The influence of Co and Cu doping on Ni-Mn-Ga Heusler alloy is investigated using the first-principles exact muffin-tin orbital method in combination with the coherent-potential approximation. Single-element doping and simultaneous doping by both elements are investigated in Ni${}_{50-x}$Co${}_x$Mn${}_{25-y}$Ga${}_{25-z}$Cu${}_{y+z}$ alloys, with dopant concentrations $x,y$, and $z$ up to 7.5 at. %. Doping with Co in the Ni sublattice decreases the ${(c/a)}_{\text{NM}}$ ratio of the nonmodulated (NM) martensite, but it simultaneously increases the cubic phase stability with respect to the NM phase. Doping with Cu in the Mn or in Ga sublattices does not change the ${(c/a)}_{\text{NM}}$ ratio significantly and it decreases the cubic phase stability. For simultaneous doping by Co in the Ni sublattice and Cu in the Mn or Ga sublattices, the effects of the individual dopants are independent and about the same as for the single-element doping. Thus, the ${(c/a)}_{\text{NM}}$ ratio can be adjusted by Co doping while the phase stability can be balanced by Cu doping, resulting in stable martensite with a reduced ${(c/a)}_{\text{NM}}$. The local stability of the cubic phase with respect to the tetragonal deformation can be understood on the basis of a density-of-states analysis.

We investigated the effects of interstitial N and C on the stacking fault energy (SFE) of an equiatomic CoCrNi medium entropy alloy. Results of computer modeling were compared to tensile deformation and electron microscopy data. Both N and C in solid solution increase the SFE of the face-centered cubic (FCC) alloy matrix at room temperature, with the former having a more significant effect by 240% for 0.5 at % N. Total energy calculations based on density functional theory (DFT) as well as thermodynamic modeling of the Gibbs free energy with the CALPHAD (CALculation of PHAse Diagrams) method reveal a stabilizing effect of N and C interstitials on the FCC lattice with respect to the hexagonal close-packed (HCP) CoCrNi-X (X: N, C) lattice. Scanning transmission electron microscopy (STEM) measurements of the width of dissociated ½ dislocations suggest that the SFE of CoCrNi increases from 22 to 42–44 mJ·m⁻² after doping the alloy with 0.5 at. % interstitial N. The higher SFE reduces the nucleation rates of twins, leading to an increase in the critical stress required to trigger deformation twinning, an effect which can be used to design load-dependent strain hardening response. GRAPHICAL ABSTRACT

The ab initio electronic structure calculations of the ${\mathrm{Ni}}_2\mathrm{MnGa}$ alloy indicate that the orthorhombic 4O structure exhibits the lowest energy compared to all known martensitic structures. The 4O structure is formed by nanotwin double layers, i.e., oppositely oriented nanotwins consisting of two (101) lattice planes of nonmodulated martensitic structure. It exhibits the lowest occupation of density of states at the Fermi level. The total energy 1.98 meV/atom below the energy of nonmodulated martensite is achieved within structural relaxation by shifting Mn and Ga atoms at the nanotwin boundaries. The same atomic shift can also be found in other martensitic nanotwinned or modulated structures such as 10M and 14M, which indicates the importance of the nanotwin double layer for the stability of these structures. Our discovery shows that the nanotwinning or modulation is a natural property of low-temperature martensitic phases in Ni-Mn-Ga alloys.

In order to explain the formation of low-temperature phases in stoichiometric Ni₂MnGa magnetic shape memory alloy, we investigate the phase transformation paths from cubic austenite with Heusler structure to low-symmetry martensitic structures. We used ab initio calculations combined with the generalized solid state nudged elastic band method to determine the minimum energy path and corresponding changes in crystal lattice. The four-, five-, and seven-layered modulated phases of martensite (4O, 10M, and 14M) are built as the relaxed nanotwinned non-modulated (NM) phase. Despite having a total energy larger than the other martensitic phases, the 10M phase will spontaneously form at 0 K, because there is no energy barrier on the path and the energy decreases with a large negative slope. Moreover, a similar negative slope in the beginning of path is found also for the transformation to the 6M premartensite, which appears as a local minimum on the path leading further to 10M martensite. Transformation paths to other structures exhibit more or less significant barriers in the beginning hindering such a transformation from austenite. These findings correspond to experiment and demonstrates that the kinetics of the transformation is decisive for the selection of the particular low-symmetry structure.