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Evidence for bandwidth-control metal-insulator transition in Ti3O5
Computational Materials Science 173 (2020) 109435
Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Letter
Evidence for bandwidth-control metal-insulator transition in Ti3O5
T
Xian-Kai Fu, Bo Yang, Wan-Qi Chen, Zhong-Sheng Jiang, Zong-Bin Li, Hai-Le Yan, Xiang Zhao, ⁎ Liang Zuo Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), School of Material Science and Engineering, Northeastern University, Shenyang 110819, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Simulation and modelling Phase transformation Crystal structure Bandwidth-controlled transition
The phase transition between lambda-Ti3O5 and beta-Ti3O5 can be driven by light irradiation, pressure, heat or electrical current, so it has broad application prospects in many fields. In this paper, the electronic and atomic structures of lambda-Ti3O5 and beta-Ti3O5 are calculated using first principle method, and the metal-insulator phase transition between lambda-Ti3O5 and beta-Ti3O5 is investigated. The study found that beta-Ti3O5 is MottHubbard insulator. Through the analysis of the arrangement of atoms of lambda-Ti3O5 and beta-Ti3O5 crystal structures, we found that the metal-insulator transition between lambda-Ti3O5 and beta-Ti3O5 conforms to the bandwidth-controlled transition.
1. Introduction There are various driving ways of phase transition between lambdaand beta-Ti3O5 [1–8]. As a promising functional material, it has received extensive attention in many fields. For example, Ohkoshi [9] found that there is a reversible laser-induced phase transition process between lambda-Ti3O5 and beta-Ti3O5, so it can be used in the field of optical storage media. Tokoro [10] found that lambda-Ti3O5 can be converted to low-temperature phase beta-Ti3O5 and release about 12 kJ/mol of heat when subjected to a pressure of 60 MPa. The betaTi3O5 changes to the high-temperature phase lambda-Ti3O5 as the temperature rises and stores latent heat. Therefore, the material can be applied to the field of thermal energy storage. Current research reports have found that the lambda-Ti3O5 exhibits metallic phase properties, while the beta-Ti3O5 exhibits insulator properties [11–15]. Therefore, these two phases have a relatively large difference in dielectric properties, making the material also have a wide application prospects in the field of electricity science [16,17]. Lambda-Ti3O5 and beta-Ti3O5 are both sub-oxide, Ti atoms provide more valence electrons than O atoms can accommodate. According to the band theory, the excess valence electrons on the Ti atom will partially occupy the orbit at the Fermi level and causes the system to exhibit metallic properties. In fact, lambda-Ti3O5 is a metal phase, but beta-Ti3O5 shows insulator properties. At present, the reasons for the properties of metal and insulator in lambda-Ti3O5 and beta-Ti3O5 are not clear, and systematic research is lacking. In order to reveal the essence of this phenomenon, in this paper we have calculated the
⁎
atomic arrangement and electronic state of Ti3O5, based on density functional theory to explore this problem. 2. Computational details All the bulk geometry optimization in this work were performed with the VASP code [18], using the GGA and GGA + U approximation in the form of the Perdew-Burke-Ernzerhof (PBE) [19] exchange-correlation functional. LDA + U approximation is also used to compare the results of verifying GGA functional calculations. The projected augmented wave method (PAW) [20] was used to describe the interaction between the valence electrons and the core. Unit cells containing 32 atoms were calculated to build the electronic properties of beta- and lambda-Ti3O5. The Monkhorst-Pack [21] scheme was applied in order to sample the Brillouin zone, and the plane wave kinetic energy cutoff is set at 660 eV. The Brillouin zone sampling mesh parameters for the kpoint set were chosen as 3 × 7 × 3 for the both phases. 3. Results and discussion Fig. 1 shows the calculated partial density of states (PDOS) using LDA + U approximations. The PDOS of lambda-Ti3O5 and beta-Ti3O5 near the Fermi level is mainly Ti-d orbit, and the proportion of O-s, O-p, Ti-s and Ti-p is very small. It can be seen that the d-orbital electron state of Ti determines whether the two phases are metallic phase properties or insulator properties. Fig. 2 shows the calculated density of states(DOS) using GGA,
Corresponding author. E-mail address: [email protected] (L. Zuo).
https://doi.org/10.1016/j.commatsci.2019.109435 Received 7 July 2019; Received in revised form 25 October 2019; Accepted 24 November 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
Computational Materials Science 173 (2020) 109435
X.-K. Fu, et al.
