Electronic properties and high-pressure behavior of wolframite-type CoWO₄

Abstract

In this work we characterize wolframite-type CoWO₄ under ambient conditions and under compression up to 10 GPa, with emphasis on its electronic structure. X-Ray diffraction and vibrational experiments, supported by ab initio calculations, show that CoWO₄ is stable under high-pressure conditions, as no structural changes are detected in the studied pressure range. Interesting findings come from optical absorption spectroscopy. On the one hand, CoWO₄ is confirmed to have one of the lowest band gaps among similar wolframites, around 2.25 eV. This makes CoWO₄ suitable for use in applications such as the photocatalysis of organic pollutants and water splitting. Additionally, a monotonic decrease of the band gap is found upon compression. This phenomenon is seldom observed in AWO₄ wolframites and is attributed to the open character of the d shell of Co²⁺. Our results are supported by theoretical ab initio simulations and are discussed with reference to other wolframites.

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1. Introduction

AWO₄ wolframites, where A is a divalent metallic cation, are crystalline compounds mainly studied for their optical properties. Depending upon the divalent cation, they may crystalize in a tetragonal structure known as scheelite or in a monoclinic structure known as wolframite.¹ Many of these compounds have multiple technological applications. They are, in fact, luminescent and scintillating materials, and are employed in high-energy physics for the detection of γ and X photons, in fluorescent devices, as dielectric ceramics in microwave applications and fiber optics.^2–5 AWO₄ wolframites have also been proposed for use in sensors for gases or nitric acid^6,7 and some of them, among which ZnWO₄ and CoWO₄, have shown promising performances in the photodegradation of organic pollutants.^8,9 CoWO₄ has also interesting magnetic properties.¹⁰ Monoclinic wolframite-type compounds share the same crystal structure (space group P2/c) and generally are semiconductors with energy gaps, E_g, covering from the near-ultraviolet to the visible.¹¹

Among wolframites, CoWO₄ has been one of the less studied compounds, even if it has recently started to get attention mainly because of its low band gap (2.3–2.7 eV), which makes it a good candidate for green technologies, in particular as a photocatalyst for degradation of pollutants present in water or for the production of hydrogen fuel by means of water splitting.^12–17 For these environmentally friendly applications, an accurate knowledge of the electronic properties of CoWO₄ is important. In particular, the band-gap energy of CoWO₄ has not yet been measured by optical-absorption spectroscopy. Some applications of CoWO₄ involve extreme environments, in particular at high pressure, and it is thus important to accurately characterize the influence of high pressure on the structural, vibrational, and optical properties of CoWO₄.

In this work, we focus our attention on wolframite-type CoWO₄. Characterizing it under ambient and high-pressure conditions, we have determined the structural stability of CoWO₄ up to at least 10 GPa, as all relevant physical magnitudes are found to vary smoothly in the studied pressure range. Structural and vibrational properties of CoWO₄, such as its bulk modulus and its anisotropic compressibility, are found to be compatible with those of analogue wolframites, along with its Raman phonons and their evolution under compression. On the other hand, interesting results come from the analysis of the optical absorption spectra. In fact, we could state that CoWO₄ is among the wolframites with the lowest band gap, E_g = 2.25(1) eV. Additionally, the band gap is shown to steeply decrease under compression, something unusual for AWO₄ wolframites and that has been reported only for MnWO₄ so far. We discuss these results on the basis of theoretical simulations and by comparison with MnWO₄ (E_g = 2.37 eV).¹⁸ We have found that the contribution of unfilled Co²⁺ 4d states to both the top of the valence band and the bottom of the conduction band is responsible for the low band gap of CoWO₄ and its negative dependence on pressure. These findings are important from the point of view of the potential application of CoWO₄, as tunable low band-gap compounds may be useful in photodegradation appliances. Also, they are likely to stimulate new research in the field of the electronic structure of AWO₄ wolframites, as significant trends are expected to be established linking the electron configuration of the A atom and the behavior of the band gap of these compounds.

2. Experimental details

Na₂WO₄ and anhydrous CoCl₂ obtained from Alfa Aesar (purity > 99%) were used as precursors for the preparation of CoWO₄. Stoichiometric quantities of the reactants were weighed, and the mixture was ground in an agate mortar with the addition of ethanol. The product was washed with distilled water to remove sodium chloride. Subsequently, it was heated at 500 °C. XRD measurements at ambient pressure were taken with the sample in the powder form using Cu K_α radiation (λ = 1.5406 Å), confirming that the obtained product was CoWO₄, with no detectable minority phases or impurities. High-Pressure (HP) XRD experiments, of up to around 10 GPa, were performed at the MSPD beamline of ALBA Synchrotron¹⁹ using a Diamond Anvil Cell (DAC) loaded with CoWO₄ in the powder form. The culets of the diamond had a diameter of 500 μm The sample was deposited in the hole of a pre-indented stainless-steel gasket (diameter 200 μm), together with ruby chips for the determination of the pressure through the ruby-fluorescence method²⁰ and a methanol : ethanol : water (MEW) mixture in the 16 : 3 : 1 volume ratio as the pressure-transmitting medium (PTM). 2D diffraction images were taken on a Rayonix CCD detector, using a wavelength λ = 0.4246 Å and transformed to intensity-2θ patterns using DIOPTAS.²¹ Rietveld and Le Bail fits were performed using POWDER CELL.²² The Equation of State (EOS) of CoWO₄ was calculated by fitting a 2nd order Birch–Murnaghan EOS to the pressure–volume data obtained from the HP experiments. Structure drawing and bond length measurements were performed with VESTA.²³

HP optical absorption experiments in the UV-vis range were performed on a pre-compressed pellet of CoWO₄ loaded in a DAC (similarly to what was done for HP XRD). Two light sources, an UV and a deuterium lamp were used. Absorption spectra were measured by comparing, at each pressure point, the spectrum of the light source through the pressure transmitting medium and through the sample (“sample-in, sample-out method”).

