The results of modeling the thermometric characteristics of the semiconductor solid solution Lu1–xZrxNiSb, which is a promising thermometric material for the manufacture of sensitive elements of thermoelectric and electro resistive thermocouples, are presented. Modeling of the electronic structure of Lu1–xZrxNiSb was performed by the Korringa–Kohn–Rostoker (KKR) method in the approximation of coherent potential and local density and by the full-potential method of linearized plane waves (FLAPW). KKR simulations were performed using the AkaiKKR software package in the local density approximation for the exchange-correlation potential with parameterization Moruzzi, Janak, Williams in the semi-relativistic one taking into account the spin-orbit interaction. The implementation of the method in the Elk software package was used to perform FLAPW calculations. To check the limits of the existence of the thermometric material Lu1–xZrxNiSb, both methods were used to calculate the change in the values of the period of the unit cell a(x) in the range x = 0 – 1.0. It is shown that there is an agreement between the change in the values of a(x) Lu1–xZrxNiSb calculated by the FLAPW method and the results of experimental studies. The obtained result indicates higher accuracy of modeling of structural parameters Lu1–xZrxNiSb by the FLAPW method in comparison with the KKR method. To study the possibility of obtaining thermometric material Lu1–xZrxNiSb and to establish the limits of its existence in the form of a continuous solid solution, modeling of thermodynamic characteristics in the approximation of harmonic oscillations of atoms within the theory of DFT density functional for a hypothetical solid solution Lu1–xZrxNiSb, x = 0 – 1.0. The change in the values of the enthalpy of mixing ΔH and the total energy E Lu1–xZrxNiSb, x = 0–1.0, allows us to state that the thermometric material exists in the form of a solid substitution solution in the concentration range x = 0 – < 0.20. At higher concentrations of impurity Zr atoms, x > 0.20, stratification occurs (spinoidal phase decay) and thermometric material does not exist. To understand the mechanisms of electrical conductivity of the thermometric material Lu1–xZrxNiSb, the methods of entry of impurity Zr atoms into the matrix of the basic semiconductor p-LuNiSb and their occupation of different crystallographic positions, as well as the presence of vacancies in them, were investigated. For this purpose, its electronic structure was modeled for different variants of the spatial arrangement of atoms and the presence of vacancies in crystallographic positions. It is shown that the most acceptable results of experimental studies are the model of the electronic structure of p-LuNiSb, which assumes the presence of vacancies in the crystallographic positions of 4a Lu atoms (~0.005) and 4c Ni atoms (~0.04). In this model of the spatial arrangement of atoms and the presence of vacancies at positions 4a and 4c, the LuNiSb compound is a semiconductor of the hole-type conductivity, in which the Fermi level eF is located near the level of the valence band eV. The kinetic characteristics of the semiconductor thermometric material Lu1–xZrxNiSb, in particular, the temperature dependences of the resistivity ρ(T, x) and the thermopower coefficient α(T, x) are modeled. It is established that at the lowest concentrations of impurity atoms Zr the Fermi level eF Lu1–xZrxNiSb passes from the bandgap to the conduction band eС. This is indicated by the negative values of the thermopower coefficient α(T, x) and the metallic conductivity type Lu1–xZrxNiSb. This changes the type of main current carriers from holes to electrons.

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