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ColZoque CS, supplEment au nO1O, Tome 4 2 , octobre 1981 page C5-867
CONTRIBUTION T O THE CHARACTERIZATION OF T H E ANELASTIC PROPERTIES OF MULTI-PHASE SYSTEMS
F.M. ~azzolai *
I s t i t u t o d i Acustica O.M. Corbino, V . Cassia 1216, Rome, I t a l y
Abstract
effects
D r e v i ous
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A c h a r a c t e r i z a t i o n o f t h e v a r i o u s k i n d s o f a c o u s t i c a l associated w i t h phase t r a n s f o n a t i o n s i s presented. Sane t h e o r e t i c a l approaches and experimental r e s u l t s concerning d i f f u s i o n-
a s s i s t e d processes are b r i e f l y o u t l i n e d , mainly f o r t h e purpose o f i l l u s t r a t i n g t h e c o n t r i b u t i o n s g i v e n t o t h i s s u b j e c t by t h e present conference.1. I n t r o d u c t i o n
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Phase t r a n s f o n a t i o n s a f f e c t a t t e n u a t i o n and v e l o c i t y o f ultrasounds according t o several s t r u c t u r a l mechanisms which can be r e l a t e d t o : a) t h e d i f f e r e n t nature o f phase t r a n s i t i o n s themselves (shear, d i ff u s i o n - a s s i s t e d etc.); b) t h e d i f f e r e n t ways o f t h e i r occurence( n u c l e a t i o n and growth, s p i nodal decanposition etc. ); c ) t h e d i f f e r e n t p r o p e r t i e s o f t h e t r a n s i t i o n products, mainly i n r e l a t i o n t o t h e degree o f l o n g o r short-range order, t h e n a t u r e o f i n t e r p h a s e boundaries and t h e d e f e c t s introduced. Due t o t h e enormous v a r i e t y o f s i t u a t i o n s , a complete a n a l y s i s o f t h e d i s s i p a t i o n processes i n v o l v e d i s q u i t e complex and beyond t h e purposes o f t h e present note. Here o n l y a general schematic c l a s s i f i c a t i o n w i l l be g i v e n which appears t o be a p p l i c a b l e t o any k i n d o f t r a n s i t i o n s ( s e c t i o n 2). The r e s t of t h e paper w i l l only deal w i t h d i f f u s i o n - a s s i s t e d transformations, shear t r a n s f o r m a t i o n being d e a l t w i t h elsewhere a t t h i s conference (1). We s h a l l b r i e f l y discuss those o r d e r - d i s o r d e r phenomena t h a t are not associated w i t h compositional changes; more e x t e n s i v e work w i l l be devoted t o t r a n s i t i o n s i n v o l v i n g long-range d i f f u s i o n , which -form t h e main s u b j e c t o f t h e papers presented a t t h i s conference, which w i l l a l s o be b r i e f l y reviewed here.
2. C l a s s i f i c a t i o n o f a c o u s t i c a l e f f e c t s
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I n t h e v a r i e t y o f t h e processes associated w i t h phase t r a n s i t i o n s an attempt o f general c h a r a c t e r i z a t i o n may appear a t f i r s t i n s i g h t o f 1 im i t e d usefulness. However, going through t h e l i t e r a t u r e i n t h i s area, i t can e a s i l y be r e a l i z e d t h a t a s u b s t a n t i a l s t a t e o f c o n f u s i o n s t i 11 e x i s t s , i n s p i t e o f t h e improvements r e c e n t l y reached by v i r t u e o f some v a l u a b l e reviews i n s e l e c t e d t o p i c s i n t h i s general f i e l d(2-
*Temporary address : University of Illinois, Department of Metallurgy and Mining at Urbana-Chafnpai~n. IL. 61801. U - S . A .
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815134
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a
5). Thus any e f f o r t aimed a t f u r t h e r c l a r i f i c a t i o n o f t h e process i n v o l v e d i n t h i s s u b j e c t appears w e l l j u s t i f i e d .
R e g a r d l e s s o f t h e n a t u r e o f a phase t r a n s i t i o n , o f t h e system i n which i t t a k e s p l a c e and of t h e phenonenology a s s o c i a t e d w i t h i t s o c c u r r e n c e , a c o u s t i c a l e f f e c t s can be u s e f u l l y c l a s s i f i e d as i n t r i n s i c o r e x t r i n s i c , a c c o r d i n g whether t h e y a r c i n t i m a t e l y r e l a t e d t o t h e processes by w h i c h t r a n s i t i o n occurs, o r t o t h e n a t u r e o f t h e t r a n s i t i o n p r o d u c t s , i n c l u d i n g among t h e s e e v e n t u a l i m p e r f e c t i o n s c r e a t e d and i nterphase b o u n d a r i e s .
