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Magnetic field-induced martensitic transformations in a few ferrous alloys
34
Journal of Magnetism and Magnetic Materials 90 & 91 (1990) 34-36 North-Holland
Magnetic field-induced martensitic transformations in a few ferrous alloys T. Kakeshita, K. Shimizu, M. Ono
a
and M. Date
a
TIle Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567, Japan a Department of Physics, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan
Martensitic transformation start temperature, M s ' increased with increasing magnetic field, and the increase was quantitatively explained by cumulative three effects of the magnetostatic energy, high field susceptibility and forced volume magnetostriction. In addition, much information was obtained as to the morphology and growth behavior of magnetic field-induced martensites.
The effect of magnetic fields on martensitic transformations in ferrous alloys and steels has. been investigated by many workers, especially by Sadovsky's group in the USSR and recently by the authors' group. The investigation by the author's group will be described in the present paper. They have clarified influences of composition, grain boundaries, crystal orientations, Invar characteristics, thermoelastic nature and austenite magnetism on the magnetic field-induced martensitic transformations in Fe-Ni, Fe-Ni-C, Fe-Pt, Fe-NiCo-Ti and Fe-Mn-C alloys, and they proposed a new formula to explain the relation between the shift of transformation start temperature, Ms' and critical magnetic field, He' for inducing the transformation. According to a previous paper by Krivoglaz and Sadovsky [1], the effect of magnetic field on martensitic transformations is due only to the magnetostatic (Zeeman) energy. They proposed the following formula to estimate the shift of transformation start temperature, AMs = M; - M s ' due to the Zeeman energy as a function of critical magnetic field He; AMs = -AM(M;)HJo/Q,
(1)
where AM(M;) = MY(M;) - Ar'(M;), MY, u-'. being the spontaneous magnetization of the austenitic and martensitic states at the shifted M s ' M;, respectively, To: the equilibrium temperature of the two phases, Q: the latent heat of transformation. However, in our investigation, a large discrepancy has been observed between experimentally measured AMs and the calculated one by using the above formula. In deriving the above formula, the Gibbs chemical free energy of austenitic and martensitic phases was assumed to be simply in a linear relation with temperature. However, the situation is not so simple in real alloy systems, and therefore the above formula should be an approximation. Thus, in the present paper, the formula itself is re-examined and a new and more exact
formula is proposed taking account the high field susceptibility and forced volume magnetostriction energies as well as the Zeeman energy, as described below. A more exact expression was adopted for the Gibbs chemical free energy, as derived by Kaufman and Cohen [2] and other researchers. In eq. (1), magnetic energy due to the high field susceptibility of austenite phase was neglected, although it was fairly large for ferromagnetic alloys. Then, the magnetic energy due to the high field susceptibility is introduced besides that due to the Zeeman energy. It may be expressed approximately as - !X~f(T)H2, because the magnetization increases linearly with magnetic field. Patel and Cohen [3] developed a theory to explain the shift of M, when a uniaxial stress or hydrostatic pressure was applied to an alloy system. By analogy with the theory, AM. vs. He relation may be expressed as follow, instead of eq. (1),
(2) where AG(M;) = GY(M;) - Ga'(M;), GY and G" being the Gibbs chemical free energies of austenitic and martensitic phases at temperature M;, respectively. This equation is a quadratic one of He' which can be obtained by solving it for specific M;, if AG, AM and X~f are known as a function of temperature. The Gibbs chemical free energies were obtained by following the equations proposed by Kaufman and Cohen [2] and other researchers. The value of AM(T) can be known from the measured spontaneous magnetization of austenitic phase and estimated one of martensitic phase (from the Slater-Pauling curve), and X~f(T) from M(t) vs. H(t) curves. By substituting these known values in eq. (2), AM~ vs. He relations have been calculated for Fe-Ni, Fe-Ni-C, Fe-Pt and Fe-Mn-C alloys. The calculated relations were almost consistent with mea-
