中文摘要：

本文在Tiwari and Patil（Scripta Metallurgica,1975,9：833）计算空位形成能的模型基础上,研究了纳米结构金属的空位形成能计算方法,通过引入形状因子,并考虑晶粒尺寸效应,计算了面心立方（fcc）、体心立方（bcc）和密排六方（hcp）结构纳米金属的空位形成能.结果表明,纳米结构金属的空位形成能随着晶粒尺寸的减小而下降 晶粒尺寸不变时,空位形成能随着晶粒形状因子的增大呈线性下降趋势.

英文摘要：

Based on the model of calculation vacancy formation energy proposed by Tiwari and Patil （Scripta Metal- lurgica, 1975, 9： 833）, we studied the calculation method of vacancy formation energy for nanostructure metals by introducing figure factor and considering grain size effect, we also calculated the vacancy formation energy of typical nar~ostructure metals, such as fcc, bcc and hcp metals. The results show that the vacancy formation energy of nano- structure metals decreases with the reducing the grain size and the vacancy formation energy decreases linearly with increasing the figure factor.