DIFFUSION MECHANISM OF IRON IN VANADIUM AT HIGH TEMPERATURE

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DIFFUSION MECHANISM OF IRON IN VANADIUM AT HIGH TEMPERATURE

C. Janot, P. Delcroix

To cite this version:

C. Janot, P. Delcroix. DIFFUSION MECHANISM OF IRON IN VANADIUM AT HIGH TEMPERATURE. Journal de Physique Colloques, 1979, 40 (C2), pp.C2-650-C2-653.

�10.1051/jphyscol:19792226�. �jpa-00218607�

JOURNAL DE PHYSIQUE

Colloque C 2 , supplgment au no 3, Tome

40,

mars

1979,

page C2-650

DIFFUSION MECHANISM OF IRON IN VANADIUF? A T H I G H T E M P E R A T U R E

C. J a n o t and P. D e l c r o i x

Laboratoire de Physique du SoZide, FacuZtd des Sciences, C.O.

n o

140, 54037 Nancy Cedes, France.

R6sumd.- On a mesurd l ' d l a r g i s s e m e n t d e s r a i e s d e r d s o n a n c e Massbauer dQ 1 l a d i f f u s i o n atomique, d a n s l e systeme

1

- 5 7 ~ o " , e n t r e 1200°C e t 1600°c, e n u t i l i s a n t une t e c h n i q u e de d d t e c t i o n d e s Clec- t r o n s de c o n v e r s i o n . P a r comparaison d e s r d s u l t a t s a v e c d e s donnges c l a s s i q u e s de d i f f u s i o n macro- s c o p i q u e , il a p p a r a 4 t q u 1 u n m d c a n i s m e b i l a c u n a i r e p o u r r a i t c o n t r i b u e r a u t r a n s p o r t de m a t i s r e au- d e s s u s d e 1450°c.

A b s t r a c t . - The d i f f u s i o n b r o a d e n i n g o f t h e MGssbauer r e s o n a n c e was measured i n a

1

- 5 7 ~ o * s y s t e m o v e r t h e t e m p e r a t u r e r a n g e 1 2 0 0 ~ ~ t o 1600°C u s i n g a n e l e c t r o n c o n v e r s i o n t e c h n i q u e . Comparing Mass- b a u e r d a t a w i t h v a l u e s o f t h e m a c r o s c o p i c d i f f u s i o n c o e f f i c i e n t s u g g e s t s t h e o c c u r e n c e o f a d i v a c a n c y mechanism f o r a t o m i c t r a n s p o r t above 1450°C.

1 . I n t r o d u c t i o n . - S t u d i e s o f d i f f u s i o n i n r e f r a c t o r y BCC rnetals have shown t h a t some o f t h e s e m e t a l s de- v i a t e from t h e s o - c a l l e d "normal d i f f u s i o n behaviour", i n p a r t i c u l a r by t h e a p p e a r a n c e o f n o n - l i n e a r i t y i n t h e A r r h e n i u s p l o t s Log D = f($ I / I / , / 2 / .

Such a n o n - l i n e a r A r r h e n i u s c u r v e f o r s e l f - d i f f u s i o n / 3 / o r i m p u r i t y d i f f u s i o n i n vanadium / 4 / , / 5 / r e s u l t s i n two d i s t i n c t s t r a i g h t l i n e s Log D f (-). T I T h i s s t r i k i n g anomalous f e a t u r e was confirmed by d i f f e r e n t a u t h o r s /6/,/7/,/8/./9/ even i f t h e tem- p e r a t u r e o f t h e ' c r o s s i n g p o i n t and t h e s l o p e s of t h e two s t r a i g h t l i n e s sometimes v a r y s i g n i f i c a n t l y from i n v e s t i g a t o r t o i n v e s t i g a t o r . Among t h e v a r i o u s ex- p l a n a t i o n s o f f e r e d t o a c c o u n t f o r t h e b e h a v i o u r ob- s e r v e d i n vanadium, i m p u r i t y e f f e c t remains t h e most ~ l a u s i b l e one / 6 / a l o n g w i t h c h a n g i n g i n t h e mechariism of a t o m i c t r a n s p o r t .

I n a r e c e n t s t u d y / l o / i t was p o s s i b l e t o measure s i m u l t a n e o u s l y t h e a c t i v a t i o n e n e r g y E: f o r s e l f d i f f u s i o n i n t h e "low" t e m p e r a t u r e r e g i o n (up t o a b o u t 1300°c) and t h e a c t u a l c o n c e n t r a t i o n Ci of i n t e r s t i t i a l i m p u r i t i e s ( 0 , N ,

...