Fig. 1. Calculated partial density of states of (a) lambda-Ti3O5 and (b) beta-Ti3O5 using LDA + U approximation. The Fermi level is set to zero.
Fig. 2. Calculated density of states of (a) lambda-Ti3O5 and (b) beta-Ti3O5 using GGA approximation. Calculated density of states of (c) lambda-Ti3O5 and (d) betaTi3O5 using GGA + U approximation. Calculated density of states of (e) lambda-Ti3O5 and (f) beta-Ti3O5 using LDA + U approximation. The Fermi level is set to zero.
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band. Fig. 3c shows the arrangement of Ti atoms on the (0 1 0) plane of lambda-Ti3O5. The minimum cycles are Ti2-Ti3-Ti3-Ti2 and Ti2-Ti1Ti1-Ti2. The sizes are 16.785 Å and 16.496 Å, respectively. Fig. 3d shows the arrangement of Ti atoms on the (0 1 0) plane of beta-Ti3O5, and all Ti atoms form infinitely long straight chains. Its minimum cycle is Ti1-Ti2-Ti3-Ti3-Ti2-Ti1-Ti1, which is 30.504 Å and also larger than lambda-Ti3O5. Therefore, the minimum cycle D of the Ti-atom arrangement of beta-Ti3O5 on the (0 1 0) plane is greater than lambdaTi3O5. From the view of atomic spacing, the maximum spacing of Ti atoms in lambda is 6.916 Å, and the maximum spacing of Ti atoms in beta is 8.998 Å. The smaller the atomic spacing, the more overlapping the atomic wave functions, and the greater the bandwidth. Therefore, lambda's bandwidth (W) is greater than beta. Kobayashi et al. [11] reported that when the U = 5 eV, the DFT calculation simulation spectra of both phases are in good agreement with the experimental valence band spectra, so it can be considered that the values of Coulomb repulsion U in lambda-Ti3O5 and beta-Ti3O5 are close. Based on the Mott-Hubbard model: it can be seen that lambda-Ti3O5 has a large W/U value and its density of state is expressed as a metal state. As lambda-Ti3O5 transform to beta-Ti3O5, the W/U value will shrink, and the original energy band will gradually split into two sub-bands. The energy gap between the sub-bands will increase as the W/U value decreases. Therefore, the metal-insulator transition between lambdaTi3O5 and beta-Ti3O5 can be considered as bandwidth-controlled transition. Fig. 4a and b are the atom arrangements of (1 0 0) plane of both phases, respectively. Its minimum cycle arrangement is Ti1-Ti3-Ti2-Ti1, which is 15.216 Å and 15.207 Å, respectively, with almost the same value. The periodic configuration of Ti atoms in the (0 0 1) plane can be divided into three categories: Ti1 plane, Ti2 plane and Ti3 plane, as shown in Fig. 4c–h. Lambda-Ti3O5’s cycles on the Ti1 plane are 5.268 Å and 7.513 Å, respectively, while beta-Ti3O5’s cycles on the Ti1 plane are 5.233 Å and 7.503 Å, respectively. Lambda-Ti3O5 has a minimum cycle of 5.268 Å on the Ti2 plane, while beta-Ti3O5 has a minimum cycle of 5.233 Å on the Ti2 plane. Lambda-Ti3O5 has a minimum cycle of 5.268 Å on the Ti3 plane, while beta-Ti3O5 has a minimum cycle of 5.233 Å on the Ti3 plane. Therefore, the cycle values on the (0 0 1) planes of the two phases are almost the same. The atomic arrangements on the (1 0 0) and (0 0 1) planes of the two phases do not conform to the bandwidth-controlled transition, while in the phase transition between
