Browsing by Author "Romaka Volodymyr"

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Features of simulation of characteristics of thermometric material Lu1–xZrxNiSb
(Lviv Politechnic Publishing House, 2021) Krayovskyy Volodymyr; Pashkevych Volodymyr; Horpenuk Andriy; Romaka Volodymyr; Stadnyk Yuriy; Romaka Lyubov; Horyn Andriy; Romaka Vitaliy
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 conc 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.
Kinetic and energetic performances of thermometric material TiCo1-xMnxSb: modelling and experiment
(Lviv Politechnic Publishing House, 2021) Krayovskyy Volodymyr; Pashkevych Volodymyr; Rokomanyuk Mariya; Haranuk Petro; Romaka Volodymyr; Stadnyk Yuriy; Romaka Lyubov; Horyn Andriy
The results of a complex study of the semiconductor thermometric material TiCo1-xMnxSb, x=0.01–0.10, for the production of sensitive elements of thermoelectric and electro resistive sensors are presented. Microprobe analysis of the concentration of atoms on the surface of TiCo1-xMnxSb samples established their correspondence to the initial compositions of the charge, and X-ray phase analysis showed the absence of traces of extraneous phases on their diffractograms. The produced structural studies of the thermometric material TiCo1-xMnxSb allow to speak about the ordering of its crystal structure, and the substitution of Co atoms on Mn at the 4c position generate structural defects of acceptor nature. The obtained results testify to the homogeneity of the samples and their suitability for the study of electrokinetic performances and the manufacture of sensitive elements of thermocouples. Modeling of structural, electrokinetic, and energetic performances of TiCo1-xMnxSb, x=0.01–0.10, for different variants of the spatial arrangement of atoms is performed. To model energetic and kinetic performances, particularly the behavior of the Fermi level , the bandgap , the density of states (DOS) distribution was calculated for an ordered variant of the structure in which Co atoms at position 4c are replaced by Mn atoms. Substitution of Co atoms (3d74s2) by Mn (3d54s2) generates structural defects of acceptor nature in the TiCo1-xMnxSb semiconductor (the Mn atom contains fewer 3d- electrons than Co). This, at the lowest concentrations of impurity atoms Mn, leads to the movement of the Fermi level from the conduction band to the depth of the bandgap . In a semiconductor with the composition TiCo0.99Mn0.01Sb, the Fermi level is located in the middle of the bandgap , indicating its maximum compensation when the concentrations of ionized acceptors and donors are close. At higher concentrations of impurity Mn atoms, the number of generated acceptors will exceed the concentration of donors, and the concentration of free holes will exceed the concentration of electrons. Under these conditions, the Fermi level approach, and then the level of the valence band TiCo1-xMnxSb cross: the dielectric-metal conductivity transition take place. The presence of a high-temperature activation region on the temperature dependence of the resistivity ln(ρ(1/T)) TiCo1-xMnxSb at the lowest concentration of impurity atoms Mn, x=001, indicates the location of the Fermi level in the bandgap of the semiconductor thermopower coefficient α(T,x) at these temperatures specify its position - at a distance of ~ 6 meV from the level of the conduction band . In this case, electrons are the main carriers of current. The absence of a low temperature activation region on this dependence indicates the absence of the jumping mechanism conductivity. Negative values of the thermopower coefficient α(T,x) TiCo0,99Mn0,01Sb at all temperatures, when according to DOS calculations the concentrations of acceptors and donors are close, and the semiconductor is maximally compensated, can be explained by the higher concentration of uncontrolled donors. However, even at higher concentrations of impurity Mn atoms in TiCo0,98Mn0,02Sb, the sign of the thermopower coefficient α(T,x) remains negative, but the value of resistivity ρ(x, T) increases rapidly, and the Fermi level deepens into the forbidden zone at a distance of ~ 30 meV. The rapid increase in the values of the resistivity ρ(x, T) in the region of concentrations x=0.01–0.02 shows that acceptors are generated in the TiCo1-xMnxSb semiconductor when Co atoms are replaced by Mn, which capture free electrons, reducing their concentration. However, negative values of the thermopower coefficient α(T,x) are evidence that either the semiconductor has a significant concentration of donors, which is greater than the number of introduced acceptors (x=0.02), or the crystal simultaneously generates defects of acceptor and donor nature. The obtained result does not agree with the calculations of the electronic structure of the TiCo1-xMnxSb semiconductor. It is concluded that more complex structural changes occur in the semiconductor than the linear substitution of Co atoms by Mn, which simultaneously generate structural defects of acceptor and donor nature by different mechanisms, but the concentration of donors exceeds the concentration of generated acceptors. Based on a comprehensive study of the electronic structure, kinetic and energetic performances of the thermosensitive material TiCo1-xMnxSb, it is shown that the introduction of impurity Mn atoms into TiCoSb can simultaneously generate an acceptor zone (substitution of Co atoms for Mn) and donor zones and of different nature. The ratio of the concentrations of ionized acceptors and donors generated in TiCo1-xMnxSb will determine the position of the Fermi level and the mechanisms of electrical conductivity. However, this issue requires additional research, in particular structural and modeling of the electronic structure of a semiconductor solid solution under different conditions of entry into the structure of impurity Mn atoms. The investigated solid solution TiCo1-xMnxSb is a promising thermometric material. Key words: Electronic structure; Resistivity; Thermopower.
