59Fe TRACER SELF-DIFFUSION IN AMORPHOUS Fe-Ni-B ALLOYS

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59Fe TRACER SELF-DIFFUSION IN AMORPHOUS

Fe-Ni-B ALLOYS

J. Horvàth, K. Pfahler, W. Ulfert, W. Frank, H. Mehrer

To cite this version:

JOURNAL DE PHYSIQUE

CoHoque C8, suppl6rnent au n012, Tome 46, dCcembre 1985 page C8-645

5 9 ~ e TRACER S E L F - D I F F U S I O N I N AMORPHOUS F e - N i - B ALLOYS

J . Horvhth, K . P f a h l e r , W. U l f e r t , W. Frank and H. ~ e h r e r +

Max-PZanck-Institut fiir MetaZZforschung, I n s t i t u t fur Physik, and Universitat S t u t t g a r t , I n s t i t u t fur Theoretische und Angewandte Physik, P.O. Box 800 665,

0-7000 S t u t t g a r t , F.R.G.

' ~ n i v e r s i t a t Miinster, I n s t i t u t fur MetaZZforschung, Domagkstrasse 75,

0-4400 Miinster, F.R. G.

RESUME

-

La d i f f u s i o n de ~ e ~ ~ dans l e s a l l i a g e s amorphes Fe4oNi40Bz0 e t -41Bl8 a @t@ mesur6e p a r l a t e c h n i q u e des r a d i o t r a c e u r s associee

a

un

sectionnement p a r bombardement i o n i q u e . L ' i n f l u e n c e de l a r e l a x a t i o n s t r u c - t u r a l e , e t u d i e e e n d 6 t a i 1 , correspond 2 une decroissance de l a d i f f u s i v i t e v e r s une l i m i t e c a r a c t e r i s t i q u e de l a temperature de d i f f u s i o n . Ceci suggPre l ' e x i s t e n c e d ' u n @ t a t amorphe m e t a s t a b l e b i e n d e f i n i q u i p e u t e t r e obtenu p a r r e c u i t thermique.

ABSTRACT- The s e l f - d i f f u s i o n o f 5 9 ~ e i n t h e amorphous a l l o y s Fe,oNi,oB20 and FeblNi ,lB was i n v e s t i g a t e d by means o f t h e r a d i o t r a c e r t e c h n i q u e i n combi- n a t i o n w i t h ion-beam s p u t t e r i n g f o r s e r i a l s e c t i o n i n g . F o r t h e f i r s t t i m e t h e i n f l u e n c e of s t r u c t u r a l r e l a x a t i o n s was s t u d i e d i n d e t a i l . I t was found t h a t d u r i n g i s o t h e r m a l a n n e a l i n g i n t h e amorphous s t a t e a r e l a x a t i o n - i n d u c e d decrease o f t h e d i f f u s i v i t y towards a v a l u e which i s c h a r a c t e r i s t i c o f t h e d i f f u s i o n temperature t a k e s place. T h i s i n d i c a t e s t h e e x i s t e n c e o f a w e l l - d e - f i n e d m e t a s t a b l e amorphous s t a t e which may be a t t a i n e d by thermal annealing. I. INTRODUCTION

D i f f u s i o n i n amorphous a l l o y s , r e c e n t l y reviewed by Limoge, Brgbec, and Adda [ I ] and Cantor and Cahn [2], i s o f i n t e r e s t f r o m v a r i o u s p o i n t s o f view. Many t e c h n o l o g i - c a l l y s i g n i f i c a n t p r o p e r t i e s o f these m a t e r i a l s such as s t r u c t u r a l r e 1 a x a t i o n s , i n - duced a n i s o t r o p y , e m b r i t t l e m e n t , and c r y s t a l 1 iz a t i o n a r e c o n t r o l l e d by t h e d i f f u s i v - i t i e s o f t h e a l l o y components. Of t h e o r e t i c a l importance a r e t h e e f f e c t s o f t h e spat- i a l v a r i a t i o n s o f t h e d i f f u s i o n a l jump d i s t a n c e and o f t h e d i f f u s i o n b a r r i e r h e i g h t .

The f a c t t h a t so f a r o n l y a small number o f r e l i a b l e d i f f u s i o n data on m e t a l l i c g l a s s e s e x i s t i s due t o two m a j o r d i f f i c u l t i e s t o which d i f f u s i o n s t u d i e s on t h e s e m a t e r i a l s a r e s u b j e c t e d : ( a ) The temperature i n t e r v a l w i t h i n which d i f f u s i o n e x p e r i - ments may be performed i s i n many cases h a r d l y l a r g e r t h a n 100 K, s i n c e on t h e h i g h - t e m p e r a t u r e s i d e i t i s l i m i t e d by t h e c r y s t a l l i z a t i o n and on t h e low-temperature s i d e by t h e smallness of t h e d i f f u s i v i t i e s .

