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SN Applied Sciences

, 1:389 | Cite as

High-pressure characterization of the optical and electronic properties of InVO4, InNbO4, and InTaO4

  • P. Botella
  • D. ErrandoneaEmail author
  • A. B. Garg
  • P. Rodriguez-Hernandez
  • A. Muñoz
  • S. N. Achary
  • A. Vomiero
Research Article
  • 95 Downloads
Part of the following topical collections:
  1. 5. Physics (general)

Abstract

We have studied the electronic properties at ambient pressure and under high pressure of InVO4, InNbO4, and InTaO4 powders, three candidate materials for hydrogen production by means of photocatalytic water splitting using solar energy. A combination of optical absorption and resistivity measurements and band structure calculations have allowed us to determine that these materials are wide band-gap semiconductors with a band-gap energy of 3.62(5), 3.63(5), and 3.79(5) eV for InVO4, InNbO4, and InTaO4, respectively. The last two compounds are indirect band-gap materials, and InVO4 is a direct band-gap material. The pressure dependence of the band-gap energy and the electrical resistivity have been determined too. In the three compounds, the band gap opens under compression until reaching a critical pressure, where a phase transition occurs. The structural transition triggers a band-gap collapse larger than 1.2 eV in the three materials, being the abrupt decrease in the band-gap energy related to an increase in the pentavalent cation coordination number. The phase transitions also cause changes in the electrical resistivity, which can be correlated with changes induced by pressure in the band structure. An explanation to the reported results is provided based upon ab initio calculations. The conclusions attained are of significance for technological applications of the studied oxides.

Keywords

Wolframite Band gap, optical properties High pressure Phase transition Electronic properties 

1 Introduction

Many ternary metal oxide compounds of the form AMO4 have been extensively studied during the last decade due to their physical properties and technological applications including their low cost and environment friendliness [1, 2, 3, 4, 5, 6]. Among this family of oxides, InMO4 compounds (M = V5+, Nb5+, or Ta5+) are of particular interest due to their excellent photocatalytic activity for water splitting under visible-light irradiation [7, 8]. Their photocatalytic properties have been empirically correlated to the crystal structure [7, 8], but their electronic structure has not yet been understood completely. In particular, the band-gap energy (Eg), a magnitude fundamental for developing the proposed technological applications, has not been accurately reported for any of the compounds. A precise determination of Eg can be achieved by means of optical absorption measurements. In addition, high-pressure (HP) studies have proven to be a formidable tool to test the robustness of the understanding of the electronic structure achieved by means of ambient-conditions studies in semiconductors [9].

InNbO4 and InTaO4 are isostructural compounds which crystallize in the wolframite structure [10]. They belong to the monoclinic space group P2/c, having two formula units per unit cell (Z = 2). In this structure, In and Nb(Ta) cations have an octahedral oxygen coordination. Under HP, both compounds undergo a phase transition to another monoclinic phase [11, 12]. The transformation to the HP phase involves a coordination increase in In and Nb(Ta). InVO4 crystallizes in a different structure compared to InNbO4 and InTaO4. This structure belongs to the orthorhombic space group Cmcm (Z = 4) [13]. The structure has InO6 octahedral units and VO4 tetrahedral units as building blocks. Under compression, InVO4 undergoes a phase transition to a wolframite-type structure [14].

Regarding the electronic properties of InMO4 compounds, the common feature is that the states at the bottom of the conduction bands are composed mainly of V 3d, Nb 4d, or Ta 5d electronic levels. On the other hand, O 2p states dominate the upper part of the valence bands. However, in the literature, it can be seen that there are significant discrepancies in the reported Eg values, which range from 1.8 to 4.8 eV, as well as about their band-gap nature, i.e., indirect or direct transition [11, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26]. In fact, in some studies, the absorption of light by defects has been mistakenly assigned to the fundamental band gap [11].

Recently, optical absorption experiments together with band structure calculations clarified the discrepancies in the case of InTaO4 [11]. This work showed that InTaO4 is a wide indirect-gap semiconductor with Eg = 3.79(5) eV, and the previous reports underestimated the band-gap value by 1.2 eV [15, 16]. In addition, investigations under HP have played an important role in the clarification of the nature of fundamental band gap. Such studies have also been shown to be an excellent tool for improving the knowledge of the influence of structural modifications on physical properties of InVO4 [14], InNbO4 [12], and InTaO4 [11]. One of the interesting phenomena observed in these compounds under compression is the color changes associated with the HP phase transition. In InTaO4, the color change has been related to an increase in the coordination number of Ta. Similar changes in the coordination number also occur in InNbO4 [12] and InVO4 [14], suggesting that HP might also trigger interesting changes in their electronic properties, reducing the band gap to values close to 2 eV, which might improve their photocatalytic activity [27].

To further understand the electronic behavior of InVO4, InNbO4, and InTaO4 at ambient pressure and under HP, we have performed a combined experimental and theoretical study. Optical absorption measurements have been carried out up to 16 GPa (20 GPa) for InVO4 (InNbO4). Resistivity measurements have been performed in the three compounds up to 10 GPa, and first-principles band structure calculations have been carried out for InNbO4. The results of these studies have been combined with optical measurements previously reported by us for InTaO4 [11] and band structure calculations already published by us for InTaO4 and InVO4 [11, 14]. Based upon all the studies mentioned above, we report an accurate determination of Eg for the orthorhombic phase of InVO4 and the wolframite phase of InNbO4 and InTaO4. We also present and discuss the effects of pressure on Eg. In particular, we report evidence of a band-gap collapse, at the structural transition pressure, for the three compounds as well as the pressure dependence of Eg for the low-pressure (LP) and HP phases. These studies have enabled us to improve the understanding of the physical properties of InVO4, InNbO4, and InTaO4 and their behavior under compression. The combination of new experimental techniques, like transport measurements, and the systematic discussion of the three compounds has allowed us a fully consistent picture for the three compounds, solving the apparent discrepancies above described. The obtained results will contribute to the optimization of technological applications [7, 8].

The paper is organized as follows. In Sect. 2, we describe the experimental and computational techniques. The results of the absorption and resistivity measurements as well as band structure calculations for the low- and high-pressure phases of the different compounds are presented and discussed in Sect. 3. Finally, a summary of the work and the conclusions are presented in Sect. 4.

2 Materials and methods

2.1 Experimental details

For the experiments, we have used polycrystalline samples synthesized by a ceramic route following the method reported in previous works [11, 12, 14]. The composition and purity of the samples were confirmed by energy-dispersive x-ray spectroscopy using a transmission-electron microscope operated at 200 keV. The crystal structure was verified by powder x-ray diffraction measurements (Cu Kα radiation). These results have been previously published [11, 12, 14].

