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Erschienen in: Physics of Metals and Metallography 11/2019

01.11.2019 | THEORY OF METALS

Effect of Anisotropy of Elastic Energy on the Electron–Phonon Drag and Temperature Dependences of Thermal EMF in Potassium Crystals at Low Temperatures

verfasst von: I. I. Kuleev, I. G. Kuleev

Erschienen in: Physics of Metals and Metallography | Ausgabe 11/2019

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Abstract

The effect of anisotropy of elastic energy on electron–phonon drag and thermoelectric phenomena in potassium crystals is studied. The temperature dependences of the thermal conductivity, thermal emf, and contributions to them from phonons of different polarizations are calculated. The calculation results are matched to the experimental data by varying the electron–phonon interaction constant for quasi-transverse phonons. It is established that the contribution of slow quasi-transverse phonons to the drag thermal emf of bulk potassium crystals is by an order of magnitude greater than the contribution of quasi-longitudinal phonons. The maximum values of the drag thermal emf in perfect potassium crystals are determined. It is shown that they do not depend on the electron–phonon interaction constants, but are determined by the second-order elastic moduli and the electron density.

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Literatur
1.
Zurück zum Zitat D. K. C. MacDonald, W. B. Pearson, and I. M. Templeton, “Thermo-electricity at low temperatures. VIII. Thermo-electricity of the alkali metals below 2 K,” Proc. R. Soc. Lond., Ser. A 256, 334 (1960). D. K. C. MacDonald, W. B. Pearson, and I. M. Templeton, “Thermo-electricity at low temperatures. VIII. Thermo-electricity of the alkali metals below 2 K,” Proc. R. Soc. Lond., Ser. A 256, 334 (1960).
2.
Zurück zum Zitat A. M. Guenault and D. K. C. MacDonald, “Electron and phonon scattering thermoelectricity in potassium and alloys at very low temperatures,” Proc. R. Soc. Lond., Ser. A 264, 41 (1961). A. M. Guenault and D. K. C. MacDonald, “Electron and phonon scattering thermoelectricity in potassium and alloys at very low temperatures,” Proc. R. Soc. Lond., Ser. A 264, 41 (1961).
3.
Zurück zum Zitat M. R. Stinson, R. Fletcher, and C. R. Leavens, “Thermomagnetic and thermoelectric properties of potassium,” Phys. Rev. B 20, 3970–3990 (1979).CrossRef M. R. Stinson, R. Fletcher, and C. R. Leavens, “Thermomagnetic and thermoelectric properties of potassium,” Phys. Rev. B 20, 3970–3990 (1979).CrossRef
4.
Zurück zum Zitat R. Fletcher, “Scattering of phonons by dislocations in potassium,” Phys. Rev. B 36, 3042–3051 (1987).CrossRef R. Fletcher, “Scattering of phonons by dislocations in potassium,” Phys. Rev. B 36, 3042–3051 (1987).CrossRef
5.
Zurück zum Zitat F. J. Blatt, P. A. Schroeder, C. L. Foiles, and D. Greig, Thermoelectric Power of Metals (Plenum, London, 1976).CrossRef F. J. Blatt, P. A. Schroeder, C. L. Foiles, and D. Greig, Thermoelectric Power of Metals (Plenum, London, 1976).CrossRef
6.
Zurück zum Zitat J. M. Ziman, Electrons and Phonons (Oxford, 1960) [in Russian]. J. M. Ziman, Electrons and Phonons (Oxford, 1960) [in Russian].
7.
Zurück zum Zitat F. Blatt, Physics of Electronic Conductivity in Solids (Izd-vo IL, Moscow, 1971) [in Russian]. F. Blatt, Physics of Electronic Conductivity in Solids (Izd-vo IL, Moscow, 1971) [in Russian].
8.
Zurück zum Zitat L. E. Gurevich, “Thermoelectric properties of conductors,” Zh. Eksp. Teor. Fiz. 16, 193 (1946). L. E. Gurevich, “Thermoelectric properties of conductors,” Zh. Eksp. Teor. Fiz. 16, 193 (1946).
9.
Zurück zum Zitat C. Herring, “Theory of the thermoelectric power of semiconductors,” Phys. Rev. 96, 1163 (1954).CrossRef C. Herring, “Theory of the thermoelectric power of semiconductors,” Phys. Rev. 96, 1163 (1954).CrossRef
10.
Zurück zum Zitat I. G. Kuleev, I. I. Kuleev, S. M. Bakharev, and V. V. Ustinov, Phonon Focusing and Phonon Transport in Single-Crystal Nanostructures (UMTs UPI, Yekaterinburg, 2018) [in Russian]. I. G. Kuleev, I. I. Kuleev, S. M. Bakharev, and V. V. Ustinov, Phonon Focusing and Phonon Transport in Single-Crystal Nanostructures (UMTs UPI, Yekaterinburg, 2018) [in Russian].
