First-principles study of doping influence on twin formation in Ni-Mn-Ga nonmodulated martensite

TL;DR

This study uses density functional theory to analyze how different dopants affect twin formation energetics in Ni-Mn-Ga martensite, revealing site-dependent influences on twinning behavior and stability.

Contribution

It provides a microscopic understanding of how specific chemical substitutions alter twin formation barriers and stability in Ni-Mn-Ga martensite.

Findings

Certain dopants lower twin nucleation barriers, promoting twinning.

Other dopants increase barriers, hindering twin formation.

Dopant site and type critically influence twin stability and energetics.

Abstract

We investigate how chemical substitution reshapes the energetics of twin formation in non-modulated (NM) Ni-Mn-Ga martensite. Using density functional theory, we compute generalized planar fault energy (GPFE) curves for the $(101)[10\bar{1}]$ shear system in stoichiometric Ni$_{2}$MnGa and in a set of doped supercells containing Cu, Co, Fe, or Zn on different sublattices. The GPFE landscape is used as a microscopic descriptor of twinning behavior: the first barrier reflects intrinsic stacking-fault formation (twin nucleation), whereas subsequent barriers govern twin thickening and boundary motion. We show that the impact of dopants is strongly site dependent. Substitutions Cu$\rightarrow$Mn, Cu$\rightarrow$Ni, Co$\rightarrow$Ni, and Zn$\rightarrow$Mn lower the nucleation barrier and generally soften the GPFE profile, indicating more favorable conditions for twin formation and propagation; these cases also correlate with a reduced tetragonality $c/a$, which implies a smaller twinning shear and a reduced energetic cost of twin formation. In contrast, Cu$\rightarrow$Ga, Co$\rightarrow$Mn, Co$\rightarrow$Ga, Fe$\rightarrow$Ga, and Zn$\rightarrow$Ga increase GPFE barriers and hinder twinning, even though such substitutions are often used to enhance martensite stability and raise $T_{m}$. Fe$\rightarrow$Mn leaves barrier heights largely unchanged, while Fe$\rightarrow$Ni produces an anomalous GPFE response indicative of unstable twin configurations. Finally, inspired by the nanotwinning characterisation of 10M/14M modulation, we link the depth of the two-layer nanotwin minimum to modulation stability. The substitutions Fe$\rightarrow$Mn, Cu$\rightarrow$Ni, and Zn$\rightarrow$Mn result in a lower energy minimum compared to the structure without the double-layered twin. The other substitutions favor the twin-free NM structure.