Experimental and theoretical study of SbPO4 under compression

SbPO4 is a complex monoclinic layered material characterized by a strong activity of the non-bonding lone electron pair (LEP) of Sb. The strong cation LEP leads to the formation of layers piled up along the a-axis and linked by weak Sb-O electrostatic interactions. In fact, Sb is 4-fold coordination with O similar to what occurs with the P-O coordination, despite the large difference of ionic radii and electronegativity between both elements. Here we report a joint experimental and theoretical study of the structural and vibrational properties of SbPO4 at high pressure. We show that SbPO4 is not only one of the most compressible phosphates but also one of the most compressible compounds of the ABO4 family. Moreover, it has a considerable anisotropic compression behavior with the largest compression occurring along a direction close to a-axis and governed by the compression of the LEP and the weak inter-layer Sb-O bonds. The strong compression along the a-axis leads to a subtle modification of the monoclinic crystal structure above 3 GPa leading from a 2D to a 3D material. Moreover, the onset of a reversible pressure-induced phase transition is observed above 9 GPa, which is completed above 20 GPa. We propose that the high-pressure phase is a triclinic distortion of the original monoclinic phase. The understanding of the compression mechanism of SbPO4 can aid in understanding the importance of the ion intercalation and catalytic properties of this layered compound.


Introduction
Inorganic functional materials composed by antimony, such as antimony orthophosphate (SbPO4), are receiving considerable attention from the scientific community, due to their potential applications in different areas. The excellent optical properties of antimony-based glasses, such as the high-linear refractive index 1,2 and the large transmittance window from ultraviolet (UV) to infrared (IR) regions 3 enables its application as optical fibers, allowing its use in photonic applications 4 . The remarkable optical properties of SbPO4 also drew a lot of attention as a photocatalyst under UV light irradiation 5,6 . Moreover, since SbPO4 belongs to a class of phosphates with a very stable layered structure, where ions can be intercalated between its layers, many research groups have studied its ion-exchange characteristics 7 and respective potential as anode in lithium-ion batteries 8,9 . SbPO4 is an A 3+ B 5+ O4 compound with layered structure that crystallizes in the monoclinic P21/m (No. 11) space group, which is isostructural to SbAsO4 10 and belongs to the same space group as the polymorph BiPO4-III 11,12 . The low-pressure (LP) structure of SbPO4 is composed by a combination of regular PO4 tetrahedra and SbO4E polyhedra disposed in a trigonal bipyramidal fashion, where E refers to the non-bonding lone electron pair (LEP) of Sb (see Figure 1(a)). For both BiPO4-III and SbPO4, P is 4-fold coordinated at room pressure; however, while SbPO4 is a layered compound, BiPO4-III is not, therefore these are not isostructural compounds. At room pressure, the Bi ion belonging to the BiPO4-III compound features a 6-fold coordination, whereas Sb has only a 4-fold coordination for SbPO4. The The vibrational properties of SbPO4 have been studied at room pressure by Raman and IR spectroscopy [13][14][15][16] , but a limited amount of information has been provided. For instance, the classification and symmetry assignment of all vibrational modes at the Brillouin zone (BZ) center (), the phonon dispersion curves (PDCs) and the phonon density of states (PDOS) have not been reported even at room pressure. High-pressure (HP) studies of several APO4 orthophosphates have been reported in the literature, i.e. where zircon-and monazite-type phosphates have been broadly studied [17][18][19][20][21][22][23][24][25][26][27] . The pressure-induced structural sequence has been understood, with several new HP phases discovered and their crystal structures solved. In addition, the influence of pressure in the vibrational properties and unit-cell parameters has been well established. The number of HP studies carried out has also helped to unveil the existing relationship between the response under compression of the microscopic and macroscopic properties of these materials. In particular, the compressibility has been explained in terms of polyhedral compressibilities 23 . Moreover, the studies of phosphates under extreme conditions have been recently extended to compounds with different crystal structures when compared to zircon or monazite. In particular, phosphates with the olivine structure as well as complex phosphates, like K2Ce(PO4)2 and isomorphic compounds, have been characterized under HP 28,29 . Finally, metastable polymorphs of BiPO4 18 , spin-Peierls distorted TiPO4 30 and CrVO4-type phosphates 31 have also been recently studied at HP. Phase transitions (PTs) driven by compression have been reported for all these compounds, with a common feature found that the PTs are always first-order, involving a collapse of the volume and the breaking and formation of chemical bonds. Moreover, HP has been found to be a successful route to penta-coordinated phosphorus, which is achieved at a pressure of 46 GPa in TiPO4 30 . In contrast with all the phosphates mentioned above, the HP behavior of SbPO4 has not yet been explored. Being this structure a layered compound and Sb possessing a strong LEP, SbPO4 is an ideal candidate for an unusual HP behavior with high compressibility and with subtle PTs at much lower pressure than that found for other APO4 orthophosphates.
In this work, we report a joint experimental and theoretical study of the structural and vibrational properties of SbPO4 at HP by means of x-ray diffraction (XRD) and Raman scattering (RS) measurements combined with ab-initio calculations. We will show that SbPO4 is one of the most compressible phosphates and ABO4 compounds. Moreover, it exhibits a considerable anisotropic behavior due to a high non-linear compression, mainly along the a-axis, as shown by respective compressibility tensor. Additionally, we will show that our measurements and calculations are compatible with the existence of an isostructural phase transition (IPT) around 3 GPa and a reversible PT above 9 GPa, which is completed around 20 GPa. After the study of several candidates for the HP phase of SbPO4 based on an updated Bastide's diagram 20,32 for ABO4 compounds containing cations with LEPs, like As 3+ , Sb 3+ , Bi 3+ , Sn 2+ and Pb 2+ , we propose a triclinic distortion of the original monoclinic phase as the HP phase above 9 GPa. The experimental and theoretical vibrational modes of both LP and HP phases at different pressures will be shown and a tentative assignment of the symmetry of each observed Raman-active mode will be provided. This work helps to better understand how layered SbPO4 behaves under compression and provides clues to design better photocatalysts and better intercalated compounds with enhanced ion-exchange characteristics based on this phosphate.
