Theoretical study on the stability, ferroelectricity and photocatalytic properties of CaBiO3

Materials with high ferroelectric polarization strength and sufficient absorption of visible light have unique advantages in photocatalysis. Based on the results of structure search, phonon frequency, and elasticity coefficient calculations, CaBiO3 has a stable R3 polar structure. First-principles calculations indicate that R3-CaBiO3 is a potentially efficient ferroelectric visible-light photocatalytic material for hydrogen production. CaBiO3 under slight strain can maintain high ferroelectric polarization strength, strong visible light absorption capacity and small effective mass. CaBiO3 under tensile strain has potentially ferroelectric photogeneration of hydrogen with a band edge position that crosses the redox potential of water. These results can expand the application of Bi-based materials in photocatalytic hydrogen production.


Introductions
Perovskite oxides exhibit a wide range of ferroelectric, piezoelectric, and thermoelectric characteristics as well as electro-optical effects, which makes them a focus in the photovoltaic and photocatalysis elds. [1][2][3] Ferroelectric materials display spontaneous polarization due to the offset of positive and negative charge centers, providing a new prospect for photovoltaic device design by promoting the separation of photoexcited carriers. 4 In addition, the internal electric eld of ferroelectric polarization also enhances inhibition of the recombination of electrons and holes. 5 Ferroelectric materials can also serve as new candidates for photocatalysis, similar to the P-N junction mechanisms, which signicantly impact surface photochemistry. 6 The non-polluting hydrogen energy generated by photocatalysis is one of the mainstays of future energy development. 7 The spontaneous polarization of ferroelectrics can provide a strong internal electric eld for the photocatalytic water separation process, which are benecial for photocatalytic hydrogen production. 8 Bismuthbased semiconductors have attracted extensive attention for their excellent photocatalytic performance under visible light due to Bi ions' unique 6s and 6p orbitals. 9,10 First-principle calculation results show that CaBiO 3 has a potentially stable R3 ferroelectric structure, 11,12 an excellent visible light-absorbing material with a bandgap of about 1.8 eV. 11 Rokesh et al. synthesized CaBiO 3 through glycine-complexation (GC) and ion-exchange (IE) methods and found that it can generate highly reactive photocatalytic free radicals to degrade pollutants. 13 For semiconductor materials to meet the conditions of photocatalytic hydrogen production, the bandgap must be larger than the standard Gibbs free energy change for the decomposition of water into H 2 and O 2 , while the band edge position must extend across the redox potential of water. 14 The CaBiO 3 crystal structure search is processed using the evolutionary algorithm implemented in the USPEX code [15][16][17] in this paper. The stability of CaBiO 3 is further veried by phonon frequencies and elasticity coefficients. Our calculation results show that CaBiO 3 under tensile conditions has excellent potential as a new ferroelectric photocatalytic semiconductor material for hydrogen production.

Calculation method
The stable structure of CaBiO 3 is searched by USPEX code with 20 atoms. The initial structure of the rst generation is set as 300, and that of the second generation is 50. The convergence standard remains unchanged for the 10th generation. Variables of 50% genetic, 20% random, 20% so mode mutation, and 10% lattice mutation were set in the calculation. As shown in Table 1, the stable structure space group number of CaBiO 3 is 146 (R3 space group), which consistent with earlier theories and experimental reports. [11][12][13] The calculated CaBiO 3 structure by USPEX soware is transformed into a conventional cell structure as shown in Fig. 1. The calculated lattice parameters a and c of CaBiO 3 are 5.88Å and 15.47Å respectively, which is closed to the early reports in the literature (a = 5.81Å, c = 15.22Å). 11 The electronic structure, elastic properties, and photoelectric properties of R3 space group CaBiO 3 are calculated using rst-principles soware packaged in VASP. 18 The PAW pseudopotential method is used to describe the interaction between electrons and nuclei, 19 and the exchange-correlation functional between electrons is treated by Perdew-Burke-Ernzerhof (PBE) functional. 20 The cutoff energy was taken at 520 eV, and the Monkhorst-Pack k-point sampling was given as 0.03Å −1 in the calculation. The energy and force convergence criteria are set as 10 −6 eV and 10 −2 eVÅ −1 , respectively. The bandgap and absorption spectra of CaBiO 3 are calculated by Modied Becke-Johnson (MBJ) exchange potential since PBE functional usually underestimates the bandgap of the material. 21 Parameter C in the MBJ functional was set as 1.7, and the bandgap result calculated was close to the earlier hybrid HSE functional (Heyd-Scuseria-Ernzerhof) report result. 11 The strain is introduced by changing the lattice parameters of a and b to relax the c axis in Fig. 1. Lattice parameters a and b are increased by 2% to relax the c lattice parameter, indicating the introduction of 2% tensile strain. The calculated lattice parameters a and c of CaBiO 3 under 2% tensile strain become 6.00Å and 15.14Å respectively. Lattice parameters a and b are reduced by 2% to relax lattice parameter c, representing the introduction of 2% compressive strain. The calculated lattice parameters a and c of CaBiO 3 under 2% compressive strain become 5.76Å and 15.87Å respectively. T-CaBiO 3 represents the introduction of tensile strain in CaBiO 3 , while C-CaBiO 3 represents the introduction of compressive strain in CaBiO 3 .

