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BEHAVIOUR OF MAGNETIC DOMAIN WALLS IN
PRESENCE OF STRUCTURAL DEFECTS IN HIGH
PURITY IRON
B. Astie, J. Degauque
To cite this version:
BEHAVIOUR OF MAGNETIC DOMAIN WALLS IN PRESENCE OF STRUCTURAL DEFECTS IN HIGH PURITY IRON
B. ASTIE AND J. DEGAUQUE
Laboratoire de Physique des Solides, associe au CNRS, INSA, Avenue de Rangueil, 31077 Toulouse Cedex, France
RdsumC
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A partir d e l a mesure du f r o t t e m e n t intCrieur magnCtomCcanique, on a CtudiC I1influence d e diffhrents dCfauts structuraux (dislocations, joints d e grains, interstitiels d e carbone et carbures p r k i p i t b ) sur l e comportement des parois d e Blochi
90" dans l e f e r pur. On determine l a distribution d e contraintes internes locales et l e f a c t e u r d e forme du cycle dlhystCrCsis magnCtom&anique, d6finis dans le mod&le d e Smith et Birchak [I]. Leurs variations sont relibes aux modifications d e densite et d'arrangement des dCfauts d e s t r u c t u r e 6tudiCs.Abstract
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Using magnetomechanical damping experiments, w e have studied t h e influence of various structural d e f e c t s (dislocations, grain boundaries, interstitial carbon a t o m s and precipitated carbides) on t h e hysteretic behaviour of 90" magnetic domain walls (DW1s) in pure iron. The distribution of internal local stresses and t h e shape f a c t o r of t h e magnetomechanical hysteresis cycle, as defined in t h e model of Smith and Birchak [ I ] , have been examined. Their variations a r e linked t o t h e modifications of density and arrangement of s t r u c t u r a l defects.I
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INTRODUCTION-
In pure iron, we have already studied t h e influence of dislocations, grain boundaries, inters itla1 carbon a t o m s and precipitated carbides on-1
. .
t h e magnetomechanical damping Q
, w h ~ c h depends only on t h e behaviour of 90°
DW's [2]. When plotted a s a function of t h e shear s t r e s sZ,
this damping, which has been measured on a reversed torsion pendulum, shows a maximum. Its position g!ves t h e average internal s t r e s s bi opposed t o t h e displacements of t h e 90" DWts 111. Looking at t h e whole of t h e Q-'( 5 ) variation, i t is possible t o deduce t h e distribution function N of t h e local internal stresses revealed by t h e irreversible displacements of 90" DW1s. Moreover if t h e calculation of t h e magnetomechanical losses at t h e maximum damping c a n be reached for every distribution function N, t h e shape f a c t o r K of t h e hysteresis loop c a n be deduced from t h e value of Q - h a The magnetomechanical energy losses a r e directly proportional t o K [l]. In this paper, a f t e r a brief description of t h e variations of Q-; and 6 . with t h e arrangements ofI
t h e structural d e f e c t s studied, w e give first t h e results concerning t h e influence of t h e modifications of N on the determination of K. Then t h e variations of these quantities a r e studied in order t o describe t h e f e a t u r e s of t h e behaviour of 90' DW's interacting with various structural d e f e c t s in polycrystalline iron. ,
I1
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DETERMINATION OF THE SHAPE FACTOR K*-
The distribution function of t h e 1local stresses N( ) is obtained by derivation s t a r t i n g from t h e values of Q- ( t )
h he
results given here c a n b e found in the thesis ofB.
Astie(D.E.,
Univ. Paul Sabatier Toulouse) (to b e published).C10-722 JOURNAL DE PHYSIQUE
N ( z ) is a distribution ,function, normalized t o I. It is zero a t Z = 0, goes towards zero when 5 4 00 and has only one maximum NM a t S = ' C N M . N can be expressed
in terms of the dimensionless parameters
Z
/ z N and N/NM. In this representation?n
it is useful t o define a "distribution width" L, w h ~ c h is t h e distance between t h e two values of
Z
/ Z N M corresponding t o N/N = 0.5. For t h e distribution function N, this width is called Lr. {-cording t o [ I ]p-bM
is given by the relation (2)where E i s the Young's modulus,
hloo
t h e saturation magnetostriction and CN a parameter which can be computed for every distribution function N. For the whole range of variation of L studied, t h e relative variation of CN is less than 7 %. So K,1
which is deduced from (2), depends mainly on t h e quantity (Q-M x
(Ti).
The relative accuracy in t h e determination of Lr and K is around 0.07.I11
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ARRANGEMENTS OF THE STRUCTURAL DEFECTS STUDIEDDislocations
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Different arranger?ents of dislokations a r e built by tensile strainings a t 300 K with strain levels between 0 and 16.4 %. Three stages appear on the stress strain curve which correspond respectively t o t h e creation of isolated dislocationsM.
with t h e strain hardening
ACT
(which is proportional t ofi,
wwh D density of c r e a t e d dislocations) but with different slopes.Grain boundaries
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By recrystallisations at different temperatures, t w o s e t s (A and 8)of specimens a r e obtained with different dislocation densities. The grain s i z e d is homogeneous throughout every specimen and increases from 0.021 mm t o 0.425 mm.
