Diffusion Dynamics of the Li Atom on Amorphous Carbon: A Direct

of magnesium ions with graphene surface. Koichi Kato , Tetsuji Iyama , Hiroto Tachikawa. Japanese Journal of Applied Physics 2014 53 (2S), 02BD02 ...
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J. Phys. Chem. B 2006, 110, 20445-20450

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Diffusion Dynamics of the Li Atom on Amorphous Carbon: A Direct Molecular Orbital-Molecular Dynamics Study Hiroto Tachikawa* and Akira Shimizu DiVision of Materials Chemistry, Graduate School of Engineering, Hokkaido UniVersity, Sapporo 060-8628, Japan ReceiVed: March 15, 2006; In Final Form: August 8, 2006

Direct molecular orbital-molecular dynamics (MO-MD) calculation was applied to diffusion processes of the Li atom on a model surface of amorphous carbon and compared with the diffusion mechanism of Li+ ion. A carbon sheet composed of C96H24 was used as the model surface. The total energy and energy gradient on the full dimensional potential energy surface of the LiC96H24 system were calculated at each time step in the trajectory calculation. The optimized structure, where the Li atom is located at the center of mass of the model surface, was used as the initial structure at time zero. Simulation temperatures were chosen in the range of 200-1250 K. The dynamics calculations showed that the Li atom vibrates around the initial position below 250 K, and it moves above 300 K. At middle temperature, the Li atom translates freely on the surface. At higher temperature (1000 K), the Li atom moves from the center to edge region of the model surface and is trapped in the edge. The activation energy calculated for the Li atom is larger than that for the Li+ ion. This difference is due to the fact that the Li atom diffuses together with an unpaired electron on the carbon surface. The diffusion mechanism of the Li atom was discussed on the basis of the theoretical results.

1. Introduction Graphite has the possibility of accommodating several species between carbon layers. Hence, this character has been applied to the anode material of a lithium secondary battery with the performance as high electromotive force and high energy density.1-7 As well as the graphite materials, amorphous carbon materials, which are composed of small carbon sheets, have higher performance than that of crystalline graphite having a layer structure. This particular feature is attributed to amorphous carbon being able to be involved with a large number of lithium ions. Actually, the theoretical maximum capacity of graphite material (LiC6) is 372 mAh/g,8 whereas amorphous carbon materials have remarkably high capacities (500-1100 mAh/ g).9 This characteristics originates from nonlayer structure where the Li atom and ion are stored in the edge region of the carbon layer. To elucidate the mechanism of the lithium battery, many experimental works have been carried out. Jungblut and Hoinkis observed the diffusion of Li on highly oriented pyrolytic graphite (HOPG) at Li dilute concentration and a temperature range from 1000 to 1300 K using isotopes 7Li and 6Li. The Li transport in HOPG was observed to be strongly anisotropic. The Li diffusion coefficient (D) in the direction of graphite plane is measured to be D ) 0.76 × 10-9 m2/s at 1070 K.10 β-Nuclear magnetic resonance (β-NMR) measurement11 revealed that the lithium diffuses as the form of ion in the graphite layer and the diffusivity is dependent upon the intercalation level. Sato et al. predicted from the analysis of lattice image and NMR spectra that the Li atom exists in the disordered carbon site.12 The interactions between Li/Li+ and the graphite surface have been investigated theoretically by several groups using lithium carbon cluster models.13-21 Using the density functional theory * Address correspondence to this author. E-mail: [email protected]. Fax. +81-11-706-7897.

(DFT) method, Marquez et al. investigated the interaction between Li+ and the hydrogen terminated cluster model (C32H18). They suggested that the Li+ ion is preferentially bound outside the cluster model (i.e, the edge site).13 Khantha et al. calculated the interaction potential of a Li atom with a graphite surface to elucidate the effect of Li-Li interaction. The binding energies of the Li atom are calculated to be 1.598 eV when Li-Li separation is 9.22 au, and 0.934 eV when the adjacent Li atom is located on or near the Li atom.14 On the basis of semiempirical MO calculations using a C96 planer carbon cluster and Li+, Nakadaira et al. suggested that the edge site is more stable than that of the ring-over site.15 Ab initio calculations for the interaction of lithium atom with graphite model clusters indicated that charge transfer from the Li atom to the graphite cluster is important in the large cluster size.17,18 Thus, the static feature about the interaction between the Li+/Li and the graphite cluster model has been extensively studied. However, the information about the dynamics feature of Li+ on the amorphous carbon surface is still unclear. Recently, we have developed a dynamics method to calculate the trajectory on the full dimensional potential energy surface obtained by ab initio and semiempirical molecular orbital (MO) methods.22-26 Using this method, we investigated the Li+ ion on the model surface of amorphous carbon to elucidate quantum chemically the diffusion dynamics.22 It was found that the Li+ ion diffuses along the node of the highest occupied molecular orbital (HOMO) of the carbon surface. In the present paper, we extended the method to a diffusion dynamics of the Li atom on the model surface of amorphous carbon to shed light on the mechanism of the lithium battery from the quantum mechanical point of view. In particular, we focus our attention on the diffusion mechanism of the Li atom on amorphous carbon because this is strongly related to the mechanism of the lithium secondary battery.

