Phase Transformation, Vibrational and Electronic Properties of K₂Ce(PO₄)₂: A Combined Experimental and Theoretical Study

Herein we report the high-temperature crystal chemistry of K2Ce­(PO4)2 as observed from a joint in situ variable-temperature X-ray diffraction (XRD) and Raman spectroscopy as well as ab initio density functional theory (DFT) calculations. These studies revealed that the ambient-temperature monoclinic (P21/n) phase reversibly transforms to a tetragonal (I41/amd) structure at higher temperature. Also, from the experimental and theoretical calculations, a possible existence of an orthorhombic (Imma) structure with almost zero orthorhombicity is predicted which is closely related to tetragonal K2Ce­(PO4)2. The high-temperature tetragonal phase reverts back to ambient monoclinic phase at much lower temperature in the cooling cycle compared to that observed at the heating cycle. XRD studies revealed the transition is accompanied by volume expansion of about 14.4%. The lower packing density of the high-temperature phase is reflected in its significantly lower thermal expansion coefficient (αV = 3.83 × 10–6 K–1) compared to that in ambient monoclinic phase (αV = 41.30 × 10–6 K–1). The coexistences of low- and high-temperature phases, large volume discontinuity in transition, and large hysteresis of transition temperature in heating and cooling cycles, as well as drastically different structural arrangement are in accordance with the first-order reconstructive nature of the transition. Temperature-dependent Raman spectra indicate significant changes around 783 K attributable to the phase transition. In situ low-temperature XRD, neutron diffraction, and Raman spectroscopic studies revealed no structural transition below ambient temperature. Raman mode frequencies, temperature coefficients, and reduced temperature coefficients for both monoclinic and tetragonal phases of K2Ce­(PO4)2 have been obtained. Several lattice and external modes of rigid PO4 units are found to be strongly anharmonic. The observed phase transition and structures as well as vibrational properties of both ambient- and high-temperature phases were complimented by DFT calculations. The optical absorption studies on monoclinic phase indicated a band gap of about 2.46 eV. The electronic structure calculations on ambient-temperature monoclinic and high-temperature phases were also carried out.本文报道了K₂Ce(PO₄)₂的高温晶体化学特性，该研究结合原位变温X射线衍射（X-ray diffraction, XRD）、拉曼光谱（Raman spectroscopy）测试与从头算密度泛函理论（density functional theory, DFT）计算。研究结果表明，常温下单斜晶相（monoclinic phase, 空间群P2₁/n）可在高温下可逆转变为四方晶相（tetragonal phase, 空间群I4₁/amd）。结合实验与理论计算，本文还预测了一种近乎零正交畸变的正交晶相（orthorhombic phase, 空间群Imma），其与四方相K₂Ce(PO₄)₂密切相关。与升温过程中测得的转变温度相比，降温循环中高温四方相可在更低温度下恢复至常温单斜晶相。XRD测试显示，该相变伴随约14.4%的体积膨胀。高温相较低的堆积密度体现在其热膨胀系数（thermal expansion coefficient）显著低于常温单斜相：常温单斜相的体积热膨胀系数α_V = 41.30 × 10⁻⁶ K⁻¹，而高温相仅为3.83 × 10⁻⁶ K⁻¹。高低温两相共存、相变时的大幅体积突变、升降温循环中显著的转变温度滞后，以及二者截然不同的结构排布，均符合该相变属于一级重构型相变（first-order reconstructive transition）的特征。变温拉曼光谱显示，783 K附近出现显著的光谱变化，对应该结构相变。原位低温XRD、中子衍射（neutron diffraction）及拉曼光谱测试未发现常温以下存在结构相变。本文还获取了K₂Ce(PO₄)₂单斜相与四方相的拉曼模频率、温度系数及约化温度系数。研究发现刚性PO₄基团的多个晶格模与外模具有强非简谐性。观测到的相变、两相结构以及常温和高温相的振动特性均通过DFT计算得到了验证。对单斜相的光学吸收测试表明其带隙（band gap）约为2.46 eV。本文同时开展了常温单斜相与高温四方相的电子结构计算。