This work helps us understand the behavior of the layered SbPO4 under compression, thus providing insights to direct and improve the design of similar photocatalysts and intercalated compounds with enhanced ion-exchange characteristics.

Experimental Method
Synthetic SbPO4 powders used in the present experiments were synthesized by M. Nalin and coworkers [2][3][4] . Energy dispersive X-ray spectroscopy (EDS) analyses performed with an Oxford Instruments detector coupled to a JEOL JSM6300 scanning electron microscope showed a good stoichiometry and no appreciable impurities. Structural characterization of powders at room pressure was carried out by XRD measurements performed with a Rigaku Ultima IV diffractometer using Cu K (1.5406 and 1.5443 Å for K and K, respectively) as the incident radiation source. Traces of other phases or of Sb2O3 were not detected. Vibrational characterization of powders at room pressure was carried out by RS measurements performed with a Horiba Jobin Yvon LabRAM HR UV microspectrometer, equipped with a thermoelectrically cooled multichannel charge-coupled device detector and a 1200 grooves/mm grating that allows a spectral resolution better than 3 cm −1 . The signal was collected in backscattering geometry exciting with a 532 nm laser with a power of less than 10 mW. Phonons were analyzed by fitting Raman peaks with a Voigt profile fixing the Gaussian linewidth (2.4 cm -1 ) to the experimental setup resolution. RS experiments allowed us also to confirm that the samples contained only a pure phase.
Powder angle-dispersive HP-XRD measurements were performed at room temperature in three different experiments. Initially, we performed two experiments (called Run 1 and Run 2) using an Xcalibur diffractometer with the lines K1 and K2 of a Mo source with λ = 0.7093 and 0.7136 Å, respectively. The sample was loaded with a 16:3:1 methanol-ethanol-water mixture in a Merrill-Bassett-type diamond anvil cell (DAC) with diamond culets of 400 m in diameter 33 .
A third powder angle-dispersive HP-XRD experiment (Run 3) was performed up to 15.2 GPa in the BL04-MSPD beamline at ALBA synchrotron facility 34 . This beamline is equipped with Kirkpatrick-Baez mirrors to focus the monochromatic beam and a Rayonix CCD detector with a 165 mm diameter-active area and was operated with a wavelength of 0.4246 Å. In the two first experiments, pressure was determined by the luminescence of small ruby chips evenly distributed in the pressure chamber 35 , while in the third experiment pressure was determined with the equation of state (EoS) of copper 36 . Integration of 2D diffraction images was performed with Dioptas software 37 while structural analysis was performed by Rietveld and Le Bail refinements using FullProf 38 and PowderCell 39 program packages. In all the experiments the DAC loading was performed taking care of avoiding sample bridging with the gasket 40 .
Finally, unpolarized HP-RS measurements up to 24.5 GPa were performed with the Horiba Jobin Yvon LabRAM HR UV microspectrometer previously mentioned. The sample was loaded with a 16:3:1 methanol-ethanol-water mixture in a membrane-type DAC and pressure was determined by the ruby luminescence method 35 . In the pressure range covered by Raman and XRD experiments pressure was determined with an accuracy of 0.1 GPa.

Theoretical details
Ab-initio calculations were performed within the framework of density functional theory (DFT) 41 to study the structural, vibrational, and elastic properties of SbPO4 under pressure.
Simulations were carried out with the Vienna ab-initio simulation package (VASP) 42 using the projector augmented wave (PAW) pseudopotentials 43 . The PAW scheme replaces core electrons by smoothed pseudovalence wave functions considering the full nodal character of the allelectron charge density in the core region. The set of plane waves employed was extended up to a kinetic energy cutoff of 520 eV because of the presence of oxygen in SbPO4. The generalized gradient approximation (GGA) was used for the description of the exchange-correlation energy within the PBEsol prescription 44 . The BZ of the monoclinic and the others analyzed structures of SbPO4 were sampled with dense Monkhorst-Pack grids of special k-points 45 . A high convergence of 1-2 meV per formula unit in the total energy is achieved with the cutoff energy and the k-point sampling employed. This ensures an accurate calculation of the forces on atoms.
At a set of selected volumes, the structure was fully relaxed to the optimized configuration through the calculation of the forces on the atoms and the stress tensor until the forces on the atoms were smaller than 0.005 eV/Å and the deviations of the stress tensor from a diagonal hydrostatic form were lower than 0.1 GPa.
Lattice-dynamics calculations were performed to study the phonons at the Γ-point of the BZ using the direct force constant approach (or supercell method). The diagonalization of the dynamical matrix provides the frequency and symmetry of the phonon modes. In order to obtain the PDCs along high-symmetry directions of the BZ and the PDOS, similar calculations were performed using appropriate supercells (2x2x2), which allow the PDCs at k-points to be obtained commensurate with the supercell size 46 . Finally, in order to study the HP mechanical stability of SbPO4, the elastic stiffness constants were determined employing the stress theorem 47 . The optimized structures were strained, at different pressures, considering their symmetry 48 .
