- Email: [email protected]
First-principles calculations for structural phase transition of LixFeS2
ARTICLE IN PRESS
Journal of Physics and Chemistry of Solids 69 (2008) 1353–1355 www.elsevier.com/locate/jpcs
First-principles calculations for structural phase transition of LixFeS2 Atsushi Honda, Shin’ichi Higai, Nobuyuki Wada, Yukio Sakabe Murata Manufacturing Co. Ltd., 1-10-1 Higashikohtari, Nagaokakyo, Kyoto 617-8555, Japan Received 30 June 2007; received in revised form 11 October 2007; accepted 30 October 2007
Abstract We investigated the crystal structure of LixFeS2 with varying the amount of Li in the range of 1pxp2 by first-principles theoretical calculations, in order to clarify its structural change and phase stability. We verified the structural phase transition around x ¼ 1.5, which was suggested by experiments. In addition, we proposed the crystal structure of LixFeS2 in 1pxp1.5 for the first time. Furthermore, the sudden change of the electronic conductivity observed around x ¼ 1.5 is properly explained with the change of the electronic band structure. r 2007 Elsevier Ltd. All rights reserved. Keywords: A. Chalcogenides; C. Ab-initio calculations; D. Crystal structure; D. Phase transitions
1. Introduction
2. Method
LixFeS2 has been well known for its high Li-ion storageability and conductivity. Brec et al. [1] studied the electrochemical property of LixFeS2 with intercalating/ deintercalating Li in the range of 0oxp2. They found that, in 1pxp2, the electrochemical potential decreases (increases) with the increase (decrease) of x. It was also found that the potential shows discontinuous change around x ¼ 1.5, so that they suggested an existence of the structural phase transition. The phase transition around x ¼ 1.5 was also supposed from the local structure analyses such as the infrared absorption [2] and Mo¨ssbauer spectroscopy [3]; the coordination numbers of cations were found to change. The crystal structure for x ¼ 2 was clarified by the X-ray diffraction analysis [4], which is shown in Fig. 1a. Though, the crystal structure for 1pxo2 has still been unrevealed. It is very meaningful to clarify details of the LixFeS2 structure for various applications. In the present study, we investigated the crystal structure of LixFeS2 with varying the amount of Li (1pxp2) by first-principles theoretical calculations.
We performed first-principles calculations based on the density functional theory [5,6] and the generalized gradient approximation [7] using the Vienna Ab-initio Simulation Package (VASP) program [8]. The projector augmented wave type atomic potentials [9] and the plane wave basis set with the cut-off energy of 340 eV were employed. The lattice constants of bcc-Li and pyrite-FeS2 are reproduced in the accuracy of 2.0% and 0.5%, respectively. In order to examine the structural phase transition of LixFeS2, two structural models for two phases were prepared. We call them A and B phases. One structure, i.e., the A phase structure for x ¼ 2 is shown in Fig. 1a, which was precisely clarified by the X-ray analysis [4]. It has the hexagonal unit cell with the space group of P3m1. The lattice constants a and c are 3.902 and 6.294 A˚, respectively. The Fe atom occupies the tetrahedral (Td) site, where its coordination number (CN) is 4. On the other hand, the Li atom occupies the Td and octahedral (Oh) sites, where its CN are 4 and 6, respectively. The other structure, i.e., the B phase structure for x ¼ 1 is presented in Fig. 1c, which was constructed based on three experimental results for the Li deintercalation. First, in 1.5pxo2, the remnant Li atom is located only at the Oh site, i.e., only Li at the Td site is deintercalated [2]. Second, CN of Fe shifts from 4 to 6 around x ¼ 1.5 [3]. Third,
Corresponding author. Tel.: +81 77 586 8209; fax: +81 77 587 1923.
