Crystal structure determination of incommensurate modulated martensite in Ni–Mn–In Heusler alloys

The crystal structure of modulated martensite in Mn-rich off-stoichiometric Ni₂Mn_1.44In_0.56 alloy was determined with high-resolution powder neutron diffraction and synchrotron X-ray diffraction in the frame of (3 + 1)-dimensional superspace theory. The average crystal structure and the modulation wave vector were firstly derived by analyzing the reflection separations induced by the martensitic transformation on the basis of the transformation orientation inheritance. This treatment could be applied to predetermine the modulated structures of materials with displacive structural transformation. The crystal structure of modulated martensite was finally refined by the Rietveld method. Results show that the martensite possesses an incommensurate 6M modulated structure of superspace group I2/m(α0γ)00, with lattice parameters a = 4.3919(4) Å, b = 5.6202(1) Å, c = 4.3315(7) Å, and β = 93.044(1)°, and the modulation wave vector q = 0.343(7) c*. The detailed site occupations for extra-Mn atoms with respect to the stoichiometric case were investigated by ab initio calculations. The extra-Mn atoms have a preference to be uniformly dispersed. A threefold layered superstructure in the 3-dimensional space was proposed to approximately describe the incommensurate modulated structure. This 6M superstructure model is considered to be representative for off-stoichiometric Ni–(Co)–Mn–In modulated martensite with martensitic transformation around room temperature. The present study is expected to offer an important basis for reliable crystallographic and microstructural characterizations on Ni–Mn–In alloys, so as to understand the underlying mechanisms of their multifunctional magneto-responsive properties.