Temperature And Pressure Dependent Geometry Optimization And Elastic Constant Calculations For Arbitrary Symmetry Crystal

Material structure and property at high temperature and high pressure has long been the interest both for experimental and theoretical research. The importance of the determination of temperature and pressure dependent crystal structure and property lies in the following aspects, the widely application of alloy in industry and understanding the seismology, geodynamics and mineral physics of the Earth’s interior.However, difficulty for experimental measurement for crystal structure and mechanical property at high temperature and pressure lies in the sample preparation, control of temperature and pressure in laboratory, increase of uncertainties of experimental values with the enlargement of temperature and pressure. Therefore, theoretical prediction becomes an irreplaceable alternative for high temperature and high pressure material property prediction. In this work, by combining first-principles and continuum elastic theory, a methodology for temperature and pressure dependent arbitrary symmetry crystal geometry optimization and elastic constants calculation is proposed. The non-equilibrium Gibbs energy as a function of temperature, pressure and deformation strain is derived, the anisotropic geometry optimization is realized by minimizing this non-equilibrium Gibbs energy with respect to the deformation strain.The temperature and pressure dependent geometry optimization has been applied to cubic symmetry diamond, hexagonal symmetry2H-diamond and hexagonal symmetry Beryllium, temperature dependent lattice parameters have been successfully predicted, calculated thermal expansion coefficient accords well with experimental ones. Then, after obtaining temperature dependent crystal structure, temperature dependent elastic constants calculations have been performed, calculated temperature dependent elastic constants of cubic diamond and hexagonal Beryllium is in accordant with available experimental values. For the hexagonal2H-diamond, the temperature dependent elastic constant is firstly predicted. Calculated results for the three kinds of material illustrate the temperature and pressure dependent geometry optimization and elastic constants calculation methodology can be applied for arbitrary symmetry crystal.The temperature and pressure dependent geometry optimization has been applied to two-dimensional lattice. Recently investigations on two-dimensional nano-film graphene and graphyne have shown that they combined wonderful electrical, optical and mechanical properties. The methodology for temperature and pressure dependent geometry optimization and elastic constants calculation proposed in this thesis is applied to two dimensional graphene and graphyne. Their lattice geometry, thermal expansion coefficient, elastic constants and ultimate strength dependence on temperature have been systematically investigated. Both the graphene and graphyne show negative TEC at low temperature region, TEC increase with the temperature slowly and finally surpass zero. Elastic constants calculation shows that graphene has superior mechanical strength and its mechanical property has a well resistance towards the temperature increase, thermal induced mechanical property softening of both graphene and graphyne are elucidated.