E-mail address: [email protected] (A. Honda). 0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2007.10.084
ARTICLE IN PRESS A. Honda et al. / Journal of Physics and Chemistry of Solids 69 (2008) 1353–1355
1354
Li(4)
Li(6) S
Fe(4) Li(4)
Fe(6)
Li
S Li
c
a
sizable change of the crystal structure was not observed through 1pxp2 [3,4]. Actually, the B phase structure is readily obtained from the A phase structure by calculations as following. We remove the Li atom at the Td site as in Fig. 1b. Then, by shifting two S atoms slightly to the upper direction, the B phase structure (Fig. 1c) is stably formed. In this structure, CN of Fe is 6. We also checked other structures by removing Li at the Oh site in the A phase structure. As shown by experiments [2], they are certainly less stable than both the A and B phases through 1pxp2. The total energy calculations of LixFeS2 were performed at x ¼ 1, 1.25, 1.5, 1.75, and 2 for both the A and B phases with employing 2 2 2 supercell. We took 3 3 2 meshed k points in the Brillouin zone. All atomic positions and lattice constants were fully optimized.
Binding energy (eV / Li atom)
Fig. 1. Crystal structures of (a) Li2FeS2 (A phase), (b) LiFeS2 (A phase), and (c) LiFeS2 (B phase). Number in parenthesis denotes the coordination number of cation. Dashed circle presents the position of Li vacancy.
1.0
0.5
3. Results and discussion Here we present our results. We calculated the binding energy (Eb) of Li for both the A and B phase structures with varying x, which is presented in Fig. 2. We defined Eb as E b ðxE Li =2 þ E FS E LFSðxÞ Þ=x,
(1)
where ELi, EFS, and ELFS(x) are the total energies of bcc-Li, pyrite-FeS2, and LixFeS2, respectively. At x ¼ 2, Eb for the A phase is larger than that for the B phase, i.e., the A phase is more stable than the B phase. As x becomes smaller, Eb for the A phase decreases, while that for the B phase does not change remarkably. At x ¼ 1.5, it is noteworthy that the stability of the A and B phases is inverted; Eb for B becomes larger than that for A. Then, in 1oxo1.5, the B phase is more stable than the A phase. Thus, it is concluded that the structural phase transition takes place from the A phase to the B phase at x ¼ 1.5. By the phase transition, CN of Fe changes from 4 to 6. With this result, the previous experimental results that suggested the phase transition at x ¼ 1.5 [1–3] are properly explained.
1.00
1.25
1.50 x in LixFeS2
1.75
2.00
Fig. 2. Binding energy of LixFeS2 (1pxp2). Solid and open circles indicate those of A and B phase, respectively.
The change of the lattice constants a and c with varying the amount of Li (x) is shown in Fig. 3a and b, respectively. We see that, with decreasing of x, both a and c shrink for the A phase. On the other hand, for the B phase, a shrinks, whereas c extends. At x ¼ 1.5, where the structural phase transition occurs, a of the A and B phases are different about 0.1 A˚, while c are almost same. This difference results in the cell volume change of 5.3% at the structural phase transition, and thus it is suggested that this phase transition is the first-order transition. However, such a critical change of the lattice constant has hardly been measured by the X-ray diffraction, because the Bragg peaks of LixFeS2 become very broad as x decreases towards x ¼ 1 [4].
ARTICLE IN PRESS A. Honda et al. / Journal of Physics and Chemistry of Solids 69 (2008) 1353–1355
1355
1.8
a 3.7
3.6
c/a
1.7
Lattice constant (Å)
3.5
1.6
b 6.1 6.0
1.5 1.00
5.9 5.8
1.25
1.50 x in LixFeS2
1.75
2.00
Fig. 4. c/a ratio of LixFeS2 (1pxp2). Solid and open circles give those of A and B phase, respectively.
5.7
4. Conclusion 1.00
1.25
1.50 x in LixFeS2
1.75
2.00
Fig. 3. Lattice constants (a) a and (b) c of LixFeS2 (1pxp2). Solid and open circles represent those of A and B phase, respectively.
