Elastic Properties, Phonon Focusing and Electronic Structures of Typical Long-Period Superstructures Al<sub>5</sub>Ti<sub>2</sub> and Al<sub>11</sub>Ti<sub>5</sub>

Abstract

The first-principles calculations were performed to systematically study the elastic properties, phonon focusing and electronic structures of typical long-period superstructures Al5Ti2 and Al11Ti5. The obtained lattice parameters are in good agreement with the experimental data. The elastic constants were calculated, and bulk modulus B, shear modulus G, Young’s modulus E and Poison’s ration ν were further obtained. Both of the numerical indicators and the three dimensional images show that Al5Ti2 and Al11Ti5 are anisotropic, and the anisotropy is slightly high for Al5Ti2. Three slowness surfaces were constructed for Al5Ti2 and Al11Ti5 to investigate the phonon focusing patterns, and the group velocity surfaces were also obtained to gain more insight into the elastic anisotropy. Due to elastic anisotropy, both of the slowness surfaces and the group velocity surfaces are nonspherical, and the anisotropy is highest for slow transverse mode, and then followed by fast transverse mode and longitudinal mode. The electronic density of states and charge density distribution of Al5Ti2 and Al11Ti5 indicate that due to strong hybridization between Al-2p and Ti-3d, there is a strong directional bonding between the Al and Ti atoms. Electronic structures reveal the underling mechanism of elastic properties and phonon focusing for Al5Ti2 and Al11Ti5.