High-pressure study of the behavior of mineral barite by x-ray diffraction

D. Santamarı́a-Pérez,1,*,† L. Gracia,2,† G. Garbarino,3 A. Beltrán,2,† R. Chuliá-Jordán,1 O. Gomis,4,† D. Errandonea,5,† Ch. Ferrer-Roca,5,† D. Martı́nez-Garcı́a,5,† and A. Segura5,† 1Departamento de Quı́mica-Fı́sica I, Universidad Complutense de Madrid, Avda. Complutense s/n, 28040, Madrid, Spain 2Departament Quı́mica Fı́sica i Analı́tica, Universitat Jaume I, 12071 Castelló de la Plana, Spain 3European Synchrotron Radiation Facility, 6 Rue Jules Horowitz, BP 220, 38043 Grenoble Cedex, France 4MALTA Consolider Team, Centro de Tecnologı́as Fı́sicas: Acustica, Materiales y Astrofisica, Universitat Politècnica de València, Camı́ de Vera s/n, 46022 Valencia, Spain 5Departamento de Fı́sica Aplicada-ICMUV, Universidad de Valencia, Edificio de Investigación, C/Dr. Moliner 50, 46100 Burjassot, Valencia, Spain (Received 22 March 2011; published 2 August 2011)


I. INTRODUCTION
Research on the mineral barite, BaSO 4 , is of great interest for Earth and material sciences.Apart from being used in drilling fluids, pigments, and as radiocontrast and catalyst agents, it has been identified in the Earth's crust and in meteorites. 1 This oxide crystallizes at ambient conditions in an orthorhombic structure (space group [S.G.]: Pnma, No. 62, Z = 4), 2 and its structure is usually very poorly described in terms of cation-centered (Ba and S) oxygen polyhedra.Using this descriptive model, this sulphate would be formed by isolated [SO 4 ] tetrahedra and complex [BaO 12 ] polyhedra.
A more recent approach allows better explaining and understanding the structures of these kinds of oxides.Vegas 3 described the structure of BaSO 4 in terms of its cation subarray BaS, which is of the FeB-type (see Fig. 1).This structure consists of triangular prisms of Ba atoms that share faces along the b direction and corners in the other two directions, with the [SO 4 ] groups inserted into these metal prisms.At high temperature, BaSO 4 transforms into a cubic F-43m phase, 4 where the Ba and S atoms adopt the same configuration that is in the corresponding sulphide at ambient conditions.][7] Barite was also studied under pressure using Raman spectroscopy and energy-dispersive x-ray diffraction.Lee et al. observed small changes in the diffraction patterns and a subtle variation of the lattice parameters at about 13 GPa, and they inferred a phase transition. 8,9The high-pressure (HP) phase was tentatively determined to be triclinic. 8More recently, however, Crichton et al. 10 have carried out Raman and angle-dispersive x-ray measurements in barite up to 21.5 GPa, using He as the pressure medium.They did not observe any phase transition in BaSO 4 , the barite-type structure remaining the highest investigated pressure.
The aim of this work is to understand the poorly known behavior of the mineral barite, BaSO 4 , under strong compression.Thus, we report an angle-dispersive x-ray diffraction (ADXRD) study up to 48 GPa, using different pressuretransmitting media.The experiments allow the accurate determination of the structural sequence and compressibility of BaSO 4 , and the obtained results were interpreted on the basis of first-principles total-energy calculations.

