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DIFFUSION AND AGING IN Cu Fe ALLOYS
P. Clark, S. Campbell
To cite this version:
P. Clark, S. Campbell. DIFFUSION AND AGING IN Cu Fe ALLOYS. Journal de Physique Colloques,
1979, 40 (C2), pp.C2-613-C2-615. �10.1051/jphyscol:19792213�. �jpa-00218593�
JOURNAL DE PHYSIQUE
Colloque C2, supplkment au n 3, Tome
40,mars 1979, page C2-6 13
DIFFUSION AND AGING IN
- Cu F eALLOYS
P.E. C l a r k and S . J . campbell*
Department of Physics, Monash University, Clayton, Vie.
3168,Australia.
' ~ e ~ a r t m e n t o f Physics, Faculty o f Military Studies, University o f New South Wales, Royal Military College, Dwltroon,
A. C. T. 2600,Australia.
R6sum6.- La s p e c t r o s c o p i e M'dssbauer s ' e s t montree u t i l e d a n s l e s 6 t u d e s q u a n t i t a t i v e s d e l a d i f f u - . s i o n du f e r d a n s l e s a l l i a g e s -e 2 l a t e m p d r a t u r e ambiante a i n s i que d a n s l ' a n a l y s e q u a l i t a t i v e du p r o c e s s u s d e r e c u i t aux h a u t e s t e m p d r a t u r e s .
Le s p e c t r e o b t e n u dynamiquement 2 400°C a p e r m i s 1 ' Q t u d e e n d e t a i l du developpement des p r 6 c i p i t Q s y-Fe d a n s les a g r e g a t s de Fe.
A b s t r a c t . - M'dssbauer s p e c t r o s c o p y h a s proved of v a l u e b o t h i n q u a n t i t a t i v e s t u d i e s of i r o n d i f f u - s i o n i n G F e a l l o y s a t room t e m p e r a t u r e and i n q u a l i t a t i v e a n a l y s i s o f t h e a g i n g p r o c e s s e s a t h i g h e r t e m p e r a t u r e . S p e c t r a o b t a i n e d d y n a m i c a l l y a t 4 0 0 ' ~ have e n a b l e d t h e development of y-Ee p r e c i p i t a t e s from Fe c l u s t e r s t o b e s t u d i e d i n d e t a i l .
T h e r e a r e s e v e r a l s i t u a t i o n s i n which ~ Z s s b a u e r s p e c t r o s c o p y may b e used t o s t u d y d i f f u s i o n a l pro- c e s s e s i n s o l i d s . I n t h e most g e n e r a l c a s e , a t o m i c d i f f u s i o n a t h i g h t e m p e r a t u r e s i s o b s e r v e d a s t h e o n s e t o f l i n e b r o a d e n i n g when t h e mean time o f s t a y of a n atom on a l a t t i c e s i t e a p p r o a c h e s t h e mean n u c l e a r l i f e t i m e 111. The l o w e s t t e m p e r a t u r e a t which t h i s t e c h n i q u e may b e u s e d depends on b o t h t h e Mijssbauer i s o t o p e and t h e m a t r i x , b u t i s t y p i - c a l l y a b o u t 9 5 0 ' ~ f o r 5 7 ~ e i n Cu. I f t h e M'dssbauer r e s o n a n c e i s e x t r e m e l y s h a r p i t i s sometimes p o s s i - b l e t o o b s e r v e f l u c t u a t i o n s i n t h e s - e l e c t r o n den- s i t y a t t h e Miissbauer n u c l e u s c a u s e d by t h e motion of t h e d i f f u s i n g s p e c i e s ; t h i s method h a s r e c e n t l y b e e n used by Heidemann e t a l . 1 2 1 t o s t u d y i n t e r - s t i t i a l d e u t e r i u m i n Ta m e t a l . A t h i r d s i t u a t i o n
o u r a p p r o a c h i s f u l l y q u a n t i t a t i v e and y i e l d s a va- l u e f o r a p a r a m e t e r c l o s e l y r e l a t e d t o t h e d i f f u - s i v i t y . At h i g h e r t e m p e r a t u r e s , a t p r e s e n t , o n l y q u a l i t a t i v e c o n c l u s i o n s may b e drawn.