In Fig. 4, the variation of the c/a ratio is shown. The c/a ratio of the A phase is almost constant around 1.6 through the Li intercalation/deintercalation process. However, that of the B phase largely changes from 1.54 (x ¼ 2) to 1.76 (x ¼ 1). Since it has been known that the usual LiMX2 type crystal structure has the c/a ratio value larger than 1.71 [3], the c/a ratio of the B phase at x ¼ 1 is considered to be reasonable. The electronic band structures of LixFeS2 were also calculated. For the A phase, the band structures are metallic, i.e., the carrier density is large, for all the Li amount (1pxp2). For the B phase, on the other hand, the band structures are semiconductor-like, i.e., the Fermi level exists near the top of the valence band and the carrier density is small. Accordingly, it is suggested that the electronic conductivity suddenly decreases with the phase transition from the A phase to the B phase. The sudden change of the conductivity by the phase transition was certainly observed [1], which is qualitatively consistent with our suggestion.
The structural change and phase stability of LixFeS2 (1pxp2) were theoretically studied in detail by firstprinciples calculations. We clarified 1. Structural phase transition around x ¼ 1.5. 2. Crystal structure of LixFeS2 in 1pxp1.5. 3. Change of lattice constants through 1pxp2. Furthermore, the sudden change of the electronic conductivity around x ¼ 1.5 is qualitatively explained with the change of the electronic band structure. References [1] R. Brec, A. Dugast, A. LeMehaute´, Mater. Res. Bull. 15 (1980) 619. [2] P. Gard, C. Sourisseau, G. Ouvrard, R. Brec, Solid State Ion. 20 (1986) 231. [3] L. Blandeau, G. Ouvrard, Y. Calage, R. Brec, J. Rouxel, J. Phys. C: Solid State Phys. 20 (1987) 4271. [4] R.J. Batchelor, F.W.B. Einstein, C.H.W. Jones, R. Fong, J.R. Dahn, Phys. Rev. B 37 (1988) 3699. [5] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [6] W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. [7] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [8] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [9] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758.
Journal of Physics and Chemistry of Solids 69 (2008) 1353–1355 www.elsevier.com/locate/jpcs
First-principles calculations for structural phase transition of LixFeS2 Atsushi Honda, Shin’ichi Higai, Nobuyuki Wada, Yukio Sakabe Murata Manufacturing Co. Ltd., 1-10-1 Higashikohtari, Nagaokakyo, Kyoto 617-8555, Japan Received 30 June 2007; received in revised form 11 October 2007; accepted 30 October 2007
Abstract We investigated the crystal structure of LixFeS2 with varying the amount of Li in the range of 1pxp2 by first-principles theoretical calculations, in order to clarify its structural change and phase stability. We verified the structural phase transition around x ¼ 1.5, which was suggested by experiments. In addition, we proposed the crystal structure of LixFeS2 in 1pxp1.5 for the first time. Furthermore, the sudden change of the electronic conductivity observed around x ¼ 1.5 is properly explained with the change of the electronic band structure. r 2007 Elsevier Ltd. All rights reserved. Keywords: A. Chalcogenides; C. Ab-initio calculations; D. Crystal structure; D. Phase transitions
1. Introduction
2. Method
LixFeS2 has been well known for its high Li-ion storageability and conductivity. Brec et al. [1] studied the electrochemical property of LixFeS2 with intercalating/ deintercalating Li in the range of 0oxp2. They found that, in 1pxp2, the electrochemical potential decreases (increases) with the increase (decrease) of x. It was also found that the potential shows discontinuous change around x ¼ 1.5, so that they suggested an existence of the structural phase transition. The phase transition around x ¼ 1.5 was also supposed from the local structure analyses such as the infrared absorption [2] and Mo¨ssbauer spectroscopy [3]; the coordination numbers of cations were found to change. The crystal structure for x ¼ 2 was clarified by the X-ray diffraction analysis [4], which is shown in Fig. 1a. Though, the crystal structure for 1pxo2 has still been unrevealed. It is very meaningful to clarify details of the LixFeS2 structure for various applications. In the present study, we investigated the crystal structure of LixFeS2 with varying the amount of Li (1pxp2) by first-principles theoretical calculations.
