Experimental and theoretical investigations on ThGeO4 at high pressure

We report here the combined results of angle-dispersive x-ray diffraction experiments performed on ThGeO4 up to 40 GPa and total-energy density-functional theory calculations. Zircon-type ThGeO4 is found to undergo a pressure-driven phase transition at 11 GPa to the tetragonal scheelite structure. A second phase transition to a monoclinic M-fergusonite type is found beyond 26 GPa. The same transition has been observed in samples that crystallize in the scheelite phase at ambient pressure. No additional phase transition or evidence of decomposition of ThGeO4 has been detected up to 40 GPa. The unit-cell parameters of the monoclinic high-pressure phase are a = 4.98(2) A, b = 11.08(4) A, c = 4.87(2) A, and beta = 90.1(1), Z = 4 at 28.8 GPa. The scheelite-fergusonite transition is reversible and the zircon-scheelite transition non-reversible. From the experiments and the calculations, the room temperature equation of state for the different phases is also obtained. The anisotropic compressibility of the studied crystal is discussed in terms of the differential compressibility of the Th-O and Ge-O bonds.


INTRODUCTION
Thorium germanate (ThGeO 4 ) is a member of the ABO 4 class of compounds with polymorphism at ambient conditions. ThGeO 4 crystallizes either in the tetragonal zircon-type structure (space group: I4 1 /amd) or the tetragonal scheelite-type structure (space group: I4 1 /a) [1]. Both structures are important mineral structures, which consist of AO 8 bisdisphenoids and BO 4 tetrahedra [2]. The members of the zircon-and scheelite-structured ABO 4 family of compounds have gained increasing attention in the past few decades due to their technological applications and their mineralogical interest [3]. In particular, high-pressure (HP) studies have been performed on them, in order to understand their mechanical properties and HP structural behaviour [3 -10]. Among these studies the majority focus on zircon-type silicates, e.g. ZrSiO 4 [8 -10], and scheelite-type tungstates, e.g. CaWO 4 [6,7]. In both cases, several pressure-induced phase transitions have been discovered and their transition mechanisms were studied [8,12]. In contrast to these oxides, AGeO 4 germanates have been poorly studied upon compression. Among them, only the equation of state (EOS) of scheelite-structured ZrGeO 4 and HfGeO 4 has been determined up to 20 GPa [13] and a phase transition from zircon to scheelite has been reported in ThGeO 4 [14]. Therefore, it is evident that additional research is needed to understand the high-pressure behaviour of ThGeO 4 and isomorphic germanates. with those previously found in other ABO 4 compounds. According to the results, ThGeO 4 is more compressible than transition metal germanates.

II. EXPERIMENTAL DETAILS
The experiments were performed on both zircon-and scheelite-structured ThGeO 4 . The samples used in the experiments were pre-pressed pellets prepared using a finely ground powder obtained from polycrystalline ThGeO 4 . In order to synthesize scheelite-type ThGeO 4 , appropriate amounts of pre-heated (1000 ºC) high-purity ThO 2 and GeO 2 were mixed thoroughly, pelletized, and reheated slowly to 1000 ºC, being held at this temperature for 24 h [1]. Then the pellet was cooled to room temperature (RT), reground, and subsequently heated at 1000 ºC for 15 h. For obtaining zircon-type ThGeO 4, the scheelite-type ThGeO 4 was heated to 1200 ºC for 24 h, being the scheelite phase transformed irreversibly to zircon-type ThGeO 4 [1]. Both products were characterized from their powder x-ray diffraction patterns recorded on a Philips X-Pert Pro diffractometer using monochromatized Cu K α radiation and by neutron diffraction data collected at the Dhruva Research Reactor at BARC [1]. The refined unit-cell parameters for both phases are given in Table I. They are in good agreement with earlier reported values [1,15].
Angle-dispersive x-ray diffraction (ADXRD) experiments were carried out on ThGeO 4 at RT and HP up to 40 GPa at Sector 16-IDB of the HPCAT -Advanced Photon Source (APS) -using a Mao-Bell type diamond-anvil cell (DAC) with an incident monochromatic wavelength of 0.3447 Å. Samples were loaded in a 100 µm hole of a 40-µm-thick rhenium gasket in the DAC with diamond-culet sizes of 300 µm.
Pressure was determined using the ruby fluorescence technique [16] and silicone oil was used as pressure-transmitting medium [17 -19]. The monochromatic x-ray beam was focused down to 20 × 20 µm 2 using Kickpatrick-Baez mirrors. The images were 4 collected using a MAR345 image plate located at 350 mm from the sample. They were integrated and corrected for distortions using FIT2D. The typical exposure time for each spectrum was 20 s. The structural analysis was performed using POWDERCELL.