A. Experimental details
To perform x-ray powder diffraction measurements, commercial barium sulphate powder with 99.99% purity (Sigma-Aldrich, Prod.Nr. 202762) was crushed in a mortar and pestle to obtain a micron-sized powder.Ambient pressure x-ray diffraction confirmed that our sample has a baritetype structure (see Fig. 2).Three independent high-pressure ADXRD experiments were conducted at room temperature.Experiment 1 was carried out up to 24 GPa with a Xcalibur diffractometer (Oxford Diffraction Ltd.).X-ray diffraction patterns were obtained on a 135-mm Atlas CCD detector placed at 120 mm from the sample using K α1 :K α2 molybdenum radiation (0.7093 and 0.7136 Å, respectively).The x-ray beam was collimated to a diameter of 300 µm.The same setup was used previously to successfully characterize the HP phases of other ABO 4 compounds in the same pressure range. 11,12easurements were performed in a modified Merrill-Bassett diamond-anvil cell (DAC) with diamond culets of 500 µm.BaSO 4 was loaded in a 160-µm-diameter hole of the stainlesssteel gasket preindented to a thickness of 40 µm.A 4:1 methanol:ethanol mixture was used as a pressure-transmitting position was used as a cleanup aperture for filtering out the tail of the x-ray beam.The images were collected using a MAR345 image plate located 426 mm from the sample.
Finally, Experiment 3 was carried out in the ID27 station of the European Synchrotron Radiation Facility (ESRF) using a monochromatic wavelength of 0.3738 Å selected by an iodine K-edge.Once the sample was placed in the stainless-steel gasket cavity, along with two ruby chips for pressure measurement, it was transferred to the high-pressure gas-loading facility.The DAC was gas loaded with He at an initial pressure of 2 kbar.Diffraction patterns were measured for 30-40 s each at up to 41 GPa, using a x-ray beam focused to 3 × 3 µm 2 and collected on a MAR CCD camera.A precise calibration of the detector parameters was developed with a reference LaB6 powder of distortion, and integration to conventional 2θ -intensity data were carried out with the Fit2D software. 13n all of the experiments, the pressure was determined using the ruby fluorescence technique. 14The indexing and refinement of the powder patterns were performed using the FULLPROF 15 and POWDERCELL 16 program packages.

B. Calculation details
Calculations were performed with the CRYSTAL09 program package. 17Sulfur and barium atoms have been described by HAYWSC-311(1d)G and DURAND-31G * pseudopotential basis set, respectively, while for oxygen atoms has been used the standard 6-31G.* The Becke's three-parameter hybrid nonlocal exchange functional 18 combined with the Lee-Yang-Parr gradient-corrected correlation functional, B3LYP, 19 has been used.Hybrid density functional methods have been extensively used for molecules and provide also an accurate description of crystalline structures as bond lengths, binding energies, and band-gap values are regarded. 20,21The diagonalization of the Fock matrix was performed at adequate k-point grids in the reciprocal space using the Pack-Monkhorst and Gilat shrinking factors IS = ISP = 4.The thresholds controlling the accuracy of the calculation of Coulomb and exchange integrals were set to 10 −8 and 10 −14 , whereas the percentage of Fock/Kohn-Sham matrices mixing was set to 40. 22Fittings of the computed energy-volume data provide values of zeropressure bulk modulus and its pressure derivative as well as enthalpy-pressure curves for the studied polymorphs. 23

