THE SNOEK-KÖSTER RELAXATION IN IRON

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THE SNOEK-KÖSTER RELAXATION IN IRON

L. Magalas, J. Dufresne, P. Moser

To cite this version:

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JOURNAL DE PHYSIQUE

CoZZoque C5, supp Zdrnent au a O l O , Tome 42, octobre 1982 page C5-127

THE SNOEK-KOSTER RELAXAT I O N I N I R O N L.B. ~ a ~ a l a s * , J.F. Dufresne and P. Moser

Centre drEtudes NucZdaires de Grenoble, D6parternent de Recherche Fondamentale Section de Physique du SoZide, 85 X - 38043 GrenobZe Cedex, France

Abstract.- An investigation on the Snoek-Kijster peak in high purity iron doped with 1000 at ppm of carbon was carried out. The study of the influence of low

temperature deformation on the S-K peak revealed that screw dislocations may not play the major part in the S-K relaxation in w-Fe. The carbon S-K peak's parameters were found to be HSK = 1.84 ? 0.03 eV and

.'EK

= 0.7 x s-I

.

It was also found that carbon-vacancy pairs might influence the S-K relaxation. However these experiments are not considered as an evidence in support of Mondino and Seeger's interpretation. The B2 and B peaks were also observed.

Y

Introduction.- In order to explain the Snoek-KBster (S-K) relaxation in b.c.c. metals Schoeck model, for a long time, has been widely accepted. Actually, this relaxation process was supposed to be caused by the motion of non specified dislocations con- trolled by the diffusion of interstitial atoms (C, N or 0) [ I ] . However a few diffi- culties arose in accounting for some striking experimental results concerned with carbon S-K peak in a-Fe. It has been claimed 161 that interstitially dissolved carbon atoms do not contribute to the S-K peak. In addition, they retard its formation or even completely suppress this effect because of precipitation on the dislocations. Puzzling results have been obtained, so far, on the question of carbon S-K peak in iron. Some results confirmed the existence of this peak [4,5,7] while the others do not [6,8,91

.

In fact, this problem has been explained by londino and Seeger f 101 in terms of the interaction of carbon atoms with vacancies. Since, not only are dislocations generated by cold work but vacancies as well the formation of C-V pairs and it's high dissociation activation enthalpies H~~~~ = 1.6 eV [ I l l may cause that the

I v-C

carbon S-K peak is not fully developped or even might be undetectably small during the first warm-up. Consequently, as suggested by Yondino, full development of the carbon S-K relaxation requires annealing above the peak temperature i.e. after dissociation of C-V paris. Nevertheless, there is no experimental evidence to bear out this hypothesis [9].

According to a recent theory of Seeger [121, the S-K relaxation in b.c.c. metals is attributed to the formation of kink pairs in screw dislocations in the pre.- Eence aofbigh local concentration of foreign interstitial atoms. This signifies that the activation enthalpy of the S--K relaxation is to be the sum of the kink pair formation enthalpy in ao/2 <Ill> screw dislocations 2 HK and the migration energy "Permanent address : Akademia ~Arniczo-~utnicza, Instytut Metalurgii, Al. Mickiewicza

30, 30-059 ~rakbw, Poland

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C5- 128 JOURNAL DE PHYSIQUE

H?l'

of t h e f o r e i g n i n t e r s t i t i a l s . A c t u a l l y , i f t h e ao/2 < I l l > screw d i s l o c a t i o n s a r e r e a l l y involved i n t h e S-K r e l a x a t i o n one would expect h i g h e r r e l a x a t i o n s t r e n g t h

when p l a s t i c deformation i s performed a t low t e m p e r a t u r e s , compared w i t h t h e same

amount of room temperature (RT) deformation. I t i s t o be noted t h a t both t h e o r i e s e x p l a i n t h e experimental r e s u l t s f a i r l y w e l l .

