中文摘要：

以Zr替代Ti（或Al）掺杂γ-Ti Al体系为研究对象,掺杂浓度（摩尔比）分别为1/54,1/36,1/24和1/16.采用基于密度泛函理论的第一性原理方法,计算研究了Zr掺杂γ-TiAl体系的晶体结构及其稳定性、延性和电子性质等.结果显示,Zr替位掺杂,可以改变γ-TiAl基合金的结构对称性.计算的形成能表明,Zr替代Ti原子会使体系的形成能降低,而Zr替代Al原子会使体系的形成能增加.因而,在掺入γ-TiAl时,Zr更倾向于替代Ti原子,但是Zr替代Al原子也具有一定的可能性,从而会产生多样的掺杂体系,对于改善合金的性质具有重要意义.对各个体系轴比的计算与分析表明,当掺杂浓度为1.85 at%—6.25 at%时,Zr替代Al原子会使体系的轴比减小、接近于1,从而改善合金的延性效果明显.能带结构显示各个Zr掺杂γ-TiAl体系均具有金属导电性.对电子态密度和布居数的分析表明,Zr替代Al原子后,Zr与其邻近Ti原子的共价键结合强度大为降低,导致合金体系中的Ti—Al（Zr）键的平均强度明显减弱,金属键增强,这是改善γ-TiAl合金延性的重要因素.

英文摘要：

This investigation aims at the Zr-doping in γ-TiAl alloy systems in which Ti （or Al） atoms are partly replaced and the impurity concentrations are 1/54, 1/36, 1/24 and 1/16 （molar ratio）, respectively. The structural, energy, plastic and electronic properties of the alloys are calculated and studied by using the first-principles method based on the density functional theory and other physical theory. From geometry optimization results it is shown that doping with Zr can change the structural symmetry of the γ-TiAl systems. These results also suggest that the cubic degree of Zr-doped γ-TiAl alloys can be increased due to the Zr-substitution. For instance, the cubic degrees of Ti12Al11Zr and Ti18Al17Zr systems are enhanced distinctly, which are positive for improving the mechanical properties of the alloys. The average formation energies obtained indicate that the Ti atom replaced by Zr can slightly decrease the formation energy of the system （〈 0.003 eV/atom）; while Zr substituting the Al atom can increase the formation energies of the systems （〈 0.07 eV/atom）. Accordingly, when Zr atoms are introduced in the γ-TiAl system, they tend to substitute Ti atoms, and can also substitute Al atoms with a certain possibility. Thus, various Zr-doped γ-TiAl regions can be produced in the system. The integral effects are of significance for improving the performance of the γ-TiAl based alloys by means of Zr-doping method. Comparing the axial ratios of Zr-doped γ-TiAl systems with that of pure γ-TiAl system, we find that Zr substituting Al atom can reduce the axial ratio of the Zr-doped alloys, which is responsible for the ductility of the materials. It should be mentioned that when the impurity concentration is in the range of 1.85 at%-6.25 at%, the doping effect will be most distinct and the axial ratio of the alloys is close to unity. It is expected that the Ti12Al11Zr system has a good ductility for its axial ratio equals to 1.007. The band structures of Zr-doped γ-TiAl systems show that they a