Raman spectroscopy was performed with a powder sample in a DAC, loaded similarly to the DACs used for HP XRD and UV-vis spectroscopy. Raman spectra were collected in the backscattering geometry using a He–Ne laser (λ = 632.8 nm), a JOBIN-YVON TRH1000 spectrophotometer, an edge filter, and a thermoelectrically cooled multichannel CCD (HORIBA SYNAPSE) as the detector.

3. Theoretical simulations

The simulations of the structural, electronic, dynamical, and elastic properties were carried out using density functional theory (DFT)²⁴ and the VASP (Vienna Ab initio Simulation Package) package.^25,26 We use the pseudopotential method with the projector augmented wave (PAW) scheme,²⁷ using a plane-wave cutoff of 540 eV to ensure high accurate convergence. The k-point integration in the Brillouin zone (BZ) was done using a big sampling of 6 × 6 × 6 grid for the primitive unit cell. Generalized Gradient Approximation, GGA with the Perdew, Burke, and Ernzerhof for solids, PBEsol prescription for the exchange–correlation energy.²⁸ Besides, we perform our simulations with the DFT+U scheme of Dudarev et al.²⁹ to treat the strongly correlated states of Co and W atoms by means of a single effective parameter, U_eff = U − J, where U and J are the screened Coulomb and exchange parameters. The selected values of U_eff were 3.32 and 6.2 eV, for the Co and W atoms, respectively.³⁰ The antiferromagnetic configuration was found to have the lowest energy. The cell parameters and the atomic positions are relaxed to obtain the optimized configurations for a given volume, where the atomic forces were less than 0.004 eV Å⁻¹, and the stress tensor is diagonal with an accuracy of less than 0.1 GPa. This procedure allows us to obtain a set of volume, energy, and pressure data from our simulations.

Phonopy package³¹ was used to perform lattice-dynamics calculations. The frequencies, and the eigenvectors of the normal vibration modes were determined at Γ point. The elastic properties were computed employing the method implemented in the VASP code.^32,33 These elastic constants are obtained for the fully optimized structures by small deformations, which produce small strains in different directions taking into account the structure symmetry.³³ The electronic band structure along the high symmetry directions of the first BZ were obtained using the relaxed theoretical structures at different pressures.

4. Results and discussion

XRD experiments

As described above, wolframite-type CoWO₄ crystallizes naturally in a monoclinic structure belonging to the P2/c space group (S.G. 13, Z = 2). The ambient-pressure XRD pattern for CoWO₄, together with the Rietveld fit, is shown in Fig. 1. All the XRD peaks are correctly indexed in the P2/c space group. Atomic positions, as calculated by us through theoretical simulations, are compatible with the values given in the literature³⁴ (see comparison in Table 1) and have been not refined in our fits. Cell parameters as obtained by XRD in open air are a = 4.670(5) Å, b = 5.687(6) Å, c = 4.951(5) Å, β = 90.08(9)° (volume V = 131.5(2) ų), in good agreement with those measured using neutron diffraction (ref. 34) and those obtained by ab initio simulations (Table S1, ESI†). According to these data, the structure of wolframite-type CoWO₄ can be described as a distorted hexagonal packing of O atoms in which Co and W both are 6-fold coordinated with oxygens. The coordination octahedral units CoO₆ and WO₆ share two edges with neighboring polyhedra of the same type, forming alternating chains of identical octahedra along the [001] axis (Fig. 2a and b). Besides, these polyhedra are slightly irregular, as the bond lengths Co–O and W–O are not all equal (Table 2).

Fig. 1 Ambient-pressure XRD pattern for CoWO₄, as obtained by a powder sample in open air (λ = 1. 1.5406 Å) and Rietveld fit. Red circles: experimental data; black line: Rietveld fit; green line: residuals; blue ticks: Bragg reflections.

Table 1 Atomic positions for wolframite-type CoWO₄, from ref. 34, and comparison with theoretical values from ab initio simulations (in parentheses)

Atom	Wyckoff	x/a	y/b	z/c
Co	2f	1/2	0.6712(8) (0.65955)	1/4
W	2e	0	0.1773(4) (0.17883)	1/4
O1	4g	0.2176(3) (0.22012)	0.1080(4) (0.10863)	0.9321(3) (0.92811)
O2	4g	0.2540(3) (0.26102)	0.3757(4) (0.38128)	0.3939(3) (0.40212)

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Fig. 2 (a) Ambient-pressure structure of wolframite-type CoWO₄. Red, blue, and grey spheres are respectively oxygen, cobalt, and tungsten atoms. The coordination polyhedra of tungsten and cobalt are shown in blue and grey, respectively; (b) projection of wolframite-type CoWO₄ unit cell onto the (010) plane, showing the alternate chains of CoO₆ and WO₆ octahedra along [001].