0304-8853/90/$03.50
T. Kakeshita et al. / Field-induced martensitic transformation
sured ones for non-thermoelastic non-Invar Fe-Ni-C and paramagnetic Fe-Mn-C alloys, but not for other alloys which were all Invar. Therefore, the inconsistency between the calculated and measured 6.Ms vs. He relations may be related to the Invar nature of those alloys. It is well known that Invar alloys have a large forced volume magnetostriction, which is defined as field-induced volume change, ow/oH, where w is a volume change per unit volume. According to previous measurements, it is isotropically positive, that is, the austenite lattice is subjected to a volume expansion. In a phenomenological point of view, it can be regarded as a negative hydrostatic pressure for the austenite lattice. This means that ow/oH corresponds to - ow/oP under hydrostatic pressure. The only difference between them is their sign, namely ow/oll> 0 while ow/oP < O. The effect of hydrostatic pressure was quantitatively studied by Patel and Cohen (3), as mentioned before. They proposed the following equation to estimate 6.Ms when a hydrostatic pressure P was applied to a ferrous alloy;
(3)
•
1001(b)
,,'fJ
80,.. Fe-24.7Ni-1.8C lot%)
6.G(Ms ) =
-
., ,
"",
, ~ 60"-
".",'
~
., ""
~
~ 40lI)
where (0: the volume change associated with martensitic transformation. The negative sign on the right-hand-side is due to the fact that (0 is inverse to P in sign. On the other hand, when a negative hydrostatic pressure (that is, isotropic expansion) is produced by the forced volume magnetostriction effect, the negative term -coP must be replaced by the positive term (o(lJw/lJH)HB, since (lJw/lJll)llB = (6.V/V)B corresponds to the hydrostatic pressure, where B is the bulk modulus. Hence, taking account of the magnetic energy due to the forced volume magnetostriction effect as well as the Zeeman and high field susceptibility energies, the 6.Ms vs. lle relations in Invar alloys must be represented by the following formula;
35
~
20-
,-'.'
o
,
I
,.'
,,
I
I
10 20 JO Magnetic Field IT) (e)
80-
g
_ 60lI)
~
~
~ 40lI)
~
20-
6.G(M;)
-6.M(M;)He -
o
hI.r(J.t;)ll;
+ (o(lJw/lJll)lle B.
(4)
In the case of thermoelastic martensitic transformation in an Invar Fe-Pt alloy, (0 becomes negative, and so the positive sign of the last term must be replaced by a negative sign. The 6.M s vs. lle relations were thus calculated for the four alloy systems by substituting the values of various physical quantities of those alloys into eq. (4), as done by using eq. (3). Of the physical quantities, the volume change (0 in Fe-Ni, Fe-Ni-C and Fe-Mn-C alloys were measured by X-ray diffraction, and that in
I
I
10 20 30 Magnetic Field lTl
Fig. 1. Comparison between calculated (- - -) and measured (e) tiM. vs. He relations for (a) Invar Fc-Ni and Fe-Pt alloys, (b) non-Invar Fe-Ni-C alloy and (c) param agnetic Fe-Mn-C alloy.
the Fe-Pt alloy was referred to a previous work. The final forced volume magnetostriction was measured by Fabry-Perot interferometry for all those alloys, and B was obtained by referring to previous works. The calculated 6.Ms vs. He relations are shown with dotted lines in fig. 1 together with the measured ones (small closed circles), (a) being for Invar Fe-31.7 and - 32.5 at %> Ni
36
T. Kakeshita et al. / Field-induced martensitic transformation
and Fe-24 at% Pt alloys, (b) for a non-Invar Fe24.7Ni-1.8C(at%) alloy and (c) for a paramagnetic Fe3.9Mn-5.0C(at%) alloy. It is clearly seen from the figure that the calculated relations are essentially in good agreement with the measured ones over the wide range of liMs and He.
References [IJ M.A. Krivoglaz and V.D. Sadovsky, Metal. Metalloved, 18 (1964) 502. [2J L. Kaufman and M. Cohen, Progr. Metal Phys. 7 (1958) 165. [3J l.R. Patel and M. Cohen, Acta Metall. 1 (1953) 531.