2.1. I n t r i n s i c E f f e c t s
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An a p p l i e d e x t e r n a l s t r e s s f i e l d p e r t u r b s t h e e q u i l i b r i u m c o n d i t i o n s o f a systetn e i t h e r t h r o u g h a c o u p l i n g between t h e colnponents o f t h e a p p l i e d s t r e s s f i e l d and a n i n t e r n a l v a r i a b l e , such as a n a p p r o p r i a t e o r d e r parameter, o r t h r o u g h t e m p e r a t u r e g r a d i e n t s e v e n t u a l l y i n d u c e d i n t h e systen~. Consequently an a p p l i e d s t r e s s c a n a c t as a d r i v i n g o r an opposing i o r c e f o r phase t r a n s i t i o n s . Any r e a d j u s t m e n t o f t h e system u n d e r s t r e s s t a k e s p l a c e a c c o r d i n g t o a r e l a x a t i o n process, whose r e l a x a t i o n t i m e s a r e u s u a l l y s t r o n g l y t e m p e r a t u r e dependent i n t h e v i c i n i t y o f t h e t r a n s i t i o n t e m p e r a t u r e Tc. Such e f f e c t s a r e i n t i m a t e l y r e l a t e d t o t h e t r a n s i t i o n p r o c e s s , i n d e p e n d e n t l y w h e t h e r i t t a k e s p l a c e t h r o u g h a movement o f an i n t e r p h a s e boundary o r t h r o u g h a b u l k e f f e c t . Such i n t r i n s i c e f f e c t s , f o r t h e s t r e s s amp1 i t u d e s u s u a l l y used i n a c o u s t i c a l s t u d i e s , o n l y appear w a r T C '-
t h ereason f o r t h a t w i l l c l e a r l y appear from n e x t s e c t i o n .
As a g e n e r a l c r i t e r i u m , such e f f e c t s a r e e x p e c t e d t o be o n l y d e t e c t a b l e , w i t h dynarnical e x p e r i m e n t s , i n systems capable o f f a s t enough r e a d j u s t m e n t s n o t i n v o l v i n g c o m p o s i t i o n a l changes (1 ong-range d i f f u s i o n ) . Exarnples o f such k i n d o f processes a r e g i v e n i n f i g s . 1, 2, and 3, where t h e a t t e n u a t i o n , a, and v e l o c i t y , V, o f u l t r a s o u n d s a r e p l o t t e d as a f u n c t i o n o f t h e t e m p e r a t u r e T o r t h e d i f f e r e n c e T-Tc, f o r v a r i o u s systems (6-8).
2.2. E x t r i n s i c E f f e c t s
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Changes i n t h e e l a s t i c and a n e l a s t i c p r o p e r t i e s o f a system may a r i s e f r o m a n e f f e c t o f t h e e x t e r n a l s t r e s s o n t h e t r a n s f o r m a t i o n p r o d u c t s r a t h e r t h a n on t h e t r a n s f o r m a t i o n process i t s e l f . I n t h i s case t h e a c o u s t i c a l b e h a v i o r r e s u l t s f r o m t h e e q u i l i b r i u m p r o p e r t i e s o r t h e k i n e t i c s o f t h e t r a n s i t i o n r a t h e r t h a n from t h e i n t r i n s i c dynamical phenomena a s s o c i a t e d w i t h t h e t r a n s i t i o n , such as f o r example c r i t i c a l f l u c t u a t i o n s . Such r e l a x a t i o n processes a r e u s u a l l y t h e r m a l l y a c t i v a t e d , t h e i r t e l i l p e r a t u r e i s n o t d i r e c t l y r e l a t e d t o t h e t r a n s i t i o n temperature.Bulk l a t t i c e r e l a x a t i o n s a r i s i n g from s t r e s s - a s s i s t e d changes i n t h e s h o r t - r a n g e o r d e r ( Z e n e r e f f e c t ) , r e o r i e n t a t i o n o f i s o l a t e d e l a s t i c d i p o l e s (Snoek e f f e c t ) and l o n g - r a n g e d i f f u s i o n (Gorsky e f f e c t ) a r e u s u a l l y a f f e c t e d
by changes i n t h e r e l a t i v e volumes and compositions o f c o e x i s t i n g phases.
Examples a r e g i v e n i n f i g s . 4, 5, and 6, where changes i n t h e r e l a x a t i o n s t r e n g t h have been recorded as a f u n c t i o n o f t i m e (9), temperature (10) or- composition (11).
E x t r i n s i c e f f e c t s associated w i t h t h e m o t i o n o f interphase-boundaries, t w i n s and d i s l o c a t i o n s , i s o l a t e d o r i n t e r a c t i n g w i t h p o i n t d e f e c t s ( l i k e l y i m p u r i t i e s ) a r e a l s o expected t o occur. Clear evidence seems now t o e x i s t o f a r e l a x a t i o n due t o t h e m o t i o n o f H - d i s l o c a t i o n complexes produced by h y d r i d e p r e c i p i t a t i o n i n t h e supersaturated s o l i d s o l u t i o n s o f hydrogen i n Ta (12), Nb (13, 14), V (15) and Pd (16). Results obtained i n Ta-H a l l o y s are reproduced i n f i g . 7, where t h e e f f e c t o f c y c l i n g i s c l e a r l y i l l u s t r a t e d . N u c l e a t i o n o f h y d r i d e p a r t i c l e s i s i n d i c a t e d by t h e abrupt increase i n t h e e l a s t i c energy d i s s i p a t i o n c o e f f i c i e n t observed a t about 230K, d u r i n g t h e f i r s t c o o l i n g run, f o l l o w i n g hydrogenation a t roan temperature (H/Ta = 0.05).
