Constant plane shift model: Structure analysis of martensitic phases in Ni50Mn27Ga22Fe1 beyond non-modulated building blocks

Martensites of Ni-Mn-Ga-based alloys consist of hierarchical twinning domains spanning from micro- to nanoscale. This affects the diffraction pattern and thus can decrease the accuracy of the determination of the crystal structure. We propose a method to obtain different martensitic phases in Ni-Mn-Ga-Fe alloy with simplified variant microstructures and domain sizes of more than 2 micrometers. The use of simplified variant microstructures allows the influence of nanometer-scale domains on diffraction line position to be circumvented and enabls the comparison of the lattice parameters of non-modulated (NM), five-layered modulated (10M), and seven-layered (14M) phases in the same temperature range due to the large hysteresis of the intermartensitic transformations. It is found that the short crystallographic axes in NM, 14M, and 10M martensites at the same temperature have different lengths. As a result, equilibrium NM structure building blocks cannot be used to build the crystal structures of 14M and 10M martensites. Instead, we introduce a constant plane shift model with identical shift values of the nearest planes (110) along [1¯10] or [11¯0] as a replacement for the tetragonal building blocks model. The work demonstrates that plane shift values differ dramatically between martensites, which agrees with ab initio calculations. The application of the constant plane shift and hard sphere models in modulated lattices for atomic-level twinning considerations is discussed.