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STUDY OF THE BEHAVIOUR OF THE MAGNETIC DOMAIN WALLIS IN Fe-C BY INTERNAL
FRICTION AND MAGNETIC MEASUREMENTS
J. Degauque, B. Astié, J. Lopez, J. Redoulès, J. Garigue
To cite this version:
J. Degauque, B. Astié, J. Lopez, J. Redoulès, J. Garigue. STUDY OF THE BEHAVIOUR OF THE MAGNETIC DOMAIN WALLIS IN Fe-C BY INTERNAL FRICTION AND MAG- NETIC MEASUREMENTS. Journal de Physique Colloques, 1987, 48 (C8), pp.C8-423-C8-428.
�10.1051/jphyscol:1987864�. �jpa-00227168�
JOURNAL DE PHYSIQUE
Colloque C8, supplement au n012, Tome.48, decembre 1987
STUDY OF THE BEHAVIOUR OF THE MAGNETIC DOMAIN WALLS IN Fe-C BY INTERNAL FRICTION AND MAGNETIC MEASUREMENTS
J. DEGAUQUE, B. ASTIB, J.M. LOPEZ, J.P. REDOULES and J. GARIGUE
Laboratoire de Physique des Solides, associe au CNRS, INSA, Avenue de Rangueil, F-31077 Toulouse Cedex, France
RESUME
Dans un alliage Fe-C
a
196 ppm poids d e carbone, maintenu a 200°C, on 6tudie la prCcipitation du carbone, par mesure du f r o t t e m e n t intgrieur magnitomCcanique et des caract6ristiques magnetiques e n champs faibles et moyens. On compare le comportement hyst6r6tique des parois de Blocha
90°, pr&s du maximum d'amortissement magn6tom&canique,a
celui des parois de Bloch a 180° dans le domaine d e Rayleigh e t pr&s du champ coercitif. Les r6sultats sont reliesa
1'6volution d e l a teneur e n interstitiels d e carbone ainsi qu'; la nature et a la taille des carbures pr6cipitCs.
ABSTRACT
In a Fe-C alloy (196 ppm.w. carbon) annealed at 200°C, the precipitation of carbon is studied by magnetomechanical damping and by magnetic measurements in low and middle range fields. We compare t h e hysteretic behaviour of t h e 90° domain walls, close t o t h e magnetomechanical damping maximum, and of t h e 180° domain walls in t h e Rayleigh region and near t h e coercive force. The results a r e linked t o t h e evolution of t h e interstitial carbon content and t o t h e kind and size of precipitated carbides.
I. INTRODUCTION
In Fe-C alloys we have already used t h e magnetomechanical damping in order t o define t h e ability of t h e 90" magnetic domain walls (DW8s) t o study t h e modifications of t h e structural arrangement of carbon a t o m s during precipitation [I]. Therefore, a s in t h e case of t h e study of various arrangements of dislocations [z], w e propose t h a t t h e magnetomechanical technique may be completed by magnetic measurements in low magnetic fields (Rayleigh region) and in middle range magnetic fields (near t h e coercive force). The aim of this paper is t o compare t h e somewhat different influence of t h e various stress fields of t h e d e f e c t s occurring during the precipitation of carbon in a dilute Fe-C alloy, on t h e one hand on t h e large displacements of 90" DW's and 180° DW8s, and on t h e small and large displacements of 180° DW's on t h e other.
2. EXPERIMENTAL TECHNIQUES
A pure iron is carburized in a liquid solution up t o 196 ppm.w. content. This carbon content is determined by chemical analysis. A f t e r thermomechanical t r e a t m e n t the grain size is homogeneous with a n average value around 200 p m . We assume t h a t
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JOURNAL DE PHYSIQUE
a f t e r annealing at 720°C for I h and quenching a t O°C, all t h e carbon has formed a n interstitial solution in U-Fe.
Magnetomechanical damping measurements a r e performed on a low frequency inverted torsion pendulum (0.7 cps). From t h e observed maximum Q-M, we deduce t h e value of 1 t h e average internal stress qi.
For t h e magnetic measurements we use a rectangular f r a m e obtained by spark cutting from t h e parallelepipedic sample of t h e damping measurements. This f r a m e constitutes t h e magnetic c o r e of a transformer. The frequency of t h e magnetic measurement is very low (0.05 cps) in order t o reduce t h e eddy currents. After numerical t r e a t m e n t by a MINC 11/73, we can obtain t h e initial susceptibility a and t h e Rayleigh's constant b from t h e virgin curve, and t h e coercive f o r c e Hc
[Z].
We give here t h e variation of Q- and of a and b in t h e usual representation where a simple function of these q u a n t ~ t i e s must increase with t h e efficiency of d e f e c t s
M
anchoring t h e DW's 131.