A r e l a x a t i o n , which seems t o be c l e a r l y r e l a t e d t o t h e motion o f t w i n s r e s u l t i n g f r a n a f c c + f c t m a r t e n s i t i c t r a n s f o r m a t i o n has been observed i n T%-In a l l o y s [17,181. E f f e c t s associated w i t h t h e m o t i o n o f i n t e r p h a s e boundaries ( t w i n s ) have a l s o been r e p o r t e d i n m u l t i p l e domain c r y s t a l s o f 6
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phase niobium h y d r i d e [19,20].
3. O r d e r - d i s o r d e r t r a n s f o r m a t i o n s
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Ordering processes can occur both by l o c a l c o o p e r a t i v e readjustments, as i n magnetic, f e r r o e l e c t r i c and c e r t a i n a t m i c o r d e r - d i s o r d e r t r a n s f o r m a t i o n s (ammonium c h l o r i d e , f o r example), o r by long-range m i g r a t i o n , as i n p r e c i p i t a t i o n of supersaturated s o l i d s o l u t i o n s . U s u a l l y d i f f u s i o n r e q u i r e s times much l o n g e r t h a n t h e p e r i o d o f a s c i l l a t i o n o f an a c o u s t i c wave, t o t a k e p l a c e over distances o f t h e order o f t h e wave length, a c c o r d i n g l y e f f e c t s accompanying transformations associated w i t h compositional changes a r e u s u a l l y e x t r i n s i c i n nature. We s h a l l b r i e f l y examine these two k i nds o f s i t u a t i o n s separately.3.1. Order-disorder transformations not i n v o l v i n g long-range diffus*.
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T h i s i s probably t h e k i n d of transformation, t h a t has been more e x t e n s i v e l y i n v e s t i g a t e d b o t h f r a n a t h e o r e t i c a l and an experimental p o i n t o f view (2-5), t h e reason i s due t o t h e f a c t t h a t t h e l a r g e i n t r i n s i c e f f e c t s associated w i t h them p r o v i d e a s e n s i t i v e method f o r i n v e s t i g a t i n g t h e i n t i m a t e f e a t u r e s o f t h e t r a n s f o r m a t i o n i t s e l f . Both the decrease i n t h e v e l o c i t y and t h e increase i n t h e
a t t e n u a t i o n o f ultrasounds (some example o f which a r e given i n fig.1-3) a r e r e l a x a t i o n a l i n nature.
F o r temperatures not t o o c l o s e t o t h e c r i t i c a l temperature
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(T-Tc)/Tc ( IO'~), t h e i n e q u a l i t y I J T < < ~ i s s a t i s f i e d (T = r e l a x a t i o n time,
=angular frequency o f t h e a p p l i e d o s c i l l a t i n g s t r e s s f i e l d ) . Under such c o n d i t i o n s , which a r e u s u a l l y s a t i s f i e d i n t h e experiments, changes i n t h e v e l o c i t y , V, w i t h temperature are e s s e n t i a l l y determined by t h e temperature dependence o f t h e r e l a x a t i o n s t r e n g t h , A, o f t h e process. P c c o r d i n g l y from data on V(T), o n l y e q u i l i b r i u m p r o p e r t i e s o f t h e c r i t i c a l p o i n t s can be deduced. The temperature dependence o f a comes both from A (T) and T (T), thus by simultaneous measurements o f V(T), and a(T), the dynamical behavior o f t h e c r i t i c a l p o i n t s can be studied.
The r e l a x a t i o n process has i n i t i a l l y been discussed by Landau and coworkers (21,22) i n t e n s o f a c o u p l i n g between t h e s t r e s s components o f t h e u l t r a s o u n d s and an i n t e r n a l v a r i a b l e such as an o r d e r parameter 6 . Two main assumptions were made: a) t h e f r e e energy o f t h e system could be expanded i n a power s e r i e s of t h e s t r e s s components and t h e order parameter; b) thermal f l u c t u a t i o n s o f 6 were n e g l i g i b l e .
As i t has been discussed a f t e r w a r d s (23) b o t h these assumptions a r e expected not t o be s a t i s f i e d i n a temperature range close t o Tc. More r e f i n e d models have consequently been developed, according t o which t h e a t t e n u a t i o n a r i s e s from an i n t e r a c t i o n o f t h e a c o u s t i c a l phonons w i t h t h e thermal f l u c t u a t i o n s o f t h e order parameter [24-271. The temperature dependence o f a, i n t h e l i m i t w T
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1 i s n o t exponential b u t r a t h e r o f t h e t Y Pea = w 2 ; (1)
where t h e c r i t i c a l exponent p assumes values depending on t h e s p e c i f i c n a t u r e o f t h e t r a n s i t i o n considered, t h e values o f ~ ( e = (T-Tc)/Tc), t h e a c o u s t i c a l mode ( l o n g i t u d i n a l , t r a n s v e r s e ) , t h e d i r e c t i o n o f p r o p a g a t i o n and t h e p o l a r i z a t i o n . Changes i n t h e sound v e l o c i t y near t h e c r i t i c a l p o i n t a r e g i v e n by
where t h e c r i t i c a l exponent a ( n o t t o be confused w i t h t h e a t t e n u a t i o n c o e f f i c i e n t ) depends on t h e a c o u s t i c a l mode (1 o n g i t u d i nal, t r a n s v e r s e ) b u t i s not very ~nuch s e n s i t i v e t o t h e nature o f t h e t r a n s f o r m a t i o n . This l a s t p r o p e r t y d e r i v e s from t h e f a c t t h a t t h e sound v e l o c i t y f o r ( w T
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I ) does n o t depend on f l u c t u a t i o n s , t h e temperature dependence being only d e t e n n i ned by e q u i l i b r i u m s t a t i c q u a n t i t i e s .Expressions s i m i l a r t o (1) and (2) had a l s o been d e r i v e d on t h e basis o f
t h e Landau t h e o r y (3); i n t h i s case t h e exponents p and a assume t h e values 2 and 1, r e s p e c t i v e l y .