III. OVERVIEW OF THE CALCULATIONS
First-principles total-energy calculations were carried out within the periodic density-functional-theory (DFT) framework using the VASP program [20,21]. The Kohn-Sham equations have been solved by means of the Perdew, Burke, and Ernzerhof (PBE) exchange-correlation functional [21], and the electron-ion interaction described by the projector-augmented-wave (PAW) pseudopotentials [23]. Hybrid densityfunctional methods have been extensively used for oxides related to ThGeO 4 , providing an accurate description of crystalline structures, bond lengths, binding energies, and band-gap values [24]. The plane-wave expansion was truncated at a cut-off energy of 400 eV and the Brillouin zones have been sampled through Monkhorst-Pack special kpoints grids that assure geometrical and energetic convergence for the ThGeO 4 structures considered in this work. All the crystal structures are optimized simultaneously on both the volume of the unit-cell and the atomic positions, computing the pressure effect by finding the values of the geometrical parameters that minimize the total energy at a number of fixed volumes. Fittings of the computed energy-volume data with a third-order Birch-Murnaghan EOS [25] provide values of zero-pressure bulk modulus and its pressure derivative as well as enthalpy-pressure curves for the three studied polymorphs [26].

IV. RESULTS AND DISCUSSIONS
The in situ ADXRD data obtained at different pressures, starting from the zircon-type ThGeO4 sample, are shown in Fig. 1. The x-ray patterns could be indexed with the zircon structure up to 8.9 GPa. At 11.1 GPa we found the appearance of diffraction peaks in addition to those assigned to the zircon phase. These peaks can be well assigned to the scheelite structure of ThGeO 4 , indicating the co-existence of the zircon and scheelite phases from 11.  [27] and SrMoO 4 [5].
When compressing the scheelite-structured sample, we found no phase transition detected. Upon decompression, the scheelite-fergusonite transition is reversible, but the zircon-scheelite transition is irreversible, as can be seen in Fig. 1. This behaviour is typical as documented in ZrSiO 4 [9] and CaWO 4 [28].
From the refinement of the x-ray diffraction patterns measured up to 24.4 GPa, we extracted the pressure dependence of the lattice parameters and unit-cell volume for zircon and scheelite ThGeO 4 . These results are summarized in Figs. 2 and 3. As in other zircon-structured ABO 4 oxides [11,30] the compression of zircon ThGeO 4 is anisotropic, the a-axis being more compressible than the c-axis (see Fig. 2). The c/a axial ratio increases from 0.904 at ambient pressure to 0.912 at 13.6 GPa. This anisotropy in the axial compressibility of zircon ThGeO 4 is comparable with that of zircon-type vanadates [11]. In scheelite ThGeO 4 we found the opposite behaviour; the c-axis is more compressible than the a-axis. In particular the c/a axial ratio decreases tetrahedra. Therefore, in this structure the a-axis is the less compressible axis, as found in the experiments. 8 The pressure dependences of the volume obtained for scheelite and zircon phases are summarized in Fig. 3. There, it can be seen that the transition from zircon to scheelite phase involves a volume collapse of approximately 10%. This is consistent with the volume collapse found in other zircons [8 -11]. We have analysed the evolution of the volume using a third-order Birch-Murnaghan EOS [26]. The EOS fits for both phases are shown as solid lines in Fig. 3. The obtained EOS parameters for the zircon phase are: V 0 = 341.8(9) Å 3 , B 0 = 184(6) GPa, and B 0 ' = 4.6(5), these parameters being the zero-pressure volume, bulk modulus, and its pressure derivative, respectively.
Empirical models have been developed for predicting the bulk moduli of zirconstructured and scheelite-structured ABO 4 compounds [28]. In particular, the bulk modulus of ThGeO 4 can be estimated from the charge density of the ThO 8 polyhedra using the relation B 0 =610 Z i /d 3 , where Z i is the cationic formal charge of thorium, d is the mean Th-O distance at ambient pressure (in Å), and B 0 is given in GPa [28]. phase. This is in agreement with the fact that scheelite provides a more efficient atomic packing than zircon.
