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

Abstract

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 $\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.

Keywords

• PbIn6Te10
• IR nonlinear optical crystal
• high temperature x-ray diffraction
• thermal expansion coefficient
• anisotropy
• Grüneisen parameter