Pressure-Induced Phase Transition and Band Gap Decrease in Semiconducting β-Cu2V2O7

The understanding of the interplay between crystal structure and electronic structure in semiconductor materials is of great importance due to their potential technological applications. Pressure is an ideal external control parameter to tune the crystal structures of semiconductor materials in order to investigate their emergent piezo-electrical and optical properties. Accordingly, we investigate here the high-pressure behavior of the semiconducting antiferromagnetic material β-Cu2V2O7, finding it undergoes a pressure-induced phase transition to γ-Cu2V2O7 below 4000 atm. The pressure-induced structural and electronic evolutions are investigated by single-crystal X-ray diffraction, absorption spectroscopy and ab initio density functional theory calculations. β-Cu2V2O7 has previously been suggested as a promising photocatalyst for water splitting. Now, these new results suggest that β-Cu2V2O7 could also be of interest with regards to barocaloric effects, due to the low phase -transition pressure, in particular because it is a multiferroic material. Moreover, the phase transition involves an electronic band gap decrease of approximately 0.2 eV (from 1.93 to 1.75 eV) and a large structural volume collapse of approximately 7%.

. Of these, copper(II) pyrovanadate, Cu 2 V 2 O 7 , has been highlighted as a favorable material for the photocatalytic splitting of water into hydrogen and oxygen due to its band gap energy. 1−3 Therefore, copper vanadate materials may play an essential role in the global shift toward renewable energy sources. Cu 2 V 2 O 7 exhibits three known polymorphs, known as α, β, and γ, all of which are formed at elevated temperatures, either naturally occurring (α and β) or synthesized in the laboratory (γ), and all of which are (meta)stable at ambient conditions. 4−9 The present work investigates β-Cu 2 V 2 O 7 under highpressure conditions at ambient temperature to explore the effect of pressure on the crystal and electronic structures. β-Cu 2 V 2 O 7 has a number of interesting and useful properties; for example, β-Cu 2 V 2 O 7 is a semiconducting antiferromagnetic material which has an (indirect) electronic band gap energy of ∼2 eV, which is optimal for absorbing energy within the solar range. 10 β-Cu 2 V 2 O 7 also exhibits interesting magnetic properties, due to its spin-1/2 honeycomb lattice of Cu 2+ [3d 9 ] ions, including quasi-1D antiferromagnetism. 11−13 Finally, β-Cu 2 V 2 O 7 is also known to exhibit a negative thermal expansion at ambient pressure. 14,15 None of the Cu 2 V 2 O 7 phases has previously been studied at high pressure; therefore, an additional motivation for this high-pressure investigation is to study mechanical similarities between the negative thermal expansion and pressure-induced volume decrease.
Herein, we report an experimental high-pressure singlecrystal synchrotron X-ray diffraction (XRD) study of β-Cu 2 V 2 O 7 under compression up to 4 GPa at ambient temperature. We present unambiguous evidence of a pressure-induced first-order phase transition from the monoclinic β-phase to the triclinic γ-phase between 0.14 and 0.40 GPa. We also investigate the electronic structure via absorption spectroscopy and ab initio density functional theory calculations, in particular the optical band gap and sub-band d−d transitions associated with Cu 2+ coordination complexes, finding the phase transition to be characterized by a 0.2 eV band gap decrease and a decrease in the average crystal field strength. We also report a detailed study of the pressure evolution of both of the crystal structures, associated crystallographic parameters and physical properties, including the bulk moduli (via a pressure−volume equation of state (EoS)) and isothermal compressibility tensors of both βand γ-phases.

Sample Preparation.