GGA + U and LDA + U approximations, respectively. The electron orbitals near the Fermi level are mainly Ti 3d valence electron orbitals, so the interaction between Ti atoms will determine whether an energy gap is generated at the Fermi level. The GGA and LDA often fail to describe systems with localized (strongly correlated) d and f electrons (this manifests itself primarily in the form of unrealistic one-electron energies). This can result in a failure to describe the energy gap that the insulator should have. As shown in Fig. 2b, the insulator properties of the beta-Ti3O5 phase cannot be correctly described using the GGA method. This can be remedied by introducing a strong atomic interaction (U) in a Hartree-Fock like manner, as an on site replacement of the GGA and LDA. The approaches are commonly known as the GGA + U and LDA + U methods. Thus GGA + U and LDA + U methods can more accurately describe the electronic state of the Ti3O5 systems. As shown in Fig. 2d and f, when using the GGA + U approximation of U = 5 eV and the LDA + U approximation of U = 5 eV, the calculated band gap is 0.14 eV, which is consistent with Ohkoshi’s report [9]. An energy gap at the Fermi level be obtained only after considering the Hubbard energy U on Ti 3d electron orbit, which means that the betaTi3O5 is Mott-Hubbard [22] type insulator. When using the GGA method, the calculated bandwidths of lambda-Ti3O5 and beta-Ti3O5 are 2.642 eV and 2.264 eV, respectively, as shown in Fig. 2a and b. When using the GGA + U method, the bandwidths of lambda-Ti3O5 and betaTi3O5 are 3.142 eV and 2.773 eV, respectively, as shown in Fig. 2c and d. Therefore, lambda-Ti3O5’s bandwidth is greater than beta-Ti3O5’s bandwidth. When the LDA + U method is used, the bandwidths of lambda-Ti3O5 and beta-Ti3O5 are 3.642 eV and 3.305 eV, respectively, and the bandwidth of lambda-Ti3O5 is also wider than that of betaTi3O5. In tight-binding model, the larger the bandwidth W, the smaller the periodic spacing D of the structure [22]. With this in mind, the atomic arrangements of lambda-Ti3O5 and beta-Ti3O5 need to be analyzed. The structures analyzed come from the reports of Ohkoshi [9] and Tokoro [10]. Fig. 3a is the local structures of lambda-Ti3O5, the Ti atom at the center has 6 nearest neighbor Ti atom coordination. Fig. 3b is the local structures of beta-Ti3O5, the Ti atom at the center has only 5 nearest neighbor Ti atom coordination. Based on the tight-binding model, the bandwidth is related to the coordination number. When taking the same interaction integral, the larger coordination number will lead to a wider
Fig. 3. The local structures of (a) lambda-Ti3O5 and (b) beta-Ti3O5 and the atomic configurations of (c) lambda-Ti3O5 and (d) beta-Ti3O5 of (0 1 0) planes. 3
Computational Materials Science 173 (2020) 109435
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Fig. 4. The atomic configurations of (a) lambda-Ti3O5 and (b) beta-Ti3O5 of (1 0 0) planes. The atomic configurations of lambda-Ti3O5 of (c) Ti1, (e) Ti2 and (g) Ti3 in (0 0 1) planes. The atomic configurations of beta-Ti3O5 of (d) Ti1, (f) Ti2 and (h) Ti3 in (0 0 1) planes.
the beta-Ti3O5 phase, indicating that the beta-Ti3O5 phase is MottHubbard insulator. Therefore, when investigating the electronic state of both phases, it is necessary to take into account the Hubbard energy U. When the periodic spacing of atoms decreases, the overlap of the atomic wave function increases, and the bandwidth W also increases. At this time, the bandwidth W and Hubbard energy U in the system determine whether the system is in a metallic state or an insulating state. Since Hubbard energy U is not sensitive to atomic spacing, changes in cycle atomic spacing will cause changes between the metal state and the insulating state of the system. The phase transition between lambda-
lambda-Ti3O5 and beta-Ti3O5, the displacement of the atoms only occurs on (0 1 0) plane. Therefore, the phase transition between lambdaTi3O5 and beta-Ti3O5 is bandwidth-controlled transition on a two-dimensional plane.