Optical absorption measurements were performed using 10-μm-thick polycrystalline pellets, with parallel faces, made by compressing the synthesized powdered samples to 1 GPa between two tungsten carbide Bridgman anvils using a hydraulic press [28]. Absorption measurements in the visible—near-infrared range were made with the optical setup described in previous studies devoted to determine the optical absorption of wide band-gap semiconductors [29]. The absorption spectrum of each material was determined from the transmittance spectra measured using the sample-in, sample-out method [30, 31]. For HP experiments, the samples were loaded in a diamond-anvil cell (DAC) with diamond anvils of culet size of 400 μm. We used an inconel gasket, pre-indented to a thickness of 50 μm with a 120-μm-diameter hole. The loading was performed carefully to avoid sample bridging between the anvils [32, 33]. Small ruby chips were used for pressure determination [34], and 16:3:1 methanol–ethanol–water mixture was used as pressure-transmitting medium [35].

Electrical resistance measurements under pressure up to 10 GPa were carried out using an opposed Bridgman-anvil setup [36] consisting of a 12-mm-face-diameter tungsten carbide anvil pair. A pair of pyrophyllite gasket of thickness 200 μm each with a central hole of 3 mm in diameter was used to contain the sample. Bismuth was employed for the pressure calibration [37] along with steatite as pressure-transmitting medium. A well-compacted and sintered powdered sample of 2 mm × 1.5 mm × 0.1 mm in dimension was utilized for the electrical resistance measurements. The ultra-low current measurements were performed at each value of pressure after a 2 min of pressure soaking time with a Keithley electrometer.

2.2 Calculation details

Band structure calculations are required to provide a rational explanation to the results from optical absorption experiments. We have already performed such calculations for InVO4 [17] and InTaO4 [11]. The simulations were carried out in the frame of density-functional theory (DFT) [38] with the Vienna ab initio simulation package (VASP) [39] and have been used here to discuss the experimental results. In the present work, similar calculations have been carried out for InNbO4. The pseudopotential projected augmented-wave method [40, 41] representing the all-electron charge density in the core region was employed. To accomplish an accurate description of InNbO4, the basis set of plane waves was extended up to an energy cutoff of 520 eV. The exchange-correlation energy was described by means of the generalized-gradient approximation (GGA) with the Perdew–Burke–Ernzerhof for solids (PBEsol) functional [42]. In addition, the Monhorst–Pack scheme [43] was employed to generate a dense special k-point sampling for the Brillouin zone (BZ) integration (6 × 6 × 6 grid). The achieved convergence in the total energy was less than 1 meV per formula unit: The forces on the atoms were lower than 0.005 eV/Å, and the deviations of the stress tensor from a diagonal hydrostatic form were smaller than 0.1 GPa. It has been previously shown that for the three studied compounds, DFT calculations provide a good description of the crystal structure at different pressures [11, 12, 17]. Using the calculated crystal structures, electronic band structure calculations, at several pressures, were performed for InNbO4 within the first Brillouin zone along the high-symmetry direction Γ-Z-D-B-Γ-A-E-Z-C2-Y2-Γ, for the low- and high-pressure structures.

3 Results and discussion

3.1 Optical absorption and band structure at ambient pressure

The optical absorption coefficient (α) as a function of photon energy measured for the LP phase of InVO4 and InNbO4 is shown in Figs. 1 and 2, respectively. At ambient conditions, in both compounds, a steep absorption is observed, which corresponds to the fundamental absorption edge, plus a low-energy absorption band. This absorption band is compatible with a typical Urbach tail [44, 45], which has been previously observed in InTaO4 [11] and in many other ternary oxides belonging to the AMO4 family [46, 47]. The nature of the low-energy tail has been the subject of considerable debate and is beyond the scope of this paper [48, 49]. In order to clarify the controversies of the band-gap values for the studied compounds and their nature at ambient conditions, the absorption spectra have been analyzed using the Tauc plot [50]. In InVO4, the absorption spectrum follows a linear behavior in the high-energy region when plotted as (αE)2 versus photon energy (E) (see the bottom panel of Fig. 1), suggesting that the compound is a direct band-gap semiconductor. This result agrees with our recent band structure calculations [17]. In the case of InNbO4, \(\sqrt {\alpha E }\) follows a linear relation with E (see the bottom panel of Fig. 2). This fact suggests that the compound is an indirect band-gap semiconductor as InTaO4 [11]. The value of Eg determined from the Tauc plots for the three compounds of interest is summarized in Table 1. The determined band gaps of InVO4, InNbO4, and InTaO4 are 3.62(5), 3.63(5), and 3.79(5) eV, respectively. In the case of InVO4, the value of Eg is slightly larger but consistent with the value reported by Yan et al. (Eg = 3.4 eV) [23]. For InNbO4, the value of Eg is slightly smaller but consistent with the value reported by Lv et al. (Eg = 3.83 eV) [20]. In the case of InTaO4, our value of Eg is only 5% smaller than the value reported by Malingowski et al. (Eg = 3.96 eV) [51]. This confirms that the studied compounds are wide-gap semiconductors.
Fig. 1

(top) Absorption spectra measured at different pressures for the LP phase of InVO4. The dashed line is the fit to the ambient-pressure absorption spectrum using the model described in the text. The insets show Eg versus pressure. The symbols are the experimental results, and the dashed line is the linear fit to the experimental data. (bottom) Tauc plot used to determine Eg. The dashed line shows the extrapolation of the linear region to the abscissa

Fig. 2

(top) Absorption spectra measured at different pressures for the LP phase of InNbO4. The dashed line is fit to the ambient-pressure absorption spectrum using the model described in the text. The insets show Eg versus pressure. The symbols are the experimental results, and the dashed line is the linear fit to experimental data. The band crossing is indicated. (bottom) Tauc plot used to determine Eg. The dashed line shows the extrapolation of the linear region to the abscissa

Table 1

Experimental and theoretical values of the band gaps (Eg) at ambient pressure

Compound

Experiment

Theory

Gap nature

Eg (eV)

Eu (eV)

References

k points

Eg (eV)

References

InVO4

Direct

3.62(5)

0.0897(5)

This work

Y → Y

4.76

[17]

4.02

[25]

InNbO4

Indirect

3.63(5)

0.1098(3)

This work

Y → Γ-B

3.29

This work

InTaO4

Indirect

3.79(5)

0.0897(5)