) . T h i s was done i n NMR e x p e r i m e n t s through measurements of s p i n - s p i n r e l a x a t i o n time T2 ( m o t i o n a l n a r r o w i n g e f f e c t ) and o f t h e d i p o l a r T: and q u a d r u p o l a r T: c o n t r i b u t i o n s t o s p i n - l a t t i c e r e l a x a t i o n t i m e ( t h e a s y m p t o t i c s l o - pes of T, and T2 v e r s u s t e m p e r a t u r e g i v e E1 and t h e D a m p l i t u d e o f t h e T: peak i s p r o p o r t i o n a l

tt

^Ci).

Thus, t h e a c t i v a t i o n e n e r g y 'E i n t h e low tempera- t u r e r e g i o n was found t o v a r y from 2.5 eV t o 3 . 2 eV, t h e l a s t b e i n g t h e upper l i m i t o b t a i n e d w i t h pro- g r e s s i v e l y improved sample p u r i t y . T h i s c o n f i r m s t h e s t r o n g i n f l u e n c e o f e x t r i n s i c e f f e c t and s u g g e s t s t h a t , up t o a b o u t 1400°C, s i n g l e v a c a n c i e s a s s o c i a - t e d t o i n t e r s t i t i a l i m p u r i t i e s c o u l d b e t h e d e f e c t s

i n v o l v e d i n t h e mechanism of s e l f - d i f f u s i o n i n vana- dium.

The p u r p o s e of t h i s p a p e r i s t o p r e s e n t MESS- b a u e r d a t a , compared t o d i f f u s i o n c o e f f i c i e n t v a l u e s o b t a i n e d by m i c r o s e c t i o n i n g t e c h n i q u e s / ] I / , i n o r - d e r t o c o n t r i b u t e t o t h e e x p l a n a t i o n of t h e n o n - l i - n e a r b e h a v i o u r i n t h e

1 -

Fe s y s t e m .

2. E x p e r i m e n t a l Method.- Experiments i n t e n d e d t o mea- s u r e t h e d i f f u s i o n b r o a d e n i n g of t h e Massbauer r e s o - n a n c e have b e e n tempted f o r a l o n g t i m e , e s p e c i a l l y i n m e t a l l i c s y s t e m / 1 2 / , / 1 3 / up t o a b o u t 1000°C.

Because of t h e i r h i g h m e l t i n g p o i n t , vanadium b a s e d a l l o y s have t o b e i n v e s t i g a t e d up t o t h e 2000K

r e g i o n and t h i s i s n o t a n e a s y a c h i e v e m e n t , f i r s t t o m a n u f a c t u r e t h e p r o p e r f u r n a c e a b l e t o h e a t a sample and keep c o n s t a n t i t s t e m p e r a t u r e i n s u c h c i r c u m s t a n c e s , second t o c a r r y o u r Massbauer spec- t r o s c o p y i n presumably v e r y low r e c o i l l e s s f r a c t i o n c o n d i t i o n s .

T h i s h a s b e e n overcome by u s i n g :

1) a s p e c i a l f u r n a c e a s d e s c r i b e d i n f i g u r e 1 , b u i l t i n a compact geometry, w i t h an e x t e r n a l double- w a l l f o r c o o l i n g by c i r c u l a t i n g w a t e r , a d i r e c t c u r r e n t low v o l t a g e power s u p p l y , a complex sys- tem f o r r a d i a t i o n s c r e e n i n g , a c y l i n d a r t u n g s t e n r e s i s t o r and two b e r y l l i u m windows ;

2 ) a s o u r c e e x p e r i m e n t geometry w i t h a

-"co*

s o u r c e o f a b o u t 5 4 mCi, o b t a i n e d by e l e c t r o d e p o s i - t i o n f o l l o w e d by a n n e a l i n g i n hydrogen. Thus, t h e sample i s k e p t t h e same f o r a l l s e r i e s o f measu- r e m e n t s , t h a t i s a 1 cm x 1 cm x 2 mm vanadium p o l y c r i s t a l l i n e i n g o t c o n t a i n i n g a b o u t 5 0 ppm o f 5 7 ~ o * and 5 7 ~ e ;

3 ) an e l e c t r o n c o n v e r s i o n t e c h n i q u e w i t h b o t h s t a n - d a r t a b s o r b e r ( p u r e i r o n f o i l o r s t a i n l e s s s t e e l )

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19792226

and d e t e c t o r moved by t h e MEssbauer t r a n s d u c e r ( s e e Fig. 1 ) .

Fig. I : Furnace and ~ s s s b a u e r arrangement.