4. Conclusions The density of states and the atomic arrangements of lambda-Ti3O5 and beta-Ti3O5 were investigated by first principle. The GGA + U and LDA + U functional can correctly describe the insulator properties of 4
Computational Materials Science 173 (2020) 109435
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Ti3O5 and beta-Ti3O5, atomic displacement occurs on (0 1 0) plane. The periodic spacing of lambda-Ti3O5 on (0 1 0) plane is less than the periodic spacing of beta-Ti3O5, so the bandwidth of lambda-Ti3O5 is greater than beta-Ti3O5. Compared to lambda-Ti3O5, beta-Ti3O5’s W/U value is smaller, so as lambda-Ti3O5 transitions to beta-Ti3O5, the arrangement of atoms changes, and the original energy band splits into two sub-bands, making the beta-Ti3O5 phase show an insulating state. Therefore, the phase transition between lambda-Ti3O5 and beta-Ti3O5 is bandwidth-controlled transition.
(2014) 106–112. [2] M.Z. Wang, W.X. Huang, Z.J. Shen, J.Z. Gao, Y.L. Shi, T.C. Lu, Q.W. Shi, J. Alloys Compd. 774 (2019) 1189–1194. [3] R. Liu, J.X. Shang, Modell. Simul. Mater. Sci. Eng. 20 (2012) 035020. [4] T. Nasu, H. Tokoro, K. Tanaka, F. Hakoe, A. Namai, S. Ohkoshi, Mater. Sci. Eng. 54 (2014) 012008. [5] Q.W. Shi, G.Q. Chai, W.X. Huang, Y.L. Shi, B. Huang, D. Wei, J.Q. Qi, F.H. Su, W. Xu, T.C. Lu, J. Mater. Chem. C 4 (2016) 10279–10285. [6] G.Q. Chai, W.X. Huang, Q.W. Shi, S.P. Zheng, D. Wei, J. Alloys Compd. 621 (2015) 404–410. [7] D. Wei, W.X. Huang, Q.W. Shi, T.C. Lu, B. Huang, J. Mater. Sci.: Mater. Electron. 27 (2016) 4216–4222. [8] K.S. Tasca, V. Esposito, G. Lantz, P. Beaud, M. Kubli, M. Savoini, C. Giles, S.L. Johnson, ChemPhysChem 18 (2017) 1385–1392. [9] S. Ohkoshi, Y. Tsunobuchi, T. Matsuda, K. Hashimoto, A. Namai, F. Hakoe, H. Tokoro, Nat. Chem. 2 (2010) 539–545. [10] H. Tokoro, M. Yoshikiyo, K. Lmoto, A. Namai, T. Nasu, K. Nakagawa, N. Ozaki, F. Hakoe, K. Tanaka, K. Chiba, R. Makiura, K. Prassides, S. Ohkoshi, Nat. Commun. 6 (2015) 7037–7044. [11] K. Kobayashi, M. Taguchi, M. Kobata, K. Tanaka, H. Tokoro, H. Daimon, T. Okane, H. Yamagami, E. Ikenaga, S. Ohkoshi, Phys. Rev. B 95 (2017) 085133. [12] Z. Shen, Q. Shi, W. Huang, B. Huang, M. Wang, J. Gao, Y. Shi, T. Lu, Appl. Phys. Lett. 111 (2017) 191902. [13] R. Liu, J.X. Shang, F.H. Wang, Comput. Mater. Sci. 81 (2014) 158–162. [14] A. Asahara, H. Watanabe, H. Tokoro, S. Ohkoshi, T. Suemoto, Phys. Rev. B 90 (2014) 014303. [15] D. Olguin, E. Vallejo, A.R. Ponce, Phys. Status Solidi B 252 (2015) 659–662. [16] S.A. Jalil, M. Akram, G. Yoon, A. Khalid, D. Lee, N.R. Hosseini, S. So, I. Kim, Q.S. Ahmed, J. Rho, M.Q. Mehmood, Chin. Phys. Lett. 34 (2017) 088102. [17] F. Hakoe, H. Tokoro, S. Ohkoshi, Mater. Lett. 188 (2017) 8–12. [18] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169–11186. [19] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865–3868. [20] P.E. Blochl, Phys. Rev. B 50 (1994) 17953–17979. [21] H.J. Monkhorst, J.D. Pack, Phys. Rev. B 13 (1976) 5188–5192. [22] M. Imada, A. Fujimori, Y. Tokura, Rev. Mod. Phys. 70 (1998) 1039–1263.