Single crystals of β-Cu 2 V 2 O 7 were grown by a flux method using SrV 2 O 6 as a flux according to ref 16. A mixture of high-purity CuO, V 2 O 5 , and SrCO 3 was ground fully and evenly with ethanol (99%) in an agate mortar. The mixture was packed into a platinum crucible (40 × 40 × 45 mm 3 ) which was then placed in a homemade electric furnace. The furnace was heated up to 950°C and kept at this peak temperature for 20 h. The furnace was then cooled slowly to 750°C at a rate of 0.5°C/h. The furnace was finally cooled down to room temperature at a rate of 100°C/h. With the above growth procedure, single crystals of β-Cu 2 V 2 O 7 with a size of 3 × 3 × 5 mm 3 were obtained by mechanical separation from the crucible. Alternative synthesis methods for β-Cu 2 V 2 O 7 also exist. 2,17 2.2. Measurements. Angle-dispersive single-crystal XRD data were acquired in two ways. First, data were acquired at ALBA Synchrotron 18 (Barcelona, Spain) on the BL04 -MSPD beamline using a monochromatic beam λ = 0.4246 Å focused to a spot size of 20 × 20 μm 2 . A SX165 Rayonix Mar CCD detector was used to record the data. Second, single-crystal XRD data were collected inhouse at the University of La Laguna. CrysAlisPro 19 was used to collect, index, scale, and apply numerical absorption corrections to the data. Single-crystal diffraction measurements (SC-XRD) were carried out at room temperature using a Rigaku SuperNOVA diffractometer equipped with an EOS CCD detector and a Mo radiation microsource (λ = 0.71073 Å). All measurements were processed with the CrysAlis software version 1.171.40.71. 20 Numerical absorption correction based on Gaussian integration over a multifaceted crystal model was applied using the ABSORB7 program. 21 For HP measurements we used a Mini-Bragg DAC from Almax-EasyLab, with an opening angle of 85°and anvil culets of 500 μm diameter, fitted with a stainless-steel gasket containing a hole of 200 μm diameter and 75 μm depth. A 4:1 methanol−ethanol mixture (ME) was used as a pressuretransmitting medium. 22 The sample was placed on one of the diamonds anvils (diffracted side) together with a small ruby sphere as a pressure sensor. 23 The structure was refined, for each pressure, using previous results as starting points, on F 2 by full-matrix least-squares refinement using the SHELXL program. 24 The optical absorption spectra were acquired using the sample-in sample-out method on the in-house optical setup at the University of Valencia, consisting of a visible−near-IR spectrometer (Ocean Optics Maya2000 Pro), a tungsten filament lamp, fused silica lenses, and reflecting optical objectives. The intensity of the light transmitted through the sample (I(ω)) was normalized against the intensity of the light transmitted through the 16:3:1 methanol−ethanol−water PTM (I 0 (ω)). Single crystals of β-Cu 2 V 2 O 7 , approximately 100 × 100 × 40 μm 3 in size, were loaded into membrane-driven DACs with culet sizes of 500 μm. Tungsten gaskets were preindented to 50 μm thickness, and then sample chambers 250 μm in diameter were drilled prior to loading the crystals. Ruby crystals were included in the sample chamber for use as a pressure gauge.
Equations of state (EoS) were fitted to the volume-pressure data using EosFit7-GUI 25 whereby the EoS were constrained to secondorder (B 0 ′ = 4) Birch−Murnaghan equations. 26 The validity of the EoS fits was checked via the associated F E versus f E plots. 27 2.3. Ab Initio Density Functional Theory Calculations. The ab initio simulations were carried out within the framework of density functional theory, DFT, 28 with the Vienna ab initio Simulation Package, VASP. 29,30 The projector augmented-wave, PAW, and pseudopotentials 31,32 were employed and the plane-wave kinetic cutoff was extended up to 540 eV to ensure highly converged results. The integrations over the Brillouin zone, BZ, were carried out with kpoints special samplings (4 × 4 × 3 and 5 × 4 × 3 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. 33,34 To treat the strongly correlated states properly, the DFT+U method of Duradev et al. 35 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 used for U eff was 6.5 eV for the Cu atoms. 36,37 In the present study, the antiferromagnetic configuration was found to be the lower one in energy.
The unit cell parameters and the atomic positions were fully optimized to obtain, at selected volumes, the relaxed structure. The criteria imposed for the optimization were that the forces on the atoms were less than 0.003 eV/Å, and the deviations of the stress tensors from a diagonal hydrostatic form were lower than 0.1 GPa. In this way, the simulations provide a data set of volumes, energies, and pressures (from the stress tensor) that are fitted with a Birch− Murnaghan equation of state 26 to obtain the theoretical equilibrium volume, the Bulk modulus, and the pressure derivatives.
