Analysis of heat conductivity mechanisms in PbSnTe solid solutions

O.Z Khshanovska; M.O. Halushchak; O.M. Matkivskyi; I.V. Horichok

doi:10.15330/pcss.24.3.564-577

Authors

O.Z Khshanovska Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
M.O. Halushchak Ivano Frankivsk National Technical University of Oil and Gas, Ivano-Frankivsk, Ukraine
O.M. Matkivskyi Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine
I.V. Horichok Vasyl Stefanyk Precarpathian National University, Ivano-Frankivsk, Ukraine

DOI:

https://doi.org/10.15330/pcss.24.3.564-577

Keywords:

thermoelectric materials, solid solutions, thermal conductivity coefficient

Abstract

In the paper, a theoretical calculation of the coefficient of thermal conductivity of solid solutions of PbSnTe was carried out. The contribution of phonon scattering on substitution atoms to the effect of reducing thermal conductivity has been established. The composition of the PbSnTe solid solution, characterized by the lowest values of the lattice component of the thermal conductivity coefficient k_lat, was determined. The concentration of intrinsic charge carriers in solid solutions is calculated and their influence on the thermoelectric parameters of the material is shown.

References

Y. Liu, H. Xie, Z. Li, Y. Zhang, C. D. Malliakas, M. Al Malki, S. Ribet, S. Hao, T. Pham, Y. Wang, X. Hu, R. dos Reis, G. J. Snyder, C. Uher, C. Wolverton, M. G. Kanatzidis, V. P. Dravid, Unraveling the Role of Entropy in Thermoelectrics: Entropy-Stabilized Quintuple Rock Salt PbGeSnCdxTe3+x, Journal of the American Chemical Society (Accepted/In press) 145(15), 8677 (2023); https://doi.org/10.1021/jacs.3c01693.

G.J. Snyder, E.S. Toberer, Complex Thermoelectric Materials, Nature Materials, 105 (2008): https://doi.org/10.1038/nmat2090.

X.L. Shi, J. Zou, Z. G. Chen, Advanced Thermoelectric Design: From Materials and Structures to Devices, Chem. Rev., 120 (15), 7399 (2020); https://doi.org/10.1021/acs.chemrev.0c00026.

T. Parashchuk, B. Wiendlocha, O. Cherniushok, R. Knura, K. T. Wojciechowski, High Thermoelectric Performance of p-Type PbTe Enabled by the Synergy of Resonance Scattering and Lattice Softening. ACS Appl. Mater. Interfaces, 13(41), 49027 (2021); https://doi.org/10.1021/ACSAMI.1C14236.

Q.H. Zhang, X.Y. Huang, S.Q. Bai, X. Shi, C. Uher, L. D. Chen. Thermoelectric Devices for Power Generation: Recent Progress and Future Challenges. Adv. Eng. Mater., 18 (2), 194 (2016); https://doi.org/10.1002/adem.201500333.

J. Shuai, Y. Sun, X. Tan, T. Mori. Manipulating the Ge Vacancies and Ge Precipitates through Cr Doping for Realizing the High-Performance GeTe Thermoelectric Material. Small, 16 (13) (2020); https://doi.org/10.1002/SMLL.201906921.

O. Khshanovska, T. Parashchuk, I. Horichok, Estimating the upper limit of the thermoelectric figure of merit in n- and p-type PbTe, Materials Science in Semiconductor Processing, 160, 107428 (13р) (2023); https://doi.org/10.1016/j.mssp.2023.107428.

Ya. Saliy, L. Nykyruy, G. Cempura, O. Soroka, T. Parashchuk, I. Horichok. Periodic nanostructures induced by point defects in Pb1-xSnxTe, Physics and Chemistry of Solid State, 24(1), 70 (2023); https://doi.org/10.15330/pcss.24.1.70-76.

O.M. Matkivskyi, V.I. Makovyshyn, T.I. Kupchak, G.D. Mateik, І.V. Horichok. Thermoelectric properties of composite materials based on lead telluride, Physics and Chemistry of Solid State, 23(2), 368 (2022); https://journals.pnu.edu.ua/index.php/pcss/article/view/5836.