10.1021/jp061603l CCC: $33.50 © 2006 American Chemical Society Published on Web 09/15/2006

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2. Method of Calculation It is known that the amorphous carbons have nonstacking structure and are composed of small sized carbon clusters.27,28 Large numbers of lithium atoms are adsorbed on the carbon layer and edge regions.15,16 Considering these features, we have chosen a cluster composed of C96H24 as a model of amorphous carbon throughout. Similar and smaller carbon clusters have been widely used as a good model of amorphous carbon29 and/ or a surface model of graphite. First, the model cluster (C96H24) was fully optimized at the semiempirical MO level (AM1). For the interaction system (LiC96H24), one Li atom was put on the center-of-mass of the model cluster (denoted by site A), and then the structures of the LiC96H24 cluster were fully optimized. It should be noted that AM1 calculation reasonably represents the structural and electronic feature of the lithium-graphite system: charge and activation energy for the diffusion are in good agreement with those of B3LYP/LANL2MB.22 Diffusion processes of the Li atom on the surface were investigated by means of the direct molecular orbital-molecular dynamics (MO-MD) method. The total energy and energy gradient on the multidimensional potential energy surface of the LiC96H24 system were calculated at each time step at the AM1-MO level of theory, and then the classical equation of motion is full-dimensionally solved. Therefore, charges and electronic states of the Li atom and all carbon and hydrogen atoms are treated exactly within the level of theory by the calculations at each time step. This point is much different from the usual classical molecular dynamics (MD) calculation where the charges of all atoms and ion are constant during the diffusion. Hence, one can obtain details of the diffusion processes of the lithium ion on amorphous carbon using the direct MO-MD method. We carried out the direct MO-MD calculations under constant temperature condition. The mean temperature of the system is defined by

T)

1

〈

3kN

∑i miVi2〉

(1)

where N is the number of atoms, Vi and mi are velocity and mass of the ith atom, and k is Boltzmann’s constant. We choose temperatures in the range 100-1100 K. The velocities of atoms at the starting point were adjusted to the selected temperature. To keep the system at a constant temperature, the bath relaxation time (τ) was introduced in the calculation.30 We have chosen τ ) 0.01 ps in all trajectory calculations. The equations of motion for n atoms in the system are given by

dQj ∂H ) dt ∂Pj ∂Pj ∂H ∂U ))∂t ∂Qj ∂Qj

(2)

where j ) 1 - 3N, H is the classical Hamiltonian, and Qj, Pj, and U are the Cartesian coordinate of jth mode, conjugated momentum, and potential energy of the system. These equations were numerically solved by the Runge-Kutta method. No symmetry restriction was applied to the calculation of the gradients. The time step size was chosen by 0.2 fs, and a total of 10 000 steps were calculated for each dynamics calculation. The drift of the total energy is confirmed to be less than (1 ×

Figure 1. Optimized structure of LiC96H24 cluster obtained at the AM1MO calculation. Notations of A-F and a-c indicate the positions of Li atom on ring-over site and in edge site, respectively.

