Effect of a magnetic field on phase transformation of steel
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Electromagnetic theory is used to characterize the magnetization processes in metals and alloys. The analysis shows that the free energy of a phase transformation may be reduced or enhanced by the magnetic field depending on the ratio of the permeability of the old and new phases. This means that the magnetic field can either stimulate or inhibit the nucleation process. The theory is in accord with the experimental results by others and us.
I. INTRODUCTION 1–3
Recent studies had discovered many effects of a magnetic field on phase transformation, including on solidification and martensitic transformation. Ohtsuka4 investigated the aging of an Fe–23.3 Ni–9.4 Al (mass%) alloy carried out both in the presence of a magnetic and in the absence of a magnetic field at 673, 873, and 973 K for 5 h. The saturation magnetic moments of the samples were measured, and a systematic difference in average magnetic moment was observed between the samples aged with and without a magnetic field. The average magnetic moment of the samples aged under a magnetic field was smaller than that aged without a magnetic field. Transmission electron microscopy (TEM) observation showed evidence of spinodal decomposition of disordered body-centered-cubic (bcc) (A2) and ordered bcc (B2) phases. The A2 phase was an Fe-containing solid solution, and the B2 was a NiAl phase. Up to now, there has not been a better explanation for the observation.
from the magnetization of the phase. The volume occupied by the particles of phase transformation we denote by V1, and that of the medium exterior to it by V2. The energy of the field owing to phase transformation is T2 = 1⁄2
HB d +
V2
兰
V1
兰 H dB B
d
,
0
(2)
and the change in energy resulting from phase transformation
兰
T = T 2 − T1 = 1 ⁄ 2 +
兰
共HB − H1B1兲 d
冉兰 H dB − ⁄ H B 冊 V2
B
V1
d
12
0
1 1
(3)
.
Owing that the relations between B and H are linear B1 = 1H1 T = 1 ⁄2
II. MODEL OF THE PHASE TRANSFORMATION ON APPLICATION OF A MAGNETIC FIELD
兰
= 1 ⁄2
兰 兰
B = 1H
,
in V2 ,
共H1B − HB1兲 d
V1
共2 − 1兲HH1 d
V1
(4)
.
A. Variation in energy by a magnetic field
Let us suppose that a magnetic field B1 from fixed sources has been established in a magnetic medium. We shall assume that the relation of B1 to H1 is linear and the medium is isotropic.5 The energy of the field is T1 = 1⁄2
兰
V
␦T = 1⁄2 H1B1 d
,
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兰␦HH
d ≈ 1⁄2
1
兰␦H
2
d
.
(5)
(1)
extended over all space. After the production of phase transformation in the medium the modified field at any point is B, and the difference B2 ⳱ B − B1 is thus the field resulting 2280
If the permeability is varied by an infinitesimal amount ␦, the consequent change in the magnetic energy is
J. Mater. Res., Vol. 16, No. 8, Aug 2001 Downloaded: 18 Aug 2014
Therefore, the change in energy resulting from phase transformation is U = 1 ⁄2
兰兰
2
1
H2 d d
.
© 2001 Materials Research Society IP address: 129.15.14.53
(6)
W. Liu et al.: Effect of a magnetic field on phase transformati
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