High-pressure polymorph of Co₃P₂O₈: phase transition to an olivine-related structure

Abstract

The monoclinic polymorph of Co₃P₂O₈ (space group P2₁/c), isomorphic to farringtonite (Mg₃P₂O₈) type orthophosphates, was studied up to 21 GPa using synchrotron powder X-ray diffraction and density-functional theory simulations to investigate the influence of pressure in the crystal structure. This study revealed a pressure induced structural phase transition for monoclinic cobalt phosphate, Co₃P₂O₈, and the details of crystal structure of the new high-pressure polymorph were delineated. The evolution of XRD pattern with pressure indicate that the onset of a phase transition occurs around 2.90(5) GPa, and the low- and high- pressure phases coexist up to 10.3(1) GPa. The high-pressure phase also has a monoclinic lattice (space group P2₁/c), and a discontinuous change of unit-cell volume of about 6.5% occurs at the transition. A reorganization of atomic positions with a change in the cobalt coordination sphere occurs in the phase transition. Notably, the high-pressure polymorph has a defect-olivine-type structure like chopinite-type orthophosphates. Using a third-order Birch–Murnaghan equation of state, the bulk moduli of the low pressure (LP) phase (75(2) GPa) and high-pressure (HP) phase (92(2) GPa) were determined. For the low-pressure polymorph, the principal axes of compression and their compressibility were also determined. Density-functional theory calculations also provided the frequencies of Raman- and infrared-active modes which can be used for mode assignment in future experiments.

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I. Introduction

The A₃B₂O₈-type orthovanadates and orthophosphates (A = divalent cation) show varieties of structure types depending on the ionic radii of the A cation as well as preparation conditions or external thermodynamic parameters like pressure and temperature.^1–3 Owing to the presence of isolated vanadate or phosphate groups, they often form loosely packed and flexible crystal structure, and hence varieties of functional properties relevant for several technological applications like laser-host, phosphors, scintillators, display devices, ion transportation, and catalysis or photocatalysis, etc. can be expected or introduced in such materials.^4–9 For larger divalent cations (A²⁺) like alkaline earth or lead cations, the A₃B₂O₈ type vanadates or phosphates usually form palmierite, apatite and related structures.^2,3,10 Such compositions can have centrosymmetric or non-centrosymmetric lattices. They are known to show high dielectric constant with low loss character, microwave dielectric properties, and ferroelectric properties. For the smaller, A²⁺ ions, they form relatively denser and distorted kagome structures, and hence display severely altered electronic properties and optical properties depending on the nature of A²⁺ ions.^7,8,11–16

Rich polymorphism under pressure with the existence of newer phases and contrasting sequences of phase transitions depending on the divalent element A has been documented for several of such A₃B₂O₈-type vanadates and phosphates. This fact has been well understood in the compounds of orthovanadate family.^11–18 Among these compounds, Cu₃V₂O₈ decomposes into CuO and V₂O₅ at 1.35 GPa,¹³ while Ca₃V₂O₈, Mn₃V₂O₈ and Sr₃V₂O₈, undergo phase transitions at 9.8,¹⁵ 10,¹⁶ and 13.8 GPa,² respectively. However, Zn₃V₂O₈, Ni₃V₂O₈, Co₃V₂O₈, and Ba₃V₂O₈ do not exhibit any phase transition up to at least 15,¹⁴ 23,¹² 20,¹² and 29 GPa,³ respectively. In contrast to their vanadate counterparts, only limited studies on the HP behaviour of the analogous phosphates are reported in literature.^19–23 Information on the high-pressure behaviour of such phosphates and the structure of high-pressure phases are mainly available on the minerals, like, sarcopside, (Fe,Mn,Mg)₃(PO₄)₂, chopinite, [(Mg,Fe)₃](PO₄)₂, and related orthophosphates.^19–25 It has been suggested that these denser polymorphs have a defective olivine-type structure and are formed by combined effects of temperature and pressure on farringotoinite by a meteoritic strike.^23–26 Thus, they also can be probably synthesized by HP-HT techniques as metastable phases.^23,26,27 Most of these studies were focused on Mg²⁺ or Fe²⁺ containing orthophosphates due to their mineralogical relevance. However, to the best of our knowledge analogous orthophosphates with smaller transition metal ions are not explored under pressure. It is well known that pressure not only affects the structural properties but also modifies bond distances and angles in the structure. Thus, it can be used to tune the vibrational and electronic properties conveniently.²⁸ In some cases, application of pressure can lead to the discovery of new metastable phases with interesting physical properties that can be achieved at ambient conditions, and hence can open new opportunities for applications.^1,29 To understand the effect of pressure on a transition metal ion bearing phosphates, a systematic study on cobalt orthophosphate, Co₃P₂O₈, under high-pressure conditions up to 20 GPa at room temperature was undertaken.

