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J. Phys. Chem. C 2009, 113, 672–676
Density Functional Theory Study for the Stability and Ionic Conductivity of Li2O Surfaces Mazharul M. Islam† and Thomas Bredow*,‡ Laboratoire de Physico-Chimie des Surfaces, CNRS-ENSCP (UMR 7045), Ecole Nationale Supe´rieure de Chimie de Paris, Paris, France, Institut fu¨r Physikalische and Theoretische Chemie, UniVersita¨t Bonn, Wegelerstrasse 12, 53115 Bonn, Germany ReceiVed: August 7, 2008; ReVised Manuscript ReceiVed: October 23, 2008
The energetic, electronic, and defect properties of two low-index Li2O surfaces were studied theoretically at density functional level. In agreement with previous theoretical studies, it was found that the (111) surface is more stable than (110). For both surfaces, a slight shift of the position of the valence band maximum and conduction band minimum with respect to the bulk Li2O was found. The formation of an isolated cation vacancy and a cation Frenkel defect in the Li2O (111) surface were studied as a function of defect concentration. The defect formation energy is ∼10% smaller on the (111) surface than in the bulk. Possible pathways for Li+ diffusion in the Li2O (111) surface were investigated. The activation energy for local hopping processes in the topmost surface layer is significantly smaller than in the Li2O bulk, which is in agreement with experimentally observed increased conductivity in nanocrystalline Li2O materials. 1. Introduction Lithium diffusion in Li2O is a subject of great technological interest due to the superionic behavior of this material.1,2 It is used in high-capacity energy storage devices for next-generation electric vehicles; in lightweight high-power-density lithium-ion batteries for heart pacemakers, mobile phones, and laptop computers;3,4 and as blanket breeding material for deuteriumtritium fusion reactors.5,6 Both theoretical and experimental investigations have been performed on defect properties7-14 and the ion conduction mechanism9,10,14-22 in Li2O. It is well-known that lattice defects have a large effect on ion conductivity of ceramics. The dominant intrinsic defects in Li2O are point defects,9,10 either as cation vacancies or of cation Frenkel type; that is, vacancies and interstitials in the Li sublattice. Schottky disorder is also observed, but it is not as predominant as the cation Frenkel defect.9 In a combined experimental and theoretical study of defects in Li2O, Chadwick et al.9 showed that Li+ ions migrate via cation vacancies. This study was performed in a combination of ac conductivity measurements and computer simulation, in which the activation energy, ∆E, for Li+ diffusion was investigated. Their measured value of ∆E, 0.49 eV, however, did not agree with the result of the simulations, ∆E ) 0.21 eV. Recently, Heitjans et al.17 investigated the ionic conductivity of ceramic oxides by NMR spectroscopy. They obtained ∆E ) 0.31 eV for Li ion diffusion in Li2O. Influenced by this study, we have performed an earlier theoretical investigation on defect properties and Li ion diffusion in bulk Li2O with density functional theory (DFT) methods and obtained ∆E ) 0.28-0.33 eV.14 This is in line with the previous theoretical studies10,15,16 for Li+ ion migration through cation vacancy sites for which activation energies of 0.34,10 0.30,15 and 0.29 eV16 were calculated. However, most of the studies are concerning the defects and ionic diffusion in crystalline bulk Li2O. In recent investigations, it has been observed that the conductivity in Li2O-B2O317-19,23 * Corresponding author. E-mail:
[email protected]. † Ecole Nationale Supe´rieure de Chimie de Paris. ‡ Universita¨t Bonn.
