THE SNOEK-KÊ-KOSTER PEAK IN Fe-P ALLOYS

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THE SNOEK-KÊ-KOSTER PEAK IN Fe-P ALLOYS

J. Ji, Z. Zhao, L. He, D. Geng

To cite this version:

J. Ji, Z. Zhao, L. He, D. Geng. THE SNOEK-KÊ-KOSTER PEAK IN Fe-P ALLOYS. Journal de Physique Colloques, 1985, 46 (C10), pp.C10-257-C10-260. �10.1051/jphyscol:19851058�. �jpa- 00225442�

JOURNAL DE P H Y S I Q U E

C o l l o q u e C10, s u p p l 6 m e n t a u 11-12, Tome 46, dgcembre 1 9 8 5 p a g e C10-257

THE SNOEK-KE-KOSTER PEAK IN Fe-P ALLOYS

,.

J . W . J I , Z.Q. ZHAO, L.D. HE' AND D.Q. GENG'

B a o t o u R e s e a r c h I n s t i t u t e of M e t a l l u r g y , B a o t o u , I n n e r Mongolia, C h i n a

' N o r t h e a s t I n s t i t u t e o f Technology, Shenyang, L i a o n i n g , China

A b s t r a c t - The S-K-K peak i n Fe-P a l l o y s h a s been s t u d i e d b y a vacuum KB-pendulum. It is found t h a t phosphorus h a s a n obvious e f f e c t on t h e IF. The experimentil r e s u l t s a g r e e w i t h S c h o e c k l s t h e o r y . The mechanism of t h e r e l a x a t i o n is a l s o d i s c u s s e d f u r - t h e r .

I

-

S c h o e c k ' s r e s u l t /I/ shows t h a t r e l a x a t i o n s t r e n g t h A (namely Q K ~ ) a n d r e l a x a t i o n time r o f t h e Snoek-Kg-~tjster(abbreviated t o S-K-K) peak a l l depend on t h e a v e r a g e d i s l o c a t i o n l e n g t h Lo between immoble p o i n t s . Schoeck ' s c a l c u l a t i o n g i v e s :

...

A = B A ~ ( 1 )

...

a n d

z

where, oc a n d @ a r e c o n s t a n t s , A i s t h e d e n s i t y of d i s l o c a t i o n , Co i s t h e i n t e r s t i t i a l c o n c e n t r a t i o n i n b u l k , t h e o t h e r l e t t e r s h a v i n g t h e i r u s u a l meaning. S o l u t e atom, e v i d e n t l y , may be a s t r o n g l o c k i n g p o i n t o f d i s l o c a t i o n i n souq.cases. Phosphorus i s a q u i t e s t r o n g h a r d e n e r i n W- i r o n , i n d i c a t i n g t h a t s t k e r e i s a v e r y l a r g e i n t e r a c t i o n between phos- p h o r u s a t o m s a n d d i s l o c a t i o n s i n i r o n , a n d a l a r g e e f f e c t o f phosphorus on t h e 3-K-K damping.Therefore, we w i l l b e a b l e t o o b t a i n some s i g n i - f i c a n t e x p e r i m e n t a l r e s u l t s a n d f u r t h e r u n d e r s t a n d t h e n a t u r e o f t h e S-K-K I F t h r o u g h i n v e s t i g a t i n g t h e CW-peak i n ~ e - ( c + N ) - P a l l o y s . I1

-

I F measurements were c a r r i e d o u t o v e r a 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 t o 4000C i n a vacuum Kh-pendulum. The a v e r a g e h e a t i n g rate was a b o u t 2 deg./min., and c o o l i n g r a t e was 1.5 deg/min.. The tempera- t u r e was k e p t c o n s t a n t d u r i n g measurements o f decay. F r e q u e n c y r a n g e f o r measurements was 0.3 t o 1.3 c p s . The maximum s t r a i n a m p l i t u d e a t t h e s u r f a c e of specimen was l e s s t h a n ^{2 x 1} 0-5. The vacuum was h i g h e r t h a n 2x10-5 t o r r . The specimen h a s a d i a m e t e r of 0.79mm. The p r e s t r a i n q u a n t i t y o f t h e specimen was 26%. The c h e m i c a l composition of t h e t e s t e d a l l o y was l i s t e d i n T a b l e 1.