A. Experimental structural study of BaSO 4
High-pressure x-ray diffraction studies using three different fluid pressure media were performed.Figure 3 shows our ADXRD data for BaSO 4 at several selected pressures with He as the pressure medium and compares them with a diffraction pattern measured at atmospheric pressure.At ambient conditions, the x-ray pattern corresponds to the orthorhombic barite-type structure previously reported (S.G.Pnma, No. 62) 2  ambient conditions, up to 27 GPa.At this pressure, two new peaks appear at 2θ = 4.916 and 7.313 (marked with arrows in the pattern at 29.5 GPa in Fig. 3).This fact indicates the onset of a phase transition in BaSO 4 .Upon further compression additional diffraction peaks appear, and the peaks of the low pressure phase almost disappear completely at 40.5 GPa.
This phase transition has also been observed in the other two high-pressure experiments, using the methanol-ethanol mixture (4:1) and the silicone oil.Some selected x-ray patterns at representative pressures using silicone oil as the pressure medium are plotted in Fig. 4, to be compared with those using He (Fig. 3).In these experiments, the diffraction peaks are significantly broader than those using helium as the pressure medium (comparing both sets of synchrotron data: (i) with silicone oil in Diamond and (ii) with He at the ESRF).In the case of the measurements carried out in our in-home diffractometer, the resolution is, of course, much worse than in both synchrotron radiation experiments.The broadening of the diffraction peaks in the experiments with MeOH-EtOH and silicone oil is clearly noticeable above 9 GPa due to nonhydrostatic compression of our sample (see Fig. 4).This lack of hydrostaticity may also drive the phase transition  The additional extra peaks that appear in these two runs at the phase transition coincide with those found with He.This is also fully consistent with the results of previous experiments reported by Lee et al. 8,9 These authors observed the appearance of two extra diffraction peaks at 13 GPa, which indicated the existence a HP phase.In this case, the experiments were done without any pressure-transmitting medium 8 or methanol-ethanol mixture, 9 and the phase transition took place at lower pressures.It is important to mention here that the HP phase was also found at high temperatures (up to 700 K) and the slope of the phase boundary between barite and the HP phase being determined to be 90 K/GPa.A comparison between our experimental and theoretical results and those of the literature can be found in Table I.
From the x-ray diffraction data, we obtained the evolution with pressure of the volume and lattice parameters of the initial barite-type phase of BaSO 4 .We also refined the atomic positions of the Ba, S, and O atoms in three diffraction patterns that correspond to the initial barite-type structure at 0.12, 13, and 24.9 GPa.We found a progressive change in the coordinates of most of the atoms (see Table II) that give rise to an increase of Ba coordination number from 12 at room pressure (see the [BaO 12 ] polyhedra in Fig. 5(a)) to 12 + 1 at 13 and 24.9 GPa.The topology of the BaS cation subarray of BaSO 4 , however, did not change much.Therefore, we can conclude that, up to the transition pressure, the distortion of the structure mainly comes from a small rotation in the [SO 4 ] tetrahedra (allowed by the S.G. symmetry).
The pressure evolution of the unit-cell parameters of barite-type structure, using the three different fluid pressuretransmitting media, is plotted in Fig. 6, where we compare them with those obtained in our theoretical calculations.The experimental data corresponding to the methanol-ethanol mixture and the silicone oil agree within accuracy up to 9 GPa.The pressure-volume (P-V) data collected using He as a pressure medium differ from those of the other media from 5 GPa.Beyond this pressure, the previous experiments (Experiment 1: MeOH-EtOH and Experiment 2: silicone oil) slightly underestimate the decrease of volume with pressure.
As it has been argued in the literature, this fact can be attributed to the larger nonhydrostatic stresses caused by the pressure media in these experiments. 24,25The pressure-volume curves were analyzed using a third-order Birch-Murnaghan equation of state (EOS).By fixing the zero-pressure volume (V 0 ) to its measured value, we obtained the bulk modulus (B 0 ) and its pressure derivative (B 0 ) for the three different experiments.These characteristic parameters are collected in Table I.We can see that the B 0 value obtained in experiments with methanol-ethanol and silicone oil as the pressure media is considerably higher than that of the He experiment as consequence of nonhydrostaticity. 26,27Experimental values of the bulk modulus and its first derivative are in relative good agreement with those obtained from ab initio calculations (see Table I).
The obtained evolution for the unit-cell parameters of the low-pressure barite phase is shown in Fig. 7.There it can be seen that the contraction of the lattice parameters is rather isotropic.For instance, according to our experiments, the relative contractions for a, b, and c between room pressure and 15 GPa in Experiment 3 (He as pressure medium) are 4.87, 5.94, and 5.92%, respectively.Similar contractions are obtained when methanol-ethanol (silicone oil) is used: 4.87% (4.46%), 5.29% (4.99%), and 4.64% (4.78%) for a, b, and c, respectively.These values are in good agreement with those from theoretical simulations, where a, b, and c axes decrease 4.05, 5.26, and 5.12%, respectively.