Taking i n t o account t h e problem of t r a n s i e n t e f f e c t i n t h e S-K r e l a x a t i o n of C i n a-Fe and t h e l a s t t h e o r y of t h e S-K peak t h i s prompted us to s t a r t t h e e x p e r i -

ments d e s c r i b e d i n t h i s paper. Simultaneously, t h e

62

and

6

peaks have been obser-

Y

ved. I n t h e f o l l o w i n g , we f i r s t d i s c u s s t h e problem of t r a n s i e n t e f f e c t of C and t h e i n f l u e n c e of low and room temperature deformation on t h e S-K peak i n a-Fe doped w i t h 1 000 a t ppm of C . I n t h e l a s t p a r t we s h a l l b r i e f l y d e a l w i t h t h e

62

and

6

peaks.

Y

Experimental procedure.- The samples a r e 0.6 mm diameter w i r e s , 100 mm i n l e n g t h , of

h i g h p u r i t y CEN-G i r o n [3] doped w i t h 1 000 a t ppm of carbon. The h e a t t r e a t m e n t in-

cluded 5 h r anneal a t 823 K i n a n atmosphere of helium followed by quench i n a flow

of helium g a s . The quenching c o o l i n g r a t e t h u s was approximately 500 KS-'. A f t e r t h i s

s o l u t i o n h e a t treatment t h e samples were q u i c k l y t r a n s f e r r e d i n t o l i q u i d n i t r o g e n where they were s t o r e d u n t i l 1 deformation procedure. Mixed deformations i n t e n s i o n

were employed, namely : 5 % a t RT + 5 % a t 77 K , 7 % a t RT

+

3 % a t 77 K , 9 % a t RT

+ 1 % a t 77 K, 10 % a t RT and a l s o d i r e c t l y 2 % a t 77 K and 2 % a t RT. Then a d d i t i o -

n a l deformations i n t o r s i o n of 3.5 % a t 77 K and 6 % a t 77 K were performed i n t h e

pendulum a f t e r g e t t i n g t h e S-K peak caused by t h e previous deformation i n t e n s i o n . I n t e r n a l f r i c t i o n and square of v i b r a t i o n frequency were simultaneously measured using an a u t o m a t i c i n v e r t e d t o r s i o n pendulum o p e r a t e d near 1 Hz and over a tempera- t u r e r a n g e from 100 t o 673 K d u r i n g l i n e a r warm up w i t h a h e a t i n g r a t e of 200 ~ h - ' .

The specimen was s u b j e c t e d t o a mean s u r f a c e s t r a i n amplitude of 9 x and immer-

sed i n a magnetic f i e l d of 100 Oe t o s u p p r e s s m a g n e t o e l a s t i c phenomenon.

The p r e c i s e v a l u e s of t h e S-K p e a k ' s parameters and i t ' s shape have been determined a f t e r s u b s t r a c t i o n of t h e background a c c o r d i n g t o t h e r e l a t i o n s h i p

where A , B and H and t h e parameters t o be determined a f t e r o p t i m a l i s a t i o n of t h e X2

f u n c t i o n . An a p p r o p r i a t e number of experimental p o i n t s , on both s i d e s of t h e peak,

a r e taken i n t o computation. The

6

parameter of lognormal d i s t r i b u t i o n h a s been e s t i -

mated according t o t h e formulas g i v e n by Nowick and Berry [ 2 ] .

Experimental r e s u l t s

.-

F i g . 1 shows t h e dependence of t h e S-K peak a f t e r background

s u b s t r a c t i o n ; i n each c a s e t h e t o t a l p l a s t i c deformation of t h e specimen a t t a i n e d 10 % b u t w i t h d i f f e r e n t r a t i o of CW a t RT and CW a t 77 K (curve a ) . A f t e r a d d i t i o n a l

CW a t 77 K of 3.5 % and 6 % i n t o r s i o n t h e dependence of t h e S-K peak i s p r e s e n t e d

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(i) With increasing degree of CW at 77 K the S-K peak is decreasing.

