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 crystallo-graphic 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) over bar 10] or [1 (1) over bar0] as a replacement for the tetragonal building blocks model. The work demonstrates that plane shift values differ dramatically between mar-tensites, 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.