[11]

Y → Γ-B

3.74

[11]

The Urbach energy (Eu) determined from the fits made for the ambient-pressure absorption spectra are also included. For the calculations, k points for the top of the valence band and the bottom of the conduction band are indicated

Previous [11, 25, 27] and present theoretical studies corroborate the conclusions extracted from the experimental results. Calculations support that InVO4 is a direct band-gap material with the gap at the Y point of the BZ. The calculated values [25, 27] tend to overestimate Eg (see Table 1). However, it should be noted here that the value of Eg is very sensitive to the functionals selected for DFT calculations [25] and differences of up to 1 eV between measured and calculated band gaps are typical [25, 46]. In spite of the overestimation of the calculated Eg, DFT confirms that InVO4 is a direct wide band-gap material and nicely describes the pressure dependence of Eg as explained in the latter section. One possible reason for the difference between the computed band gap and experimental value of Eg might be the contribution of electron excitonic effects [25]. In the case of InTaO4, the agreement between experiments and calculations is not only qualitative but quantitative [11] (see Table 1). This material is an indirect wide band-gap material with the top of the valence band at the Y point of the BZ and bottom of the conduction band at a point in the Γ-B direction.

For InNbO4, we have obtained qualitatively similar results. The band structure is shown in Fig. 3. As happens in InTaO4, calculations found InNbO4 to be an indirect gap material with the bottom (top) of the conduction (valence) band at the same points of the BZ. In the case of InNbO4, calculations underestimate Eg by 0.3 eV. Therefore, the combination of experiments and calculations indicates that the small band gaps previously reported (1.9 eV for InVO4, 2.5 eV for InNbO4, and 2.6 eV for InTaO4) [15, 16] are probably underestimated values. This could be caused by a wrong interpretation of the low-energy Urbach tail, which in the diffused reflectance measurements reported earlier was assumed to be the fundamental intrinsic absorption. The fact that the low-energy tail does change under compression, while the step edge we assigned to the fundamental absorption blueshifts; it is a confirmation that the low-energy absorption is not due to electronic transitions from the valence band to the conduction band.
Fig. 3

Band structure of InNbO4 at ambient pressure

From the calculations, we also obtained the density of states of InNbO4, which is shown in Fig. 4. In the figure, it can be seen that O 2p states dominate the upper part of the valence bands and Nb 4d states dominate the lower conduction bands with a small contribution from O 2p and In 5s states. Thus, the orbital composition of the band structure near the Fermi level is qualitatively similar in InNbO4, InTaO4, and InVO4, being the band gap determined as first approximation by the molecular electronic structure of the NbO43−, TaO43−, and NbO43− ions in analogy with the behavior observed in other AMO4 compounds [52]. This fact will determine the pressure evolution of the band gap as we will discuss in next section.
Fig. 4

Total electronic density of states (solid black line) and partial electronic density of states (in colors as denoted in the inset) of InNbO4 at ambient pressure

In order to provide more evidence supporting that the absorption spectrum of the different compound corresponds to a fundamental gap plus a low-energy Urbach tail, we have fit the experimental results using a model in which the fundamental absorption dominates the absorption coefficient above a critical energy (Ecrit) and the Urbarch tail dominates it below Ecrit [53]. In this model, the absorption coefficient as a function of the photon energy is given by:
$$\alpha (E) = \left\{ {\begin{array}{*{20}l} {A_{1} e^{{\frac{{E - E_{\text{g}} }}{{E_{\text{u}} }}}} } \hfill & {h\nu \le E_{\text{g}} + E_{\text{crit}} } \hfill \\ {A_{2} (E - E_{\text{g}} )^{n} } \hfill & {h\nu \ge E_{\text{g}} + E_{\text{crit}} } \hfill \\ \end{array} } \right.$$
where the parameters A1 and A2 are correlated by imposing continuity of the function α(E) and its derivative. These conditions also determine the critical energy (Ecrit), below which the Urbach exponential absorption is assumed. In the equation, Eu is the Urbach energy and n is equal to 1/2 or 2 for direct or indirect transitions, respectively. Assuming the Eg values determined from the Tauc plots (see Table 1) and using an iterative procedure, we have fitted the ambient-pressure absorption spectra shown in Figs. 1 and 2(top). As it can be seen, the fits (dashed red lines) reproduce well the experimental results (solid black lines), confirming that assuming a direct band gap for InVO4 plus an Urbach tail and an indirect band gap for InNbO4 plus an Urbach tail is a reasonable hypothesis to describe the absorption spectra of both compounds. From the fits, we have also determined Eu, which is also related to the steepness parameter of the absorption tail. The obtained values are summarized in Table 1. They are comparable with the values obtained in related ternary oxides [44, 53].

3.2 High-pressure behavior of the band gap

In Figs. 1, 2, 5, and 6, we show optical absorption spectra at selected pressures for the low-pressure orthorhombic phase of InVO4 and wolframite phase of InNbO4. The maximum pressure represented for each compound, i.e., 6.3 GPa in InVO4 and 11 GPa in InNbO4, is just below the transition pressure in each compound. In both materials, we have observed a blueshift in the absorption spectra under compression, similar to the one reported for the low-pressure wolframite phase of InTaO4 [11]. Following the same procedure that we used with the ambient-pressure absorption spectra, we have determined Eg for different pressures. The results are shown in the inset of Figs. 1 and 2. The behavior of Eg in InVO4 is linear with pressure. Eg moves at a rate of dEg/dP = 13.3(5) meV/GPa. This value is comparable with the pressure coefficient obtained from calculations, dEg/dP = 8.9 meV/GPa [17]. The opening of the band gap is caused by the fact that the conduction bands move toward higher energy faster than the valence bands which are less sensitive to pressure. The same phenomenon induces the blueshift of the band gap in InNbO4 (see Fig. 2) and InTaO4 [11]. However, these two compounds have a slightly different behavior, with a kink in the pressure dependence of Eg near 6.5 GPa (see Fig. 2). In InNbO4, Eg moves at a rate of 26.8(1.1) meV/GPa up to a pressure of 6.6 GPa. After this pressure, the pressure dependence of Eg slows down to 10.4(2) meV/GPa. According to our band structure calculations, this feature is due to a band crossing. This is caused by the fact that there is a relative maximum in the valence band at the Z point of the BZ which moves faster toward higher energies than absolute maximum of the valence band located at the Y point at ambient pressure. As a consequence, the Z point becomes the absolute maximum beyond 6 GPa. The different pressure dependence of both maxima not only drives the band crossing but also cause the change on the pressure dependence of Eg that we commented when describing the experiments.
Fig. 5