(ii) The difference between Q-I after 10% at RT and 9 % at RT

+

I % at 7 7 K is max

always negligible.

(iii) The aforementioned relationship is valid for additional CCJ at 77 K of 3.5 X and 6 %.

This experimental part of the work was repeated twice so as to be sure of getting a correct answer on the question of the influence of low temperature cold work on S-K

peak. The results were exactly the same.

We must notice, too, that after a small deformation of 2 % at 77 K and 2

X

at RT the S-K peak is very slightly different, indeed. The exact values are the follo- wing : for deformation at RT

dl

= 4.4 x l o 3 ,

max Tmax = 558 K, B = 3 . 5 and for deformation at 77 K

<-&

= 4 . 0 x l o 3 , Tmax = 556 K, R = 3 . 5 . Generally, on the first runaf- ter deformation in tension a Snoek peak with a very small contribution on both sides is observed. Then, starting from 450 K a peak is rising ; it's maximum varies within atemperature range of 530-600 K depending on the deformation (Fig. Za, b, curves 1). Immediately after reaching 673 K a measurement is continued with cooling down (curves

2 ) . The cooling rate is also 200 K s-l. In this case, an extremely stable peak at

5 4 5 K (f = 1 Hz) is observed. This is a carbon Snoek-Ksster peak in a-Fe. Several runs up and down may be performed and the S-R peak is unbelievably repeatable within an error in an estimation of < i x a n d T of 1 %.

max

Thechanges in internal friction and modulus are very similar after -deformation performed in all "mixed" deformation and after additional cold work at 77 K with the only one exception of the so-called S-K peak on the first run when warming-up after deformation in tension (Fig. ?a, b, curves 1). For this reason only one more typical curve is to be presented. Fig. 3 illustrates characteristic spectra of a specimen deformed 10 % at RT plus additional 3 . 5 % in torsion at 77 I<. The 270 K and 350 K peaks are usually observed. The S-K peaks in the up (curve 1 ) and down (curve 2 ) runs are very similar. In the later case, however, high temperature background is lower and perfectly flat spectrum below 400 K is observed. High temperature backgrounddamp- ing removal and a real S-K peak is also presented. Moreover, a pinning stage caused by carbon atoms starts at about 320 K after all variants of "mixed" cold work in tension. After additional CW at 77 K this stage starts below 300 K. This is to emphasize the coexistence of all the already mentioned peaks, namely : 270 K, 350 K, the S-K peak and the pinning stage in the up runs after additional Cil in torsion at 77 K.

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C5- 130 JOURNAZ, DE PHYSIQUE

annealing a t 370 K f o r 8 min.

Discussion.- I n t h e p r e s e n t i n v e s t i g a t i o n a f t e r d i f f e r e n t k i n d s of 10 % c o l d work

and 2 % c o l d work of pure i r o n doped w i t h 1 000 atm ppm of carbon t h e Snoek-K6ster

peak i s n o t f u l l y developed i n t h e f i r s t r u n up, b u t when cooling down. This peak i s

h i g h l y s t a b l e and i t ' s shape and

B

parameter i s e x a c t l y t h e same when second and

f o l l o w i n g r u n s a r e made, and a l s o a f t e r ageing a t 673 K f o r 1 hour i n absence of Snoek peak. The absence of t h e e n t i r e S-K peak i n t h e f i r s t r u n ups and i t ' s appea- rance when cooling down i . e . when 673 K was reached can be explained i n terms of carbon-vacancy i n t e r a c t i o n ( f o r d e t a i l s s e e [ 1 9 , 2 0 ] ) . I n f a c t , f u l l y developed S-K

peak may a l s o be o b t a i n e d when t h e h i g h e s t temperature during r u n ups was 600 K ;

t h i s temperature i s s u f f i c i e n t f o r d i s s o c i a t i o n of C-V p a i r s . F i n a l l y , r e l e a s e d carbon atoms do t a k e p a r t i n t h e S-K r e l a x a t i o n . These r e s u l t s a r e i n agreement w i t h t h e i n t e r p r e t a t i o n of Mondino and Seeger [IO].