and Li2O-Al2O3 nanocomposites24 is higher than in nanocrystalline Li2O, although B2O3 and Al2O3 are insulators. This surprising effect was attributed to an increased fraction of structurally disordered interfacial regions among the nanoparticles.17 Therefore, it is an interesting matter to investigate the defects and ionic diffusion in Li2O surfaces. The present study is part of a series of theoretical investigations of lithium diffusion in Li2O-B2O3 systems. In earlier work, we studied structural, energetic, and electronic bulk properties of the basic compounds Li2O14 and B2O3-I31 and of various Li2O-B2O3 compounds.30,32 Later we focused on defect formation and ionic conductivity of Li2O-B2O3 solid compounds and nanocomposites.23,33,34 In the present study, we perform a theoretical investigation of the cation vacancy and cation Frenkel defect formation and mobility at Li2O surfaces, as a reference to the Li2O-B2O3 nanocomposites in which surface effects were found to dominate the diffusion mechanism.23 The two most stable Li2O surfaces, (111) and (110),25,26 are considered. We employ the same DFT hybrid method that was used in our previous study of bulk Li2O.14 It will be briefly described in the following section. 2. Computational Method The energetic, electronic, and defect properties of Li2O surfaces were calculated with the Hartree-Fock (HF)/DFT hybrid method PW1PW. In the PW1PW hybrid method,27 the exchange functional is a linear combination of the HF expression (20%) and the Perdew-Wang (PW)28,29 exchange functional (80%). Electron correlation is described with the PW91 correlation functional.28,29 The agreement between calculated properties and experimental data was in general considerably better than with pure density functionals or other hybrid functionals, such as B3LYP.14,27,30,31 PW1PW was used as implemented in the crystalline orbital program CRYSTAL03.35 In CRYSTAL, the Bloch functions are linear combinations of atomic orbitals. Two different basis sets (BS) were employed in the present study; namely, BS A and BS B (obtained by augmenting BS A with diffuse s and d polarization functions), which have been used previously.14
10.1021/jp807048p CCC: $40.75 2009 American Chemical Society Published on Web 12/18/2008
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TABLE 1: Calculated Lattice Parameters, a (Å), and Li-O Bond Distances (Å) for Bulk Li2O, and Surfaces (111) and (110) 14
bulk Li2O
a Li-O asa Li-Os asa Li-Os
Li2O(111) (this study) Li2O(110) (this study)
a Surface lattice parameter (≡ a/2). distance after surface relaxation.
b
BS A
BS B
4.56 1.975 3.22 1.953 b 3.22 1.911 b
4.57 1.977 3.23 1.956 b 3.23 1.915 b
Es
Surface oxygen-lithium
Truncation thresholds for integral calculation were set to 10 times stricter values than the default (7, 7, 7, 7, 14). Convergence of the surface energy with respect to the number of k points and the number of layers in the slab models was checked in each case. Different from plane-wave calculations, no vacuum distance between the slabs has to be specified with CRYSTAL because the models are truly two-dimensional. 3. Results and Discussion In this section, we present the results for the structural, energetic, and electronic properties for selected low-index Li2O surfaces (111) and (110), followed by the defect properties and the energy barriers for Li+ ion migration in the Li2O (111) surface. 3.1. Surface Relaxation. The (111) and (110) surfaces were modeled with a series of slabs with increasing number of atomic layers (n ) 3, 6, 9, 12, 15, 18, 21, 24 and n ) 2, 4, 5, 6, 10, respectively). The lattice parameters of the slab were obtained from the optimized PW1PW bulk values of our previous investigation on Li2O14 using the same basis sets. All atomic layers of the slab models were fully relaxed. The calculated lattice parameters and Li-O bond distances (Å) for bulk Li2O, Li2O(111), and Li2O(110) surfaces are compiled in Table 1. It can be seen that the basis set has a negligible effect on the structural parameters. As expected, the outermost oxygen atoms move inward due to their reduced coordination, and consequently, the Li-O bond lengths are reduced by 0.02-0.06 Å. The relative stability of the surfaces was estimated according to their surface energy (Es), calculated as
