晶格振动模式密度研究

Investigation on the mode density of lattice vibration

晶格振动模式密度(声子态密度)即单位频率间隔内的模式数,是反映声子在波矢空间分布疏密程度的物理量.为了准确地求出晶格热容量随温度的变化关系,必须用较精确的办法计算出晶格振动的模式密度,进而掌握材料的热力学性质.一般教材中对该部分的讲解晦涩难懂,本文从晶格振动的物理意义开始,分析说明并推导一维、二维、三维不同体系的晶格振动模式密度公式,进而求出德拜模型下不同体系晶格热容公式.

The mode density of the lattice vibration（ phonon density of states）,i.e.,the mode number in the unit frequency interval,is a physical quantity reflecting the density of the phonon in the space of the wave vector. In order to calculate accurately the lattice heat capacity varying with temperature,one must calculate the density of lattice vibration by using more accurate method,and then grasp the thermodynamic properties of materials. Some general textbooks on the part of the explanation are obscure and difficult. This paper starts from the physical meaning of the lattice vibration,analysis and derivation of 1 D,2 D and 3 D different systems of lattice vibration mode density formula,then the lattice heat capacity formula of Debye model for different systems is presented.