The effect influence of elastic energy anisotropy on the mutual drag of electrons and phonons and the electrical resistance of potassium crystals at low temperatures have investigated. We have analyzed the momentum exchange between the electron and three phonon flows corresponding to three branches of the vibrational spectrum in the hydrodynamic approximation. The actual mechanisms of phonon momentum relaxation have taken into account: scattering at sample boundaries, dislocations, and in the processes of phonon-phonon transfer. It have shown that in the limiting case of strong mutual drag of electrons and phonons, the electrical resistance will be much lower than that given by the Bloch–Grüneisen theory, and the phonon and electron drift velocities are close and they are determined by the total phonon relaxation rate in resistive scattering processes. In the opposite case, when resistive scattering processes dominate for phonons and the phonon system remains in equilibrium, then the electrical resistance follows the Bloch–Grüneisen theory. In this case, the drift velocities of all modes are different and much less than the electron drift velocity.

Исследовано влияние фокусировки фононов на фононный транспорт в полупроводниковых и диэлектрических кристаллах с различным типом анизотропии упругой энергии при низких температурах. Рассчитаны эффекты МакКарди в теплопроводности упруго анизотропных кристаллов в режиме кнудсеновского течения фононного газа. Проанализировано влияние фокусировки фононов на распространение и граничное рассеяние фононов в образцах с квадратным и прямоугольным сечениями, и дано физическое объяснение эффектам МакКарди.

The influence of the anisotropy of elastic energy on the phonon propagation and phonon transport in single crystal nanofilms with different types of anisotropy of elastic energy in a Knudsen flow of a phonon gas is studied. The angular distribution of phonon mean free paths in the planes of the films and in their cross section is analyzed. The physical reasons leading to the dependence of the thermal conductivity on the orientation of the film planes and the directions of the heat flux relative to the crystal axes are studied. An analysis of the effect of focusing on the phonon propagation made it possible to explain the qualitative difference between the anisotropy of phonon mean free paths in films of cubic nanocrystals of various types having different orientations of the planes.

The effect of the anisotropy of elastic properties on the thermal conductivity of GaAs/AlGaAs heterostructures at low temperatures is investigated. The effect of phonon focusing on the anisotropy of the thermal conductivity is analyzed. The parameters of the specular reflection of phonons from the boundaries of the heterostructures, which characterize the heat flux in the Knudsen mode of the phonon gas flow, are determined. The angular dependences of the mean free paths of phonons of different polarizations, which determine the thermal conductivity anisotropy of heterostructures with orientations {100} and {110}, are calculated.