High-Pressure Structural Behavior and Equation of State of Kagome Staircase Compound, Ni3V2O8

We report on high-pressure synchrotron X-ray diffraction measurements on Ni3V2O8 at room-temperature up to 23 GPa. According to this study, the ambient-pressure orthorhombic structure remains stable up to the highest pressure reached in the experiments. We have also obtained the pressure dependence of the unit-cell parameters, which reveals an anisotropic compression behavior. In addition, a room-temperature pressure–volume third-order Birch–Murnaghan equation of state has been obtained with parameters: V0 = 555.7(2) Å3, K0 = 139(3) GPa, and K0′ = 4.4(3). According to this result, Ni3V2O8 is the least compressible kagome-type vanadate. The changes of the crystal structure under compression have been related to the presence of a chain of edge-sharing NiO6 octahedral units forming kagome staircases interconnected by VO4 rigid tetrahedral units. The reported results are discussed in comparison with high-pressure X-ray diffraction results from isostructural Zn3V2O8 and density-functional theory calculations on several isostructural vanadates.


Introduction
Metal orthovanadates with formula M 3 V 2 O 8 , where M is a divalent metal, have been the focus of research in recent years, mainly because of their optical, dielectric, and magnetic properties [1][2][3][4]. These properties make the M 3 V 2 O 8 family of compounds useful in several technological applications, from photocatalytic water splitting [3] to light-emitting diodes [5] and ion batteries [6]. In addition, compounds such as Co 3 V 2 O 8 and Ni 3 V 2 O 8 have very interesting magnetic and ferroelastic properties [2], which are intimately related to the presence of kagome staircase two-dimensional (2D) magnetic layers [2]. M 3 V 2 O 8 compounds are also intriguing from a crystallographic perspective [7,8]. They share a particular type of crystal structure, which is shown schematically in Figure 1. The structure is orthorhombic (space group Cmca, No. 64) with eight formula units per unit cell. In the crystal structure, the M atoms are octahedrally coordinated by oxygen atoms (see Figure 1a). In particular, the MO 6 octahedral units exhibit an edge-sharing pattern, forming a quasi-planar kagome staircase (see Figure 1b), which, in the case of Ni 3 V 2 O 8 , results in inequivalent super-exchange interactions within the magnetic lattice [9]. Consequently, an anisotropic magnetic coupling develops in the stair-like kagome layers, leading to the emergence of multiple temperature-induced magnetic phase transitions [9]. The kagome staircases are separated by VO 4 tetrahedral units, giving the M 3 V 2 O 8 family of compounds a pseudo-two-dimensional layered characteristic, which, as discussed below, leads to an anisotropic compressional behavior when an external pressure is applied.
AVO4 orthovanadates, where A is a trivalent atom, have been extensively studied under highpressure (HP) conditions [10,11]. As a result, first-order phase transitions, involving large volume changes, have been discovered at pressures below 10 GPa (for instance, the zircon-scheelite and zirconmonazite transitions in alkaline earth vanadates [10,11]). Many of these transitions lead to interesting phenomena such as a collapse of the electronic band gap [12]. In contrast, very little effort has been dedicated to study kagome staircase orthovanadates under HP. Indeed, only two works can be found in the literature [7,9]. One of them reports powder X-ray diffraction (XRD) data on Zn3V2O8 up to 15 GPa [7]. No phase transition was detected and an anisotropic response to compression was determined. The second one reports the influence of pressure on the magnetic properties of Ni3V2O8 up to 2 Gpa [9]. Therefore, despite the interesting physics involved, the HP behavior of M3V2O8 orthovanadates is an underexplored research area.
Here, we report a study of the HP behavior of the structural properties of Ni3V2O8. The information obtained from such studies can form a foundation for future studies on the influence of pressure in physical properties, including magnetic properties. We have performed synchrotron powder XRD experiments in Ni3V2O8 up to 23 Gpa at ambient temperature, thereby obtaining information on the structural stability of compressibility of the compound. The rest of the paper is organized as follows. Section 2 is devoted to the description the experimental methods. In Section 3, the results are reported and discussed in comparison with Zn3V2O8 and other isostructural M3V2O8 vanadates. Concluding remarks are given in Section 4. Figure 1. (a) Crystal structure of Ni3V2O8. NiO6 octahedra are shown in grey and VO4 tetrahedra are in red. Small red circles are oxygen atoms. (b) Projection of the crystal structure showing VO4 tetrahedra (in red) and Ni atoms (in gray) connected to make more evident the kagome staircase framework. Three unit cells are included in (b). The unit cell is shown is black solid lines.