P r e v i o u s s t u d i e s of d i l u t e a l l o y s of i r o n i n c o p p e r 1 4 1 have s e r v e d t o d e l i n e a t e t h e Mbssbauer parame- t e r s a s s o c i a t e d w i t h i s o l a t e d i r o n atoms and s m a l l c l u s t e r s of i r o n atoms. We have re-examined s e v e r a l samples which were p r e p a r e d i n t h e a s - r o l l e d (AR) o r f a s t - q u e n c h e d (FQ) s t a t e s and i n i t i a l l y examined a b o u t f i v e y e a r s ago 141. As e x p e c t e d , e a c h sample had aged a t room t e m p e r a t u r e ; t h i s was e v i d e n c e d a s a n i n c r e a s e i n t h e component due t o c l u s t e r e d i r o n atoms a t t h e e x p e n s e o f t h e i s o l a t e d i r o n . The main changes f o r specimens c o n t a i n i n g 0.05
-
2.71 a t . % Fe a r e summarized i n t a b l e I.a r i s e s 1 3 1 f o l l o w i n g t h e f o r m a t i o n of i m p u r i t y -
T a b l e I : Room t e m p e r a t u r e a g i n g i n w e i n t e r s t i t i a l complexes when t h e Debye-Waller f a c t o r
of one component of t h e s p e c t r u m shows a r a p i d de- c r e a s e i n a narrow t e m p e r a t u r e i n t e r v a l s i g n i f y i n g t h e o n s e t o f c a g e d i f f u s i o n .
We r e p o r t h e r e t h e a p p l i c a t i o n o f ~ ' d s s b a u e r t e c h n i - q u e s i n a s t u d y of t h e d i f f u s i o n a l p r o c e s s e s l e a d i n g t: t h e f o r m a t i o n of c l u s t e r s and p r e c i p i t a t e s o f i r o n atoms i n a c o p p e r m a t r i x . The approach we have a d o p t e d c a n be. a p p l i e d t o any m e t a l l u r g i c a l s y s t e m which i s s u b j e c t t o c l u s t e r f o r m a t i o n and i s p a r t i -
c u l a r l y u s e f u l i n t h a t i t c o v e r s t h e t e m p e r a t u r e r a n g e from room t e m p e r a t u r e upwards. F o r tempera- t u r e s s u f f i c i e n t l y low t h a t t h e G s s b a u e r s p e c t r u m i s c o l l e c t e d i n a time v e r y much s h o r t e r t h a n t h e t i m e between hops of an i n d i v i d u a l d i f f u s i n g atom
I
Estimated hopping rate p (s-')
8.7 x 10-10
10.8 x 10-lo
7.5 * 10-O
3.7 r 10-lO
6.4 10-lo
5.6 x 10-lo
5.9 x 10-lo Nominal
I
Fractional contribution dueconcentration at.X Fe
0.05 AR
0.24 AR
0.26 YQ
0.46 YQ
0.89 YQ
2.12 AR
2.12 FQ
to isolated iron atoms initial area
&to)
0.91
0.86
0.93
0.77
0.59
0.48
0.38
final area
*It)
0.77
0.69
0.81
0.72
0.53
0.43
0.36
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19792213
C2-6
14 JOURNAL DE PHYSIQUEThis t a b l e a l s o c o n t a i n s an e s t i m a t e of t h e minimum hopping r a t e of t h e i s o l a t e d i r o n atoms a s deduced from t h e e x p r e s s i o n
-
*(')x$ ,
where A(0) and A(t)= A(0)
r e p r e s e n t t h e f r a c t i o n a l c o n t r i b u t i o n due t o i s o l a - t e d i r o n atoms i n t h e i n i t i a l and f i n a l s p e c t r a res- p e c t i v e l y . As t h e c o n c e n t r a t i o n dependence of p appears s m a l l , t h e mean v a l u e of
p
%7x10-' s-' w i l l be r e p r e s e n t a t i v e of t h e time s c a l e involved.Bulk d i f f u s i o n s t u d i e s of 5 9 ~ e i n Cu using t r a c e r s e c t i o n i n g techniques /5/ show t h a t t h e d i f f u s i o n c o e f f i c i e n t f o l l o w s an Arrhenius r e l a t i o n s h i p of t h e form D = D exp(-Q/RT) over t h e range 920
-
1350K.A simple e x t r a p o l a t i o n y i e l d s Dz. loe3' cm2 s-I a t room temperature, whereas t h e hopping r a t e obtained from t h e G s s b a u e r d a t a i n d i c a t e s a v a l u e of cmz s-1. We have demonstrated t h a t t h i s gross d i s a - greement can be r e s o l v e d by n o t i n g t h a t t h e ~ G s s b a u e r specimens ( t h i n f o i l s annealed a t 1000°C and quen- ched r a p i d l y ) have a nonequilibrium vacancy concen- t r a t i o n and by allowing f o r t h i s .
From t h e known d i f f u s i o n parameters f o r vacancies i n Cu / 6 / t h e vacancy e q u i l i b r i u m temperature i n the quenched specimens i s c a l c u l a t e d t o be %650K. I r o n d i f f u s e s i n Cu predominantly by a vacancy mechanism / 5 / , and assuming t h a t t h e a c t i v a t i o n energy f o r vacancy formation i n Cu i s temperature independent, t h e ~ Z s s b a u e r value f o r y i e l d s an a c t i v a t i o n ener- gy f o r movement of an i r o n atom a t room temperature of 1.0
+
0.04 eV. T h i s v a l u e i s s i m i l a r t o t h e high temperature bulk d i f f u s i o n r e s u l t of 1.04+
0.01 eV/ 5 / , and thus confirms t h e u s e f u l n e s s of Mijssbauer techniques i n t h e s t u d y of atomic d i f f u s i o n a t low temperatures.