3.2 O r d e r - d i s o r d e r t r a n s f o r m a t i o n s associated w i t h long-range d i f f u s i o n
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R e l a t i v e l y l i t t l e t h e o r e t i c a l work has been done on t h i s s u b j e c t (28, 29).
K r i v o g l a z (28) has analyzed the e f f e c t of an e l a s t i c p e r t u r b a t i o n i n a two- phase system i n t h e case o f one o r two components. Here t r a n s f o r m a t i o n s a s s o c i a t e d w i t h c o ~ n p o s i t i o n a l changes a r e d e a l t ~ i t h , thus only r e s u l t s f o r a two crwnponent system w i l l b r i e f l y be i l l u s t r a t e d . The basic assumptions made a r e t h e f o l l o w i n g : a) t h e heat d i f f u s i v i t y i s h i g h enough t o e s t a b l i s h isothermal c o n d i t i o n s ; b) t h e e l a s t i c continous i s i s o t r o p i c . The main r e s u l t o f t h i s i n v e s t i g a t i o n i s t h a t , i n p r i n c i p l e , a r e l a x a t i o n process i s expected t o occur, w i t h a r e l a x a t i o n time which assumes d i f f e r e n t expressions according t o whether t h e r a t e c o n t r o l l i n g process i s t h e speed o f t h e i n t e r p h a s e boundary motion, o r the d i f f u s i o n f l o w towards t h e interphase boundary. We s h a l l only discuss t h e second case, which appears t o be t h e more r e a l i s t i c one. Assuming t h a t t h e second phase c o n s i s t s o f a small q u a n t i t y o f s p h e r i c a l p a r t i c l e s , o f mean r a d i u s r T i s g i v e n by
0'
where KO and Kao a r e t h e b u l k moduli a t low ( w ~ < < l ) and a t h i g h ( w ~ > > l ) frequencies, Dl i s t h e i n t e r d i f f u s i o n c o e f f i c i e n t i n t h e m a t r i x ( f i r s t phase) and X2 t h e volume f r a c t i o n o f t h e second phase. As i t can be e a s i l y seen from r e l a t i o n (3), T i s expected t o be extremely l o n g f o r s u b s t i t u t i o n a l a1 l o y s (assuming ~ = 1 0 - ~ ~ c m ~ / s e c , ~ ~ = 1 0 - ~ , Ko/Kw=l, T cones o u t t o be 10 sec). 6 F o r a1 l o y s having 0,C o r N as a component, T can be estimated t o be ) 10 sec.
Thus, w i t h t h e e x c e p t i o n o f hydrogen, f o r which T can become as small as 10- sec, i t i s u n l i k e l y t h a t an i n t r i n s i c e f f e c t o f t h i s type can be 3 d e t e c t e d i n a dynamic experiment.
F o l l o w i n g methods developed by Eshel by (30)
,
Schoeck (29) has c a l c u l a t e d t h e i n t e r a c t i o n energy o f a p r e c i p i t a t e p a r t i c l e w i t h an e x t e r n a l f i e l d . His conclusions a r e t h a t only r e l a x a t i o n e f f e c t s associated w i t h t h e s l i d i n g o f incoherent i nterphase boundaries, o r w i t h t h e m o t i o n o f d i s l o c a t i o n s s i t u a t e d i n semicoherent boundaries, can occur. Pccording t o Schoeck s t r e s s - a s s i s t e d p r e c i p i t a t i o n and d i s s o c i a t i o n a r e only expected t o g i v e r i s e t o a background d i s s i p a t i o n , m o n o t o n i c a l l y i n c r e a s i n g w i t h te~nperature. Nevertheless, on t h e b a s i s o f Schoeck arguments i t seems t h a t t h e p o s s i b l i t y o f a r e l a x a t i o n e f f e c t due t o p r e c i p i t a t e f o r m a t i o n and d i s s o l u t i o n cannot, i n p r i n c i p l e , be r u l e d out. However, as discussed before, T i s expected t o be exceedingly h i g h f o rJOURNAL DE PHYSIQUE
dynamical i n v e s t i g a t i o n s .
Concluding t h i s section, i t seems t h a t only e x t r i n s i c e f f e c t s can be u s u a l l y observed i n systems which undergo compositional changes d u r i n g phase t r a n s f o n a t i o n .