The k-path for the electronic band structure calculations was chosen with the SeeK-path tool. 38 The band structure analysis was carried out with the sumo package. 39

RESULTS AND DISCUSSION
3.1. Visual Observations. The pressure-induced β → γ phase transition is unambiguously confirmed by single-crystal XRD and ab initio density functional theory calculations (see the next section). Here, we begin by presenting two visual observations of the β → γ phase transition in the sample. First, the ∼2 eV band gap, which transmits light in the lower energy part of the visible spectrum (red/orange), is sensitive to pressure. In Figure 1 it is clear that the color of the Cu 2 V 2 O 7 crystal becomes darker across the β → γ phase transition, which is associated with a band gap closure of ∼0.2 eV (see "Electronic Structure" section for further details). Second, as indicated by the arrow in Figure 1b, crystal fractures were  Figure 2, and basic crystallographic information is presented in Table 1. Comprehensive crystallographic information is provided in Tables S1−S3. The crystal structures have previously been described elsewhere, determined from ambient pressure XRD measurements; 9 however, for the sake of discussion, the structures of βand γ-Cu 2 V 2 O 7 , as determined in the current work, are briefly described here.
The The structure of the γ-Cu 2 V 2 O 7 phase is shown in Figure  2b,d. The γ-Cu 2 V 2 O 7 structure has two symmetrically independent Cu 2+ cations. Half of the Cu 2+ cations are penta-coordinated in the same way as those in β-Cu 2 V 2 O 7 ; however, the other half are hexa-coordinated, thereby forming CuO 6 units with octahedral coordination configuration (shown in green in Figure 2b,d). All CuO 5 (CuO 6 ) units, share edges to form continuous 1D chains, shown in blue (green). All CuO 5 and CuO 6 chains point along the a-axis, or in the [1,0,0] direction. The chains are also organized into layers, which   Figure 2 that the crystal structures of βand γ-Cu 2 V 2 O 7 are closely related. Both structures are characterized by alternating layers of chains of CuO x units, whereby the layers are interconnected by mutually parallel V 2 O 7 units. The orientation of the V−V vectors (red) relative to the CuO 5 chains (blue) is the same in both structures (shown in Figure  1). Therefore, the β → γ phase transition can be qualitatively described by two factors: (1) an increase of coordination number, from 5 to 6, of all CuO 5 units in alternating layers and (2) a transformation of those layers (approximately by a reflection in the ac-plane) so that all CuO 6 chains become parallel to the CuO 5 chains.
Cu 2 V 2 O 7 has not been studied previously under highpressure conditions; therefore, this is the first time that the β → γ phase transition has been observed to be induced by pressure. Bearing in mind that β-Cu 2 V 2 O 7 has been found to occur naturally in fumarloic areas and that the low pressure required to induce the β → γ phase transition (<0.4 GPa) occurs naturally in the earth's crust, the present work shows that γ-Cu 2 V 2 O 7 may also occur naturally although it has not yet been discovered. The β → γ phase transition has previously been observed to be induced by high temperatures (∼700°C) at ambient pressures. 7,8 Therefore, the β → γ phase boundary must have a steep negative slope in pressure−temperature space because it can be crossed by increasing either temperature (∼700°C) or pressure (<0.4 GPa) from ambient conditions. Ab initio density functional theory (DFT) calculations of enthalpy, for the beta and gamma phases, found that the triclinic phase becomes the more stable phase at 0.1 GPa and 0 K (see Figure S1).
