中文摘要：

采用第一性原理方法详细研究了氟化钙结构的多种金属氢化物MH2（M=La，Nd，Gd，Tb，Y,Dy,Ho，Er_Lu，sc，Ti，Zr,Hf）的力学性质（弹性常数、体弹模量、剪切模量、杨氏模量）．计算结果表明，MH2（M=La，Nd，Gd，Tb，YDy,Ho，Er,Lu，Sc）在低温下具有稳定的氟化钙结构，其抵抗体积形变，切应变和拉伸（或压缩）形变的能力从LaH2，NdH2，GdH2，TbH2，YH2，DyH2，HoH2，ErHz，Lull2到ScH2逐次递增，而MH2（M=Ti，Zr,Hf）在低温下的氟化钙结构不稳定．通过对两种稳定的氢化物（TbH2，ErH2）和两种不稳定的氢化物（TiH2，HfH2）的电子态密度以及差分电荷密度进行对比，发现它们的稳定性与金属和氢之间的相互作用有密切关系．

英文摘要：

The mechanical properties of MH2 （M = La, Nd, Gd, Tb, Y, Dy, Ho, Er, Lu, Sc, Ti, Zr, Hi） are studied by the first-principles calculations. The results show that the fluorite structures of MH2 （M = La, Nd, Gd, Tb, Y, Dy, Ho, Er, Lu, Sc） are stable at low temperatures. Their bulk moduli, shear moduli and Young＇s moduli increase in the order of LaH2, NdH2, GdH2, TbH2, YH2, DyH2, HoH2, ErH2, Lull2 and ScH2. However, the cubic phases of MH2 （M = Ti, Zr, Hi） are unstable at low temperatures. According to the densities of states and charge densities of TbH2, ErH2, TiH2 and HfH2, it can be found that the stabilities of metal dihydrides depend on the interaction between metal and hydrogen atoms.