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19851058

JOURNAL DE PHYSIQUE

T a b l e 1 . Chemical c o m p o s i t i o n o f t e s t e d a l l o y s (wt.pprn)

a l l o y _{C N P} B a l a n c e

number

A-0 1 7 120 70 Fe

A-I 1 7 8 5 210 ^I)

A-2 1 7 63 370 II

A-3 1 7 45 640 ^1,

A-4 1 7 18 2400 1,

111

-

It i s found t h a t t h e I F reduced and s h i f t e d t o lower t e m p e r a t u r e a s a n i n c r e a s e i n t h e phosphorus c o n c e n t r a t i o n Cp and a d e c r e a s e i n t h e con- c e n t r a i o n C(N+C) of b o t h c a r b o n a n d n i t r o g e n ( s e e F i g . 1 ) . The

-1

137ppm t o 35ppm. It can b e s e e n , from a comparison w i t h work /2/, t h a t t h e i n f l u e n c e o f phosphorus on t h e I F is predominent b e c a u s e u n d e r t h e same change of C ( N + ~ th e changes of t h e IF maximum and peak tempera- ture i n t h e p u r e Pe-A system a r e o n l y 2 x 1 0 ~ 3 a n d 150C, namely 1/4.5 and 1/5 times of t h e s e i n t h e Fe-P a l l o y s , s e p a r a t e l y .

-

.

o - Fe-lmppmCWal0pp.p 8

l2 _-

.

0 - ^Fa- ~ . ~ D p P " P

-

7 Q m

a

/

2 - /I

0 2 4 B

& x l o Z

100 m m 4n

'

I? ( 'C ) Fig.2 The r e l a t i o n s h i p between t h e peak h e i g h t a n d t h e concen- F i g . 1 The S-K-K peak i n t e s t e d t r a t i o n o f phosphorus

a l l o y s

A Q E ~ - C ~ c u r v e i s g i v e n i n F i g . 2 , where t h e Qh i s t h e peak h e i g h t ob- -1 t a i n e d by d e d u c t i n g background from t h e Q-1-T c u r v e s . Th f i g u r e shows t h a t t h e r e is a l i n e a r r e l a t i o n s h i p b e t x e n QEI and when Cp is i n a r a n g e from 70 t o 640ppm(namely Q-273 is i n r a n g e of I ,4x10-2 t o 5.4~10'2).

Table 2. The activation energy of both relaxation and

interstitial diffusion and the binding energy between the interstitial and dislocation

alloy H Hd Hb

number (eV> (ev) (eV)

A-0 1 . 6 2 f 0 . 0 2 0.91 0 . 7 1

A- 1 1 . 4 1 f 0 . 0 1 0 . 5 0

A-2 1.37 + ^{0 . 0 1} 0 . 4 6

A- 3 1 . 2 7

*

A-4 1.22 f 0 . 0 1 0 . 3 1

The v a l u e s of H o b t a i n e d from t h e s l o p e s of a n A r r h e n i u s p l o t a r e l i s t e d i n T a b l e 2. It i s i n d i c a t e d t h a t t h e a c t i v a t i o n e n e r g y of t h e r e l a x a t i o n i s v a r i a b l e s i n c e c o m p o s i t i o n c h a n g e s , and t h e a c t i v a t i o n e n e r g y de- c r e a s e s from 3 7 . 3 ~ c a l . / m o l e . i n a l l o y A-0 t o 2 8 . 1 ~ c a l . / m o l e . i n a l l o y A-4.

-

Phosphorus o b v i o u s l y r e d u c e s t h e IF peak h e i g h t . The r e l a t i o n s h i p be- tween Q ~ I a n d Cp c a n be e x p r e s s e d by f o r m u l a ( 3 ) when Cp i s i n a r a n g e from 70 t o 640ppm ( s e e F i g . 2 ) :

Q ~ ~ = ~ ~ c ~ - ~ / ~ + r

... ...

where 6' and r a r e c o n s t a n t s . ~ p - ~ / 3 c a n be w r i t t e n a s ( ~ p l / 3 ) - ~ and cp1/3 is t h e l i n e c o n c e n t r a t i o n of phosphorus. The phosphorus i n t h e a l l o y s o f A-0 t o A-3 is i n s o l i d s o l u t i o n , a n d t h e r e i s no s e g r e g a t i o n o f phosphorus t o d i s l o c a t i o n . The phosphorus atoms i n s o l i d s o l u t i o n c a n be c o n s i d e r e d a s s t r o n g p i n n i n g p o i n t s t o d i s l o c a t i o n . The l e n g t h h0 of movable d i s l o c a t i o n segment, which i s r e s p o n s i b l e f o r t h e I F , c a n be ex- p r e s s e d b y a formula:

L ~ ~ = ( o c ~ c ~ ~ / ~ ) -I

...

where oc* i s a p i n n i n g c o e f f i c i e n t of phosphorus t o d i s l o c a t i o n . of cour- s e , t h e a l l o y A-4 i s a n e x c e p t i o n because t h e c o n t e n t of phosphorus i n t h e a l l o y o b v i o u s l y e x c e e d s i t s s o l u b i l i t y . I n t h e p r e s e n t s t u d y , t h e d i s l o c a t i o n d e n s i t y A c a n be c o n s i d e r e d a s c o n s t a n t , t h e n t h e r e w i l l be

Q ~ ; ~ = @ ~ A L : ~ + r

... ...

where @ " = 6 t w t 2 / ~ is a c o n s t a n t . The e x p r e s s i o n ( 5 ) q u i t e a g r e e s w i t h t h e formula ( 1 ) g i v e n by S c h o e c k t s t h e o r y , i n d i c a t i n g t h a t t h e S-K-K peak h e i g h t l i n e a r l y i n c r e a s e s w i t h a n i n c r e a s e i n l e n g t h s q u a r e of movable d i s l o c a t i o n segment. It w i l l be n o t i c e d t h a t Lno g i v e n by f o r m u l a ( 4 ) o n l y r e p r e s e n t s t h e l e n g t h o f non-screw(edge) d i s l o c a t i o n b e c a u s e phos- p h o r u s atom a s a s u b s t i t u t i o n a l s o l u t e c a u s i n g a s p h e r i c a l symmetric d i s t o r t i o n i n M-Fe o n l y i n t e r a c t s on non-screw(edge) d i s l o c a t i o n r a t h e r t h a n p u r e s c r e w d i s l o c a t i o n . That i s t o say: t h a t t h e d i s l o c a t i o n r e s - p o n s i b l e f o r t h e S-K-K r e l a x a t i o n is non-screw(edge) o n e , a n d phosphorus s h o r t e n s t h e d i s l o c a t i o n l e n g t h r e s u l t i n g i n t h e r e d u c t i o n i n q g l .

Peak t e m p e r a t u r e

I f we s u b s t i t u t e L f o r Lo i n t h e f o r m u l a ( 2 ) a n d t a k e f o r m u l a ( 4 ) i n t o formula ( 2 ) , a s we!?? as t a k e i n t o c o n s i d e r a t i o n of C c I ~ ) = C o , t h e n t h e f o l l o w i n g e x p r e s s i o n of t h e r e l a x a t i o n t i m e c a n be o i t a i n e d :

rEwt'TC( C + N ) c ~ - ~ / ~ ~ x ~ ( H / K T )

... . ..

where O L ~ ' = O L / ( ~ ~ ~ ) ~ i s a c o n s t a n t . We s h a l l n e g l e c t t h e change i n t h e va- r i a b l e T i n f r o n t of exponent f o r convenience of d i s c u s s i o n s i n c e i t s e f f e c t on 't i s much less t h a n T w i t h i n t h e exponent. I n t h i s way, it i s v e r y e v i d e n t t h a t t o k e e p c c o n s t a n t i n peak t e m p e r a t u r e t o t h e same f r e e n c y u s e d , t h e t e m p e r a t u r e T must l o w e r s when t h e v a r i a b l e s C ( C + N ) ,

27

Cp- 3 a n d H i n t h e a l l o y s A 4 t o A-3 a l l d e c r e a s e s u c c e s s i v e l y . A c t i v a t i o n e n e r g y

Scheock c o n s i d e r e d t h a t t h e a c t i v a t i o n e n e r g y of t h e S-K-K r e l a x a t i o n c o n s i s t s of t h e d i f f u s i o n a c t i v a t i o n e n e r g y of i n t e r s t i t i a l atoms and t h e b i n d i n g e n e r g y between t h e i n t e r s t i t i a l atoms and d i s l o c a t i o n , na- mely, H=Hd+Hb. I f we t a k e t h e v a l u e of Hd t o be 2 1 ~ c a l . / m o l e . ( O . g l e v ) f o r t h e t e s t a l l o y s and assume t h a t i s t h e same t o a l l t h e a l l o y s , t h e v a l u e s o f Hb f o r a l l o y s A-0 t o A-4 can b e o b t a i n e d by H minus Hd. The b i n d i n g e n e r g y d e c r e a s i n g w i t h a n i n c r e a s e of Cp ( s e e T a b l e 2 ) c a n b e e x p l a i n e d as f o l l o w s : The phosphorus atoms on d i s l o c a t i o n r e d u c e t h e

