Investigation of the anisotropic thermal expansion of PbIn6Te10 crystal by high temperature x-ray diffraction measurements

The PbIn 6 Te 10 crystal, an IR laser frequency conversion material, grown via the Bridgman method with dimensions ϕ 35 mm × 90 mm in a four-zone furnace, was subject to the investigation of its thermal expansion behavior using high-temperature x-ray diffraction in the range of 25–450 °C. Based on the obtained data, the average thermal expansion coefficients of 15.21 × 10 −6 K −1 for α a and 6.44 × 10 −6 K −1 for α c were determined utilizing the least square method. The study revealed that the linear and volume thermal expansion coefficients of PbIn 6 Te 10 crystals satisfy the relationships α a > α c > 0, α V = 2 α a + α c , and α a increased while α c decreased with increasing temperature, accentuating a substantial anisotropy in thermal expansion between the crystal’s principal axes. A detailed exploration pinpointed that the variations in the PbTe 6 octahedron primarily governed the changes in the PbIn 6 Te 10 unit cells, with further investigation uncovering its association with variations in the nearest neighboring bonds, which is mainly related to Pb-Te 4 and Pb-Te 2 bonds. Additionally, the determination of temperature-dependent anisotropic thermal expansion coefficient α was complemented by calculating Grüneisen parameter γ using Quasi-harmonic Debye model. Remarkably, these parameters also exhibited anisotropic behaviors ( γ ⊥ increases with temperature whereas γ / / decreases, α ⊥ > α ∥ ), contributing additional insights into the crystal thermal characteristics.