Original ArticlesChemical ordering in Ni-Mn-Ga Heusler alloys
Introduction
Heusler alloys have attracted attention for their potential as actuators in electromechanical systems because several of the alloys, including Ni2MnGa, exhibit a BCC → BCT (c/a = 0.94) martensitic transition at temperature Ms (1). Heusler alloys, with the stoichiometric formula A2BC, have an ordered L21 structure. This ordering can arise from the high temperature disordered A2 phase either directly (A2→ L21) or via the intermediate B2′ phase (A2→B2′→L21) (2).
A good deal is known about the martensitic and ferromagnetic phase transitions in Ni2MnGa 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13. To understand the coupling of the phase transitions, it is necessary to characterize the chemical order-disorder transition, since the physical properties of the ordered and disordered phases are different. However, little experimental data 14, 15 exists regarding the A2→B2′→L21 chemical ordering sequence in Ni50MnxGa50-x during cooling. Hence, the purpose of this investigation is to characterize the chemical ordering transition in Ni50MnxGa50-x over a composition range of 15 ≤ x ≤ 35 by performing in situ neutron diffraction measurements.
Experimental results are compared to the predictions of a model based on the Bragg-Williams-Gorski (BWG) approximation. Long range order parameter η vs. temperature T and a quasibinary temperature-composition diagram are considered. The T-c diagram, with a composition range of 15 ≤ x ≤ 35, is presented to describe the A2→B2′→L21 ordering transition and the alloy melting transition. Phase transitions in selected Ni50MnxGa50-x alloys are verified using differential thermal analysis (DTA).
A simple, analytical calculation by which the A2→B2′→L21 ordering sequence of Ni2MnGa may be modeled is based on the Bragg-Williams approximation (16). The BWG approximation has been used in numerous investigations 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29 over the years for characterization of order-disorder phenomena in alloys. One such calculation by Murakami et al. (25) considered off-stoichiometric Heusler alloys using a BWG model with four order parameters.
Calculations of long range order parameters and T-c diagrams for complex ordering ternary systems such as Heusler alloys have been performed using the cluster variation method (CVM). Sanchez et al. (30), present the fundamental statistical-thermodynamical foundation of this method, which is based on a generalized 3-D Ising model. A set of generalized prototype CVM calculations were performed by McCormack et al.(2) for a stoichiometric A2BC Heusler system to illustrate the qualitative features of the phase transition. According to these prototype calculations, the A2→B2′ transition is of 2nd order while the order of the B2′→L21 transition depends on the ratio between nearest and next-nearest neighbor pair interaction energies. Experimentally, both 1st and 2nd order transitions have been observed for B2′→L21 ordering (31).
Section snippets
A. Bragg-Williams-Gorski approximation
A BWG model, similar to a calculation by Murakami, is used to characterize the classical ordering sequence that is postulated to occur in Ni50MnxGa50-x upon cooling. The BWG model is modified by using the static concentration wave method of Khatchaturyan (32) to establish a set of lattice occupation probabilities pik that are required to construct a model of the A2→B2′→L21 phase transition. The order parameters η1 and η2 are defined as
A. preparation of Ni50MnxGa50-x alloys
Alloys of composition Ni50Mn15Ga35, Ni50Mn20Ga30, Ni50Mn22Ga28, Ni50Mn25Ga25, Ni50Mn27Ga23, Ni50Mn29Ga21, Ni50Mn30Ga20, Ni50Mn33Ga17 and Ni50Mn35Ga15 were prepared by the Materials Preparation Center-Ames Laboratory. The alloys were formulated by pouring measured amounts of 99.99999 at. % solid Ga and electrolytic flake Mn in a small formed dish of 99.9999 at. % sheet Ni. The Ni-Mn-Ga buttons were arc melted, allowed to solidify and remelted several times to ensure compositional homogeneity (33)
A. differential thermal analysis
The DTA data for Ni50Mn15Ga35, Ni50Mn20Ga30, Ni50Mn25Ga25, Ni50Mn27Ga23, Ni50Mn30Ga20, Ni50Mn33Ga17 and Ni50Mn35Ga15 exhibit shallow “peaks” and baseline step changes during heating and cooling which may be attributed to B2′→L21 transitions as verified by neutron diffraction data. DTA cooling scans for Ni50Mn20Ga30, Ni50Mn25Ga25 and Ni50Mn30Ga20 are presented in Figures 1 (a)-(c). The melting and B2′→L21 transition temperatures of several of the Ni50MnxGa50-x alloys, as observed by DTA, are
Conclusions
- 1.
The B2′→L21 transition is observed by neutron diffraction measurements in all Ni50MnxGa50-x alloys except for Ni50Mn15Ga35. The B2′→L21 transition in Ni50Mn15Ga35 is observed by DTA.
- 2.
Thermal peaks and baseline step changes corresponding to latent heats of the B2′→L21 transitions are very small, but present in all of the Ni50MnxGa50-x alloys evaluated by DTA.
- 3.
The A2→B2′ transition is not observed in any Ni50MnxGa50-x alloys by DTA. However incomplete B2′ order is observed in Ni50Mn15Ga35, Ni50Mn20
Acknowledgements
The authors wish to thank Dr. William Boettinger and Ms. Maureen Williams of the Materials Science and Engineering Laboratory at the National Institute of Standards and Technology for providing the differential thermal analysis data used in this study. We also wish to thank B.H. Toby, J.K. Stalick and F.B. Altorfer of the NIST Center for Neutron Research for expert advice on powder diffraction data analysis and technical assistance.
References (34)
- et al.
Scripta Metall.
(1992) Acta Metall.
(1959)- et al.
Acta Metall.
(1971) - et al.
Acta Metall.
(1983) - et al.
Physica
(1984) - et al.
Phil. Mag. A.
(1998) - et al.
Phys. Rev. B.
(1996) J. Appl. Phys.
(1960)- et al.
Phys. Met. Metall.
(1989) - et al.
Scripta Metall.
(1995)
Phys. Met. Metall.
Phys. Met. Metall.
Sov. Phys. JETP.
Phys. Met. Metall.
J. Phys. III Fr.
J. Phys. Cond. Matter.
Cited by (136)
Magnetocaloric effect in large temperature window on off-stoichiometric Ni-Mn-Ga-based Heusler alloys
2023, Journal of Alloys and CompoundsBi-doping engineering of Ni-Mn-Ga polycrystals and resulting grain particles for smart Ni-Mn-Ga/polymer composites
2023, Journal of Materials Research and TechnologyOrdering mechanism and kinetics in Ni<inf>2</inf>Mn<inf>1−x</inf>Cu<inf>x</inf>Ga ferromagnetic shape memory alloys
2021, Journal of Alloys and Compounds