Pressure and Temperature Dependent Structural Studies on Hollandite Type Ferrotitanate and Crystal Structure of a High Pressure Phase

The structural stability and phase transition behavior of tetragonal (<i>I</i>4/<i>m</i>) hollandite type K₂Fe₂Ti₆O₁₆ have been investigated by <i>in situ</i> high pressure X-ray diffraction using synchrotron radiation and a diamond anvil cell as well as by variable temperature powder neutron and X-ray diffraction. The tetragonal phase is found to be stable in a wider range of temperatures, while it reversibly transforms to a monoclinic (<i>I</i>2/<i>m</i>) structure at a moderate pressure, viz. 3.6 GPa. The pressure induced phase transition occurs with only a marginal change in structural arrangements. The unit cell parameters of ambient (t) and high pressure (m) phases can be related as <i>a</i>_<i>m</i> ∼ <i>a</i>_<i>t</i>, <i>b</i>_<i>m</i> ∼ <i>c</i>_<i>t</i>, and <i>c</i>_<i>m</i> ∼ <i>b</i>_<i>t</i>. The pressure evolution of the unit cell parameters indicates anisotropic compression with β_a = β_b ≥ β_c in the tetragonal phase and becomes more anisotropic with β_a ≪ β_b < β_c in the monoclinic phase. The pressure–volume equations of state of both phases have been obtained by second order Birch–Murnaghan equations of state, and the bulk moduli are 122 and 127 GPa for tetragonal and monoclinic phases, respectively. The temperature dependent unit cell parameters show nearly isotropic expansion, with marginally higher expansion along the <i>c</i>-axis compared to the <i>a-</i> and <i>b-</i>axes. The tetragonal to monoclinic phase transition occurs with a reduction of unit cell volume of about 1.1% while the reduction of unit cell volume up to 6 K is only about 0.6%. The fitting of temperature dependent unit cell volume by using the Einstein model of phonons indicates the Einstein temperature is about 266(18) K

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 (<i>P</i>2₁<i>/n</i>) phase reversibly transforms to a tetragonal (<i>I</i>4₁<i>/amd</i>) structure at higher temperature. Also, from the experimental and theoretical calculations, a possible existence of an orthorhombic (<i>Imma</i>) 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 (α_V = 3.83 × 10^–6 K^–1) compared to that in ambient monoclinic phase (α_V = 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

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 (<i>P</i>2₁<i>/n</i>) phase reversibly transforms to a tetragonal (<i>I</i>4₁<i>/amd</i>) structure at higher temperature. Also, from the experimental and theoretical calculations, a possible existence of an orthorhombic (<i>Imma</i>) 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 (α_V = 3.83 × 10^–6 K^–1) compared to that in ambient monoclinic phase (α_V = 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

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 (<i>P</i>2₁<i>/n</i>) phase reversibly transforms to a tetragonal (<i>I</i>4₁<i>/amd</i>) structure at higher temperature. Also, from the experimental and theoretical calculations, a possible existence of an orthorhombic (<i>Imma</i>) 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 (α_V = 3.83 × 10^–6 K^–1) compared to that in ambient monoclinic phase (α_V = 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