Computational Materials Science 74 (2013) 50–54
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First-principles calculations of the vacancy defects in BiOF as cathode materials for Li-ion batteries Zhenhua Yang a,b,c,⇑, Yong Pei b,⇑, Shuncheng Tan a, Xianyou Wang b,c, Li Liu b,c, Xuping Su c,d a
Faculty of Materials, Optoelectronics and Physics, Key Laboratory of Low Dimensional Materials & Application Technology of Ministry of Education, Xiangtan University, Xiangtan 411105, Hunan, China b School of Chemistry, Xiangtan University, Xiangtan 411105, Hunan, China c Key Laboratory of Materials Design and Preparation Technology of Hunan Province, Xiangtan University, Xiangtan 411105, Hunan, China d School of Materials Science and Engineering, Changzhou University, Changzhou 213164, Jiangsu, China
a r t i c l e
i n f o
Article history: Received 13 January 2013 Received in revised form 2 March 2013 Accepted 4 March 2013 Available online 9 April 2013 Keywords: Vacancy formation energy Conductivity Electronic structure Electrochemical properties
a b s t r a c t The structural relaxation, formation energies, electronic structure and electrochemical properties of BiOF with vacancy defects were studied by ﬁrst-principles calculations. Some typical native Bi-related, oxygen-related and ﬂuoride-related vacancy defects in their relevant charge state were discussed, respectively. Calculated vacancy formation energies indicate that Bi3 charged vacancy is easiest to fabricate in BiOF when Fermi level lies closer to the conduction band. Besides, BiOF with Bi3 charged vacancy has the best conductivity and electrochemical properties. Ó 2013 Elsevier B.V. All rights reserved.
1. Introduction Recently, metal ﬂuorides based on reversible conversion reaction have aroused great interest in the Li-ion batteries due to their high theoretical voltage and capacity [1–7]. The overall reaction for conversion reaction can be summarized as follows: þ
mLi þ me þ MFn () nLim=n F þ M
where M stands for a metal cation. It is clear that all the oxidation states of the metal ﬂuorides in the conversion reaction are utilized, thereby leading to much higher capacity and energy densities than in the intercalation reactions used in Li-ion batteries. Besides, metal ﬂuorides are more ionic than metal oxides, which makes conversion reaction output higher voltage than metal oxides in the cathode applications. On the other hand, the effect of the higher ionicity of M F makes metal ﬂuorides have wider band gap than metal oxides, inhibiting the application of metal ﬂuoride electrodes. In order to improve the conductivity of metal ﬂuorides, some methods can be employed. Common ways are via adding conductive agents, such ⇑ Corresponding authors. Address: Faculty of Materials, Optoelectronics and Physics, Key Laboratory of Low Dimensional Materials & Application Technology of Ministry of Education, Xiangtan University, Xiangtan 411105, Hunan, China. Tel.: +86 0731 58292195 (Z. Yang). E-mail addresses: [email protected]
(Z. Yang), [email protected]
(Y. Pei). 0927-0256/$ - see front matter Ó 2013 Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.commatsci.2013.03.012
as carbon, MoS2 , V2O5  and MoO3 . However, the wide band gap of metal ﬂuorides cannot be radically solved and the speciﬁc capacity of metal ﬂuorides are demolished by adding conductive agents. Among metal ﬂuorides, BiF3 is one of the most promising cathode materials for Li-ion batteries due to its high voltage (3.13 V) and theoretical energy density (945 W h/kg) . However, BiF3 also suffers from poor electronic conductivity due to its high ionicity. In order to improve conductivity of BiF3 and avoid the loss of its speciﬁc capacity, new methods have to be considered. It has been reported that introducing covalent M–O bonds into metal ﬂuoride system is an effective method to improve the electronic conductivity and electrochemical property of metal ﬂuorides. Moreover, the electrochemical behavior of BiOF cathode material was investigated in the experiment  and the results suggest that introducing M–O bonds can signiﬁcantly improve the electrochemical property of metal ﬂuorides. Although it has better conductive and electrochemical properties than BiF3, BiOF still belongs to semiconductor and the conductivity still requires further improvement. It is well known that introducing anion or cation vacancy in material is one of the most excellent methods to improve the conductivity of material. However, to the best of our knowledge, no theoretical and experimental investigations are carried out to study the effect of vacancy defects on the BiOF. Hence, in this work, we employ ﬁrst-principles calculations to study the effect of vacancy defects on the conductive and electrochemical properties of BiOF, which will offer guidelines for the design of Li-ion batteries.
