Theory of thermal expansion in 2D crystals
Theory of thermal expansion in 2D crystals
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二维晶体的热膨胀理论
DOI：
10.1002/pssb.201552286
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发表时间：
2015
期刊：
影响因子：
--
通讯作者：
F. Peeters
中科院分区：
文献类型：
--
作者：
K. Michel;S. Costamagna;F. Peeters
层状晶体的热膨胀系数αT是一个重要的理论和技术问题。正如我所建议的。M. Lifshitz在1952年提出，在薄固体膜（结晶膜）中，αT的负贡献是由于面内拉伸模和面外弯曲（弯曲模）之间的非谐耦合。真正的面内非谐性对αT有正贡献。这两种效应之间的竞争可以导致符号（交叉）的变化，从温度（T）范围T≤Tα的αT的负值到层状晶体中T>Tα的αT的正值。在这里，我们提出了一个二维（2D）六方晶体的这些现象的分析晶格动力学理论。我们开始从一个哈密顿量，其中包括第三和第四阶的晶格位移的非调和项。对于不同尺寸的晶体，研究了平面内和面外对热膨胀的贡献随T的变化。此外，弯曲模态频率的重正化在确定交叉温度Tα中起着关键作用。数值例子给出了石墨烯的非谐耦合从实验中确定。该理论适用于任何已知非谐耦合的其它层状晶体。
The thermal expansion αT in layered crystals is of fundamental and technological interest. As suggested by I. M. Lifshitz in 1952, in thin solid films (crystalline membranes) a negative contribution to αT is due to anharmonic couplings between in‐plane stretching modes and out‐of‐plane bending (flexural modes). Genuine in‐plane anharmonicities give a positive contribution to αT . The competition between these two effects can lead to a change of sign (crossover) from a negative value of αT in a temperature (T) range T≤Tα to a positive value of αT for T>Tα in layered crystals. Here, we present an analytical lattice dynamical theory of these phenomena for a two‐dimensional (2D) hexagonal crystal. We start from a Hamiltonian that comprises anharmonic terms of third and fourth order in the lattice displacements. The in‐plane and out‐of‐plane contributions to the thermal expansion are studied as functions of T for crystals of different sizes. Besides, renormalization of the flexural mode frequencies plays a crucial role in determining the crossover temperature Tα . Numerical examples are given for graphene where the anharmonic couplings are determined from experiments. The theory is applicable to other layer crystals wherever the anharmonic couplings are known.