Stability analysis
The search results for USPEX suggest that CaBiO 3 with R3 space group is a potentially stable structure. The elastic properties and phonon frequencies of CaBiO 3 with R3 space group are calculated to verify the stability furtherly. CaBiO 3 with R3 space group has seven independent elastic coefficients. The  1 The structure and lattice parameters of pristine R3-CaBiO 3 and R3-CaBiO 3 under strain. Table 2 The calculated elastic coefficient (GPa) independent elastic coefficients must satisfy the following inequalities group (1) to achieve mechanical stability. 22 The calculated elastic coefficients are shown in Table 2, which meet all the requirements of the inequality group for mechanical stability. 2 × 2 × 2 supercell contained 80 atoms have been used to calculate the phonon frequency of pristine CaBiO 3 and CaBiO 3 under strain conditions. The calculated phonon frequency of pristine CaBiO 3 with the R3 space group in Fig. 2 shows that there is no imaginary frequency in the whole Brillouin region, indicating that it is a potentially metastable structure. CaBiO 3 under compressive or tensile strain conditions can still maintain stability due to the calculated elastic coefficients and phonon frequency results in Table 2 and Fig. 2. The elastic coefficients and phonon frequency of CaBiO 3 under compressive strain condition become larger since the shorter bond lengths of Ca-O and Bi-O in the Fig. 3 could lead to the increased atomic interactions. Conversely, the tensile strain effect causes the bond length of CaBiO 3 to be larger for reducing the atomic interactions, which leading to the lower elastic coefficients and phonon frequencies.

Calculated ferroelectric properties
The ferroelectric properties of the R3-CaBiO 3 polarized structure are calculated by the modern polarization theory of the Berry Phase method, 23,24 and R 3 is chosen as the centrosymmetric phase. The calculation results are shown in Fig. 4, and l is the linear interpolation scale value between the polarized and centrosymmetric phase structures. R3-CaBiO 3 forms a noticeable double potential well curve with atomic movement, and the position of the potential well represents the ferroelectric polarized phase. The calculated ferroelectric polarization strength is 59.63 mc cm −2 , which is close to the value of 56 mc cm −2 reported in the earlier literature, 11 and close to the ferroelectric polarization strength of conventional ferroelectric oxide R3c ZnSnO 3 . 25,26 Next, we consider the effect of strain on the ferroelectric properties of R3-CaBiO 3 . R3-CaBiO 3 , under the presence of a slight strain, can still maintain ferroelectric polarization strength larger than 50 mc cm −2 as well. The ferroelectric driving mechanism of R3-CaBiO 3 is similar to that of the R3c structures BiFeO 3 and ZnSnO 3 , which is mainly determined by the action of the A-site ions (Ca, Bi or Zn) and O ions. 27,28 The offset of Ca ions decreases from 0.40Å to 0.34Å under 2% tensile strain in Table 3, which reduces the ferroelectric polarization strength. The offset of Ca ions increases to 0.46Å under compressive strain, which improves the ferroelectric polarization strength. Ca ion at A site of CaBiO 3 under strain conditions has the most direct effect on the ferroelectric properties of the system.

