Towards the grain boundary phonon scattering problem: evidence for a low-temperature crossover

Abstract

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...

Low-temperature thermal conductivity in polycrystalline graphene

“…1). In this case, the phonon-GB scattering can be expressed as [11] l −1 where ν is the Frank index, n i is the areal density of BWDDs,…”

“…The GB-induced phonon scattering has a marked impact on the thermal conductivity, κ, at low temperatures. In bulk materials, the well-pronounced crossover from κ ∼ T 2 to κ ∼ T 3 has been proved with the crossover temperature strongly depending on the GB size [11,12]. Therefore, one can expect a similar effect in two-dimensional polycrystalline materials like graphene.…”

Disclination dipoles as the basic structural elements of dielectric glasses

“…Actually, we reexamine the old ideas of the previous two paragraphs from another point of view. The model proposed here was inspired by a recent finding that a biaxial WDD is a rather unique scatterer [18]. Namely, it has been shown that the mean free path l D of thermal phonons scattered by biaxial WDD with nonskew axes of rotation behaves like l D ∼ q −1 at small q while l D → const with q increasing.…”

“…It has long been known that there is a close connection between grain boundaries in materials with pronounced cluster structure and wedge disclination dipoles (WDD) [17]. Recently, this analogy has been successfully applied for description of the old experiments in polycrystals on the basis of the WDD-induced scattering [18]. As was mentioned in [3], the scattering in polycrystals has a close parallel in amorphous solids.Another approach which takes into account topological defects in glasses came from geometrical and topological considerations.…”

“…We will try to answer some of these questions below within our model. First of all, let us reproduce briefly the main results of the previous paper where the scattering of thermal phonons by WDD was studied [18]. For simplicity, in what follows we consider only biaxial WDD with nonskew axes of rotation (below the term "biaxial WDD" will refer only to this type of biaxial WDD).…”