三维氯化钠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 3-D NaCl Iron Crystal

作　　者：周群益 莫云飞 侯兆阳 周丽丽[4] Zhou Qunyi;Mo Yunfei;Hou Zhaoyang;Zhou Lili(College of General Education,Guangzhou Institute of Science and Technology,Guangzhou Guangdong 510540,China;School of Electronic and Communication Engineering,Changsha University,Changsha Hunan 410022,China;School of Science,Chang’an University,Xi’an Shanxi 710064,China;School of Information Engineering,Gannan Medical University,Ganzhou Jiangxi 341000,China)

机构地区：[1]广州理工学院通识教育学院,广东广州510540 [2]长沙学院电子信息与电气工程学院,湖南长沙410022 [3]长安大学理学院应用物理系,陕西西安710064 [4]赣南医学院信息工程学院,江西赣州341000

出　　处：《衡阳师范学院学报》2021年第3期50-54,共5页Journal of Hengyang Normal University

基　　金：国家自然科学基金项目(11747123);广东省高校科研特色创新项目(2020KTSCX209)。

摘　　要：研究发现在三维氯化钠晶体结构中存在两种晶胞:氯心晶胞和钠心晶胞,两种晶胞是互嵌晶胞。提出两种晶胞互相嵌入形成各级晶体的方法,根据各级晶体表面离子的分布规律,总结得出马德隆常数的累加法的递推公式。埃夫琴采用电中性的晶体计算马德隆常数,大大地提高了收敛速度。分析出埃夫琴法实际上只考虑晶体内部离子和表面离子的内部部分对马德隆常数的贡献,应称为内埃夫琴法。证明了各级晶体都是电中性的,推导了外埃夫琴法的公式,其意义是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。提出了晶胞嵌入-外埃夫琴法,用迭代算法高效率地计算出多级马德隆常数的多位精确值。There are two types of unit cells centered Cl and centered Na,and they nest with each other.The structure of NaCl 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 according the distribution of ions on the surface,but the convergence rate is slow.The Evjen method can enhance the convergence rate according to the neutral crystal unit.Furthermore,a new method of calculating Madelung constant is proposed by us,by considering the contribution of ions in the outer surface of crystal cell,and this method is called outer Evjen method.This method can eliminate the surface effect,and it is an amendment of accumulation method.The accurate value of Madelung constant for 3-D NaCl ion crystal is obtained by outer Evjen method.

关 键 词：氯化钠 嵌套 埃夫琴法 马德隆常数 

分 类 号：O48[理学—固体物理]