HAL Id: jpa-00221005
https://hal.archives-ouvertes.fr/jpa-00221005
Submitted on 1 Jan 1981
HAL is a multi-disciplinary open access
archive for the deposit and dissemination of
sci-entific research documents, whether they are
pub-lished or not. The documents may come from
teaching and research institutions in France or
abroad, or from public or private research centers.
L’archive ouverte pluridisciplinaire HAL, est
destinée au dépôt et à la diffusion de documents
scientifiques de niveau recherche, publiés ou non,
émanant des établissements d’enseignement et de
recherche français ou étrangers, des laboratoires
publics ou privés.
OF THE ANELASTIC PROPERTIES OF
MULTI-PHASE SYSTEMS
F. Mazzolai
To cite this version:
JOURNAL DE PHYSIQUE
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
-
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
-
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
-
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 .
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
-
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-
t h eC '
reason 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
-
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.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
-
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
-
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*.
-
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 ea 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.
(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
<<
1 i s n o t exponential b u t r a t h e r o f t h e t Y Pe2
a = w ;
(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
<<
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 .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
-
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 by0'
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
6
(assuming ~ = 1 0 - ~ ~ c m ~ / s e c , ~ ~ = 1 0 - ~ , Ko/Kw=l, T cones o u t t o be 10 sec). 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 small3
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 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 ddynamical 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
-
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
-
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).
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 decreasein
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),
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.
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 ei 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 .
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
REFERENCES
P. F. Gobin and 0. M e r c i e r : This Conference.
C. W. Garland: Physical k o u s t i c s Vol. V I I (P. W. Masor, ed.), Pcademic Press, N.Y. (1970).
A. S. Nowick and 6. S. Berry: A n e l a s t i c R e l a x a t i o n i n C r y s t a l l i n e S o l i d s , Chapter 16, Academic Press, N.Y. (1972).
W. Rewhald: Mv. Phys. 22, 721 (1973).
6.
L u t h i , T. J. Moran and R. J. P o l l i n a : J. Phys. Chem. S o l i d s , 31, 1741 (1970).A. G. Chynoweth and W. G. Schneider: J. Chem. Phys., 20, 1777 (1952).
6. Golding: Phys. Rev. L e t t e r s , 20, 5 (1968).
E. L i t o v and Uehling : Phys. Rev. L e t t e r s , 21, 809 (1968). C. U e r t :
J.
Appl. Phys., 20, 943 (1949).J. Tretkowski : J u l - B e r i c t
,
Jul-1049-FF (1974).F. M. Mazzolai, P. G. Bordoni and F. A. Lewis: J. Phys. F: Metal Phys.,
11, 337 (1981).
G. C a n n e l l i and F. M. Mazzolai: Nuovo Cimento, 648, 171 (1969).
C. A. Wert, D. 0. Thoinpson and 0. Buck:
J.
Phys. Chern. Sol. 31, 1973 (1970).G. Ferron, M. Q u i n t a r d and J. de Fouquet: Nuovo Cimento, 336, 76 (1976). 0. Yoshinari, M. Koiwa, H. Asano and M. Hi rabayashi : I n t e r n a l F r i c t i o n and U l t r a s o n i c A t t e n u a t i o n i n Sol i d s (R. R. H a s i g u t i ed.), U n i v e r s i t y o f Tokyo Press, 495 (1977).
F. M. Mazzolai, P. G. Bordoni and F. A. Lewis: J. Phys. F: Metal Phys., 10, 781 (1980).
M. E. de Morton: J. Pppl. Phys., 40, 208 (1969). J. W. C h r i s t i a n : J. I n s t . Metals, 93, 546 (1965).
M. Anano, T. Matsumoto and Y. Sasaki: S c r i p t a Met., 7, 371 (1973).
M. h a n o and H. K. Birnbaum: I n t e r n a l F r i c t i o n and Ultrasound A t t e n u a t i o n i n S o l i d s (R. R. H a s i g u t i ed.) U n i v e r s i t y o f Tokyo Press, p. 323 (1977).
L. D. Landau and I. M. K h a l a t n i k o v : Dokl. Akad. Nauk USSR 96, 469 (1954).
I. A. Yakovlev and I. S. V e l i c h k i n a : Sov. Phys. Usn. 63, 5,552 (1957).
1.
P. Kadanoff, W. Gotze, D. Hamblem, R. Hecht, E.A.S. Lewis, V. V. Pal Ciavskas, M: Rayl, J. S w i f t , D. Aspnes and J. Kane: Rev. Mod. Phys; 39, 395 (1967).A. P. Levanyuk: S o v i e t Phys. JETP, 22, 901 (1966).
F. Schwabl, Phys. Rev. B 7, 2038 (1973).
G. E. Laramore and L. P. Kadanoff: Phys. Rev. 187, 619 (1969).
N. A. K r i v o g l az : Fiz. Metal. Netal loved. 10 Vol. 4, 497 (1960).
G. Schoeck: Phys. Stat. Sol. 32, 651 (1969). J. D. Eshelby: Proc. Roy. Soc. A 241, 376 (1957).
A. C. Damask and A. S. Nowick: J. Appl. Phys. Stat. Sol. 32, 31 (1961). G. Schoeck and E. Bisogni: Phys. S t a t . Sol. 32, 31 (1969).
R.
E. Miner, T. L. Wilson and J. M. Jackson: Trans. AIME, 245, 1375 (1969).J. M e r l i n , P. Merle, F. Fouquet and J. M. P e l l e t i e r : S c r i p t a Met. 12, 227 (1978).
C. W. Owen and T. E. S c o t t : S c r i p t a Met., 13, 923 (1973).
G.
Ferron and M. Q u i n t a r d : S c r i p t a Met., 13, 923 (1973).$. Gahr, M. L. Grossbeck and H. K. Birnbaum: k t a . Met., 25, 125 (1977). K. N u t t a l l : J. I n s t . Metals: 99, 266 (1971).
A. S. Nowick: J. Pppl. Phys., 22, 925 (1951).
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.
.
.
.
.
.
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
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