(top) Absorption spectra measured at different pressures for the HP phase of InVO4. The dashed line is the fit to the 6.5 GPa absorption spectrum using the model described in the text. The insets show Eg versus pressure. The band-gap collapse is indicated. The symbols are the experimental results, and the dashed line is the linear fit to them. (bottom) Tauc plot used to determine Eg. The dashed line shows the extrapolation of the linear region to the abscissa

Fig. 6

(top) Absorption spectra measured at different pressures for the HP phase of InNbO4. The dashed line is the fit to the 11.5 GPa absorption spectrum using the model described in the text. The insets show Eg versus pressure. The band-gap collapse is indicated. The symbols are the experimental results, and the dashed line is the linear fit to them. (bottom) Tauc plot used to determine Eg. The dashed line shows the extrapolation of the linear region to the abscissa

The band-crossing phenomenon discovered near 6.5 GPa in InNbO4 has been observed for InTaO4 at a similar pressure (P ~ 7 GPa) [11] and is typical of wolframite-type compounds [10]. For instance, it has been found in CdWO4 around 5 GPa [54] and it is a consequence of the non-isotropic compressibility of wolframite and the distortion induced by pressure in the TaO6 (NbO6) octahedron. In contrast, the VO4 tetrahedron is much less compressible than these units, resulting in the lesser sensitivity of the band structure topology with pressure.

Increasing the pressure beyond 6.3 GPa (11 GPa) in InVO4 (InNbO4), we observed a color change in the samples from colorless to yellow. This color change is due to a band-gap collapse which can be clearly seen by comparing Figs. 1 and 2 with Figs. 5 and 6. The pressure where the abrupt collapse of the band-gap is observed is consistent with the structural phase transition found by XRD and Raman experiments in both compounds [12, 14]. The same band-gap collapse has been detected in InTaO4 at the phase transition near 13 GPa [11]. A similar analysis as for the LP phase has been done for the HP phase to study its band-gap nature and value. We found that the absorption spectrum of both compounds follows a linear behavior in the high-energy region when is plotted as (αE)2 versus photon energy (E) (see Fig. 5 and 6 bottom panel), suggesting that in the HP phase, both compounds are direct band-gap semiconductors. To corroborate these findings, we used the model employed for the absorption coefficient of the low-pressure phase to fit the absorption spectra of the HP phase assuming a direct band gap. As it can be seen in Fig. 5 and 6, the experimental data and the adjusted model are in good agreement in both the compounds. The values obtained for Eg in the HP phase are given in Table 2. There it can be seen that in the three compounds, there is a band-gap collapse, being the band gap considerably smaller in the HP phase than in the LP phase. In addition, after the phase transition, we noticed an increase in the Urbach energy which becomes approximately 0.130(5) eV for the HP phase of the three compounds, which suggest an increase in the crystal lattice disorder.
Table 2

Experimental and theoretical values of the band gaps (Eg) of the HP phase and pressure coefficient for the LP and HP phases

Compound

Study type

dEg/dP (meV/GPa) (LP)

dEg/dP (meV/GPa) (LP BC)

Gap nature (HP)

Eg (eV)

ΔEg collapse (eV)

dEg/dP (meV/GPa) (HP)

References

InVO4

Exp.

13.3(5)

 

Direct

2.20(5)

1.51(10)

8.5(3)

This work

Theo.

8.9

 

Direct

3.06

1.77

9.3

[17]

InNbO4

Exp.

26.8(1.1)

10.4(2)

Direct

2.70(5)

1.20(10)

− 9.6(2)

This work

Theo.

14.8

5.0

Direct

2.02

1.45

− 5.1

This work

InTaO4

Exp.

20.1(9)

15.1(9)

Direct

2.70(5)

1.3(10)

− 8.0(3)

[11]

Theo.

19.8

16.4

Direct

2.25

1.61

− 3.9

[11]

The letters BC refer to the low-pressure phase of InNbO4 and InTaO4 for pressures after the band crossing and before the phase transition. The band-gap collapse at the phase transition (∆Eg) is also given

In the inset of Figs. 5 and 6, we show the pressure dependence of Eg. In both insets, the band-gap collapse is quite evident. It can also be seen that the band gap follows a linear behavior with pressure in the HP phase. However, there is a difference between both compounds. In InVO4, after the transition, Eg increases with pressure. This is consistent with the fact that the HP phase of InVO4 is isostructural to the low-pressure phase of InNbO4 and InTaO4, so a blueshift is expected for the HP phase of InVO4 as happen in the LP phase of the other two compounds. In contrast, in the HP phase of InNbO4, the band gap redshifts under compression, exactly as happened in InTaO4. From the measurements made up to the maximum pressure reached in the experiments, 16 GPa for InVO4 and 20 GPa for InNbO4, we determined dEg/dP about 8.5(3) meV/GPa in the case of InVO4 and − 9.6(2) meV/GPa in the case of InNbO4, which is very similar to the pressure coefficient of − 8.0(3) eV reported for InTaO4. All these results are summarized in Table 2.

Before discussing the calculations carried out for the HP phases, we would like to remark the fact that in the three HP phases, the band gap is in the range 2.2 eV < Eg < 2.7 eV, which makes these phases more suitable than the LP phases for photocatalytic water splitting [55]. Given the possibility of synthesizing the HP polymorphs of InNbO4, InTaO4, and InVO4 as metastable phases at ambient conditions, by means of soft-chemistry methods [56] or using a large-volume apparatus [57], it would be possible in the immediate future to test their photocatalytic properties with the aim of using them in technological applications. Such studies are beyond the scope of this work.