A t h i g h e r aging temperatures, more f r e q u e n t atom movements mean t h a t even s h o r t - t e r m , dynamic MESS- bauer s p e c t r a can d i s c e r n only t h e i n t e g r a t e d r e s u l t of many s e p a r a t e atom movements a s t h e i r o n c l u s t e r s grow. The s p e c t r a l a n a l y s i s t o determine t h e d i f f u - s i v i t y would t h e r e f o r e r e q u i r e a complex t h e o r e t i c a l model. Nonetheless, t h e ~ E s s b a u e r technique h a s s t i l l found a p p l i c a t i o n i n o u t l i n i n g t h e broad f e a t u r e s of t h e aging process.
The d i f f u s i o n a l p r o c e s s e s involved i n t h e formation of l a r g e i r o n c l u s t e r s , and subsequently y-Fe p r e c i - p ' i t a t e s , i n &Fe have been s t u d i e d dynamically i n a 0.89 a t . % Fe sample maintained a t 400°c. The s e r i e s of t e n s p e c t r a o b t a i n e d have been f i t t e d on t h e basis of our e a r l i e r model /4/ i n which a s i n g l e Lorentzian l i n e r e p r e s e n t s a unique atomic environment, such a s i s o l a t e d i r o n atoms o r a y-Fe c o n f i g u r a t i o n of i r o n
atoms, w i t h d o u b l e t s r e p r e s e n t i n g c l u s t e r s of i r o n atoms. Three such d o u b l e t s were found t o be s u f f i - c i e n t , and from t h e s y s t e m a t i c behaviour of t h e i r isomer s h i f t s and quadrupole s p l i t t i n g s t h e y have been i d e n t i f i e d with c l u s t e r s c o n t a i n i n g % 2 , Q 4-5 and 'L 6-7 i r o n atoms r e s p e c t i v e l y . The time develop- ment of t h e v a r i o u s components of t h e Miissbauer s p e c t r a w i t h aging a t 400°C i s shown i n f i g u r e I from which t h e following f e a t u r e s of aging i n &Fe may be noted :
a ) t h e s i n g l e t due t o i s o l a t e d i r o n atoms d e c r e a s e s e x p o n e n t i a l l y w i t h aging time;
b) t h e c o n t r i b u t i o n s of i r o n p a i r s ( d o u b l e t L) and c l u s t e r s of % 4-5 atoms ( d o u b l e t M) d e c r e a s e r a p i - d l y a t f i r s t , and t h e n p e r s i s t a s small components.
c ) t h e decreased c o n t r i b u t i o n from s i n g l e atoms aqd small c l u s t e r s i s matched by an i n c r e a s e i n d o u b l e t N , which corresponds t o c l u s t e r s c o n t a i n i n g % 6-7 atoms ;
d) t h e development a f t e r % 180 min. of t h e s i n g l e t due t o y-Fe o c c u r s , w i t h i n experimental e r r o r , a t t h e same r a t e a s the d e c r e a s e i n doublet N;
e ) t h e p e r s i s t e n c e of d o u b l e t s L and M can be l i n k d w i t h t h e occurrence of y-Fe, s u g g e s t i n g t h a t when a g i n g i s w e l l developed d o u b l e t s L and M t h e n repre- s e n t s u r f a c e atoms of a y-Fe globule / 7 / .
TIME I m~nutcr I
F i g . 1 : Time development of t h e s e p a r a t e components f o r a 0.89
X
Fe i n Cu specimen aged a t 400°C.I t t h e r e f o r e appears t h a t w e ages by s o l u t i o n i r o n atoms combining t o form small c l u s t e r s , t o a limit of % 6 t o 7 atoms. These c l u s t e r s then combi- ne t o form y-Fe g l o b u l e s which r a p i d l y grow i n t o y-Fe p r e c i p i t a t e s .
I n sumrnary, Mijssbauer spectroscopy has been shown
to yield quantitative information on the very slow diffusion processes involved in clustering in S F e alloys at room temperature. The more rapid proces- ses at higher temperatures have been outlined in terms of y-Fe formation by cluster accretion.
References
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Mullen, J.G. and Knauer, R.C., MGssbauer Effect
Methodology, vol 5, (Plenum Press, New York) 1970, p 197.
121
Heidemann, A., Wipf, H., and Wortmann, G., Hyp. Int.,i
(1978) 844./31 Vogl, G., Mansel, W., Petry, W,, and ~rgger,
V., Hyp. Int.,
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Clark, P.E. and Liddell, P.R., J. Phys.
F
:Metal Phys., 2 (1972) L114; Campbell, S.J. and Clark,P.E.
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:~ e t a i ~ h y s . (1974) 1073.
/5/
Mullen, J.G., Phys. Rev. 121
(1961) 1649.161 Shewmon, P.G., Diffusion in Solids (McGraw Hill, New York) 1963, p 66.
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