nach oben

Physics of Metals and Metallography

Erschienen in:

01.12.2023 | THEORY OF METALS

Effect of Phonon Focusing and Shear Waves on Drag Thermopower in Potassium Single-Crystal Nanostructures at Low Temperatures. Review 3

verfasst von: I. I. Kuleyev, I. G. Kuleyev

Erschienen in: Physics of Metals and Metallography | Sonderheft 1/2023

Einloggen

Aktivieren Sie unsere intelligente Suche, um passende Fachinhalte oder Patente zu finden.

search-config

KI-gestützte Suche

Aus

Abstract

The effect of phonon focusing on electron–phonon drag and thermopower in nanostructures based on potassium single crystals at low temperatures is studied. The role of quasi-longitudinal and quasi-transverse phonons, as well as shear waves, in the drag thermopower of the nanostructures is considered. It is shown that, in the Knudsen flow regime of a phonon gas, the slow quasi-transverse t₂ mode makes the dominant contribution to the drag thermopower of the nanostructures and, only in directions close to the focusing of longitudinal phonons (L-phonons), their contribution become comparable to the contribution of the t₂ mode. The directions of heat flux in which the maximum and minimum values of drag thermopower are achieved in nanowires, films, and nanoplates based on potassium single crystals are determined. The study of the effect of focusing on the phonon propagation in potassium single crystals made it possible to calculate a number of new, unusual effects in the anisotropy of drag thermopower in potassium-based nanostructures. These effects are mainly due to the competition between the contributions of the t₂ mode and L-phonons to the drag thermopower. Since the relaxation rate of L-phonons on electrons in potassium is 25 times higher than for the t₂ mode, with an increase in the transverse dimensions of potassium nanostructures, the anisotropy of the drag thermopower in them, in contrast to the anisotropy of thermal conductivity in dielectric nanostructures, changes nonmonotonically. It first increases, reaching a maximum, then decreases, and vanishes when the dimensions become macroscopic (D ≥ 10^–1 cm). One of the interesting effects calculated in this work is the orientational anisotropy of drag thermopower in potassium nanoplates. In two identical nanoplates with a rectangular cross section, the thermopower in the direction of the temperature gradient [011] for the orientation of the wide faces of the {100} plates turns out to be significantly greater than for the {110} orientation. With increasing plate width, the orientational anisotropy of thermopower increases to 37%. It is shown that the orientational anisotropy of the thermopower is due to the effect of focusing on the phonon propagation in the plates. The competition between the contributions of the t₂ mode and L-phonons, which determine the maximum and minimum values, leads to a nonmonotonic dependence of the orientational anisotropy of the drag thermopower on the thickness of the nanoplate. It is shown that, for square potassium films with {100} and {111} orientations of planes, the drag thermopower is isotropic in the film plane, but, for the {110} orientation, it becomes ellipsoidal with its major axis in the [001] direction. A characteristic feature of drag thermopower in square films is orientation anisotropy. For the [011] directions of the temperature gradient, the drag thermopower in potassium films with the {100} orientations of planes turns out to be significantly greater than with the {110} orientations. It behaves nonmonotonically, reaching a maximum of 57% at a thickness D = 2.2 × 10^–5 cm. It is obvious that the effects calculated in this work open up new prospects for experimental studies of electron–phonon drag in metal films.

Vorheriger Artikel Phonon Focusing and Electron Transport in Potassium Single Crystals. Review 2

Nächster Artikel Effect of Anisotropy of Elastic Energy and Shear Waves on Electron–Phonon Relaxation and Electrical Resistivity of Noble Metals. Review 4

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Online-Abonnement

Mit Springer Professional "Wirtschaft+Technik" erhalten Sie Zugriff auf:

über 102.000 Bücher
über 537 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Finance + Banking
Management + Führung
Marketing + Vertrieb
Maschinenbau + Werkstoffe
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Wirtschaft"

Online-Abonnement

Mit Springer Professional "Wirtschaft" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 340 Zeitschriften

aus folgenden Fachgebieten:

Bauwesen + Immobilien
Business IT + Informatik
Finance + Banking
Management + Führung
Marketing + Vertrieb
Versicherung + Risiko

Jetzt Wissensvorsprung sichern!

