Structural properties and thermodynamic stability of Ba-doped silicon type-I clathrates synthesized under high pressure

Abstract

We present a joint experimental and theoretical study of the stability and structural properties of Ba-doped silicon type-I clathrates ${\mathrm{Ba}}_{8}{\mathrm{Si}}_{46}$ synthesized under high pressures. The thermodynamic stability of ${\mathrm{Ba}}_{8}{\mathrm{Si}}_{46}$ under high pressure has been discussed from the total energy calculations of some barium silicides within the local density approximation (LDA). We have theoretically found that pressure favors the formation of the clathrate phase as experimentally observed. We have also performed a synchrotron x-ray-diffraction experiment of ${\mathrm{Ba}}_{8}{\mathrm{Si}}_{46}$ prepared under high pressures. Some of the missing endohedral Ba elements in the small cage of Si(20) have been observed by x-ray crystallography, while big cages of Si(24) are found to be completely occupied by Ba elements. The stabilization energies of Ba atoms in the endohedral sites estimated within the present LDA calculation suggest that this is presumably attributed to the energetical site preference of Ba atoms between $d(6)$ and $a(2)$ sites. In addition, the isothermal parameter of Ba in the big cage of Si(24) has been found to be larger than that in the small Si(20) unit, which is consistent with some theoretical predictions in earlier works.