Cite this Article
Farid Ul Islam AKM, Nurul Huda Liton Md, Tariqul Islam HM, Al Helal Md, Kamruzzaman Md. Mechanical and thermodynamical stability of BiVO4 polymorphs using first-principles study. Chinese Physics B, 2017, 26(3): 036301  
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Mechanical and thermodynamical stability of BiVO4 polymorphs using first-principles study
Farid Ul Islam AKM1, †, Nurul Huda Liton Md2, Tariqul Islam HM3, Al Helal Md2, Kamruzzaman Md4
Department of Computer Science and Engineering, Begum Rokeya University, Rangpur, Rangpur-5400, Bangladesh
Department of Physics, Begum Rokeya University, Rangpur, Rangpur-5400, Bangladesh
Department of Chemistry, Begum Rokeya University, Rangpur, Rangpur-5400, Bangladesh
Department of Physics and Materials Science and Center of Super-Diamond and Advanced Films (COSDAF), City University of Hong Kong, Hong Kong SAR, China

 

† Corresponding author. E-mail: farid_ru@yahoo.com

Abstract

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.

PACS: 63.20.dk;71.20.nr;74.25.Ld;73.22.-f
Keyword:BiVO4;crystal structure;lone pair;mechanical stability
1. Introduction

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.

2. Computational details

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.

3. Results and discussion
3.1. Crystal structure

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 1. Our optimized lattice parameters are consistent with the available theoretical[47, 52, 53] and experimental values.[14, 51, 54]

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. 1(a)–1(d). It is seen that V forms VO4 tetrahedron for all polymorphs, whereas, Bi forms BiO6 octahedron for m-BiVO4, BiO4 tetrahedron for zt-BiVO4 and op-BiVO4, and BiO8 dodecahedron for st-BiVO4. Some researcher reported that for m-BiVO4, Bi forms BiO8 dodecahedron,[54] but in our study Bi forms BiO6 octahedron. This may happen due to the lone pair activity of Bi 6s electrons. This is the key factor for the electrical conductivity of m-BiVO4. It is also seen that both m-BiVO4 and op-BiVO4 form a layered structure of Bi–V–O units stacked along the c-axis. On the contrary, there is no distinct Bi–O–V layer observed in zt-BiVO4 and st-BiVO4, because in these structures, Bi forms a bond with oxygen of the next Bi–O–V layer.

(color online) Crystal structures of (a) m-BiVO4, (b) op-BiVO4, (c) zt-BiVO4, and (d) st-BiVO4.

3.2. Electronic structure

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. 2(a)–2(d). Here, the Fermi energy is set to zero. The energy band structures of BiVO4 were calculated along the high symmetry points of the Brillioun zone. From our calculation, it is seen that the valence band maximum (VBM) is on the Z–G line for m-BiVO4 and st-BiVO4, the Y-line for op-BiVO4, and the conduction band minimum (CBM) is located at the A-line for m-BiVO4 and st-BiVO4, and the X-line for op-BiVO4. The observed indirect band gaps of m-BiVO4, op-BiVO4, and st-BiVO4 are 2.193 eV, 2.461 eV, and 2.169 eV, respectively. Whereas, zt-BiVO4 is a direct band gap material and its band gap is 2.598 eV. Its VBM and CBM are located on the G–Z line. Our calculated band gaps are consistent with the available theoretical values[15, 37, 47] but less than the experimental ones[3, 5, 16, 39–42] due to the well-known underestimation of DFT.

(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. 3(a)–3(d). From the figure, it is observed that the upper valence band is spread between 0 and −5.5 eV with respect to the highest occupied states. In the upper valence band, the electronic character is mainly due to the O 2p state, which are the common characteristics of oxide semiconducting materials. The V 3d, Bi 6s and 6p states also contribute to the upper valence band. Although there are s, p, and d orbitals but only the p–d hybridization occurs at the top of the valence band. Since Bi 6s and O 2p show anti-bonding nature between −1.63 eV and −3.02 eV, we can say that Bi 6s acts as a lone pair, which may be confirmed from Mulliken charge analysis, bond populations, and also from the crystal structures. The energy bands at −7.0 eV to −10 eV and −16 eV to −18 eV are the deep level valence states which consist of Bi 6s and O 2s states. It is also observed that the conduction band is mainly derived from V 3d states with p–d hybridization among the V 3d, O 2p, and Bi 6p states.

(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 2. The higher value of charge transfer indicates higher overlap of the electron clouds of two bonding atoms, which causes ionic bonding. The higher value of bond population implies the strong covalency whereas the lower value exhibits the strong iconicity.

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 , which confirms that no lone pair electron presents in the V atom but creates an ionic bond with Bi3+ for BiVO4. Therefore, we can say that V–O bonds are directly related to the interactive forces between Bi3+ and V5+. However, in op-BiVO4, zt-BiVO4, and st-BiVO4 structures, Bi shows +5 valency instead of +3 and there is no lone pair activity. From Table 2, it is also observed that the distortion of Bi–O bond length occurs due to 6s2 lone pair of Bi3+. This characteristic plays an important role for the high photocatalytic activity of the visible light irradiation.[55] m-BiVO4 may show more photocatalytic activities as compared to other BiVO4 polymorphs.

3.3. Elastic properties

The calculated elastic coefficients and stiffness constants are tabulated in Table 3. The conditions of mechanical stability are important to estimate the stability of a compound. The calculated elastic constants of m-BiVO4 should satisfy the Born stability criterion[56, 57] for monoclinic structure: ; ; ; ; ; ; ; where

Table 3.

Calculated elastic constants of different BiVO4 polymorphs.

.