O.M. Matkivsky, Y.P. Saliy, I.V. Horichok. Scattering Mechanisms in pressed PbTe, Physics and Chemistry of Solid State, 21(1), 82 (2020); https://journals.pnu.edu.ua/index.php/pcss/article/view/2974/3759.

D.M. Freik, S.I. Mudryi, I.V. Gorichok, R.O. Dzumedzey, O.S. Krunutcky, T.S. Lyuba, Charge carrier scattering mechanisms in thermoelectric PbTe:Sb, Ukr. J. Phys., 59 (7), 706 (2014).

B. M. Askerov, Electron Transport Phenomena in Semiconductors, 1994; https://doi.org/10.1142/1926.

L. Zhirifalko, Statistical Physics of Materials, Wiley, New York, 1973.

H. Wang, Y. Pei, A. D. LaLonde, and G. J. Snyder, Heavily Doped p-Type PbSe with High Thermoelectric Performance: An Alternative for PbTe, Adv. Mater., 23, 1366 (2011). https://doi.org/10.1002/adma.201004200.

Y. Zhang, X. Ke, C. Chen, J. Yang and P. R. C. Kent, Thermodynamic properties of PbTe, PbSe, and PbS: First principles study, Phys. Rev. B: Condens. Matter, 80, 024304 (2009); https://doi.org/10.1103/PhysRevB.80.02430.

H. Wang , Y. Pei , A. D. LaLonde , and G. J. Snyder, Heavily Doped p-Type PbSe with High Thermoelectric Performance: An Alternative for PbTe, Adv. Mater., 23, 1366–1370 (2011). https://doi.org/10.1002/adma.201004200.

R. Knura, T. Parashchuk, A. Yoshiasa and K.T. Wojciechowski, Origins of low lattice thermal conductivity of Pb1−xSnxTe alloys for thermoelectric applications, Dalton Trans., 50, 4323 (2021); https://doi.org/10.1039/d0dt04206d.

Alekseva G.T. Thermal conductivity of lead chalcogenides and their solid materials based on PbTe, Dissertation for the development of the scientific level of a candidate of physical and mathematical sciences. L. (1984).

E. S. Toberer, A. Zevalkink, G. J. Snyder, Phonon Engineering through Crystal Chemistry, J. Mater. Chem., 21 (40), 15843 (2011); https://doi.org/10.1039/c1jm11754h.

R. Knura, T. Parashchuk, A. Yoshiasa, and K. T. Wojciechowski, Evaluation of the double-tuned functionally graded thermoelectric material approach for the fabrication of n-type leg based on Pb0.75Sn0.25Te, Appl. Phys. Lett., 119, 223902 (2021); https://doi.org/10.1063/5.0075126.

T. Parashchuk, L. Chernyak, S. Nemov, and Z. Dashevsky, Influence of Deformation on Pb1-xInxTe1-yIy and

Pb1-x-ySnxInyTe Films, Phys. Status Solidi B, 2000304 (2020). https://doi.org/10.1002/pssb.202000304.

N.Kh. Abrikosov, L.E. Shelimova, Semi-conductor materials based on A4B6 compounds. M.: Science (1975).

T. Tritt, Thermal conductivity: theory, properties, and applications, Edited by Terry Tritt, Kluwer Academic, Plenum Publishers, New York, 2004. ISBN 0-306-48327-0.

R.P.Tye, Thermal conductivity. Edited by R.P.Tye, Dynatech Corporation, Cambridge Massachusetts, USA, Academic press. London and New York, V.1. 1969.

A.M. Kosevich, Fundamentals of the mechanics of a crystal lattice, M. Nauka (1972).

P.G. Klemens, Thermal Resistance due to Point defects at high temperatures, Phys.Rev., 119 (2), 507 (1960); https://doi.org/10.1103/PhysRev.119.507.

Yu.N. Zhuravlev, D.V. Korabelnikov, M.V. Aleinikova. Ab initio calculations of the thermodynamic parameters of lithium, sodium, and potassium oxides under pressure, Physics of the Solid State, 54 (7), 1518 (2012).

F. Ren, E.D. Case, J.R. Sootsman, M. G. Kanatzidis, H. Kong, C. Uher, E. Lara-Curzio, R. M. Trejo, The high-temperature elastic moduli of polycrystalline PbTe measured by resonant ultrasound spectroscopy, Acta Materialia, 56, 5954 (2008). https://doi.org/10.1016/j.actamat.2008.07.055.