Table 2 Bond distances d in the CoO₆ WO₆ octahedra of CoWO₄ and their volume V at ambient pressure

Bond	Multiplicity	d (Å)	V (Å^3)
Co–O1	2	2.033(4)	12.1456
Co–O2	2	2.1198(18)
Co–O2	2	2.157(5)
W–O1	2	2.1164(4)	9.3647
W–O1	2	1.916(3)
W–O2	2	1.785(3)

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The evolution of the XRD patterns of CoWO₄ under compression in nearly hydrostatic conditions³⁵ is summarized in Fig. 3. As shown, all the patterns up to 9.5 GPa can be indexed in the same P2/c space group. The shrinking of the unit cell is pointed out by the progressive shifting of the Bragg reflections towards higher values of 2θ. Apart from this, the only notable change in the patterns is the splitting of some peaks, which is more evident in the 8–10° angular range. These splitting are due to the variation of the β angle of the monoclinic structure, which is initially very close to 90° and increases with a positive pressure coefficient of ∂β/∂P = 0.088(4) deg GPa⁻¹ (Table 3 and Fig. 4). At ambient pressure, the most intense diffraction peak is an overlap of the (1̄11) and (111) reflections (at 8.34° and 8.35°, respectively); these appear clearly separated at 9.5 GPa. Similarly, the (002) and (021) peaks (9.84° and 9.88° at ambient pressure), which are strictly convoluted at low pressure, greatly increase their separation at higher pressure (see Fig. 3). In short, despite a steady increase of the monoclinic β angle, no phase transitions are detected in the studied pressure range. As we will see in the following, this conclusion is corroborated by Raman spectroscopy and theoretical simulations.

Fig. 3 Powder XRD patterns of CoWO₄ at selected pressures. Blue ticks indicate the positions of the Bragg reflections. Reflections for which the splitting at high pressure is more evident have been indicated.

Table 3 Linear functions describing the pressure dependence of unit-cell parameters of CoWO₄. Intercept and slope are referred to the linear fits of the values of cell parameters vs. pressure

Parameter	Intercept	Slope	k i (10^−3 GPa^−1)
a	4.669(2) Å	−0.0091(4) Å GPa^−1	1.95(9) × 10^−3 GPa^−1
b	5.683(3) Å	−0.0182(7) Å GPa^−1	3.2(1) × 10^−3 GPa^−1
c	4.949(1) Å	−0.0073(2) Å GPa^−1	1.48(4) × 10^−3 GPa^−1
β	90.12(2) deg	0.089(4) deg GPa^−1	—

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Fig. 4 CoWO₄ unit-cell parameters a, b and c as a function of pressure. The trend of the monoclinic β angle is shown in the inset. Red lines are linear fits of the data.

In the following, the compressibility of CoWO₄ is analyzed from the powder XRD data. Fig. 4 summarizes the variation of the cell parameters as a function of pressure. As anticipated, a, b, and c smoothly decrease upon increasing pressure.

The axial compressibility of CoWO₄, (, for the a_iaxis, a⁰_i being the cell parameter at ambient pressure) can be studied from the linear fits of the cell parameters vs. pressure. The values in Table 3 show that the compressibility along the b axis is much higher than along the a and c axes. This anisotropic behavior, and the increase of the monoclinic angle, is commonly observed in wolframites, and has been reported previously for MgWO₄, CdWO₄ and MnWO₄, among others.^36–38

A more rigorous insight on the axial compressibility of CoWO₄ comes from the analysis of its compressibility tensor. For monoclinic structures, the tensor is symmetric and has only four non-zero components, whose values can be calculated using the analytical expressions given by Knight.³⁹ These components for CoWO₄ are summarized in Table 4, in which also the eigenvalues and eigenvectors of the compressibility tensor are shown. One of the eigenvectors is parallel to the unique crystallographic b-axis, while the other two define a plane perpendicular to it. Compressibility is clearly anisotropic, as it varies between 9.0252 × 10⁻⁴ and 3.2095 × 10⁻³ GPa⁻¹ and the axis with the maximum compressibility is the unique b-axis (β₂₂ component). On the other hand, the direction of minimum compressibility lies in the ac plane, forming an angle of 53.65° with the c axis (from c to a), corresponding to the crystallographic direction [3̄,0,4].³⁹ To first order, the isothermal compressibility of CoWO₄ is given by the trace of the compressibility tensor, ,³⁹ corresponding to an approximate value of the bulk modulus B₀ = 150.76 GPa. For completeness, we also show the compressibility indicatrix, calculated using PASCal, in Fig. S1 (ESI†).⁴⁰

Table 4 Isothermal compressibility tensor coefficients, β_ij, their eigenvalues, λ_i, and eigenvectors, ev_i, and angle of minimum direction of compression, ψ, for CoWO₄

β 11 (GPa^−1)	1.952 × 10^−3
β 22 (GPa^−1)	3.209 × 10^−3
β 33 (GPa^−1)	1.471 × 10^−3
β 13 = β31 (GPa^−1)	7.726 × 10^−4
λ 1 (GPa^−1)	2.5209 × 10^−3
ev1	(0.80540, 0, 0.59273)
λ 2 (GPa^−1)	3.2095 × 10^−3
ev2	(0, 1, 0)
λ 3 (GPa^−1)	9.02527 × 10^−4
ev3	(−0.59273, 0, 0.8054)
ψ (deg)	53.65

