Effect of pressure on the Raman-active modes of zircon (ZrSiO₄): a first-principles study

Density-functional theory (DFT) was employed in a first-principles study of the effects of pressure on the Raman-active modes of zircon (ZrSiO₄), using both the generalized gradient and local density approximations (GGA and LDA, respectively). Beginning with the equilibrium structure at zero pressure, we conducted a calibration of the effect of pressure in a manner procedurally similar to an experimental calibration. For pressures between 0 and 7 GPa, we find excellent qualitative agreement of frequency–pressure slopes ∂ω/ ∂P calculated from GGA DFT with results of previous experimental studies. In addition, we were able to rationalize the ω vs. P behavior based on details of the vibrational modes and their atomic displacements. Most of the ∂ω/ ∂P slopes are positive as expected, but the symmetry of the zircon lattice also results in two negative slopes for modes that involve slight shearing and rigid rotation of SiO₄ tetrahedra. Overall, LDA yields absolute values of the frequencies of the Raman-active modes in good agreement with experimental values, while GGA reproduces the shift in frequency with pressure especially well.