Anharmonic phonons of NaZr2(PO4)3studied by Raman spectroscopy, first-principles calculations, and x-ray diffraction

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Raman spectroscopy, x-ray diffraction, and ab initio calculations are carried out to gain insight into the thermal expansion properties of ${\mathrm{NaZr}}_{2}{({\mathrm{PO}}_{4})}_{3}$. In situ Raman studies at high pressure in a diamond anvil cell indicate that two low-energy phonons corresponding to a combination of PO${}_{4}$ tetrahedral librations and Zr translations contribute negatively to its thermal expansion, and temperature-dependent Raman studies reveal the modes that are truly anharmonic. To complement the spectroscopic measurements the phonon spectrum is computed and mode assignments are carried out employing first-principles calculations. The computed atomic displacements corresponding to the lowest-energy Raman mode indicates that it involves PO${}_{4}$ rotations and Zr translations, and its Gruneisen parameter is found to be negative, in agreement with our measured value. The thermal expansion coefficient calculated using mode Gruneisen parameters obtained from computed phonon spectra at different volumes ($7.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}/\mathrm{K}$) is in good agreement with the reported value ($4.5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}6}/\mathrm{K}$). In situ x-ray diffraction measurements in a diamond anvil cell are carried out up to 20 GPa. There are clear indications of a phase transformation above 5.5 GPa, and the transformation is reversible with little hysteresis. From our x-ray diffraction measurements and density functional theory calculations the bulk modulus of rhombohedral ${\mathrm{NaZr}}_{2}{({\mathrm{PO}}_{4})}_{3}$ is determined to be 47 and 45 GPa, respectively, and these values are used to obtain the respective Gruneisen parameters.