SIMULATION OF CHARACTERISTICS OF SENSITIVE ELEMENTS OF TEMPERATURE CONVERTERS BASED ON TiCo1-xCrxSb
Authors:   Lviv Politecnic National University, Krayovskyy Volodymyr , Haraniuk Petro ,   Lviv Politecnic National University, Horpeniuk Andrii ,   Lviv Politechnic National University, Romaka Volodymyr ,   Lviv Politechnic National University, Stadnyk Yuriy ,   Ivan Franko National University of Lviv, Ukraine, Romaka Lyubov ,   Ivan Franko National University of Lviv, Horyn Andriy ,   Ivan Franko National University of Lviv
Published: December 2024

The results of modeling the thermodynamic, structural, and kinetic properties of the thermometric material TiCo1-xCrxSb, x=0–0.10, as well as the conversion functions of sensitive elements of a thermoelectric converter based on it in the temperature range of 4.2–1000 K are presented. The results presented continue the research of sensitive elements of temperature converters based on basic semiconductor thermometric material TiCoSb. Previous studies of the structural, energetic, and kinetic properties of TiCoSb showed that its crystal structure is disordered, and there are vacancies in the crystallographic positions of the 4c Co atoms and 4a Ti atoms. In the semiconductor TiCoSb, the Fermi level εF is located in the band gap εg, the width of which is εg≈257 meV.

The sensitive elements of the temperature transducers are made of thermometric material TiCo1-xCrxSb, obtained by doping the base semiconductor TiCoSb with Cr atoms (3d54s1), introduced into the structure by substitution of Co atoms (3d74s2) in the crystallographic position 4c. Since the Cr atom has fewer 3d-electrons than Co, such doping should have generated impurity acceptor states in the band gap εg. In this way, it is planned to change the degree of compensation of TiCo1-xCrxSb and the mechanisms of electrical conductivity. In turn, having a mechanism for changing the concentration of energy states, we can predictably optimize the kinetic properties of the TiCo1-xCrxSb thermometric material. This will increase the sensitivity and accuracy of sensitive elements of resistance thermometers and thermoelectric converters.

Thermometric materials TiCo1-xCrxSb, x=0.01–0.10, were produced by fusing a charge of components in an electric arc furnace with a tungsten electrode (cathode) in an atmosphere of purified argon under a pressure of 0.1 kPa on a copper water- cooled base (anode). Titanium was used as a getter. Heat treatment of alloys consisted of homogenizing annealing at a temperature of 1073 K for 720 hours. in vacuumed quartz ampoules (up to 1.0 Pa) with temperature control with an accuracy of ±10 K. Arrays of diffraction data were obtained on a STOE STADI-P powder diffractometer (Cu Kα1-radiation), and structural characteristics of TiCo1-xCrxSb were calculated using the Fullprof program. The chemical and phase compositions of the samples were monitored using metallographic analysis (scanning electron microscope Tescan Vega 3 LMU).

DFT calculations were performed using the Vienna Ab initio Simulation Package VASP v. 5.4.4 with potentials of the PAW type. The Perdew-Burke-Enzerhoff exchange-correlation functional in the Monkhorst-Pack generalized gradient approximation (GGA) for the 11×11×11 k-grid was used. In all calculations, the plane wave cutoff was set to 400 eV. A supercell approach was used for mixed-arrangement crystal structures. In this case, lattice symmetry was reduced and all unique atom distributions were generated using a combinatorial approach. The lattice parameters for such structures were optimized by varying the lattice volume, which was then fitted by the universal equation of state. The electronic kinetic coefficients were calculated using the Exciting code (FLAPW – Full Potential Linearized Augmented Plane Waves method) by solving the linearized Boltzmann equation in the approximation of a constant relaxation time. The modeling of the distribution of the density of electronic states (DOS) was performed using the Korringa-Kohn-Rostoker (KKR) method (AkaiKKR software package) in the Coherent Potential Approximation (CPA) and Local Density Approximation (LDA) for the exchange-correlation potential with by the Moruzzi-Janak-Williams (MJW) parameterization]. The accuracy of calculating the position of the Fermi level εF is ±6 meV. Modeling of thermometric characteristics of sensitive elements of electroresistive and thermoelectric thermometers in the temperature range of 4.2–1000 K was carried out using the FLAPW method, Elk software package.