3.3. Electronic Structure. The optical properties, and thus the piezo-and thermochromic properties, exhibited by βand γ-Cu 2 V 2 O 7 can be explained by the optical transmission window defined by the interband charge transfer transitions (optical band gaps) and the sub-band absorption of Cu 2+ dlevels (see Figure 3). The relative variations in transition  Inorganic Chemistry pubs.acs.org/IC Article energies and oscillator strength (absorption coefficient) with temperature and/or pressure determine these properties. Therefore, understanding these properties requires a precise knowledge of how structural variations (determined via XRD) affect the electronic structure. The electronic structures of βand γ-Cu 2 V 2 O 7 were investigated via absorption spectroscopy measurements and ab initio simulations. There are two regions of interest in the adsorption spectra in Figure 3: first, on the right-hand side (above 1.8 eV), the optical band gap edges; second, on the lefthand side (below 1.8 eV), the absorption associated with d−d electronic transitions of Cu 2+ .
3.3.1. Band Structure. We first discuss the optical band gap energies. The band gap energies of βand γ-Cu 2 V 2 O 7 were experimentally determined to be 1.91 and 1.73 eV, respectively, thereby corresponding to a band gap collapse of 0.18 eV (∼9%) across the β → γ phase transition (as shown by arrow 1 in Figure 3 Figure S3. The experimental band gaps as a function of pressure up to 2.4 GPa are shown in the inset in Figure 3. Additionally, the DOS (total density of states) and the projected density of states ( Figure S4) are very similar for both phases. The upper level of the valence band is contributed to mainly by Cu-3d and O-2p states, while the O 2s states are located in the lower part of the valence band. As for the conduction band, the major contribution comes from the V 3d states.
3.3.2. Sub-Band Absorption. We now discuss the sub-band absorption (below 1.8 eV) associated with d−d electronic transitions of Cu 2+ . The broad Gaussian-shaped absorbing regions observed in the sub-band gap energy region below 1.8 eV (see Figure 3) are due to d−d electronic transitions of Cu 2+ and the transition energies can be thoroughly explained by crystal-field (CFM) and angular overlap (AOM) models. 42,43 The maxima, bandwidth, and oscillator strength of these bands strongly depend on the Cu 2+ local symmetry of the CuO 5 or CuO 6 coordination complexes. 44 Figure 3b shows schematic energy level diagrams of the elongated octahedral CuO 6 (nearly D 4h ) and elongated pyramidal CuO 5 (nearly C 4v ) complexes, and the corresponding energies as a function of the σ and π bonding AOM parameters e σ and e π for the equatorial (eq) and axial (ax) ligands. 42 The crystal-field strength scales with the bond distance in oxides as a power of 5:10Dq(R) = C/(R 5 ), where R is the bond length. This R-dependence is found from basic CF theory, 43,45,46  The derivation of eq 1 is provided in the Supporting Information. Taking the average R eq β = 1.95 Å and R eq γ = 2.01 Å from the experimental XRD data, the reduction in E(e → b 1 ) along the β → γ phase transition should be 0.86 according to the model. The experimental energy ratio between 1.41 eV (β) and 1.18 (γ) gives a ratio of 0.84 in excellent agreement with the model.
It must be noted that although R eq β and R eq γ are derived as an average of the four short Cu−O distances obtained from XRD for CuO 5 the standard deviation of such distances is below σ = 0.012 Å in the β-phase and 0.07 Å in the γ-phase. In fact, the slight double-humped band observed in both phases (Figure 3a) may be due to low-symmetry local distortion of CuO 5 beyond C 4v . This symmetry lowering would additionally split the doubly degenerate e levels into two singlets (xz, yz) yielding additional broadened bands.
In Figure 3, both sub-band absorption spectra are completely determined by the CuO 5 polyhedra because d−d transitions are, in the first approximation, parity-forbidden in centrosymmetric compounds like CuO 6 (Laporte rule), although they can occur via electron−phonon coupling, thereby contributing only weakly to the observed spectrum. An additional simplification is that the e(d xz ,d yz ) → b 1 (d x 2 −y 2 ) electric-dipole transition, which is allowed in CuO 5 , has an oscillator strength which is an order of magnitude higher than any of the other d−d transitions in CuO 5 (involving the b 2 (d xy ) and a 1 (d 3z 2 −r 2 ) levels), or in the nearly D 4h elongated CuO 6 (e g , b 2g , a 1g → b 1 ). 45,52 Therefore, only one transition is needed to explain the sub-band absorption peaks.
