† Corresponding author. E-mail:
First principles calculations of structural, electronic, mechanical, and thermodynamic properties of different polymorphs of BiVO4 are performed using Bender-type plane/wave ultrasoft pseudopotentials within the generalized gradient approximation (GGA) in the frame of density functional theory (DFT). The calculated structural and electronic properties are consistent with the previous theoretical and experimental results. The electronic structures reveal that m-BiVO4, op-BiVO4, and st-BiVO4 have indirect band gaps, on the other hand, zt-BiVO4 has a direct band gap. From the DOS and Mulliken’s charge analysis, it is observed that only m-BiVO4 has 6s2 Bi lone pair. Bond population analysis indicates that st-BiVO4 shows a more ionic nature and a similar result is obtained from the elastic properties. From the elastic properties, it is observed that st-BiVO4 is more mechanically stable than the others. st-BiVO4 is more ductile and useful for high electro-optical and electro-mechanical coupling devices. Our calculated thermodynamic properties confirm the similar characteristics found from electronic and elastic properties. m-BiVO4 is useful as photocatalysts, solid state electrolyte, and electrode and other polymorphs are applicable in electronic device fabrications.
At the present, finding an alternative energy source is a great demand due to the decreasing of available fossil and inadequate natural energy sources in the technology dependent world, which can also reduce environmental pollution. These limitations can be overcome by degrading toxic pollutants and splitting water for hydrogen production. To fulfill this purpose, photocatalyst may play an important role.
Since solar energy is one of the abundant energy sources, it can be widely used for electrical and thermal power generation. Due to the enormous sources of chemical energy such as H2, as compared to electricity and its environmental stability and potentially higher efficiency solar cell is able to make a concentration as one of the promising technological concepts. It is well known that wide band gap semiconductors, such as TiO2 (3.2 eV) and ZnO (3.4 eV), are extensively used as photocatalysts.[1, 2] The control of both sizes and shapes of semiconductor photocatalysts is very important for their photocatalytic activity because the photocatalytic reaction occurs at the interface between photocatalyst and electrolyte. However, the utilization of solar energy, i.e., the solar cell efficiency, is greatly affected by the mismatch between the large band gap of the semiconductor and the sunlight spectrum. TiO2 and ZnO based solar cells are effective only in the ultraviolet region (utilization of about 4% of the sunlight energy). Therefore, a photocatalyst with a narrow band gap responding to visible light is highly desired.
Ti-free narrow band gap semiconducting oxides containing bismuth, such as BiVO4, Bi2WO6, and BiMoO6, have recently received a great deal of attention because of their visible light responsive photocatalytic activities.[3–8] Among these materials, BiVO4 is one of the most active O2 evolution photocatalyst in the field of semiconductor and photoelectrode[3, 6] due to its relatively low band gap of about 2.4 eV, enabling it to the more efficient use of visible light and an adequate position of the conduction and valance bands as compared to the oxidation potential of water.[6] In addition, BiVO4 is a relatively abundant,[6, 8] non-toxic material[9] and it also displays various interesting and desirable physical properties, such as ionic conductivity[10] and ferro-elasticity.[11]
There are different polymorphs of BiVO4, the well known polymorphs are monoclinic clinobisvanite (m-BiVO4), orthorhombic pucherite (op-BiVO4, zircon tetragonal dreyerite (zt-BiVO4, and scheelite tetragonal (st-BiVO4.[5, 12] Among them, m-BiVO4 with a band gap of 2.4 eV shows higher photocatalytic activity for O2 evolution, chemical reaction induced visible light irradiation, photo decomposition of organic pollutants, water decomposition, carbon dioxide reduction, and generation of photo-current.[3–5, 13–19] Several methods, such as solid-state reaction, co-precipitation, hydrothermal treatment, chemical bath deposition, organometallic decomposition, and sonoechemical routes have been reported for the fabrication of BiVO4.[11, 16, 20–23] Aqueous, hydrothermal, and solvothermal processes are different solution based methods that have been developed to fabricate m-BiVO4 nanostructures, such as nanoellipsoids,[24–26] nanowires/nanofibers,[27, 28] nanosheets/nanoplates,[29, 30] hyperbranched crystals,[31] and mesocrystals.[32]
On the other hand, recent high quality experimental results highlighted that the photo-electrochemical (PEC)-induced oxidation under visible light irradiations represents a challenging test of modern electronic structure of BiVO4.[18, 33–36] The electronic and optical properties of BiVO4 are studied by using density function theory (DFT) and these studies show that it is a direct band gap material with a band gap of 2.16 eV.[15, 37] UV–vis spectra suggest that BiVO4 has a dipole-allowed direct band gap,[18, 38] but the experimental value is 2.4 eV.[3, 5, 16, 39–42] Several authors recently studied its electronic properties introducing GGA with PBSol,[43] hybrid functions (HSE 06)[44–46] to improve the calculated energy band gap.
