Role of anisotropy on topological structures of elasticity, anisotropy, brittleness and phonon in Al3Ti

Based on tensor theory and Bond matrix model, the anisotropy, brittleness/plasticity, and stress-strain under bulk and point stresses are systematically studied, in order to find the effect of anisotropy on their structures. The applications of the Kelvin-Christoffel tensor are mainly focused on phonon focusing and phonon image with Gaussian curvature method. The investigation of phonon entropy shows that the 3-branche lattice waves are mainly composed of long acoustic waves and long optical waves. The slowness of the three lattice waves is influenced by anisotropy as follows: the slow shear wave is the largest, the fast shear wave is the second, and the longitudinal wave is the smallest. This is well explained by the 3D anisotropy of phonon amplification coefficients. PACS: 62.20.D-; 74.25.Ld; 62.30. +d; 63.20.-e; 74.25.Ld; 94.20.Bb