B. High-pressure phase
We also propose a crystalline structure for the HP phase.As it can be seen in Figs. 3 and 8, the diffraction pattern of the HP phase (40.5 GPa) obtained with He as the pressure medium still has very well-defined peaks.Two small peaks correspond to the low-pressure phase.The rest of the peaks could be indexed in an orthorhombic cell with lattice constants: a = 6.55( 5 A distorted barite-type structure model was refined by the Rietveld method, leading to the atomic parameters collected in Table III.The diffraction pattern is shown in Fig. 8 to illustrate the quality of the refinement.The refined parameters were the overall scale factor, the cell parameters, the pseudo-Voigt profile function with terms to account for the reflection anisotropic broadening, the fractional atomic coordinates, and the background.During the refinement process, displacement factors of two atoms were physically meaningless.For this reason, the overall displacement parameter was fixed at B = 0.5 Å2 .The structure of the HP phase is basically a strong distortion of the initial barite phase (see Fig. 9).The a axis contracts approximately 18.3%, the b axis expands approximately 20%, and the c axis remains nearly constant at the transition pressure, with the volume of both phases differing in only ∼2%.This lattice transformation entails a small displacement and tilting movement of the  .This phase transition is fully reversible, with the Pnma orthorhombic structure being recovered after decompression (see Fig. 4).The reversibility of the phase transition was observed in the experiments using silicone oil and the methanol:ethanol mixture as the pressure media.In the case of He, no x-ray diffraction pattern was recorded at room pressure after decompression.
Pressure-volume results in the pressure range where both phases coexist are plotted in Fig. 10.As can be seen, the volume collapse is of ∼2%, as mentioned above.The variation of the unit cell volumes of the HP phase of BaSO 4 with pressure could be fitted to a third-order Birch-Murnaghan equation of state where the values of the bulk modulus (B 0 ) and cell volume at zero pressure (V 0 ) are left to vary freely and B 0 is fixed to 4. The characteristic parameters for the P2 1 2 1 2 1 phase are V 0 = 325(3) Å3 and B 0 = 78(4) GPa.It is important to remember that the P-V data of the HP phase have been obtained when both the initial and the HP phase coexist.This fact could slightly affect the V 0 and B 0 values.In the inset of Fig. 10, it can be seen that in the sample studied under silicone oil (less hydrostatic medium), the transition starts at lower pressures than in the sample studied using He, and the pressure range of the transition is wider.This fact has also been observed in other materials, such as Ti. 26 Finally, we will make an attempt to relate the found HP phase transition in BaSO 4 to other sequences of pressureinduced phase transitions in ABX 4 compounds, whose stability has been recently discussed in terms of an updated version of Bastide's diagram. 28In this diagram, phase transitions in ABO 4 compounds can be "somehow" predicted by considering the role played by cationic radii, r A and r B , with respect to anion radius, r O , and the north-east rule.Because of its r A /r O and r B /r O ratios, BaSO 4 is located very close to the boundary with the cubic Fm-3m KBF 4 -type structure (a NaCl-type cation subarray), which would suggest that this structure-type could be that of our HP-phase.Despite our lattice parameters tending to approach each other, our cation subarray is still much closer to the FeB-type than to the NaCl-type structure.
Previous studies have found that monazite-type ABO 4 compounds tend to transform upon compression either to the scheelite or the barite structure.For instance, the latter behavior was observed in the phosphate LaPO 4 29 and in the sulphate CaSO 4 30 at high pressures.The new orthorhombic HP phase reported here could therefore be a potential structure for both the monazite-and the barite-type structures at high pressures.Thus, for example, Huang et al. recently reported a phase transition in the barite-type BaCrO 4 compound at about 9 GPa, which could not be identified. 31For this experiment, the authors used a 4:1 MeOH:EtOH mixture as the pressure transmitting medium.X-ray patterns above this pressure seem to present similar features of those observed in our experiment, so this new HP-structure of BaCrO 4 could therefore be a potential P2 1 2 1 2 1 postbarite structure.Further experiments using softer pressure media (He, preferably) are needed to confirm this hypothesis.