Co₃P₂O₈ crystallizes in a monoclinic structure described by space group P2₁/c (it is also described in the literature by the non-standard space group P2₁/n).³⁰ It is isostructural with γ-Zn₃(PO₄)₂ ³¹ and Mg₃(PO₄)₂,³² farringtonite-type orthophosphates.³⁰ The crystal structure of ambient pressure phase of Co₃P₂O₈ is depicted in Fig. 1a. In the structure, cobalt atoms occupy two different coordination polyhedra, a slightly distorted octahedron (CoO₆) and a penta-coordinated polyhedron (CoO₅), in a ratio of one to two respectively. The penta-coordinated CoO₅ polyhedron can be described as a distorted trigonal bipyramid. The presence of such polyhedra in related vanadates, like Zn₃V₂O₈, has been related to the existence of pressure induced phase transitions.¹⁴ Zn₃V₂O₈ undergoes a phase transition by hydrostatic pressure below 4 GPa, which has been attributed to the displacement of an oxygen atom towards ZnO₅ units under the influence of pressure and that leads to a closely packed structure and transforms the ZnO₅ units to ZnO₆ octahedral units. We hypothesized that such structural changes could be a common phenomenon in such orthovanadates and phosphates, and that further motivate us to explore the high-pressure behaviour and possible pressure induced phase transitions in Co₃P₂O₈, which has not yet been studied under compression. In fact, Co₃P₂O₈ is also scarcely studied at ambient conditions and more commonly investigated in the interest of its use as a pigment in ceramics, (it was the favourite violet pigment of Claude Monet who used it in the famous Water-Lilies painting³³), as a catalytic material,³⁴ as an electrode in super-capacitors when hydrated,³⁵ as well as due to its interesting magnetic properties.^36,37 However, neither experimental nor theoretical data on its mechanical properties or lattice vibrations are reported in literature.

Fig. 1 The crystal structure of (a) the ambient-pressure phase of Co₃P₂O₈, and (b) the high-pressure phase of Co₃P₂O₈. The CoO₅ and CoO₆ polyhedra are shown in blue and the VO₄ tetrahedra are shown in grey. The red circles represent the oxygen atoms. The unit-cell is represented with black solid lines.

To understand the properties and HP behaviour of Co₃P₂O₈, we have performed a combined in situ HP powered X-ray diffraction (XRD) measurements as well as density-functional theory (DFT) calculations. A structural phase transition was discovered at 2.90(5) GPa, and the crystal structure of the new phase has been determined. Compressibility, elastic constants and bulk moduli for both ambient and high-pressure phases were obtained experimentally and theoretically. The frequencies and assignments of Raman- and infrared-active modes for both ambient and high-pressure phases have been calculated, and to our believes these are being reported for the first time.

II. Materials and methods

Co₃P₂O₈ was prepared by a multistep reaction of Co₃O₄ (Alfa Aesar, 99.9%) and (NH₄)₂HPO₄ (Thomas Baker, 99.5%). All the reactants were used as received. The weighed quantities of the reactants were thoroughly mixed and heated at 300 °C on a hotplate using a platinum crucible. The mixture was heated until the complete melting and decomposition of (NH₄)₂HPO₄ was ensured. Once cooled, the solidified mass was then homogenized, pressed into pellet and then heated at 750 °C for 12 h. This step was repeated after homogenization of the product. Further the sample was crushed and pressed to pellet and heated at 900 °C for 5 h. All the heat treatments were carried out in air using a platinum boat as sample holder. A crystalline single phase monoclinic Co₃P₂O₈ was confirmed from powder XRD measurements of the sample. The ambient pressure unit-cell parameters observed from the powder XRD data are: a₀ = 5.0629(5) Å, b₀ = 8.3611(8) Å, c₀ = 8.7882(8) Å, and β₀ = 121.0(5)°, and they agree with crystal structure reported in literature.^24,30

