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

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.

Figures (6)

• Figure 1: Generalized planar fault energy (GPFE) $\gamma$ as a function of $u/s$ for Ni$_{2}$MnGa Heczko2024-of, Ni$_{50}$Mn$_{28.125}$Ga$_{21.875}$Heczko2026-vx, and Ni$_{2}$FeGa Zeleny2023-wu. Solid lines with filled markers correspond to non-optimized atomic configurations, while dashed lines with open markers represent energies obtained after optimization. The horizontal dashed line indicates zero energy reference.
• Figure 2: Schematic illustration of the nanotwin growth process, where each image represents an individual stable configuration during the nanotwin formation, i.e., a minimum on the GPFE curve. Blue, red, and green spheres represent Ni, Mn, and Ga atoms, respectively, while orange sphere represent positions of dopant atom.
• Figure 3: Simulation cell used in the present atomistic model for stoichiometric Ni$_{2}$MnGa NM martensite. Blue, red, and green spheres represent Ni, Mn, and Ga atoms, respectively. The translation vectors are indicated by arrows, and the simulation cell used in the present atomistic model is marked by a thick black line while the dashed lines represent. (a) View of the simulation cell from [010] direction. (b) Three-dimensional view of the simulation cell highlighting the periodic boundary conditions.
• Figure 4: The generalized planar fault energy (GPFE) curves obtained for Cu-, Co-, and Fe-doped systems are presented in a matrix layout. The rows correspond to the dopant chemical species (Cu, Co, and Fe), whereas the columns specify the host chemical species in Ni$_{2}$MnGa that is substituted by the dopant (Mn, Ga, or Ni). For comparison, the GPFE curve of the stoichiometric Ni$_{2}$MnGa system is displayed in the background. Individual dopant configurations are further distinguished by color, as indicated in the respective panels.
• Figure 5: Generalized planar fault energy (GPFE) profiles for Zn-doped Ni–Mn–Ga NM martensite. Two substitutional configurations are examined: Zn substituting Mn (Zn$\rightarrow$Mn) and Zn substituting Ga (Zn$\rightarrow$Ga). Solid curves denote the non-optimized GPFE obtained directly from the imposed shear displacement, whereas dashed curves represent the optimized GPFE refined using the GADGET algorithm in conjunction with the nudged elastic band (NEB) method. For reference, the GPFE curve of stoichiometric Ni$_{2}$MnGa is plotted in grey.