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

Abstract

The PbIn₆Te₁₀ crystal, an IR laser frequency conversion material, grown via the Bridgman method with dimensions ϕ35 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 PbIn₆Te₁₀ crystals satisfy the relationships α_a > α_c > 0, α_V = 2α_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 PbTe₆ octahedron primarily governed the changes in the PbIn₆Te₁₀ unit cells, with further investigation uncovering its association with variations in the nearest neighboring bonds, which is mainly related to Pb-Te⁴ and Pb-Te² bonds. Additionally, the determination of temperature-dependent anisotropic thermal expansion coefficient α was complemented by calculating Grüneisen parameter $\gamma$ using Quasi-harmonic Debye model. Remarkably, these parameters also exhibited anisotropic behaviors (${\gamma }_{\perp }$ increases with temperature whereas ${\gamma }_{//}$ decreases, α_⊥ > α_∥), contributing additional insights into the crystal thermal characteristics.