The sub-band absorption maxima are found at 1.41 and 1.18 eV for βand γ-Cu 2 V 2 O 7 , respectively, thereby corresponding to a decrease in the transition energy of approximately 0.23 eV across the phase transition (as indicated by arrow 2 in Figure  3). The transition energy (or d-level splitting) in CuO 5 is determined by the strength of the crystal field, which is in turn determined by the Cu−O bond lengths. The decrease in transition energy across the phase transition implies a decrease in crystal field strength and therefore an increase in Cu−O bond length. This is consistent with the Cu−O bond lengths determined from our XRD data (see Figure S5). The observed oscillator strength (absorption coefficient) largely depends on the orientation of the transition dipole, which in this case is in the basal plane of the CuO 5 polyhedra, and the electric field vector of the incident light used in the experiment. Because the γ-phase has exactly half the number of CuO 5 polyhedra of the β-phase, a drop in oscillator strength would be expected across the phase transition, however the opposite is observed (as shown by arrow 3 in Figure 3). This can be attributed to the spatial orientation of the single crystal sample relative to the incident light. It is not possible to comment on the crystallographic orientation in the absorption Inorganic Chemistry pubs.acs.org/IC Article spectra because the XRD measurements were carried out independently on different single crystal samples.

Bulk Modulus.
The β → γ phase transition is unambiguously categorized as first-order according to the plot of the normalized unit cell volume (V/Z) as a function of pressure, as shown in Figure 5a. A volume collapse of approximately 7% is observed across the phase transition in both experimental and calculated data. The normalized ambient pressure volumes, V 0 , and bulk moduli, B 0 , were determined by fitting Birch−Murnaghan (BM) equations of state (EoS) truncated to second-order in energy (B 0 ′ = 4) to the data. Due to the low phase transition pressure, only four experimental data points were obtained for β-Cu 2 V 2 O 7 . Therefore, the theoretical data (black dashed line in Figure  5a) are used for the discussion. The excellent reliability of the calculated data is clearly shown in Figure 5 (dashed lines) by the close agreement with the experimentally determined lattice parameters.
The normalized volume at ambient pressure, V 0 , and bulk modulus, B 0 , for both βand γ-Cu 2 V 2 O 7 (summarized in Figure 5a) are as follows: For the low-pressure phase, β-  Figure 5b shows the normalized stress, F E , as a function of Eulerian strain, f E . The F E versus f E plot provides assessment of the quality of the fitted EoS, whereby a zero-gradient fit to the data indicates that a second-order truncation of the BM EOS is suitable (see ref 27 for more details). as is the case for γ-Cu 2 V 2 O 7 (see Figure 5b).
3.5. Isothermal Compressibility. The isothermal compressibility tensor describes the principal axes of compression which, for any crystal system, constitute a unique set of orthogonal axes along which compressibility is described by a linear function of pressure. 57 The magnitudes (compressibil- Inorganic Chemistry pubs.acs.org/IC Article ities, K) and directions of the principal axes of compression (X 1 , X 2 , and X 3 ) for βand γ-Cu 2 V 2 O 7 are presented in Table  2.
The principal axes of compression of β-Cu 2 V 2 O 7 reveal a pronounced anisotropic compressibility (see Figures 2 and 6) which is herein rationalized in terms of the underlying crystal structure. The principal axis of minimal compression, in this case X 2 , points in the [0,1,0] direction and has a compressibility of 5.2 × 10 −3 GPa −1 . Therefore, the least compressible direction in β-Cu 2 V 2 O 7 exactly corresponds to the crystallographic b-axis and points exactly between the layers of chains of edge-sharing CuO 5 units (which lie in the ab-plane). Additionally, X 2 dissects the smallest angle between the two different types of chains (see Figure 2a) thereby pinpointing the direction of maximum strength.