( I ) Double w a l l f o r c o o l i n g w a t e r , (2) Screen s e t f o r thermic r a d i a t i o n , (3) Berylliumwindows, ( 4 ) Power supply, (5) R e s i s t o r , ( 6 ) Radioactive sample, ( 7 ) Mijssbauer t r a n s d u c e r . (8) E l e c t r o n d e t e c t o r , (9) ~ g s s b a u e r a b s o r b e r . I n such a way, Miissbauer s p e c t r a were measu-

red up t o temperatures never reached b e f o r e . As ty- p i c a l l y shown i n f i g u r e 2, t h e r a t i o of s i g n a l over background i s s t i l l about 2 a t 940 K and 0.10 a t

1824 K w i t h a s t a i n l e s s s t e e l a b s o r b e r , and very n i c e s p e c t r a can be o b t a i n e d up t o 1600 K w i t h a pure i r o n a b s o r b e r .

U n f o r t u n a t e l y , t h e d i f f u s i o n broadening mea- surements had t o be r e s t r i c t e d t o only a few v a l u e s of the temperature i n t h e narrow range 1473 K t o

1 8 2 4 ' ~ because of unmeasurable broadening a t lower temperature and d r a s t i c e v a p o r a t i o n of t h e s o u r c e . The d i f f u s i o n broadenings AT were d i r e c t l y deduced from t h e l i n e widths and a r e given i n t h e second Polumn of t a b l e I. A s i t i s w e l l known / 1 2 / , t h i s can b e considered a s an a b s o l u t e d e t e r m i n a t i o n

of the average atomic jump frequency :

1 - f - Ar

T C 2l4

( f c i s t h e so-called c o r r e l a t i o n c o e f f i c i e n t ) . A d i f f u s i o n c o e f f i c i e n t D(<12>) can be c a l c u l a - t e d from 1 / ~ , provided t h a t t h e average l e n g t h <12>

of the elementary jump i s known, by t h e r e l a t i o n :

I n t h e t h i r d c o l u m of t a b l e I, D(ao) has been c a l c u l a t e d assuming a n e a r e s t neighbour d i s t a n c e f o r t h e elementary jump. The f o u r t h calm r e p o r t s t h e macroscopic d a t a D" o b t a i n e d by c l a s s i c a l microsec- t i o n i n g techniques / I l l f o r t h e d i f f u s i o n of i r o n i m p u r i t y i n vanadium and the l a s t column g i v e s t h e r a t i o / < T > / a o o b t a i n e d by a d j u s t i n g D(<12>) t o D*.

JOURNAL DE PHYSIQUE

n o t be invoked n e i t h e r s i n c e they would suppose

-

J < 1 2 > / a o = I . 16 which i s s t i l l too s m a l l . In a d i - vacancy mechanism, t h e jumping atom would perform two s u c c e s s i v e displacements, each of them c o r r e s - ponding t o a d i s t a n c e a. ; b u t a c t u a l l y t h e r e i s no s t o p between them and t h i s w i l l account f o r

_- one

jump i n Mgssbauer spectroscopy, w i t h a

4<l2>

value corresponding t o t h e t r u e d i s t a n c e between i n i t i a l and f i n a l s i t e s , a s n a i v e l y p i c t u r e d i n f i g u r e 3

I

where t h e d i f f e r e n t p a t h s w i t h t h e i r r e s p e c t i v e

s t a t i s t i c weights a r e shown. Thus, a s e a s i l y calcu- l a t e d , a pure divacancy mechanism would r e s u l t i n

-

a r a t i o J < 1 2 > / a o = 1.66. The experimental value a t 1 5 5 0 ' ~ b e i n g about 1.3 means c o n t r i b u t i o n t o d i f - f u s i o n from both s i n g l e and d i v a n c i e s . Then, t h e measured d i f f u s i o n broadening A r and t h e to-

t o t a l

t a l d i f f u s i o n c o e f f i c i e n t D total can be expressed F i g . 2 : Typical Mgssbaunr s p e c t r a a t high tempera-

t u r e measured with a s t a i n l e s s s t e e l absor- by : b e r .

Table I

3. Discussion and Conclusion.- Up t o about 1 4 0 0 ~ ~ i t i s c l e a r t h a t d i f f u s i o n c o e f f i c i e n t s c a l c u l a t e d from t h e ~ g s s b a u e r l i n e broadening can be reasonably ad- j u s t e d t o t h e m i c r o s e c t i o n i n g d a t a , w i t h i n e x p e r i - mental accuracy, assuming elementary jumps between n e a r e s t neighbour s i t e s . This i s c o n s i s t e n t w i t h a d i f f u s i o n mechanism i n which s i n g l e vacancies a r e involved and confirms both macroscopic / ] I / and NMR

-

d a t a / l o / . The r a t i o J < 1 2 > / a o b e i n g a l i t t l e s m a l l e r than one, j u s t account f o r t h e w e l l known e x i s t e n c e of a m i g r a t i o n volume.