( p )

I n t h e amorphous s t a t e t h e d i f f u s i v - i t i e s may change as a f u n c t i o n o f t h e a n n e a l i n g t i m e ue t o s t r u c t u r a l r e l a x a t i o n s .

5%

I n t h i s work t h e s e l f - d i f f u s i o n o f r a d i o a c t i v e e t r a c e r atoms i n

Fe,oNi40B20 and FeklNi 41B18 produced by me1 t s p i n n i n g a t Vacuumschmelze, Hanau, was i n v e s t i g a t e d i n t h e temperature range between 512 K and 643 K. By combining t h e r a - d i o t r a c e r method w i t h t h e i o n - b e a m - s p u t t e r i n g t e c h n i q u e i t was p o s s i b l e t o measure e x t r e m e l y small d i f f u s i o n c o e f f i c i e n t s , viz., down t o 8.7 x m2s-l. I n c o n t r a s t t o p r e v i o u s i n v e s t i g a t i o n s on t h e d i f f u s i o n ( o f m o s t l y f o r e i g n atoms) i n amorphous a l l o y s , i n t h e p r e s e n t s t u d i e s s p e c i a l a t t e n t i o n was p a i d t o t h e p r e p a r a t i o n of t h e specimens and t o t h e e f f e c t o f r e l a x a t i o n processes o c c u r r i n g d u r i n g pre- and d i f f u s i o n - a n n e a l i n g t r e a t m e n t s on t h e d i f f u s i v i t y .

11. EXPERIMENTAL

C8-646 JOURNAL

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c a l c l o t h . I n t h i s way s u r f a c e d e f e c t s were avoided, which was checked by l i g h t o r scanning e l e c t r o n microscopy. The decent p o l i s h i n g t r e a t m e n t i s a p r e r e q u i s i t e o f mea- s u r i n g a c c u r a t e l y t h e v e r y low d i f f u s i v i t i e s by means o f t h e r a d i o t r a c e r technique, which, t h u s a p p l i e d , r e p r e s e n t s t h e most s e n s i t i v e and most d i r e c t method. The S9Fe r a d i o t r a c e r s were d e p o s i t e d e l e c t r o c h e m i c a l l y i n an about 1 nm t h i n s u r f a c e l a y e r . Both pre-anneals and d i f f u s i o n anneals were c a r r i e d o u t i n evacuated q u a r t z ampoules a t about 0.2 mPa. The n o n - c r y s t a l l i n i t y o f t h e specimens was t e s t e d b e f o r e and a f t e r t h e d i f f u s i o n anneals by c o e r c i v e - f i e l d measurements. I n p r e v i o u s i n v e s t i g a t i o n s i t has been found t h a t i n many f e r r o m a g n e t i c amorphous a l l o y s t h e c o e r c i v e f i e l d i s v e r y s e n s i t i v e t o t h e o n s e t o f c r y s t a l l i z a t i o n [3,4]. A d d i t i o n a l l i g h t and scanning- e l e c t r o n - m i c r o s c o p y s t u d i e s served t o cross-check t h e amorphism o f t h e specimens.

I n t h e measurements o f t h e c o n c e n t r a t i o n p r o f i l e s o f t h e i n - d i f f u s e d t r a c e r s m i c r o s e c t i o n i n g was done by ion-beam s p u t t e r i n g . T y p i c a l s e c t i o n t h i c k n e s s e s were 2 nm. The s p u t t e r i n g r a t e s were c a l c u l a t e d from t h e mass l o s s d u r i n g s p u t t e r i n g ( a b o u t 60 llg) and f r o m t h e area and volume d e n s i t y o f t h e specimens. The m a t e r i a l r e - moved by s p u t t e r i n g was c o l l e c t e d s e c t i o n w i s e on M y l a r f o i l s . The r a d i o a c t i v i t y o f each s e c t i o n was determined by means o f a G e ( L i ) - y spectrometer o r a l i q u i d - s c i n t i l l a t i o n counter. F u r t h e r e x p e r i m e n t a l d e t a i l s a r e g i v e n i n [5-71. 111. RESULTS