It i s a l s o confirmed t h a t t h e peak temperature i s d e c r e a s i n g when t h e degree

of CW i s i n c r e a s e d [6]. A f t e r deformation of 2 % a t RT t h e Tmax = 557 K while a f t e r

10 % a t RT Tmax = 545 K .

Thanks t o t h e s t a b i l i t y of t h e S-K peak we determined t h e a c t i v a t i o n energy, however, i n a comparatively small frequency range of 0.3-1.5 Hz. Thus, t h e a c t i v a t i o n

energy i s 1.84 f 0.03 eV and t h e pre-exponential f a c t o r i s 0.7 x lo-'' s-'.

Let u s now c o n s i d e r t h e S e e g e r ' s h y p o t h e s i s , according t o which, i n a-Fe t h e S-K r e l a x a t i o n i s caused by t h e kink-pair f o r m a t i o n i n screw d i s l o c a t i o n s i n t h e presence of a h i g h l o c a l c o n c e n t r a t i o n of carbon atoms ( h e r e i n t h i s s t u d y ) . The d a t a r e p o r t e d (Fig. 1 ) s u g g e s t t h a t i t i s n o t t h i s c a s e . Moreover, when t h e amount of 77 K deformation i s i n c r e a s e d t h e S-K peak i s d e c r e a s e d . Before d e f i n i t e c o n c l u s i o n s can b e drawn, however one must t a k e i n t o account comparatively small

changes i n t h e of t h e S-K peak a f t e r deformation of 10 % a t RT and 5 % a t RT

+

5 % a t 77 K . V i r t u a l l y , i t i s 18 % d e c r e a s e . The same r a t i o i s v a l i d f o r a d d i t i o n a l cold work i n t o r s i o n a t 77 K .

A l b e i t , we have t o r e s o r t t o a n o t h e r experimental d a t a on Fe-40 ppm N by Ino and

Sugeno [13]. They showed t h a t t h e S-K peak i s d r a s t i c a l l y decreased when deformation temperature i s d e c r e a s i n g . For t h e sake of c l a r i t y , l e t us g i v e t h e v a l u e s of t h e

S-K peak a f t e r defamations a t 473, 303, 203 K i .e. Q-' = 8.9 x Q-' = 4 x

Q-' = 1 . 2 x r e s p e c t i v e l y . I n view of t h e above i t seems u n l i k e l y t h a t

a012 < I l l > screw d i s l o c a t i o n s play t h e major p a r t i n t h e S-K r e l a x a t i o n i n a-Fe i n both systems Fe-C and a l s o i n Fe-N.

The 270 K and 350 K peaks i n high p u r i t y i r o n doped w i t h carbon may be iden-

t i f i e d a s 8 2 and B peaks a s i n pure i r o n [14,16]. I n accordance w i t h t h e s e r e s u l t s

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t h e B 2 peak has t o i n v o l v e screw segments of d i s l o c a t i o n s and i n t r i n s i c p o i n t d e f e c t s c r e a t e d by cold work performed d i r e c t l y a t 77 K o r w i t h p r e s t r a i n a t RT ( F i g . 2b, 3 ) . To observe B peak t h e presence of f r e s h d i s l o c a t i o n i s c l e a r l y needed. I n o r d e r t o

Y

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employed. Detailed consideration on the mechanism of the B 2 and 6 peaks willbedes-

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cribed elsewhere 1171.

Conclusions.

-

Within the scope of this present investigation it is concluded that : 1. It is confirmed that the existence of C-V pairs mask the Snoek-Kb'ster relaxation in a-Fe. Although, after dissociation of C-V pairs released carbon atoms do take part in the S-K relaxation and a symetrical S-K peak is observed.

