High-pressure phase transitions and compressibility of wolframite-type tungstates

This paper reports an investigation on the phase diagram and compressibility of wolframite-type tungstates by means of x-ray powder diffraction and absorption in a diamond-anvil cell and ab initio calculations. The diffraction experiments show that monoclinic wolframite-type MgWO4 suffers at least two phase transitions, the first one being to a triclinic polymorph with a structure similar to that of CuWO4 and FeMoO4-II. The onset of each transition is detected at 17.1 and 31 GPa. In ZnWO4 the onset of the monoclinic-triclinic transition has been also found at 15.1 GPa. These findings are supported by density-functional theory calculations, which predict the occurrence of additional transitions upon further compression. Calculations have been also performed for wolframite-type MnWO4, which is found to have an antiferromagnetic configuration. In addition, x-ray absorption and diffraction experiments as well as calculations reveal details of the local-atomic compression in the studied compounds. In particular, below the transition pressure the ZnO6 and equivalent polyhedra tend to become more regular, whereas the WO6 octahedra remain almost unchanged. Fitting the pressure-volume data we obtained the equation of state for the low-pressure phase of MgWO4 and ZnWO4. These and previous results on MnWO4 and CdWO4 are compared with the calculations, being the compressibility of wolframite-type tungstates systematically discussed. Finally Raman spectroscopy measurements and lattice dynamics calculations are presented for MgWO4.


Introduction
Materials belonging to the tungstate family (AWO 4 with A being a divalent element) have a long history of practical application and have been the object of extensive research. Their optical and luminescence properties have received great attention as these compounds are widely used as scintillating detectors in high-energy particle physics, rare-event searches, and medical diagnosis among other applications [1]. From the fundamental and geophysical standpoints, AWO 4 oxides are also interesting compounds [2]. Tunsgtates of large divalent cations (Ca, Ba, Pb, Sr, and Eu) usually crystallize in the tetragonal scheelite structure (space group: I4 1 /a, Z = 4) and those compounds of small divalent cations (Cd, Zn, Mg, Mn, etc.) can take the wolframite structure (space group: P2/c, Z = 2) [3]. In wolframite (shown in Fig. 1), both A and W cations have octahedral oxygen coordination and each octahedron shares two corners with its neighbors [4].
In the last years there has arisen renewed interest in AWO 4 compounds and their evolution under pressure. In the case of wolframites, high-pressure (HP) Raman spectroscopy studies have been performed in CdWO 4 [5,6] and ZnWO 4 (the mineral sanmartinite) [7,8]. Ab initio calculations have been also carried out to study their structural stability [6,8]. In ZnWO 4 a pressure-induced phase transition has been detected beyond 30 GPa [8] and a subsequent transition suggested near 58 GPa. A monoclinic β-fergusonite-type structure (space group: C2/c, Z = 4) has been proposed for the HP phase. In CdWO 4 two transitions take place around 20 and 35 GPa, being two coexisting phases found within this pressure range one with tetragonal and another with triclinic symmetry. At 35 GPa CdWO 4 transforms to a β-fergusonite-type structure. Under the current status of the research, HP x-ray diffraction studies are needed to further progress on the understanding of the structural properties of wolframites. However, in contrast with scheelite-structured tungstates [1,9,10], such studies have been rarely performed in wolframites. Indeed CdWO 4 , MgWO 4 , and MnWO 4 (the mineral hübnerite) have been studied only up to a pressure lower than 8 GPa [11]. Therefore the information available is limited to the compression of the wolframite phase at low pressures.