Es )
Eslab - mEbulk 2A
TABLE 2: Convergence of Calculated Surface Energies Es (J m-2) of Li2O(111) with the Number, n, of Atomic Layers in the Slab Models
(1)
where Eslab is the total energy of the two-dimensional slab with m Li2O formula units; Ebulk is the total energy per unit of the Li2O bulk, again taken from our previous study;14 and A is the surface area of the slab. The division by 2 in eq 1 implies that the slab has two identical surfaces. Our slab models were constructed according to this requirement. They contain either a central mirror plane, an inversion center, or a 2-fold axis. In this way, artificial polarization effects due to dipole moments along the surface normal are avoided. In Tables 2 and 3, the surface energies and their convergence with increasing number n of layers are presented for unrelaxed and relaxed slabs. For both surfaces, fast convergence with n was obtained, in line with the ionic character of lithium oxide. Es has converged within 0.001 J m-2 with a six-layer slab for Li2O(111) (Table 2) and with a five-layer slab for Li2O(110) (Table 3). There is a slightly larger relaxation effect for the (110) surface as compared to the (111) surface. It was observed that increasing the basis set from BS A to BS B leaves geometric
BS A
BS B
n
(unrelaxed)
(relaxed)
(unrelaxed)
(relaxed)
3 6 9 12 15 18 21 24
0.859 0.870 0.869 0.869 0.869 0.869 0.869 0.869
0.835 0.832 0.849 0.843 0.837 0.832 0.851 0.845
0.815 0.819 0.820 0.821 0.822 0.823 0.825 0.823
0.799 0.789 0.790 0.790 0.794 0.793 0.795 0.793
TABLE 3: Convergence of Calculated Surface Energies, Es (J m-2), of Li2O(110) with the Number, n, of Atomic Layers in the Slab Models Es BS A
BS B
n
(unrelaxed)
(relaxed)
(unrelaxed)
(relaxed)
2 4 5 6 10 15
1.583 1.617 1.617 1.618 1.619 1.622
1.224 1.351 1.367 1.366 1.369 1.369
1.363 1.433 1.438 1.438 1.440 1.442
1.118 1.224 1.243 1.240 1.240 1.247
parameters virtually unchanged and decreases the surface energies only slightly. We therefore assume that further extension of the atomic basis sets will not significantly alter the present results. The converged Es value of the (111) surface is 0.79 J m-2, significantly smaller than that of the (110) surface, 1.24 J m-2. The relative stability of the two surfaces agrees well with the ab initio study of Li2O surfaces by Lichanot et al.26 3.2. Electronic Structure. Li2O is a wide-gap (band gap 7.99 eV) insulator.36 The calculated band gap obtained with the PW1PW method (BS B) is 8.37 eV,14 which agrees reasonably well with experiment, in line with previous studies.27 In Figure 1, the density of states (DOS) of bulk Li2O (Figure 1a) is compared with the DOS of the Li2O (111) and (110) surfaces. The qualitative features of the projected DOS of both the surfaces are similar to those of the bulk: the valence band (VB) is formed mainly by the oxygen 2p orbitals with only small contributions from Li, whereas the conduction band (CB) is dominated by Li states. However, there is an upward shift of the VB top and a downward shift of the CB bottom for the surfaces, thereby reducing the band gap as compared to the bulk. This is in agreement with an electron energy loss spectroscopic study on the surface valence-to-conduction band transition for Li2O.37 According to our results, surface excitons are more pronounced in the case of the Li2O (110) surface. 3.3. Defect Properties. Two dominant point defect types, cation vacancies and cation Frenkel defects, are studied for the most stable Li2O (111) surface. The convergence of defect formation energy was checked with respect to increasing supercell size (decreasing defect concentration), increasing number of slab layers, and basis set size. 3.3.1. Cation Wacancy. Using optimized structural parameters for the perfect crystal, 2 × 2 and 4 × 4 surface supercells were constructed containing 6-, 9-, and 12-layer slabs parallel to the (111) surface for Li2O. The vacancy was created by removing one Li atom (site A1, see Figure 2) from the supercell, keeping
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Ede(V) ) E(Li2n-1On) + E(Li) - E(Li2nOn)
Figure 1. Projected density of states (a) of the Li2O bulk, (b) of the Li2O (111) surface, and (c) of the Li2O (110) surface.