However, there is still an incomplete understanding of the physical properties of BiVO4 that leads to a high photocatalytic activity as well as the formation process correlated with this phenomenon. To study the durability of photocatalyst, solid state electrolyte and electrode, we need to know the mechanical stability. Yuan et al.[47] reported on the pressure dependent mechanical stability, but there is no theoretical or experimental study on the thermodynamical stability of BiVO4 polymorphs which will support many applications. Elastic properties of materials provide information regarding the bonding characteristics between crystal planes of the atoms and the anisotropic character of the bond is useful to determine the structural stability of the crystal. In addition, the thermodynamic properties of photocatalytic compounds are important because the Gibbs free energy, Debye temperature, and heat capacity can determine the thermodynamical stability of the system.
In this paper, we investigate the electronic structure, elastic and thermodynamic properties of BiVO4 polymorphs and also study their interrelation using first principles calculations.
The calculations were performed using the CASTEP code.[48] The geometrical structures and physical properties such as electronic, elastic, and thermodynamic properties were calculated with ultrasoft pseudopotential using density function theory (DFT).[49] We employed Perdew–Burke–Ernzerhof GGA[50] to calculate the exchange and correlation potentials. The valence configurations are 6s26p3 for Bi, 2s22p4 for O, and 3d34s2 for V. Here, we considered two formula units of BiVO4 in a primitive cell. The kinetic energy cutoff for the plane waves was 480 eV and the energy convergence criterion was chosen to be 10−6 eV. The maximum force on each atom and stress were less than 0.01 eV/Å and 0.05 GPa, respectively, and the displacement of atoms during the geometry optimization was less than 0.0005 Å. The Brillouin zone was sampled using the Monkhorst–Pack scheme with a 12 × 12 × 6 k-point set.
The optimized lattice parameters of m-BiVO4 (space group I2/b),[14] op-BiVO4 (space group Pnca),[51] zircon tetragonal (zt-BiVO4 (space group I41/amd),[52] and st-BiVO4 (space group I41/a)[14] are tabulated in Table Calculated, theoretical, and experimental lattice parameters of different BiVO4 polymorphs.
Polymorphs
Present work
Theoretical[47, 52, 53]
Experimental[14, 51, 54]
a/Å
b/Å
c/Å
a/Å
b/Å
c/Å
a/Å
b/Å
c/Å
m-BiVO4
5.1684
5.1301
11.6887
5.183
5.074
11.711
5.1935
5.0898
11.6972
op-BiVO4
5.3863
5.0509
11.9070
–
–
–
–
5.33
5.06
12.02
zt-BiVO4
7.3633
7.3633
6.4337
7.350
7.350
6.434
7.303
7.303
6.584
st-BiVO4
5.1496
5.1496
11.6380
5.121
5.121
11.647
5.147
5.147
11.7216
The basic unit structures of BiVO4 polymorphs are shown in figs. (color online) Crystal structures of (a) m-BiVO4, (b) op-BiVO4, (c) zt-BiVO4, and (d) st-BiVO4.
The investigation of the electronic band structure for understanding the electronic properties of BiVO4 polymorphs is very useful. The band structure of BiVO4 is shown in figs. (color online) GGA calculated band structures of (a) m-BiVO4, (b) op-BiVO4, (c) zt-BiVO4, and (d) st-BiVO4 along some high-symmetry lines in the Brillouin zone.
The total and partial densities of states corresponding to the electronic band structures of BiVO4 polymorphs are shown in figs. (color online) Total DOS and PDOS of (a) m-BiVO4, (b) op-BiVO4, (c) zt-BiVO4, and (d) st-BiVO4 calculated by GGA.