10-3)% throughout at all steps in the trajectory. The momentum of the center of mass and the angular momentum are assumed to zero. Static density functional theory (DFT) calculation, B3LYP/ LANL2DZ, and AM1 calculations for the potential energy curves (PECs) along a diffusion path on carbon cluster were carried out with the Gaussian 03 program package.31 3. Results A. Structures of the Model Cluster of Amorphous Carbon. The structures of the free carbon cluster C96H24 and the lithium atom-surface cluster LiC96H24 are optimized. The structure of the carbon cluster is purely planar. The fully optimized structure of the LiC96H24 cluster is illustrated in Figure 1. We assume that the Li atom is located at site A for the initial point. The Li atom at site A is located 2.152 Å above the carbon surface at the optimized structure. The LiC96H24 cluster has a lens structure. The charge of the Li atom is calculated to be Q(Li) ) +0.70, which means 70% of the electron of the Li atom is diffused into the carbon surface. The structure of the carbon model surface is slightly changed by the interaction of the Li atom. The C-C bond lengths around site A before and after the interaction with the Li atom are calculated to be 1.427 and 1.434 Å, respectively. This C-C bond elongation is caused by the slight electron transfer from the Li atom to the π*(CdC) orbital of the carbon surface. To check reliability of the AM1 level, the B3LYP/LANL2DZ calculation is carried out for the LiC96H24 system. The charge of the Li atom is calculated to be +0.75 (LANL2DZ), which are in good agreement with that of the AM1 calculation. B. Diffusion of the Li Atom at Low Temperatures (250500 K). First, the dynamics calculations are carried out at lower temperature below 250 K. However, the Li atom does not move on the surface, whereas it vibrates around its equilibrium point. The diffusion takes place above 300 K. The snapshots for the Li atom superimposed on the carbon surface at 500 K are illustrated in Figure 2. It is assumed that the Li atom is located in site A at time zero. After thermal

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Figure 2. Geometrical parameters around Li atom at site A and snapshots of the LiC96H24 system at 500 K. The insert indicates a bonding feature of the Li atom to the carbon atom (C1′′).

Figure 4. Time propagation of spin density during the diffusion of the Li atom at 800 K. Isosurface indicates spin density on carbon surface.

Figure 3. Time propagation of the position of the Li atom on the carbon surface at 500 K plotted as a function of time.

activation, the Li atom moves and passes near the C1′ carbon at time 0.15 ps, and then reaches the next carbon atom (site B) at 0.18 ps. After that, the Li atom returns to the direction for site A. The Li atom is positioned again in site A at 0.40 ps. It should be noted that the Li atom moves mainly along the C-C bond. At 2.00 ps, the Li atom binds to the C1′′ atom. To elucidate the dynamics in more details, time propagation of the bond distances (R1 and R1′′) is monitored and the values are plotted in Figure 3, where R1 and R1′′ are the C1-Li and C1′′-Li distances, respectively. The distances R1 and R1′′ are equivalent to 2.587 Å at time zero (site A). After thermal activation, both distances increase with increasing time, meaning that the Li atom moves gradually on the surface. At time 0.180.25 ps, the Li atom is located around site B, and then Li returns

again to site A. The Li atom vibrates three times between sites A and B in the range 0.0-1.0 ps. Finally, the Li atom binds to the C1′′ atom. C. Time Propagation of Spin Densities of the System. A lithium atom has an unpaired electron, so that spin density is generated in the lithium-carbon cluster system. The time propagation of spin density is illustrated in Figure 4. At time zero, spin is widely distributed in sites A, B, C, and D. This distribution corresponds to the singly occupied molecular orbital (SOMO) of the carbon cluster. Once diffusion is started, the unpaired electron moves together with the Li atom. The spin is localized around the Li atom. Especially, the electron localization around the Li atom becomes stronger when the atom is close to the edge region. This result strongly indicates that the Li atom moves together with the unpaired electron on the carbon surface. It should be noted that the lithium atom diffuses together with the unpaired electron on the carbon surface. D. Diffusion of the Li Atom at 1000 K. Snapshots and trajectory of the Li atom at 1000 K superimposed on the carbon surface are given in Figures 5 and 6, respectively. The Li atom starting from site A runs against the edge region of the carbon cluster. The atom moves along the carbon atoms and puts down in the edge region at 0.3 ps. After that, the atom transfers along the edge. An extended view in Figure 6 shows the binding

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Figure 5. Trajectory of the Li atom superimposed on the carbon surface at 1000 K. The Li atom is started from site A.

Tachikawa and Shimizu

Figure 7. Position of the Li atom on the carbon surface at 1000 K plotted as a function of time. R1, R2, R3, and R4 are distances of the Li atom from C1, C2, C3, and C4 atoms, respectively.

Figure 8. Diffusion coefficients (D) of the Li atom on the C96H24 cluster calculated by direct MO-MD calculation at the AM1 level.

