Structure and stability of ${\mathrm{ZrSiO}}_4$ under hydrostatic pressure

We present the results of a combined experimental and theoretical investigation aimed to determine structural and equation-of-state parameters and phase stability thermodynamic boundaries of ${\mathrm{ZrSiO}}_4$ polymorphs. Experimental unit-cell data have been obtained for a powdered sample in a diamond-anvil cell using energy-dispersive synchrotron x-ray diffraction with emphasis on the pressure range $0–15\mathrm{GPa}$. Static total-energy calculations have been performed within the density functional theory at local density and generalized gradient approximation levels using a plane-wave pseudopotential scheme. Our quantum-mechanical simulations explore the pressure response of the two observed tetragonal structures (zircon- and scheelite-type reidite) as well as of other potential post-scheelite polymorphs up to about $60\mathrm{GPa}$. We find very good agreement between our experimental and calculated pressure-volume values for the low-pressure phase of ${\mathrm{ZrSiO}}_4$. A microscopic analysis of the bulk compressibility of zircon and reidite in terms of polyhedral and atomic contributions is proposed to clarify some of the discrepancies found in recent theoretical and experimental studies. Our results show the relevant role played by the oxygen atoms in the description of this property. The zircon-reidite equilibrium phase transition pressure is computed around $5\mathrm{GPa}$. No other post-scheelite phase is found stable above this pressure though a decomposition into ${\mathrm{ZrO}}_2$ (cottunite) and ${\mathrm{SiO}}_2$ (stishovite) is predicted at about $6\mathrm{GPa}$. These two transition pressure values are well below the experimental ranges detected in the laboratory in concordance with the large hysteresis associated with these transformations.

Figure 1

Energy-dispersive x-ray diffraction spectrum of zircon at ambient pressure. The small peak at about $30\mathrm{keV}$ is due to zirconium oxide. The Bragg angle is $\theta =4.01°$. The strong zirconium fluorescence lines (at 15.7 and $16.7\mathrm{keV}$) are not shown.

Figure 2

(Color online) Volume (a) and normalized volume (b) versus pressure diagrams. Symbols stand for the experimental data of this work (solid squares), Ref. 3 (crosses), and Ref. 4 (stars). Standard deviations of the volume in the range $0.01–0.02{\mathrm{\AA }}^3$ (Ref. 3) and (most of the points) in the ranges $0.02–0.04{\mathrm{\AA }}^3$ (Ref. 4, zircon) and $0.03–0.08{\mathrm{\AA }}^3$ (Ref. 4, reidite). Lines correspond to our calculated data under the LDA (solid) and GGA (dashed) approximations. Arrows represent calculated volume collapses at the LDA and GGA $\mathrm{zircon}\to \mathrm{reidite}$ transition pressures (see Sec. 3D).

Figure 3

(Color online) Pressure effects on (a) the $c∕a$ ratio and (b) the normalized oxygen coordinates for zircon and reidite polymorphs according to our LDA calculations.