High-pressure angle-dispersive powder XRD experiments were performed at ambient temperature at the Materials Science and Powder Diffraction beamline (BL04-MSPD) of ALBA synchrotron.³⁸ We employed a membrane-type diamond-anvil cell (DAC) with diamond culets of 500 μm in diameter. A 200 μm thick Inconel gasket, pre-indented to a thickness of 50 μm, with a 250-μm diameter hole drilled in the center was used as the pressure chamber. A mixture of methanol–ethanol–water (16 : 3 : 1) was used as the pressure-transmitting medium (PTM). This PTM remains quasi-hydrostatic up to 10 GPa,³⁹ but it has been successfully used to study high pressure behavior of oxides up to significantly higher pressure than that of the present study.⁴⁰ A Cu grain was loaded next to the sample in DAC to use as pressure marker. Pressure at the sample was determined from the position of the Cu 111 reflection in the XRD pattern and the equation of state (EOS) for Cu reported by Dewaele et al.⁴¹ During the process of sample loading, great attention was given to ensure that only a minor portion of the pressure chamber was occupied by the loaded sample and Cu. This was done to minimize the likelihood bridging between sample and diamond anvils. For HP XRD, a monochromatic X-ray beam of wavelength 0.4642 Å focused down to a spot size of 20 × 20 μm (full-width-at-half-maximum) and collimated with a pinhole. XRD images were collected on a two-dimensional Rayonix SX165 CCD detector. The two-dimensional diffraction images were integrated using DIOPTAS.⁴² Rietveld refinements were performed using FullProf software package.⁴³

Total-energy ab initio simulations were performed within the framework of density-functional theory, DFT,⁴⁴ with the Vienna ab initio Simulation Package, VASP.^45,46 In this study we utilized projector augmented-wave (PAW) pseudopotentials^47,48 and extended the plane-wave kinetic cut-off up to 540 eV to guarantee highly converged outcomes. The integrations over the Brillouin zone, BZ, were carried out with k-special points samplings (6 × 4 × 4 and 4 × 6 × 6 grids for the low- and high-pressure phases, respectively). The exchange–correlation energy was described by means of the generalized-gradient approximation, GGA, with the Armiento and Mattsson, AM05, prescription.⁴⁹ To treat the strongly correlated states appropriately, the DFT+U method of Dudarev et al.⁵⁰ was employed. This method utilizes a single parameter, U_eff = U − J, where U and J are the effective on-site Coulomb and exchange parameters, respectively. The value of U_eff for the Co atoms used was 3.32 eV.⁵¹ In the present study, the antiferromagnetic configuration was found to be the lower energy one. The unit-cell parameters and the atomic positions were fully optimized to obtain the relaxed structure at selected volumes. The criteria imposed for the optimization process were that the forces on the atoms should be smaller than 0.003 eV Å⁻¹ and the deviations of the stress tensors from a diagonal hydrostatic form were smaller than 0.1 GPa. In this manner, the simulations provide a data set of volumes, energies, and pressures (from the stress tensor). These were fitted with a third-order Birch–Murnaghan equation of state⁵² to obtain theoretical equilibrium volume, bulk modulus and its pressure derivative. Lattice-dynamic calculations of the phonon modes were carried out at the zone centre (Γ point) of the BZ with the direct force-constant approach.⁵³ These calculations give the frequencies of the normal modes, their symmetries, and their polarization vectors. This allows the identification of the irreducible representations and the character of the phonon modes at the Γ-point. A 2 × 2 × 2 supercell was used to obtain the phonon dispersion and to check the dynamical stability of the analysed structures. Mechanical properties were studied from the calculations of the elastic constants using the stress–strain methodology implemented in VASP using the Le Page⁵⁴ methodology. From these elastic constants, we derived the different elastic moduli and analyzed the mechanical stability.

III. Results and discussion

A. XRD experiments

We performed two HP XRD experiments, one up to 20.60(5) GPa (experiment 1) and the another (experiment 2) only up to 4.60(5) GPa. In the first experiment we observed the onset of a phase transition at 2.90(5) GPa. The second experiment was performed only up to pressures slightly above the transition pressure to confirm the results of the first experiment and to collect more data for the EOS determination of the low-pressure phase. In experiment 2, the transition pressure was 2.85(5) GPa, which agrees with the first experiment. In Fig. 2, we present a selection of HP XRD patterns recorded in the first experiment at different pressure conditions. In the figure, it can be seen that XRD patterns at 0.30(5) and 2.20(5) GPa agree well with a crystal structure (low-pressure, LP) isomorphic to that of the farringtonite-type phase. Rietveld refinement plots are included to support this statement. The goodness of fit parameters for the experiment performed at 0.30(5) GPa are R_p = 2.85%, R_wp = 3.62%, and χ² = 1.24. Similar values were obtained for the low-pressure phase in both experiments at different pressures confirming the correctness of the structural model. The refined crystal structure parameters at 0.15(5) GPa are given in Table 1, and the corresponding CIF file can be downloaded from the Cambridge Crystallographic Data Centre (CCDC), using the deposition number 2354014. The present observed crystal structure is very similar to the structure of Co₃P₂O₈ reported at ambient conditions^24,30 with only small changes in lattice parameters and atomic positions. Relevant bond distances in the structure are given in Table 1. They agree with those previously reported in the literature^24,30 at ambient conditions.