4. C o n t r i b u t i o n s presented a t t h i s conference
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P6 p o i n t e d out i n t h e p r e v i o u s section, i n t r i n s i c e f f e c t s a r e u n l i k e l y t o occur, f o r dynamical experiments, on phase t r a n s f o r m a t i o n s associated w i t h compositional changes.C e r t a i n l y most o f t h e phenomena d e a l t w i t h i n t h e papers presented a t t h i s conference (which i n t h e f o l l o w i n g w i l l be quoted by adding t h e l e t t e r c ) , can c l e a r l y be i d e n t i f i e d as e x t r i n s i c e f f e c t s . fs i t has schematically been i n d i c a t e d i n s e c t i o n 2, such e f f e c t s w i l l be c l a s s i f i e d as
&,
interphase- boundary and l a t t i c e - d e f e c t s e f f e c t s , a f u r t h e r d i s t i n c t i o n being made betweenr e l a x a t i o n and n o n - r e l a x a t i o n processes.
4.1. B u l k - l a t t i c e e f f e c t s
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I n t h i s category t h e most important r e l a x a t i o n phenomena are t h e Zener and t h e Snoek e f f e c t s , whose m o d i f i c a t i o n s have been f o l l o w e d i n a number o f papers ( l c - 4 c ) .One o f t h e most i n t e r e s t i n g systems t o be i n v e s t i g a t e d by i n t e r n a l f r i c t i o n r e s u l t s t o be t h e A l - k ~ system, where one ( o r more) r e l a x a t i o n has been observed, whose i n t e r p r e t a t i o n has been c o n t r o v e r s i a l . (31-34) f o r many years. The b a s i c problem i s t o understand whether t h i s e f f e c t i s due t o stress-induced changes i n t h e shape of p r e c i p i t a t e s (31), t o t h e m o t i o n o f semicoherent i n t e r p h a s e boundaries (32) o r t o short-range order changes (Zener e f f e c t ) ( l c ) . The o b s e r v a t i o n made By S c h a l l e r e t al. ( l c ) , t h a t t h e peak reaches h i s maximm h e i g h t f o r a s i l v e r content o f about 59.5 at%, t h a t i s f o r a s i n g l e phase s i t u a t i o n , seems t o s t r o n g l y support t h e i r conclusion t h a t t h i s i s a Zener type o f r e l a x a t i o n .
The i m p o r t a n t r o l e played by Zener e f f e c t i n i n v e s t i g a t i n g o r d e r - d i s o r d e r phenomena i s c l e a r l y e v i d e n t f r a n the work by De Rooy e t a l . (2c) i n a- CuNiZn a l l o y s , where i t has s u c c e s s f u l l y been used t o i n v e s t i g a t e t h e temperature dependence o f Ni and Zn m o b i l i t y near Tc. A gradual decrease i n t h e r e l a x a t i o n t i m e w i t h T, observed when approaching Tc f r a n l w temperatures, c l e a r l y shows t h a t t h e m o b i l i t y o f Zn increases w i t h t h e degree o f d i s o r d e r . However such a b i g increase (more t h a n one o r d e r o f magnitude) seems not e x p l a i n a b l e i n t e r n s o f a change i n t h e c o r r e l a t i o n f a c t o r only, as i t has been assumed by t h e above a u t h o r s (2c).
An a p p l i c a t i o n o f t h e a n e l a s t i c techniques, which i s o f t e c h n o l o g i c a l
importance, has been made by Chin-Hsiou Tang e t al. (3c). The temper e m b r i t t l e m e n t o f s t e e l s has been found t o be associated w i t h p r e c i p i t a t i o n o f
Fe3C(N)
,
which causes a decrease in t h e c o n c e n t r a t i o n o f C ( Y ) i n t h e a-phase as w e l l as a p i n n i n g o f d i s l o c a t i o n s , thus g i v i n g r i s e t o a simultaneous decrease o f t h e Snoek and Koester e f f e c t s .A w e l l developed peak has been observed i n n i t r i t e d Fe-16.6 wt % Cr quenched from 1100 o r 800°C (4c). A l t e r a t i o n s i n t h e h e i g h t and temperature o f the peak w i t h changing t h e n i t r o g e n content and/or t h e quenching temperature show t h a t t h e peak i s s e n s i t i v e t o m i c r o s t r u c t u r e , however t h e o r i g i n o f t h e peak has not been e s t a b l ished y e t .
Background d i s s i p a t i o n and e f f e c t s not r e l a x a t i o n a l i n nature have been i n v e s t i g a t e d i n a group o f papers (5c-8c), which deal w i t h a number o f d i f f e r e n t m a t e r i a l s .
A phenomenological d i s c u s s i o n of t h e changes i n t h e background d i s s i p a t i o n t o be expected a t o r d e r - d i s o r d e r phase t r a n s f o r m a t i o n s of f i r s t o r d e r i s made by B e r r i s f o r d e t al. (5c). From a comparison o f t h e r e s u l t s o f such a n a l y s i s and those o f t h e experiments i t i s concluded t h a t t h e 8-0' and
6-6.' phase t r a n s f o r m a t i o n s i n Mg-In a l l o y s i s o f f i r s t order. It i s t o be p o i n t e d o u t t h a t t h e background d i s s i p a t i o n considered here i s n o t i n t r i n s i c a l l y r e l a t e d t o t h e t r a n s f o r m a t i o n process, b u t r a t h e r t o mechanisms o p e r a t i n g i n t h e bulk o f t h e t r a n s f o r m a t i o n products. The a p p l i c a b i l i t y o f t h e c o n s i d e r a t i o n s made appears t o be l i m i t e d t o the cases where i n t e r p h a s e boundaries do not a p p r e c i a b l y c o n t r i b u t e .