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 and compliances , respectively. In particular, the bulk and shear moduli in the Voigt approach are

The corresponding expressions for the Reuss procedure are

Thus, the Hill-averaged bulk and shear ( moduli can be determined by using

By using these average values of B and G, the Young modulus E and the Poisson ratio ν can be computed by the following equations:

All the calculated elastic constants are shown in Table 4 for different crystal systems of BiVO4. The bulk modulus B is a measure of resistance to volume change by applied pressure and it is related to the bond length.[65] From our calculation, it is seen that the order of bulk moduli is , hence st-BiVO4 has stronger resistance to the volume change caused by applied pressure than the other polymorphs of BiVO4. From this point of view, st-BiVO4 is more useful for hard coating than the others. On the other hand, high bulk modulus indicates the strong strength of the bonds in the solid.

Calculated bulk modulus B (GPa), shear modululs G (GPa), Young’s modulus E (GPa), G/B, Poisson ratio υ, anisotropy factors , and , Klemman parameter ξ, and Vicker’s hardness of different BiVO4 polymorphs. The subscripts V, R, H, and V represent the Voigt, Reuss, Hill, and Vicker approximations, respectively.

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 materials are ductile (ionic), otherwise brittle (covalent) in nature.

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 . Therefore, st-BiVO4 shows more ductility and no fracture will occur readily upon mechanical pressure when it is used as solid state electrolyte.

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 ( ) for a covalent material; where as it is greater than or equal to 0.25 for ionic materials. The Poisson ratio also reflects the stability of the crystal against shear. The values 0.25 and 0.5 are the lower and upper limits, respectively for central force in solids. In the present calculation, the Poisson ratios are 0.295, 0.295, 0.330, and 0.313 for m-BiVO4, op-BiVO4, zt-BiVO4, and st-BiVO4, respectively at zero pressure. This result reveals that the ionic contribution is dominated in these compounds, which makes them useful for high electro-optical and electromechanical coupling.[68] The obtained Poisson ratio indicates that all BiVO4 have central interatomic forces.

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]

From the elastic constants, we obtain the shear anisotropy factors for the tetragonal structure[70]

The calculated anisotropy factors are tabulated in Table 4. The small anisotropy may minimize cracking propagation during sample preparation.[71] The elastic anisotropy is closely related to the inter-atomic bond strength.

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

and its value usually lies between 0, showing minimum bond bending, and 1, showing minimum bond stretching.[74] Our calculated ξ are tabulated in Table 4. It shows that bond bending is preferred in these materials and this tendency is greater in m-BiVO4 than the others.

Finally, we analyze the hardness of these materials by adopting the empirical scheme[75] which correlates Vicker’s hardness and Pugh’s ratio k via the formula

The calculated values are tabulated in Table 4. It is seen that m-BiVO4 is harder than the others. It is also observed that all the elastic properties are strongly agreed with the electronic properties.

3.4. Thermodynamical stability

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. 4. From the figure, it is found that the Gibbs free energy at the same temperature gradually decreases in the sequence: . The smaller Gibbs free energy is favorable for the thermodynamic stability of the compound.[76] From this point of view, the thermal stabilities of these compounds gradually increase in the sequence: . The rapid change of Gibbs free energy with temperature is logical for semiconductor crystal.[77]

(color online) Temperature dependent free energy of different BiVO4 polymorphs.

Debye temperature is another thermodynamic parameter, at which all the phonon vibrations have the same frequency. It is also used to distinguish between high and low temperature regions for a solid. The Debye temperature is a suitable parameter to describe phenomena of solid-state physics which are associated with lattice vibration, elastic constants, specific heat, and melting point. The temperature dependent Debye temperatures for BiVO4 polymorphs are shown in Fig. 5. The observed Debye temperatures of m-BiVO4, op-BiVO4, zt-BiVO4, and st-BiVO4 are 243.12 K, 146.83 K, 125.83 K, and 166.49 K, respectively at 0 K. At low temperature, the vibrational excitations arise solely from acoustic vibrations and the Debye temperature can also be calculated from elastic constants using the following equations:[78]

where,

(color online) Temperature dependent Debye temperature of different BiVO4 polymorphs.

The calculated , and using the elastic constants for different polymorphs of BiVO4 are tabulated in Table 5 and the sequence of is , which is consistent with the observed trend of Young’s and shear moduli and also with thermodynamic data.

Calculated volume V (Å3), density ρ ( ), longitudinal ( ), transverse ( ), and average sound velocity ( ), Debye temperature (K), and Gruneisen parameter γ of different BiVO4 polymorphs.

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 is known as an important parameter closely related to many physical properties such as specific heat and melting temperature. The specific heat capacity at constant volume for BiVO4 polymorphs as a function of temperature is calculated and shown in Fig. 6. It is seen that increases with increasing temperature. These results indicate that phonon thermal softening occurs when the temperature is raised. At the low temperature limit, of all BiVO4 polymorphs obeys the expected Debye law. At high temperature (T ∼ 840 K), it follows the Dulong and Petit law and approaches the classical asymptotic limit. These natures of the curves indicate that atomic interactions in BiVO4 polymorphs especially occur at low temperature. The heat capacity of a substance not only provides essential insight into its vibrational properties, but is also mandatory for many applications.

Fig. 6. (color online) Temperature dependent constant-volume heat capacity of different BiVO4 polymorphs.

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]

where the Poisson ratio ν can be derived from the longitudinal and transverse ( ) sound waves using the following relation:[80, 81]

The calculated Gruneisen parameters of BiVO4 are tabulated in Table 5 and their values increase in the order of . The high γ results in low thermal conductivity and indicates a degree of anharmonicity in a crystal lattice of BiVO4 which may be associated with the presence of trivalent Bi.[82]

4. Conclusion

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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