Fig. 2 Rietveld refinement profiles of powder XRD patterns measured in Co₃P₂O₈ at selected pressures shown in the figure. Pressures are given in the figure with the uncertainties given between brackets. The black circles are the experimental data, and the red (black) lines are the refinements (residuals). Vertical black (red) ticks are the calculated positions of the reflections of the low(high)-pressure phase. The Cu peaks used to measure pressure are indicated. Black (red) asterisks are the peaks of the low(high)-pressure phase discussed in the text.

Table 1 Experimental unit-cell parameters, atomic positions, and bond-distances (in Å) of the low-pressure phase of Co₃P₂O₈ at 0.15(5) GPa. CCDC 2354014

a = 5.0635(1) Å, b = 8.3594(2) Å, c = 8.7865(2) Å, and β = 121.05(2)°
Atom	Site	x	y	z
P–O2 = 1.542(5), P–O1 = 1.545(9), P–O4 = 1.547(4), and P–O3 = 1.567(4). Co1–O2 = 1.976(6), Co1–O4 = 1.979(9), Co1–O4 = 1.983(5), Co1–O3 = 2.023(9), and Co1–O1 = 2.207(6). Co2–O2 = 2.143(4) (x2), Co2–O1 = 2.044(8) (x2), and Co2–O3 = 2.153(4) (x2).
Co1	4e	0.5169(4)	0.8589(4)	0.6119(10)
Co2	2b	0.5	0	0
P	4e	0.8385(2)	0.1940(2)	0.8006(2)
O1	4e	0.7687(9)	0.1424(9)	−0.0549(9)
O2	4e	0.1882(9)	0.1956(4)	0.8739(4)
O3	4e	0.6875(4)	0.3637(4)	0.7419(4)
O4	4e	0.6888(4)	0.0775 (5)	0.6410(4)

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In experiments 1 and 2, we detected the appearance of extra diffraction peaks at 2.90(5) GPa and 2.85(5) GPa, respectively. This can be seen in Fig. 2 which depicts the data from experiment 1. Some of the more prominent additional peaks are marked with red asterisks in Fig. 2. In the same figure at 2.90(5) GPa we identify with black asterisks peaks that undoubtedly belong to the low-pressure phase. We associated the appearance of extra peaks as the onset of a structural phase transition. As pressure was increased, we found that the peaks of the low-pressure phase became weaker, and the peaks of the high-pressure phase became stronger. However, there are peaks of the low-pressure phase that can be identified up to 10.3(1) GPa. They are denoted by black asterisk in Fig. 2. The peaks of the low-pressure phase completely disappear at 10.5(1) GPa supporting the completion of the phase transition. We believe the coexistence of the low-pressure and high-pressure phase might be connected to a kinetic barrier similar to that observed in the related phosphate, LiNiPO₄.⁵⁵ As we will describe below, the reported phase transition is reconstructive involving the modification of primary chemical bonds. Consequently, the phase transformation needs to overcome an energy barrier (the kinetic barrier) which makes the transition slow and favours the coexistence of the low- and high-pressure phases. The phase coexistence is not due to non-hydrostatic conditions or pressure gradients because in this pressure range the conditions are quasi-hydrostatic.³⁹ This argument is consistent with the fact that there is no significant peak broadening in the XRD experiment under HP.

For the structural assignation of the HP phase, we first indexed the XRD pattern measured at 10.5(1) GPa using DICVOL⁵⁶ and then assigned the symmetry. It is found that the space group P2₁/c gives the best figure of merit, and that the unit-cell parameters determined after indexation resembled those of the metastable olivine-type Co₃P₂O₈ reported by Berthet et al. which is isostructural to chopinite.²⁷ Then, we refined the atomic positions by Rietveld refinement method using atomic positions reported by Berthet et al.²⁷ as initial position coordinates. Fig. 2 shows the Rietveld refinement plot for the XRD data obtained at 10.5(1) GPa. The refined structure gives small residuals and goodness-of-fit parameters, R_p = 2.85%, R_wp = 4.44%, and χ² = 1.57. The unit-cell parameters and atomic position determined at 10.5(1) GPa are summarized in Table 2. This table also include bond distances which are similar to those reported at ambient pressure in the literature.²⁷ The CIF file can be downloaded from CCDC under deposition number 2355641. The crystal structure of the HP phase is shown in Fig. 1b. In the structure of HP phase, all the Co atoms are in octahedral coordination. The relevant bond distances are given in Table 2. XRD patterns measured upon further compression can be fitted with the same structural model as shown in Fig. 2 for the measurement at 20.5(2) GPa. After decompression, at the lowest pressure, the recovered sample contained both the HP and LP phases, supporting the hypothesis that the transition might be hindered by a kinetic barrier.⁵⁷

