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.

The problem of phonon scattering by grain boundaries is studied within the wedge disclination dipole (WDD) model. It is shown that a specific q-dependence of the phonon mean free path for biaxial WDD results in a low-temperature crossover of the thermal conductivity, κ. The obtained results allow to explain the experimentally observed deviation of κ from a T 3 dependence below 0.1K in LiF and N aCl.The effect of low-angle grain boundaries on the thermal conductivity, κ, of LiF and N aCl over the temperature range 0.08-5 K has been investigated in [1,2]. The main conclusions are the following: (i) the boundaries are sessile, (ii) the dominant phonon-scattering process comes from static strain fields caused by boundaries, and (iii) the experimental results are compatible with predictions of the theoretical model [3] where a grain boundary is represented as a wall of edge dislocations. In experiments, however, in addition to the expected behavior κT −3 = const, a remarkable increase in κT −3 below T * ∼ 0.1K was detected. A similar deviation, but beginning near 2K, was observed in sapphire [4]. There is still no satisfactory explanation of this phenomenon. In particular, in [1] it was supposed that the measured increase can be caused by the onset of partial specular reflection from the lightly sandblasted walls. Similarly, it was suggested that [4] "a frequency independent scattering mechanism should be present in these samples which becomes ineffective below 1K".In 1955 Klemens [3] studied the problem of the scattering of lattice waves by grain boundaries within the Born approximation. Considering the grain boundary as an array of edge dislocations lying in the plane of the boundary, he found that the phonon mean free path is frequency independent. Hence a T 3 dependence of the thermal conductivity at low temperatures was associated with the boundary scattering. While this finding explains well the experimental results [1,2,4] above some characteristic temperature, T * , it fails to describe the observed anomaly below T * . It is important to note in this connection that the result [3] was obtained under assumption that the dislocation wall is infinitely long. For a finite wall of well separated dislocations the problem of the phonon scattering becomes difficult and is still unresolved.An alternative model for description of grain boundaries has been presented in [5]. It was proposed that grain boundaries being rather rotational than translational defects can be described more naturally by disclinations. Moreover, what is important, the far strain fields caused by wedge disclination dipoles (WDD) were found to agree with those from finite walls of edge dislocations [6,7]. For this reason, the WDD-based model allows us to study important effects due to finiteness of grain boundaries.Notice also that additional interest to this problem was inspired by recent consideration of disclinations and dipoles of disclinations in the context of metal glasses [8,9], graphite films [10], and nanostructures [11]. For example, an...

The problem of phonon scattering by strain fields caused by Stone-Wales (SW) defects in graphene is studied in the framework of the deformation potential approach. An explicit form of the phonon mean free path due to phonon-SW scattering is obtained within the Born approximation. The mean free path demonstrates a specific q-dependence varying as q (-3) at low wavevectors and taking a constant value at large q. The thermal conductivity of graphene nanoribbons (GNRs) is calculated with the three-phonon umklapp, SW and rough edge scatterings taken into account. A pronounced decrease of the thermal conductivity due to SW defects is found at low temperatures whereas at room temperatures and above the phonon-phonon umklapp scattering becomes dominant. A comparison with the case of vacancy defects shows that they play more important role in the reduction of the thermal conductivity in GNRs over a wide temperature range.

In the framework of a gauge approach the problem of an electron localization in elastic materials with disclinations is investigated. The straight wedge disclinations, both topologically stable and unstable, as well as the disclination monopole, are considered. It is shown that for the topologically stable wedge, a disclination strongly localized in the core region electron states appears. For the topologically unstable negative wedge disclination and disclination monopole, the localization process is found to depend essentially on the depth of the deformation potential. The levels of localized electrons as well as the exact form of the normalized wavefunctions of the ground state are obtained numerically.

The effect of grain boundary (GB) structure, size and shape on thermal conductivity of polycrystalline graphene is studied in the framework of the deformation potential approach. Precise analytical expressions for the phonon mean free path (MFP) are obtained within the Born approximation. We found exactly two types of behavior in the long-wavelength limit: MFP varies as ω −1 for open GBs of any shape while it behaves as ω −3 for closed configurations (loops). In the short-wavelength limit MFP tends to a constant value for any configuration. Oscillatory behavior is observed for all GBs which indicates that they serve as diffraction grating for phonons. This property is also inherent in GBs with irregularities caused by partial disclination dipoles. The thermal conductivity is calculated in the framework of Callaway's approach with all main sources of phonon scattering taken into account. Reduction of the heat conductivity with decreasing grain size is obtained in a wide temperature range. Most interesting is that we found a marked decrease in the thermal conductivity of polycrystalline graphene containing GBs with changes in their misorientation angles.