F i g s . 1 and 2 show t y p i c a l 59Fe p e n e t r a t i o n p r o f i l e s . I n these f i g u r e s t h e spe- c i f i c a c t i v i t y C o f t h e r a d i o t r a c e r s i n t h e removed l a y e r s ( f u l l c i r c l e s ) , which i s p r o p o r t i o n a l t o t h e t r a c e r c o n c e n t r a t i o n , i s p l o t t e d as a f u n c t i o n o f x2/td, where x and t d mean t h e o r i g i n a l d i s t a n c e o f t h e l a y e r s f r o m t h e t r a c e r - c o v e r e d s u r f a c e and t h e d i f f u s i o n time, r e s p e c t i v e l y . A1 1 p r o f i l e s match w e l l t h e s o - c a l l e d t h i n - f i l m s o l u t i o n

o f F i c k ' s second law, _{T T}

C = C o ( n D t d ) - ' I 2 exp(-x2/4D t d ) .

(1)

-

T

I n ( 1 ) D denotes t h e t r a c e r d i f f u s i o n c o e f f i c i e n t and Co t h e t o t a l amount o f t r a c e r atoms d e p o s i t e d on t h e surface. The d i f f e r e n t slopes o f t h e s t r a i g h t l i n e s i n F i g s . 1 and 2 i n d i c a t e t h a t DT depends on t h e a n n e a l i n g time, so t h a t t h e values o f t h e d i f f u s i v i t y deduced from t h e s e p l o t s must be i d e n t i f i e d w i t h t h e t i m e average

The t i m e dependence o f t h e t r a c e r d i f f u s i v i t y was determined a t 573 K, 593 K, and 613 K on Fe40Ni40B20 ( F i g . 3 ) and a t 613 K on Fe41Ni41B18 (Fig.4). Since i n t h e s e s e r i e s o f measurements t h e specimens had been pre-annealed i n t e n t i o n a l l y a t t h e d i f f u s i o n temperatures f o r d i f f e r e n t times t and d i f f u s e d f o r d i f f e r e n t times td, i n F i g s . 3 and 4 t h e CDT) values ( f u l l symboys) taken f r o m t h e p e n e t r a t i o n p r o f i l e s were p l o t t e d versus t z tp + td/2. The s o l i d curves may h e l p t o v i s u a l i z e t h e depend- ences o f <DT) on t h i s e f f e c t i v e anneal i n g t i m e a t g i v e n temperatures. From these d a t a i n s t a n t a n e o u s values o f t h e d i f f u s i o n c o e f f i c i e n t , D T ( t d ) , were d e r i v e d w i t h t h e a i d o f t h e r e l a t i o n s h i p f o l l o w i n g from (21,

D T ( t d ) = d ( <DT> t d l / d t d , ( 3 )

-

and d i s p l a y e d i n F i g . 3 as dashed curves. Note t h a t f o r t h e s e ~ ' ( t d ) curves t h e t i m e t g i v e n on t h e abscissae i s i d e n t i c a l w i t h td. U n f o r t u n a t e l y , t h e r e l i a b i l i t y o f t h e D T ( t d ) curves i s f a i r l y low, i n p a r t i c u l a r a t s h o r t d i f f u s i o n times a t which t h e t r a c e r p e n e t r a t i o n depths are o f t h e o r d e r o f a few nm o n l y and a t which t o o small a number o f p r o f i l e s have been measured. I r r e s p e c t i v e o f these d e f i c i e n c i e s t h e data p r e s e n t e d i n Figs. 3 and 4 show t h a t i n Fe40Ni4&320 and Fe4,Ni4,B18 t h e d i f f u s i v i t y of

59Fe decreases r a p i d l y towards a p l a t e a u v a l u e D R, which depends on t h e d i f f u s i o n temperature. A f u r t h e r decrease o f t h e d i f f u s i v i t y i n a l a t e r s t a t e o f annealing, which i s due t o t h e onset o f c r y s t a l l i z a t i o n [5-81, has been o m i t t e d i n Figs. 3 and 4.

F i g . 1. 5 9 ~ e d i f f u s i o n p r o f i l e s i n F i g . 2. 5 9 ~ e d i f f u s i o n p r o f i l e s i n m 0 B 2 0 a f t e r d i f f u s i o n anneals W 1 B l 8 a f t e r d i f f u s i o n anneals a t

a t 593 K f o r the times given. One 613 K f o r the times given. Two specimens specimen was pre-annealed a t 593 K were pre-annealed a t 613 K f o r t = 4 h o r f o r tp = 30 h. 12 h, r e s p e c t i v e l y . P t [ h l 30 1 0 - ~ 0

-

613 K

-

_.