Table 2 Experimental unit-cell parameters, atomic positions, and bond-distances (in Å) of the HP phase of Co₃P₂O₈ at 10.50(5) GPa. CCDC 2355641

a = 5.7858(1) Å, b = 4.7475(2) Å, c = 9.9344(2) Å, and β = 91.72(2)°
Atom	Site	x	y	z
P–O2 = 1.528(17), P–O3 = 1.536(13), P–O1 = 1.557(9), and P–O4 = 1.586(12). Co1–O1 = 2.055(11) (x2), Co1–O4 = 2.077(13) (x2), and Co1–O2 = 2.093(9) (x2). Co2–O3 = 1.975(11), Co2–O2 = 2.037(16), Co2–O4 = 2.056(11), Co2–O1 = 2.061(16), Co2–O3 = 2.072(12), and Co2–O4 = 2.219(13).
Co1	2b	0.5	0	0
Co2	4e	0.7616(9)	0.5143(9)	0.2279(9)
P	4e	0.7471(9)	0.0753(9)	0.4058(9)
O1	4e	0.7316(15)	0.7481(15)	0.4013(15)
O2	4e	0.7493(15)	0.3057(15)	0.0487(15)
O3	4e	−0.0544(15)	0.1932(15)	0.3233(15)
O4	4e	0.5296(15)	0.2281(15)	0.3377(15)

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The observed phase transition involves a structural reorganization and an abrupt decrease of the unit-cell volume, as discussed below. These observations suggest the phase transformation is a first-order reconstructive phase transition. An important structural change in the phase transformation is related to the coordination number of Co atoms. The low-pressure phase the Co1O₆ octahedra and Co2O₅ units share edges to form a zig-zag –Co1O₅–Co2O₆–Co1O₅– chain. In contrast, the high-pressure phase has a closely similar framework formed by edge sharing Co2O₆–Co1O₆–Co2O₆ octahedral chains. The presence of penta-coordinated Co ions near a vacant coordination site is conducive to the formation of additional Co–O bonds at relatively low compression, thereby favouring the observed phase transition. The high-pressure phase is an olivine-type structure with ordered vacancies. The structure can be seen as a monoclinic distortion of orthorhombic Co₂Li₂P₂O₈ (space group Pnma),⁵⁸ where the two Li atoms are substituted by one cobalt atom and a vacancy, forming [Co₃□]P₂O₈. The presence of ordered vacancies favors tilting of CoO₆ octahedra which triggers the reduction of symmetry of the crystal structure. In fact, the HP chopinite-type structure can be obtained by a group–subgroup transformation from the structure of Co₂Li₂P₂O₈ by letting the β angle deviate from 90°. The occurrence of the observed phase transition is consistent with the fact that chopinite has been found as a HP polymorph of Mg-dominant farringtonite in meteoritic minerals found in Antarctica.²³

From the Rietveld refinements of the XRD patterns acquired on sample compression, we determined the pressure dependence of the unit-cell parameters. The pressure dependence of the unit-cell parameters is presented in Fig. 3. In the figure, we also show the results from density functional theory (DFT) calculations for comparison. DFT calculated results agree quite well with experiments for the LP phase. For the HP phase the calculated data show slightly underestimated lattice parameters a, b, and c while a slightly overestimated angle β. As a consequence, the volume is underestimated by 3% in DFT simulations. This difference is typical of DFT calculations performed within the GGA approximation as it is related to the approximation used to describe the exchange–correlation energy. Such differences are also observed in the elastic constants. The causes for such differences have historically been discussed in the literature.^59,60 In the LP phase the parameter a follows a non-linear behaviour, decreasing up to around 3 GPa (i.e., the transition pressure) and then increasing with pressure. The other two parameters have a similar compressibility, and the angle β increases with pressure enhancing the monoclinic distortion of the structure. In the HP phase, a, b, and c have a similar compressibility and β increases with pressure. Regarding the pressure dependence of the volume, in both phases we found that it can be described by a third-order Birch–Murnaghan equation of state (BM EOS).⁵² According to the fits shown in Fig. 3, for the LP phase the experimental unit-cell volume at zero pressure, bulk modulus, and its pressure derivative are: V₀ = 319.3(2) ų, B₀ = 75(2) GPa, and B′₀ = 2.1(3), respectively, while the corresponding values for the HP phase are: V₀ = 299.4(2) Å, B₀ = 92(2) GPa and B′₀ = 4.2(2). The increase in B₀ and B₀′ after the phase transition indicates a decrease of the compressibility, which is consistent with the abrupt decrease of the volume by 6.5%, which makes the HP phase denser than the LP phase. The discontinuity of the volume at the phase transition is consistent with a first-order nature for the transition and consistent with coexistence of both LP and HP phases in wider pressure range. The bulk modulus we report for LP Co₃P₂O₈ (farringtonite-type) is similar to that of α-Ca₃P₂O₈ (B₀ = 79(2) GPa and B′₀ = 4).⁶¹ The bulk modulus of HP Co₃P₂O₈ (chopinite-type) is similar to that reported recently for isostructural Mg₃P₂O₈ (B₀ = 82(2) GPa and B′₀ = 4),⁶² Sr₃P₂O₈ (B₀ = 89(2) GPa and B′₀ = 6.6(3)),⁶³ and olivine-type LiNiPO₄ (B₀ = 88(2) GPa and B′₀ = 3.5(5)).⁵⁵ Among related phosphates, only compounds where one of the cations is potassium are more compressible, such as K₂Ce(PO₄)₂ (B₀ = 52(3) GPa and B′₀ = 5.7(6)).⁶⁴ This is because of the relative weakness of K–O bonds which exhibit significant compressibility under pressure.

