e t r y , t h e w e l l known r e l a t i o n s d e r i v e d by e a r l i e r a u t h o r s t o d e s c r i b e t h e g e o m e t r i c c h a n g e s i n s u c h s y s t e m s f o r e a c h i n d i v i d u a l mechanism /3'2//33/ may be i n s e r t e d i n t o ( 1 ) w i t h t h e r e s u l t :

( d x / d t ) = ksx'6+ kvx-4+kbx-5 ; ( d y / d t ) = k ; i 3 + k i n - 4 ( 2 ) where: k and k ' a r e t e m p e r a t u r e - d e p e n d e n t c o n s t a n t s ; v , b, and

s t a n d f o r volume, g r a i n boundary, and s u r f a c e d i f f u s i o n , r e s p e c t i v e l y . From ( 1 ) and ( 2 ) f o l l o w s t h a t :

k ~ x - ~ + k i x - 4

( d y / d x )

-

kSxm6+ kvx-4+ kbx-5 ( 3 )

R e l a t i o n ( 4 ) p e r $ i t s t o a s s e s s t h e i n f l u e n c e o f g e o m e t r i c c h a n g e s due t o s u r f a c e d i f f u s i o n upon t h e e f f e c t i v e s h r i n k a g e due t o a p p r o a c h o f p a r t i c l e c e n t r e s by volume and g r a i n boundary d i f f u s i o n a t a g i v e n s t a - g e o f s i n t e r i n g c h a r a c t e r i s e d by a g i v e n w i d t h of t h e n e c k ,

a t t a i n - ed. Taking, e.g., x1=1.10-9 m and x2= 0 . 5 r , where r i s t h e r a d i u s o f p a r t i c l e s , t h e s h r i n k a g e i n c r e c e n t s Ay and h y ' h a v e been c a l c u l a t e d , where b y i s t h e s h r i n k a g e i n c r e m e n t when a l l t h e t h r e e d i f f u s i o n a l mechanisms a r e o p e r a t i n g i n t h e t w o - s p h e r e s model and Ay' i s t h e i n - c r e m e n t i n a b s e n c e o f mass t r a n s p o r t by s u r f a c e d i f f u s i o n , r e s p e c t i v e - l y . T a b l e 1 p r e s e n t s t h e r a t i o s &/Ay' o b t a i n e d i n t h i s way, f o r o x i d e and m e t a l l i c s y s t e m s f o r which t h e r e a r e r e l i a b l e d a t a of s u r f a - c e , g r a i n boundary, and volume d i f f u s i o n , t h e d a t a r e l a t i n g t o two p a r - t i c l e s i z e s and two homologous t e m p e r a t u r e s , T/Tm, where Tm i s t h e mel- t i n g p o i n t . A s a l r e a d y s u g g e s t e d by F i g . 3 , t h e o p e r a t i o n o f s u r f a f e d i f - f u s i o n d o e s n o t a f f e c t s u b s t a n t i a l l y t h e s h r i n k a g e due t o c e n t r e s ap- p r o a c h by volume and g r a i n boundary d i f f u s i o n of t h e m e t a l l i c s y s t e m s , e s p e c i a l l y i n c a s e o f l a r g e r p a r t i c l e s . On t h e c o n t r a r y , t h i s i s n o t s o w i t h t h e o x i d e s y s t e m s where t h e o c c u r r e n c e of s u r f a c e d i f f u s i o n s h o u l d d e c r e a s e t h e s h r i n k a g e a s s o c i a t e d w i t h a p p r o a c h o f p a r t i c l e c e n t r e s by two t o s i x o r d e r s o f magnitude.

These r e s u l t s s u g g e s t s t r o n g l y t h a t a p p r o a c h o f p a r t i c l e c e n t r e s due t o

volume and boundary d i f f u s i o n s h o u l d n o t be t h e p r e d o m i n a n t phenomenon

l e a d i n g t o s h r i n k a g e o f o x i d e micropowders of t h e s y s t e m s a n a l y s e d .

Looking f o r o t h e r phenomena which may b r i n g a b o u t s h r i n k a g e and p o r e

e l i m i n a t i o n i n s u c h s y s t e m s l e t u s m e n t i o n two o f them which h a v e been

p r o p o s e d r e c e n t l y . A thermodynamic a n a l y s i s h a s i n d i c a t e d / 2 7 / / 2 8 / t h a t

t h e p r o b a b i l i t y o f e l i m i n a t i o n of p o r e s , i r r e s p e c t i v e j o f ' t h e i r s i z e , i s

t h e h i g h e r t h e l o w e r t h e i r c o o r d i n a t i o n numberlis. S i n c e c o a l e s c e n c e of

p a r t i c l e s by s u r f a c e d i f f u s i o n l e a d s t o growth of p a r t i c l e s a d j a c e n t t o

t h e ( g r o w i n g ) p o r e s and t h u s d e c r e a s e s t h e c o o r d i n a t i o n number o f p o r e s

i t s h o u l d be h e l p f u l i n t h e s i n t e r i n g p r o c e s s . The second phenomenon may

be t h e development o f t r a n s i e n t s t r e s s e s due t o s h r i n k a g e - r a t e d i f f e r e n -

t i a l between z o n e s h a v i n g a d i f f e r e n t g r a i n and p o r e s i z e / 2 9 / - / 3 1 / . T h i s

s i t u a t i o n i s t y p i c a l f o r s u r f a c e d i f f u s i o n - a c c o m p a n i e d s i n t e r i n g .

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