CRediT authorship contribution statement Xian-Kai Fu: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Visualization, Investigation. Bo Yang: Data curation, Writing - review & editing. Wan-Qi Chen: Visualization, Investigation. Zhong-Sheng Jiang: Visualization, Investigation. ZongBin Li: Supervision. Hai-Le Yan: Software, Validation. Xiang Zhao: Supervision. Liang Zuo: Conceptualization, Writing - review & editing, Data curation, Software, Validation. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1][1] A. Ould-Hamouda, H. Tokoro, S. Ohkoshi, E. Freysz, Chem. Phys. Lett. 609
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Contents lists available at ScienceDirect
Computational Materials Science journal homepage: www.elsevier.com/locate/commatsci
Letter
Evidence for bandwidth-control metal-insulator transition in Ti3O5
T
Xian-Kai Fu, Bo Yang, Wan-Qi Chen, Zhong-Sheng Jiang, Zong-Bin Li, Hai-Le Yan, Xiang Zhao, ⁎ Liang Zuo Key Laboratory for Anisotropy and Texture of Materials (Ministry of Education), School of Material Science and Engineering, Northeastern University, Shenyang 110819, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Simulation and modelling Phase transformation Crystal structure Bandwidth-controlled transition
The phase transition between lambda-Ti3O5 and beta-Ti3O5 can be driven by light irradiation, pressure, heat or electrical current, so it has broad application prospects in many fields. In this paper, the electronic and atomic structures of lambda-Ti3O5 and beta-Ti3O5 are calculated using first principle method, and the metal-insulator phase transition between lambda-Ti3O5 and beta-Ti3O5 is investigated. The study found that beta-Ti3O5 is MottHubbard insulator. Through the analysis of the arrangement of atoms of lambda-Ti3O5 and beta-Ti3O5 crystal structures, we found that the metal-insulator transition between lambda-Ti3O5 and beta-Ti3O5 conforms to the bandwidth-controlled transition.