2. The experimental results on S-K relaxation in Fe-C and Fe-N systems are not in agreement with the Seeger's theory on the S-K relaxation in b.c.c. metals. It is to be pointed out that when the deformation temperature is decreased or the amount of cold work at 77 K is increased the height of the S-K peak is decreasing. However, further supporting evidences are desired since these results are not consistent with recent results on Nb-0 system 1181.

3. It is also worthwhile to point out that the S-K peak may be observed when there is no carbon atoms in solid solution since no Snoek peak was detected after thefirst run. It is therefore expected to consider all carbon atoms in an extended Cottrell atmosphere.

4. A detailed analysis should be carried out for the 523 K peak in ferrous martensi- te. It is probably safe to assume that the S-K peak and 523 K peak in ferrousmarten- site might be caused by a nearly similar relaxation process.

To clarify the interpretation of the S-K mechanism further work is clearly necessary.

Acknowledgments.

-

The authom are grateful to Mr.Z.Kabsch for his assistance throughout the experiments.

References

[

1 1 G. Schoeck, Acta Met. 11, 617 (1%3).

1

21 A.S. Nowick, B.S. Berry, IBM Journal 5, 297 (1961). [ 31 F. Vanoni, Thesis, Grenoble (1973).

[ 41 K. Kamber, D. Keefer, C. LJert, Acta Net. 9, 403 (1961). [ 51 J. Mc Grath, R. Rawlings, Acta Net. 14, 1 , (1966). [ 6 1 D.P. Pettara, D.N. Beshers, Acta Net. 15, 791 (1967).

71 R. Kamel, S.A. Mahmoud, F.11. Mansy, Phys. Stat. Sol. (a) 41, K113 (1977). [ 81 G. Ferron, J. Parisot, J. de Fouquet, Scripta Ilet. 7, 855 (1973).

[

91 L.E. Buchanan, R. Kennedy, Proc. ICIFUAS 5, vol. 11, Ed. D. Lenz and K. Liicke, Springer-Verlag, Berlin (1975) p. 362.

[I01 M. Mondino, A. Seeger, Scripta Met. 11, 817 (1977). [ll] 1.1. Weller, J. Diehl, Scripta Met. 10, 101 (1976).

[I21 A. Seeger, Phys. Stat. Sol. (a) 55, 457 (1979). [I31 H. Ino, T. Sugeno, Acta Met. 15, 1197 (1967).

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C5-132 JOURNAL DE PHYSIQUE

[16] V. Hivert, P. Groh, I i . Frank, I.G. Bitchie, P. ?foser, Phys. Stat. Sol. (a) 46, 89 ( 1 9 7 8 ) .

[17] L.B. Magalas, J.F. Dufresne, P. !loser, to be published.

[ I 8 1 C. Oytana, D. Varchon, Acta Net. 27, 17 ( 1 9 7 9 ) .

[ I 9 1 T. Takeyama, H. Takahashi, 3. Phys. Soc. Japan 3 5 , 939 (1973).

1201 P. Hautojzrvi, 3. Johansson, A. Vehanen, J. Yli-Kauppila, P. Maser, Phys. Rev. Lett. 44, 1326 (1980).

Fig. 1-The dependence of the S-K Fig. 3-Internal friction spectrun for a spe- ~eak's height as a function cimen predeformed 10 % at RT with ad- of cold work performed at ditional deformation of 3 , 5 % at 77 K RT and 77 R. Total deforma- in torsion. Curve 1

-

run-up, curve 2

tion was 10 %, curve a. run-down ;

Curves b and c correspond

-.-.-.

computed background, to additional deformation

..-..-

real S-K peak. of 3 , 5 % and 6 % in torsion

at 77 K, respectively.

Fig. 2

-

Internal friction spectrun and square of the frequency as a function of temperature for a specimed deforned 10 % at RT (figure a) and 5 % at RT + 5 Z at 77 K (figure b).