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Physics of Metals and Metallography

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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

Authors: I. I. Kuleyev, I. G. Kuleyev

Published in: Physics of Metals and Metallography | Special Issue 1/2023

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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.

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

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

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Title: Effect of Phonon Focusing and Shear Waves on Drag Thermopower in Potassium Single-Crystal Nanostructures at Low Temperatures. Review 3
Authors: I. I. Kuleyev
I. G. Kuleyev
Publication date: 01-12-2023
Publisher: Pleiades Publishing
Published in: Physics of Metals and Metallography / Issue Special Issue 1/2023
Print ISSN: 0031-918X
Electronic ISSN: 1555-6190
DOI: https://doi.org/10.1134/S0031918X23602160

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Other articles of this Special Issue 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

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

Preface