Materials and Methods
Powder samples of Ni3V2O8 were synthesized via a solid-state reaction starting from NiO (99.995% purity) and V2O5 (99.9% purity). The starting reagents were obtained from Alfa Aesar (Tewksbury, MA, United States). They were mixed meticulously and subsequently heated in an Al2O3 crucible in air at 800 °C for 16 h. The product was then ground and pressed into a pellet, to be afterward sintered at 900 °C for an additional 16 h. The obtained sample was finally ground manually in an agate mortar to obtain a micron size powder. In order to characterize it, we performed powder XRD measurements using a X'Pert Pro diffractometer from Panalytical (Almelo, The Netherlands) with Cu Kα1 radiation (λ = 1.5406 Å). The measurements were performed in the angular range 10° < 2θ < 70°, by continuous scanning with a step size of 0.02° and total step time of 200 s.
Angle-dispersive X-ray diffraction experiments at room-temperature and high pressure were performed at beamline I15 of the Diamond Light Source using a membrane-type diamond-anvil cell (DAC) with diamond-culet sizes of 450 μm in diameter and monochromatic X-rays of λ = 0.42466 Å. The X-ray beam was focused down to 10 × 10 μm 2 . A rocking (±10°) of the DAC was used to improve the homogeneity of the Debye rings. A fine powder of Ni3V2O8 was loaded in a 150 μm hole of a rhenium gasket pre-indented to a 40 μm thickness. One grain of Cu was loaded together with the

Materials and Methods
Powder samples of Ni 3 V 2 O 8 were synthesized via a solid-state reaction starting from NiO (99.995% purity) and V 2 O 5 (99.9% purity). The starting reagents were obtained from Alfa Aesar (Tewksbury, MA, United States). They were mixed meticulously and subsequently heated in an Al 2 O 3 crucible in air at 800 • C for 16 h. The product was then ground and pressed into a pellet, to be afterward sintered at 900 • C for an additional 16 h. The obtained sample was finally ground manually in an agate mortar to obtain a micron size powder. In order to characterize it, we performed powder XRD measurements using a X'Pert Pro diffractometer from Panalytical (Almelo, The Netherlands) with Cu K α1 radiation (λ = 1.5406 Å). The measurements were performed in the angular range 10 • < 2θ < 70 • , by continuous scanning with a step size of 0.02 • and total step time of 200 s.
Angle-dispersive X-ray diffraction experiments at room-temperature and high pressure were performed at beamline I15 of the Diamond Light Source using a membrane-type diamond-anvil cell (DAC) with diamond-culet sizes of 450 µm in diameter and monochromatic X-rays of λ = 0.42466 Å. The X-ray beam was focused down to 10 × 10 µm 2 . A rocking (±10 • ) of the DAC was used to improve the Crystals 2020, 10, 910 3 of 11 homogeneity of the Debye rings. A fine powder of Ni 3 V 2 O 8 was loaded in a 150 µm hole of a rhenium gasket pre-indented to a 40 µm thickness. One grain of Cu was loaded together with the sample and used as internal standard for pressure determination. For this purpose, we used the equation of state (EOS) determined by Dewaele et al. under hydrostatic conditions [13]. A 16:3:1 methanol-ethanol-water (MEW) mixture was used as a pressure-transmitting medium [14,15]. The powder XRD patterns were collected using a Pilatus 2M detector (DECTRIS, Baden, Switzerland) and transformed into one-dimensional patterns using the DIOPTAS suite [16]. The sample-to-detector distance was measured following standard procedure from the diffraction rings of LaB 6 .

Results and Discussion
The results of the ambient-conditions XRD measurements are shown in Figure 2. All of the observed reflections can be accounted for by the orthorhombic crystal structure reported in the literature (space group Cmca, No. 64) [17], leading to small residuals (see Figure 2) and converging to small R-factors: R p = 2.39% and R WP = 3.79%. The resulting unit-cell parameters were a = 5.928(4) Å, b = 11.384(6) Å, and c = 8.241(5) Å, which agree to within 0.1% of literature values [17]. The obtained atomic positions are reported in Table 1, being also in good agreement with the literature [17].  [13]. A 16:3:1 methanol-ethanol-water (MEW) mixture was used as a pressure-transmitting medium [14,15]. The powder XRD patterns were collected using a Pilatus 2M detector (DECTRIS, Baden, Switzerland) and transformed into one-dimensional patterns using the DIOPTAS suite [16]. The sample-to-detector distance was measured following standard procedure from the diffraction rings of LaB6.