Fig. 3 Pressure dependence of the unit-cell parameters a, b, c, and β and volume, for both the LP and HP phases of Co₃P₂O₈. Empty circles (squares) are from experiment 1 (2). The black triangles are the results at ambient conditions. Black (red) colour is used for the LP (HP) phase. The solid lines are the results from DFT simulations, and the dashed blue lines are the equations of state fitted to the experimental data described in the text. The associated errors are smaller than symbols.

B. DFT calculations

In Fig. 4 we present the enthalpy versus pressure, and energy versus volume (inset) for the LP and HP phases of Co₃P₂O₈. The calculations show that LP farringtonite-type Co₃P₂O₈ is the structure with the lowest energy and lowest enthalpy at 0 GPa. Thus, the farringtonite-type structure is the thermodynamically most favourable structure of Co₃P₂O₈. As pressure increases, the volume decreases, and beyond 2.1 GPa, the HP chopinite-type structure becomes the most stable structure for Co₃P₂O₈. These results support the occurrence of a structural phase transition at 2.1 GPa in agreement with experiments. From calculations we determined the EOS parameters for both phases as: V₀ = 318.4(2) ų, B₀ = 78(2) GPa, and B′₀ = 2.0(3) (for low-pressure phase) and V₀ = 286.9(2) ų, B₀ = 91(1) GPa, and B′₀ = 4.2(2) (for high-pressure phase). The values of the bulk moduli and their pressure derivatives are also consistent with those extracted from experiments.

Fig. 4 (a) DFT calculated enthalpy vs. pressure for the low-pressure (black) and high-pressure (red) phases of Co₃P₂O₈. The vertical blue dashed line shows the pressure where the enthalpy curves cross intersect. (b) DFT calculated energy vs. volume for the same phases. To identify phases in (b), we have used the same colour code than in (a).

Our calculations also support the mechanical and dynamical stability of the two structures. Tables 3 and 4 show the calculated elastic constants for both structures. All the eigenvalues of both elastic tensors are positive indicating elastic stability of both phases. The obtained constants also fulfil the Born criteria⁶⁵ and confirm that the structures are mechanically stable. From the elastic constants, we have calculated the elastic moduli using the average between the values obtained with the Hill and Reuss approximations.⁶⁶ The obtained bulk moduli for the low-pressure (80.6 GPa) and high-pressure phases (100.7 GPa) agree with the values obtained from experiments and total-energy calculations. The Young's modulus, in the low(high)-pressure phase is 12% (20%) larger than the bulk modulus, indicating that in both phases the tensile and compressive stiffness when the force is applied lengthwise is larger than their resistance to bulk compression. We also found that in both phases the shear modulus is considerably smaller than the bulk modulus indicating that shear deformations are favoured over volume contraction, making both phases of Co₃P₂O₈ susceptible to large non-hydrostatic stresses.⁶⁷ In addition, according to the B/G ratio (>1.75), we can postulate that the two phases of Co₃P₂O₈ are ductile.⁶⁸ The values of the Poisson's ratio (ν) are also consistent with this conclusion.⁶⁹

Table 3 Calculated elastic constants C_ij (in GPa) for LP Co₃P₂O₈ at 0 GPa. The bulk (B), shear (G), and Young (E) moduli, Poisson's ratio (n), and B/G ratio are also included. B, G, and E are given in GPa

