The contribution of surfaces and interfaces to the crystal thermal conductivity

IF 8.2 1区 化学 Q1 CHEMISTRY, PHYSICAL
M. Kazan , P. Masri
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引用次数: 13

Abstract

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.

表面和界面对晶体导热性的贡献
本文综述了表面和界面在固体导热中的作用的理论认识。试图收集在实验分析中使用的各种方法。评估了这些方法的充分性和有效性范围,并就可能的理论和实验研究提出了建议,这些研究似乎是可取的。论文的主要部分是描述表面振动模式、表面导热性、缺陷与晶体表面的相互作用以及晶体表面的声子散射。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,在用松弛时间描述散射过程的情况下计算热流,并推导出晶格导热系数的一般形式。特别考虑了边界散射和边界热导的影响。在前几节中,尽管考虑了边界散射,但导热系数的计算采用循环边界条件进行。这样的处理虽然在数学上很方便,但却消除了研究真实晶体自由表面附近原子动力学性质的可能性,因为表面层中的晶体结构可能与晶体主体的结构不同。作用在表层原子上的力与作用在整体原子上的力是不同的,因为表层的原子比晶体内部的原子有更少的近邻、次近邻等。因此,人们会期望晶体表层原子的动力学性质和由此产生的热导率与晶体整体中的原子不同。此外,当晶体尺寸变小到表面体积比不可忽略时,自由表面对晶体频率分布函数的修正,即本质上是二维晶体的贡献,将改变热导率的温度依赖性,并产生明显的尺寸对热导率的影响。此外,控制晶体物理性质的选择规则起源于无限扩展晶体的对称性、平动性和旋转性,对于有限晶体或晶体表层的原子,这些对称性不再成立,选择规则可以放宽。因此,人们会期望发现薄膜或小颗粒的热导率将显示出块状材料所没有的特定特征。为了从理论上理解尺寸和表面对晶格热导率的影响,我们在最后几节中提出了热导率的理论晶格动力学讨论,其中自由边界表面的存在对晶格振动的修改起着主导作用。
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来源期刊
Surface Science Reports
Surface Science Reports 化学-物理:凝聚态物理
CiteScore
15.90
自引率
2.00%
发文量
9
审稿时长
178 days
期刊介绍: Surface Science Reports is a journal that specializes in invited review papers on experimental and theoretical studies in the physics, chemistry, and pioneering applications of surfaces, interfaces, and nanostructures. The topics covered in the journal aim to contribute to a better understanding of the fundamental phenomena that occur on surfaces and interfaces, as well as the application of this knowledge to the development of materials, processes, and devices. In this journal, the term "surfaces" encompasses all interfaces between solids, liquids, polymers, biomaterials, nanostructures, soft matter, gases, and vacuum. Additionally, the journal includes reviews of experimental techniques and methods used to characterize surfaces and surface processes, such as those based on the interactions of photons, electrons, and ions with surfaces.
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