氯化铯离子晶体的嵌套结构和马德隆常数的迭代计算

Nesting Structure and Iteration Calculation of Madelung Constant of CsCl Iron Crystal

分析了氯化铯晶体的嵌套结构,说明了马德隆常数的迭代计算方法。氯化铯结构的晶体存在两种互嵌单胞:氯心单胞和铯心单胞。通过单胞嵌入,可形成具有嵌套结构的晶体,这种形成晶体的方法称为嵌入法。马德隆常数的基本计算方法是累加法,文章提出了氯化铯结构的马德隆常数的累加法公式和递推公式。氯化铯结构有两种不同的表面,因而有两个不同的累加法的马德隆常数,两个常数都不收敛,其平均值也不代表马德隆常数。埃夫琴采用多个电中性的埃夫琴单胞组成的晶体,提高了马德隆常数的收敛速度。埃夫琴法实际上是计算晶体内部的离子和内表面离子对马德隆常数贡献的方法,因而可称为内埃夫琴法。该文推导了外埃夫琴法的公式。晶体外表面离子对马德隆常数只有负面贡献,可当作表面效应,外埃夫琴法是一种消除晶体表面效应的马德隆常数的计算方法,是对累加法的修正。将单胞嵌入法和外埃夫琴法结合起来,就形成单胞嵌入—外埃夫琴法,这种方法应用范围十分广泛。

In this paper,the nesting structure of CsCl iron and the iteration calculation of its Madelung constant are analyzed.There are two types of nesting cell centered Cl and centered Cs,and they nest with each other.The structure of CsCl ion crystal is constructed by means of nesting these unit cells,and this method is called nesting method.The recursive formula of calculating its Madelung constant is obtained,which belongs to accumulation method.There are two different Madelung constants calculating by the accumulation method due to the two different surfaces of CsCl structure.Meanwhile,the formula of Evjen method is deduced,which can enhance the convergence rate.Furthermore,a new method of cell nesting—outer Evjen method,is proposed by us,by considering the contribution of ions in the outer surface of crystal cell.This method can eliminate the surface effect,and it is an amendment of accumulation method.