C ij		Property
C 11	184.5	B	80.6
C 22	129.3	G	34.4
C 33	100.6	E	90.4
C 44	39.0	ν	0.313
C 55	30.1	B/G	2.34
C 66	32.9
C 12	77.4
C 13	66.7
C 15	−2.8
C 23	40.1
C 25	3.4
C 35	−13.8
C 46	−0.7

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Table 4 Calculated elastic constants C_ij (in GPa) for HP Co₃P₂O₈ at 0 GPa. The bulk (B), shear (G), and Young (E) moduli, Poisson's ratio (n), and B/G ratio are also included. B, G, and E are given in GPa

C ij		Property
C 11	133.5	B	100.7
C 22	202.5	G	48.8
C 33	206.1	E	126.1
C 44	59.1	ν	0.291
C 55	37.8	B/G	2.06
C 66	44.9
C 12	57.1
C 13	66.1
C 15	−8.2
C 23	80.4
C 25	−17.7
C 35	−11.2
C 46	−13.6

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To conclude, we present the results of our phonon calculations. The calculated phonon dispersion of each phase is shown in Fig. 5. The phonon dispersions indicate that there are no imaginary phonon branches in the structures examined in this study. This provides evidence for the dynamic stability of the two phases of Co₃P₂O₈. We have also calculated the phonon frequencies and the symmetries for the Raman-active and infrared (IR)-active modes. The results are summarized in Table 5. Since there are no Raman or IR experiments reported for the studied materials, our results can be used as a guide for future experiments. Using group theory, the following 78 vibrational modes are predicted for both phases at the Γ point of the BZ; Γ = 18A_g + 18B_g + 21A_u + 21B_u. Of these modes, one A_u mode and two B_u modes are the acoustic modes. All of the remaining modes are optical modes. Out of the modes present, 36 can be observed in Raman spectroscopy (18A_g + 18B_g), and 39 can be observed in IR spectroscopy (20A_u + 19B_u). In the low-pressure phase, the distribution of Raman modes resembles the Raman spectra of Mg₃P₂O₈ ⁶⁹ and Ca₃P₂O₈.⁷⁰ A principal characteristic of the Raman and IR spectra of the low-pressure phase is the phonon gap from 600 to 915 cm⁻¹. This is related to the fact that modes above 915 cm⁻¹ are associated to internal vibrations of the PO₄ tetrahedron. The rest of the modes correspond mainly to lattice vibrations involving Co atoms and PO₄ tetrahedra moving as rigid units. Among the internal modes the A_g modes with frequencies of 987.7 and 1032.1 cm⁻¹ are the symmetric and asymmetric stretching modes of the PO₄ tetrahedron. Note that their frequencies are nearly the same as those observed for the equivalent modes in Mg₃P₂O₈, which are 987 and 1029 cm⁻¹ respectively.⁶⁹ This is a consequence of the fact that the PO₄ tetrahedron is nearly identical in orthophosphates. The Raman and IR spectra of the HP phase are qualitatively similar to those of the LP phase. The main difference is the decrease of the phonon gap which in the HP phase is between 625 and 880 cm⁻¹. We also notice a decrease of the frequency of the internal stretching modes, which in the HP phase are 940.4 and 1027.2 cm⁻¹. Similar decrease in frequency of these modes is found when comparing the Raman spectra of farringtonite-type and chopinite-type Mg₃P₂O₈.⁶⁹ Such decrease in the frequency of phonon modes is related to the distortion of the PO₄ tetrahedron.

Fig. 5 Phonon dispersion of (a) the low-pressure phase of Co₃P₂O₈ at 0 GPa and (b) the high-pressure phase of Co₃P₂O₈ at 5.5 GPa.

Table 5 Calculated optical phonon frequencies ω (in cm⁻¹) at the Γ point for the low-pressure phase of Co₃P₂O₈ at 0 GPa and the high-pressure phase at 5.5 GPa