An i n v e s t i g a t i o n on t h e i n f l u e n c e of an a p p l i e d s t r e s s on a s e l f - t w i s t i n g e f f e c t , o f a t o r s i o n pendulum, which occurs d u r i n g h y d r i d e p r e c i p i t a t i o n i n Vanadium (35.36) has l e d Yoshinari e t a l . (6c) t o the c o n c l u s i o n t h a t t h i s phenomenon i s r e l a t e d t o a p r e f e r e n t i a l p r e c i p i t a t i o n ( d i s s o l u t i o n ) o f h y d r i d e p l a t e l e t s on c e r t a i n s e t s o f h a b i t planes r a t h e r than on others. This e x p l a n a t i o n i s i n keeping w i t h t h e r e s u l t s o f p r e v i o u s s t a t i c experiments on s t r e s s - i nduced p r e c i p i t a t i o n ( d i s s o l u t i o n ) i n hydride-forming metals, c a r r i e d o u t by Bi rnbaum and coworkers (37).
The e v o l u t i o n o f background d i s s i p a t i o n i n Cu-21 a t % A1 d u r i n g temper o f p r e v i o u s l y quenched m a t e r i a l shows (7c) several stages, some o f which appear t o be r e l a t e d t o annealing and c l u s t e r i n g o f quenched-in vacancies, o t h e r s t o o r d e r i n g processes. A s e p a r a t i o n and a f u l l understanding of-phenomena i n v o l v e d appears t o be premature a t t h e moment. t h e
The work by Fargeot e t at ( 3 c ) , performed i n an extremely wide temperature range, c l e a r l y shows t h a t p o l y c r y s t a l l i n e (A1 0 ) MgO (n=3, 3.5),
2 3 n
C5-874 JOURNAL DE PHYSIQUE
prepared by plasma spraying i s i n a metastable phase. E v o l u t i o n towards an equi 1 ib r i u l n s t a t e (coexistence o f and phases) gives r i s e t o r e l e v a n t changes i n t h e Young modulus above 1000°C w h i l e changes below 1000°C appear t o be r e l a t e d t o t h e annealing out o f quenched-in defects. Stages are a l s o observed i n s i n g l e c r y s t a l s prepared w i t h a Vermeuil method.The work i s an i n t e r e s t i n g a p p l i c a t i o n o f a c o u s t i c a l techniques f o r i n v e s t i g a t i n g m i c r o s t r u c t u r a l changes i n systems n o t y e t as e x t e n s i v e l y i n v e s t i g a t e d as metals and a l l o y s .
4.2. Interphase-boundary e f f e c t s
-
The experimental evidence of e f f e c t s a s s o c i a t e d w i t h interphase-boundary m o t i o n i s less c l e a r t h a n f o r t h e o t h e r two c a t e g o r i e s o f e x t r i n s i c e f f e c t s . It i s g e n e r a l l y accepted t h a t such processes a r i s e from s l i d i n g o f incoherent interphases, according t o mechanisms analogous t o those a s s o c i a t e d w i t h h i g h angle g r a i n boundaries. I n t h i s s e c t i o n we s h a l l examine r e s u l t s obtained i n sane h i g h damping a l l o y s i n which d i s s i p a t i o n i s associated w i t h interphase-boundary processes ( 9 c - l l c ) .Experiments c a r r i e d out by M i l l e t e t a l . (9c) i n grey cast i r o n show t h a t t h e damping c a p a c i t y o f such m a t e r i a l r e s u l t f r a n g r a p h i t e p r e c i p i t a t e s , w h i l e mechanical p r o p e r t i e s i s e s s e n t i a l l y determined by t h e m i c r o s t r u c t u r e . These o b s e r v a t i o n s a l l o w t h e p r o d u c t i o n o f a grey c a s t i r o n w i t h h i g h damping as w e l l as h i g h s t r e n g t h . The s p e c i f i c d i s s i p a t i o n mechanisms have not been c l e a r l y i d e n t i f i e d , however t h e a v a i l a b l e r e s u l t s seem t o i n d i c a t e t h a t they may be p a r t l y r e l a t e d t o i n t e r f a c e s m o t i o n i n s i d e t h e hexagonal form o f g r a p h i t e and p a r t l y t o t h e m o t i o n of interphase boundaries,
s e p a r a t i n g the rombohedral from t h e hexagonal phase.
The e f f e c t o f a d d i t i o n s o f Mg on t h e mechanical and a c o u s t i c a l p r o p e r t i e s of quenched c a s t i n g s o f Zn-A1 (8-203 Al) has been i n v e s t i g a t e d by T. Otani e t a l . (10c). It i s found t h a t Mg a d d i t i o n s markedly reduce damping, w h i l e they i n c r e a s e t h e s t a b i l i t y a g a i n s t decomposition d u r i n g ageing. It i s concluded t h a t amounts o f Mg lower t h a n 0.02% should be used t o o b t a i n b e n e f i c i a l e f f e c t s f r a n a l l o w i n g w i t h Mg.