Studies of thermometric material Lu1-xZrxNiSb
(Lviv Politechnic Publishing House, 2022) Pashkevych Volodymyr; Krayovskyy Volodymyr; Rokomanyuk Mariya; Haranuk Petro; Romaka Volodymyr; Stadnyk Yuriy; Romaka Lyubov; Horyn Andriy; Fruchart Daniel
The results of experimental research of perspective thermometric material Lu1-xZrxNiSb which can be used for the production of sensitive elements of thermoelectric and electroresistive thermometers are presented. Thermometric materials Lu1–xZrxNiSb, x = 0.01 – 0.10, were made 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 hearth (anode). Heat treatment of alloys consisted of homogenizing annealing at a temperature of 1073 K. Annealing of samples was carried out for 720 h in vacuumed up to 1.0 Pa ampoules of quartz glass in muffle electric furnaces with temperature control with an accuracy of ±10 K. Diffraction arrays were obtained on a diffractometer DRON-4.0 (FeKα radiation), and the structural characteristics of Lu1–xZrxNiSb were calculated using the Fullprof program. The chemical and phase compositions of the samples were monitored using a scanning electron microscope (Tescan Vega 3 LMU). The study of the temperature dependences of the resistivity ρ(T, x) and the thermopower coefficient α(T, x) Lu1–xZrxNiSb was performed in the temperature range of 80÷400 K on samples in the form of rectangular parallelepipeds measuring ~1.0×1.0×5.0 mm3. Measurements of the values of the specific magnetic susceptibility χ(x) of Lu1–xZrxNiSb samples were performed by the relative Faraday method at a temperature of 273 K using a thermogravimetric installation with an electronic microbalance EM-5-ZMP in magnetic fields up to 10 kGs. Microprobe analysis of the concentration of atoms on the surface of Lu1–xZrxNiSb samples, x = 0.01–0.10, established their correspondence to the initial compositions of the charge, and X-ray phase analysis showed no traces of extraneous phases on the sample diffractograms, except for the main phase. The nonmonotonic nature of the change in the values of the unit cell period of the thermometric material an(x) Lu1–xZrxNiSb, x = 0.01 – 0.10, which differs from the results of modeling structural characteristics using software packages AkaiKKR and Elk. The nonmonotonic change in the values of the period of the unit cell a(x) Lu1–xZrxNiSb and the presence of the extremum dependence suggests that the impurity Zr atoms introduced into the matrix of the LuNiSb basic semiconductor can simultaneously occupy partially different crystallographic positions in different ratios. The temperature resistivities ρ and the thermopower coefficient α of the LuNiSb base semiconductor contain high- and low-temperature activation regions, which is characteristic of doped and compensated semiconductors. The introduction into the LuNiSb structure of the lowest concentration of impurity Zr atoms in the experiment (x = 0.01) radically changes both the behavior of the temperature dependences of the resistivity ρ and the thermopower coefficient α and the type of the main electric current carriers. The values of the resistivity ρ(T, x) Lu1–xZrxNiSb only increase with increasing temperature, which is characteristic of the metallic type of electrical conductivity and is due to the mechanisms of scattering of current carriers. This nature of the change in electrical resistance ρ(T, x) is evidence that the Fermi level εF has left the bandgap εg and is in the conduction band εC. This is indicated by the negative values of thermopower coefficient α(T, x) at all сoncentrations and temperatures. Studies of the magnetic susceptibility χ(x) showed that the samples as a basic semiconductor LuNiSb, as well as the thermometric material Lu1–xZrxNiSb, at all concentrations of impurities Zr, are Pauli paramagnetic. There is a synchronicity of the behavior of χ(x) with the dependences of the resistivity ρ(x, T) and the thermopower coefficient α(x, T), which is due to the change in the density of states at the Fermi level g(εF). The results of experimental studies of the Lu1–xZrxNiSb thermometric material completely coincide with the results of modeling its kinetic characteristics under the presence of vacancies in the crystallographic positions 4a and 4c of the Lu and Ni atoms, respectively. Such studies allow making adjustments in the structural studies of thermometric material with an accuracy that significantly exceeds the accuracy of X-ray research methods. The obtained results will allow us to clarify the spatial arrangement of atoms in the nodes of the unit cell, as well as to identify the mechanisms of electrical conductivity to determine the conditions for the synthesis of thermosensitive materials with maximum efficiency of thermal energy conversion into electricity.