C10-260 JOURNAL DE _PHYSIQUE

e n e r g y o f t h e s t r e s s f i e l d of d i s l o c a t i o n , r e s u l t i n g i n t h e r e d u c t i o n i n t h e b i n d i n g e n e r g y beween i n t e r s t i t i a l atom a n d d i s l o c a t i o n . Such t h e e f f e c t of phosphorus i n c r e a s e s w i t h a n i n c r e a s e o f its c o n c e n t r a t i o n . I n a d d i t i o n , t h e p a r t i c l e s of t h e s e c o n d phase i n a l l o y A-4 a n d t h e i r i n t e r f a c e s w i t h m a t r i x w i l l a l s o a f f e c t t h e d i s t r i b u t i o n of i n t e r s t i t i a l s , namely a f f e c t Hb, t o o ( o f c o u r s e , phosphorus may r e d u c e t h e a c t i v a t i o n e n e r g y o f t h e d i f f u s i o n of c a r b o n a n d n i t r o g e n i n ol-iron).

The above d i s c u s s i o n i n d i c a t e s t h a t t h e S-K-K I F i n t h e t e s t a l l o y s con- forms t o S c h o e c k ' s t h e o r y , a n d non-screw(edge) d i s l o c a t i o n is r e s p o n s i - b l e f o r t h i s r e l a x a t i o n .

I F mechanism

It c a n be p o i n t e d o u t t h a t " t h e enhanced Snoek peak" o c c u r r e d a t s l i - g h t l y h i g h e r t e m p e r a t u r e t h a n t h e Snoek peak t e m p e r a t u r e o f c a r b o n i n i r o n is c a u s e d by t h e motion o f t h e d r a g g i n g by b o t h s c r e w d i s l o c a t i o n a n d edge d i s l o c a t i o n o f Snoek a t m o s p h e r e of i n t e r s t i t i a l s . The Snoek o r d e r w i l l n o t be r e s p o n s i b l e f o r t h e S-K-K I F a p p e a r e d a t even h i g h e r t e m p e r a t u r e b e c a u s e as soon a s t h e t e p e r a t u r e is o v e r t h a t of Snoek o r d e r , t h e p r o c e s s i n c o n v e r s i o n of Snoek o r d e r i n t o C o t t r e l l atmos- p h e r e w i l l o c c u r ,

It i s w e l l known t h a t C o t t r e l l a t m o s p h e r e h a s a l r e a d y formed a n d may produce a dynamic s t r a i n a g e i n bcc m a t e r i a l s c o n t a i n i n g enough amount o f i n t e r s t i t i a l s a t t h e t e m p e r a t u r e , where t h e S-K-K peak a p p e a r s . More- o v e r , t h e v a l u e o f t h e a c t i v a t i o n e n e r g y f o r t h e d i s a p p e a r a n c e o f t h e s e r r a t i o n s i n a s t r a i n - s t r e s s c u r v e is q u i t e similar t o t h a t f o r t h e S-K-K I F /3/, It c a n be p o i n t e d o u t , from t h e s e f a c t s , work/4/ a n d p r e - s e n t work, t h a t t h e p h y s i c a l model, " t h e d r a g g i n g by d i s l o c a t i o n of a C o t t r e l l a t m o s p h e r e of s o l u t e atoms by m i g r a t i o n o f t h e s o l u t e a t o m s w c a u s i n g t h e 3-K-K r e l a x a t i o n , advanced by Kg e t a1./5,6/, i s c o r r e c t on t h e whole, b u t t h e d i s l o c a t i o n moves, a s d e s c r i b e d by Schoek, by t h e bowing o f p i n n e d d i s l o c a t i o n segments /1/ r a t h e r t h a n by t h e f o r m a t i o n and motion of k i n k s /7/.

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/3/ Keh, A. S., Nakada, Y. a n d L e s l i e , W. C . , D i s l o c a t i o n Dynamics, e d i t e d by R o s e n f i e l d , A. R. e t a l , Megrow-Hill ( 1968) 381.

/4/ Oytana, C. a n d Varchon, D., Acta M e t a l l . 3 ( 1 9 7 9 ) 17.

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/6/ Kg, T. S . , S c r i p t a M e t a l l .

fi

/7/ S e e g e r , A . , Phys. S t a t . S o l . ( a ) (1979) 457.