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An alternative estimate of the bulk modulus B₀ is obtained by fitting the experimental pressure–volume data to a 2nd-order Birch–Murnaghan EOS (Fig. 5), which gives a comparable result of B₀ = 131(3) (V₀ = 131.43(10) ų) GPa. These values are in line with the bulk moduli of other wolframites such as MgWO₄, MnWO₄, and ZnWO₄ (see Table 5 for a comparison).^36,41,42Ab initio simulations of the volume at ambient pressure agree within a 1% with the experimental values. Also, fitting a 2nd-order Birch–Murnaghan EOS on the theoretical pressure–volume data, as shown in Fig. S2 (ESI†), gives a compatible, although slightly overestimated, value of B₀ (Table 5). It is interesting to notice that the experimental value of B₀ is very close to the one expected from the phenomenological rule proposed by Ruiz-Fuertes et al. (B₀ = 137 GPa), which relates the bulk modulus with the inverse of A–O distance in AWO₄ wolframites (A being a divalent element).⁴¹ It is noteworthy that our ab initio simulations predict that atomic positions are nearly constant across the studied pressure range, with a maximum variation around 0.3% over an increase of 1 GPa in pressure for an oxygen atom. This value is comparable with the experimental uncertainty on the atomic positions in CoWO₄ (see Table 1). Hence, in the following we will assume that atomic positions are constant in the entire pressure range. Therefore, the CoO₆ and WO₆ octahedra will have the same bulk modulus of the CoWO₄ unit cell, given that their volume varies accordingly to the volume of the whole unit cell in the absence of atomic displacements. In turn, this implies that CoO₆ and WO₆ octahedra are equally compressible and contribute equally to the volume reduction of the unit cell under compression, unlike that observed in other AWO₄ wolframites.³⁶

Fig. 5 Pressure–volume data for wolframite-type CoWO₄ (black spheres) and fit with a 2nd-order Birch–Murnaghan EOS (red line). Errors are comparable to symbol size.

Table 5 Values of the bulk modulus (B₀), its derivative (B₀′) and the volume at ambient pressure (V₀) for CoWO₄ and analogue wolframites. The experimental value of B₀ in parenthesis for CoWO₄ has been estimated as the inverse of the trace of the compressibility tensor. The theoretical value of B₀ in parentheses for CoWO₄ has been obtained directly by ab initio simulations

Compound	V 0 (Å^3)	B 0 (GPa)	B 0′	Ref.
CoWO4
Experiment	131.43(10)	131(3) (150.76)	4	This work
Theory	129.114(13)	164.3(5) (161.15)	4	This work
MgWO4
Experiment	131.1(3)	160(13)	4.5(3)	41
Experiment	—	144(3)		36
MnWO4
Experiment	—	131(2)	4	36
Experiment	138.8(2)	145(3)	4.3(2)	42
ZnWO4
Experiment	132.9(5)	145(6)	6.6(9)	41

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Vibrational spectroscopy

The Raman spectrum of monoclinic-type CoWO₄ at ambient pressure, together with its evolution up to 10 GPa, is shown in Fig. 6. Group theory predicts a total of 18 Raman active modes for monoclinic-type CoWO₄, with a mechanical representation at the Γ point given by Γ = 8A_g + 10B_g.⁴³ All of the predicted modes have been detected in our experiments (Fig. 6 and Table 6), including one at 244 cm⁻¹ which, to the best of our knowledge, had not been reported before. For AWO₄ wolframites, active Raman modes can be classified into internal, high-frequency stretching modes of the WO₆ octahedron, and external modes, originated by the motion of the A cation and the WO₆ octahedron as a unit.³⁸ The distribution of the modes in CoWO₄ is the archetypical one for similar tungstates (4 modes above 600 cm⁻¹, 2 isolated modes in the 500–550 cm⁻¹ range, and 12 modes below 405 cm⁻¹).⁴¹ Nonetheless, for CoWO₄, the frequency of some of the modes differs significantly between previous experimental reports.^38,44–47 These discrepancies are mostly observed in the low-frequency range, i.e. mostly external modes are affected. It is thus reasonable to argue that these differences may arise from different preparation methods, which may impact sample purity and cell parameters.

Fig. 6 Raman spectra of wolframite-type CoWO₄ at ambient conditions (bottom) and at selected pressures. The symmetry and position of each peak are shown for the spectrum at ambient pressure (ticks).

Table 6 Symmetry, frequency under ambient conditions (ω₀), linear pressure coefficient and the Grüneisen parameter (dP/dω and γ, respectively) of the Raman active phonons for CoWO₄, as obtained from experiments and ab initio simulations. The asterisk indicates a phonon which had not been experimentally reported before

Mode	Experiment			Theory
Exp	ω 0 (cm^−1)	dω/dP (cm^−1 GPa^−1)	γ	ω 0 (cm^−1)	dω/dP (cm^−1 GPa^−1)	γ
Bg	88(1)	0.66(4)	0.89(7)	92.83	0.79	1.11
Ag	125(1)	0.12(3)	0.12(3)	128.42	0.74	0.75
Bg	154(1)	0.45(4)	0.35(4)	157.27	1.03	0.86
Bg	181(1)	0.27(3)	0.18(2)	183.66	0.60	0.43
Bg	200(1)	0.93(3)	0.56(4)	189.19	0.54	0.37
Ag	244(1)*	2.74(10)	1.34(9)	222.88	2.70	1.59
Bg	271(1)	2.24(13)	0.99(8)	277.89	2.61	1.23
Ag	278(1)	1.26(13)	0.54(6)	294.77	0.70	0.31
Bg	316(1)	3.44(18)	1.31(10)	309.94	1.77	0.75
Ag	333(1)	3.67(16)	1.32(10)	338.56	3.50	1.35
Bg	373(1)	3.80(17)	1.22(9)	358.51	3.95	1.44
Ag	403(1)	1.45(7)	0.43(3)	399.97	1.17	0.38
Bg	495(1)	3.45(8)	0.83(5)	494.23	2.96	0.78
Ag	529(1)	3.60(14)	0.82(6)	523.69	3.06	0.77
Bg	657(1)	5.2(4)	0.94(9)	629.86	3.83	0.80
Ag	686(1)	3.52(15)	0.61(4)	677.89	2.64	0.51
Bg	766(1)	4.49(19)	0.70(5)	756.31	4.07	0.70
Ag	881(1)	3.37(8)	0.46(3)	853.38	2.66	0.41