In order to analyze the Sb-O interatomic interactions of SbPO4 at different pressures, we computed the electron density and its Laplacian at the Sb-O bond critical points using the VASP code and the CRITIC2 program 49 . The CRITIC2 code implements the Quantum Theory of Atoms in Molecules (QTAIM) 50 . Within this theory, the 1-saddle critical points of the electron density (bond critical points, BCPs), and their corresponding atomic interaction lines (bond paths), determine which atoms are bonded to which. In addition, the value of  at the BCP correlates with the strength of the bond between two nuclei, provided the comparison is restricted to pairs of atoms of the same species. The Laplacian of the charge density at the BCP, ∇ 2 ρ(r) = 0, can be used to determine the covalent (if ∇ 2 ρ(r) < 0) character of the bond. We note that the charge density computed from the present PAW-DFT calculations using VASP solely contains the valence states; consequently, the calculated charge density values are only relevant for distances larger than the PAW radius of each atom (far enough from the core). However, it is this region where the BCPs appear and therefore the analysis of the density can still be used to characterize the Sb-O bond. We also performed an analysis of the electron localization function (ELF) along the Sb-O bonds. For the ELF analysis, we used the Elk software 51 version 6.3.2 with structural parameters obtained from the VASP optimization. The Elk software provides allelectron full-potential linearized augmented plane-wave (FPLAPW) calculations. We used a 4x4x4 uniform grid for the reciprocal space sampling, a Rmin*Kmax equal to 7.0, and a Gmax for the interstitial expansion of the density and potential equal to 22.0 a.u. To have smoother ELF profiles, we increased the number of radial points inside the muffin tins to 1000, except in the 20.8 GPa case, where this causes SCF convergence difficulties.

Structural and vibrational properties at ambient conditions
The XRD diffractogram of SbPO4 at room pressure is shown in Figure 2(a). Rietveld refinement of the XRD pattern was performed using, as initial model, the monoclinic P21/m (space group No. 11) structure of SbPO4 reported in literature 9 . The refined parameters were the overall scale factor, the zero shift, the cell parameters, the pseudo-Voigt profile function with terms to account for the reflection anisotropic broadening (including anisotropic micro-strains), the fractional atomic coordinates, and the background. The Rietveld refinement yielded the following lattice parameters at 1 atm: a = 5.10303(4) Å, b = 6.77210(3) Å, c = 4.74424(3) Å,  = 94.6089(4)º, a unit-cell volume V0 = 163.422(2) Å 3 , and the atomic coordinates collected in Table 1. These values agree with values reported in the literature: a = 5.0868, b = 6.7547 Å, c = 4.7247 Å,  = 94.66º and V0 = 161.8 Å 3 11 . Our experimental values agree with those from our own ab-initio calculations (see Table S1 in Supplementary Information (SI)). We have found that the theoretical V0 underestimates the experimental V0 by only a 0.4%; a value that is within the uncertainty in GGA-PBESol calculations. At room pressure, the monoclinic structure of SbPO4 has one Sb, one P and three O atoms at independent Wyckof sites: all atoms are at 2e (x,1/4,z) sites except one O that is at a 4f (x,y,z) sites. Therefore, the monoclinic structure has eleven free atomic parameters.    [52][53][54][55][56] , the presence of a strong non-bonding cation LEP in SbPO4 causes a distortion in the structure that usually leads to a layered structure.  (7) As regards the lattice dynamics of SbPO4, Figure 2(b) shows the experimental RS spectrum of SbPO4 observed at room pressure. The RS spectrum accounts for 13 peaks at room pressure and is dominated by a strong mode close to 356 cm -1 . In fact, our RS spectrum is similar to the only one that has been published up to our knowledge 15 and is similar in appearance to that of BiPO4-III 12 Table 2.  It is also noteworthy of mentioning that for SbPO4 the internal modes associated with the PO4 tetrahedron, are bending and stretching P-O modes located on the medium and highfrequency regions, respectively (see PDOS in Figure 2(c)). In fact, as in many phosphates, the vibrational modes of SbPO4 can be understood as internal and external modes of the PO4 units. It is known that the internal modes of the free tetrahedral PO4 3− molecule with Td symmetry are: the symmetric stretching A1 mode (aka ν1), the triply degenerated (F2) asymmetric stretching (aka ν3), the doubly degenerated (E) bending mode (aka ν2); and the triply degenerated (F2) bending mode (aka ν4). These vibrations are located at 938, 1017, 420 and 567 cm −1 , respectively 61 . In SbPO4, the highest frequency modes (above 900 cm -1 ) are mainly asymmetric stretching modes, except the symmetrical P-O stretching mode (Ag mode of 936 cm -1 ) in which the four O atoms vibrate in phase against the P atom (see Figure S4 in SI). The mediumfrequency modes between 400 and 650 cm -1 are mostly related to P-O bending: i) above 540 cm -1 these correspond to P-O bending modes combined with Sb-O stretching modes and ii) below 540 cm -1 these correspond to P-O and Sb-O bending modes of both PO4 and SbO4 units.
Therefore, we understand that the phonon gap found on SbPO4 is clearly due to the separation of the internal stretching and bending modes evidenced inside the PO4 units.
Finally, the vibrational modes of the low-frequency region below 400 cm -1 can be related to translations (T) and rotations (R) of the PO4 units; i.e. the external modes of the PO4 units (see Table 2 and Table S3 in SI). In particular, the Au mode of 220 cm -1 corresponds to the rotation of the PO4 units (see Figure S5 in SI) and other modes at frequencies between 200 and 330 cm -1 also show partial rotation of the PO4 units.  19 . We would like to point out that, despite the description given above, is possible to perform more elaborated analyzes of the origin of the SbPO4 vibrational modes using, for example, the concept of bond stiffness 62-64 .

