Theoretical description of the phase transitions in Ni-Mn-Ga shape memory alloys under an external stress along [110] axis

Sergey V. Taskaev ,  Vasiliy D. Buchelnikov ,  Nikolay M. Didenko 

Chelyabinsk State University (ChelSU), Br. Kashirinykh Str, 129, Chelyabinsk 454021, Russian Federation


Cubic Heusler Ni-Mn-Ga shape memory alloys are of special attention, because of their structural and magnetic properties. In this kind of Heusler alloys martensitic phase transitions happen in the ferromagnetic state.
To present the phase diagrams of the cubic ferromagnet we take an expression of free energy [1] that contains only order parameter components causing structural and magnetic transitions with the account of external stress along [110] axis. The dimensionless expression for energy in the case ТМ<ТС when a structural transition occurs in a ferromagnetic state is

F=T(e32+e22)/2+sgn(b)e3(e32-3e22)/3+(e32+e22)2/4+B(21/2e2sin2θcos2φ/2+ 61/2e3(3cos2θ-1)/6)+K(sin22θ+sin4θsin22φ)/4+σ(61/2/6e3+1/2ξsin2θsin2φ)

Here T is the dimensionless temperature, ξ, B is the dimensionless magnetostriction constants, K is the dimensionless magnetic anisotropy constant, σ is the dimensionless stress, е2 and е3 are the combinations of the strain tensor, θ and φ are the polar and azimuthal angles of magnetization. In this work we consider the case of B>0 and K>0.
By minimization of free energy (1) with е2, е3, θ, φ we can obtain the following states.
1. The tetragonal phase T1 with magnetization || [001] axes.
2. The orthorhombic phase R1 with magnetization || [001] axes.
3. The tetragonal phase T2 with magnetization || [110] axes.
4. The tetragonal phase T3 with magnetization || [-110] axes.
5. The orthorhombic phase R2 with magnetization ∈ (001) plane.
The phase diagram with b<0 allows us to describe the experimental sequence of the phase transitions which is observed in [2].
This work was particially sponsored by Human Capital Foundation, RF and CRDF Y2-P-05-19, RFBR 05-08-50341, RFBR 06-02-16266, RFBR and JSPS 05-02-19935, RFBR and NNSF 06-02-39030, RFBR 07-02-96029-r_ural_a, RF President MK-5658.2006.2 grants.
[1] V.D.Buchelnikov et al., JETP, 92, (2001) 1019.
[2] V.V.Kokorin et al., Fiz. Tverd. Tela (Leningrad) 33, 1250-1252.

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Presentation: Oral at E-MRS Fall Meeting 2007, Symposium E, by Sergey V. Taskaev
See On-line Journal of E-MRS Fall Meeting 2007

Submitted: 2007-05-11 10:51
Revised:   2009-06-07 00:44
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