We will now comment in more detail on the calculated band structure of the HP phase of InNbO4 which is shown in Fig. 7. By comparing it with the band structure of the low-pressure phase, it can be noticed that the band structure of the HP phase is much more dispersive than the one of the LP phase. In addition, it resembles very much the band structure of the HP phase of InTaO4 [11]. On the other hand, the calculations indicate that the HP phase of InNbO4 is a direct gap semiconductor (as the one of InTaO4). The maximum of the valence band and the minimum of the conduction band are located at the Γ point of the BZ. This result is in agreement with the conclusion extracted from the analysis of absorption spectra of the HP phase. The theoretical value of Eg at 16.3 GPa is 2.02 eV. This value is 0.7 eV smaller than the measured Eg, being the difference within the range of the typical differences between DFT calculations and experiments. In spite of it, calculations confirm that there is large band-gap collapse at the phase transition in InNbO4 as it also happens in InTaO4. In addition, calculations give a similar evolution of Eg with pressure than the experiments. Specially, they confirm the redshift of the band gap of the HP phase under compression, which is different than the behavior of the LP phases of InVO4, InNbO4, and InTaO4, and the HP phase of InVO4 in which the band gap blueshift under compression.
Fig. 7

Band structure of HP InNbO4 at 16.3 GPa

As happen in the HP phase of InTaO4, the band gap of the HP phase of InNbO4 redshifts because the top of the valence band moves faster toward higher energies than the bottom of the conduction band. This phenomenon can be understood by taking a look to the electronic density of states which is shown in Fig. 8. The main qualitative difference of it with the LP phase is the contribution of In 4d states to the top of the valence band. These states shift with pressure in direction of higher energies faster than O 2p and Nb 4d states, and therefore, the top of the valence band shifts to higher energies faster than the bottom of the conduction band, causing the observed small redshift of Eg. The role of In 4d states is analogous to the role of Mn 3d states in wolframite-type MnWO4 [58], in which the band gap closes under compression as opposed to the behavior of other wolframite like CdWO4, ZnWO4 and MgWO4.
Fig. 8

Total electronic density of states (solid black line) and partial electronic density of states (in colors as denoted in the inset) of HP InNbO4 at 16.3 GPa

3.3 Resistivity measurements

Resistivity measurements were carried out up to 10 GPa on all the compounds studied in this work including InTaO4. The results obtained from the experiments are shown in Fig. 9. As can be seen there, all the compounds at room conditions present a large resistivity of the order of MΩ.cm. These resistivity values suggest that the charge transport cannot be caused by the thermal activation of electrons from the valence band to the conduction band. At ambient conditions (1 bar and 300 K), the thermal energy (the product of the Boltzmann constant and the temperature) available to promote electrons from the valence to the conductions band is 25 meV. Thus, in our compounds, due to their wide band-gap energy (Eg > 3.62 eV), the thermal energy is approximately 1/150 Eg. Therefore, the intrinsic density of free electrons in the conduction band is negligible. As a consequence, the wide band-gap semiconductors InNbO4, InTaO4, and InVO4 cannot be in the intrinsic regime [59]. Notice that even in a narrow-gap semiconductor like GaAs, the intrinsic resistivity is of the order of 108 Ω.cm [60], i.e., two orders of magnitude larger than in InVO4, InNbO4, and InTaO4.
Fig. 9

Resistivity as a function of pressure measured for the three studied compounds. The compounds are identified in the inset

In a recent work by R. van de Krol et al. [58], it has been determined for thin films of InVO4 an electrical conductivity of ~ 4 × 10−8 Ω−1 cm−1 (resistivity ~ 25 × 106 Ω cm) which is consistent with our result at ambient conditions of 13.0(5) × 106 Ω cm for such compound. Also, at room temperature, the carrier concentration is estimated to be 1011 cm−3. Then, assuming an electron mobility of 10 cm2/(V s) typical of polycrystalline materials [61] (like our samples), it will lead a resistivity of the order of 10 MΩ cm as measured. The electrical conductivity on InVO4 has been attributed to the presence of donor states at ~ 0.7 eV below the conduction band [62]. The presence of these donor states has been related mainly to deviations from the ideal In:V ratio of 1:1. Notice that a deviation of 0.05% corresponds to a donor density of approximately 6 × 1019 cm−3. The low bulk conductivity is because only a small fraction of these donors will be ionized [62].

Under compression up to nearly 1.6 GPa, the resistivity increases with pressure in the three compounds. If we assumed that the electron mobility is not affected by pressure up to 1.6 GPa, from the pressure dependence of the resistivity, the pressure evolution of the activation energy of donor states has been calculated to be 8.9(8), 2.5(3), and 4.5(2) meV/GPa for InVO4, InNbO4 and InTaO4, respectively. In all the cases, the activation energy increases as pressure increases in order to explain the behavior of the resistivity. This is consistent with the widening of the band-gap under pressure which will favor the increase in the effective mass of the electrons in the conduction band, making the donor states to move further away from the bottom of the conduction band [63].

At the pressure of about ~ 1.6 GPa, the resistivity of InVO4 shows a sharp discontinuity. This discontinuity in the resistivity can be attributed to the structural phase transition and the collapse of the band-gap that the compound experiences under quasi-hydrostatic conditions at 6.3 GPa. The reduction in the transition pressure in the resistivity measurements is related to the fact that these experiments have been performed under non-hydrostatic conditions, which usually induces a lowering of the transition pressure [63, 64, 65, 66], in some cases up to 10 GPa [67, 68]. From 1.6 GPa to the maximum pressure achieved in the experiments, the resistivity of InVO4 follows a smooth behavior which is consistent with the fact that a second-phase transition in InVO4 is only expected to occur at 28 GPa [17].

We will comment now the results on the other two compounds. Near 1.6 GPa, InNbO4 and InTaO4 present a kink in the pressure dependence of the resistivity, which could be presumably associated with the band crossing that it has been observed near 6.5 GPa in both materials. The phenomenon is more evident in InNbO4 than in InTaO4. In particular, the band crossing might lead to a reduction in the activation energy of donors, leading to an increase in the carrier concentration which necessarily will be reflected in the pressure dependence of the resistivity. However, the observed behavior could be caused by many other factors like a change of the carrier mobility. To clarify this issue, measurement as a function of temperature at different pressures should be performed, which is beyond the scope of this work.

In InNbO4, a discontinuity has been observed in the resistivity at 9.5 GPa which evidences the existence of the phase transition. In contrary to InTaO4, no discontinuity has been observed up to 10 GPa. The detection of the transition in InNbO4 at 9.5 GPa and not at 11 GPa is related with the presence of non-hydrostatic stresses in the resistivity experiments, as we already discussed for the reduction in the transition pressure in InVO4. In InTaO4, the transition occurs at 13 GPa and therefore is not surprising that it is not detected in the resistivity measurements (maximum pressure 10 GPa). One hypothesis to explain the increase in the resistivity at the phase transition in InNbO4 is the generation of defects. Indeed, as commented before, we have observed that the Urbach energy increases considerably after the phase transition in InNbO4. This supports the hypothetical formation of defects at the transition. The defects can act as recombination centers, reducing the carrier concentration and leading to the observed increase in the resistivity.