A t h i g h e r temperature d i f f u s i o n c o e f f i c i e n t s o b t a i n e d from ~ i j s s b a u e r spectroscopy and microsec- t i o n i n g techniques can be a d j u s t e d t o each o t h e r on- l y i f t h e elementary jump d i s t a n c e i s supposed l a r - g e r than a o . Thus, t h e d a t a cannot be analysed any l o n g e r i n terms of a s i n g l e vacancy mechanism. D i - r e c t jumps between n e x t n e a r e s t . n e i g b o u r s i t e s can-

A r t o t a l =

Arlv

⁺

Ar2v

D t o t a l = D ~ v ⁺ D2v

(where t h e s u b s c r i p t s Iv and 2v r e f e r t o s i n g l e and d i v a n c i e s r e s p e c t i v e l y ) .

F i g . 3 : The v a r i o u s p o s s i b l e exchange processes of an impurity atom w i t h a divacancy i a BCC metal.

A : 1 = *a0, weight : I ; B : 1 =

$

^{a. = 1.63 ao,}

weight :

9

^{; C : 1 =}

4

a. = 1.16 a o , weight:;

.

w i t h t h e f o l l o w i n g r e l a t i o n s :

( 1 . 3 a o ) 2

D t o t a l =- 12H ' r t o t a l ( a t 1550:~)

Using t h e d a t a from t a b l e I a t 1 5 5 0 ' ~ r e s u l t s i n c a l c u l a t i n g t h e e q u a t i o n s :

T a k i n g i n t o a c c o u n t t h e c l a s s i c a l e x p r e s s i o n s 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 s a s o b t a i n e d from t h e r - modynamics, D2V/DIV c a n b e approximated by :

C2v E;"

i n which

- -

^exP

^{- ki}

^{Eg i s} t h e c o n c e n t r a t i o n C l v

r a t i o of d i v a c a n c y t o s i n g l e vacancy, : E i s t h e f o r - mation e n e r g y o f a vacancy, EB i s t h e b i n d i n g e n e r g y o f d i v a c a n c y and hEm i s t h e d i f f e r e n c e i n m i g r a t i o n e n e r g y of s i n g l e and d i v a c a n c y . Thus :

t o b e u s e d a l o n g w i t h t h e v a l u e o f a c t i v a t i o n e n e r g y f o r d i f f u s i o n i n t h e low t e m p e r a t u r e s t a g e where t h e s i n g l e vacancy mechanism h a s t h e m a j o r c o n t r i b u t i o n , t h a t i s :

As p o i n t e d o u t by Kimura 1141, t h e m i g r a t i o n e n e r g y s h o u l d b e l a r g e r t h a n t h e f o r m a t i o n e n e r g y i n V, Nb, Ta and EB i s e x p e c t e d t o b e o f t h e o r d e r o f EF 1 3 , s a y I v :

E? = 1 . 5 eV E~~ = 1 . 7 e V

m

E~ = 0.5 eV

Then, t h e MEssbauer d a t a a t 1 5 5 0 ' ~ would c o r r e s p o n d t o :

which i s b o t h r e a s o n a b l e and i n a c c e p t a b l e agreement w i t h r e c e n t macroscopic d a t a f o r d i f f u s i o n of i r o n

i m p u r i t i e s i n vanadium / I I / .

R e f e r e n c e s

/ I / A b l i t z e r , D., Philos.Mag.

36

(1977) 391.

/ 2 / A b l i t z e r , D . , Philos.Mag.

35

(1977) 1239.

/ 3 / P e l l e g , J . , Philos.Mag.

2

(1974) 383.

1 4 1 P e l l e g , J . , Philos.Mag.

32

(1975) 593.

1 5 1 P e l l e g , J . , Philos.Mag.

2

(1977) 349.

1 6 1 P e l l e g , J . , Philos.Mag.

2

(1977) 725.

1 7 1 P e a r t , R.F., J. Phys. Chem. S o l i d s

2

⁽¹⁹⁶⁵⁾

1853.

1 8 1 Lundy, T.S., Mc Hargue, C.J., T r a n s . AIME

233

(1965) 243.

/ 9 / Coleman, M.G., Wert, C.A., P e a r t , R.F., Phys.

Rev.

175

(1968) 788.

/ 101 C h a b r e , Y . , P r i v a t e Communication.

/ 1 1 / A b l i t z e r , D., P r i v a t e Communication.

1121 J a n o t , C., J. P h y s i q u e

21

(1976) 253.

1131 C a r p e n t e r , J . S . , Cathey, W . N . , Phys. L e t t .

64A

(1977) 313.

/14/ Kimura, H., i n " P r o g r e s s i n t h e s t u d y o f p o i n t d e f e c t " , Ed. by Doyama M. and Yoshida S., (Uni- v e r s i t y o f Tokyo P r e s s ) 1977, Chap. 3 , p. 119.