In this work, using density functional theory based electronic structure calculations, we carry out a comparative study of geometric, mechanical, electronic, magnetic, and thermoelectric properties of Co x TaZ alloys, where Z = Si, Ge and Sn and x = 1 and 2. In the present study, a systematic approach has been taken to perform calculations to probe the possibility of existence of a tetragonal (martensite) phase in these alloys and also to perform a comparative study of various physical properties of the six systems, mentioned above, in the cubic and possible tetragonal phases. From our calculations, a tetragonal phase has been found to be stable up to about 400 K in case of Co2TaSi and Co2TaGe alloys, and up to about 115 K for Co2TaSn, indicating the presence of room temperature cubic phase in the latter alloy unlike the former two. Further, the results based on the energetics and electronic structure have been found to corroborate well with the elastic properties. All the above-mentioned full Heusler alloys (FHAs) show magnetic behavior with metallicity in both the phases. However, their half Heusler counterparts exhibit non-magnetic semi-conducting behavior in the cubic phase. We calculate and compare the thermoelectric properties, in detail, of all the materials in the cubic and possible tetragonal phases. In the cubic phase, the half Heusler alloys exhibit improved thermoelectric properties compared to the respective FHAs. Furthermore, it is observed that the FHAs exhibit higher (by about an order of magnitude) values of Seebeck coefficients in their cubic phases, compared to those in the tetragonal phases (which are of the order of only a few micro-volts/Kelvin). The observed behaviors of the transport properties of the probed materials have been analyzed using the topology of the Fermi surface.
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