Electronic Structure And Elastic Properties Of The Layered Ternary Carbide Ti₃AlC₂

The ternary layered carbide Ti3AlC2 is a new Thermodynamically stable nanolaminates. The Ti3AlC2 combines unusual properties of both ceramics and metals, having broad application prospects in the fields of high temperature material and electric contacting material.The CASTEP code is a plane-wave pseudopotential total energy calculation method that is based on density functional theory. It was used in the present calculation, wherein the Vanderbilt-type ultrasoft pseudopotential and generalized gradient approximation (GGA-PW91) were employed. The plane-wave basis set cutoff was 380 eV for all calculations. The special points sampling integration over the Brillouin zone was employed by using the Monkhorst-Pack method with a 9×9×2 special k-points mesh.Lattice parameters, including lattice constants and internal atomic coordinates, were modified independently to minimize the enthalpy and interatomic forces. The Broyden-Fletcher-Goldfarb-Shanno (BFGS) minimization scheme was used in geometry optimization. The tolerances for geometry optimization are difference on total energy within 5x10-6 eV/atom, maximum ionic Hellmann-Feynman force within 0.01 eV/A, maximum ionic displacement within 5x10-4 A and maximum stress within 0.02 GPa. The calculated results are in good agreement with experimental measurements and other theoriral results. To better understand the nature of the interatomic bonding, the electronic structure and Mulliken population was examined.The elastic coefficients were determined by applying a set of given homogeneous deformations with a finite value and calculating the resulting stress with respect to optimizing the internal degrees of freedoms. Two strain patterns, one with nonzero s33 components and the other with a nonzeroε11 andε23, generated stresses related to all five independent elastic coefficients for a unit cell with a hexagonal symmetry. We determined the elastic stiffness from a linear fit of the calculated stress as a function of strain. Other mechanical parameters, such as the bulk modulus(GPa), Young's moduli(GPa), and Poisson's ratio(GPa) were calculated from the compliance tensor. The shear modulus(GPa) was calculated according to the Voigt approximation. The external pressure was imposed upon the simulated unit cell as isotropic hydrostatic pressure. Calculations were performed for various pressures between 0 and 50 GPa, and the atomic configuration at zero pressure was referred to as the equilibrium state in this paper. The lattice parameters and internal atomic positions were fully optimized throughout the simulations until local minimizations of the total energy were realized. The elastic coefficients and modulis at various pressures were obtained to understand the role how external pressure influence the elastic properties of TiAlC2.