_U) "1 593 K E u +A 10-2'

c

l

573 K v I I I I I I I I 0 20 40 60 80

.

-

.

-

I I I I I I I I I I I I I 0 200 LOO 600 800 0 5 10 15 2 0 t [ h l t t h l

Fig. 3. Time dependence o f 5 y ~ e s e l f - Fig. 4. Time dependence o f the 5 9 ~ e s e l f - -on c o e f f i c i e n t s i n Fe40Ni40B2p -on c o e f f i c i e n t i n Fe41Ni41B18 a t a t 573 K, 593 K, and 613 K ( f o r d e t a i l s 613 K ( f o r d e t a i l s see t e x t ) .

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r = r o exp(HR/kT) ( 4 )

f o r Fe4,Ni 40B20 we estimated TO = 10- s and the r e l a x a t i o n enthalpy HR = 1 eV. From the preceding discussion i t i s c l e a r t h a t d i f f u s i v i t i e s measured i n the re- gime o f r e l a x a t i o n , i n which they are s t r o n g l y time-dependent (Figs. 3 and 41, may s c a t t e r considerably, and indeed t h i s i s the case f o r many previous d i f f u s i v i t y data [2 Even more important i s t o r e a l i z e t h a t i t i s p h y s i c a l l y meaningless t o determine t h e temperature dependence o f a d i f f u s i v i t y i n an unrelaxed amorphous a l l o y , since d u r i n g r e l a x a t i o n the system passes i l l - d e f i n e d , unstable non-equilibrium states. Hence, i n t h e Arrhenius p l o t s o f Fig. 5 only DTR values measured on specimens which had been re1 axed by pre-anneal i n g are included. Obviously, i n both a1 1 oys i n v e s t i g a t e d DTR f o l l o w s an Arrhenius law,

T D~ = D: exp (-H I~T).

R ( 5 )

I n Fe40Ni40B20 th e pre-exponential f a c t o r , D:, and the t r a c e r d i f f u s i o n enthalpy, HT are equal t o 2.7 x m2s- and 2.4 eV, r e s p e c t i v e l y ; f o r Fe41Ni41B18 we found DT0 = 1.1 x m2s-I and HT = 2.3 eV.

I V . DISCUSSION

The r e s u l t s r e p o r t e d i n Sect. I 1 1 l e a d t o the f o l l o w i n g p i c t u r e o f 5 9 ~ e s e l f - d i f f u s i o n i n amorphous F e 4 0 N ~ 4 p B 2 0 and Fe41Ni41B18. The f a c t t h a t t h e decrease o f the d i f f u s i v i t y d u r i n g t h e t r a n s i t i o n from t h e as-quenched t o the r e l a x e d amorphous s t a t e (Figs. 3 and 4) i s accompanied by an increase o f the volume d e n s i t y [9], i.e. by e l i - mi n a t i o n o f excess f r e e volume, suggests t h a t the enhancement o f the d i f f u s i v i t y i n t h e as-quenched s t a t e over t h a t i n the r e l a x e d s t a t e a r i s e s from i n d i r e c t d i f f u s i o n o f t h e t r a c e r atoms v i a excess quasi-vacancies. The e l i m i n a t i o n o f these vacancies dur- i n g r e l a x a t i o n appears t o take place p r e f e r e n t i a l l y v i a t h e i r m i g r a t i o n t o t h e spe- cimen surfaces, as i n d i c a t e d by t h e magnitude o f the pre-exponential f a c t o r TO i n (4). The a c t i v a t i o n enthalpy o f r e l a x a t i o n , HR, may t h e r e f o r e be i d e n t i f i e d w i t h the m i g r a t i o n enthalpy o f quasi-vacancies i n the as-quenched s t a t e .

The observation t h a t the d i f f u s i o n c o e f f i c i e n t i n pre-annealed specimens i s equal t o DTR from the very beginning o f a d i f f u s i o n anneal even i f the d i f f u s i o n temperature

I I

r

!;; ;l ri ne;; do;iui;

1

;l;

1

[K] [103s] [K] [103s]

Table 1. Pre-annealing and d i f f u s i o n data on FekONi ,,B2,.

