爱因斯坦固体模型中的化学势疑难及其解决  

On chemical potentials of atoms and phonons in Einstein solid model

作　　者：彭君波 陈擎 刘全慧 PENG Jun-bo;CHEN Qing;LIU Quan-hui(School for Theoretical Physics,College of Physics and Electronics,Hunan University,Changsha,Hunan 410082,China)

机构地区：[1]湖南大学物理与微电子科学学院理论物理研究所

出　　处：《大学物理》2019年第8期63-65,共3页College Physics

基　　金：国家自然科学基金(11675051);高教社《热统》在线开放课程资源建设项目(20171015);教育部高等学校物理学类专业教学指导委员会项目(20171231);湖南大学教改基金(20161231)资助

摘　　要：一般而言,固体系统具有单一的自由能和其它热力学函数,但是有两个化学势,一个来自振子一个来自声子,前者非零而后者为零.爱因斯坦利用的是玻尔兹曼统计,发现固体原子的单个振动的配分函数可以解释成为单一频率声子气体的配分函数,其中声子的化学势为零,但是固体原子的化学势却不能解释成为声子的化学势.本文采用微正则系综,同时给出了固体原子和声子的化学势.In general,for a thermodynamic system each thermodynamic function has only one expression.However,solid has two chemical potentials,one for solid atoms and another for phonons,which have finite and vanishing value,respectively.Einstein utilized the Boltzmann statistics to discuss the heat capacity of the solid especially at low temperature,in which the partition function for single oscillating degree of freedom of the solid atoms can as well be intepreted on the base of phonon gas.It is evident that the chemical potential for the solid atoms can not be taken to be that of the phonon gas.How to simultaneouly determine the values of both chemical potentials is explicitly illustrated with microcanonical ensemble.

关 键 词：声子 固体原子 振子 化学势 微正则系综 

分 类 号：O414.21[理学—理论物理]