In contrast, the intermediate and major principal compression axes (X 1 and X 3 ) in β-Cu 2 V 2 O 7 are approximately 6 times more compressible than X 2 , with mutually comparable compressibilities of 31.8 × 10 −3 and 32.1 × 10 −3 GPa −1 respectively. Both X 1 and X 3 lie in ac-plane, and as per the definition of the principal axes of compression, they are related by a rotation of 90°since their directions are [4,0,3] and [4,0,−3], respectively. It is important that both of X 1 and X 3 lie in the ac-plane because they share this description with all of the CuO 5 lone electron pairs (LEPs) (see Figure 6a,c). Specifically, each penta-coordinated CuO 5 units possesses an axial LEP, opposite the axial oxygen atom, which points toward the location where a sixth oxygen would make a complete octahedron. The directions of the LEPs are indicted by blue arrows in Figure 6. The LEPs are exactly perpendicular to the principal axis of minimal compression, X 2 (equivalently, the baxis); therefore, it is clear that the LEPs are responsible for the highly anisotropic compressibility of β-Cu 2 V 2 O 7 . A similar phenomenon has also been observed in iodates. 58 The principal axes of compression of γ-Cu 2 V 2 O 7 reveal a much less pronounced anisotropic compressibility in contrast to that of β-Cu 2 V 2 O 7 . Where the principal axes of major and minor compression in the β-phase respectively had compressi- The principal compression axes (X 1 , X 2 , and X 3 ) are represented by black arrows in Figures 2 and 6. The data in the table were calculated using the lattice parameters from the single crystal XRD analysis (Tables S1−S3) and the PASCal principal axis strain calculator. 56 . . Interestingly, the most compressible axis in the γ-phase phase is roughly equivalent to the least compressible axis in the β-phase in terms of compressibility. 3.6. Pressure-Induced Structural Evolution/Relation to Nonlinear Thermal Expansion. The β-Cu 2 V 2 O 7 structure exhibits negative thermal expansion (NTE) at ambient pressures. The primary mechanism for the NTE is believed to relate primarily to a transverse vibrational mode associated with the oxygen atom which bridges the VO 4 tetrahedra in the V 2 O 7 units (O 3 V−O−VO 3 ). The V 2 O 7 units interlink the chains of edge-sharing CuO x units; therefore, a vibrational mode perpendicular to the V−O−V bridge causes a reduction in the time-averaged distance between the vanadium atoms, thereby pulling the layers closer together and reducing the unit volume. 14,15 Since the layers lie in the ab-plane, a reduction in the lattice constant c corresponds to a decrease in the interlayer distance. As shown in Figure 5c, all lattice constants for both phases decrease monotonically with increasing pressure. In the present work, the interlayer spacing abruptly decreases from 4.7429 to 4.5294 Å across the β → γ phase transition, thereby corresponding to a change in interlayer spacing of −0.2135 Å. Because only the time-averaged atomic positions can be observed in XRD measurements, the vibrational modes cannot be observed directly. However, the time-averaged V 2 O 7 unit provides insight regarding the pressure-induced structural behavior. For example, Figure 7a shows the intervanadium (V−V) distance as a function of pressure. The V−V distance decreases with pressure in both phases; however, it jumps by +0.1 Å across the β → γ phase transition. The normalized unit cell volume decreases across the transition, therefore the V−V distance is clearly not the dominating factor in the volume decrease. Additionally, as shown in Figure 7b, the V−O−V angle, formed by the bridging oxygen atom, appears to remain constant in the β-phase, whereas it decreases with pressure in the γ-phase and exhibits no clear jump across the phase transition. Therefore, the V−O−V angle is also not responsible for the large volume collapse. The Cu−O bond distances also remain roughly constant over the full pressure range (see Figure S5), and in fact, the volume of the CuO x coordination complexes appears to increase (see Figure S6). The key to the volume collapse of ΔV ≈ 7% therefore likely lies with the mutual rotation of the VO 4 units. According to the XRD data, when viewed along the V−V direction (as shown in Figure 7c  Inorganic Chemistry pubs.acs.org/IC Article plotted as a function of pressure in Figure 7d, whereby it is clear that the dihedral angles in the γ-phase exhibit a larger deviation from 60°than those in the β-phase. This is important because it suggests that the relative rotation of the VO 4

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