Jetzt informieren

Springer Professional "Technik"

Online-Abonnement

Mit Springer Professional "Technik" erhalten Sie Zugriff auf:

über 67.000 Bücher
über 390 Zeitschriften

aus folgenden Fachgebieten:

Automobil + Motoren
Bauwesen + Immobilien
Business IT + Informatik
Elektrotechnik + Elektronik
Energie + Nachhaltigkeit
Maschinenbau + Werkstoffe

Jetzt Wissensvorsprung sichern!

Jetzt informieren

I. I. Kuleyev and I. G. Kuleyev, “Effect of phonon focusing on the drag thermopower in single-crystal potassium nanowires at low temperatures,” Phys. Met. Metallogr. 122, 75–82 (2021). https://doi.org/10.1134/S0031918X21020071ADSCrossRef

I. G. Kuleyev and I. I. Kuleyev, “Effect of phonon focusing and shear waves on anisotropy of drag thermopower in potassium nanoplates,” Chin. J. Phys. 72, 351–359 (2021). https://doi.org/10.1016/j.cjph.2021.05.007MathSciNetCrossRef

I. I. Kuleyev and I. G. Kuleyev, “Phonon focusing and anisotropy of drag thermopower in potassium thin films at low temperatures,” J. Phys. Chem. Solids 170, 110948 (2022). https://doi.org/10.1016/j.jpcs.2022.110948CrossRef

I. I. Kuleev and I. G. Kuleev, “Dynamic properties and focusing of phonons in metallic and dielectric crystals of cubic symmetry. Review 1,” Phys. Met. Metallogr. 124 (2023).

I. I. Kuleyev and I. G. Kuleyev, “Phonon focusing and anisotropy of the lattice thermal conductivity of potassium crystals at low temperatures,” Phys. Met. Metallogr. 119, 1141–1147 (2018). https://doi.org/10.1134/S0031918X18120098ADSCrossRef

I. I. Kuleyev and I. G. Kuleyev, “Role of quasi-longitudinal and quasi-transverse phonons in the drage thermopower of potassium crystals at low temperatures,” J. Exp. Theor. Phys. 129, 46–58 (2019). https://doi.org/10.1134/S1063776119060141ADSCrossRef

I. G. Kuleyev and I. I. Kuleyev, “The effect of phonon focusing on the electron-phonon relaxation and electron transport in potassium crystals,” Chin. J. Phys. 68, 886–895 (2020). https://doi.org/10.1016/j.cjph.2020.10.005MathSciNetCrossRef

I. I. Kuleyev and I. G. Kuleyev, “Drag thermopower in nanowires and bulk potassium crystals under the conditions of competition between the boundary and bulk mechanisms of phonon relaxation,” J. Phys.: Condens. Matter 31, 375701 (2019). https://doi.org/10.1088/1361-648x/ab271fCrossRefPubMed

I. I. Kuleev and I. G. Kuleev, “Effect of anisotropy of elastic energy on the electron–phonon drag and temperature dependences of thermal emf in potassium crystals at low temperatures,” Phys. Met. Metallogr. 120, 1033–1039 (2019). https://doi.org/10.1134/S0031918X19110103ADSCrossRef

10.

I. I. Kuleev and I. G. Kuleev, “The role of shear waves in electron–phonon drag in potassium crystals at low temperatures,” Phys. Met. Metallogr. 121, 921–928 (2020). https://doi.org/10.1134/s0031918x20100063ADSCrossRef

11.

H. B. G. Casimir, “Note on the conduction of heat in crystals,” Physica 5, 495–500 (1938). https://doi.org/10.1016/s0031-8914(38)80162-2ADSCrossRef

12.

