This review provides theoretical understanding of the role of the surface and interface in the thermal conductivity of solids. An attempt is made to collect the various methods used in the analysis of experiments. The adequacy and range of validity of these methods are evaluated, and suggestions are made concerning possible theoretical and experimental investigations which seem desirable. A major part of the paper is devoted to the description of the surface vibrational modes, the surface thermal conductivity, the interaction of defects with crystal surfaces, and the phonon scattering from crystal surfaces.

First, a review is made of the general form of the interatomic potential energy and lattice vibrations. Certain aspects related to the three- and four-phonon processes are discussed. Then, the heat current is calculated in the presence of scattering processes described by a relaxation time, and a general formalism for the lattice thermal conductivity is derived. A special consideration is given to the effect of boundary scattering and boundary thermal conductance. In the first sections, despite the consideration of boundary scattering, the calculation of the thermal conductivity is carried out with adopting of the cyclic boundary conditions. Such a treatment, while mathematically convenient, eliminates the possibility of studying the dynamical properties of atoms in the neighborhood of a free surface of a real crystal because the crystal structure in the surface layers may differ from the structures in the bulk of the crystal. The forces acting on atoms in the surface layers will be different from the forces acting on atoms in the bulk since an atom in the surface layers has fewer nearest neighbors, next-nearest neighbors, etc., than an atom in the interior of a crystal. Therefore, one would expect that the dynamical properties and the resultant thermal conductivity are different for atoms in the surface layers of a crystal than for atoms in the bulk of the crystal. Moreover, when crystal size becomes small enough that the ratio of surface to volume is not negligible, the modification of the frequency distribution function of the crystal by the presence of free surfaces, which is the addition of a contribution from an essentially two-dimensional crystal, will alter the temperature dependence of thermal conductivity and give rise to distinct size effects on the thermal conductivity. Furthermore, selection rules governing physical properties in crystals, which have their origins in symmetry properties, translational and rotational, of an infinitely extended crystal, can be relaxed for finite crystals or for atoms in the surface layers of crystals for which these symmetry properties no longer hold. Thus, one would expect to find that the thermal conductivity of a thin film or small particle will show specific features that do not appear for the case of bulk material. In order to present theoretical understanding of the effect of size and surface contribution to the lattice thermal conductivity, we present in the last sections a theoretical lattice dynamical discussion of the thermal conductivity in which the modification of the lattice vibration by the presence of free boundary surfaces play a dominant role.

该综述提供了对表面和界面在固体热导率中的作用的理论理解。试图收集用于实验分析的各种方法。对这些方法的充分性和有效性范围进行了评估，并就可能需要的理论和实验研究提出了建议。本文的主要部分致力于表面振动模式，表面热导率，缺陷与晶体表面的相互作用以及声子从晶体表面的散射的描述。

首先，回顾了原子间势能和晶格振动的一般形式。讨论了与三声子和四声子过程有关的某些方面。然后，在存在由弛豫时间描述的散射过程的情况下，计算热电流，并得出晶格热导率的一般形式。要特别考虑边界散射和边界热导的影响。在第一部分中，尽管考虑了边界散射，但采用循环边界条件进行了热导率的计算。这种处理虽然在数学上很方便，由于表面层中的晶体结构可能不同于晶体主体中的结构，因此消除了研究真实晶体自由表面附近原子的动力学特性的可能性。由于表面层中的原子比晶体内部的原子具有更少的最近邻居，下一个最近邻居等，因此作用在表面层中的原子的力将不同于本体中的原子的力。 。因此，人们可以预期，对于晶体表面层中的原子而言，动力学特性和所得的热导率与对于晶体主体中的原子而言是不同的。此外，当晶体尺寸变得足够小以至于表面积与体积之比不可忽略时，通过自由表面的存在来改变晶体的频率分布函数，这是本质上是二维晶体的贡献，这将改变热导率的温度依赖性，并且对热导率产生明显的尺寸影响。电导率。此外，对于有限的晶体或晶体表层中不再具有这些对称属性的原子，可以放宽控制晶体物理属性的选择规则，这些规则的源于无限扩展晶体的对称属性，平移和旋转。抓住。因此，人们将期望发现薄膜或小颗粒的导热性将显示出对于块状材料而言不会出现的特定特征。