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All in all, the frequencies as obtained in our experiments and those calculated by ab initio simulations are in good agreement, and the same can be said for the Grüneisen parameters, defined as (Table 6). Minor discrepancies between theory and experiments are not unusual for wolframite-type compounds.³⁸ For CoWO₄, the phonons which appear to be more sensitive to pressure are the one at 244 cm⁻¹ and the three in the range from 316 to 373 cm⁻¹, with a value of γ well above 1 (Table 6). A similar situation is found in wolframite-type MgWO₄, for which the highest Grüneisen parameters are low-frequency external modes within similar ranges.⁴¹ The data in Fig. 6 support the stability of wolframite-type CoWO₄, as no qualitative differences are detectable among the Raman spectra at different pressure. Given that all phonons’ linear pressure coefficients are positive (Table 6), no vanishing or splitting phonons are found in the studied pressure range, confirming the absence of structural transitions. As shown in Fig. 7, all Raman modes consistently blueshift upon compression.

Fig. 7 Frequency of Raman modes vs. pressure for wolframite-type CoWO₄ (circles). Dashed lines are the linear fits used for the calculation of the pressure coefficients and Grüneisen parameters.

Our ab initio simulations support the experimental results. As shown in Fig. S3 (ESI†), theoretical calculations correctly predict all phonons hardening under high pressure conditions. Therefore, no phonons become imaginary at any pressure point, ruling out the presence of phase transitions.

Wolframite-type CoWO₄ also has 15 IR active phonons, whose mechanical representation at the Γ point is Γ = 7A_u + 8B_u (excluding acoustic modes).⁴³ Although experimental IR spectroscopy data for CoWO₄ are not available by us at the moment, we have calculated the IR phonons and their evolution under pressure (see Fig. S4 and Table S2, ESI†). The distribution of calculated IR modes is in good agreement with previous results.⁴⁶ Similarly to the Raman modes, IR phonons generally harden with pressure. Only one B_u mode around 247 cm⁻¹ appears to have a small negative pressure coefficient. However, this cannot be interpreted as a sign of dynamical instability, as in the studied pressure range, all modes keep their real (positive) character.

The volumetric thermal expansion coefficient α of an oxide like CoWO₄ can be obtained using a statistical thermodynamic approach by assuming that all the energy of a crystal resides in its vibrations.^48,49 This has been successfully done in the past for BaWO₄ using Raman and IR frequencies.⁴⁹ Using this approach and the calculated frequencies and pressure dependences for different modes, we have estimated the thermal expansion for CoWO₄ at ambient pressure and as a function of pressure. This information is relevant for the use of CoWO₄ as an oxidation protection layer of ferritic stainless steel.⁵⁰ We found that at ambient pressure α = 11 × 10⁻⁶ K⁻¹, in agreement with results reported from recent high-temperature XRD studies.⁵⁰ Under compression, we have determined that the thermal expansion coefficient α of CoWO₄ linearly decreases with pressure at a rate of −2 × 10⁻⁷ K⁻¹ GPa⁻¹, α = 9 × 10⁻⁶ K⁻¹ at 10 GPa. This behavior is similar to that reported for BaWO₄.⁴⁹

Elastic properties

In the following we will discuss the elastic behavior of CoWO₄. The monoclinic structure of CoWO₄ only allows 13 independent non-zero components for the symmetric 6 × 6 elasticity matrix C, i.e. the diagonal C_ii components (i = 1,…,6) plus C₁₂, C₁₃, C₁₅, C₂₃, C₂₅, C₃₅, C₄₆.⁵¹ The values of these coefficients are shown in Table 7.

Table 7 Elastic constants C_ij (in GPa) at 1 bar for of wolframite-type CoWO₄

C 11	C 22	C 33	C 44	C 55	C 66	C 12	C 13	C 23	C 15	C 25	C 35	C 46
222	252	307	77	83	71	125	116	116	11	3	29	−9

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The C_ij parameters of CoWO₄ in Table 7 are roughly similar to those reported previously for CdWO₄ and ZnWO₄ and may be thus considered typical for AWO₄ compounds^52,53 even when they are calculated using an orthorhombic approximation for the structure of these compounds.⁵⁴

The eigenvalues λ₁ (i = 1,…,6) of the C matrix, as shown in Table 8, are all positive under ambient conditions, thus satisfying one of the four equivalent formulations of the Born elastic stability criterion. The positivity of all eigenvalues in fact, states a necessary and sufficient condition for the stability of the wolframite structure under ambient conditions.⁵⁵

Table 8 Eigenvalues λ₁ (in GPa, i = 1,…,6) of the elasticity matrix C of wolframite-type CoWO₄

