First-principles investigation of structural, electronic, vibrational, and thermoelectric properties of some quaternary half-heusler materials

Half-Heusler materials having 18 valence electrons exhibit semiconductor behavior and are intensively studied because of their thermoelectric properties. Quaternary half-Heusler materials with four different atoms are also have 18 valence electrons similar to the ternary half-Heusler materials and are promising due to their low thermal conductivities. In this study, structural, electronic, vibrational and thermoelectric properties of ternary half-Heusler TiCoSb and ScNiSb and quaternary half-Heusler Ti$_2$FeNiSb$_2$ and MgTiNi$_2$Sb$_2$ materials are calculated from first principles. Calculations are carried out using density functional theory (DFT) within generalized gradient approximation (GGA). Equilibrium lattice parameters are obtained by geometrical optimization. Bulk modulus, pressure dependence of bulk modulus, electronic band structures, total and partial electronic density of states and vibrational properties are calculated and results are compared with available experiments and other calculations. Thermoelectric properties such as Seebeck coefficient, electrical conductivity, and electronic thermal conductivity are calculated within the framework of the semi-classical Boltzmann transport theory and with relaxation time approximation. ZT values are predicted with the help of lattice thermal conductivity and a guessed constant relaxation time coefficient results obtained by available experimental and theoretical studies. The p-type ZT value (0.58) of Ti$_2$FeNiSb$_2$ material which is created by substituting the Co atom in the TiCoSb material with the Fe and Ni atoms was found to be 40\% lower than TiCoSb value (0.94) at 800K. However, it has been shown that the substitution of Mg and Ti atoms instead of Sc atoms in ScNiSb material provides a two-fold increase in MgTiNi$_2$ Sb$_2$ compared to that of ScNiSb (0,42).