Journal of Magnetism and Magnetic Materials 90 & 91 (1990) 34-36 North-Holland
Magnetic field-induced martensitic transformations in a few ferrous alloys T. Kakeshita, K. Shimizu, M. Ono
a
and M. Date
a
TIle Institute of Scientific and Industrial Research, Osaka University, Ibaraki, Osaka 567, Japan a Department of Physics, Faculty of Science, Osaka University, Toyonaka, Osaka 560, Japan
Martensitic transformation start temperature, M s ' increased with increasing magnetic field, and the increase was quantitatively explained by cumulative three effects of the magnetostatic energy, high field susceptibility and forced volume magnetostriction. In addition, much information was obtained as to the morphology and growth behavior of magnetic field-induced martensites.
The effect of magnetic fields on martensitic transformations in ferrous alloys and steels has. been investigated by many workers, especially by Sadovsky's group in the USSR and recently by the authors' group. The investigation by the author's group will be described in the present paper. They have clarified influences of composition, grain boundaries, crystal orientations, Invar characteristics, thermoelastic nature and austenite magnetism on the magnetic field-induced martensitic transformations in Fe-Ni, Fe-Ni-C, Fe-Pt, Fe-NiCo-Ti and Fe-Mn-C alloys, and they proposed a new formula to explain the relation between the shift of transformation start temperature, Ms' and critical magnetic field, He' for inducing the transformation. According to a previous paper by Krivoglaz and Sadovsky [1], the effect of magnetic field on martensitic transformations is due only to the magnetostatic (Zeeman) energy. They proposed the following formula to estimate the shift of transformation start temperature, AMs = M; - M s ' due to the Zeeman energy as a function of critical magnetic field He; AMs = -AM(M;)HJo/Q,
(1)
where AM(M;) = MY(M;) - Ar'(M;), MY, u-'. being the spontaneous magnetization of the austenitic and martensitic states at the shifted M s ' M;, respectively, To: the equilibrium temperature of the two phases, Q: the latent heat of transformation. However, in our investigation, a large discrepancy has been observed between experimentally measured AMs and the calculated one by using the above formula. In deriving the above formula, the Gibbs chemical free energy of austenitic and martensitic phases was assumed to be simply in a linear relation with temperature. However, the situation is not so simple in real alloy systems, and therefore the above formula should be an approximation. Thus, in the present paper, the formula itself is re-examined and a new and more exact
formula is proposed taking account the high field susceptibility and forced volume magnetostriction energies as well as the Zeeman energy, as described below. A more exact expression was adopted for the Gibbs chemical free energy, as derived by Kaufman and Cohen [2] and other researchers. In eq. (1), magnetic energy due to the high field susceptibility of austenite phase was neglected, although it was fairly large for ferromagnetic alloys. Then, the magnetic energy due to the high field susceptibility is introduced besides that due to the Zeeman energy. It may be expressed approximately as - !X~f(T)H2, because the magnetization increases linearly with magnetic field. Patel and Cohen [3] developed a theory to explain the shift of M, when a uniaxial stress or hydrostatic pressure was applied to an alloy system. By analogy with the theory, AM. vs. He relation may be expressed as follow, instead of eq. (1),
(2) where AG(M;) = GY(M;) - Ga'(M;), GY and G" being the Gibbs chemical free energies of austenitic and martensitic phases at temperature M;, respectively. This equation is a quadratic one of He' which can be obtained by solving it for specific M;, if AG, AM and X~f are known as a function of temperature. The Gibbs chemical free energies were obtained by following the equations proposed by Kaufman and Cohen [2] and other researchers. The value of AM(T) can be known from the measured spontaneous magnetization of austenitic phase and estimated one of martensitic phase (from the Slater-Pauling curve), and X~f(T) from M(t) vs. H(t) curves. By substituting these known values in eq. (2), AM~ vs. He relations have been calculated for Fe-Ni, Fe-Ni-C, Fe-Pt and Fe-Mn-C alloys. The calculated relations were almost consistent with mea-
