中文摘要：

采用第一性原理的密度泛函理论平面波赝势法，通过广义梯度近似研究了Ti3AC2相（A=Si，Sn，Al，Ge）的相结构、能量、电子结构和弹性性质．首先对六方晶相结构的Ti3AC2（A=Si，Sn，Al，Ge）四个相进行几何优化，对其能带结构、总态密度、分态密度和电荷密度分布以及弹性性质进行研究，并计算各相的内聚能与形成能．计算结果表明：Ti3GeC2较其他三相稳定，Ti3AlC2的形成能最低，说明Ti3AlC2较Ti3SiC2，Ti3SnC2和Ti3GeC2更易生成；TiaAC2（A=Si，Sn，Al，Ge）各相在费米能级处的电子态密度较高，材料表现出较强的金属性，同时各相的导电性为各向异性．Ti3AC2（A-Si，Sn，Al，Ge）各相的导电性主要由Ti的3d电子决定，A（A=Si，Sn，Al，Ge）的P态电子和C的2p态电子也有少量贡献．决定材料电学性质的主要是Ti的3d，A的P和C的2p态电子的p—d电子轨道杂化，而p—d电子轨道杂化成键则使材料具有比较稳定的结构；对TiaAC2相（4=Si，Sn，Al，Ge）弹性性质的研究表明Ti3AlC2的原子间结合力较弱，而TiaGeC2的原子间结合力相对较强，材料的强度较大．

英文摘要：

A first-principles plane-wave pseudo potential method based on the density functional theory is used to investigate the phase structures, energies, electronic structures and elastic properties of Ti3AC2 （A = Si, Sn, Al, Ge） phases. In this paper, Ti3AC2 （A = Si, Sn, Al, Ge） crystal structures are first optimized, then the band structures, total and part density of states, charge density distributions and elastic properties of these compounds are analyzed, and the cohesive energies and formation energy of these phases are also calculated. The results show that the Ti3GeC2 is more stable than other compounds, the formation energy of Ti3AlC2 is the lowest in these compounds, which indicates that Ti3AlC2 is easier to generate; Ti3AC2 （A = Si, Sn, Al, Ge） each have a higher density of states at Fermi level, which shows the strong metallicity, meanwhile, the electrical conductivity of each phase is anisotropic. The DOS at the Fermi energy is mainly from the Ti-d electrons, which should be involved in the conduction properties although d electrons are considered to be inefficient conductors. The lowest valence bands are formed by the C-s states with a small mixture of Ti-p＋d, and A-s＋p states. The electrical properties are mainly decided by the p-d hybridizations between 3d electrons in Ti and the p electrons in A （A =Si, Sn, Al, Ge） and 2p electrons in C, and the strong hybridization of p-d states make the materials have stable structures. It should be noted that the calculated bond length of Ti-Ge is shorter than those of Ti-A （A =Si, Sn, Al） bonds. This implies that the Ti--Ge bond is stronger than Ti-A （A =Si, Sn, Al） bonds. Yhrthermore, the Fermi level of Ti3GeC2 is relatively low, which also indicates the relatively high stability of Ti3GeC2. The charge density provides a measure of the strength of the ionic bond, so that Ti3GeC2 and Ti3SiC2 have stronger ionic bonds than Ti3SnC2 and Ti3AlC2. The strong M-A bonds in Ti3GeC2 lead to a decreasing and c lattice parameter value increasing.