λ 1	64.5
λ 2	77.9
λ 3	83.5
λ 4	110.5
λ 5	172.8
λ 6	502.8

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Under hydrostatic compression, the magnitudes which describe the elastic properties of a crystal are the components B_ij of the elastic stiffness tensor B. These are related to the C_ij coefficients by the following relationships:

B_ii = C_ii − P (i = 1,…,6);

B₁₂ = C₁₂ + P, B₁₃ = C₁₃ + P, B₂₃ = C₂₃ + P;

B₁₅ = C₁₅, B₂₅ = C₂₅, B₃₅ = C₃₅, B₄₆ = C₄₆,

where P is the pressure.⁵⁶ Under simulated hydrostatic compression, all of the B_ij stiffness coefficients increase steadily, except for B₄₆ which presents a moderate decrease. On the other hand, B₄₄ and B₂₅ reach a maximum around 3 and 4 GPa, respectively, before decreasing slowly (Fig. 8a).

Fig. 8 (a) Elastic stiffness coefficients B_ij as a function of pressure; (b) generalized stability criteria for wolframite-type CoWO₄.

In the presence of an external load, such as non-zero hydrostatic compression, the equilibrium conditions for a crystal structure are given by the Born generalized criterion, which implies that the B matrix must be definitely positive.^56,57 This is equivalent to saying that the following six inequalities must be fulfilled:

M₁ = B₁₁ > 0

M₂ = B₁₁B₂₂ − B₁₂² > 0

M₃ = (B₂₂B₃₃ − B₂₃²)B₁₁ − B₃₃B₁₂² + 2B₂₃B₁₂B₁₃ − B₂₂B₁₃² > 0

M4 = B₄₄ > 0

M₅ = B₁₂²B₃₅² − B₃₃B₅₅B₁₂² + 2B₅₅B₁₂B₁₃B₂₃ − 2B₁₂B₁₃B₂₅B₃₅

−2B₁₂B₁₅B₂₃B₃₅ + 2B₃₃B₁₂B₁₅B₂₅ + B₁₃²B₂₅² − B₂₂B₅₅B₁₃²

−2B₁₃B₁₅B₂₃B₂₅ + 2B₂₂B₁₃B₁₅B₃₅ + B₁₅²B₂₃² − B₂₂B₃₃B₁₅²

−B₁₁B₅₅B₂₃² + 2B₁₁B₂₃B₂₅B₃₅ − B₁₁B₃₃B₂₅² − B₁₁B₂₂B₃₅² + B₁₁B₂₂B₃₃B₅₅ > 0

M₆ = B₄₄B₆₆ − B₄₆² > 0

As shown in Fig. 8b, M_i values are all positive across the entire pressure range and, plausibly, also well above 10 GPa. The wolframite structure of CoWO₄ is thus expected to be stable even at pressures greater than 10 GPa. This result is compatible with our vibrational analysis, whose extrapolation excludes the appearance of phonons with negative frequency, and thus of dynamic instabilities, in the range immediately above 10 GPa.

Knowing the C matrix and its inverse S = C⁻¹ (compliance tensor), elastic parameters such as the bulk modulus, B₀, the shear modulus, G, the Young's modulus E, and the Poisson ratio, ν, can be calculated at ambient pressure, using the expression reported by Zhao et al.,⁵⁸ in both the Voigt and the Reuss approximations. These parameters are summarized in Table 9 for CoWO₄ and all of them are in line with those already reported for CdWO₄ and ZnWO₄.^52–54

Table 9 Bulk modulus, B, shear modulus, G, the Young's modulus, E, and the Poisson's ratio, ν, of wolframite-type CoWO₄ at ambient pressure. The B/G ratio is also shown

	Voight	Reuss	Average
B 0 (GPa)	166	162	164
G (GPa)	75	71	73
E (GPa)	194	186	190
ν	0.305	0.308	0.307
B 0/G ratio	2.232	2.27	2.251

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The average bulk modulus B₀ = 164 GPa calculated using the C matrix is slightly overestimated with respect to the experimental value, even if such discrepancies are not uncommon for wolframites.^38,53 Nonetheless, the bulk modulus calculated using the elastic matrix is in perfect agreement with theoretical values shown in Table 5. Finally, the high B₀/G ratio (>2) indicates that CoWO₄ is a malleable material. Elastic parameters as a function of pressure are resumed in Fig. S5 (ESI†). While the bulk modulus increases uniformly under compression, the shear modulus slightly decreases, probably in connection with the increase of the monoclinic β angle observed experimentally, which may also be the reason behind the decrease of the Young's modulus above 4 GPa (Fig. S5a–c, ESI†). Although increasing with pressure, the Poisson ratio has a value ν < 0.5 across the studied pressure range (Fig. S5d, ESI†), thus reflecting both the slightly anisotropic compressibility of wolframite-type CoWO₄ (see results in the XRD section) and an increasing ionic character of the chemical bond.^59,60 Finally, the bulk/shear ratio also increases under compression, indicating the high ductility of CoWO₄ (Fig. S5d, ESI†).

Given the scarcity of studies regarding the elastic properties of AWO₄ wolframites, these results represent a valuable addition to the knowledge of those compounds, and we hope that they may stimulate more research on this subject, as significant trends may be thus established between the elastic properties of AWO₄ materials and composition/external conditions (pressure/temperature).