Low pressure phase				High pressure phase
Raman		IR		Raman		IR
Mode	ω	Mode	ω	Mode	ω	Mode	ω
Bg	95.4	Au	83.6	Bg	111.2	Au	90.9
Ag	102.8	Bu	111.7	Ag	113.5	Bu	126.9
Ag	114.2	Au	120.0	Bg	143.5	Bu	149.1
Ag	145.1	Bu	132.7	Ag	146.4	Au	150.6
Bg	152.0	Au	148.9	Ag	159.9	Au	168.6
Ag	157.6	Bu	153.9	Bg	181.1	Bu	188.8
Bg	160.4	Au	180.1	Bg	193.9	Au	191.9
Ag	201.4	Au	186.4	Ag	200.9	Au	203.6
Bg	202.2	Bu	188.8	Ag	235.5	Bu	206.1
Bg	216.5	Bu	194.5	Bg	244.4	Au	213.6
Ag	234.9	Au	200.0	Ag	254.1	Bu	240.4
Bg	235.9	Au	219.7	Bg	265.9	Bu	253.3
Ag	267.1	Bu	234.2	Ag	291.8	Au	253.7
Ag	287.8	Au	250.7	Ag	309.5	Au	285.0
Bg	294.9	Bu	254.2	Bg	311.9	Bu	292.1
Bg	312.5	Au	272.3	Bg	333.6	Au	343.5
Bg	321.9	Bu	286.7	Ag	334.2	Bu	344.9
Ag	332.7	Au	316.9	Bg	349.9	Au	353.4
Bg	421.8	Bu	316.9	Ag	388.9	Au	356.0
Ag	431.4	Bu	329.3	Bg	397.8	Bu	358.0
Ag	461.5	Au	332.6	Ag	477.3	Bu	380.5
Bg	474.7	Bu	427.7	Bg	491.0	Au	433.7
Bg	528.6	Au	430.7	Ag	525.8	Bu	442.4
Ag	532.4	Au	485.9	Bg	534.2	Au	485.8
Ag	572.1	Bu	493.7	Ag	583.7	Bu	489.2
Bg	584.0	Bu	529.0	Bg	595.2	Au	517.6
Ag	584.3	Au	538.9	Ag	612.2	Bu	532.2
Bg	594.6	Au	564.8	Bg	626.2	Bu	553.7
Ag	919.6	Bu	572.4	Bg	885.1	Au	565.8
Bg	928.8	Bu	598.9	Ag	893.2	Au	595.4
Ag	972.6	Au	609.1	Bg	934.2	Bu	609.2
Ag	989.7	Au	916.1	Ag	940.4	Bu	881.6
Bg	1004.5	Bu	922.3	Bg	1025.5	Au	891.4
Ag	1032.1	Au	955.4	Ag	1027.2	Bu	933.7
Bg	1041.3	Bu	973.4	Ag	1041.2	Au	952.4
Bg	1079.9	Bu	988.1	Bg	1048.0	Bu	1031.0
		Au	998.2			Au	1033.9
		Bu	1014.3			Bu	1050.3
		Au	1029.4			Au	1114.1

---

IV. Conclusions

Through high-pressure X-ray diffraction experiments and density-functional theory calculations it has been concluded that Co₃P₂O₈ experiences a phase transition beyond 2.9 GPa. The crystal structure of the new high-pressure phase has been determined. The occurrence of phase transition is connected to the presence of CoO₅ trigonal bipyramids in the low-pressure phase and the formation of an additional Co–O bond induced by compression. We have also established the pressure dependence of the unit-cell parameters and a room-temperature equation of state for each phase. The obtained bulk moduli are discussed in comparison with related orthophosphates. Calculations also give the details about the elastic constants and moduli, and phonon frequencies, they may be important roles for using Co₃P₂O₈ in various applications.

Author contributions

Robin Turnbull, Josu Sánchez Martín, Akun Liang, Daniel Díaz-Anichtchenko, Catalin Popescu, K. Sandeep Rao, S. Nagabhusan Achary, and Alfonso Muñoz: investigation, writing – review & editing. Vinod Panchal: formal analysis, writing – review & editing. Daniel Errandonea: conceptualization, formal analysis, funding acquisition, investigation, project administration, writing – original draft, writing – review & editing.

Data availability

All relevant data are available from the corresponding author upon reasonable request.

Conflicts of interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

The authors thank the financial support from the Spanish Ministerio de Ciencia, Innovación y Universidades, MCIU, (https://doi.org/10.13039/501100011033) under Projects PID2022-138076NB-C41/44, and RED2022-134388-T. They also acknowledge the financial support of Generalitat Valenciana through grants PROMETEO CIPROM/2021/075 and MFA/2022/007. R. T. acknowledges funding from the Generalitat Valenciana for Postdoctoral Fellowship no. CIAPOS/2021/20. J. S.-M. acknowledges the Spanish MCIU for the PRE2020-092198 fellowship. C. P. recognizes the financial support from the Spanish Ministerio de Ciencia e Innovacion through project PID2021-125927NB-C21. This study forms part of the Advanced Materials program and is supported by MCIU with funding from European Union Next Generation EU (PRTR-C17.I1) and by the Generalitat Valenciana. The authors thanks ALBA for providing beamtime under experiment no. 2022085940.

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