Investigation of the Anisotropic Thermal Expansion Mechanism of AgxGaxGe1–xSe2 Crystals

Quaternary nonlinear optical single crystals AgxGaxGe1-xSe2 (x = 0.250, 0.167) were grown by the Bridgman method in a four-zone furnace. The thermal expansion behavior of AgxGaxGe1-xSe2 (x = 0.25, 0.167) was studied by the method of single-crystal X-ray diffraction from 150 to 295 K and powder X-ray diffraction in the range of 298-773 K. Both results show the crystals have positive linear thermal expansion coefficients in different directions and a positive volume thermal expansion coefficient, and it is observed that they satisfy the relationship of αa > αc > αb and αV ≈ αa + αb + αc for the orthorhombic structure. It is found that the AgxGaxGe1-xSe2 (x = 0.25, 0.167) unit cells varying with temperature were mainly dominated by variations in framework geometry (AgSe4 tetrahedron), and the thermal motion of Ag atoms in the AgSe4 tetrahedron. As it was revealed, according to the powder X-ray diffraction, it is found that the isotropic thermal atomic displacement parameter of the Ag atoms is much larger than those of the Se and Ga(Ge) atoms in the AgSe4 tetrahedron. Furthermore, anisotropic atomic displacement parameters (ADPs) of Ag atoms are extracted from the single-crystal diffraction; the ADPs along the a axis, b axis, and c axis have a significant difference, which means the thermal vibration of Ag atoms is anisotropic. It is of great significance for improving crystal growth technology and understanding the thermal properties of this kind of crystals.