Study of thermometric material Er1-xScxNiSb. II. Experimental results
(Lviv Politechnic Publishing House, 2021) Krayovskyy Volodymyr; Pashkevych Volodymyr; Horpenuk Andriy; Romaka Volodymyr; Stadnyk Yuriy; Romaka Lyubov; Horyn Andriy
The results of a comprehensive study of the crystal and electronic structures, kinetic and energetic performances of the semiconductor thermometric material Er1-xScxNiSb (x = 0 – 0.1) are presented. Microprobe analysis of the concentration of atoms on the surface of Er1-xScxNiSb samples established their correspondence to the initial compositions of the charge, and the diffractograms of the samples are indexed in the structural type of MgAgAs. Because the atomic radius Sc (rSc = 0.164 nm) is smaller than that of Er (rEr = 0.176 nm), it is logical to reduce the values of the unit cell's period a(x) Er1-xScxNiSb, which correlate with the results of mathematical modeling. The temperature dependences of the resistivity ln(ρ(1/T)) contain high- and low-temperature activation regions, which are specific for semiconductors and indicate the location of the Fermi level in the bandgap, and positive values of the thermopower coefficient a (x, T) specify its position – near the valence band . This result does not agree with the results of modeling the electronic structure for its ordered version. The presence of a low-temperature activation region on the ln(ρ(1/T)) p-ErNiSb dependence with an activation energy = 0.4 meV indicates the compensation of the sample provided by acceptors and donors of unknown origin. A decrease in the values of the resistivity ρ(x, T) and the thermopower coefficient a(x, T) points to an increase in the concentration of holes in p-Er1-xScxNiSb in the area of concentrations x = 0 – 0.03. This is possible in a p-type semiconductor only by increasing the concentration of the main current carriers, which are holes. The fact of increasing the concentration of acceptors in Er1-xScxNiSb at insignificant concentrations of impurity atoms is also indicated by the nature of the change in the values of the activation energy of holes from the Fermi level to the valence band . Consequently, if in p-ErNiSb the Fermi level was at a distance of 45.4 meV from the level of the valence band , then at the concentration Er1-xScxNiSb, x = 0.01, the Fermi level shifted towards the valence band and was located at a distance of 13.6. Since the Fermi level reflects the ratio of ionized acceptors and donors in the semiconductor, its movement by x = 0.01 to the valence band is possible either with an increase in the number of acceptors or a rapid decrease in the concentration of ionized donors. At even higher concentrations of Sc impurity in p-Er1-xScxNiSb, x ≥ 0.03, low-temperature activation sites appear on the ln(ρ(1/T)) dependences, which is a sign of compensation and evidence of the simultaneous generation of acceptor and donor structural defects in the crystal nature. This is also indicated by the change in the position of the Fermi level in the bandgap of the semiconductor Er1-xScxNiSb, which is almost linearly removed from the level of the valence band : (x = 0.05) = 58.6 meV and (x = 0.10) = 88.1 meV. Such a movement of the Fermi level during doping of a p-type semiconductor is possible only if donors of unknown origin are generated. For a p-type semiconductor, this is possible only if the concentration of the main current carriers, which are free holes, is reduced, and donors are generated that compensate for the acceptor states. This conclusion is also confirmed by the behavior of the thermopower coefficient a(x, T) at concentrations x ≥ 0.03. The results of structural, kinetic, and energy studies of the thermometric material Er1-xScxNiSb allow us to speak about a complex mechanism of simultaneous generation of structural defects of acceptor and donor nature. However, the obtained array of experimental information does not allow us to unambiguously prove the existence of a mechanism for generating donors and acceptors. The research article offers a solution to this problem. Having the experimental results of the drift rate of the Fermi level as the activation energy (x) from the Fermi level to the valence band by calculating the distribution of the density of electronic states (DOS) sought the degree of compensation, which sets the direction and velocity of the Fermi level as close as possible to the experimental results. DOS calculations are performed for all variants of the location of atoms in the nodes of the unit cell, and the degree of occupancy of all positions by their own and/or foreign atoms. It turned out that for ErNiSb the most acceptable option is one that assumes the presence of vacancies in positions 4a and 4c of the Er and Ni atoms, respectively. Moreover, the number of vacancies in the position Er (4a) is twice less than the number of vacancies in the position Ni (4c). This proportion is maintained for Er1-xScxNiSb. Vacancies in the positions of Er (4a) and Ni (4c) atoms Er1-xScxNiSb are structural defects of acceptor nature, which generate two acceptor zones and in the semiconductor. The introduction of impurity Sc atoms into the ErNiSb structure by substituting Er atoms in position 4a is also accompanied by the occupation of vacancies by Sc atoms and a reduction in their number. Occupying a vacancy, the Sc atom participates in the formation of the valence band and the conduction band of the semiconductor Er1-xScxNiSb, acting as a source of free electrons. We can also assume that the introduction of Sc atoms into the structure of the compound ErNiSb is accompanied by a process of ordering the structure of Er1-xScxNiSb and Ni atoms occupy vacancies in position 4c. This process also, however, 2 times slower, leads to a decrease in the concentration of structural defects of acceptor nature. In this case, Ni, giving valence electrons, now act as donors.