中文摘要：

本文采用第一性原理研究了六角相ErAx（A=H，He）的弹性性质，其中X=0，0．0313，0．125，0．25，分别讨论了体系中不同浓度的氢和氦对体系弹性性质的影响．计算结果表明，六角相铒．氢体系晶体的弹性常数、体弹模量、剪切模量、杨氏模量基本上随着晶体中氢的浓度增加而增加，然而，铒．氦体系的弹性常数、体弹模量、剪切模量和杨氏模量几乎随着氦浓度的增加而降低．从电荷转移方面分析了氢和氦与Er的相互作用，发现六角相ErHx的弹性性质随H浓度的变化机理与ErHex随He浓度的变化机理不同．

英文摘要：

The elastic properties of hexagonal phase ErAx （A = H, He） have been calculated by the first-principles method, where x = 0, 0.0313, 0.125, 0.25. Effects of different concentrations of hydrogen and helium on the elastic properties of ErAx systems have been investigated in detail. Results show that the elastic constants, Young＇s modulus, bulk modulus and shear modulus of ErHx systems increase mainly with increasing hydrogen concentration, whereas, those elastic properties of ErHex systems almost decrease with increasing helium concentration. We have investigated the changes in the charge densities of Er atoms produced by A atoms. It was found that the mechanism for the change of the elastic properties of hexagonal phase ErHx with increasing hydrogen atoms is different from that of ErHex with increasing helium atoms.