The s t r u c t u r a l sources o f h i g h damping p r o p e r t i e s o f Zn-A1 have been reexamined by Kawabe e t a l . ( l l c ) ; p r e v i o u s f i n d i n g s by N u t t a l l a r e s u b s t a n t i a l l y confirmed. Both authors observe a h i g h peak i n t h e as-quenched m a t e r i a l , ho:rever t h e peak temperature f r a n N u t t a l l (38) data i s a p p r e c i a b l y higher. A comparison w i t h data by Nowick (39) appears l e s s d i r e c t i n view o f t h e l a r g e d i f f e r e n c e i n compositions used. The main r e s u l t o f t h e most recent- i n v e s t i g a t i o n seems t o be t h e a s s o c i a t i o n o f t h e h i g h damping p r o p e r t i e s w i t h l a r g e s l i d i n g processes o c c u r r i n g a t t h e i nterphase-boundary surfaces. An
e x t r a c o n t r i b u t i o n t o d i s s i p a t i o n seems t o a r i s e a t t h e t r a n s i t i o n temperature whose n a t u r e i s not e a s i l y understandable a t t h e moment.
4.3. E x t r i n s i c e f f e c t s associated w i t h l a t t i c e - d e f e c t s
-
I n view o f t h e l a r g e defonnations u s u a l l y associated w i t h phase transformations, a n e l a s t i c e f f e c t s due t o l a t t i c e d e f e c t s are e a s i l y predicted. I n a d d i t i o n t o these a r e a l s o t o be considered phenomena which occur as a consequence o f t h e m o d i f i c a t i o n s induced by phase t r a n s f o r m a t i o n s on p r e e x i s t i n g o r i n t e n t i o n a l l y i n t r o d u c e d l a t t i c e i m p e r f e c t i o n s . Papers d e a l i n g w i t h such e f f e c t s (12c-15c) w i l l be examined i n t h i s section.The a c o u s t i c emission associated w i t h h y d r i d e p r e c i p i t a t i o n has been s t u d i e d by Cannelli e t a1 (12c) i n Nb (H/Nb=0.04). I n t h i s case t h e d e f e c t s o f i n t e r e s t are o f macroscopic nature (cracks). The most i n t e r e s t i n g o b s e r v a t i o n made i s t h a t the emission a c t i v i t y , as measured d u r i n g repeated c o o l i n g s (room temperature--225K) i n a specimen, t h a t has been annealed a t 150°C b e f o r e each measurement run, i s h i g h e r than t h a t observed when t h e i ntermediate anneal i ng treatment i s not appl ied. This d i f f e r e n c e has been a t t r i b u t e d t o oxygen m i g r a t i o n t o d i s l o c a t i o n s punched o u t by h y d r i d e p r e c i p i t a t i o n , however an incomplete d i s s o l u t i o n , a t l e a s t i n t h e specimen not annealed a t 150°C, appears a l s o t o be a p o s s i b l e cause o f t h e observed d i f f e r e n c e s .
A second paper (13c) i n t h i s group deals w i t h a p e c u l i a r narrow peak observed i n /U3(Xl quenched f r a n 1073K (disordered s t a t e ) and subsequently p l a s t i c a l l y deformed. A s t r u c t u r a l mechanism f o r t h e peak has t e n t a t i v e l y been proposed. It i s assumed t h a t t h e s t r e s s induced motion o f d i s l o c a t i o n s causes some s o r t o f o r d e r - d i s o r d e r process i n regions, where a h i g h c o n c e n t r a t i o n o f t h e as-quenched vacancies has been produced by d i s l o c a t i o n movement d u r i n g p l a s t i c deformation.
The mutual i n f l u e n c e o f p r e c i p i t a t i o n and r e c r y s t a l l i z a t i o n i s t h e s u b j e c t o f t h e l a s t two papers (14c,15c). One o f t h e main r e s u l t s o f t h e f i r s t one i s t h a t o f showing how t h e background d i s s i p a t i o n due t o d i s l o c a t i o n s can be s u c c e s s f u l l y used t o d e t e c t p r e c i p i t a t i o n and r e c r y s t a l l i z a t i o n processes. I n t h e case o f Al-Mn a l l o y s (1-2% Mn) i t has been found t h a t Mn atoms i n s o l u t i o n p i n t h e d i s l o c a t i o n s and r e t a r d r e c r y s t a l l i z a t i o n . A d e l i c a t e p o i n t , which has probably not been f u l l y e l u c i d a t e d y e t , i s t o understand t o which e x t e n t the observed phenomena a r e determined by Mn a t o m i n s o l u t i o n o r by p r e c i p i t a t e s .
Data concerning e f f e c t o f p r e c i p i t a t i o n on r e c r y s t a l l i z a t i o n by K i s s e t
C5-876 JOURNAL DE PHYSIQUE
a l . (15c) a r e i n s u b s t a n i a l agreement w i t h those by D i a l l o e t a l . (14c). Ol~e i n t e r e s t i n g r e s u l t o f t h e above study (15c) i s t h a t g r a i n boundary r e l a x a t i o n i s p r o g r e s s i v e l y reduced by i n c r e a s i n g t h e amount o f Mn, and g r a d u a l l y replaced by an i n t e r p h a s e boundary r e l a x a t i o n .