Electronic properties

According to our calculations, wolframite CoWO₄ is predicted to have two electronic gaps around 2.3 eV under ambient conditions, which are very close in energy: a direct gap at the Γ point and an indirect Γ → Z gap (Fig. 9a). On the other hand, when (αhv)^1/2 is plotted versus hν (where α is the absorbance and hν the energy of the incident light), a linear trend is found for energies above 2.3 eV (Tauc plot, Fig. 10), meaning that the fundamental gap in wolframite CoWO₄ is of an indirect nature. This is not surprising, as AWO₄ wolframites whose A²⁺ cation has unfilled d subshells have been shown to have indirect gaps.^18,61

Fig. 9 Electronic band structure of wolframite CoWO₄; (a) under ambient conditions, and (b) at 10 GPa.

Fig. 10 Tauc plot of the absorbance spectrum of wolframite CoWO₄ at ambient pressure. The fit of the linear region is shown in red.

The band gap energy E_g of CoWO₄, as extracted from the data in Fig. 10, is E_g = 2.25(1) eV, in full agreement with theoretical calculations (E_g = 2.33 eV). These values suggest that the previous studies slightly overestimate E_g.^12,62 This can be understood considering that these values were determined either from indirect electrical measurements or from diffuse reflectance measurements in nanoparticles, two techniques that are less accurate that optical absorption. The value here determined for the band gap is also lower than those of analogue orthotungstates, which have gaps in the range of 2.37–4.06 eV (Table 10), CoWO₄ being the wolframites with the lowest band gap so far.^11,18 Interestingly, our result is in line with the predictions of Lacomba-Perales et al., which highlight a correlation between the band gap and the cationic radii in AWO₄ wolframites.¹¹ The value we determined for the band gap of CoWO₄ (2.25(1) eV), makes it an excellent candidate as a semiconductor electrode for efficient visible light photolysis of water.⁶³

Table 10 Band gap E_g of wolframite-type CoWO₄ with pressure coefficient as measured in this work and comparison with analogue wolframites (from ref. 18)

Compound	Theory Eg (eV)	Experiments Eg (eV)	Experiments dEg/dP (meV GPa^−1)
MgWO4	3.22	4.06	13.9
ZnWO4	2.79	3.98	12.7
CdWO4	2.91	4.02	12.0
MnWO4	1.83	2.37	−22.2
CoWO4	2.33	2.25(1)	−28.1(4)

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The small band gap of CoWO₄ can be understood by analyzing the electronic contributions to its density of states (DOS). In AWO₄ wolframites with large energy gaps, such as MgWO₄, ZnWO₄ and CdWO₄, the bottom of the conduction band is dominated by W 5d states hybridized with the O 2p state, while the upper part of the valence band is dominated by O 2p states slightly hybridized with 5d states of W. The contribution of the A²⁺ cation to both bands is negligible. On the other hand, for MnWO₄, which has a narrower band gap, 2d states of Mn²⁺ contribute to both the valence and the conduction bands.¹⁸ Given the similar electronic configuration of Mn and Co, it is thus fair to assume that for wolframite CoWO₄, the Co²⁺ 3d states are the reason behind the reduced band gap. Indeed, our calculations (Fig. 11a) show that under ambient conditions, the top of the valence band is contributed predominantly by 3d states of CO²⁺ which still give a significant contribution to the bottom part of the conduction band along with W 5d states and, to a lesser extent, O 2p states. Other AWO₄ wolframites, with an A⁺² having unfilled d states, such as FeWO₄ and NiWO₄, are also expected to exhibit a comparatively small band gap.^11,61,64 This strengthens the hypothesis regarding the fundamental contribution of the open d states to the band gap of these compounds.

Fig. 11 Partial density of state of CoWO₄ (a) under ambient conditions and (b) at a pressure of 10 GPa.

In the following, we will discuss the behavior of the band gap of CoWO₄ under high pressure conditions. Fig. 12 shows the (αhv)^1/2vs. hν Tauc plot of the absorption tail of CoWO₄ at selected pressures. Same as in Fig. 10, all plots present a linear region above a certain energy hν of the incident light, meaning that the band gap of wolframite CoWO₄ retains its indirect character in this pressure range. This can be explained by the limited changes in the topology of the band structure of CoWO₄ under compression (see Fig. 9a and b). On the other hand, it is evident how, unlike analogue wolframites, the band gap of CoWO₄ closes with pressure (Fig. 13). Again, the absence of structural phase transitions in the studied pressure range is reflected in the smooth decrease of the band gap, without any discontinuous collapse. The decrease is linear, with a large negative pressure coefficient dE_g/dP = −28.1(4) meV GPa⁻¹, a dependence on pressure even larger than that of wolframite MnWO₄ (−22.2 meV GPa⁻¹). The experimental result is in perfect agreement with ab initio calculations, which give a similar value of −24.9(3) meV GPa⁻¹ for the pressure coefficient. The relative contribution of Co, W and O states to the DOS of CoWO₄ remains unaffected in the studied pressure range, as shown in Fig. 11b. Nonetheless, features such as the two-peak shape structure in the −1.5 to 0 eV range become more evident at high pressure. An analogous behavior is seen, again, in MnWO₄, in which a similar feature is available in the DOS.¹⁸ The unfilled Mn²⁺ 3d states are split by the octahedral crystal field into twofold e_g and threefold t_g states, which give place to a two-peaks feature in the DOS of around −0.75 eV The splitting is enhanced by the pressure due to the shortening of the Mn–O bonds.^18,36 Again, it is reasonable to expect a similar reason behind the behavior of the peak-like feature of the DOS of CoWO₄ at the top of the valence band.