1. Introduction There are various driving ways of phase transition between lambdaand beta-Ti3O5 [1–8]. As a promising functional material, it has received extensive attention in many fields. For example, Ohkoshi [9] found that there is a reversible laser-induced phase transition process between lambda-Ti3O5 and beta-Ti3O5, so it can be used in the field of optical storage media. Tokoro [10] found that lambda-Ti3O5 can be converted to low-temperature phase beta-Ti3O5 and release about 12 kJ/mol of heat when subjected to a pressure of 60 MPa. The betaTi3O5 changes to the high-temperature phase lambda-Ti3O5 as the temperature rises and stores latent heat. Therefore, the material can be applied to the field of thermal energy storage. Current research reports have found that the lambda-Ti3O5 exhibits metallic phase properties, while the beta-Ti3O5 exhibits insulator properties [11–15]. Therefore, these two phases have a relatively large difference in dielectric properties, making the material also have a wide application prospects in the field of electricity science [16,17]. Lambda-Ti3O5 and beta-Ti3O5 are both sub-oxide, Ti atoms provide more valence electrons than O atoms can accommodate. According to the band theory, the excess valence electrons on the Ti atom will partially occupy the orbit at the Fermi level and causes the system to exhibit metallic properties. In fact, lambda-Ti3O5 is a metal phase, but beta-Ti3O5 shows insulator properties. At present, the reasons for the properties of metal and insulator in lambda-Ti3O5 and beta-Ti3O5 are not clear, and systematic research is lacking. In order to reveal the essence of this phenomenon, in this paper we have calculated the
⁎
atomic arrangement and electronic state of Ti3O5, based on density functional theory to explore this problem. 2. Computational details All the bulk geometry optimization in this work were performed with the VASP code [18], using the GGA and GGA + U approximation in the form of the Perdew-Burke-Ernzerhof (PBE) [19] exchange-correlation functional. LDA + U approximation is also used to compare the results of verifying GGA functional calculations. The projected augmented wave method (PAW) [20] was used to describe the interaction between the valence electrons and the core. Unit cells containing 32 atoms were calculated to build the electronic properties of beta- and lambda-Ti3O5. The Monkhorst-Pack [21] scheme was applied in order to sample the Brillouin zone, and the plane wave kinetic energy cutoff is set at 660 eV. The Brillouin zone sampling mesh parameters for the kpoint set were chosen as 3 × 7 × 3 for the both phases. 3. Results and discussion Fig. 1 shows the calculated partial density of states (PDOS) using LDA + U approximations. The PDOS of lambda-Ti3O5 and beta-Ti3O5 near the Fermi level is mainly Ti-d orbit, and the proportion of O-s, O-p, Ti-s and Ti-p is very small. It can be seen that the d-orbital electron state of Ti determines whether the two phases are metallic phase properties or insulator properties. Fig. 2 shows the calculated density of states(DOS) using GGA,
Corresponding author. E-mail address: [email protected] (L. Zuo).
https://doi.org/10.1016/j.commatsci.2019.109435 Received 7 July 2019; Received in revised form 25 October 2019; Accepted 24 November 2019 0927-0256/ © 2019 Elsevier B.V. All rights reserved.
Computational Materials Science 173 (2020) 109435
X.-K. Fu, et al.
Fig. 1. Calculated partial density of states of (a) lambda-Ti3O5 and (b) beta-Ti3O5 using LDA + U approximation. The Fermi level is set to zero.
Fig. 2. Calculated density of states of (a) lambda-Ti3O5 and (b) beta-Ti3O5 using GGA approximation. Calculated density of states of (c) lambda-Ti3O5 and (d) betaTi3O5 using GGA + U approximation. Calculated density of states of (e) lambda-Ti3O5 and (f) beta-Ti3O5 using LDA + U approximation. The Fermi level is set to zero.
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X.-K. Fu, et al.
