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