(3 + 1)D superspace description of the incommensurate modulation in the premartensite phase of Ni₂MnGa: a high resolution synchrotron x-ray powder diffraction study

Abstract

Le Bail and Rietveld analysis of high resolution synchrotron x-ray powder diffraction (SXRPD) data shows unambiguous signatures of the failure of the commensurate 3M modulation model. Using (3 + 1) dimensional superspace group formalism, we have not only confirmed the incommensurate modulation in the premartensite phase with a modulation wavevector of q = 0.337 61(5)c* but also determined the superspace group (Immm(00γ)s00), atomic positions and amplitude of modulations for the incommensurate premartensite phase of Ni2MnGa for the first time. Our results may have important implications in the understanding of the martensitic transition and hence the magnetic field induced strains.

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

“…Thus, both incommensurate and commensurate cases can be treated equally under this scheme, which is considered as the most appropriate and elegant option for determining the complete crystal structure of modulated martensite. So far, the validity of this general approach has been demonstrated in Heusler-type alloys with different kinds of modulated martensite [28,[31][32][33].…”

High-resolution synchrotron x-ray powder diffraction study of the incommensurate modulation in the martensite phase ofNi2MnGa: Evidence for nearly 7M modulation and phason broadening

“…[14,15] The structure of the low temperature martensite phase of Ni 2 MnGa has been extensively investigated using different diffraction techniques (x-ray, neutron and electron diffraction) for single crystal [16,17,18,19,20,21], powder [19,22,23,24] and epitaxial thin film [1] samples. However, the actual crystal structure and the nature of the modulation in the martensite phase, for which both commensurate and incommensurate modulations have been reported [16,22,23,24], are still controversial.…”

Elasticity and magnetism of Ni2 MnGa premartensitic tweed

“…Despite of the overall cubic symmetry, high resolution synchrotron X‐ray diffraction () shows that the premartensite phase/tweed exhibits the modulation or shuffling with approximate wave vector [1/3, 1/3, 0]. There is a discussion whether this modulation is commensurate () or incommensurate (), but it does not change the overall picture that the premartensite can be considered as consisting of fine (approximate) 6 M modulated phase with all possible modulation directions randomly distributed, or, equivalently, as adaptive phase with () 2 shuffling period .…”