Structural properties under compression
All XRD peaks shift to larger angles on increasing pressure up to 15.2 GPa as observed in Figure S6. This result is consistent with the decrease of interplanar distances at increasing pressure. In addition to that, from room pressure up to 8.4 GPa, the only noticeable change on the XRD pattern is the gradual increase of the intensity of the peak at the lowest angle. This phenomenon is the consequence of changes in the coordinate of Sb, which slowly moves from the room pressure position to that of Bi in BiPO4-III, favoring the approximation of Sb to two second-neighboring oxygen atoms; a fact supported by our ab initio simulation. Above 8.4 GPa, we observe the progressive appearance of four additional diffraction peaks (see Figure S6). The new peaks increase in intensity continuously up to the maximum pressure of our XRD study and these are not related to the monoclinic SbPO4 structure. On pressure release, the obtained diffraction pattern is identical to that of the initial sample, thus showing the reversibility of the pressure-induced PT (see top of Figure S6).  65 was fitted to our P-V data to obtain the zero-pressure volume, V0, bulk modulus, B0, and its pressure derivative, B0'. If the volume vs pressure data are fitted in the whole range, a B0' larger than 10 is obtained, thus suggesting an anomalous compressibility behavior. As will be commented below, there is an IPT above 3 GPa. Therefore, we have obtained the EoS at two different pressure ranges: before the IPT (1atm to 3 GPa) and after the IPT (3 GPa to 8 GPa). In addition, since the results of the three runs do not present significant divergences, only one adjustment was made on all the experimental points. Both experimental and theoretical data are summarized in Table 3 showing rather good agreement.   (2) GPa. The increase of B0 is directly related to an increase of the structure rigidity after the IPT that is common in layered materials 59,66,67 . It is noteworthy of mentioning that, with a B0 around 34 GPa, SbPO4 is the most compressible phosphate 18 . Interestingly, the bulk modulus of SbPO4 is almost half of that of barite-type compounds, such as PbSO4 and BaSO4 68-70 and is even smaller than the bulk modulus of the distorted barite-type structure of SnSO4 and respective different layered phases 71 . This is noteworthy because the strong LEP of Sn 2+ of SnSO4 leads to layered structures with a 3-fold coordinated Sn at the distorted barite-type Pnma structure and 3+1-fold coordinated Sn in the P21/a phase above 0.2 GPa 71 . Consequently, we can safely conclude that SbPO4 is not only the most compressible phosphate but also one of the most compressible ABO4 compounds.
Up to 3 GPa 162.6 (6) 36 ( Table 3 and is in good agreement with our theoretical results. As previously, the adjustment was performed for two different pressure ranges: before the IPT (1 atm to 3 GPa) and after the IPT (3 GPa to 8 GPa). As expected for this layered material, the aaxis (direction perpendicular to the layers) presents the largest compressibility due to the high compressibility of the Sb LEP and the weak inter-layer Sb-O distances, and the b-axis evidenced the lowest value due to the small compressibility of the Sb-O3 and P-O3 bonds mainly directed along this axis. The parameter a and c present a significant decrease in the pressure coefficient at pressures higher than 3 GPa, thus supporting the hypothesis of an IPT around this pressure value.
The  angle also presents a smooth decrease with pressure and, although our theoretical values present a discrepancy of ~2º in absolute value with respect to the experimental values, a similar evolution of the experimental and theoretical data with increasing pressure is evidenced. This result indicates that our theoretical data provides a correct description of the evolution of the lattice parameters and  angle of the monoclinic structure of SbPO4 under compression.
Since SbPO4 is a monoclinic material, we have calculated and diagonalized the experimental and theoretical isothermal compressibility tensor, βij, in order to evaluate the magnitudes and directions of the principal axes of compressibility 17 . The tensor has been calculated using the linear Lagrangian approximation (LLA) 72 and the infinitesimal Lagrangian approximation (ILA) 73 . For the LLA, a linear fit of the unit-cell parameters was carried out between the pressure range 0-5 GPa.  Table 4. These values are considerably larger than in BiPO4 and BiSbO4 17,74 which is consistent with the layered structure of SbPO4. The inverse trace of the compressibility tensor, expected to be equal to the bulk modulus, is 48 GPa, which agrees with the result obtained from the BM-EoS.
123 (4)  139 123 (4)  137 The eigenvalues and eigenvectors computed for the isothermal compressibility tensor are also reported in Table 4. Considering the eigenvector ev2, the minor compression direction is along the b-axis. On the other hand, the major compression direction occurs along the (0 1 0) plane at the given angle Ψ (see Table 4) to the c-axis (from c to a). The direction of maximum compressibility, considering the value of the β angle is at 30 (4) The strong change observed in the slopes of the c/a and b/a axial ratios and the F-f plot above 3 GPa seem to suggest an IPT around that pressure range, which will be further discussed. Considering the good correlation between our experimental and theoretical results for monoclinic SbPO4, we can use the theoretical results to extract additional information that is not available through the LeBail fit, such as the evolution of the free atomic positions, bond lengths and polyhedron distortion at HP. In Figure 6, we can observe the pressure dependence of the theoretical Sb-O and P-O bond lengths. As can be noticed in Figure 6(a), the shortest Sb-O1 bond length shows no significant change with pressure, but the shortest Sb-O2 and Sb-O3 bond lengths (see solid lines in Figure 1(b)) tend to converge to the same value as the pressure increases. In this context, it is worth mentioning the increase of the Sb-O2 bond length between 0 and 3 GPa and its change of slope above 3 GPa. Similar changes of slope close to 3 GPa can also be observed at other Sb-O distances. As regards the largest Sb-O lengths (marked with * in Figure 6(a)), which correspond to the two inter-layer Sb-O3 distances and the two dashed lines shown in Figure 1(b), these show a considerable decrease below 3 GPa. Above this pressure value, this tendency decreases, but is still reminiscent. Similarly, all P-O bond lengths ( Figure   6(b)) decrease with pressure, except the P-O3 bond that remains almost constant below 3 GPa and decreases above this pressure. As already commented, changes of the slopes for the many bond lengths of the monoclinic SbPO4 are observed around 3-4 GPa, especially for distances related to the O3 atom; i.e. the external O atoms of the layers, while smaller changes are associated to O1 and O2 atoms; and the internal O atoms of the layers (see Figures 1(a) and (b)). To trace the origin of those changes we have plotted in Figure S8 of SI the pressure dependence of the Wyckoff sites of monoclinic SbPO4. In order to assure the good agreement between our theoretical and experimental data, the experimental values obtained by Rietveld refinement at room pressure were also included in Figure S8. As can be observed, the z value of all sites tends to decrease with pressure, except for Sb. It is also possible to observe that the evolution of all positions presents a minor change of the slope around 3 GPa; however, the largest variation of the slope is observed for the x position of both O2 and O3 and the y position of O3 (Figures S8(d) and S8(e)). These trend variations are indicative of a pressure-induced IPT close to 3 GPa, as previously commented. Further discussion about the IPT will be provided when we discuss the behavior of the electron topology at HP.
