Structural study of topological insulator Bi$_{2}$(Se$_{3-x}$Te$_{x})$

With neutron diffraction, we systematically investigated the local and average structures of topological insulator Bi$_{2}$(Se$_{3-x}$Te$_{x})$ (x=0, 1, 1.5, 2, and 3) from 5 to 500 K. The average crystal structure of Bi$_{2}$Se$_{3}$ is rhombohedral R-3m symmetry with 2 unique chalcogen sites. This gives rise to 2 types of Bi-(Se/Te) bonds in quintuple layer composed of Se1-Bi-Se2 --Bi-Se1 layers, covalent Se1-Bi bond with the bonding length of 2.85 {\AA} and ionic Se2-Bi bond with the bonding length of 3.07 {\AA} at 5 K. The Se1-Se1 bonds between quintuple layers are governed by Van der Walls of the length of 3.47 {\AA} at 5 K. With increasing temperature, it is observed that the quintuple layer unit contracts from the anti-parallel motion of the Bi-(Se1)$_{3}$ tetrahedra toward the Se2-center layer. Also such a contraction implies the Van der Waals bonding between quintuple layers weakens with temperature. A similar temperature dependence of atomic structure is observed on Bi$_{2}$Se$_{3}$.