The results of modeling the properties of the semiconductor solid solution Lu1-xScxNiSb, x=0–0.10, which is a promising thermometric material for the manufacture of sensitive elements of thermocouples, are presented. Modeling of the electronic structure of Lu1-xScxNiSb 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. The Elk software package was used in the FLAPW calculations. To check the limits of the existence of the thermometric material Lu1-xScxNiSb by the KKR method, the change of the values of the period of the unit cell a(x) in the range x=0–0.10 was calculated. It is established that the substitution of Lu atoms in the crystallographic position 4a by Sc atoms is accompanied by a decrease in the values of the unit cell period a(x) Lu1-xScxNiSb. This behavior of a(x) Lu1-xScxNiSb is since the atomic radius Sc (rSc=0.164 nm) is smaller than that of Lu (rLu=0.173 nm). In this case, structural defects of neutral nature are generated in Lu1-xScxNiSb, because the atoms Lu (5d 1 6s 2 ) and Sc (3d 1 4s 2 ) are located in the same group of the Periodic Table of the Elements and contain the same number of d-electrons. To study the conditions for obtaining thermometric material Lu1-xScxNiSb, x=0–0.10, and to establish the energy feasibility of its formation in the form of a continuous solid solution, modeling of thermodynamic characteristics in the approximation of harmonic oscillations of atoms within the DFT density functional theory. The low values of the enthalpy of mixing ΔHmix(x) and the nature of the dependence behavior indicate the energy expediency of substitution in the crystallographic position 4a of Lu atoms for Sc atoms and the existence of a solid substitution solution for the studied samples Lu1-xScxNiSb, x=0–0.10. To understand the mechanisms of electrical conductivity of the thermometric material Lu1-xScxNiSb, x=0–0.10, various models of crystal and electronic structures of the basic semiconductor LuNiSb are considered. Assuming that the crystal structure of Lu1-xScxNiSb is ordered (crystallographic positions are occupied by atoms according to the MgAgAs structural type), the Elk software package was used to model the DOS electronic state density distribution for LuNiSb and Lu0.875Sc0.125NiSb. It is shown that in the LuNiSb compound the Fermi level lies in the middle of the band gap , and the bandwidth is =190.5 meV. DOS simulations for the ordered variant of the Lu0.875Sc0.125NiSb crystal structure show a redistribution of the density of DOS electronic states and an increase in the band gap . In this case, the Fermi level , as in the case of LuNiSb, lies in the middle of the band gap , and the generated structural defects are neutral. The DOS calculation for the disordered variant of the crystal structure of the LuNiSb compound was performed using a model that can be described by the formula Lu1+yNi1-2ySb. In this model, the Lu atoms partially move to the 4c position of the Ni atoms, and in this position, a vacancy (y) occurs simultaneously. Moreover, as many Lu atoms additionally move to the 4c position of Ni atoms, so many vacancies arise in this position. In this model of the crystal structure of the LuNiSb compound and the absence of vacancies (y=0), the calculation of the DOS electronic state density distribution indicates the presence of the band gap εg , and the Fermi level εF lies near the valence band εV. In the model of the structure of the LuNiSb compound at vacancy concentrations y=0.01, the DOS calculation also shows the presence of the band gap εg , and the Fermi level εF still lies near the valence band εV. Since Ni atoms make the greatest contribution to the formation of the conduction band εC, even at a concentration of y=0.02, the DOS calculation shows that the Fermi level εF now lies near the conduction band εC. This means that the main carriers of the electric current of the LuNiSb compound at y=0.02 are electrons, which does not correspond to the results of experimental studies. Based on the above model of the disordered crystal structure of the LuNiSb compound, the density distribution of DOS electronic states was calculated for the disordered variant of the crystal structure of the thermometric material Lu1-xScxNiSb, which is described by the formula Lu1-x+yScxNi1-2ySb. In this model of the Lu1-xScxNiSb crystal structure, the calculation of the DOS electronic state density distribution shows the presence of a band gap εg , in which small energy levels ("tail tails") are formed, which overlap with the zones of continuous energies. In this case, the Fermi level εF is localized at low energy levels, which makes it impossible to accurately determine the depth from the Fermi level εF. The proposed model is correct only for a small number of impurity Sc atoms since the partial occupation of the 4c position of Ni atoms by Lu atoms significantly deforms the structure with its subsequent decay. The results of experimental studies of the kinetic, energy, and magnetic properties of the thermometric material Lu1-xScxNiSb will show the degree of adequacy of the proposed model.

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