Motivated by the above-described facts, we have undertaken a comparative study of the structural properties of CdWO 4 , MgWO 4 , MnWO 4 , and ZnWO 4 under compression. In this paper, we report HP angle-dispersive x-ray diffraction (ADXRD) experiments in MgWO 4 (ZnWO 4 ) up to nearly 50 (26) GPa as well as x-ray absorption spectroscopy (XAS) measurements in ZnWO 4 up to 18 GPa at the Zn K-edge. The obtained results are interpreted with the help of ab initio total-energy calculations. In MgWO 4 , we observe two phase transitions and propose a triclinic structure for the first HP phase. For ZnWO 4 an intermediate phase with P1 symmetry has been found at lower pressure than the proposed phase with C2/c symmetry [8], pointing towards the same sequence followed by MgWO 4  Unpolarized confocal micro-Raman scattering measurements were performed at room temperature in a double monochromator Jobin-Yvon U1000 equipped with a N 2 cooled charge coupled device (CCD) detector, in the backscattering geometry. The 520 and 646 nm lines (wavelengths longer than that of the MgWO 4 band gap [15]) of an Coherent Innova Argon-Kripton laser were used at an incident power of 10 mW on the sample, which proved to be low enough to avoid spurious effects caused by the laser induced heating of the sample. This was verified by varying the incident power and observing that neither the Stokes to anti-Stokes intensity ratio nor the frequency of the Ag mode at 916.8 cm -1 varied within experimental precision. The laser spot diameter on the sample was 1 µm and the spectral resolution was better that 1 cm -1 .

III. Calculations
First-principles total-energy and lattice-dynamics calculations were done within the framework of the density-functional theory (DFT) and the pseudopotential method using the Vienna ab initio simulation package (VASP) [16 -18]. The exchange and correlation energy was initially taken in the local-density approximation (LDA) [19] for MgWO 4 and the generalized-gradient approximation (GGA) according to Perdew-Burke-Ernzerhof prescription for MnWO 4 [20]. The projector-augmented wave (PAW) scheme [21,22] was adopted and the semicore 5p electrons of W were also explicitly phase resembles the structure of CuWO 4 [27] and FeMoO 4 -II [28]. This structure is a distorted version of wolframite, which is topologically related to it. Note that the triclinic space group is a subgroup of the monoclinic space group and consequently the proposed transition appears to be continuous. This is consistent with our finding that the coordination of the Mg and W atoms does not change at the transition. Comparing both structures in Fig. 1, it can be seen that the phase transition mainly consists on a movement of the oxygen and A atoms, implying a rotation of the octahedron and a distortion of it. This distortion is enough to reduce the symmetry to triclinic. Basically, the proposed transition involves a tilting and distortion of the MgO 6 octahedra, which produces a local symmetry breakdown into the triclinic symmetry. In the triclinic phase, the Mg atoms have a more irregular coordination compared with wolframite. As we will show later, a similar structure is predicted by our ab initio calculations for the HP phase of MgWO 4 . Another evidence supporting the occurrence of a phase transition at 17.1 GPa is given in Fig. 5, where the full-width at half maximum (FWHM) of three Bragg peaks is represented as a function of pressure. A steep increase in their width is seen at that pressure, coinciding with the transition onset. This fact can be explained by comparing the diffraction patterns of both structures. As it is characteristic of secondorder transitions, the wolframite peaks can be also accounted for with the new triclinic structure. However, the triclinic distortion gives rise to a contribution from extra peaks that split from the original wolframite peaks explaining the observed peak broadening.
For ZnWO 4 , our x-ray diffraction experiments suggest that the HP phase has the same triclinic structure as HP MgWO 4 . This is apparently in contradiction with previous Raman-spectroscopy experiments [8], which reported the onset of a phase transition to a monoclinic β-fergusonite-type phase (C/2c) beyond 30.6 GPa. However, the 15.1 GPa transition pressure is very close to the pressure were a domain formation was observed in single-crystalline ZnWO 4 together with a relative change of the Raman peak intensities [8]. Note that the triclinic structure was also observed in CdWO 4 as an intermediate phase between the low-pressure wolframite structure and the high-pressure β-fergusonite phase [6]. Therefore, in addition to MgWO 4 and CdWO 4 , the triclinic phase can be also pressure-induced in ZnWO 4 several GPa below the β-fergusonite phase.