C. First-principles structural study of BaSO 4
In order to identify the HP phase transition, we initially carried out first-principles calculations of the initial barite structure and five potential different phases at high-pressure: monazite-type (S.G.: P2 1 /n), scheelite-type (S.G.: I4 1 /a), AgMnO 4 -type (S.G.: P2 1 /n), KBF 4 -type (S.G.: Fm-3m), and fergusonite-type (S.G.: I2 1 /a) structures.The structural candidates considered were selected by empirical crystallochemical arguments such as the Bastide's diagram and the behavior under pressure of the cation subarrays in oxides.Thus, the monazite-and scheelite-type structures could be HP phases in BaSO 4 as it occurs, for example, in other ABO 4 compounds like TbPO 4 or YPO 4 . 12,32However, the location of these candidates in the Bastide's diagram, at the left-hand side of the initial barite-type structure, makes them unlikely stable structures for BaSO 4 at high pressure.Another possible HP phase was the AgMnO 4 -type structure, which is a monoclinic distortion of the barite structure.This structure has recently been observed in CaSO 4 under pressure after the barite structure. 30The KBF 4 -type structure has also been considered as a potential HP phase in BaSO 4 due to the fact that it is located at right-hand side of Bastide's diagram.This Fm-3m cubic phase was described in the F4-3m subgroup so that the O atoms could be located at a fixed crystallographic position.The fergusonite-type structure was analyzed because it has been observed in BaMoO 4 at high pressure. 33ur theoretical study indicates that barite is the structure of BaSO 4 with the lowest enthalpy at ambient pressure.A fit with a Birch-Murnaghan third-order equation of state gives values in relatively good agreement with experimental results presented in the previous section using different pressure transmitting media: V 0 = 364.99Å3 , B 0 = 62(2) GPa, and B 0 = 4.5 (3).The equilibrium volume V 0 is overestimated by ∼5% with respect to the experimental value.Full structural information of the barite structure shows a good agreement between theory and experiment.At high pressures, all the potential candidates have been found to be energetically noncompetitive for BaSO 4 .Subsequently after these calculations, the structure of the HP phase was solved and refined from the x-ray pattern at 40.5 GPa.It turned out to be a huge orthorhombic distortion of the initial barite structure with a large contraction of the a axis and a large expansion of the b axis, as discussed previously.Figure 11 shows the energy as a function of volume curves for the initial and HP calculated structures.It can be clearly seen that both curves cross each other at high pressure.As shown in the enthalpy as a function of pressure curves of Fig. 11, the HP-phase becomes more stable than barite at 32 GPa, after a transition in which the volume change is about 2%.This is in excellent agreement with the experimental data obtained using He as a pressure medium, where the onset of the phase transition was observed at 27 GPa.It should be noted that, to our knowledge, this high-pressure orthorhombic phase (P2 1 2 1 2 1 ) has never been observed in other ABO 4 compounds.Structural data of the HP-phase are collected in Table IV, to be compared with the experimental values of Table III.As described above, in the HP structure at 32 GPa, there are still four S-O bond lengths of ∼1.52 Å, as in the barite phase at this pressure, and thus the environment of the S atom almost does not change.However, the tilting movement of the [SO 4 ] tetrahedra led to a change in the environment of the Ba atoms and, consequently, to the phase transition.Furthermore, our ab initio calculations provide the variation of the energy with volume for the new HP phase.The thirdorder Birch-Murnaghan equation of state was fitted to our data giving the following characteristic parameters: V 0 = 354.9Å3 , B 0 = 75.07GPa, and B 0 = 3.1.These results are in excellent agreement with those obtained from the experimental data (see above).

IV. CONCLUDING REMARKS
The high-pressure structural stability of barite BaSO 4 has been studied by means of x-ray diffraction experiments using three different fluid pressure-transmitting media as well as by ab initio calculations.From our experimental data, we have determined that the compression of the initial Pnma barite phase is rather isotropic and that the values of the bulk modulus and its first derivative are B 0 = 58.6(2)GPa and B 0 = 4.82(4), respectively (using He as the pressure medium).We have also found that compression induces a phase transition at 27 GPa from the barite Pnma structure to another orthorhombic structure, P2 1 2 1 2 1 , which can be seen as a significant distortion of the initial phase.This transition involves a contraction of the a axis of approximately 18.3% and an expansion of the b axis of approximately 20%, with the c axis remaining nearly constant at the transition.Furthermore, we have found that the onset of the phase transition is highly dependent on the hydrostaticity of our pressure media.Thus, the less hydrostatic the medium is, the lower the transition pressure.Our results are supported by theoretical total energy calculations, which also provide the equation of state of the new HP phase, giving the following parameters: V 0 = 354.9Å3 , B 0 = 75.07GPa, and B 0 = 3.1 (to be compared with those obtained from experimental data: V 0 = 325(3) Å3 , B 0 = 78(4) GPa, and a fixed value B 0 = 4).

