PROOF OF THE VALIDITY OF THE VIRIAL THEOREM IN THE EQUATION OF STATE BY THE THOMAS-FERMI-DIRAC MODEL

The present paper is to demonstrate the validity of the virial theorem for electrons in the revised Thomas-Fermi-Dirac model, which has not yet received a rigorous proof. The theorem has actually a wider sense in application both in classical and quantum-mechanical dynamics.     

弹-塑性流体动力学数值模拟计算的一种新自由面格式

提出了适用于电子束或X射线辐照、爆炸和高速碰撞等问题的弹-塑性流体动力学数值模拟计算的一种新自由面格式。一些数值模拟计算的结果表明,所给出的新自由面格式明显优于目前一直沿用的Richtmyer格式,尤其适用于电子束及X射线辐照材料时产生的热-力学效应的数值模拟计算。     

一、二维弹塑性流体动力学数值计算的高精度新自由面格式

提出了适用于X射线或电子束辐照、爆炸和高速碰撞等问题的一、二维弹塑性流体动力学数值模拟计算的一种新自由面格式。对于X射线及电子束辐照材料与结构的热-力学效应的数值计算结果表明,该新自由面格式明显优于目前一直沿用的Richtmyer格式。从理论上证明了该新自由面格式具有三阶精度,而Richtmyer格式为一阶精度。     

冷压状态方程计算的新方法和材料相图的研究

本文运用位力(virial)定理严格地给出了材料的冷压状态方程.本文的理论没有引入对系统势能的任何假定,只需计算系统的总动能,因而在状态方程的研究上得到了新的进展.本文采用了经典TFD统计模型,给出了计算材料状态方程的新方法.此方法可以运用于整个凝聚体系统,从零压开始计算材料各个压缩度下的压力,考虑到经典TFD模型的统计与真实量子力学统计之间的差异.此方法对每种元素的总动能计算作了修正.用此状态方程的新方法计算,可以得到在整个压缩度范围(包括零压附近)压力与实测值一致的冷压状态方程, 对Li,Na,Al,Fe,Ag和U等元素以及Fe-Ni,Al-Cu等二元合金进行了数值计算,结果与实测值符合得较好. 文中还探讨了材料相图的理论研究.冷压状态方程计算的新方法和相图的理论研究将为材料的设计提供依据.      

COMPUTATION ON HEAT OF FORMATION AND EOS OF ALLOY BY A REFINED TFD MODEL

A new method of calculation of EOS and heat of formation of alloy by a modified TFD model is proposed. For elements, only their specific volumes at zero pressure and temperature are required as basic parameters, and the quantum corrections to the kinetic energy are admitted for a better accuracy in later calculations. Nothing more is demanded to be known a priori. Thus computations and analyses for some binary alloys such as Al-Cu, Al-Ni and Al-Co on their EOS as well as heat of formation have been car-ried out in detail. Results obtained are in good agreement with measurements. The theory also provides an explanation for the Miedema's empirical relations between the heat of formation and the eletronic characteristics in alloys. In a subsequent paper it will be shown that there is an intimate correlation between the present theory and the covalent bond theory of Pauling and Yu. It is quite plausible that the TFD model has far wider fields of application and may serve as a probe to both research and design of materials.