4 Conclusions

By means of the combination of optical absorption measurements and band structure calculations, we have shown that InVO4, InNbO4, and InTaO4 are wide band-gap materials with energy band gaps of 3.62(5), 3.63(5), and 3.79(5) eV, respectively. We have also determined the pressure dependence of the band-gap energy up to nearly 20 GPa. In the low-pressure phase of the three compounds, the band gap blueshifts under compression. In all of them, we have also observed a band-gap collapse that can be correlated with the previously observed phase transitions. Band structure calculations provide a rational explanation to the observed behaviors. In particular, a picture that satisfactorily explains the electronic properties at ambient and high pressure has been proposed. Finally, resistivity measurements are consistent with the optical experiments. They have been useful to determine that the three materials are not intrinsic semiconductors. Possible reasons for the behavior of the resistivity have been discussed. We consider the reported results are a contribution to deepen the understanding of the electronic properties of the photocatalytic materials InVO4, InNbO4, and InTaO4. The accurate determination of band-gap energies and the consistence between different experimental techniques and computer simulations make our findings relevant for the optimization of applications like photocatalytic production of hydrogen from water splitting.

Notes

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 Nos: MAT2016-75586-C4-1-P/3-P and MAT2015-71070-REDC and by Generalitat Valencia through the grant Prometeo/2018/123 EFIMAT. P. B. and A. V. acknowledge the Kempe Foundation and the Knut och Alice Wallenberg Foundation for their financial support. S. N. Achary and A. B. Garg acknowledge the support provided by Universitat de Valencia by means of a visitor grant to perform a research stay (Atracció de Talent, VLC-CAMPUS).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