Modeling of the cell period change a(x) for the ordered version of the TiCo1-xCrxSb structure, x=0–0.1, showed a linear increase in the cell period, since the atomic radius of Cr (rCr=0.128 nm) is greater than the atomic radius of Co (rCo=0.125 nm) . Experimental studies of the structure of samples TiCo1-xCrxSb, x=0–0.1, established that the change in the period a(x) does not correspond to the simulation results. In the concentration range x=0–0.02, the values of the period a(x) increase, which was expected when replacing Co atoms (3d74s2) with Cr atoms (3d54s1), because the atomic radius of Cr is larger than the atomic radius of Co. Such changes will lead to a redistribution of the electron density and the appearance of defects of an acceptor nature, since the Cr atom contains fewer d-electrons than the Co atom. Occupancy by Cr atoms of vacancies in the 4a position of Ti atoms and 4c of Co atoms, which are present in TiCoSb, can also cause an increase in the values of the cell period a(x) of TiCo1-xCrxSb. The presence of vacancies gives rise to structural defects of an acceptor nature, and acceptor states will appear in the band gap εg. If Ti atoms (3d24s2) are replaced by Cr atoms in position 4a or they occupy vacancies in TiCo1-xCrxSb, structural defects of the donor nature will be generated (Cr has more d-electrons than Ti).

For the ordered version of the structure of the hypothetical thermometric material TiCo1-xCrxSb, x=0–1.0, the calculation of thermodynamic characteristics in the approximation of harmonic oscillations of atoms was carried out within the framework of the DFT density functional theory. The results of calculating the change in the values of the Gibbs thermodynamic potential ΔGmix(х) of the thermometric material TiCo1-xCrxSb show a negligible solubility of Cr atoms.

Calculation of the electronic structure of the semiconductor thermometric material TiCo1-xCrxSb, x=0–0.10, for the ordered variant of the crystal structure showed that in the basic thermometric material TiCoSb the Fermi level εF lies in the band gap εg near its middle. Doping TiCoSb with the lowest concentration of Cr atoms (x=0.005) leads to the appearance of defects of an acceptor nature (Cr has fewer d-electrons than Co). As a result, corresponding acceptor states εА will appear in the band gap εg, which are located near the valence band εV. The Fermi level εF in TiCo0,995Cr0,005Sb will move from the middle of the band gap εg to the valence band εV. In the experiment, we will obtain a thermometric material with positive values of the thermopower coefficient α(T,x), which will serve as one branch of the thermoelectric temperature converter.

When the concentration of Cr admixture increases, for example in TiCo0,98Cr0,02Sb, the concentration of acceptor states will increase, which will force the Fermi level εF to cross the edge of the valence band εV and be located in the zone of continuous energies. Finding the Fermi level εF in the valence band εV will change the type of electrical conductivity of the thermometric material TiCo1-xCrxSb from activation to metallic.

Having calculated the electronic structure of TiCo1-xCrxSb, we will obtain a tool for modeling the behavior of the resistivity ρ(х,T) and the thermopower coefficient α(T,x) when acceptor states appear in the band gap εg. At the lowest concentration of the acceptor impurity Cr, х=0.002, the electrical conductivity has a metallic character, and the values of ρ(T,x) are the highest. The increase in the values of the specific resistance ρ(х,T) TiCo1-xCrxSb with increasing temperature is due to the mechanisms of scattering of current carriers. High values of the thermopower coefficient α(T,x) at temperatures T=40–800 K show that the thermometric material TiCo1-xCrxSb remains a highly doped semiconductor, whose Fermi level εF lies in the valence band εV. This is indicated by the positive values of the thermopower coefficient α(T,x). An increase in the concentration of the acceptor impurity Cr is accompanied by an increase in the concentration of holes, and this leads to a decrease in the values of the specific resistance ρ(x,T), and the holes continue to be the main current carriers of the thermometric material TiCo1-xCrxSb. The simulation showed that the introduction of Cr atoms into the TicoSb structure changes its electronic structure and redistributes the density of electronic states at the Fermi level g(εF).

The transformation functions of the Pt-TiCo0.99Cr0.01Sb thermoelectric pair are presented. We can see that the obtained sensitive elements of thermotransducers based on the latest thermometric materials have high sensitivity. The ratio of change of thermopower values to the range of temperature measurements in thermocouples is greater than all known industrial thermocouples. However, due to the metallization of the conductivity of the thermometric material TiCo1-xCrxSb, x>0.005, the temperature coefficient of resistance (TCR) of the obtained resistance thermometers is greater than the TCR of metals, but it is inferior to the value of TCR of sensitive elements made of semiconductor materials.