1
bi
and l/Q-M increase linearly with t h e density of grain boundaries. The slope of t h e s e variations i s nearly similar f o r t h e two s e t s b u t t h e level is higher f o r s e t A which corresponds t o t h e higher dislocation density [2].Fe-C alloy
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A pure iron-carbon alloy (180 ppm.w carbon) is annealed a t two temperatures. A t 40°C only precipitates ofE
carbide appear, whose density increases1
in function of time. l / Q - M decreases when
6
remains practically constant. This is connected with t h e counterbalance of t h e anchoring e f f e c t of precipitates by a "release effect" due t o t h e decrease of t h e restoring force of t h e interstitial carbon a t o m s on t h e 90° DW's [3]. At 200°C, a f t e r 10 mn of annealing, t h e precipitation of1
&
carbide i s followed by t h a t of cementite. 1 / ~ - ~ and6.
increase markedly a t t h e beginning of this second stage, which is connected with t h e efficient anchoring e f f e c t of precipitates whose s i z e becomes comparable t o t h e DW1s width i 3 1 -Fig. 2
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K vs-
strain hardening(a)
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reciprocal grain size (b)-
annealing t i m e in hC10-724 JOURNAL DE PHYSIQUE
IV
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EXPERIMENTAL RESULTS AND DISCUSSIONDislocations
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Lr increases in t h e stages I and I1 with t h e density D of c r e a t e d dislocations and i s constant in s t a g e I11 (Fig. 1 a). The corresponding values of L show t h a t t h e reduced distribution function of internal stresses depends more o n t h e arrangement of isolated dislocations than on t h e density. N/NM becomes less homogeneous (L increases) in s t a g e I, when isolated dislocations a r e created. Then N/NM keeps i t s shape in s t a g e 11, when t h e newly c r e a t e d dislocations cluster in tangles. In s t a g e 111, N/NM becomes homogeneous again, when cells of dislocations a r e forming, with decreasing density of isolated dislocations inside them.The coefficient K decreases uniformly when D increases, with a stronger r a t e in s t a g e I (Fig. 2 a). The shape of t h e magnetomechanical loop is mainly a f f e c t e d by t h e isolated dislocations and much less by tangles o r walls of dislocations.
Grain boundaries
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L decreases similarly f o r t h e t w o s e t s A and B (Fig.1 b). So, t h e reduced distributions N/NM show t h e s a m e trend towards homogeneity when t h e density of grain boundaries increases. The distributions corresponding t o set B a r e more homogeneous due t o t h e lower density of dislocations. The coefficient Kdecreases with t h e average grain s i z e (Fig.2 b). K i s also a f f e c t e d by t h e higher density of dislocations of set A. '
Fe-C alloy
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For t h e annealing at 40°C, Lr and L have similar variations showing t h a t t h e reduced N/NM becomes more homogeneous when t h e content of interstitial carbon a t o m s decreases and t h e density of&
carbides increases (Fig.1 c). The surprising behaviour of t h e shape f a c t o r K ( F i g . 2 ~ ) which is different from t h a t observed above, i s attributed t o t h e "release effect" previously discussed.According t o t h e variations of Lr and L, t h e precipitation of cementite, during annealing at 200°C, is linked t o a decrease of t h e homogeneity of t h e reduced distribution N/NM, when t h e
size
of t h e precipitates becomes comparable t o t h e width of DW's (Fig.1 d). A t longer annealing t i m e s ( t>
500 mn), when t h e density of precipitates decreases, N/NM is more homogeneous. The increase of K a t t h e beginning of t h e annealing is due t o t h e "release e f f e c t u (Fig.2 d). K decreases markedly (for t>
20 mn), a s t h e density of precipitates does not change very much [3]. So t h e decrease of K is connected t o t h e increasing compatibility of t h e s i z e of t h e precipitates and t h e DW's width. The c e m e n t i t e carbides act as pinning c e n t e r s which induce strong local perturbations on t h e 90°DWts.V
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CONCLUSION-
In pure iron, structural d e f e c t s a c t differently, according t o their density and their arrangement, on t h e behaviour of 90" DWts. Isolated dislocations, grain boundaries and c e m e n t i t e carbides of s i z e comparable t o t h e width of t h e DWts, a f f e c t markedly t h e homogeneity of t h e distribution of internal stresses, opposed t o t h e displacements of 90°DW's, and t h e shape f a c t o r of t h e magnetomechanical loop. This shape f a c t o r is more sensitive t o t h e braking e f f e c t of t h e interstitial carbon a t o m s t h a n t o t h e anchoring e f f e c t by t h e precipitates of carbide.REFERENCES
[ I ] Smith, G.W., Birchak, J.R., J.A. Phys.,