From the analysis of our x-ray diffraction data, we extracted the pressure dependence of the lattice parameters for both wolframite MgWO 4 and ZnWO 4 . These results are summarized in Fig. 6. This behaviour is in agreement with that reported by Macavei et al. from single crystal studies up to 8 GPa [11]. In Fig. 7 we report the evolution of the unit-cell volumes of MgWO 4 and ZnWO 4 obtained in our experiments as well as the volume data obtained previously [11] for MgWO 4 , MnWO 4 and CdWO 4 .
In the case of MgWO 4 our data are in good agreement with single-crystal diffraction data within the pressure range covered by these measurements [11]. We have analyzed the volume changes using a third-order Birch-Murnaghan EOS [30]. B. X-ray absorption measurements positions are similar to those obtained when a structural refinement was performed at different pressures [11]. The only differences are seen for the longest bond that shows to be more compressible than in the ab initio calculations and our ADXRD results.  Table II the calculated infrared active modes as well as their pressure coefficients and Grüneisen parameters are shown for completeness. There are three infrared modes that soften upon compression.

D. Theoretical Results
In order to help with the interpretation of our experimental results, ab initio total-energy and lattice-dynamics calculations were performed for MgWO 4 . Similar calculations were performed for MnWO 4 and previously for CdWO 4 [6] and ZnWO 4 [8]. These results will be systematically compared with the bulk of experimental results  Table III together with the orthorhombic structure (Cmca) predicted to become stable beyond 48 GPa as well as the structural information about wolframite. The proposed transition to the β-fergusonite structure is possible given the evidence available in CdWO 4 and ZnWO 4 [6,8]. The stabilization of the orthorhombic structure involves a coordination increase for Mg from 6 to 10. The coordination of W remains unaltered. The appearance of this structure is in agreement with the HP systematic developed by Bastide [1] and with the structural sequence found in other tungstates [33]. The confirmation of the existence of the β-fergusonite and Cmca structures is waiting for future experiments.
Regarding the triclinic P1 structure, the calculations also predict that in the pressure range where it was experimentally observed, it is energetically competitive with wolframite. This means that possible uniaxial stresses induced by the use of a pressure medium like silicone oil could be enough to induce a phase transition from the wolframite structure to the triclinic one. This fact could probably be the cause of the finding of the triclinic phase instead of the β-fergusonite phase beyond 17.1 GPa. In Table III we report the calculated structural information for the P1 structure at 29 GPa.
The agreement with the experimental values is good.
As we mentioned above, calculations have been performed for the low-pressure phase of MnWO 4 . Since this compound could be magnetic due to the presence of the Mn cation, we considered different magnetic configurations. We found the low-pressure phase of MnWO 4 to have a wolframite structure with an antiferromagnetic configuration. In this configuration, Mn has a magnetic moment of 4.319 µB while in the ferromagnetic configuration is 4.356 µB. The structural information for this phase is summarized in Table IV. The agreement with the literature [11] is good. For this phase we also calculated its EOS obtaining the following parameters: V 0 = 157.4 Å 3 , B 0 = 125 GPa, and B 0 ' = 4.3. The bulk modulus agrees well with the previously reported experimental value [11].
To conclude we would like to compare the different compressibilities reported for MgWO 4 , MnWO 4 , CdWO 4 and ZnWO 4 . A summary of their bulk moduli and unitcell volume are given in Table V. It is straightforward to see there, that there is an inverse correlation between the volume and the bulk modulus. As expected the densest compounds are the less compressible. It can be also seen that our experimental values agree with previous values within 10%. The same conclusion can be extracted for our calculations.
Some insight on the compressibility of wolframites can be extracted from their polyhedral compressibility. As we discussed above, W-O bonds are much more rigid than A-O bonds. Then, the compression of wolframite can be attributed dominantly to changes in the A-O bond lengths. The same trend has been found in scheelite-structured orthotungstates and orthomolybdates [33,34], leading to a phenomenological rule that correlates the bulk modulus with the inverse of the A-O distance. If the same rule is applied to wolframite, we estimate the bulk modulus given in the right hand-side column of Table V. As can be seen there, the estimated values reproduce the tendency followed by the bulk compressibility of wolframites, but slightly underestimates the bulk modulus. However, we think, the phenomenological rule [33] can be used to