11.
Zurück zum Zitat F. I. Fedorov, Theory of Elastic Waves in Crystals (Nauka, Moscow, 1965). F. I. Fedorov, Theory of Elastic Waves in Crystals (Nauka, Moscow, 1965).
12.
Zurück zum Zitat I. G. Kuleev and I. I. Kuleev, “Elastic waves in cubic crystals with positive or negative anisotropy of second-order elastic moduli,” Phys. Solid State 49, No. 3, 437–444 (2007).CrossRef I. G. Kuleev and I. I. Kuleev, “Elastic waves in cubic crystals with positive or negative anisotropy of second-order elastic moduli,” Phys. Solid State 49, No. 3, 437–444 (2007).CrossRef
13.
Zurück zum Zitat I. G. Kuleev and I. I. Kuleev, “The role of quasi-longitudinal and quasi-transverse phonons in the thermoelectric power of entrainment of potassium crystals at low temperatures,” J. Exp. Theor. Phys. 155, No. 6, 56–70 (2019). I. G. Kuleev and I. I. Kuleev, “The role of quasi-longitudinal and quasi-transverse phonons in the thermoelectric power of entrainment of potassium crystals at low temperatures,” J. Exp. Theor. Phys. 155, No. 6, 56–70 (2019).
14.
Zurück zum Zitat B. Truel, C. Elbaum, and B. B. Chick, “Ultrasonic methods in solid state physics,” (Academic, New York–London, 1969). B. Truel, C. Elbaum, and B. B. Chick, “Ultrasonic methods in solid state physics,” (Academic, New York–London, 1969).
15.
Zurück zum Zitat I. I. Kuleev and I. G. Kuleev, “Phonon focusing and anisotropy of the lattice thermal conductivity of potassium crystals at low temperatures,” Phys. Met. Metallogr. 119, 1141–1147 (2018).CrossRef I. I. Kuleev and I. G. Kuleev, “Phonon focusing and anisotropy of the lattice thermal conductivity of potassium crystals at low temperatures,” Phys. Met. Metallogr. 119, 1141–1147 (2018).CrossRef
16.
Zurück zum Zitat I. G. Kuleev, I. I. Kuleev, S. M. Bakharev, and V. V. Ustinov, “Phonon focusing and electron–phonon drag in semiconductor crystals with degenerate charge-carrier statistics,” J. Exp. Theor. Phys. 150, 567–585 (2016). I. G. Kuleev, I. I. Kuleev, S. M. Bakharev, and V. V. Ustinov, “Phonon focusing and electron–phonon drag in semiconductor crystals with degenerate charge-carrier statistics,” J. Exp. Theor. Phys. 150, 567–585 (2016).
17.
Zurück zum Zitat L. E. Gurevich and I. Ya. Korenblit, “The influence of electron drag by phonons and their mutual drag on kinetic coefficients of semimetals,” Fiz. Tverd. Tela 6, 856–863 (1964). L. E. Gurevich and I. Ya. Korenblit, “The influence of electron drag by phonons and their mutual drag on kinetic coefficients of semimetals,” Fiz. Tverd. Tela 6, 856–863 (1964).
18.
Zurück zum Zitat G. D. Mahan, L. Lindsay, and D. A. Broido, “The Seebeck coefficient and phonon drag in silicon,” J. Appl. Phys. 116, 245 102 (2014).CrossRef G. D. Mahan, L. Lindsay, and D. A. Broido, “The Seebeck coefficient and phonon drag in silicon,” J. Appl. Phys. 116, 245 102 (2014).CrossRef
19.
Zurück zum Zitat J. W. Ekin and B. W. Maxfield, “Electrical resistivity of potassium from 1 to 25° K,” Phys. Rev. B 4, 4215–4225 (1971).CrossRef J. W. Ekin and B. W. Maxfield, “Electrical resistivity of potassium from 1 to 25° K,” Phys. Rev. B 4, 4215–4225 (1971).CrossRef
20.
Zurück zum Zitat A. P. Zhernov and A. V. Inyushkin, Isotopic Effects in Solids (RNTs Kurchatovskii Institut, Moscow, 2001) [in Russian]. A. P. Zhernov and A. V. Inyushkin, Isotopic Effects in Solids (RNTs Kurchatovskii Institut, Moscow, 2001) [in Russian].
21.
Zurück zum Zitat P. G. Klemens, “The scattering of low-frequency lattice waves by static imperfections,” Proc. Phys. Soc. Sect. A 68, No. 12, 1113–1128 (1955).CrossRef P. G. Klemens, “The scattering of low-frequency lattice waves by static imperfections,” Proc. Phys. Soc. Sect. A 68, No. 12, 1113–1128 (1955).CrossRef
Metadaten
Titel
Effect of Anisotropy of Elastic Energy on the Electron–Phonon Drag and Temperature Dependences of Thermal EMF in Potassium Crystals at Low Temperatures
verfasst von
I. I. Kuleev
I. G. Kuleev
Publikationsdatum
01.11.2019
Verlag
Pleiades Publishing
Erschienen in
Physics of Metals and Metallography / Ausgabe 11/2019
Print ISSN: 0031-918X
Elektronische ISSN: 1555-6190
DOI
https://doi.org/10.1134/S0031918X19110103

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