Temperature dependence of elastic properties of Ni2+xMn1-xGa and Ni2Mn(Ga1-xAlx) from first principles

The temperature dependence of the elastic properties of Ni2+xMn1-xGa and Ni2Mn(Ga1-xAlx) (x = 0.0, 0.1, and 0.2) random alloys are investigated by using the first-principles exact muffin-tin orbitals method. At 0 K, the calculated equilibrium parameters in both cubic L2(1) and nonmodulated tetragonal beta'''-Ni2MnGa are in good agreement with the available experimental data and other theoretical results. Separating the thermal effects into single electron excitation, volume expansion, phonon smearing, and magnetic terms, we find that phonon smearing gives the dominating positive tetragonal elastic constant (C') versus temperature (T) slope for the cubic phase. For Ni2+xMn1-xGa, the competition between the negative alloying effect (partial derivative C'/partial derivative x < 0) and the positive temperature effect (partial derivative C'/partial derivative T > 0) leads to nearly constant C'[x, T-M(x)] at the martensitic transition temperature T-M(x). For Ni2Mn(Ga1-xAlx), where both partial derivative C'/partial derivative x and partial derivative C'/partial derivative T are positive, however, due to the significantly decrease of T-M(x), the critical C'[x, T-M(x)] slightly decreases with Al doping. Furthermore, it is demonstrated that both the composition and the temperature dependence of C' are indispensable to get a reasonable theoretical T-M(x).