A. K. McCurdy, H. J. Maris, and C. Elbaum, “Anisotropic heat conduction in cubic crystals in the boundary scattering regime,” Phys. Rev. B 2, 4077–4083 (1970). https://doi.org/10.1103/physrevb.2.4077ADSCrossRef

13.

H. J. Maris, “Enhancement of heat pulses in crystals due to elastic anisotropy,” J. Acoust. Soc. Am. 50, 812–818 (1971). https://doi.org/10.1121/1.1912705ADSCrossRef

14.

D. Li, Yi. Wu, P. Kim, L. Shi, P. Yang, and A. Majumdar, “Thermal conductivity of individual silicon nanowires,” Appl. Phys. Lett. 83, 2934–2936 (2003). https://doi.org/10.1063/1.1616981ADSCrossRef

15.

W. Liu and M. Asheghi, “Phonon–boundary scattering in ultrathin single-crystal silicon layers,” Appl. Phys. Lett. 84, 3819–3821 (2004). https://doi.org/10.1063/1.1741039ADSCrossRef

16.

M. Asheghi, M. N. Touzelbaev, K. E. Goodson, Y. K. Leung, and S. S. Wong, “Temperature-dependent thermal conductivity of single-crystal silicon layers in SOI substrates,” J. Heat Transfer 120, 30–36 (1998). https://doi.org/10.1115/1.2830059CrossRef

17.

M. Asheghi, Y. K. Leung, S. S. Wong, and K. E. Goodson, “Phonon-boundary scattering in thin silicon layers,” Appl. Phys. Lett. 71, 1798–1800 (1997). https://doi.org/10.1063/1.119402ADSCrossRef

18.

A. D. McConnell and K. E. Goodson, “Thermal conduction in silicon micro- and nanostructures,” Annu. Rev. Heat Transfer 14, 129–168 (2005). https://doi.org/10.1615/annualrevheattransfer.v14.120CrossRef

19.

D. G. Cahill, P. V. Braun, G. Chen, D. R. Clarke, S. Fan, K. E. Goodson, P. Keblinski, W. P. King, G. D. Mahan, A. Majumdar, H. J. Maris, S. R. Phillpot, E. Pop, and L. Shi, “Nanoscale thermal transport. II. 2003–2012,” Appl. Phys. Rev. 1, 011305 (2003). https://doi.org/10.1063/1.4832615CrossRef

20.

I. G. Kuleyev, I. I. Kuleyev, and S. M. Bakharev, “Phonon focusing and temperature dependences of the thermal conductivity of silicon nanowires,” J. Exp. Theor. Phys. 118, 253–265 (2014). https://doi.org/10.1134/S1063776114020022ADSCrossRef

21.

I. I. Kuleyev, S. M. Bakharev, I. G. Kuleyev, and V. V. Ustinov, “Phonon focusing and temperature dependences of thermal conductivity of silicon nanofilms,” J. Exp. Theor. Phys. 120, 638–650 (2015). https://doi.org/10.1134/S1063776115020144ADSCrossRef

22.

I. G. Kuleyev, I. I. Kuleyev, S. M. Bakharev, and V. V. Ustinov, Phonon Focusing and Phonon Transport: In Single-Crystal Nanostructures, Texts and Monographs in Theoretical Physics (De Gruyter, Berlin, 2020). https://doi.org/10.1515/9783110670509

23.

J. Ziman, Electrons and Phonons (Oxford Univ. Press, Oxford, 1960).

24.

B. M. Mogilevskii and A. F. Chudnovskii, Heat Conductivity of Semiconductors (Nauka, Moscow, 1972).

25.

R. Berman, Thermal Conduction in Solids (Oxford Univ. Press, Oxford, 1976).

26.

M. Knudsen, “Die Gesetze der Molekularströmung und der inneren Reibungsströmung der Gase durch Röhren,” Ann. Phys. 333, 75–130 (1909). https://doi.org/10.1002/andp.19093330106CrossRef

27.