We performed first-principles calculations based on the density functional theory [5,6] and the generalized gradient approximation [7] using the Vienna Ab-initio Simulation Package (VASP) program [8]. The projector augmented wave type atomic potentials [9] and the plane wave basis set with the cut-off energy of 340 eV were employed. The lattice constants of bcc-Li and pyrite-FeS2 are reproduced in the accuracy of 2.0% and 0.5%, respectively. In order to examine the structural phase transition of LixFeS2, two structural models for two phases were prepared. We call them A and B phases. One structure, i.e., the A phase structure for x ¼ 2 is shown in Fig. 1a, which was precisely clarified by the X-ray analysis [4]. It has the hexagonal unit cell with the space group of P3m1. The lattice constants a and c are 3.902 and 6.294 A˚, respectively. The Fe atom occupies the tetrahedral (Td) site, where its coordination number (CN) is 4. On the other hand, the Li atom occupies the Td and octahedral (Oh) sites, where its CN are 4 and 6, respectively. The other structure, i.e., the B phase structure for x ¼ 1 is presented in Fig. 1c, which was constructed based on three experimental results for the Li deintercalation. First, in 1.5pxo2, the remnant Li atom is located only at the Oh site, i.e., only Li at the Td site is deintercalated [2]. Second, CN of Fe shifts from 4 to 6 around x ¼ 1.5 [3]. Third,
Corresponding author. Tel.: +81 77 586 8209; fax: +81 77 587 1923.
E-mail address: [email protected] (A. Honda). 0022-3697/$ - see front matter r 2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.jpcs.2007.10.084
ARTICLE IN PRESS A. Honda et al. / Journal of Physics and Chemistry of Solids 69 (2008) 1353–1355
1354
Li(4)
Li(6) S
Fe(4) Li(4)
Fe(6)
Li
S Li
c
a
sizable change of the crystal structure was not observed through 1pxp2 [3,4]. Actually, the B phase structure is readily obtained from the A phase structure by calculations as following. We remove the Li atom at the Td site as in Fig. 1b. Then, by shifting two S atoms slightly to the upper direction, the B phase structure (Fig. 1c) is stably formed. In this structure, CN of Fe is 6. We also checked other structures by removing Li at the Oh site in the A phase structure. As shown by experiments [2], they are certainly less stable than both the A and B phases through 1pxp2. The total energy calculations of LixFeS2 were performed at x ¼ 1, 1.25, 1.5, 1.75, and 2 for both the A and B phases with employing 2 2 2 supercell. We took 3 3 2 meshed k points in the Brillouin zone. All atomic positions and lattice constants were fully optimized.
Binding energy (eV / Li atom)
Fig. 1. Crystal structures of (a) Li2FeS2 (A phase), (b) LiFeS2 (A phase), and (c) LiFeS2 (B phase). Number in parenthesis denotes the coordination number of cation. Dashed circle presents the position of Li vacancy.
1.0
0.5
3. Results and discussion Here we present our results. We calculated the binding energy (Eb) of Li for both the A and B phase structures with varying x, which is presented in Fig. 2. We defined Eb as E b ðxE Li =2 þ E FS E LFSðxÞ Þ=x,
(1)
where ELi, EFS, and ELFS(x) are the total energies of bcc-Li, pyrite-FeS2, and LixFeS2, respectively. At x ¼ 2, Eb for the A phase is larger than that for the B phase, i.e., the A phase is more stable than the B phase. As x becomes smaller, Eb for the A phase decreases, while that for the B phase does not change remarkably. At x ¼ 1.5, it is noteworthy that the stability of the A and B phases is inverted; Eb for B becomes larger than that for A. Then, in 1oxo1.5, the B phase is more stable than the A phase. Thus, it is concluded that the structural phase transition takes place from the A phase to the B phase at x ¼ 1.5. By the phase transition, CN of Fe changes from 4 to 6. With this result, the previous experimental results that suggested the phase transition at x ¼ 1.5 [1–3] are properly explained.
