中文摘要：

采用基于密度泛函理论的第一性原理方法,计算研究了压力对Ti_2AlC与Ti_2AlN结构、力学性能的影响.研究发现压力的增大会使体系的体积比降低,Ti_2AlC压缩性较Ti_2AlN好.力学性能研究发现,压力的增大使材料抵抗变形能力增强,体系的延展性有了很大的提升,当压力超过40 GPa后,Ti_2AlC与Ti_2AlN从脆性材料转变为延性材料,体模量与剪切模量的比值达到1.75,延展性有了很大的提升.通过准谐德拜模型,分析了压力与温度对Ti_2AlC与Ti_2AlN体模量、热容及热膨胀系数的影响.结果表明,随着温度的升高,Ti_2AlN与Ti_2AlC的体模量下降.定容热容与定压热容的变化趋势相同,但在高温下,定容热容遵循Dulong-Petit极限,温度对热容的影响效果较压力明显.温度与压力对Ti_2AlN与Ti_2AlC线膨胀系数的影响主要发生在低温区域.

英文摘要：

The MAX phase has attracted much attention due to its unique properties combined with the merits of both metal and ceramic,including the low density,high electrical conductivity and good oxidation resistance,which makes it significant for possible applications in various high temperature or other environments.There is a lot of research work on Ti_2AlX（X=C,N）.However little research about thermodynamic properties at high pressure is carried out.So we study the structural,mechanical and thermodynamic properties of Ti_2 AlC and Ti_2 AlN at various pressures and temperatures.The first-principles calculations based on electronic density-functional theory framework are used to investigate the properties at various pressures.The cut-off energy is 350 eV.Converged results are achieved with 10×10×2 special K-point meshes.The self-consistent convergence of total energy is set to be 5.0 × 10~（-6） eV/atom.According to the calculated structural parameters at various pressures,we can find that the ratios V/V_0（V_0 denotes the system volume at 0 GPa） of Ti_2AlX are reduced by 20.59%and 18.93%,respectively,so the compressibility of the system is strong.As the internal pressure increases,the curves of V/V_0 become gentle.Then we calculate elastic constants at pressures ranging from 0 to 50 GPa in steps of 10 GPa.It is obvious that the Ti_2AlX is mechanically stable because all of the elastic constants satisfy the Born stability criteria.The bulk modulus,shear modulus and Young＇s modulus linearly increase with internal pressure increasing,implying that the pressure can improve the resistance to volume deformation.The ductility and brittleness can be judged according to Pugh＇s criterion（ratio of bulk modulus to shear modulus B/G）,and the brittle nature turns into ductile nature in a pressure range of 40-50 GPa for the Ti_2AlX since the value of B/G exceeds 1.75.Finally,we study the thermodynamic properties at various pressures and temperatures based on the quasi-harmonic Debye approximation theory,including t