R. Berman, F. E. Simon, and J. M. Ziman, “The thermal conductivity of diamond at low temperatures,” Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 220, 171–183 (1953). https://doi.org/10.1098/rspa.1953.0180

28.

R. Berman, E. L. Foster, and J. M. Ziman, “Thermal conduction in artificial sapphire crystals at low temperatures I. Nearly perfect crystals,” Proc. R. Soc. London, Ser. A: Math. Phys. Sci. 231, 130–144 (1955). https://doi.org/10.1098/rspa.1955.0161

29.

I. I. Kuleyev, I. G. Kuleyev, S. M. Bakharev, and A. V. Inyushkin, “Relaxation times and mean free paths of phonons in the boundary scattering regime for silicon single crystals,” Phys. Solid State 55, 31–44 (2013). https://doi.org/10.1134/S106378341301023XADSCrossRef

30.

I. I. Kuleyev, I. G. Kuleyev, S. M. Bakharev, and A. V. Inyushkin, “Features of phonon transport in silicon rods and thin plates in the boundary scattering regime. The effect of phonon focusing at low temperatures,” Phys. B: Condens. Matter 416, 81–87 (2013). https://doi.org/10.1016/j.physb.2013.02.020ADSCrossRef

31.

I. I. Kuleyev, I. G. Kuleyev, S. M. Bakharev, and A. V. Inyushkin, “Effect of phonon focusing on the temperature dependence of thermal conductivity of silicon,” Phys. Status Solidi (b) 251, 991–1000 (2014). https://doi.org/10.1002/pssb.201350332CrossRef

32.

I. I. Kuleyev, I. G. Kuleyev, and S. M. Bakharev, “Phonon focusing and features of phonon transport in silicon nanofilms and nanowires at low temperatures,” Phys. Status Solidi (b) 252, 323–332 (2015). https://doi.org/10.1002/pssb.201451364CrossRef

33.

I. G. Kuleev and I. I. Kuleev, “Phonon focusing and electron transport in potassium monocrystals. Review 2,” Phys. Met. Metallogr. 124, Suppl. 1, S31–S58 (2023). https://doi.org/10.1134/S0031918X23602093

34.

R. Fletcher, “Scattering of phonons by dislocations in potassium,” Phys. Rev. B 36, 3042–3051 (1987). https://doi.org/10.1103/physrevb.36.3042ADSCrossRef

35.

I. G. Kuleyev and I. I. Kuleyev “The role of shear waves in electron–phonon relaxation and electrical resistivity of noble metals,” Chin. J. Phys. 83, 103–112 (2023). https://doi.org/10.1016/j.cjph.2022.12.010

36.

I. I. Kuleyev and I. G. Kuleyev, “Phonon focusing and anisotropy of drag thermopower in potassium thin films at low temperatures,” J. Phys. Chem. Solids 170, 110948–110957 (2022). https://doi.org/10.1016/j.jpcs.2022.110948CrossRef

37.

F. J. Blatt, P. A. Schroeder, C. L. Foiles, and D. Greig, Thermoelectric Power of Metals (Plenum Press, New York, 1976). https://doi.org/10.1007/978-1-4613-4268-7CrossRef

38.

M. P. Zaitlin, L. M. Scherr, and A. C. Anderson, “Boundary scattering of phonons in noncrystalline materials,” Phys. Rev. B 12, 4487–4492 (1975). https://doi.org/10.1103/physrevb.12.4487ADSCrossRef

39.

K. Fuchs, “The conductivity of thin metallic films according to the electron theory of metals,” Math. Proc. Cambridge Philos. Soc. 34, 100–108 (1938). https://doi.org/10.1017/s0305004100019952ADSCrossRef

40.

E. H. Sondheimer, “The mean free path of electrons in metals,” Adv. Phys. 1, 1–42 (1952). https://doi.org/10.1080/00018735200101151ADSCrossRef

41.