P.G. Klemens. The thermal conductivity of dielectric solids at low temperature, Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences, 208(1092), 108 (1951), https://doi.org/10.1098/rspa.1951.0147.

P. G. Klemens, The scattering of lowfrequency lattice waves by static imperfections, Proc. Phys. Soc., London, Sect. A, 68, 1113 (1955); https://doi.org/10.1088/0370-1298/68/12/303.

M. K. Zhitinskaya, S. A. Nemov , Yu. I. Ravich, Effect of phonon scattering from neutral and charged impurity centers on the lattice heat conductivity of PbTe:(Tl, Na), Physics of the Solid State, 40 (7), 1098 (1998).

V.V. Prokopiv, L.V. Turovska, L.I. Nykyruy, I.V. Horichok, Quasichemical modeling of defect subsystem of tin telluride crystals, Chalcogenide letters, 13 (7), 309(2016).

G. A. Slack and S. Galginaitis, Thermal conductivity and phonon scattering by impurities in CdTe, Phys. Rev., 133, A253 (1964); https://doi.org/10.1103/PhysRev.133.A253.

J. Callaway, Model for lattice thermal conductivity at low temperatures, Phys. Rev., 113, 1044 (1959); https://doi.org/10.1103/PhysRev.113.1046.

M. Roufosse and P. G. Klemens, Thermalconductivity of complex dielectric crystals, Phys. Rev. B: Solid State, 7, 5379 (1973); https://doi.org/10.1103/PhysRevB.7.5379.

Dissertation presente par Tania Claudio Weber en vue de l'obtention du grade de Docteur en Sciences. Lattice Dynamics of Nanostructured Thermoelectric Materials, Julich Centre for Neutron Science JCNS and Peter Grunberg Institut PGI. Annee academique 2012-2013.

L.E. Shelimova, Debye temperature of A4B6 semiconductors, NM, 24, 1597 (1988).

T. Chonan and S. Katayama, Molecular-Dynamics simulation of lattice thermal conductivity in Pb1-xSnxTe and Pb1-xGexTe at high temperatures, J. Phys. Soc. Jpn., 75 (6), 064601 (2006), https://doi.org/10.1143/JPSJ.75.064601.

E. P. Papadakis, Ultrasonic Phase Velocity by the Pulse‐Echo‐Overlap Method Incorporating Diffraction Phase Corrections, J Acoustю. Soc. Am., 42, 1045 (1967); https://doi.org/10.1121/1.1910688.

O. Madelung, Festkorpertheorie I, II, Springer-Verlag. Berlin. Heidelberg, New York, 1972.

J.D. Chung, A.J.H. McGaughey, M. Kaviany, Role of Phonon dispersion in Lattice Thermal Conductivity Modeling, Transactions of the ASME, 126, 376 (2004).

I. Bolesta, Solid State Physics. Handbook, Lviv, LNU Ivan Franko publishing (2003).

S. A. Aliev, R. I. Selim-zade, S. S. Ragimov. Heat-transfer phenomena in alloys Ві1-хSbx, Semiconductors, 44 (10), 1275 (2010).

A. Ward and D. A. Broido, Intrinsic phonon relaxation times from first-principles studies of the thermal conductivities of Si and Ge, Phys. Rev. B, 81, 085205 (2010); https://doi.org/10.1103/PhysRevB.81.085205.

A. Ward, D. A. Broido, D. A. Stewart, G. Deinzer. Ab initio theory of the lattice thermal conductivity in diamond, Phys. Rev. B, 80, 125203 (2009); https://doi.org/10.1103/PhysRevB.80.125203.

I. G. Kuleev, Electron-phonon entrainment, thermodynamic effects, and the thermal conductivity of degenerate conductors, Physics of the Solid State, 41 (10), 1608 (1999).

H.H. Boghossian, K.S. Dubey. Peripheral phonons and phonon conductivity of the doped semiconductor, Solid State Communication, 27, 1065 (1978); https://doi.org/10.1016/0038-1098(78)91111-0.

D. Greig, Thermoelectricity and Thermal conductivity in the Lead Sulfide Group of semiconductors, Phys. Rev., 120 (2), 358 (1960); https://doi.org/10.1103/PhysRev.120.358.