References

  1. 1.
    Minakshi M, Watcharatharapong T, Chakraborty S, Ahuja R (2018) A combined theoretical and experimental approach of a new ternary metal oxide in molybdate composite for hybrid energy storage capacitors. APL Mater 6:047701CrossRefGoogle Scholar
  2. 2.
    Errandonea D, Manjon FJ (2008) Pressure effects on the structural and electronic properties of ABX4 scintillating crystals. Prog Mater Sci 53:711CrossRefGoogle Scholar
  3. 3.
    Rui M, Li X, Gan L, Zhai T, Zeng H (2016) Ternary oxide nanocrystals: universal laser hydrothermal synthesis, optoelectronic and electrochemical applications. Adv Funct Mater 26:5051CrossRefGoogle Scholar
  4. 4.
    Noureldine D, Takanabe K (2016) State-of-the-art Sn2+-based ternary oxides as photocatalysts for water splitting: electronic structures and optoelectronic properties. Catal Sci Technol 6:7656CrossRefGoogle Scholar
  5. 5.
    Errandonea D, Garg AB (2018) Recent progress on the characterization of the high-pressure behaviour of AVO4 orthovanadates. Prog Mater Sci 97:123CrossRefGoogle Scholar
  6. 6.
    Panchal V, Garg N, Poswal HK, Errandonea D, Rodriguez-Hernandez P, Muñoz A, Cavalli E (2017) High-pressure behavior of CaMoO4. Phys Rev Mater 1:043605CrossRefGoogle Scholar
  7. 7.
    Zhang X, Zhang J, Yu J, Zhang Y, Yu F, Jia L, Tan Y, Zhu Y, Hou B (2019) Enhancement in the photocatalytic antifouling efficiency over cherimoya-like InVO4/BiVO4 with a new vanadium source. J Colloid Interface Sci 533:358CrossRefGoogle Scholar
  8. 8.
    Oshikiri M, Boero M, Ye J, Zou Z, Kido G (2002) Electronic structures of promising photocatalysts InMO4 (M = V, Nb, Ta) and BiVO4 for water decomposition in the visible wavelength region. J Chem Phys 117:7313CrossRefGoogle Scholar
  9. 9.
    Errandonea D, Segura A, Sanchez-Royo JF, Muñoz V, Grima P, Chevy A, Ulrich C (1997) Investigation of conduction-band structure, electron-scattering mechanisms, and phase transitions in indium selenide by means of transport measurements under pressure. Phys Rev B 55:16217CrossRefGoogle Scholar
  10. 10.
    Errandonea D, Ruiz-Fuertes J (2018) A brief review of the effects of pressure on wolframite-type oxides. Crystals 8:71CrossRefGoogle Scholar
  11. 11.
    Errandonea D, Popescu C, Garg AB, Botella P, Martinez-García D, Pellicer-Porres J, Rodríguez-Hernández P, Muñoz A, Cuenca-Gotor V, Sans JA (2016) Pressure-induced phase transition and band-gap collapse in the wide-band-gap semiconductor InTaO4. Phys Rev B 93:035204CrossRefGoogle Scholar
  12. 12.
    Garg AB, Errandonea D, Popescu C, Martinez-García D, Pellicer-Porres J, Rodríguez-Hernández P, Muñoz A, Botella P, Cuenca-Gotor VP, Sans JA (2017) Pressure-driven isostructural phase transition in InNbO4: in situ experimental and theoretical investigations. Inorg Chem 56:5420CrossRefGoogle Scholar
  13. 13.
    Baran EJ (1998) Materials belonging to the CrVO4 structure type: preparation, crystal chemistry and physicochemical properties. J Mater Sci 33:2479CrossRefGoogle Scholar
  14. 14.
    Errandonea D, Gomis O, García-Domene B, Pellicer-Porres J, Katari V, Achary SN, Tyagi AK, Popescu C (2013) New polymorph of InVO4: a high-pressure structure with six-coordinated vanadium. Inorg Chem 52:12790CrossRefGoogle Scholar
  15. 15.
    Ye J, Zou Z, Arakawa H, Oshikiri M, Shimoda M, Matsushita A, Shishido T (2002) Correlation of crystal and electronic structures with photophysical properties of water splitting photocatalysts InMO4 (M = V5+, Nb5+, Ta5+). J Photochem Photobiol A Chem 148:79CrossRefGoogle Scholar
  16. 16.
    Zou Z, Ye J, Arakawa H (2000) Structural properties of InNbO4 and InTaO4: correlation with photocatalytic and photophysical properties. Chem Phys Lett 332:271CrossRefGoogle Scholar
  17. 17.
    López-Moreno S, Rodríguez-Hernández P, Muñoz A, Errandonea D (2017) First-principles study of InVO4 under pressure: phase transitions from CrVO4- to AgMnO4-type structure. Inorg Chem 56:2697CrossRefGoogle Scholar
  18. 18.
    Lu M, Li Q, Zhou C, Zhang C, Shi H (2018) Effects of nonmetal elements doping on the electronic structures of InNbO4: first-principles calculations. Mater Res Express 5:075505CrossRefGoogle Scholar
  19. 19.
    Lin HY, Chen YF, Chen YW (2017) Water splitting reaction on NiO/InVO4 under visible light irradiation. Int J Hydrog Energy 32:86CrossRefGoogle Scholar
  20. 20.
    Lv J, Kako T, Zou Z, Ye J (2010) Enhanced N-doping efficiency and photocatalytic H2 evolution rate of InNbO4 by mechanochemical activation. J Mater Res 25:159CrossRefGoogle Scholar
  21. 21.
    Li GL, Yin Z (2011) Theoretical insight into the electronic, optical and photocatalytic properties of InMO4 (M = V, Nb, Ta) photocatalysts. Phys Chem Chem Phys 13:2824CrossRefGoogle Scholar
  22. 22.
    Lee DS, Chen HJ, Chen YW (2012) Photocatalytic reduction of carbon dioxide with water using InNbO4 catalyst with NiO and Co3O4 cocatalysts. J Phys Chem Solids 73:661CrossRefGoogle Scholar
  23. 23.
    Yan M, Yan Y, Wang C, Lu W, Shi W (2014) Ni2+ doped InVO4 nanocrystals: one-pot microwave-assisted synthesis and enhanced photocatalytic O2 production activity under visible-light. Mater Lett 121:215CrossRefGoogle Scholar
  24. 24.
    Feng H, Hou D, Huang Y, Hu X (2014) Facile synthesis of porous InNbO4 nanofibers by electrospinning and their enhanced visible-light-driven photocatalytic properties. J Alloys Compd 592:301CrossRefGoogle Scholar
  25. 25.
    Mondal S, Appalakondaiah S, Vaitheeswaran G (2016) High pressure structural, electronic, and optical properties of polymorphic InVO4 phases. J Appl Phys 119:085702CrossRefGoogle Scholar
  26. 26.
    Chaison J, Wetchakun K, Wetchakun N (2017) Investigation of the physical, optical, and photocatalytic properties of CeO2/Fe-doped InVO4 composite. J Phys Chem Solids 111:95CrossRefGoogle Scholar
  27. 27.
    Zou Z, Ye J, Sayama K, Arakawa H (2001) Direct splitting of water under visible light irradiation with an oxide semiconductor photocatalyst. Nature 414:625CrossRefGoogle Scholar
  28. 28.
    Errandonea D (2010) The melting curve of ten metals up to 12 GPa and 1600 K. J Appl Phys 108:033517CrossRefGoogle Scholar
  29. 29.
    Lacomba-Perales R, Errandonea D, Segura A, Ruiz-Fuertes J, Rodriguez-Hernandez P, Radescu S, Lopez-Solano J, Mujica A (2011) A combined high-pressure experimental and theoretical study of the electronic band-structure of scheelite-type AWO4 (A = Ca, Sr, Ba, Pb) compounds. J Appl Phys 110:043703CrossRefGoogle Scholar
  30. 30.
    Panchal V, Errandonea D, Segura A, Rodriguez-Hernandez P, Muñoz A, Lopez-Moreno S, Bettinelli M (2011) The electronic structure of zircon-type orthovanadates: effects of high-pressure and cation substitution. J Appl Phys 110:043723CrossRefGoogle Scholar
  31. 31.
    Errandonea D, Martinez-Garcia D, Lacomba-Perales R, Ruiz-Fuertes J, Segura A (2006) Effects of high pressure on the optical absorption spectrum of scintillating PbWO4 crystals. Appl Phys Lett 89:091913CrossRefGoogle Scholar
  32. 32.
    Errandonea D, Muñoz A, Gonzalez-Platas J (2014) Comment on “High-pressure x-ray diffraction study of YBO3/Eu3+, GdBO3, and EuBO3: pressure-induced amorphization in GdBO3”. J Appl Phys 115:216101CrossRefGoogle Scholar
  33. 33.
    Errandonea D (2013) Exploring the properties of MTO4 compounds using high-pressure powder x-ray diffraction. Cryst Res Technol 50:729CrossRefGoogle Scholar
  34. 34.