FIG. 1 .
FIG. 1.(a) Structure of barite at ambient conditions projected on to the ac-plane.Light, medium, and dark grey circles represent Ba, S, and O atoms, respectively.This structure is formed by trigonal prisms of Ba in which the [SO 4 ] units are inserted.The skeleton of the cation subarray (BaS) of BaSO 4 is similar to the structure of the alloy FeB, represented in (b).
FIG. 3. Selected x-ray powder diffraction patterns of BaSO 4 using He as the pressure-transmitting medium (Experiment 3, ID27, ESRF).Backgrounds subtracted.The arrows indicate the appearance of new peaks corresponding to the HP phase at 29.5 GPa.Upon further compression additional diffraction peaks appear, and the peaks of the low-pressure phase almost disappear completely at 40.5 GPa.

FIG. 4 .
FIG. 4. Selected x-ray powder diffraction patterns of BaSO 4 using silicone oil as the pressure-transmitting medium (Experiment 2, I15, Diamond).Backgrounds subtracted.The arrows indicate the appearance of new peaks corresponding to the HP phase at about 19 GPa.The upper pattern at 6.4 GPa was taken in the decompression process and shows the reversibility of the phase transition.

FIG. 5 .
FIG. 5. (a) [BaO 12 ] polyhedra sharing a common edge at room pressure.In addition to this type of polyhedral connectivity, [BaO 12 ] also shares triangular faces with adjacent [BaO 12 ] polyhedra at ambient conditions.(b) [BaO 12 ] polyhedra sharing a quadrangular face in the structure of the HP phase.
FIG. 7. Evolution of the lattice parameters of the low-pressure phase of barite (Pnma) with pressure according to our experimental (Xcalibur: empty squares; Diamond: solid dark grey circles; ESRF: solid light grey stars) and ab initio data (solid black triangles).As can be seen, the contraction of the lattice parameters is rather isotropic.a high figure of merit (M(20) = 21.2).Therefore, this structure implies a volume change of about 2% at the transition.The systematic absences in the indexed lattice planes are consistent with symmetry elements (screw axes) of the S.G.P2 1 2 1 2 1 .A distorted barite-type structure model was refined by the Rietveld method, leading to the atomic parameters collected in TableIII.The diffraction pattern is shown in Fig.8to illustrate the quality of the refinement.The refined parameters were the overall scale factor, the cell parameters, the pseudo-Voigt profile function with terms to account for the reflection anisotropic broadening, the fractional atomic coordinates, and the background.During the refinement process, displacement factors of two atoms were physically meaningless.For this reason, the overall displacement parameter was fixed at B = 0.5 Å2 .

FIG. 8 .
FIG. 8. Observed, calculated, and difference x-ray diffraction profiles for the HP phase of BaSO 4 at 40.5 GPa.Vertical markers indicate Bragg reflections of the new orthorhombic P2 1 2 1 2 1 structure (above) and the initial orthorhombic Pnma structure (below).
FIG. 9. Structure of the new HP phase of BaSO 4 at 40.5 GPa projected on to the ac-plane.Light, medium, and dark grey circles represent Ba, S, and O atoms, respectively.In this structure, the trigonal prisms of Ba in which the [SO 4 ] units were inserted are highly distorted as a consequence of the tiliting of these [SO 4 ] tetrahedra.To be compared with Fig. 1(a).

FIG. 10 .
FIG.10.Volume-pressure data of both the low-and the HP phases of BaSO 4 in the coexistence region.Inset: Relative fraction of the HP phase versus pressure using He and silicone oil as pressure media.

FIG. 11 .
FIG. 11.Internal energy as a function of volume per formula unit for the initial Pnma barite structure and the P2 1 2 1 2 1 HP-phase.The enthalpy variation versus pressure curve for both polymorphs is depicted in the inset (taking the Pnma barite structure as reference).

TABLE I .
10perimental details, transition pressures, bulk moduli, and the first derivatives with pressure of our three different experiments and our theoretical study.For comparison purpose, the details and values reported by Lee et al.8and Crichton et al.10are also given.

TABLE II .
Rietveld-refined lattice parameters and fractional coordinates of the barite-type structure of BaSO 4 (S.G.Pnma, No. 62) at three different pressures.