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2. Computational method and structural model
3. Results and discussion
2.1. Computational method
3.1. Relaxed structure
The calculations have been performed using the ab initio totalenergy and molecular-dynamics program VASP (Vienna ab initio simulation program) developed at the institut für Materialphysik of the Universität Wien [9–11]. Generalized gradient approximation (GGA) of Perdew–Burke–Ernzerhof parameterization and projected augmented wave (PAW) method were used to treat electronic exchange–correlation energy .The cut-off energy and the Brillouin zone sampling are ﬁxed to 550 eV and 3 3 4, respectively. Both lattice parameters and internal atomic coordinates were fully optimized by a Quasi Newton (QN) algorithm until the Hellmann–Feynman forces on all atoms were less than 0.02 eV/Å.
The calculated lattice parameters of BiOF are a = b = 3.794 Å, c = 6.228 Å. It is obvious that the calculated lattice parameters are in good agreement with the experimental results , which indicates that our calculated method is reasonable.
2.2. Structural model BiOF compound has tetragonal crystal structure of space group P 4/nmmS (No.129) with six atoms in the crystal cell, as shown in Fig. 1. The Wyckoff positions of the atoms are Bi 2c (0, 0.5, 0.2077), O 2a (0,0,0), F 2c (0,0.5,0.6524).The BiOF crystal contains two molecules and its lattice parameters are a = b = 3.756 Å, c = 6.234 Å, a = b = c = 90°  For the simulation of vacancy defects in BiOF, we used a 2 2 2 supercell containing 48 atoms. Three types of vacancy defects, i.e., Bi vacancy (VBi), O vacancy (VO) and F vacancy (VF), were investigated. The vacancy model for BiOF is built by removing one atom (Bi, O or F) from the corresponding supercell.
3.2. Formation energy of intrinsic vacancies in BiOF Usually, vacancy formation energy is often employed to assess the level of difﬁculty in introducing vacancy (cation or anion vacancy) in materials. If the vacancy formation energy is more negative, introducing vacancy in materials will become easier. The calculated methods of vacancy formation energy in materials have been reported in previous lectures and they have been successfully applied in the calculations for various semiconductors and insulator [14–18]. The formation energies of charged point defects in BiOF were calculated by
DH ¼ EðV i ; qÞ EðperfectÞ þ
ni ðDli þ lelement Þ þ qðEVBM i
þ DV þ E F Þ
where E(Vi, q) and E(perfect) are the total energies of the supercell with and without vacancies, respectively. q is the valence state. lelement is the chemical potential of element i (i = Bi, O or F) and its i value is the energy per atom i. ni is the number of Bi, O and F atoms removed from perfect BiOF supercell. Dli is the chemical potential relative to lelement . Dli þ lelement is the chemical potential under difi i ferent growth condition. EVBM is the energy at the valence band maximum and DV is the ‘‘potential alignment’’ used to align the potentials in the perfect and defective supercells. EF is the Fermi level relative to EVBM ,varying from 0 to band gap of perfect supercell (Eg). EVBM and Eg can be obtained by
EVBM ¼ ET ðperfect : 0Þ ET ðperfect : þ1Þ
Eg ¼ ½ET ðperfect : 1Þ ET ðperfect : 0Þ ½ET ðperfect : 0Þ ET ðperfect : þ1Þ
Here, ET(perfect:1), ET(perfect:0) and ET(perfect:+1) are the total energies of a perfect super-cell with one negative charge, no charge and one positive charge. From Eq. (2), it is obvious that vacancy formation energy has close relationship with Dli þ lelement . i In order to obtain the chemical potentials of Bi, O and F, we ﬁrstly calculated formation enthalpies of BiF3, Bi2O3 and BiOF according to Eqs. (5)–(7).
Fig. 1. The structure models of the perfect BiOF.
