A high resolution synchrotron x-ray powder diffraction study of the incommensurate modulation in the martensite phase of Ni2MnGa: Evidence for nearly 7M modulation and phason broadening

摘要

The modulated structure of the martensite phase of Ni2MnGa is revisited usinghigh resolution synchrotron x-ray powder diffraction (SXRPD) measurements,which reveals higher order satellite reflections up to the 3rd order and phasonbroadening of the satellite peaks. The structure refinement, using the (3+1)dimensional superspace group approach, shows that the modulated structure ofNi2MnGa can be described by orthorhombic superspace group Immm(00$\gamma$)s00with lattice parameters a= 4.21861(2) {\AA}, b= 5.54696(3) {\AA}, and c=4.18763(2) {\AA} and an incommensurate modulation wave vector q= 0.43160(3)c*=(3/7+$\delta$)c*, where $\delta$=0.00303(3) is the degree of incommensurationof the modulated structure. Additional satellite peak broadening, which couldnot be accounted for in terms of the anisotropic strain broadening based on alattice parameter distribution , has been modeled in terms of phasons usingfourth rank covariant strain tensor representation for incommensuratestructures. The simulation of single crystal diffraction patterns from therefined structural parameters unambiguously reveals a rational approximantstructure with 7M modulation. The inhomogeneous displacement of differentatomic sites on account of incommensurate modulation and the presence of phasonbroadening clearly rule out the adaptive phase model proposed recently byKaufmann et al.[1] and suggests that the modulation in Ni2MnGa originates fromsoft-mode phonons.