The bonding behavior of BiVO4 can be studied from the Mulliken charge analysis and bond populations. The atomic charges, chemical bond lengths, and bond populations are listed in Table Calculated bond length, bond population, charge, and band gap of different BiVO4 polymorphs.
Polymorphs
Bond length
Population
Bond length
Population
Charge/e
Band gap/eV
Bi–O/Å
Bi
V–O/Å
V
Bi
V
O
m-BiVO4
2.397, 2.402, 2.469, 2.575
0.06, 0.13, 0.05, 0.07
1.720, 1.761, 2.978
0.67, 0.61, –0.03
1.84
0.87
–0.71
2.193
op-BiVO4
2.359, 2.380, 2.562, 2.616
0.16, 0.05, 0.03, –0.03
1.691, 1.791, 2.796
0.72, 0.54, 0.02
1.83
0.87
–0.75
2.461
zt-BiVO4
2.399, 2.509
0.19, 0.05
1.728
0.66
1.87
0.89
–0.69
2.598
st-BiVO4
2.439, 2.474
0.06, 0.10
1.739
0.64
1.85
0.87
–0.68
2.165
In all of the polymorphs of BiVO4, the charge transfers from V and Bi to O are about 0.89 and 1.87 electrons, respectively, and the V–O bond populations (0.67, 0.72, 0.66, 0.64) are larger than those (0.13, 0.16, 0.19, 0.10) of the Bi–O bonds. Therefore, the strength of covalent bonding in the V–O bond is stronger than that in the Bi–O bond and the bonding behavior of BiVO4 is mixed covalent-ionic, where m-BiVO4 and op-BiVO4 show relatively more covalency nature than the other polymorphs. From the crystal structure and electronic properties of BiVO4, we conclude that the V atom makes both ionic and covalent bonds with O to form
The calculated elastic coefficients and stiffness constants are tabulated in Table
![]() |
![]() | Table 3.
Calculated elastic constants |
Similarly, for the orthorhombic crystal, the mechanical stability conditions are[58, 59]
For the tetragonal crystal, the mechanical stability conditions are[60]
By using the calculated data, it is seen that the elastic constants satisfy the above criteria, so we can say that m-BiVO4, op-BiVO4, zt-BiVO4, and st-BiVO4 are mechanically stable.
Voigt,[61] Reuss and Angew[62] separately proposed the average relations expressing the strain in terms of the given stress. Hill[63, 64] proved that the approximations made by Voigt and Reuss represent the upper and lower bounds of the elastic constants, respectively. The resulting Voigt and Reuss moduli are expressed in terms of the stiffness constants
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Thus, the Hill-averaged bulk
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All the calculated elastic constants are shown in Table Calculated bulk modulus B (GPa), shear modululs G (GPa), Young’s modulus E (GPa), G/B, Poisson ratio υ, anisotropy factors
Polymorphs
m-BiVO4
111.34
52.91
108.52
51.28
52.10
109.93
134.97
0.474
0.295
1.116
0.921
1.399
0.66
5.43
op-BiVO4
107.24
51.58
98.52
46.06
48.82
102.88
126.46
0.475
0.295
0.669
0.423
1.067
0.63
5.13
zt-BiVO4
112.48
47.56
105.45
36.30
41.93
108.97
111.49
0.385
0.330
0.578
–
1.647
0.36
2.82
st-BiVO4
132.38
58.46
131.89
54.20
56.33
132.13
147.96
0.426
0.313
0.997
–
1.917
0.64
4.80
Shear modulus G is a quantity for measuring the stiffness of a material, which is also a measure of resistance to reversible deformation upon shear stress. Larger shear modulus indicates that the directional bonding between atoms is more pronounced.
Materials with high B and G are likely to be hard materials. The ratio of G/B gives the information about covalent and ionic behavior of materials on the basis of their brittle and ductile character in solids.[66] The upper limits of G/B are 1.1 for brittle and 0.6 for ductile character, i.e., if
The ductility/brittleness is very important in the battery fabrication, since the electrode/electrolyte interface contact is crucial for better electrical conductance. Ductile electrode/electrolyte material can be able to change its shape without fracture. Ductile electrolyte material demonstrates good performance in terms of device fabrication, cycling performance, and safety.
