Mie-Grüneisen状态方程的物理力学释义

A Physical Mechanics Paraphrase on Mie-Grüneisen Equation of State

通过建立一种简单的固体一维点阵定容热振动的物理力学模型,完全由力学方程推演出了Mie-Grüneisen形式的固体状态方程,并从力学本质上明确了热压力的物理意义是原子热振动时均值所造成的作用力偏载量。所得Grüneisen系数与频率的关系说明,真实三维晶体的Grüneisen系数与晶体结构相关。在简单立方晶体的情况下,获得了与Dugdale-MacDonald公式形式相同的Grüneisen系数-冷压微分关系式。研究结果证明,在状态方程构建方面,"物理力学"是一种非常有效的研究工具。

A one-dimensional model of lattice physical mechanics was built up to study the atomic ther- mal vibration in a constant volume state. According to the lattice dynamics model, An equation of state of solids which is similar to the Mie-Griineisen＇s,was deduced absolutely from vibration mechanics. The mechanical implication of thermal pressure was ascertained, that thermal pressure was the average value of thermal vibration force in time domain. The relationship between GriJneisen parameter and thermal vibration frequency shows that the Grtineisen parameter of a real solid corelates with its crystal structure. The differential expression between GrLineisen parameter derivated from a simple cubic crystal and cold pressure was obtained,which agrees with the D-M relation.