Let's compare now the experimental data presented above with the results of the ab initio calculations for ThGeO 4 . The zircon, scheelite, and M-fergusonite structures have been considered in these calculations to test the experimental results. Figure 4 shows the energy vs volume curves for these structures. The common tangent construction enables to deduce the transition pressure and the equilibrium pressure [33,34]. According to the calculations zircon is the most stable structure from ambient pressure up to 2 GPa. Beyond this pressure the scheelite structure become energetically more favorable, which agrees with the zircon-scheelite phase transition detected in the ADXRD experiments. The transition-pressure difference between experiments and calculations may be possible due to a kinetic hindrance of the equilibrium phase transformation, a frequent phenomenon in ABO 4 oxides [6], which in some cases leads to a polymorphism zone in the P-T phase diagram [35].
For the zircon structure at ambient pressure, the calculations gave a = 7.3269 Å and c = 6.6416 Å. The obtained atomic positions are summarized in Table I. The calculated unit-cell parameters are slightly larger than the experimental values (see Table I). This small overestimation is within the typical reported systematic errors in On the other hand, our calculations give an anisotropic compressibility for the unit-cell parameters comparable with the experiments.
As pressure increases, the zircon structure becomes unstable against scheelite at 2 GPa. For the scheelite structure at ambient pressure, the calculations gave a = 5.2128 Å and c = 11.6022 Å. The obtained atomic positions are summarized in Table I. As in the case of zircon ThGeO 4 , the calculated unit-cell parameters also slightly overestimate the experimental values (see Table I This behaviour is also similar to that of most of the ABO 4 compounds that undergo the scheelite-fergusonite transition [3]. It should be noted here that, in the range of stability of the fergusonite phase, the energy differences between scheelite and fergusonite are slightly smaller than DFT errors. Indeed, in Fig. 4 it is hard to differentiate both structures. Therefore, to clearly show that the M-fergusonite phase becomes more stable than the scheelite one, we have plotted the energy difference between both structures in the inset of Fig. 4. In spite of this small energy difference, from the total-energy and enthalpy calculations it is found that M-fergusonite becomes the most favourable structure beyond 31 GPa. Therefore, in agreement with our experimental observation, the calculations also suggest that monoclinic fergusonite is the post-scheelite phase of ThGeO 4 . This conclusion is also consistent with the systematic HP sequence found for orthotungstates, orthomolybdates, and orthovanadates [3,11]. It is important to note that the high-pressure monoclinic phase reported here has been never found before in germanates. In this regard our results can contribute to a successful anticipation of highpressure forms in other germanates. In Table II According with this, the fergusonite and scheelite phase have a very similar compressibility, which is in agreement with the behaviour of other ABO 4 compounds [3]. Consequently, the volume change at the phase transition is smaller than 1%, as found in the experiments. Regarding the anisotropy of the M-fergusonite structure, the calculations indicate that the monoclinic distortion increase upon compression. In particular the β angle reaches 90.5º at 40 GPa, and the difference between the unit-cell parameters a and c increases from 0.02 to 0.05 Å (see Fig. 2). This behaviour is characteristic of the M-fergusonite structure, which distorts upon compression favouring a gradual coordination increase and leading to a pseudo-tetrahedrally coordinated B cation [6].     Note that the crystallographic settings commonly used to describe the scheelite and fergusonite phases are related in such a way that the c-axis of the tetragonal unit cell corresponds to the b-axis of the monoclinic unit cell     24 Figure 5