In order to find the origin of the new peaks above 8.4 GPa, we provide an indexation of the XRD pattern above that pressure assuming the possibility of a phase coexistence between the LP phase and a new HP phase or assuming a single HP phase. To search for possible HP structures of ABO4 compounds, we resorted to the Bastide's diagram 20,32 by taking into account the position of SbPO4 in that diagram (rSb/rO = 0.563, rP/rO = 0.126). We have plotted a renewed form of the Bastide's diagram in Figure 7 highlighting the location of many compounds containing cations with LEPs, such as As 3+ , Sb 3+ and Bi 3+ , which have been positioned in respective diagram for the first time. We must stress that there are many compounds with As 5+ in the diagram, with As 5+ behaving similarly to P 5+ , but there is only one compound of As 3+ (in red), which is precisely AsPO4 with P 5+ . We must also stress that there are many compounds with P 5+ in the diagram, but no compound with P 3+ is mentioned.
According to the north-east rule in Bastide's diagram, SbPO4 should crystallize in the orthorhombic CrVO4-type structure with    Figure 7). However, neither these structures allow us to explain the new peaks observed in Figure S6. Since BiPO4-III transforms into the monazite structure above 0.8 GPa 12 , we have also tried the comparison of the peaks with the monazite structure. However, the position of the new diffraction peaks cannot be explained with a possible PT to this structure either, despite the monazite structure being energetically more favorable than the monoclinic structure at HP.
Since Sb is 4-fold coordinated for the monoclinic structure instead of 6-fold coordinated, as expected from the Sb 3+ ionic radius, we have considered that the real position of SbPO4 could be that of AsPO4, which is predicted to have 4-fold coordination for As, despite of existing a real 3-fold coordination of As at room pressure 75 . In such a case, monoclinic SbPO4 could transform under pressure into the CrVO4 or wolframite structures (see red arrow in Figure 7); however, the positions of the new diffraction peaks cannot be explained with a possible PT to these structures  Finally, we found a possible solution by considering the coexistence of the LP monoclinic phase of SbPO4 with a respective triclinic distortion. Such coexistence has been observed in other monoclinic oxides at HP 71,76 . In our case, we have built the candidate triclinic structure, which belongs to the P-1 (No. 2) space group, by using the group-subgroup relationships between space groups n o 2 and 11. By considering the coexistence of the LP monoclinic structure and the HP triclinic structure, we have been able to clarify the diffraction patterns measured above 8.4 GPa. Our XRD patterns suggest that the LP phase is the dominant phase up to 11.2 GPa, being the HP phase the dominant phase above this pressure value. In  Table S2). This result and the group-subgroup relationship between both structures suggest that the PT could be a very weak first order transformation, as suggested by the coexistence of both monoclinic and triclinic structures at HP and the reversibility of the XRD pattern at room pressure previously mentioned. inter-layer distances with the same length. Above this pressure, the HP phase becomes more stable and the evolution of the ECoN of Sb of the HP phase presents the same growth rate as that of the LP phase, thus reaching an ECoN of 5.19 at 18.5 GPa. We will see later that this value is consistent with a 4+2+1-fold coordination for Sb coordination for this pressure range. The increase of ECoN with pressure is followed by the decrease of the distortion index (Figure 9(b)) that, above 4.7 GPa presents a decrease of the distortion rate and remains constant in the HP phase. Moreover, the increase of the Sb coordination in the monoclinic phase from 4 to 4+2 can be related to the strong decrease of the Sb eccentricity of the SbO6 polyhedron between 1 atm and (see Figure S10).
Finally, we must stress that the ECoN value of Sb in SbPO4 at 18.5 GPa is close to that of Bi for BiPO4-III at room pressure (5.16); therefore, we can conclude that around 18 GPa the SbPO4 compound behaves as BiPO4-III at room pressure 19 . In other words, pressure promotes the approach of the layers in SbPO4, thus favoring the bond between the Sb 3+ of one layer and the O 2atoms of the adjacent layer, therefore converting the 2D-type structure of SbPO4 at room pressure into a 3D-type structure that reaches a similar coordination to that of BiPO4-III at pressures close to 18 GPa.
We conclude by mentioning that the proposed pressure-induced IPT at 3 GPa and monoclinic-triclinic PT above 9 GPa does not involve a change of the coordination of P, although a considerable increase of the coordination of Sb from 4 at room pressure to 4+2 above 3 GPa is observed; moreover respective coordination increases to 4+2+2 above 9 GPa (see

Vibrational properties under compression
Raman scattering (RS) spectra at selected pressures up to 24.5 GPa are presented in Figure S11. Once the sample is inside the pressure cell, it is possible to observe some peaks that probably are not related to the SbPO4 sample (see blue arrows in Figure S11) since these do not appear on the RS spectra at room pressure either before or after the HP cycle (see bottom and top RS spectra in Figure S11). These peaks could be due to some unintentionally impurity loaded on the DAC. The pressure dependence of these peaks is plotted as blue symbols in Figure 10 and some of them can be observed up to the maximum pressure of our RS experiment.