Discussions on photocatalytic properties
The optical properties of materials are closely related to the band structure. As shown in Fig. 5, the calculated energy band structure of CaBiO 3 is an indirect bandgap. Although an indirect bandgap is not an optimal function for light absorption, it could reduce the probability of photoelectron-hole radiation recombination. The calculated band gap of the pristine CaBiO 3 is 1.58 eV by MBJ functional, which is consistent with the value reported by HSE functional in the literature. 11 The optical absorption properties of the material are closely related to the bandgap of the material itself. In order to further understand the absorption of visible light, we also calculated the optical absorption spectrum. The relation between the optical absorption coefficient a(u) of CaBiO 3 and the real 3 r and the imaginary 3 i of the dielectric function is shown below eqn (2).
u is the circular photon frequency, and C is the speed of light. The pristine CaBiO 3 begins to absorb visible light when the incident photon energy is close to 1.6 eV and forms the prominent absorption peak (about 2.2 eV) in Fig. 6, indicating that it has a strong visible light absorption capacity. The slight red shi appears in the absorption coefficient of CaBiO 3 under tensile strain due to the longer bong length and lower band gap, while the opposite reaction occurs in the compressive strain condition.
The band edge of CaBiO 3 was calculated according to the following empirical formula 29 to explore the photocatalytic hydrogen production ability of CaBiO 3 .
where E g is the bandgap, c is the mean electronegativity, and E 0 is the frame of reference as a scale factor concerning the normal hydrogen electrode (NHE) of the vacuum. As shown in Fig. 7, the CBM band edge position of pristine CaBiO 3 is close to the reduction potential of H + /H 2 , while the band edge position of VBM is lower than the oxidation potential of O 2 /H 2 O, showing a potential photocatalytic hydrogen production capacity. The empirical formula above was also used for the band edge positions of photocatalytic materials TiO 2 , NaBiO 3 , and KBiO 3 . [30][31][32] Their band edge positions all cross the redox potential of water and satisfy the condition of decomposition water to produce hydrogen. The calculated density of the state of CaBiO 3 shows that the conduction band and valence band are mainly composed of O-2p and Bi-6s orbitals, which is similar to other Bi-based photocatalytic materials. 33 The effective mass of the electron in CaBiO 3 under strain conditions is also relatively small, which is close to NaBiO 3 (0.4 m 0 ) and KBiO 3 (0.8 m 0 ), as shown in Table 4, suggesting that the photogenerated carriers  of CaBiO 3 could be easy to separate. The higher transfer rate of photogenerated carriers and lower recombination rate could be produced due to the larger D value. D is dened as the ratio of the hole effective mass to the electron effective mass. The D values of CaBiO 3 at a slight strain in Table 4 range from 2.5 to 2.8, which is slightly larger than that of the conventional photocatalytic ferroelectric material BaTiO 3 (D = 2.44) calculated by the MBJ functional. 34,35 Meanwhile, the large ferroelectric strength and strong visible light absorption of CaBiO 3 will further contribute to the improvement of photocatalytic performance. The band edge positions of T-CaBiO 3 and C-CaBiO 3 are corrected by the 1 s core energy level of Bi atoms in pristine CaBiO 3 . As shown in Fig. 7, the CBM band edge position of CaBiO 3 under the tensile strain condition moves up and becomes higher than the hydrogen reduction potential, which could be favorable to hydrogen production. The CBM band edge of C-CaBiO 3 moved down and was lower than hydrogen reduction potential, which reduced hydrogen production efficiency. CaBiO 3 under tensile strain can still maintain high ferroelectric polarization strength and strong visible light absorption ability, further promoting photocatalytic hydrogen production.

Conclusion
The USPEX soware was used to explore the CaBiO 3 structure in this paper. The results show that the stable structure of CaBiO 3 is the R3 space group conguration. The phonon frequencies and elasticity coefficients calculations also indicate that R3-CaBiO 3 satises the stability condition. The ferroelectric polarization of R3-CaBiO 3 is mainly generated by the shi of the symmetry center of Ca-O ions. The shi of Ca ions signicantly affects the ferroelectric polarization of R3-CaBiO 3 under strain conditions. The offset of Ca ions decreases under tensile strain with reduced ferroelectric polarization strength, while the opposite case is in the compressive strain condition. R3-CaBiO 3 can preserve the high ferroelectric polarization strength and visible light absorption capacity under the slight strain. The band edge position of CaBiO 3 under tensile strain can cross the redox potential of water and maintain a small electron-effective mass with the large ratio of hole and electron masses, which is favorable for photocatalytic hydrogen production. CaBiO 3 is a potential ferroelectric photocatalytic material for hydrogen production under visible light.

Conflicts of interest
The authors declared that they have no conicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conict of interest in connection with the work submitted.