    Mao HK, Xu J, Bell PM (1986) Calibration of the ruby pressure gauge to 800 kbar under quasi-hydrostatic conditions. J Geophys Res 91:4673CrossRefGoogle Scholar
  35. 35.
    Klotz S, Chervin JC, Munsch P, Le Marchand G (2009) Hydrostatic limits of 11 pressure transmitting media. J Phys D Appl Phys 42:075413CrossRefGoogle Scholar
  36. 36.
    Errandonea D, Segura A, Martínez-García D, Muñoz-San Jose V (2009) Hall-effect and resistivity measurements in CdTe and ZnTe at high pressure: electronic structure of impurities in the zinc-blende phase and the semimetallic or metallic character of the high-pressure phases. Phys Rev B 79:125203CrossRefGoogle Scholar
  37. 37.
    Errandonea D, Martinez-Garcia D, Segura A, Ruiz-Fuertes J, Lacomba-Perales R, Fages V, Chevy A, Roa L, Muñoz V (2006) High-pressure electrical transport measurements on p-type GaSe and InSe. High Press Res 26:513CrossRefGoogle Scholar
  38. 38.
    Hohenberg P, Kohn W (1964) Inhomogeneous electron gas. Phys Rev 136:3864MathSciNetCrossRefGoogle Scholar
  39. 39.
    Kresse G, Furthmüller J (1996) Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set. Phys Rev B 54:11169CrossRefGoogle Scholar
  40. 40.
    Blöch E (1994) Projector augmented-wave method. Phys Rev B 50:17953CrossRefGoogle Scholar
  41. 41.
    Kresse G, Joubert D (1999) From ultrasoft pseudopotentials to the projector augmented-wave method. Phys Rev B 59:1758CrossRefGoogle Scholar
  42. 42.
    Perdew JP, Ruzsinszky A, Csonka GI, Vydrov O, Scuseria GE, Constantin LA, Zhou X, Burke K (2008) Restoring the density-gradient expansion for exchange in solids and surfaces. Phys Rev Lett 100:136406CrossRefGoogle Scholar
  43. 43.
    Monkhorst HJ, Pack JD (1976) Special points for Brillouin-zone integrations. Phys Rev B 13:5188MathSciNetCrossRefGoogle Scholar
  44. 44.
    Urbach F (1953) The long-wavelength edge of photographic sensitivity and of the electronic absorption of solids. Phys Rev 92:1324CrossRefGoogle Scholar
  45. 45.
    Studenyak I, Kranj M, Kurik M (2014) Urbach rule in solid state physics. Int J Opt Appl 4:76Google Scholar
  46. 46.
    Errandonea D, Muñoz A, Rodríguez-Hernández P, Proctor JE, Sapiña F, Bettinelli M (2015) Theoretical and experimental study of the crystal structures, lattice vibrations, and band structures of monazite-type PbCrO4, PbSeO4, SrCrO4, and SrSeO4. Inorg Chem 54:7524CrossRefGoogle Scholar
  47. 47.
    Itoh M, Yokota H, Horimoto M, Fujita M, Usuki Y (2002) Urbach rule in PbWO4. Phys Status Solidi B 231:595CrossRefGoogle Scholar
  48. 48.
    Sumi H, Toyozawa Y (1971) Urbach-Martienseen rule and exciton trapped momentarily by lattice vibrations. J Phys Soc Jpn 31:342CrossRefGoogle Scholar
  49. 49.
    Dow JD, Redfield D (1972) Toward a unified theory of Urbach’s rule and exponential absorption edges. Phys Rev B 5:594CrossRefGoogle Scholar
  50. 50.
    Tauc J (1968) Optical properties and electronic structure of amorphous Ge and Si. Mater Res Bull 3:37CrossRefGoogle Scholar
  51. 51.
    Malingowski AC, Stephens PW, Huq A, Huang Q, Khald S, Khalifah PG (2012) substitutional mechanism of ni into the wide-band-gap semiconductor InTaO4 and its implications for water splitting activity in the wolframite structure type. Inorg Chem 51:6096CrossRefGoogle Scholar
  52. 52.
    Errandonea D (2017) High-pressure phase transitions and properties of MTO4 compounds with the monazite-type structure. Phys Status Solidi B 254:1700016CrossRefGoogle Scholar
  53. 53.
    Ruiz-Fuertes J, Errandonea D, Manjón FJ, Martínez-García D, Segura A, Ursaki VV, Tiginyanu IM (2008) High-pressure effects on the optical-absorption edge of CdIn2S4, MgIn2S4, and MnIn2S4 thiospinels. J Appl Phys 103:063710CrossRefGoogle Scholar
  54. 54.
    Ruiz-Fuertes J, Friedrich A, Errandonea D, Segura A, Morgenroth W, Rodríguez-Hernández P, Muñoz A, Meng Y (2017) Optical and structural study of the pressure-induced phase transition of CdWO4. Phys Rev B 95:174105CrossRefGoogle Scholar
  55. 55.
    Takanabe K (2017) Photocatalytic water splitting: quantitative approaches toward photocatalyst by design. ACS Catal 7:8006CrossRefGoogle Scholar
  56. 56.
    Gai S, Li C, Yang P, Lin J (2014) Recent progress in rare-earth micro/nanocrystals: soft chemical synthesis, luminescent properties, and biomedical applications. Chem Rev 114:2343CrossRefGoogle Scholar
  57. 57.
    Hua FB, Liang K-C, Kung J, Hsu W-L, Wang Y (2012) A large volume multi-anvil apparatus for the earth sciences community in Taiwan. Terr Atmos Ocean Sci 23:647CrossRefGoogle Scholar
  58. 58.
    Ruiz-Fuertes J, Lopez-Moreno S, Lopez-Solano J, Errandonea D, Segura A, Lacomba-Perales R, Muñoz A, Radescu S, Rodrıguez-Hernandez P, Gospodinov M, Nagornaya LL, Tu CY (2012) Pressure effects on the electronic and optical properties of AWO wolframites (A = Cd, Mg, Mn, and Zn): the distinctive behavior of multiferroic MnWO4. Phys. Rev. B 86:125202CrossRefGoogle Scholar
  59. 59.
    Kittel Ch (1996) Introduction to solid state physics. Wiley, HobokenzbMATHGoogle Scholar
  60. 60.
    Sze SM, Irvin JC (1968) Resistivity, mobility and impurity levels in GaAs, Ge, and Si at 300 K. Solid State Electron 11:599CrossRefGoogle Scholar
  61. 61.
    van de Krol R, Ségalini J, Enache CS (2011) Influence of point defects on the performance of InVO4 photoanodes. J. Photonics Energy 1:016001CrossRefGoogle Scholar
  62. 62.
    Joshi DP, Sen K (1983) Effect of grain size on the resistivity of polycrystalline material. Solar Cells 9:261CrossRefGoogle Scholar
  63. 63.
    Yu P, Cardona M (1996) Fundamentals of Semiconductors. Springer, BerlinCrossRefGoogle Scholar
  64. 64.
    Lei L, Li Y, Hong L, Ying L, Chun-Qiang Z, Long-Xing Y, Gui-Ping L (2018) First principles calculation of the non-hydrostatic effects on structure and Raman frequency of 3C-SiC. Sci Rep 8:11279CrossRefGoogle Scholar
  65. 65.
    Jenei Z, Liermann HP, Cynn H, Klepeis J-HP, Baer BJ, Evans WJ (2011) Structural phase transition in vanadium at high pressure and high temperature: influence of non-hydrostatic conditions. Phys Rev B 83:05410CrossRefGoogle Scholar
  66. 66.
    Guennou M, Bouvier P, Haumont R, Garbarino G, Kreisel J (2011) High-pressure phase transitions in BiFeO3: hydrostatic versus non-hydrostatic conditions. Phase Transit 84:474CrossRefGoogle Scholar
  67. 67.
    Errandonea D, Meng Y, Somayazulu M, Häusermann D (2005) Pressure-induced α → ω transition in titanium metal: a systematic study of the effects of uniaxial stress. Physica B 355:116CrossRefGoogle Scholar
  68. 68.
    Garg AB, Errandonea D, Rodríguez-Hernández P, Muñoz A (2017) ScVO4 under non-hydrostatic compression: a new metastable polymorph. J Phys Condens Matter 29:055401CrossRefGoogle Scholar

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Division of Materials Science, Department of Engineering Science and MathematicsLuleå University of TechnologyLuleåSweden
  2. 2.Departamento de Física Aplicada-Instituto de Ciencia de Materiales, MALTA Consolider TeamUniversidad de ValenciaValenciaSpain
  3. 3.High-Pressure and Synchrotron Radiation Physics DivisionBhabha Atomic Research CentreMumbaiIndia
  4. 4.Homi Bhabha National InstituteMumbaiIndia
  5. 5.Departamento de Física, Instituto de Materiales y Nanotecnología, MALTA Consolider TeamUniversidad de La LagunaLa LagunaSpain
  6. 6.Chemistry DivisionBhabha Atomic Research CentreTrombay, MumbaiIndia

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