Fig. 12 Tauc plot of the absorbance spectrum of wolframite CoWO₄ at selected pressures (shown above each curve). The fits of the linear regions are shown in red.

Fig. 13 Band gap E_g of wolframite CoWO₄ as a function of pressure (circles) with corresponding linear fits (lines). Closed (open) symbols and solid (dashed) lines correspond to experimental (theoretical) results.

As mentioned, the decrease of the band gap with pressure is unusual for AWO₄ wolframites. Akin to what was observed for MnWO₄, in CoWO₄ the unfilled 3d states of Co contribute to the bottom of the conduction band. These d states are pushed down in energy by pressure, contrary to what happens for wolframites with filled d states such as MgWO₄, ZnWO₄, and CdWO₄.^18,37 On the other hand, for all of the mentioned compounds, the top of the valence band is unaffected by pressure. The net result is a decrease (resp. increase) of the band gap with pressure for AWO₄ wolframites with an open (resp. closed) d shell.

On the basis of our findings and previous results, a trend may thus be established, by which AWO₄ wolframites with an A²⁺ cation with open d shell are expected to exhibit a comparatively small band gap, which further decreases under high-pressure conditions. Further experimental studies are required to confirm this hypothesis.

To conclude the discussion of the electronic properties of CoWO₄, we will comment on the effective mass of electrons and holes (m_e and m_h, respectively), which we have obtained from DFT calculations. This parameter is related to the carrier mobility, which directly affects the separation and diffusion rate of photo-induced charge carriers, one of the most important factors determining being the photocatalytic activity of a semiconductor. The effective mass of holes and electrons has been calculated from the second derivative of the energy with the wave vector. Due to the monoclinic structure of wolframite, the effective masses of carriers will be also anisotropic, being described by a non-diagonal tensor.⁶⁵ For instance, it can be seen in Fig. 8 that the top valence band in the band structure of CoWO₄ is more dispersive along G–A and G–B than along G–Z and G–Y₂. A similar anisotropy is observed in the bottom conduction band of the band structure around the Z point (the minimum of the conduction band). For practical purposes, an average effective mass can be defined as [a], where m_i are the eigenvalues of the effective mass tensor. By following this procedure, we have determined that at ambient pressure and . The first value is very high in comparison with the typical electron-mobility of semiconductors suggesting that CoWO₄ has a low performance as an n-type semiconductor. In contrast, the second value is comparable to the hole-mobility of the best p-type semiconductors.⁶⁶ These observations are consistent with the experimental observation that un-doped CoWO₄ is a p-type semiconductor.⁶² On the other hand, it is known that the relative ratio of effective mass determines the recombination rate of carriers.⁶⁷ In our case , which means that electrons and holes should easily recombine and show short lifetimes. Therefore, our study indicates that CoWO₄ as the ideal band-gap energy to be used as a photocatalytic electrode; but also has the same limitations regarding photocurrent that a typical photocatalytic material as BiVO₄ or TiO₂ has.^68,69

5. Conclusions

A multifaceted characterization was performed on wolframite-type CoWO₄ under room conditions and at high pressures, of up to 10 GPa, by means of XRD, Raman spectroscopy, optical absorption spectroscopy, and ab initio simulations. All these techniques agree in that CoWO₄ is stable in the studied pressure range, as no signs of phase transitions could be detected. The bulk modulus of CoWO₄ has been found to be in line with the values of other AWO₄ wolframites, and its compressibility is equally anisotropic. The elastic constants of CoWO₄ have been calculated and are found to be in line with those of analogue wolframites. For completeness, we have also discussed the elastic properties of CoWO₄ under compression, as the characterization of the elastic behavior of wolframite is often neglected in the study of these compounds. The most intriguing experimental results are those regarding the electronic structure of CoWO₄, which has been found to be an indirect semiconductor with a reduced band gap, of around 2.25 eV, when other wolframites such as CdWO₄, MgWO₄ and ZnWO₄ have large direct gaps, with values around 4 eV. In addition, the band gap redshifts upon compression, something which may be beneficial for photocatalytic applications, and that has been seldom observed in AWO₄ wolframites. These results are attributed to the open character of the d shell of Co²⁺, which contribute to both the bottom of the conduction band as well as to the top of the valence band. These allow us to draw broad conclusions as, by comparison with previous results, the electronic structure of wolframite AWO₄ appears to be strongly influenced by the open or closed character of the d shell of the A²⁺ cation. As such, other wolframites, such as FeWO₄ and NiWO₄, are expected to behave similarly to CoWO₄. In this respect, new studies and experiments are required to confirm significant trends in analogue compounds.

Author contributions

The manuscript was written through the contributions of all authors. All authors have approved the final version of the manuscript.

Conflicts of interest

There are no conflicts of interest to declare.

Acknowledgements

This research was supported by the Spanish Ministerio de Ciencia, Innovación y Universidades, the Spanish Research Agency, and the European Fund for Regional Development under Grant No. PID2019-106383GB-C41/43, FIS2017-83295-P and RED2018-102612-T and by Generalitat Valenciana under Grant Prometeo/2018/123 (EFIMAT). E. B would like to thank the University of Valencia for his “Attracció de Talent” postdoctoral contract (UV-INV_POSTDOC19-1026935). Powder X-ray diffraction experiments were performed at the Materials Science and Powder Diffraction beamline of ALBA Synchrotron (experiment no. 2016081784).

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Footnote

† Electronic supplementary information (ESI) available. See DOI: 10.1039/d1ma00510c

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