Results and Discussion
The results of the ambient-conditions XRD measurements are shown in Figure 2. All of the observed reflections can be accounted for by the orthorhombic crystal structure reported in the literature (space group Cmca, No. 64) [17], leading to small residuals (see Figure 2) and converging to small R-factors: Rp = 2.39% and RWP = 3.79%. The resulting unit-cell parameters were a = 5.928(4) Å, b = 11.384(6) Å, and c = 8.241(5) Å, which agree to within 0.1% of literature values [17]. The obtained atomic positions are reported in Table 1, being also in good agreement with the literature [17].     Figure 3, it can be seen that over the complete pressure range of the experiments, all the reflections can be assigned to the known orthorhombic structure of Ni 3 V 2 O 8 and to Cu (the pressure marker), which is supported by a profile matching analysis using the Le Bail method. Therefore, no phase transition is observed in Ni 3 V 2 O 8 up to 23 GPa. More details of the HP X-ray patterns can be seen in Figures 4 and 5. Figure 4 shows results for P ≤ 7 GPa and Figure 5 shows results from 7.6 to 23 GPa. Beyond 20 GPa, we detected the presence of one extra reflection originating from the Re gasket, which appears because of the reduction in the size of the sample chamber. The data in Figures 3 and 4 show a change of relative peak intensities under increasing compression. This is related to the development of preferred crystallite orientation relative to the X-ray beam. Under compression, we also observe that the position of peaks indexed as 0k0 is less sensitive to pressure, and that they move less towards higher angles than the rest of the peaks. This can be observed in Figure 4 by comparing the pressure evolution of peaks identified with planes (131) and (040), since the (131) peak approaches the stationary (040) peak. As we will discuss below, this observation is rooted in the non-isotropic behavior of Ni 3 V 2 O 8 . Another consequence of the anisotropic behavior is the gradual merging of peaks; for instance, those identified with planes (221) and (023). Their merging under compression can be seen in Figure 3, Figure 4, and Figure 5. In addition, beyond 7.6 GPa, we have observed a gradual broadening of the peaks ( Figure 5), which is related to the gradual loss of quasi-hydrostaticity [15,18].
Crystals 2020, 10, 910 4 of 11 Figures 3,4, and 5 show sequential integrated XRD patterns acquired up to 23 GPa on compression of Ni3V2O8. In Figure 3, it can be seen that over the complete pressure range of the experiments, all the reflections can be assigned to the known orthorhombic structure of Ni3V2O8 and to Cu (the pressure marker), which is supported by a profile matching analysis using the Le Bail method. Therefore, no phase transition is observed in Ni3V2O8 up to 23 GPa. More details of the HP Xray patterns can be seen in Figure 4 and Figure 5. Figure 4 shows results for P ≤ 7 GPa and Figure 5 shows results from 7.6 to 23 GPa. Beyond 20 GPa, we detected the presence of one extra reflection originating from the Re gasket, which appears because of the reduction in the size of the sample chamber. The data in Figures 3 and 4 show a change of relative peak intensities under increasing compression. This is related to the development of preferred crystallite orientation relative to the Xray beam. Under compression, we also observe that the position of peaks indexed as 0k0 is less sensitive to pressure, and that they move less towards higher angles than the rest of the peaks. This can be observed in Figure 4 by comparing the pressure evolution of peaks identified with planes (131) and (040), since the (131) peak approaches the stationary (040) peak. As we will discuss below, this observation is rooted in the non-isotropic behavior of Ni3V2O8. Another consequence of the anisotropic behavior is the gradual merging of peaks; for instance, those identified with planes (221) and (023). Their merging under compression can be seen in Figures 3, 4, and 5. In addition, beyond 7.6 GPa, we have observed a gradual broadening of the peaks ( Figure 5), which is related to the gradual loss of quasi-hydrostaticity [15,18].  shown with black lines. The difference between the observed data and Le Bail refinement is shown in green. Ticks indicate the positions of Ni3V2O8 peaks. Through performing Le Bail refinements of the powder XRD patterns, we have obtained the pressure dependence of the unit-cell parameters. The XRD patterns at all pressures can be identified with the ambient-pressure orthorhombic structure of Ni3V2O8; however, the XRD patterns measured at pressures higher than 15.1 GPa have been excluded from this analysis due to the partial overlap of the Cu peak used to determine pressure with a diffraction peak from the sample (see Figure 5), because this could lead to inaccuracies in the pressure determination larger than 0.2 GPa. The unit-cell parameters as a function of pressure are shown in Figure 6. This information is important for modeling Through performing Le Bail refinements of the powder XRD patterns, we have obtained the pressure dependence of the unit-cell parameters. The XRD patterns at all pressures can be identified with the ambient-pressure orthorhombic structure of Ni 3 V 2 O 8 ; however, the XRD patterns measured at pressures higher than 15.1 GPa have been excluded from this analysis due to the partial overlap of the Cu peak used to determine pressure with a diffraction peak from the sample (see Figure 5), because this could lead to inaccuracies in the pressure determination larger than 0.2 GPa. The unit-cell parameters as a function of pressure are shown in Figure 6. This information is important for modeling the suppression of ferroelectricity by pressure in Ni 3 V 2 O 8 [9]. The response of the crystal structure to compression is clearly non-isotropic, with the b and a axes, respectively, having the smallest and largest compressibility. The