3 DHðBiF3 Þ ¼ Etotal ðBiF3 Þ Etotal ðBiÞ Etotal ðF2 Þ 2
3 DHðBi2 O3 Þ ¼ Etotal ðBi2 O3 Þ 2Etotal ðBiÞ Etotal ðO2 Þ 2
1 1 DHðBiOFÞ ¼ Etotal ðBiOFÞ Etotal ðBiÞ Etotal ðO2 Þ Etotal ðF2 Þ 2 2
where Etotal is the total energy of each component. For the calculation of the total energies of O2 and F2, spin-polarized calculations are performed, two F and O atoms are placed together at the distance of 1.42 Å and 1.21 Å in the cubic box with periodic conditions, respectively. The cubic box has the lattice constant of 10 Å. The calculated total energies of O2 and F2 are 9.86 and 3.72 eV, respectively. And calculated results of corresponding formation enthalpies were also given in Table 1. It is evident that our calculated
Z. Yang et al. / Computational Materials Science 74 (2013) 50–54
formation enthalpies of Bi2O3 excellently agree with present experimental value . The equilibrium of BiOF should be maintained. Under thermal equilibrium grow conditions, DlBi, DlO and DlF satisfy following relationship:
DlBi þ DlO þ DlF ¼ DHðBiOFÞ
Here, DH(BiOF) is the formation enthalpy of BiOF. Besides, In order to avoid precipitation of solid elemental crystal and the formation of extra phases (such as Bi2O3 and BiF3), DlBi, DlO and DlF must satisfy further constrains:
DlBi 6 0; DlO 6 0; DlF 6 0
2DlBi þ 3DlO 6 DHðBi2 O3 Þ
DlBi þ 3DlF 6 DHðBiF3 Þ
These conditions determine the range of the chemical potentials for the formation of BiOF. Considering Eqs. (2)–(4), the calculated formation energies of charged defects in BiOF have close relationship with the chemical potential of component and the Fermi-level positions. Therefore, DlBi, DlO and DlF are constrained in a small region within A–D as shown in Fig. 2. Where A, B, C and D are four representative chemical potential points. A and B points represent rich-O growth conditions while C and D points stand for rich-Bi growth conditions. The exact value of chemical potentials at points A, B, C and D are (3.898, 0, 1.642 eV), (3.268, 0, 2.272 eV), (0, 2.179, 3.361 eV) and (0, 2.599, 2.941 eV) for DlBi, DlO and DlF, respectively. Hence, the oxygen chemical potential can be varied within 2:599eV 6 DlO 6 0 and the ﬂuoride chemical
Table 1 Formation enthalpies (eV) of compounds per chemical formula obtained from the ﬁrst-principles calculations. Compounds
BiF3 Bi2O3 BiOF
Cubic Monoclinic Tetragonal
FM3-M P121/C1 P4/NMMS
Formation enthalpies Present
8.823 6.536 5.540
potential can be varied within 3:361eV 6 DlF 6 0. They are often practically used for controlling the sintering of BiOF in experiments. Fig. 3 shows the formation energies of various vacancy defects as a function of the Fermi level under different growth conditions. Bi0, Bi3, O0, O1+, O2+, F0 and F1+ vacancies in BiOF were labeled as 0 1þ 2þ 0 1þ V 0Bi ; V 3 Bi ; V O ; V O ; V O ; V F and V F , respectively. The slope of a line indicates the charged state. Positive slope corresponds to the positively charged state of vacancy defect in BiOF, while negative slope shows negatively charged state of vacancy defect in BiOF. The change in slope suggests a transition between different charged states. It can be seen from Fig. 3 that neutral and charged vacancies of Bi, O and F vary their formation energies under the different growth conditions. Moreover, neutral vacancies of Bi, O and F all have positive formation energies for whole part of the band gap, indicating that neutral vacancies of Bi, O and F are very difﬁcult to form under usual conditions. While the charged vacancies of Bi, O and F have negative formation energies for some part of the band gap, which shows that charged vacancies of Bi, O and F are more stable than neutral vacancies of Bi, O and F under some growth conditions. In Fig. 3a, corresponding to rich-O and rich-F growth conditions, the +1/+2 transition of oxygen vacancy occurs at about 1.75 eV relative to valence band. Formation energies of V 1þ are slower than F 2þ those of V 1þ O and V O for the most part of the band gap, which sug1þ 2þ gests that V 1þ F is easier to fabricate than V O and V O . When Fermi level is located near valence band, the charged vacancies of Bi, O and F are difﬁcult to form in BiOF due to their positive values of vacancy formation energies. However, the formation energy of Bi vacancy decreases and becomes negative in some part of band gap when the Fermi level shifts from valence band to conduction. Hence, it is easiest to fabricate V 3 Bi compared with O and F vacancies. When the growth conditions shift from A point to B point, as shown in Fig. 3b, the formation energies of V 2þ O become slight smaller, which indicates that decreasing the chemical potential of F can conduce to V 2þ under rich-O growth conditions. Under rich-Bi O growth conditions, as shown in Fig. 3c and d, V 2þ O vacancy is found to be most stable at the top of the valence band. And V 3 Bi vacancy is the most stable at the bottom of conduction. By comparison of for1þ 2þ mation energies of V 2þ O and V F , the formation of V O vacancy is 1þ easier while formation of V F vacancy becomes difﬁcult as the growth condition shifts from point C to point D. 3.3. Inﬂuence of vacancy defect on the electronic structure of BiOF
Fig. 2. Stability phase for BiOF as determined from ﬁrst-principles calculations.