Fig. 5. Arrhenius diagrams o f the 5 9 ~ e ~ f f u s i o n c o e f f i c i e n t s , DTR i n

d i f f e r s from the pre-annealing temperature may have t h e f o l l o w i n g reasons: ( i ) I n pre- annealed specimens atomic quasi-defects ( = quasi-vacancies and/or q u a s i - s e l f -

i n t e r s t i t i a l s ) are present i n concentrations which are temperature-independent and thus c h a r a c t e r i s t i c o f the relaxed amorphous s t a t e . I f the t r a c e r atoms undergo i n d i r e c t d i f f u s i o n v i a these defects, HT i s i d e n t i c a l w i t h the m i g r a t i o n enthalpy o f t h e dominat- i n g quasi-defect species i n the r e l a x e d s t a t e . ( i i ) I n r e l a x e d specimens quasi-

d e f e c t s are present i n q u a s i - e q u i l i b r i u m concentrations. A f t e r a temperature change w i t h i n the re1 axed state, the new e q u i l i b r i um i s e s t a b l i s h e d undetectably f a s t v i a quasi-defect emission from o r absorption a t r e s i d u a l unrelaxed regions s u r v i v i n g up t o c r y s t a l l i z a t i o n . Then i n the case o f i n d i r e c t t r a c e r d i f f u s i o n HT means the sum of t h e formation and m i g r a t i o n enthalpy o f t h e dominating quasi-defect species. ( i i i ) The t r a c e r atoms d i f f u s e w i t h o u t the a i d o f quasi-defects (site-exchange o r d i r e c t quasi- i n t e r s t i t i a l mechanism), and HT i s t h e i r m i g r a t i o n enthal py. - A t present a d i s c r i m i - n a t i o n between the a l t e r n a t i v e s ( i ) t o ( i i i ) i s n o t possible.

As demonstrated c o n v i n c i n g l y i n t h i s work, the 59Fe d i f f u s i o n i n FebpNi 4oB20 and Fe4,Ni4,B,, i s c o n t r o l l e d by unique d i f f u s i o n e n t h a l p i e s HT over t h e e n t i r e ranges o f d i f f u s i o n temperatures i n v e s t i g a t e d , and t h e values o f D ~ , are by two orders o f ma- g n i t u d e l a r g e r than i n usual c r y s t a l l i n e metals. These observations become understand- a b l e i f the elementary d i f f u s i o n a l jumps and/or the formation o f quasi-defects i n - v o l v e the c o l l e c t i v e motion o f several atoms [7,10]. I n a r e c e n t study o f the 59Fe t r a c e r s e l f - d i f f u s i o n i n Fe,$i over a wide Zemperature regime (551 K

-

783 K)

[ll] both a r e l a x a t i o n e f f e c t and a unique d i f f u s i o n enthalpy (2.1 eV) were observ- ed, too, whereas D~~ (4.6 x m2s-,I was found t o be comparable t o the values i n t y p i c a l c r y s t a l l i n e metals.

The d i f f u s i o n i n Fe40Ni40B20 has been i n v e s t i g a t e d f o r t h r e e more elements, viz., P[8], Au[12], and B[13]. Whereas the d i f f u s i v i t i e s o f P and Au are s i m i l a r t o t h a t o f Fe, B d i f f u s e s f a s t e r by two orders o f magnitude. This may i n d i c a t e t h a t - f r o m the mechanisms ( i t o ( i i i ) expected t o occur i n amorphous a l l o y s - f o r Fe, P, and Au the same mechanism operates whereas B d i f f u s e s v i a another one. Concerning t h e r e l a x - a t i o n e f f e c t , f o r P t h e evidence f o r such a phenomenon was l e s s c l e a r than f o r Fe. T h i s may be due t o the f a c t t h a t a t very low d i f f u s i v i t i e s t h e i m p l a n t a t i o n technique, which had t o be a p p l i e d t o study the d i f f u s i o n o f P, does n o t reach the h i g h

accuracy o f the method used f o r Fe. The studies on B d i f f u s i o n were done e x c l u s i v e l y on pre-annealed specimens [13]. I n t h e case o f Au no d i f f e r e n c e was found between t h e d i f f u s i o n i n as-quenched and pre-annealed specimens [12]. Provided ( 4 ) i s a p p l i c a b l e t o [ 1 2 ] and [13], i n these experiments the annealing times have been too s h o r t f o r a l l o w i n g t h e specimens t o reach the r e l a x e d amorphous state.

The authors wish t o thank Professor Dr. H. Kronmuller f o r h i s i n t e r e s t i n t h i s work. F i n a n c i a l support by the Deutsche Forschungsgemeinschaft i s acknowledged. REFERENCES

[I] Y. Limoge, G. Brgbec, and Y. Adda, i n : Dimeta 82 ( D i f f u s i o n and D e f e c t Monograph Series No.71, e d i t e d by F.J. Kedves and D.L. Beke,

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