As regards to the peaks that may be considered as first-order modes of SbPO4, some of these begin to widen and lose intensity and other new peaks start to rise above 7.7 GPa (see red arrows in Figures S11(a), (b) and (c)), thus giving support to the existence of a PT above this pressure range. In particular, the peak that rises at 12.8 GPa around 134.7 cm -1 and at 24.5 GPa around 160.4 cm -1 (Figure S11(a)) becomes the most intense peak of the RS spectrum of the HP phase. Other seven less intense new peaks can be observed between the pressure range of 7.7 and 16.2 GPa. Notably, the peaks initially observed at 355 cm -1 (the strongest one of the LP phase) and at 888 cm -1 (probable second-order mode of the LP phase) progressively disappear with increasing pressure, thus indicating that the PT seems to be completed around 20 GPa. This result could explain why our XRD measurements up to 15 GPa cannot clearly resolve the HP phase since this phase is not completely developed at this pressure range. Note also that the region, which presents less changes of the Raman spectrum is the high-frequency region related to the stretching P-O vibrations of the PO4 unit. This means that the HP phase is most likely to be a phase with tetrahedral coordination of P, in good agreement with the proposed triclinic HP phase and with the higher pressure phase at which the P coordination has been observed to increase on other phosphates 30,84 .   Table 2. For the sake of completeness, we also plotted the dependence of the theoretical IR-active modes at HP in Figure   S12 in SI, which data are summarized in Table S3 in SI. Comparing the evolution of the theoretical and experimental results at HP, we can note that results obtained from ab-initio calculations underestimate the frequencies of all Raman-active modes. This underestimation (typically within 3-5%) is especially evident in the medium-and high-frequency regions, where frequency values differ up to 30 cm -1 . However, comparing the pressure evolution of both data, we can tentatively assign the symmetry irreducible representations of some experimental Ramanactive modes with the aid of theoretical calculations (see Table 2 and Figure 10). For this purpose, we have calculated the pressure coefficients of the Raman peaks up to 3 GPa ( Table 2) due to the IPT observed above 3 GPa. Curiously, all experimentally observed peaks at room pressure can be associated to the Ag modes, except for the peak located at 151 cm -1 , which we attribute to the Bg mode at 151 cm -1 . Finally, it must be mentioned that the signature of the experimental broad peak initially observed at 107 cm -1 is not clear since it was observed only at 1 atm outside the DAC (before and after the pressure cycle).
As can be observed in Figure 10, many vibrational modes present a change in the pressure coefficient between 3 and 6 GPa, reinforcing the idea of the existence of a pressureinduced IPT around 3 GPa. In particular, experimental Raman-active modes Ag(T) (near 215 cm -1 ) and Ag(R) (near 356 cm -1 ) as well as a number of theoretical Raman-active modes (at 75,106,118,152,200,324,347, and 990 cm -1 at 0 GPa in Table 2) show a change of slope close to 3 GPa in Figure 9. Moreover, all the vibrational modes of SbPO4 that show a negative pressure coefficient at 0 GPa change to a positive pressure coefficient above 3 GPa. This result is in good agreement with the pressure-induced 2D-to-3D phase transition that takes place in layered SbPO4 above 3 GPa upon increasing Sb coordination from 4 to 4+2-fold. On the other hand, the non-linear behavior of the theoretical vibrational modes located at 926 and 937 cm -1 at room pressure, is the result of an anticrossing of these two Ag modes, which is reproduced by the experimental results at a slightly higher-pressure value (~12 GPa - Figure 10(c)). A change of pressure coefficient around 3 GPa can also be observed for many theoretical IR-active modes (Figure S12), where a couple of anticrossings seem also to be observed for the Bu peaks 183 and 207 cm -1 (Figure S12(a)) and at 930 and 937 cm -1 (Figure S12(c)), respectively. The change of the pressure coefficient of the Raman-active and IR-active modes near 3 GPa can be related to the approximation of the atomic layers that begin to interact more strongly and lead to the increase of Sb coordination. Note that the compression of the LEP is much larger than that of other bonds, thus leading to a large compression of the inter-layer distance below 3 GPa (compression is less pronounced at higher pressures).
At this point, we can discuss the pressure coefficients of the vibrational modes. It can be observed that the largest pressure coefficients correspond mostly to the P-O vibrations stretching located at the high-frequency region. In particular, the highest-pressure coefficient is that of the symmetric stretching Ag mode and the respective IR analogue, the Bu mode. A similar high response to pressure of the stretching P-O vibrations, and in particular of the symmetric stretching modes, has been found for other orthophosphates 19,20,26,[85][86][87][88] . Large pressure coefficients are also observed for the rotational modes of the PO4 unit (theoretical Au and Bg modes at 220 and 224 cm -1 , respectively). Again, this behavior has already been observed for other orthophosphates 19,20,26,[85][86][87][88] .
As regards to the rigid layer modes, the shear rigid layer modes positioned at 75 cm -1 (Bg mode) and at 89 cm -1 (Ag mode) have pressure coefficients of 4.5 and 0.5 cm -1 /GPa, respectively.
On the other hand, the longitudinal rigid layer mode at 106 cm -1 (Ag mode) has a pressure coefficient of -0.6 cm -1 /GPa (see Table 2). For typical layered materials, with van der Waals interaction between the layers, such as GaSe and InSe, the longitudinal rigid layer mode has a larger pressure coefficient (above 3 cm -1 /GPa) when compared to that of the shear rigid layer mode (between 0.5 and 1.5 cm -1 /GPa, see discussion in Refs. 59 and 89). The situation of SbPO4 is completely different to that of typical layered compounds but also different to that of BiTeBr and BiTeI with polar interactions between the layers 59 . On one hand, the lowest-frequency Ag mode is a typical shear rigid layer mode (see Figure S2) and evidences a pressure coefficient below 1 cm -1 /GPa. On the other hand, the shear rigid layer Bg mode shows an extraordinarily high-pressure coefficient. This can be explained taking into account the atomic vibrations of this latter mode (see Figure S1). It can be observed that the Bg mode is not a pure shear mode and bending of Sb-O1 and Sb-O3 bonds within the SbO4E unit. Therefore, the negative pressure coefficient for this mode in SbPO4 is most likely related to a decrease of the Sb-O2 bond strength which is in good agreement with the increase of the Sb-O2 bond distance between 0 and 3 GPa (see Figure 6). Note that the change of the pressure coefficients of many vibrational modes is also in agreement with the changes of the Sb-O distances observed in Figure 6, thus providing additional support to the occurrence of a second-order IPT for SbPO4 around 3 GPa.
Several new Raman-active modes ( Figure S11)  where Ag are Raman-active (R) and Au are IR-active, except for the three acoustic modes.