Figure 6. Snapshots of the LiC96H24 system at 1000 K. The insert indicates an expanded view of a bonding structure of the Li atom to the carbon atom in the edge region.

structure of Li to the carbon atom in the edge region. The structure around the carbon atom is changed from planar to bent form by interacting with the Li atom, indicating that the electronic state of the carbon atom is changed from the sp2- to sp3-like hybrid orbital by the interaction with the Li atom. However, the binding of Li to the carbon atom is relatively

weak, so that the C-Li bond is easily dissociated at 1000 K, and the Li atom transfers to the next carbon atom. To elucidate the movement of the Li atom in more detail, the distances of Li from several carbon atoms are plotted as a function of time in Figure 7. The distance R1 is 2.587 Å at time zero. Starting the diffusion, R1 is gradually increased, but R2 and R3 are decreased, indicating that the Li atom goes away from site A (1st stage). The distance R2 is minimized at the 2nd stage, indicating that the Li atom is bound to the C2 atom of the carbon surface. At the 3rd and 4th stages, the Li atom binds to C3 and C4 atoms, respectively. The Li atom is returned to the C3 atom at the 5th stage. Thus, the Li atom moves while making the C-Li bond along the carbon atoms at the edge site. This feature is much different from that of the Li+ ion. In the case of the Li ion, the binding does not take place during the diffusion. E. Diffusion Coefficients. The diffusion coefficients of the Li atom (D) are calculated for all temperatures in the range 3001250 K. The calculated diffusion coefficients are plotted in Figure 8. The values increase with increasing temperature. The diffusion coefficients for 300, 700, and 1000 K are calculated to be 3.99 × 10-11, 3.27 × 10-10, and 5.95 × 10-10 m2/s, respectively. An Arrhenius plot of the diffusion coefficient of the Li atom is given in Figure 9 together with that of the Li+ ion. The diffusion coefficient for the Li atom is smaller than that of the Li+ ion. The activation energies for the diffusion of the Li atom and Li+ are calculated to be 1.08 and 0.81 kcal/mol, respectively. The experimental value for diffusion of Li+ is 1.22 kcal/mol in

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Figure 9. Arrhenius plots of diffusion coefficients of the Li atom on the model surface. The values for the Li+ ion are cited from our previous paper [Tachikawa, H.; Shimizu, A. J. Phys. Chem. B 2005, 109, 13255].

graphite,32 which is in excellent agreement with the calculated value. This agreement implies that the present calculation would be valid to simulate the diffusion processes of Li/Li+-carbon systems. 4. Discussion A. Diffusion of the Li Atom on the Carbon Surface. In the present work, direct MO-MD calculation was applied to the diffusion dynamics of the Li atom on the carbon model surface. The diffusion coefficient at 300 K was calculated to be D(Li,300 K) ) 3.99 × 10-11 m2/s, which is one-order of magnitude slower than that of the Li+ ion D(Li+,300 K) ) 5.40 × 10-10 m2/s. The decrease of the diffusion coefficient of the Li atom is caused by the deformation of the carbon skeleton during the diffusion: namely, the Li atom walks while trailing the distribution of spin density. On the other hand, diffusion of the Li+ ion does not cause the lattice deformation. Hence, the diffusion rate of the Li atom becomes slower. B. Comparison with the Diffusion Mechanism of the Li+ Ion. In our previous paper,22 we reported that the Li+ ion diffuses along the node of the highest occupied molecular orbital (HOMO). Also, it was found that the Li+ ion behaves as an electron acceptor on the carbon surface. The present calculation indicaes that the diffusion path of the Li atom is much different from that of the Li+ ion: the Li atom moves while feeling interaction with the singly occupied molecular orbital (SOMO) of the carbon surface. The Li atom behaves as an electron donor in the carbon surface. The excess electron is transferred from the Li atom to the carbon surface, and the Li atom moves together with the excess electron on the carbon surface. Thus, the present study strongly suggests that the diffusion mechanisms of the Li atom and teh Li ion are essentially different. It should be noted that these features are not obtained by a usual classical MD calculation, only direct MO-MD calculation gives the important information for the diffusion mechanism. A model of the diffusion process of the Li atom on the amorphous carbon is illustrated in Figure 10. At lower temperatures (below 250 K), the Li atom vibrates around the equilibrium point and displacement is significantly small. At intermediate temperatures (ca. 300 < T < 800 K), the Li atom moves on the carbon surface. At higher temperatures, the atom moves and falls in the edge region, and then the atom diffuses along the edge region. In the case of diffusion of the Li+ ion, the ion moves freely on both surface and edge regions at 800-1000 K, which is slightly deferent from that of the Li atom. Thus,

Figure 10. Model for the diffusion of the Li atom on the amorphous carbon surface. (A) Temperature effects on the diffusion process and (B) mechanism of diffusion of the Li atom.

