Crystal structure of 7M modulated Ni–Mn–Ga martensitic phase
Introduction
Ferromagnetic shape memory materials such as Ni–Mn–Ga Heusler alloys attract much attention because they exhibit the giant magnetic-field-induced-strain (MFIS) effect (see, e.g., Refs. [1], [2] and references therein) and remarkable magnetocaloric properties [3], [4]. These ferromagnetic alloys are characterized by a martensitic transformation below or above the Curie temperature TC. They are also characterized by the unusual combination of strong magnetoelastic coupling and extremely mechanically soft crystal lattice [1]. The observed MFIS is due to the magnetic field-induced twin rearrangement in the martensitic phase.
A number of martensitic structures have been found in the Ni–Mn–Ga system [5], [6]. The basic martensitic structure is a result of the spontaneous uniform lattice distortion of the parent cubic phase with a L21 structure type. The distorted lattice can be tetragonal, orthorhombic or monoclinic, depending on the composition of Ni–Mn–Ga alloy and the temperature [5]. In addition, evidenced by the presence of satellites in diffraction experiments, lattice modulations (periodic shuffling of nearly close-packed planes) can appear [5], [6].
Despite the intense research dedicated to this important material, the role of the martensitic structure in defining the MFIS mechanism and the magnetic properties is not completely understood. In particular, the giant magnetostrain effect is observed only for Ni–Mn–Ga modulated martensites [7], [8]. As MFIS is strongly dependent on magnetostress value and twin boundary mobility [1], [2], [7], the crystal structure determination of these modulated martensites is of fundamental importance.
The most frequently observed modulated Ni–Mn–Ga martensitic structures have been indicated as 5M and 7M, depending on the number of unit cells of basic structure involved in the related superstructure [6]. The description of the displacive modulation of atomic layers at the basis of these complex structures has been the object of several structural investigations [5], [6], [9]. Recently, accurate determination of the “5M” crystal structure of stoichiometric martensite Ni2MnGa has been achieved by the application of superspace theory on powder diffraction data [10]. These studies have demonstrated that the “5M” modulation in Ni–Mn–Ga alloys can be commensurate or incommensurate [11].
However, the crystal structure of 7M martensite in Ni–Mn–Ga (known also as 14M-type [5]) is still not well established. The 7M martensitic structure is characterized by a diffraction pattern with six satellites between the main reflections associated with the distorted basic structure [5], [6], [12]. The lattice distortion with respect to the original parent L21 structure has been generally described in terms of the orthorhombic structure with a > b > c [6], [8], [11], [12]. The first observation of this type of structure was reported in an experiment where a stoichiometric Ni2MnGa single crystal was subjected to external tensile or compression loads along the cubic 〈1 0 0〉 or 〈1 1 0〉 crystallographic directions, respectively, at room temperature [6]. Furthermore, investigations devoted to the composition dependence of structural and magnetic properties evidenced the presence of temperature-induced 7M modulated martensite in Mn-rich [13], [14] and Ni-rich [15] Ni–Mn–Ga alloys. Such a Ni–Mn–Ga martensite displays some analogies with the Ni–Al layered martensitic structure [16]. The Ni-rich binary Ni–Al alloys show a martensitic phase, called 7R or, more recently, 7M [5], with a monoclinic structure with seven-layered modulation. Elastic neutron scattering experiments revealed the periodicity of the modulation to be consistent with a modulation vector q close to 1/7[1 1 0]c (subscript c indicates the B2-ordered parent cubic lattice) [17]. This structure has been described in terms of a (5, ) stacking sequence (related to Zhdanov’s notation) of the (1 1 0)c nearly close-packed atomic planes. The same model has been applied to the Ni-rich Ni–Mn–Ga martensitic phase showing 7M modulation. This composition has been investigated by transmission electron microscopy (TEM) analysis [14], and the reported high resolution electron microscopy (HREM) images along [2 1 0] and [0 1 0] monoclinic zone axes were compared with a model consisting of a (5, )2 stacking arrangement of (1 1 0)c atomic planes. Although this structural model is considered the most similar to the martensitic structure shown by HREM projections, the authors reported non-perfect periodicity of the stacking sequence.
The main object of the present study is a precise determination of the crystal structure of the 7M-type modulated Ni–Mn–Ga martensitic phase. For this purpose, a powdered sample of Mn-rich composition was investigated by X-ray diffraction (XRD). The structure was found to show an incommensurate “7M” modulation which has been solved by the superspace approach. The Rietveld refinement achieved the convergence, giving a structure comparable with a (5, )2 layers stacking. Moreover, the crystal structure obtained by this procedure has also been applied to a martensitic phase of Ni-rich composition investigated in the present work by powder neutron diffraction (PND).
Section snippets
Experimental
Polycrystalline ingots with nominal composition Ni2Mn1.2Ga0.8 and Ni2.15Mn0.85Ga were prepared by melting the pure elements of electrolytic Ni 99.97 at.%, electrolytic Mn 99.5 at.% and Ga 99.9 at.% in a non-consumable-electrode arc furnace in Ar atmosphere. Several re-melts were performed to ensure good homogeneity. The samples were thermally treated in Ar flow at 800 °C for 5 h. Energy dispersion spectrometry (EDS) was used to check the sample composition. Both martensitic and Curie transition
Results
The powder diffraction pattern of Ni2Mn1.2Ga0.8 martensite, collected at room temperature and shown in Fig. 1, was analyzed in order to determine the unit cell parameters of the fundamental lattice. The system is found to belong to a monoclinic symmetry with unit cell parameters: a = 4.222 Å, b = 5.507 Å, c = 4.267 Å and β = 93.3°. As already remarked, the 7M martensite is frequently associated with a pseudo-orthorhombic lattice based on the parent L21 structure, whose unit cell parameters are derived
Structural analysis
This section is dedicated to the crystal structure analysis in comparison with the models previously proposed to explain the structural characteristic of the 7M martensitic phase.
The values of and parameters shown in Table 2 evidence that the major atomic displacement from the basic positions corresponds to the x-coordinate. Fig. 2 shows a graphical representation of the modulation function superimposed onto a two-dimensional projection (with y = 0.5 and z = 0) of the fourth-dimensional
Concluding remarks
For the first time, a Ni–Mn–Ga 7M modulated structure has been solved by XRD analysis. The crystal structure presented in this work represents the first crystallographic model of this type of modulated Ni–Mn–Ga martensitic phase provided by a structural refinement. Several new insights emerge from the determination of the 7M crystal structure found for Ni2Mn1.2Ga0.8 martensite stable at room temperature. The modulation is not commensurate with a sevenfold superstructure but, on the contrary, is
Acknowledgements
The authors are grateful to the Institute Laue-Langevin (Grenoble, France) for providing technical and financial support. VAC is grateful to Fondazione Cariplo (Project 2004.1819-A10.9251) for financial support.
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