Fizika Nizkikh Temperatur: Volume 43, Number 10 (October 2017), p. 1459-1471    ( to contents , go back )

Tunnel-thermally activated mechanism of vacancy diffusion in a quantum crystal

V.D. Natsik1,2 and S.N. Smirnov1

1B. Verkin Institute for Low Temperature Physics and Engeneering of the National Academy of Sciences of Ukraine 47 Nauky Ave., Kharkiv 61103, Ukraine

2Karazin Kharkov National University, 4, Svobody Sq., Kharkov 61077, Ukraine

Received April 27, 2017


The vacancy model in a quantum crystal as a pseudo-particles is considered. The vacancy has the meta-stable quantum states localized at the lattice sites in potential wells of the crystalline field. It is assumed that quantum dynamics of such a vacancy can be described in the semiclassical approximation, and its spectrum consists of a broad band and one or two discrete levels splited from the band. The diffusion migration of the vacancy in the bulk of the crystal is reduced to a sequence of random tunnel and thermally activated jumps between the lattice sites. It is shown that the temperature dependence of the vacancy diffusion coefficient has a specific feature: a monotonic decrease upon cooling with a sharp transition from the exponential law typical for high-temperature thermally activated diffusion to the athermal tunneling process at extremely low temperatures. The similar feature was recently recorded in the experimental study of mass transfer in 4He and 3He crystals (Low Temp. Phys. 41, 169 (2015); Low Temp. Phys. 42, 1075 (2016). This mechanism of diffusion of vacancies and its analysis supplement the previously proposed, by A.F. Andreev and I.M. Lifshitz, concept of the diffusion flow of a defecton-quasiparticles quantum gas with a band energy spectrum (ZhETF (rus.) 56, 2057 (1969); UFN (rus.) 118, 251 (1976)).

PACS: 62.20.F– Deformation and plasticity;
PACS: 67.80.–s Quantum solids;
PACS: 67.80.D– Solid 3He;
PACS: Defects, impurities, and diffusion.

Key words: solid helium, plastic flow, activation energy, quantum diffusion, vacancies, dislocations.

Published online: August 27, 2017

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