anisotropic compressibility observed Ni 3 V 2 O 8 is fully compatible with the anisotropic thermal expansion of the same compound [9]. Both results can be rationalized based on the layered characteristic of the kagome staircase in the crystal structure and the relative compressibilities of the constituent polyhedra, as discussed below. the suppression of ferroelectricity by pressure in Ni3V2O8 [9]. The response of the crystal structure to compression is clearly non-isotropic, with the b and a axes, respectively, having the smallest and largest compressibility. The anisotropic compressibility observed Ni3V2O8 is fully compatible with the anisotropic thermal expansion of the same compound [9]. Both results can be rationalized based on the layered characteristic of the kagome staircase in the crystal structure and the relative compressibilities of the constituent polyhedra, as discussed below.  Table 2, where it can be seen that they increase  Table 2, where it can be seen that they increase following the sequence κ b < κ c < κ a . The a and c-axes have larger compressibilities than the b-axis by approximate factors of 1.5 and 1.3, respectively. A similar behavior has previously been observed in Zn 3 V 2 O 8 .
following the sequence b < c < a. The a and c-axes have larger compressibilities than the b-axis by approximate factors of 1.5 and 1.3, respectively. A similar behavior has previously been observed in Zn3V2O8. The reason for the anisotropic behavior of Ni3V2O8 and Zn3V2O8 (and probably all isomorphic vanadates) might be related to the kagome layered characteristic of the crystal structure. It is wellknown that in other ternary oxides, such as NiWO4 and ZnWO4 [19], the pressure-induced changes in crystal structure are largely determined by the NiO6 and ZnO6 octahedral units because of their large compressibility relative to the VO4 tetrahedron. The much smaller VO4 tetrahedron has been determined from the study of many different vanadates to be an essentially rigid unit, which, due to V 3d -O 2p hybridization [20], changes little under compression [10]. As we have already described (see Figure 1), the crystal structure of M3V2O8 compounds is composed of 2D kagome staircases of compressible MO6 octahedra, which therefore constitute compressible layers that lie perpendicular to the b-axis. In between these layers of NiO6 and ZnO6 octahedra, there are located the less compressible VO4 tetrahedra, which are arranged to form pillars between the kagome layers, reducing the compressibility along the b-axis. In fact, the in-plane effective bulk modulus [21] for kagome layers is 132 GPa, and the effective bulk modulus in the perpendicular direction is 186 GPa. Thus, the layered characteristic of the crystal structure of kagome-type vanadates provides a rational explanation to their anisotropic behavior under compression. The present results suggest that it is not unreasonable to speculate that anisotropic compressibility would be a finger print of the broad family of kagome-type compounds. Such anisotropic behavior is expected to affect super-exchange interactions between magnetic atoms, thereby modifying the temperature of different magnetic transitions. This would modify the Néel temperature as reported for Ni3V2O8 [9]. By extrapolating the result reported by Chaudhury et al. [9], it can be speculated that under compression the Néel temperature can be increased from 9.8 K at ambient pressure to a temperature close to 15 K at 20 GPa. The reason for the anisotropic behavior of Ni 3 V 2 O 8 and Zn 3 V 2 O 8 (and probably all isomorphic vanadates) might be related to the kagome layered characteristic of the crystal structure. It is well-known that in other ternary oxides, such as NiWO 4 and ZnWO 4 [19], the pressure-induced changes in crystal structure are largely determined by the NiO 6 and ZnO 6 octahedral units because of their large compressibility relative to the VO 4 tetrahedron. The much smaller VO 4 tetrahedron has been determined from the study of many different vanadates to be an essentially rigid unit, which, due to V 3d -O 2p hybridization [20], changes little under compression [10]. As we have already described (see Figure 1), the crystal structure of M 3 V 2 O 8 compounds is composed of 2D kagome staircases of compressible MO 6 octahedra, which therefore constitute compressible layers that lie perpendicular to the b-axis. In between these layers of NiO 6 and ZnO 6 octahedra, there are located the less compressible VO 4 tetrahedra, which are arranged to form pillars between the kagome layers, reducing the compressibility along the b-axis. In fact, the in-plane effective bulk modulus [21] for kagome layers is 132 GPa, and the effective bulk modulus in the perpendicular direction is 186 GPa. Thus, the layered characteristic of the crystal structure of kagome-type vanadates provides a rational explanation to their anisotropic behavior under compression. The present results suggest that it is not unreasonable to speculate that anisotropic compressibility would be a finger print of the broad family of kagome-type compounds. Such anisotropic behavior is expected to affect super-exchange interactions between magnetic atoms, thereby modifying the temperature of different magnetic transitions. This would modify the Néel temperature as reported for Ni 3 V 2 O 8 [9]. By extrapolating the result reported by Chaudhury et al. [9], it can be speculated that under compression the Néel temperature can be increased from 9.8 K at ambient pressure to a temperature close to 15 K at 20 GPa. Table 2. Linear compressibilities at zero pressure (left) and room-temperature equation of state (EOS) parameters of Ni 3 V 2 O 8 . The center (right) column shows the converged fitting parameters for the third-order Birch-Murnaghan EOS for P ≤ 7.6 (15.1) GPa. V 0 is the ambient-pressure volume. K 0 is the bulk modulus. K 0 is the pressure derivative of the bulk modulus.
