RESEARCH OF THERMOMETRIC MATERIAL Er1-xScxNiSb. I. MODELLING OF PERFORMANCES
Authors:   Lviv Polytechnic National University, Krayovskyy Volodymyr , Pashkevych Volodymyr ,   Lviv Polytechnic National University, Horpenuk Andriy ,   Lviv Polytechnic National University, Romaka Volodymyr ,   Lviv Polytechnic National University, Stadnyk Yuriy ,   Ivan Franko National University of Lviv, Romaka Lyubov ,   Ivan Franko National University of Lviv, Horyn Andriy ,   Ivan Franko National University of Lviv, Romaka Vitaliy ,   Leibniz Institute for Solid State Research
Published: May 2021

Automated The results of modeling performances of the semiconductor solid solution Er1-xScxNiSb are presented, which can be a promising thermometric material for the manufacture of sensitive elements of thermoelectric and electroresistive thermocouples. Fullprof Suite software was used to model the crystallographic characteristics of the Er1-xScxNiSb thermometric material. Modeling of the electronic structure of Er1-xScxNiSb was performed by Coring-Kon-Rostocker methods in the approximation of coherent potential and local density using the exchange-correlation potential Moruzzi-Janak-Williams and Linear Muffin-Tin Orbital in the framework of DFT density functional theory. The Brillouin zone was divided into 1000 k-points, which were used to model energetic performances by calculating DOS. The width of the energy window was 22 eV and was chosen to capture all semi-core states of p-elements. Full potential (FP) was used in the representation of the linear MT orbital in the representation of plane waves. The accuracy of calculating the position of the Fermi level was εF ± 6 meV. To verify the existence of a continuous solid solution, Er1-xScxNiSb substitution, the change in the values of the period of the unit cell a (x) was calculated within the framework of the DFT density functional theory in the range x = 0–1.0. It is presented that the calculated and experimentally obtained dependences of the period of the unit cell a(x) Er1-xScxNiSb are almost parallel, which confirms the correctness of the used tools and the obtained modeling results. To research the possibility of obtaining thermometric material Er1-xScxNiSb in the form of a continuous solid solution was performed modeling of thermodynamic calculations in the approximation of harmonic oscillations of atoms in the theory of DFT density functional for a hypothetical solid solution Er1-xScxNiSb, x = 0–1.0. It is shown that the change in the values of free energy ΔG(x) (Helmholtz potential) passes through the minimum at the concentration x≈0.1 for all temperatures of possible homogenizing annealing of the samples, indicating the solubility limit of Sc atoms in the structure of the ErNiSb compound. The presence of this minimum indicates that the substitution of Er atoms for Sc atoms in the ErNiSb compound is energetically advantageous only up to the concentration of impurity atoms Sc, x≈0.1. At higher concentrations of Sc atoms, x> 0.10, stratification occurs (spinoidal phase decay). It is shown that modeling of the mixing entropy behavior S even at a hypothetical temperature T = 4000 K shows the absence of complete solubility of Sc atoms in Er1-xScxNiSb. To model the energetic and kinetic performances of the semiconductor thermometric material Er1-xScxNiSb, particularly the behavior of the Fermi level F e , bandgap width g e the distribution of the density of electronic states (DOS) and the behavior of its electrical resistance ρ(x, T) is calculated for an ordered variant of the structure in which the Er atoms in position 4a are replaced by Sc atoms. It is shown that the ErNiSb compound is a semiconductor of the electronic conductivity type, in which the Fermi level is located near the level of the conduction band C e . The modeling showed that at higher concentrations of Sc atoms, the number of generated acceptors exceeds the concentration of uncontrolled donors, and the concentration of free holes exceeds the concentration of electrons. Under these conditions, the Fermi level F e approaches, and then the level of the valence band Er1- xScxNiSb crosses: the dielectric-metal conductivity transition occurs. The experiment should change the sign of the thermo-emf coefficient α(x, T) Er1-xScxNiSb from negative to positive, and the intersection of the Fermi level F e and the valence band changes the conductivity from activating to metallic: on the dependences ln(ρ(1/T)) the activation sites disappear, and the values of resistivity ρ increase with temperature.