0304-8853/90/$03.50
T. Kakeshita et al. / Field-induced martensitic transformation
sured ones for non-thermoelastic non-Invar Fe-Ni-C and paramagnetic Fe-Mn-C alloys, but not for other alloys which were all Invar. Therefore, the inconsistency between the calculated and measured 6.Ms vs. He relations may be related to the Invar nature of those alloys. It is well known that Invar alloys have a large forced volume magnetostriction, which is defined as field-induced volume change, ow/oH, where w is a volume change per unit volume. According to previous measurements, it is isotropically positive, that is, the austenite lattice is subjected to a volume expansion. In a phenomenological point of view, it can be regarded as a negative hydrostatic pressure for the austenite lattice. This means that ow/oH corresponds to - ow/oP under hydrostatic pressure. The only difference between them is their sign, namely ow/oll> 0 while ow/oP < O. The effect of hydrostatic pressure was quantitatively studied by Patel and Cohen (3), as mentioned before. They proposed the following equation to estimate 6.Ms when a hydrostatic pressure P was applied to a ferrous alloy;
(3)
•
1001(b)
,,'fJ
80,.. Fe-24.7Ni-1.8C lot%)
6.G(Ms ) =
-
., ,
"",
, ~ 60"-
".",'
~
., ""
~
~ 40lI)
where (0: the volume change associated with martensitic transformation. The negative sign on the right-hand-side is due to the fact that (0 is inverse to P in sign. On the other hand, when a negative hydrostatic pressure (that is, isotropic expansion) is produced by the forced volume magnetostriction effect, the negative term -coP must be replaced by the positive term (o(lJw/lJH)HB, since (lJw/lJll)llB = (6.V/V)B corresponds to the hydrostatic pressure, where B is the bulk modulus. Hence, taking account of the magnetic energy due to the forced volume magnetostriction effect as well as the Zeeman and high field susceptibility energies, the 6.Ms vs. lle relations in Invar alloys must be represented by the following formula;
35
~
20-
,-'.'
o
,
I
,.'
,,
I
I
10 20 JO Magnetic Field IT) (e)
80-
g
_ 60lI)
~
~
~ 40lI)
~
20-
6.G(M;)
-6.M(M;)He -
o
hI.r(J.t;)ll;
+ (o(lJw/lJll)lle B.
(4)
In the case of thermoelastic martensitic transformation in an Invar Fe-Pt alloy, (0 becomes negative, and so the positive sign of the last term must be replaced by a negative sign. The 6.M s vs. lle relations were thus calculated for the four alloy systems by substituting the values of various physical quantities of those alloys into eq. (4), as done by using eq. (3). Of the physical quantities, the volume change (0 in Fe-Ni, Fe-Ni-C and Fe-Mn-C alloys were measured by X-ray diffraction, and that in
I
I
10 20 30 Magnetic Field lTl
Fig. 1. Comparison between calculated (- - -) and measured (e) tiM. vs. He relations for (a) Invar Fc-Ni and Fe-Pt alloys, (b) non-Invar Fe-Ni-C alloy and (c) param agnetic Fe-Mn-C alloy.
the Fe-Pt alloy was referred to a previous work. The final forced volume magnetostriction was measured by Fabry-Perot interferometry for all those alloys, and B was obtained by referring to previous works. The calculated 6.Ms vs. He relations are shown with dotted lines in fig. 1 together with the measured ones (small closed circles), (a) being for Invar Fe-31.7 and - 32.5 at %> Ni
36
T. Kakeshita et al. / Field-induced martensitic transformation
and Fe-24 at% Pt alloys, (b) for a non-Invar Fe24.7Ni-1.8C(at%) alloy and (c) for a paramagnetic Fe3.9Mn-5.0C(at%) alloy. It is clearly seen from the figure that the calculated relations are essentially in good agreement with the measured ones over the wide range of liMs and He.
References [IJ M.A. Krivoglaz and V.D. Sadovsky, Metal. Metalloved, 18 (1964) 502. [2J L. Kaufman and M. Cohen, Progr. Metal Phys. 7 (1958) 165. [3J l.R. Patel and M. Cohen, Acta Metall. 1 (1953) 531.