3. RESULTS
-
Precipitation of carbonFigure 1 shows t h e fraction (1
-
X) of t h e carbon which remains in interstitial solution a t t i m e t. After a f a s t drop corresponding t o t h e f i r s t s t a g e of precipitation( 6
carbide), (1-
X) shows a plateau. Then a f t e r 40 mn of annealing a second slower drop occurs, which is linked t o t h e precipitation of F e C according t o previous 3 studies on Fe-C alloys 141. The STEM and TEM observations confirm t h a t during t h e f i r s t s t a g e of precipitation only E. carbide appears, whose habit plane is {100) (phot. a and b). A f t e r 6 hours of annealing (phot. c ) we observe some precipitates of F e C , which become more numerous a f t e r 55 h of annealing (phot. d).3
Magnetomechanical measurements
-
The variation of I/Q-M and of 1 q. (which a r e connected t o t h e irreversible displacements of t h e 90° DW's) a r e quite s i h i l a r (Fig. 2).After a slight decrease of l/Q-M only, a t t h e be inning of t h e precipitation, these I
- k
two quantities increase (more markedly f o r 1/Q roughly a t t h e s a m e t i m e of annealing (250 mn).
Magnetic measurements
-
The variations of l/a and I /n,
given on figures 3 and 4, show a g r e a t decrease a t t h e beginning of t h e annealing, followed by a marked maximum just about t h e same t i m e (around 350 mn). The coercive f o r c e shows t h e s a m e maximum a f t e r 350 mn of annealing (Fig. 5), but t h e initial decrease observed o n t h e variations of I / a and Iffi
is missing.4. DISCUSSION
4.1. Magnetomechanical measurements
At t h e beginning of t h e precipitation, t h e irreversible displacements of t h e 90" DW's a r e braked by t h e magnetic a f t e r e f f e c t pressure due t o t h e interstitial carbon. The decrease of t h e interstial content makes t h e movements of these DWts easier a s long a s t h e anchoring e f f e c t of t h e precipitated carbides does not dominate. Thus t h e increase of
Q-L
is due t o t h e major "release effect" linked t o t h e interstitials. The internal s t r e s s Qi does not show t h e s a m e variation. But this discrepancy, in t h e framework of Smith and Birchak's model, c a n be linked t o t h e modification of t h e shape f a c t o r of t h e magnetomechanical cycle, when t h e precipitation is in progress 151-At longer t i m e s of annealing, t h e braking e f f e c t of t h e precipitates may become predominant when their size is comparable t o t h e width of DW1s [6]. For t h e
90° DW's this should occur for t h e maximum of l/Q-M and Gi, i.e. a f t e r 250 mn of 1 annealing. This e f f e c t corresponds t h e n t o t h e second s t a g e of precipitation. Thus t h e precipitates of Fe3C seem to be anchoring d e f e c t s more e f f e c t i v e than E. carbides for 90° DW1s. A t t h e end of t h e precipitation, t h e magnetic closure domains built around t h e precipitates increase t h e a r e a of 90°DW1s, which decreases l/QrM and G i 1 (phot. el.
4.2 Magnetic measurements
Rayleigh region
-
The reversible and irreversible small range displacements of 180°DW's a r e very sensitive t o t h e magnetic a f t e r e f f e c t pressure. This may explain t h e f a s t drop of l/a and 1/61,
which a r e linked t o these displacements, with t h e decrease of t h e interstitial c o n t e n t at t h e beginning of t h e precipitation. Indeed t h e measured variation of I / a is in very good agreement with t h e computed one, using t h e classical model which gives a linear decrease of I / a with t h e decrease of interstitial content 171. The maximums of I / a and I/l6
a f t e r 350 mn of annealing a r e due to t h e anchoring e f f e c t of t h e precipitates of cementite. These maximums a r e not higher than t h e initial values of I / a and I /6,
which shows t h a t t h e restoring f o r c e of t h e interstitials is more o r less equal t o t h e anchoring one of t h e F e C precipitates.3
L a r g e displacements of DW9s
-
The coercive f o r c e corresponds t o t h e whole of t h e DW1s. In this case t h e a f t e r e f f e c t pressure does not brake t h e displacement of t h e 180° DW1s. So at t h e beginning of t h e f i r s t s t a g e of precipitation, t h e6
carbides e x e r t a slight anchoring e f f e c t on these DW1s. This e f f e c t becomes more e f f e c t i v e a f t e r 40 mn of annealing, at t h e s t a r t of t h e second stage.The observed maximum of Hc is connected t o t h e agreement between t h e s i z e of t h e precipitates and t h e DW's width. From t h e model of Dijkstra and Wert [ 6 ] , Hc may be expressed a s a function of t h e volume fraction of t h e precipitated carbon and of t h e diameter d of t h e precipitates. From our values of Hc, we obtain 0.07 p m for t h e values of d, which i s not t o o f a r from t h e a c t u a l value of t h e DW's width in iron ( ~ 0 . 1 p m ) .