To obtain how electronic states change in the presence of Bi, O and F vacancies, the densities of states (DOS) of BiOF with and without vacancies were calculated. Fig. 4b–d presents the total DOS (TDOS), as well as their partial DOS (PDOS) of BiOF with 2þ 1þ V 3 Bi ; V O and V F , respectively. For comparison, the TDOS and PDOS of perfect BiOF are also plotted (see Fig. 4a). The Fermi energy is taken as the zero of energy. As can be seen in Fig. 4a, the conduction bands and the upper valence bands are composed mainly of O 2p orbits, F 2p orbits and Bi 6p orbits. Strong hybridization exits between O 2p orbits and Bi 6p orbits. Moreover, strong hybridization between F 2p orbits and Bi 6p orbits also occurs in these regions. The perfect BiOF belongs to materials with wide band gap and the calculated band gap is 3.10 eV, which is very close to Ref.  obtained results (3.00 eV). In the cases of 1þ 3 2þ 1þ V 3 Bi ; and V F , the TDOS proﬁles of BiOF with V Bi ; V O and V F all shift towards low energy region due to the existence of vacancies defect. Consequently, the corresponding band gap decreases. 2þ 1þ The band gaps of BiOF with V 3 are 1.56, 2.62 and Bi ; V O and V F 3 2.92 eV, respectively. Hence, introducing V Bi is one best way to evidently decrease the band gap of BiOF and improve its electronic conductivity.
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Fig. 3. The formation energies of charged vacancies in BiOF as a function of the Fermi level under different growth conditions. (a) A point; (b) B point; (c) C point and (d) D point.
3.4. Inﬂuence of vacancy defect on the electrochemical properties of BiOF To fully understand the vacancy effect on the electrochemical properties of BiOF, we further consider the case of vacancy defect in the BiOF crystals containing Bi, O and F vacancies (Bi1xO1yF1z), respectively. Usually, Bi1x O1y F1z and Li metal are taken as cathode and anode materials in Li-ion batteries, respectively. And Bi1x O1y F1z often takes conversion reaction with Li metal and the following equation can be written as:
Bi1x O1y F1z þ ð3 2y zÞLi ! ð1 xÞBi þ ð1 yÞLi2 O þ ð1 zÞLiF
According to Eq. (12), Gibbs free energy (DG) can be obtained by the following equation:
DG ¼ ð1 xÞEBi þ ð1 yÞELi2 O þ ð1 zÞELiF ð3 2y zÞELi EBi1x O1y F1z
where EBi, ELi2 O , ELiF, ELi and EBi1xO1y F1z are the energies of bulk Bi, Li2O, LiF, Li and Bi1x O1y F1z . Therefore, the average voltage (V) can be calculated according to the equation:
Here, m is the number of electrons and F is the Faraday constant. The expected theoretical capacity(C) of EBi1xO1y F1z during a conversion reaction with Li can be calculated according to following equation:
nN0 e 1 3 M0 1 10 3600
where n is the number of Li involved in reactions, N0 is the Avogadro’s constant, e is the electron charge and M0 is the relative molecular mass of EBi1xO1y F1z . Average voltage (V) and theoretical capacity(C) of BiOF, Bi15/ 16OF, BiO15/16F and BiOF15/16 were calculated and listed in Table 2. Bi15/16OF has the highest average voltage and theoretical capacity by comparison, which indicates that introducing Bi vacancy in BiOF is the best method to improve its electrochemical properties. 4. Conclusions In summary, the structural relaxations, formation energies, electronic structure and electrochemical properties of various vacancy defects in BiOF have been investigated by ﬁrst-principles calculations. It was found that the calculated lattice parameters of BiOF are in good agreement with available experimental data, indi-
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cating that our approach is a suitable method for calculating a system like BiOF material. Neutral vacancies of Bi, O and F are very difﬁcult to form in usual conditions. Bi3, O1+, O2+ and F1+ vacancies can occur depending on the external chemical potentials and Fermi level. Under rich-O growth conditions, Bi, O and F vacancy defects at the valence band are difﬁcult to form due to their positive vacancy formation energies. V 2þ O remains most stable under rich-Bi growth conditions. V 3 Bi is easy to fabricate under rich-O and richBi growth conditions vacancy when the Fermi level lies very close to conduction band compared with O and F vacancies. It is observed that the band gaps of BiOF with Bi3, O2+ and F1+ vacancy are 1.56, 2.62 and 2.92 eV, respectively. Hence, introducing Bi3 vacancy can evidently improve the electronic conductivity of BiOF. Additionally, introducing Bi3 vacancy can markedly improve the electrochemical properties of BiOF. Acknowledgements This work was ﬁnancially supported by Project supported by Hunan Provincial Natural Science Foundation of China (Grant No. 12JJ6041) and Start-up funds for doctor supported by Xiangtan University (Grant No. 12QDZ02). Y.P is partially supported by the Academic Leader Program in Xiangtan University (10QDZ34) and Natural Science Foundation of China (Grant No. 21103144). References
Fig. 4. TDOS and PDOS of BiOF systems with and without vacancy defects. (a) 2þ 1þ Perfect BiOF; (b) BiOF with V3 Bi ; (c) BiOF with VO ; and (d) BiOF with VF . Table 2 The expected average voltage and capacity of BiOF with and without vacancy during a conversion reaction with Li. Compound
Voltage (V) Capacity (mA h/g)
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