Therefore, there are eighteen Raman-active and fifteen IR-active modes. The eighteen Ramanactive and fifteen IR-active theoretical modes have been plotted in Figures 10 and S13, respectively. As observed in Figure 10, the theoretical Raman-active modes for the HP phase of SbPO4 show similar frequencies and pressure coefficients to those of the LP phase. Table 5 summarizes the frequencies and pressure coefficients of the experimental and theoretical modes of the HP triclinic phase of SbPO4. Despite of not existing a very good agreement between the experimentally measured modes of the HP phase and the calculated ones, we have provided in Table 5 a tentative assignment of the experimental modes to this triclinic phase. The theoretical frequencies and pressure coefficient of the IR-active modes of the proposed triclinic HP phase of SbPO4 are also summarized in Table S4 in SI. Regarding the relative disagreement between calculated and experimental triclinic Raman-active modes in Table 5, we think that it can be due to experimental problems of appearance of second-order modes instead of first-order modes of the triclinic phase or to theoretical problems regarding the simulation of the correct triclinic phase since the experimental triclinic phase could be slightly different to the simulated one.
Regarding this point, we must note that simulation of triclinic phases is very challenging since energy minimization procedures can lead to local minima and not to absolute minima. This means that we have found a triclinic phase that is competitive with the monoclinic one at HP, but we cannot assure that this is the only triclinic competitive phase and therefore we cannot assure that the simulated one is exactly the experimental one.
In summary, our unpolarized HP-RS measurements of SbPO4 exhibit most of the Ramanactive modes of the monoclinic (P21/m) phase with Ag symmetry, but very few modes with Bg symmetry. The assignment of vibrational modes as internal or external of the PO4 units has been provided and their pressure coefficients, especially those for rigid layer modes, properly discussed. HP-RS results support the occurrence of an IPT around 3 GPa and a PT above 8 GPa that complete respective formation around 20 GPa, in good agreement with the XRD measurements. Finally, the Raman-active modes of the HP phase of SbPO4 have been measured and their frequencies have been compared to the theoretically predicted modes for the HP triclinic phase.

Electronic properties under compression
In order to understand the electronic properties of SbPO4, we have calculated the theoretical electronic band structure of SbPO4. Figure 11 shows the theoretical electronic band structure and PDOS of SbPO4 at 0 GPa and 5.1 GPa. As observed in Figure 11  In Figure 11(b) it is possible to observe that at 5.1 GPa, the minimum of the conduction band is located at point Y2, indicating that the bandgap at this pressure range is measured between the high-symmetry points of C2 and Y2. The pressure dependence of both indirect C2-B and C2-Y2 bandgaps is plotted in Figure 12. As can be observed, the indirect C2-B bandgap increases with pressure whereas the indirect C2-Y2 bandgap decreases with pressure.
Consequently, an indirect-to-indirect crossover in the conduction band minimum occurs around 2.4 GPa; i.e. close to the IPT pressure. Above this pressure, the minimum indirect bandgap is found to be between the C2 and Y2 high-symmetry points of the BZ.  Fig. 9(a)). The ELF analysis is shown in Fig. 13 where some remaining non-smoothness of the curves are due to the impossibility of raising the number of radial points further. We note that an all-electron wave function is needed to get a reliable picture of the ELF, since this function is not separable into core and valence contributions. The value of the ELF along lines connecting Sb to its O neighbors were calculated by three-dimensional interpolation from the ELF grid generated by Elk using the CRITIC2 software 49 . For the AIM electron density analysis, we have computed the electronic charge density and respective Laplacian at the BCPs also using CRITIC2 software (see Table S5). With this information, we have analyzed the Sb-O interatomic interactions in the different SbPO4 structures in order to study the variation in Sb coordination as a function of pressure. At 0 GPa, Sb is 4-fold coordinated in monoclinic SbPO4 with four Sb-O distances (d1, d2 and two d3) below 2.2 Å (see Fig. 6(a)). All four bonds show a similar ELF profile and a minimum near 0.44 of the normalized distance in Fig. 13(a) and also similar values of the electron density at their BCPs. On the other hand, the remaining four Sb-O distances (two d4, d5 and d6 above 2.7 Å) present completely different ELF profiles that show the existence of a maximum near 0.4 of the normalized distance that corresponds to the Sb LEP and a minimum close to 0.52 for d4, 0.53 for d5 and 0.54 for d6. Regarding the electron density, the d4 and d6 Sb-O distances show charge densities at the corresponding BCPs that are significantly smaller than in the short contacts, and the d5 contact does not even have a BCP (see Table S5). These observations evidence the negligible Sb-O interaction along these directions, which agrees with the ECoN results regarding the 4-fold coordination of Sb for the monoclinic SbPO4 systems at 0 GPa. Above 3 GPa, monoclinic SbPO4 shows four Sb-O bond lengths (d1 to d3) below 2.2 Å and two Sb-O bonds (d4) below 2.6 Å (see Fig. 6(a)). The four shortest distances show ELF profiles similar to those at 0 GPa and the other two distances (d4) show an ELF profile where the LEP maximum is almost gone and there is a minimum closer to 0.44; i.e. similar to those of d1 to d3 distances ( Fig. 13(b)); thus indicating that the ELF domain associated to the LEP has shrunk.
Similarly, at this pressure, the charge density of the d4 has increased significantly compared to the evolution of the density at the d1, d2, and d3 BCPs. This picture of the ELF and charge density at the BCP is consistent with the 4+2-fold Sb coordination that occurs above the IPT.
Moreover, the BCP along the d5 distance appears at pressures above 3 GPa, thus giving support to the occurrence of an IPT above this pressure involving a change from 4-fold to 4+2-fold Sb coordination. Note that at 7.1 GPa the ELF of the d5 and d6 distances still show the LEP maxima near the 0.4 normalized distance ( Fig. 13 (b)) and the charge densities at the BCPs of these two distances are smaller than the others (see Table S5), thus supporting the 4+2-fold coordination of SbPO4 of the monoclinic phase up until 8 GPa. We also point out that the Laplacian of all BCPs is positive, thus evidencing the ionic character of all Sb-O bonds, regardless of bond distance.
