High-resolution synchrotron x-ray powder diffraction study of the incommensurate modulation in the martensite phase of Ni_2MnGa: Evidence for nearly 7M modulation and phason broadening

摘要

The modulated structure of the martensite phase of Ni_2MnGa is revisited using high-resolution synchrotron x-ray powder diffraction measurements, which reveal higher-order satellite reflections up to the third order and phason broadening of the satellite peaks. The structure refinement, using the (3+1) dimensional superspace group approach, shows that the modulated structure of Ni_2MnGa can be described by orthorhombic superspace group Immm(00γ)s00 with lattice parameters a = 4.21861(2) A, b = 5.54696(3) A, and c = 4.187 63(2) A, and an incommensurate modulation wave vector q = 0.431 60(3)c~* = (3/7 + δ)c~*, where δ = 0.00303(3) is the degree of incommensuration of the modulated structure. Additional satellite peak broadening, which could not be accounted for in terms of the anisotropic strain broadening based on a lattice parameter distribution, has been modeled in terms of phasons using fourth-rank covariant strain-tensor representation for incommensurate structures. The simulation of single-crystal diffraction patterns from the refined structural parameters unambiguously reveals a rational approximant structure with 7M modulation. The inhomogeneous displacement of different atomic sites on account of incommensurate modulation and the presence of phason broadening clearly rule out the adaptive phase model proposed recently by Kaufmann et al. [S. Kaufmann, U. K. Roessler, O. Heczko, M. Wuttig, J. Buschbeck, L. Schultz, and S. Faehler, Phys. Rev. Lett. 104, 145702 (2010)] and suggest that the modulation in Ni_2MnGa originates from soft-mode phonons.