band. Fig. 3c shows the arrangement of Ti atoms on the (0 1 0) plane of lambda-Ti3O5. The minimum cycles are Ti2-Ti3-Ti3-Ti2 and Ti2-Ti1Ti1-Ti2. The sizes are 16.785 Å and 16.496 Å, respectively. Fig. 3d shows the arrangement of Ti atoms on the (0 1 0) plane of beta-Ti3O5, and all Ti atoms form infinitely long straight chains. Its minimum cycle is Ti1-Ti2-Ti3-Ti3-Ti2-Ti1-Ti1, which is 30.504 Å and also larger than lambda-Ti3O5. Therefore, the minimum cycle D of the Ti-atom arrangement of beta-Ti3O5 on the (0 1 0) plane is greater than lambdaTi3O5. From the view of atomic spacing, the maximum spacing of Ti atoms in lambda is 6.916 Å, and the maximum spacing of Ti atoms in beta is 8.998 Å. The smaller the atomic spacing, the more overlapping the atomic wave functions, and the greater the bandwidth. Therefore, lambda's bandwidth (W) is greater than beta. Kobayashi et al. [11] reported that when the U = 5 eV, the DFT calculation simulation spectra of both phases are in good agreement with the experimental valence band spectra, so it can be considered that the values of Coulomb repulsion U in lambda-Ti3O5 and beta-Ti3O5 are close. Based on the Mott-Hubbard model: it can be seen that lambda-Ti3O5 has a large W/U value and its density of state is expressed as a metal state. As lambda-Ti3O5 transform to beta-Ti3O5, the W/U value will shrink, and the original energy band will gradually split into two sub-bands. The energy gap between the sub-bands will increase as the W/U value decreases. Therefore, the metal-insulator transition between lambdaTi3O5 and beta-Ti3O5 can be considered as bandwidth-controlled transition. Fig. 4a and b are the atom arrangements of (1 0 0) plane of both phases, respectively. Its minimum cycle arrangement is Ti1-Ti3-Ti2-Ti1, which is 15.216 Å and 15.207 Å, respectively, with almost the same value. The periodic configuration of Ti atoms in the (0 0 1) plane can be divided into three categories: Ti1 plane, Ti2 plane and Ti3 plane, as shown in Fig. 4c–h. Lambda-Ti3O5’s cycles on the Ti1 plane are 5.268 Å and 7.513 Å, respectively, while beta-Ti3O5’s cycles on the Ti1 plane are 5.233 Å and 7.503 Å, respectively. Lambda-Ti3O5 has a minimum cycle of 5.268 Å on the Ti2 plane, while beta-Ti3O5 has a minimum cycle of 5.233 Å on the Ti2 plane. Lambda-Ti3O5 has a minimum cycle of 5.268 Å on the Ti3 plane, while beta-Ti3O5 has a minimum cycle of 5.233 Å on the Ti3 plane. Therefore, the cycle values on the (0 0 1) planes of the two phases are almost the same. The atomic arrangements on the (1 0 0) and (0 0 1) planes of the two phases do not conform to the bandwidth-controlled transition, while in the phase transition between
GGA + U and LDA + U approximations, respectively. The electron orbitals near the Fermi level are mainly Ti 3d valence electron orbitals, so the interaction between Ti atoms will determine whether an energy gap is generated at the Fermi level. The GGA and LDA often fail to describe systems with localized (strongly correlated) d and f electrons (this manifests itself primarily in the form of unrealistic one-electron energies). This can result in a failure to describe the energy gap that the insulator should have. As shown in Fig. 2b, the insulator properties of the beta-Ti3O5 phase cannot be correctly described using the GGA method. This can be remedied by introducing a strong atomic interaction (U) in a Hartree-Fock like manner, as an on site replacement of the GGA and LDA. The approaches are commonly known as the GGA + U and LDA + U methods. Thus GGA + U and LDA + U methods can more accurately describe the electronic state of the Ti3O5 systems. As shown in Fig. 2d and f, when using the GGA + U approximation of U = 5 eV and the LDA + U approximation of U = 5 eV, the calculated band gap is 0.14 eV, which is consistent with Ohkoshi’s report [9]. An energy gap at the Fermi level be obtained only after considering the Hubbard energy U on Ti 3d electron orbit, which means that the betaTi3O5 is Mott-Hubbard [22] type insulator. When using the GGA method, the calculated bandwidths of lambda-Ti3O5 and beta-Ti3O5 are 2.642 eV and 2.264 eV, respectively, as shown in Fig. 2a and