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中文摘要：
基于马儿可夫链理论和Bragg-Williams型方程，建立了描述反位缺陷占位几率的基本方程和转移几率；推导出了平衡时空位与反位缺陷浓度的表达式。利用所建模型结合第一性原理平面波赝势法系统研究了NiAl中各种点缺陷，从定量计算和电子结构角度论证了平衡状态下，在Ni：Al=1附近，Ni和A1原子的占位服从Fermi．Dirac统计，并且当温度从800增加到1300K时，NiAJ几率比A1Ni几率大10^6～10^9倍，反位缺陷以NiAl为主。VNi浓度比AlNi浓度大10^5～10^7倍、而NiAl浓度比vAl浓度大10^6～10^（10）。倍。对于同一原子而言，NiAl比vNi稳定，AlNi比VAl稳定。
英文摘要：
Based on the Markov Chain in Probability Theory and the Bragg-Williams-type equations for equilibrium defect concentrations, the occupancy probability equations and transfer probability of describing antisite defect have been established. At the same time, antisite and vacant site defect concentrations＇ equations have also been derived. Using the established equations, the transfer probability and the first-principles plane-wave pseudopotential method, the various point defects of NiA1 were studied. It is proved from the calculation and the electron structure that the occupancy probability of antisite defect obeys Fermi-Dirac statistics and when the temperature changes from 800 to 1300 K with Ni：Al=1, NiA1 anti-site probability is more about 10^6-10^9 times than AlNi antisite probability, which proves that NiAl is the dominant point defect. VNi vacant site concentration is more about 10^5-10^7 times than A1Ni antisite concentration, while NiAl antisite concentration is more about 10^6-10^（10） times than VAl vacant site concentration.
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