I. I. Kuleyev, I. G. Kuleyev, and S. M. Bakharev, “Low-temperature anisotropy of the thermal conductivity of single-crystal nanofilms and nanowires,” J. Exp. Theor. Phys. 119, 460–472 (2014). https://doi.org/10.1134/S1063776114090040CrossRef

42.

I. I. Kuleyev, S. M. Bakharev, I. G. Kuleyev, and V. V. Ustinov, “Influence of phonon focusing on the Knudsen flow of phonon gas in single-crystal nanofilms of spintronic materials,” Phys. Met. Metallogr. 118, 316–327 (2017). https://doi.org/10.1134/S0031918X17040068ADSCrossRef

43.

M. Smoluchowski, “Zur kinetischen Theorie der Transpiration und Diffusion verdünnter Gase,” Ann. Phys. 338, 1559–1570 (1910). https://doi.org/10.1002/andp.19103381623CrossRef

44.

H. J. Maris and Sh.-I. Tamura, “Heat flow in nanostructures in the Casimir regime,” Phys. Rev. B 85, 54304 (2012). https://doi.org/10.1103/physrevb.85.054304ADSCrossRef

45.

I. I. Kuleev, S. M. Bakharev, I. G. Kuleev, and V. V. Ustinov, “Effect of phonon focusing on Knudsen flow of phonon gas in single-crystal nanowires made of spintronics materials,” Phys. Met. Metallogr. 118, 10–20 (2017). https://doi.org/10.1134/s0031918x17010033ADSCrossRef

46.

J. Philip and K. S. Viswanathan, “Phonon magnification in cubic crystals,” Phys. Rev. B 17, 4969–4978 (1978). https://doi.org/10.1103/physrevb.17.4969ADSCrossRef

47.

A. G. Every, “Ballistic phonons and the shape of the ray surface in cubic crystals,” Phys. Rev. B 24, 3456–3467 (1981). https://doi.org/10.1103/physrevb.24.3456ADSCrossRef

48.

C. Jasiukiewicz, T. Paszkiewicz, and D. Lehmann, “Phonon focussing patterns: Calculation of response of finite area detectors to pulsed ballistic beams of dispersive and dispersionless phonons,” Z. Phys. B Condens. Matter 96, 213–222 (1994). https://doi.org/10.1007/BF01313286ADSCrossRef

49.

M. Lax and V. Narayanamurti, “Phonon magnification and the Gaussian curvature of the slowness surface in anisotropic media: Detector shape effects with application to GaAs,” Phys. Rev. B 22, 4876–4897 (1980). https://doi.org/10.1103/physrevb.22.4876ADSMathSciNetCrossRef

Titel: Effect of Phonon Focusing and Shear Waves on Drag Thermopower in Potassium Single-Crystal Nanostructures at Low Temperatures. Review 3
verfasst von: I. I. Kuleyev
I. G. Kuleyev
Publikationsdatum: 01.12.2023
Verlag: Pleiades Publishing
Erschienen in: Physics of Metals and Metallography / Ausgabe Sonderheft 1/2023
Print ISSN: 0031-918X
Elektronische ISSN: 1555-6190
DOI: https://doi.org/10.1134/S0031918X23602160

Springer Professional

Abstract

Bitte loggen Sie sich ein, um Zugang zu Ihrer Lizenz zu erhalten.

Sie haben noch keine Lizenz? Dann Informieren Sie sich jetzt über unsere Produkte:

Springer Professional "Wirtschaft+Technik"

Springer Professional "Wirtschaft"

Springer Professional "Technik"

Weitere Artikel der Sonderheft 1/2023

Phonon Focusing and Electron Transport in Potassium Single Crystals. Review 2

Effect of Anisotropy of Elastic Energy and Shear Waves on Electron–Phonon Relaxation and Electrical Resistivity of Noble Metals. Review 4

Preface

Dynamic Properties and Focusing of Phonons in Metallic and Dielectric Crystals of Cubic Symmetry. Review 1