b. When using the GGA + U method, the bandwidths of lambda-Ti3O5 and betaTi3O5 are 3.142 eV and 2.773 eV, respectively, as shown in Fig. 2c and d. Therefore, lambda-Ti3O5’s bandwidth is greater than beta-Ti3O5’s bandwidth. When the LDA + U method is used, the bandwidths of lambda-Ti3O5 and beta-Ti3O5 are 3.642 eV and 3.305 eV, respectively, and the bandwidth of lambda-Ti3O5 is also wider than that of betaTi3O5. In tight-binding model, the larger the bandwidth W, the smaller the periodic spacing D of the structure [22]. With this in mind, the atomic arrangements of lambda-Ti3O5 and beta-Ti3O5 need to be analyzed. The structures analyzed come from the reports of Ohkoshi [9] and Tokoro [10]. Fig. 3a is the local structures of lambda-Ti3O5, the Ti atom at the center has 6 nearest neighbor Ti atom coordination. Fig. 3b is the local structures of beta-Ti3O5, the Ti atom at the center has only 5 nearest neighbor Ti atom coordination. Based on the tight-binding model, the bandwidth is related to the coordination number. When taking the same interaction integral, the larger coordination number will lead to a wider
Fig. 3. The local structures of (a) lambda-Ti3O5 and (b) beta-Ti3O5 and the atomic configurations of (c) lambda-Ti3O5 and (d) beta-Ti3O5 of (0 1 0) planes. 3
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Fig. 4. The atomic configurations of (a) lambda-Ti3O5 and (b) beta-Ti3O5 of (1 0 0) planes. The atomic configurations of lambda-Ti3O5 of (c) Ti1, (e) Ti2 and (g) Ti3 in (0 0 1) planes. The atomic configurations of beta-Ti3O5 of (d) Ti1, (f) Ti2 and (h) Ti3 in (0 0 1) planes.
the beta-Ti3O5 phase, indicating that the beta-Ti3O5 phase is MottHubbard insulator. Therefore, when investigating the electronic state of both phases, it is necessary to take into account the Hubbard energy U. When the periodic spacing of atoms decreases, the overlap of the atomic wave function increases, and the bandwidth W also increases. At this time, the bandwidth W and Hubbard energy U in the system determine whether the system is in a metallic state or an insulating state. Since Hubbard energy U is not sensitive to atomic spacing, changes in cycle atomic spacing will cause changes between the metal state and the insulating state of the system. The phase transition between lambda-
lambda-Ti3O5 and beta-Ti3O5, the displacement of the atoms only occurs on (0 1 0) plane. Therefore, the phase transition between lambdaTi3O5 and beta-Ti3O5 is bandwidth-controlled transition on a two-dimensional plane.
4. Conclusions The density of states and the atomic arrangements of lambda-Ti3O5 and beta-Ti3O5 were investigated by first principle. The GGA + U and LDA + U functional can correctly describe the insulator properties of 4
Computational Materials Science 173 (2020) 109435
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Ti3O5 and beta-Ti3O5, atomic displacement occurs on (0 1 0) plane. The periodic spacing of lambda-Ti3O5 on (0 1 0) plane is less than the periodic spacing of beta-Ti3O5, so the bandwidth of lambda-Ti3O5 is greater than beta-Ti3O5. Compared to lambda-Ti3O5, beta-Ti3O5’s W/U value is smaller, so as lambda-Ti3O5 transitions to beta-Ti3O5, the arrangement of atoms changes, and the original energy band splits into two sub-bands, making the beta-Ti3O5 phase show an insulating state. Therefore, the phase transition between lambda-Ti3O5 and beta-Ti3O5 is bandwidth-controlled transition.
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CRediT authorship contribution statement Xian-Kai Fu: Conceptualization, Methodology, Software, Data curation, Writing - original draft, Visualization, Investigation. Bo Yang: Data curation, Writing - review & editing. Wan-Qi Chen: Visualization, Investigation. Zhong-Sheng Jiang: Visualization, Investigation. ZongBin Li: Supervision. Hai-Le Yan: Software, Validation. Xiang Zhao: Supervision. Liang Zuo: Conceptualization, Writing - review & editing, Data curation, Software, Validation. Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. References [1][1] A. Ould-Hamouda, H. Tokoro, S. Ohkoshi, E. Freysz, Chem. Phys. Lett. 609
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