Regarding the triclinic phase, we find four distances below 2.15 Å, two distances below 2.5 Å and the remaining two distances below 2.7 Å above 8 GPa. At 14.4 GPa, all d1 to d8 distances show ELF profiles (see Figure 13(c)) similar to those found in monoclinic SbPO4 at 7.1 GPa (see Figure 13(b)). The degeneracy of bonds d3 and d4 in the monoclinic phase is broken in the triclinic phase, thus we find d1 to d4 (d5 to d6) distances in the triclinic phase showing similar ELF profiles to those of d1 to d3 (d4) distances in the monoclinic phase.
Similarly, d7 and d8 distances in the triclinic phase show similar ELF profiles to those of d5 and d6 in the monoclinic phase. This is consistent with the 4+2 coordination of Sb in triclinic SbPO4 at 14.4 GPa. At 20.8 GPa, the picture is slightly different because the ELF maximum due to the Sb LEP is gone for the d7 distance; i.e. d7 distance shows a similar ELF profile to that of d5 and d6 distances (see Fig. 13 (d)). This suggests an increase of coordination to 4+2+1 for Sb. This interpretation is in agreement with the fact that the charge density at the BCPs of the d7 distance has values comparable to those in the d4 distance of the monoclinic phase. Moreover, this conclusion is in agreement with the fact that the Sb coordination in SbPO4 reaches the effective coordination found for Bi in BiPO4-III at 0 GPa. Note that the charge density value of the d8 distance is smaller than the others and the ELF profile of the d8 distance still exhibits the maximum of the Sb LEP at 20.8 GPa. We interpret this as indicating that the triclinic structure Sb does not undergo a 4+2+1+1 coordination up to higher pressure (likely above ca. 25 GPa).
In summary, we have demonstrated with the calculated ELFs and the charge densities and respective Laplacians at the BCPs of the shortest Sb-O distances that in SbPO4: i) a change in the number of BCPs of Sb occurs at the IPT close to 3 GPa, and ii) an increase of Sb coordination can be evidenced by the charge density accumulation at the BCPs, and by the disappearance of the Sb LEP maximum of the ELF, supporting the conclusion related to the increase of Sb coordination previously shown by the ECoN.

Conclusions
We have reported a joint experimental and theoretical study of the structural and vibrational properties of SbPO4 at HP by means of XRD and RS measurements combined with ab-initio calculations. From the structural point of view, we have shown that SbPO4 is one of the most compressible materials (bulk modulus around 20 GPa), not only among phosphates but also among ABO4 compounds. Moreover, its compressibility tensor evidences a considerable anisotropic behavior due to a high non-linear compression, mainly along the a-axis.
Additionally, our results have shown that SbPO4 undergoes an IPT around 3 GPa and a PT above 9 GPa, which is completed around 20 GPa.
After the study of several candidates for the HP phase of SbPO4 on the light of an updated Bastide's diagram containing many ABO4 compounds with strong cation LEPs, we have proposed a triclinic distortion of the original monoclinic phase as the HP phase above 9 GPa.
The Raman-active modes of both LP and HP phases have been measured and properly discussed at different pressures. In general, a rather good agreement is observed between the experimental and theoretical data for the structural and vibrational data. Finally, we have provided the electronic band structure of monoclinic SbPO4 at different pressures, showing that this compound is an indirect bandgap material (bandgap value above 3.8 eV) that is transparent in the visible, UVA and UVB spectral regions in the whole pressure range up to 9 GPa.
Theoretical data have helped us to understand the microscopic mechanisms of the compression of monoclinic SbPO4, evidencing that monoclinic SbPO4 undergoes a transition from 2D-type structure with a 4-fold coordination of Sb at room pressure to a 3D structure with 4+2 coordination above 3 GPa. Changes of the Wyckoff positions, changes of the slopes of c/a and b/a ratios, and changes on the pressure dependence of interatomic distances, even of P-O3 bond distances (expected to be rather strong and incompressible bonds), clearly show the occurrence of an IPT around 3 GPa. This IPT is further confirmed by the changes in the pressure coefficients of different vibrational modes around 3 GPa. Moreover, all vibrational modes of SbPO4 that show a negative pressure coefficient at room pressure change to a positive pressure coefficient above 3 GPa. This result is in good agreement with the pressure-induced 2D-to-3D phase transition taking place in layered SbPO4 above 3 GPa. The Sb cation increases the coordination number up to 4+2+1-fold for the triclinic phase above 15 GPa and the effective coordination of SbPO4 around 18 GPa becomes similar to BiPO4-III at room pressure.
Finally, we want to stress that the ability of pressure to modulate the LEP activity and convert the 2D structure of SbPO4 into the 3D network of BiPO4-III may have important implications for technological applications for SbPO4-based compounds since the role played by external pressure can be mimicked by chemical pressure. In particular, partial substitution of Sb cations in SbPO4 by Bi cations (with smaller LEP) or by other cations with valence 3+ and without an active LEP, like In, is expected to lead to a closing of the inter-layer space of the SbPO4 structure; i.e. will promote the 3D nature of the compound. Conversely, partial substitution of Sb cations by As cations (with a much stronger LEP) is expected to promote the opening of the structure and consequently the 2D nature of the compound. Thus, our work suggests a way to open or close the structure of layered SbPO4 that can help to enhance the catalytic and atomic-insertion properties of SbPO4-based compounds

Acknowledgments
Authors thank the financial support from Brazilian Conselho Nacional de

Synopsis
Here we report a joint experimental and theoretical study of the monoclinic SbPO4 at high pressure. We show that SbPO4 is not only one of the most compressible phosphates but also one of the most compressible compounds of the ABO4 family. The strong compression along a-axis leads to an isostructural phase transition above 3 GPa and a reversible phase transition to a triclinic phase above 9 GPa, which is completed above 20 GPa.  Figure S1. Atomic vibrations (along the b-axis) of the Bg mode of 75 cm -1 , which is one of the shear layer modes of SbPO4. Sb (big purple), P (medium-size orange) and O (small red).