From our calculation, it is observed that BiVO4 polymorphs are ductile in order of
The Young modulus E is important for technological and engineering applications. The larger E indicates more stiffer materials. High E indicates higher binding energies and shorter interatomic bond length in the materials.[67] Hence st-BiVO4 is stiffer than the other three.
The Poisson ratio measures the degree of directionality of the covalent bonds. The Poisson ratio is small (
The anisotropy of a material is another important parameter used to determine whether the structural properties are the same in all directions or not. In practice, all single crystals are anisotropic, so an appropriate parameter is needed to characterize the extent of anisotropy. For orthorhombic and monoclinic structures, the shear anisotropic factors are[69]
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The calculated anisotropy factors are tabulated in Table
Klemman[72] introduced an important parameter called internal strain parameter ξ, which describes the relative positions of the cation and anion sub-lattices under volume conserving strain distortions, for which positions are not fixed by symmetry[73] using the relation tendency of bond bending to bond stretching. It is defined as
![]() |
Finally, we analyze the hardness of these materials by adopting the empirical scheme[75] which correlates Vicker’s hardness
![]() |
In this paper, we used the thermodynamic property to describe the structural stabilities of different polymorphs of BiVO4 with the elevated temperature.
Gibbs free energy G is one of the most important thermodynamic parameters to describe the stability of a compound. The variations of Gibbs free energy of different polymorphs of BiVO4 with temperature are shown in Fig. (color online) Temperature dependent free energy of different BiVO4 polymorphs.
Debye temperature
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(color online) Temperature dependent Debye temperature of different BiVO4 polymorphs.
The calculated Calculated volume V (Å3), density ρ (
Polymorphs
V
m-BiVO4
298
7.22
4986
2687
2999.65
242.94
1.744
op-BiVO4
323
6.64
5029
2711
3026.46
238.57
1.743
zt-BiVO4
349
6.17
5170
2607
2923.46
224.71
1.971
st-BiVO4
309
6.97
5453
2843
3180.82
254.58
1.859
Debye temperature
![]() | Fig. 6. (color online) Temperature dependent constant-volume heat capacity ![]() |
The Gruneisen parameter γ is often referred to as a temperature dependent anharmonicity parameter that reflects how many phonon vibrations in a crystal lattice deviate from harmonic oscillation. It also describes how the thermal properties of the material vary with the unit cell size. Anharmonicity of the chemical bond drives the phonon–phonon umklapp and normal processes that limit the lattice thermal conductivity.[79] The Gruneisen parameter γ of BiVO4 polymorphs has been calculated using the following relation:[80]
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![](cpb_26_3_036301/cpb_26_3_036301_eq109.gif)
![](cpb_26_3_036301/cpb_26_3_036301_eq110.gif)
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The calculated Gruneisen parameters of BiVO4 are tabulated in Table
To study the structural, mechanical stability, electronic and thermodynamic properties of BiVO4 polymorphs, we employed first principles calculations with GGA. Our calculated optimized lattice parameters of this compound are in good agreement with the available theoretical and experimental results. From the band structure, it is revealed that m-BiVO4, op-BiVO4, and st-BiVO4 structures are indirect band gap materials, while zt-BiVO4 is a direct band gap material. Mulliken charge analysis indicates that all the polymorphs are mixed covalent-ionic in nature. The presence of a lone pair in m-BiVO4 makes it a good candidate for photocatalytic application. The obtained elastic properties indicate that all polymorphs are mechanically stable and st-BiVO4 possesses more ductile (ionic) properties. These technologically promising compounds are hard materials due to their higher bulk, Young’s, and shear moduli. The lower shear anisotropic factors indicate smaller elastic anisotropy. The Gibbs free energy, Debye temperature, heat capacity, and Grüneisen parameter have been derived from the calculated elastic constants, which are essential for thin film growth of BiVO4. The calculated thermodynamic properties confirm their thermodynamical stability and are also consistent with the elastic properties. The results recommend that BiVO4 has potential structural and photocatalytic applications in various forms such as a nano-material. From our investigation, we conclude that m-BiVO4 is useful for photocatalysts, solid state electrolyte, and electrode, on the other hand other polymorphs of BiVO4 are applicable in electronic device fabrications. Our study would be helpful to the scientific community to select their application areas according to their desired properties.
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