Investigation of the Anisotropic Thermal Expansion Mechanism of Ag_xGa_xGe_{1- x}Se₂ Crystals

Quaternary nonlinear optical single crystals Ag_xGa_xGe_1-xSe₂ (x = 0.250, 0.167) were grown by the Bridgman method in a four-zone furnace. The thermal expansion behavior of Ag_xGa_xGe_1-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 α_a > α_c > α_b and α_V ≈ α_a + α_b + α_c for the orthorhombic structure. It is found that the Ag_xGa_xGe_1-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.