The effect of long-range strain fields on transport properties of disclinated materials

Abstract

The problem of both phonon and electron scattering by long-range strain fields caused by wedge disclination dipoles (WDD) is studied in the framework of the deformation potential approach. The exact analytical results for the mean free path are obtained within the Born approximation. The WDD-induced contribution to the residual resistivity in nanocrystalline metals is estimated. Phonon scattering due to randomly distributed WDDs is shown to result in a clear crossover from T 3-to T 2-behaviour in the thermal conductivity, κ, at low temperatures. A combination of two scattering processes, the phonon scattering due to biaxial WDD and the Rayleigh-type scattering, is suggested to be of importance for amorphous dielectrics. Our results are in good agreement with the experimentally observed κ for a-SiO 2 , a-GeO 2 , a-Se, and polystyrene. Numerical calculations show that κ is very sensitive to the size of the dipole separation, which is fixed near 20 Å.

Effects of resonant phonon scattering from internal molecular modes on the thermal conductivity of molecular glasses

“…The liquid sample was put into the container of the measuring cell under 4 He superlinear gas flow. The container once filled with the sample was vacuum-tight covered with a copper cap and an indium ring.…”

“…27 Somewhat similar phenomena have been reported for clathrates, 28 where the remarkable linear or ͑T͒ ϰ T 3/2 dependences at low temperatures are understood as a consequence of the coupling of rattling motions of off-center atoms to phonons. 3,29 Also, phenomenological treatments considering strain fields caused by wedge disclination dipoles 4 lead to a clear crossover from T 3 to T 2 in the thermal conductivity at low temperature.…”

“…Amongst those, the behavior of the temperature dependence of the thermal conductivity ͑T͒ of glasses and disordered crystals continues to attract a significant research effort. 1 The most intriguing manifestation of the scattering of heat waves by either topological, 1 orientational, 2 chemical disorder, 3 defect crystals, 4 or even crystals with minimum disorder 5 concerns the quantitative similitude of ͑T͒ within a relatively wide range of temperatures ͑0.1-10 K͒, independent of the chemical composition. In stark contrast, most of our understanding of such phenomena relies on phenomenological constructs such as the two-level systems 1 ͑TLSs͒ or soft-potential 6 models ͑SPMs͒.…”

Residual resistivity due to wedge disclination dipoles in metals with rotational plasticity

“…In the case when l 1 = l 2 = 0, we have biaxial WDD with shifted axes of rotation (see, e.g., [17,18]). …”

“…It means that only normal to disclination line component of electron wave vector k ⊥ are involved in scattering process. As a result, the problem reduces to the two-dimensional scattering where the matrix element which determines the transition of electron from Fermi state with wave vector k F = k ⊥ + k z to state k ′ can be written as [2,18] …”