4.3. Connection between magnetomechanical and magnetic measurements
In order t o compare t h e f o r c e of interaction between t h e structural d e f e c t s studied and t h e two types of DW1s, we use t h e former magnetic theory of Becker and Diking [8], which assumes t h a t t h e energy of t h e DW's is mainly determined by t h e internal stresses. From t h e values of G i determined by magnetomechanical damping i t is possible t o deduce t h e values of a [9]
4 152
a = j ( - ) X (-
A loo*
where
hlOO
is t h e saturation magnetostriction and I t h e spontaneous magnetization.The values of b and
H,
have been determined in t h e s a m e way S :C8-426 JOURNAL DE PHYSIQUE
The range of s i z e of t h e computed values agrees with t h e measured quantities f o r b and Hc, which correspond like G i t o t h e irreversible movements of t h e DW's. On t h e o t h e r hand t h e computed values of a a r e 100 t i m e s higher than t h e measured ones. Moreover t h e observed variations of bi a r e close t o those of Hc, but at t h e f i r s t t i m e s of annealing, when t h e influence of interstitials is predominant, they d o not a g r e e with those of 1 /
\Ji;:
I t is then obvious t h a t t h e behaviour of t h e 90"DW's and 180" DW's a r e really comparable mainly in t h e range of their large displacements.
CONCLUSION
In a Fe-C alloy annealed a t 200°C, we have shown t h a t t h e study of t h e irreversible displacements of large amplitude of t h e 90°DW's o n t h e one hand and of t h e 18O0DW's on t h e other, gives roughly similar results when comparing t h e variation and t h e a c t u a l value of t h e internal s t r e s s opposed t o t h e movements of e a c h type of wall. The reversible or irreversible displacements of small amplitude of t h e 180" DW's show quite t h e s a m e sensitivity a s those of large amplitude in presence of precipitated carbides of a s i z e comparable t o t h e DW's width. On t h e other hand mainly t h e displacements of small amplitude of 180°DW*s display t h e modification of t h e interstitial carbon content in this alloy.
ACKN0WLEM;EMEN-r
The authors would like t o express their gratitude t o DrsR.A.Taylor and J.P. Jakubovics of Oxford University Metallurgy Department for t h e electron microscopy and magnetising experiments o n t h e HVEM microscope in Oxford.
REFERENCES
1 ASTIE, B. DEGAUQUE, J. Proc. ECIFUAS 3, C.C. Smith ed. (Pergamon Press 1980) 211
2 LOPEZ, J.M. DEGAUQUE, 3. ASTIE, B. GARIGUE, J. REDOULES, J.P. Mem. Sc.
Rev. Metallurgie (March 198 51, 147
3 ASTIE, B. DEGAUQUE, J. PORTESEIL, J.L. VERGNE, R. IEEE Trans. on Magn. 17 (Nov. 1981) 2929
4 PARISOT, J. Thesis (Universit6 d e Poitiers) (1970)
5 ASTIE, B. DEGAUQUE, 3. Proc. ICIFUAS 8, J. Phys. CIO, 46 (1985) 721 6 DIJKSSTRA, L.D. WERT, C. Phys. Rev. 79, (19501, 979
7 NEEL L. J. Phys. Rad. 12 (19511, 339
8 BECKER, R. DORING, W. Ferromagnetismus, Ed. S. Springer Verlag (1939) 9 SMITH, G.W. BIRCHAK, J.L. J. Appl. Phys. 41 n"8 (1970) 3315
10 KERSTEN, M. Zeit. Physik, 124 (1948) 714.
Fig. 1
Fig. 3
t m n
I I I
1 10 l o 2 103 l o C
Fig. 2
Fig. 4
Fig. 5
Interstitial carbon fraction (Fig. I) ; l/Q-M and I Ci: (Fig. 2 ) ; l / a (Fig. 3) ; 11
6
(Fig. 4) ; Hc ( ~ i g . 5 )vs annealing time at 200°C.
C8-428 J O U R N A L DE PHYSIQUE
a ) 2 h (x 3,200) STEM observations b) 2 h (x 12,500) STEM observations
C ) 6 h (x 4,800) TEM observations
d) 5 h (x 4,800) TEM observations
e ) 55 h (x 30 000) Lorentz TEM (180" and 90° DWfs).