the diffusion process of teh Li atom on the model cluster is strongly dependent on teh temperature, and the diffusion mechanism is different from that of teh Li+ ion: namely, the Li atom moves together with the unpaired electron and causes the structural deformation of the carbon lattice. Hence, the activation energy of the diffusion of the Li atom is larger than that of the Li+ ion. Unfortunately, there are no experimental data for comparison of diffusions for Li+/Li in amorphous carbon. To prove this model, a detailed experiment is needed. C. Comparison with Previous Studies. The static properties for the interactions between lithium ion (atom) and carbon clusters have been investigated theoretically by several groups.13-18 The binding of Li+/Li on each trapping site was investigated by means of DFT and semiempirical MO calculations. These calculations showed that the Li atom and Li+ ion are more stabilized at the edge site than at the ring-over site.15,29,30 For example, Panapek et al.29b investigated the interaction between Li+ ions and disordered carbon-hydrogen alloy (amorphous carbon) by means of semiempirical MNDO and AM1 methods using C54H18 model cluster. They showed that large amounts of Li ions can adsorb to the edge region of the carbon surface. In particular, Li+ was preferentially bound to H-terminated edges of hexagonal carbon fragments. Hankinson and Almlo¨f carried out a pioneering calculation for the interaction of the Li atom with a carbon layer at the ab initio calculations.18 They showed that the Li atom interacting with the carbon layer exists as a positive ion. These results are in good agreement with that of the present calculation. D. Concluding Remarks. In this section, we discuss approximations used in the present study. A model of amorphous carbon was assumed to a C96H24 carbon model cluster. This cluster has 37 hexagons. From X-ray diffraction experiment, it is suggested that the amorphous carbon has a few-layer graphitic fragment of order 40 lateral dimension corresponding to 20-

20450 J. Phys. Chem. B, Vol. 110, No. 41, 2006 30 contiguous hexagons.33 Also, the amorphous carbon has no stacked layer structure.27,28 Therefore, the model cluster (C96H24) would be enough to represent the structure of actual amorphous carbon. However, dynamics calculations with several sized cluster models would be required to obtain more accurate information on the diffusion process on amorphous carbons. Next, the multidimensional potential energy surface calculated by the AM1 method is used in the trajectory calculations throughout. This level of theory would be adequate to discuss qualitatively the diffusion dynamics of the lithium-carbon system as shown in a previous paper.22 In particular, the AM1 calculation represents well the barrier height and shape of potential energy curve along the diffusion path calculated by a more sophisticated level (B3LYP/LANL2MB). For example, static activation barriers between ring-over sites for diffusion of Li atom are calculated to be 1.86 (AM1) and 1.69 kcal/mol (B3LYP/LANL2MB). Also, the charge of the Li atom is explicitly represented by the AM1 calculation. Hence, the direct MO-MD calculations at this level of theory would give a reasonable feature on the diffusion process of the Li atom on the carbon cluster. However, more accurate wave functions may provide deeper insight in the detailed diffusion dynamics. We used one sheet of the carbon cluster in the present work. The stacking structures of carbon surface would affect the diffusion constant of the Li atom. It is considered that the diffusion constant of the Li atom becomes larger in the stacking structure because the Li atom couples with a phonon mode of the carbon cluster and moves. Also, we treated a single lithium atom for a diffusion model of the lithium atom. However, there is a report that the lithium atom exists as a dimer (Li)2 in higher density state.12 Therefore, we will investigate the diffusion of (Li)2 in the near future. Thus, despite the several assumptions introduced here, the results enable us to obtain valuable information on the mechanism of the diffusion of the Li atom on an amorphous carbon cluster. Acknowledgment. The authors are indebted to the Computer Center at the Institute for Molecular Science (IMS) for the use of the computing facilities. H.T. also acknowledges partial support from a Grant-in-Aid from the Ministry of Education, Science, Sports and Culture of Japan. Supporting Information Available: Full description of the material. This material is available free of charge via the Internet at http://pubs.acs.org. References and Notes (1) For a review article see: Inagaki, M. J. Mater. Res. 1989, 4, 1560. (2) For a review articlesee: Koksbang, R.; Barker, J.; Shi, H.; Saidi, M. Y. Solid State Ionics 1996, 84, 1. (3) Inagaki, M. In Chemical Physics of Intercalation; NATO ASI Ser. B, 172; Legrand, A. P., Flandrois, S., Eds.; Plenum: New York, 1987; p 105. (4) Inagaki, M.; Tachikawa, H.; Nakahashi, T.; Konno H.; Hishiyama, Y. Carbon 1998, 36, 1021.

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