Determination of the high-pressure crystal structure of $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ and $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$

We report the results of both angle-dispersive x-ray diffraction and x-ray absorption near-edge structure studies in $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ and $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$ at pressures of up to $56\mathrm{GPa}$ and $24\mathrm{GPa}$, respectively. $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ is found to undergo a pressure-driven phase transition at $7.1\mathrm{GPa}$ from the tetragonal scheelite structure (which is stable under normal conditions) to the monoclinic fergusonite structure whereas the same transition takes place in $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$ at $9\mathrm{GPa}$. We observe a second transition to another monoclinic structure which we identify as that of the isostructural phases $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4\text{−}\mathrm{II}$ and $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4\text{−}\mathrm{III}$ (space group $P{2}_1∕n$). We have also performed ab initio total-energy calculations which support the stability of this structure at high pressures in both compounds. The theoretical calculations further find that upon increase of pressure the scheelite phases become locally unstable and transform displacively into the fergusonite structure. The fergusonite structure is, however, metastable and can only occur if the transition to the $P{2}_1∕n$ phases were kinetically inhibited. Our experiments in $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ indicate that it becomes amorphous beyond $47\mathrm{GPa}$.

Figure 1

Room-temperature ADXRD data of (a) $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ and (b) $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$ at different pressures. In all diagrams the background was subtracted. To better illustrate the appearance of the (020) Bragg reflection of the fergusonite structure around $2\theta \approx 4°$ a section of one of the fergusonite patterns is enlarged and shown in the inset. In (b) to illustrate the quality of the Le Bail refinement obtained for the fergusonite structure at $10.1\mathrm{GPa}$ the difference between the measured data and the refined profile is shown (dotted line). The bars indicate the calculated positions of the reflections of the fergusonite structure.

Figure 2

Evolution of the lattice parameters (a) and (b), volume (c), and axial ratios (d) of $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ and $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$ under pressure. Empty squares correspond to data of the scheelite phase and empty (gray) circles to data of the fergusonite phase of $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ $\left(\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4\right)$. Solid circles,[19] solid triangles,[16] and crosses[7] illustrate the data of the scheelite phase obtained from the literature. Empty triangles are the fergusonite data reported in Ref. 16. In (c) the solid lines represent the EOS described in the text. In (a), (b), and (d) they are just a guide to the eye. The plotted EOS corresponds to the true compressibility of the scheelite phase. However, it represents very well also the pressure dependence of the volume of the fergusonite phase.

Figure 3

Pressure dependence of the interatomic bond distances in the scheelite and fergusonite phases of $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ and $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$. Squares represent the calculated distances and circles the distances extracted from the present experiments.

Figure 4

ADXRD pattern of $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ at $7.3\mathrm{GPa}$ and $10.9\mathrm{GPa}$. The background was subtracted. The dotted lines represent the difference between the measured data and the refined profiles. The bars indicate the calculated positions of the reflections.

Figure 5

Ab initio simulation of XANES spectra at the W $L_3$-edge of $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ (a) and $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$ (b) in several different phases. The structural data used in simulations are taken from Tables , and from Refs. 26, 31, 47 (see text for details). Resonance B is present when the W coordination is fourfold, but it is not present when the W coordination is sixfold.

Figure 6

Experimental XANES spectra (W $L_3$-edge) of $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ (a) and $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$ (b) at different pressures. The spectra collected on pressure release are marked with $d$. The analysis of the spectra (see text) reveals a coordination change at $9.8\mathrm{GPa}$ in the case of $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$. In its turn, $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$ transits to a sixfold coordinated fergusonite between 9 and $10.5\mathrm{GPa}$. Subtle changes in the spectra suggest a second phase transition in $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$ at $16.7\mathrm{GPa}$.

Figure 7

Total-energy versus volume ab initio calculations for $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4$ (a) and $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4$ (b) in different structures. The insets extend the pressure range to the region where the $\mathrm{Ba}\mathrm{W}{\mathrm{O}}_4\text{−}\mathrm{II}$ and $\mathrm{Pb}\mathrm{W}{\mathrm{O}}_4\text{−}\mathrm{III}$ structures becomes unstable.