The unit-cell volume of Ni 3 V 2 O 8 as a function of pressure is shown in Figure 7. The results show an apparent change in compressibility at 7.6 GPa, which cannot be related to a phase transition, since the XRD data provide no evidence for it up to the maximum pressure investigated (23 GPa). A similar behavior has been recently reported in other ternary oxides near this pressure [22]. The apparent change in compressibility is in fact related to the known hydrostatic limit for MEW [15]. Fitting a third-order Birch-Murnaghan (BM) EOS [23] (using EosFit [24]) in the hydrostatic regime (P ≤ 7.6 GPa) gives the parameters given in the central column of Table 2. To illustrate the importance of constraining EOS fits to hydrostatic data, for comparison, we also fitted the EOS with all data up to 15.1 GPa, leading to the values given in the right column of Table 2. The inclusion of non-hydrostatic data leads to an underestimation of the ambient pressure bulk modulus (K 0 ) and to an unusual large pressure derivative (K 0 = 11.1(9)).  The unit-cell volume of Ni3V2O8 as a function of pressure is shown in Figure 7. The results show an apparent change in compressibility at 7.6 GPa, which cannot be related to a phase transition, since the XRD data provide no evidence for it up to the maximum pressure investigated (23 GPa). A similar behavior has been recently reported in other ternary oxides near this pressure [22]. The apparent change in compressibility is in fact related to the known hydrostatic limit for MEW [15]. Fitting a thirdorder Birch-Murnaghan (BM) EOS [23] (using EosFit [24]) in the hydrostatic regime (P ≤ 7.6 GPa) gives the parameters given in the central column of Table 2. To illustrate the importance of constraining EOS fits to hydrostatic data, for comparison, we also fitted the EOS with all data up to 15.1 GPa, leading to the values given in the right column of Table 2. The inclusion of non-hydrostatic data leads to an underestimation of the ambient pressure bulk modulus (K0) and to an unusual large pressure derivative (K0′ = 11.1(9)). Where not shown, error bars are comparable to symbols' size. The black solid (red dashed) line is the equation of state obtained from data for P ≤ 7.6 (15.1) GPa. As stated in the text, results deviate from the quasi-hydrostatic EOS for P ≥ 7.6 GPa likely due to the influence of nonhydrostaticity.
We will now comment on the bulk modulus of Ni3V2O8 within the context of other M3V2O8 vanadates [25,26] using the bulk moduli summarized in Table 3. In Table 3, it can be seen that Ni3V2O8 is the most incompressible compound within M3V2O8 family of isomorphic vanadates. For the discussion, based on the fact that NiO6 units are more compressible than rigid VO4 units [10,19], we Where not shown, error bars are comparable to symbols' size. The black solid (red dashed) line is the equation of state obtained from data for P ≤ 7.6 (15.1) GPa. As stated in the text, results deviate from the quasi-hydrostatic EOS for P ≥ 7.6 GPa likely due to the influence of non-hydrostaticity.
We will now comment on the bulk modulus of Ni 3 V 2 O 8 within the context of other M 3 V 2 O 8 vanadates [25,26] using the bulk moduli summarized in Table 3. In Table 3, it can be seen that Ni 3 V 2 O 8 is the most incompressible compound within M 3 V 2 O 8 family of isomorphic vanadates. For the discussion, based on the fact that NiO 6 units are more compressible than rigid VO 4 units [10,19], we will assume