Thermal expansion of mullite-type Bi{sub 2}Al{sub 4}O{sub 9}: A study by X-ray diffraction, vibrational spectroscopy and density functional theory
Polycrystalline Bi{sub 2}Al{sub 4}O{sub 9} powder samples were synthesized using the glycerine method. Single crystals were produced from the powder product in a Bi{sub 2}O{sub 3} melt. The lattice thermal expansion of the mullite-type compound was studied using X-ray diffraction, Raman spectroscopy and density functional theory (DFT). The metric parameters were modeled using Grüneisen approximation for the zero pressure equation of state, where the temperature-dependent vibrational internal energy was calculated from the Debye characteristic frequency. Both the first-order and second-order Grüneisen approximations were applied for modeling the volumetric expansion, and the second-order approach provided physically meaningful axial parameters. The phonon density of states as well as phonon dispersion guided to set the characteristic frequency for simulation. The experimental infrared and Raman phonon bands were compared with those calculate from the DFT calculations. Selective Raman modes were analyzed for the thermal anharmonic behaviors using simplified Klemens model. The respective mode Grüneisen parameters were calculated from the pressure-dependent Raman spectra. - Graphical abstract: Crystal structure of mullite-type Bi{sub 2}Al{sub 4}O{sub 9} showing the edge-sharing AlO{sub 6} octahedra running parallel to the c-axis. - Highlights: • Thermal expansion of Bi{sub 2}Al{sub 4}O{sub 9} was studied using XRD, FTIR, Raman and DFT. • Metric parameters were modeled using Grüneisen approximation. • Phonon DOS and phonon dispersion helped to set the Debye frequency. • Mode Grüneisen parameters were calculated from the pressure-dependent Raman spectra. • Anharmonicity was analyzed for some selective Raman modes.