1.00
1.25
1.50 x in LixFeS2
1.75
2.00
Fig. 2. Binding energy of LixFeS2 (1pxp2). Solid and open circles indicate those of A and B phase, respectively.
The change of the lattice constants a and c with varying the amount of Li (x) is shown in Fig. 3a and b, respectively. We see that, with decreasing of x, both a and c shrink for the A phase. On the other hand, for the B phase, a shrinks, whereas c extends. At x ¼ 1.5, where the structural phase transition occurs, a of the A and B phases are different about 0.1 A˚, while c are almost same. This difference results in the cell volume change of 5.3% at the structural phase transition, and thus it is suggested that this phase transition is the first-order transition. However, such a critical change of the lattice constant has hardly been measured by the X-ray diffraction, because the Bragg peaks of LixFeS2 become very broad as x decreases towards x ¼ 1 [4].
ARTICLE IN PRESS A. Honda et al. / Journal of Physics and Chemistry of Solids 69 (2008) 1353–1355
1355
1.8
a 3.7
3.6
c/a
1.7
Lattice constant (Å)
3.5
1.6
b 6.1 6.0
1.5 1.00
5.9 5.8
1.25
1.50 x in LixFeS2
1.75
2.00
Fig. 4. c/a ratio of LixFeS2 (1pxp2). Solid and open circles give those of A and B phase, respectively.
5.7
4. Conclusion 1.00
1.25
1.50 x in LixFeS2
1.75
2.00
Fig. 3. Lattice constants (a) a and (b) c of LixFeS2 (1pxp2). Solid and open circles represent those of A and B phase, respectively.
In Fig. 4, the variation of the c/a ratio is shown. The c/a ratio of the A phase is almost constant around 1.6 through the Li intercalation/deintercalation process. However, that of the B phase largely changes from 1.54 (x ¼ 2) to 1.76 (x ¼ 1). Since it has been known that the usual LiMX2 type crystal structure has the c/a ratio value larger than 1.71 [3], the c/a ratio of the B phase at x ¼ 1 is considered to be reasonable. The electronic band structures of LixFeS2 were also calculated. For the A phase, the band structures are metallic, i.e., the carrier density is large, for all the Li amount (1pxp2). For the B phase, on the other hand, the band structures are semiconductor-like, i.e., the Fermi level exists near the top of the valence band and the carrier density is small. Accordingly, it is suggested that the electronic conductivity suddenly decreases with the phase transition from the A phase to the B phase. The sudden change of the conductivity by the phase transition was certainly observed [1], which is qualitatively consistent with our suggestion.
The structural change and phase stability of LixFeS2 (1pxp2) were theoretically studied in detail by firstprinciples calculations. We clarified 1. Structural phase transition around x ¼ 1.5. 2. Crystal structure of LixFeS2 in 1pxp1.5. 3. Change of lattice constants through 1pxp2. Furthermore, the sudden change of the electronic conductivity around x ¼ 1.5 is qualitatively explained with the change of the electronic band structure. References [1] R. Brec, A. Dugast, A. LeMehaute´, Mater. Res. Bull. 15 (1980) 619. [2] P. Gard, C. Sourisseau, G. Ouvrard, R. Brec, Solid State Ion. 20 (1986) 231. [3] L. Blandeau, G. Ouvrard, Y. Calage, R. Brec, J. Rouxel, J. Phys. C: Solid State Phys. 20 (1987) 4271. [4] R.J. Batchelor, F.W.B. Einstein, C.H.W. Jones, R. Fong, J.R. Dahn, Phys. Rev. B 37 (1988) 3699. [5] P. Hohenberg, W. Kohn, Phys. Rev. B 136 (1964) 864. [6] W. Kohn, L.J. Sham, Phys. Rev. A 140 (1965) 1133. [7] J.P. Perdew, K. Burke, M. Ernzerhof, Phys. Rev. Lett. 77 (1996) 3865. [8] G. Kresse, J. Furthmuller, Phys. Rev. B 54 (1996) 11169. [9] G. Kresse, D. Joubert, Phys. Rev. B 59 (1999) 1758.