Elastic and electronic properties of the Ti5X3 (X=Si, Ge, Sn, Pb) compounds from first-principles calculations

The structural stabilities, elastic and electronic properties of Ti5X3 (X=Si, Ge, Sn, Pb) compounds with D88 structure have been systematically investigated within the frame work of density functional theory. With increase of atomic number of the element X, the calculated lattice constants of Ti5X3 compounds are found to increase, while stabilities of these compounds decrease because the formation enthalpies increase. Moreover, with exception of C12, the calculated elastic constants Cij are reduced with increase of atomic number of element X, the bulk, shear, Young’s modulus and Debye temperature are also lowered, while Poisson’s ratio is larger, and the ductility is slightly improved. The elastic anisotropies were further studied, especially the 3D direction dependence of these elastic modulus was visually described. The density of states and charge density distribution reveal bonding feature of Ti5X3. Especially, the X–X and Ti–X covalent bonding strength is found to decrease with increase of atomic number of element X.

Graphical abstractThe charge density contour plots on the (0 0 0 1) plane for Ti5Si3 (a), Ti5Ge3 (b), Ti5Sn3 (c) and Ti5Pb3 (d).Figure optionsDownload full-size imageDownload as PowerPoint slideHighlights► The elastic constants except C12 were lowered with increase of atomic number of X. ► The bulk and shear modulus as well as Young’s modulus was also decreased. ► The elastic anisotropies of Ti5X3 were further studied visually. ► The X–X and Ti–X covalent bonding strength was lowered.