5. Conclusions
-
It has been shown t h a t : a) an u s e f u l d i s t i n c t i o n can be made b e t r ~ e e n i n t r i n s i c and e x t r i n s i c e f f e c t s ; b) phase t r a n s f o r m a t i o n i n v o l v i n g compositional changes u s u a l l y i n v o l v e e x t r i n s i c e f f e c t s .Several i n t e r e s t i n g r e s u l t s have been described i n t h e papers submitted a t t h e conference which can be summarized as f o l l o w s : 1) The s t r u c t u r a l mechanism of i n t e r n a l f r i c t i o n i n A 1 - 4 ( l c ) and Al-Zn ( l l c ) has been f u r t h e r c l a r i f i e d ; 2) New e f f e c t s have been p h e n m e n o l o g i c a i l y c h a r a c t e r i z e d even i f not completey understood (4c,13c); 3) I n f o r m a t i on o f p h y s i c a l i n t e r e s t have been found on atomic m o b i l i t i e s i n a-CuNiZn (2c), and on r e c r y s t a l l i z a t i o n o f A1 -Mg a1 l o y s (14c,15c); 4) T e c h n o l o g i c a l l y important r e s u l t s have been obtained on temper-embrittlement o f a l l o y i n g s t e e l s (3c), on l a t t i c e d i s r u p t i o n and p r e c i p i t a t i o n c h a r a c t e r i s t i c s o f hydrides i n Nb and V
(6c,12c), on h i g h damping p r o p e r t i e s o f M - Z n ( 1 0 c , l l c ) and o f grey cast i r o n (9c), as w e l l as on t h e phase separations i n (A1203), MgO (8c).
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This conference
l c . R. S c h a l l e r and W. Benoit: P r e c i p i t a t i o n stages
. . .
2c. A. De Rooy, P. M. Bronsveld and J. Th. M. De Mossom: I n t e r n a l F r i c t i o n
.
. . .
3c. Chi-Hsiou Tang, Mei Su and Ting-Chuan L e i : R e l a t i o n s h i p s Between
. . .
4c. M. Lebienvenu and 6. Dubois: I n f l u e n c e o f
. . . . .
5c. R. A. B e r r i s f o r d and G. M. Leak: An I n t e r n a l F r i c t i o n
. . . . .
6c. 0. Yoshinari and M. Koiwa: On the t w i s t
. . . . . "
7c. M. Lewbienvenu, E. Capelle, G. Oca~npo and B. Dubois: I n t e r n a l F r i c t i o n 8c. D. Fargeot, C. Gault, F. P l a t o n and P. Boch: E l a s t i c
. . . . .
9c. P. M i l l e t , R. S c h a l l e r and W. Beniot: C h a r a c t e r i s t i c
. . . . .
10c. T. Otani, K. Hoshino and T. Kurosawa: Damping c a p a c i t y
. . .
l l c . H. Kawabe and K. Kuwahara: High Damping
. . . . .
12c. G. Cannell i and R. Cantel 1 i : The I n f l u e n c e
. . . . . .
13c. K. Iwasaki: An Anoinalous
. . . . . .
14c. C. D i a l l o , M. Mondino and W. B e n o i t : P r e c i p i t a t i o n
. . .
15c. S. Kiss, F. J. Kedves, I. Z. Harangozo: Grain boundary
. . . . .
TEMPERATURE ('C) TEMPERATURE ('Cl FIG. I TEMPERATURE DEPENDENCE OF a AND v IN A VAPOR-LlaUIO PHASE
TRANSITION ( X E N O N ) (REF. 6 )
FIG. 3 TEMPERATURE DEPENDENCE OF a IY A FERROELECTRIC PHASE TRANSITION ( U 0 2 P 0 4 ) (REF 8
F I B . 2 TEMPERATURE DEPENDENCE OF a A N J v IN A N ANTIFERROMAG- NETIC PHASE TRANSITION (RbMnF,) (PE?. 7 )
FIG. 4
STRENGTH OF SNOEK EFFECT DURING ISO- . T H E R M A L PRECIPITA- T I O N OF Fe3N I N IRON (REF. 9 )
JOURNAL DE PHYSIQUE
I " " I " " '
/ /
FIG. 5. - L / / J INVERSE OF THE STRENGTH OF
"..I/(d7" j GORSKY EFFECT VS TEMPERA- TURE NEAR T H E a ' - a TR4N- S l T l O N TEMPERATURE I N Nb-H (REF. 10)
0 '
400 450 500 550
T ( K )-
1.5
1r---r---r-
FIG. 6
STRENGTH OF ZENER EFFECT FOR VARIOUS HYDROGEN CONTENTS I N Pd - H (Ref II )
T I ' K ) r ( * c )
FIG. 7 R E L A X A T I O N DUE TO DISLOCA- B RELAXATION OUE TO THC T I O N - H COMPLEXES PRODUCED MOTION OF TWINS PRODUCE0 BY HYORIDE P R E C I P I T A T I O N AT B Y T H E fcc
-
f c t2 3 0 L (REF. 12) H A R T E N S I T I C T R 4 N S F O R M I - T I O N ( R E F 181