(2)
Here, E(Li2n-1On) and E(Li2nOn) denote the total energy of the supercell with and without vacancy, respectively, and E(Li) is the energy of free Li atom. Effects from the zero point energy were neglected. The relaxation energy, ER is calculated by subtracting the energies of the relaxed slab from the unrelaxed one. In Table 4, calculated cation vacancy formation energies are presented. Ede(V) is calculated with eq 2 for unrelaxed and fully relaxed systems. As found for bulk Li2O,14 Ede(V) has a small BS dependence, the difference between BS A and BS B being only 1-2 kJ/mol. Ede(V) decreases with decreasing defect concentration (i.e., increasing supercell size). This indicates a long-range repulsive interaction between lithium vacancies located in neighboring cells. The observed trend can also be due to the effect of relaxation of the lattice atoms around the vacancy. The movement of the atoms out of their lattice positions due to the presence of the defect is restricted by the periodic boundary conditions introduced on the supercell. This can be best seen by the smaller relaxation energy of the 2 × 2 supercell (ER is ≈60-65 kJ/mol), as compared to that of the 4 × 4 supercell (ER is in the range of 110-130 kJ/mol). For both 2 × 2 and 4 × 4 supercells, Ede(V) is converged with 6-layer slabs. The converged Ede(V) value for the Li2O(111) surface is 540 kJ/mol. This has to be compared with the bulk value for Li2O, 576 kJ/mol, obtained with the same method and basis sets.14 Therefore, we conclude that the surface of Li2O contains a higher percentage of defects than the bulk Li2O. The calculated geometrical relaxation effects around a Li vacancy are shown in Table 5. The three oxygen atoms in the first coordination shell (first-nearest neighbors, 1-NN) increase their distance to the vacant Li site by 5%. This is reasonable, since the electrostatic attraction by the Li+ cation is missing. The removal of one neutral Li atom creates a hole in the valence band. According to a Mulliken analysis of the crystal orbitals, one of the surrounding 1-NN O atoms (formally O2-) is oxidized to O-, and spin density is localized on this O atom. Three Li atoms in the second coordination shell (2-NN) show an inward TABLE 4: Effect of relaxation and basis set size on the cation vacancy formation energy Ede(V) (kJ/mol) in Li2O(111) supercell
n
structure
BS A
BS B
2×2
6
unrelaxed relaxed unrelaxed relaxed unrelaxed relaxed unrelaxed relaxed unrelaxed relaxed unrelaxed relaxed
633 553 638 552 641 552 663 543 685 542 710 543
608 550 612 551 615 551 650 539 670 540
9 12 4×4
6 9 12
Figure 2. A six-layer slab for the 4 × 4 supercell of Li2O (111) surface. White circles represent lithium atoms and gray circles represent oxygen atoms.
the system neutral. Thus, the defective cell contains an odd number of electrons, and its ground state is a doublet. The calculations were performed with the spin-polarized method (unrestricted Kohn-Sham, UKS). The formation energy of cation vacancy Ede(V) is calculated as
TABLE 5: Distances, r (Å), of Neighboring Atoms from the Vacancy and Changes of the Distances, ∆r (%), for Relaxed Atoms for the Cation Vacancy (Site A1, see Figure 2) atom
r
unrelaxed
relaxed
∆r
O(3) Li(3) Li(9) O(6) Li(4) Li(3)
r1 r2 r3 r4 r5 r6
1.98 2.28 3.23 3.79 3.96 4.57
2.08 2.15 3.28 3.76 3.99 4.59
+ 5.05 - 5.70 + 1.50 - 0.80 + 0.76 + 0.40
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TABLE 6: Effect of Model and Basis Set Size on the Frenkel Formation Energy Ede(F) (kJ/mol) for Li2O(111); 4 × 4 Supercell Model n
BS A
BS B
exptl (Li2O)9
calcd (Li2O)23
6 9
154 152
151 150
244
216
relaxation of -6%. Due to the reduced electrostatic repulsion, the 2-NN Li atoms tend to move toward the vacancy. The 9 Li atoms in the third coordination shell (3-NN) show an outward relaxation. All other atoms with larger distances to the defect position show only small displacements. Thus, the lattice relaxation is mainly restricted to the nearest and the secondnearest neighbor atoms of the defect site. This is in line with the structural relaxations around a cation vacancy observed in bulk Li2O.14 3.3.2. Cation Frenkel Defect. On the basis of our experience from the cation vacancy investigation, only 4 × 4 supercells containing six and nine layer slabs were employed. To simulate the cation Frenkel defects, one Li atom was removed from the regular site and was placed at interstitial sites at different distances. The Frenkel formation energy, EF, was calculated as the energy needed to move a Li+ ion from its regular lattice site to an interstitial site. The lowest EF was obtained for a distance of 3.60 Å between the interstitial and the regular sites. As in the case of cation defects, small dependencies from model parameters were observed for the Frenkel defect formation (Table 6): EF changes by only 2-3 kJ/mol when the BS is increased from A to B and by only 1 kJ/mol when the number of atomic layers is increased from six to nine. The similarity of the trends obtained for Ede(V) and EF is not surprising, since both defects involve the formation of an empty Li lattice site. Due to the different references, the absolute values of EF are much smaller than those of Ede(V). The two defect types can be regarded as extreme cases of real lattice defects, where the dislocated Li is close to the vacancy (Frenkel defect) or at infinite distance (hole vacancy). EF in the Li2O(111) surface is 151 kJ/mol, considerably smaller than the measured bulk value (244 kJ/mol).9 3.4. Li+ Migration. In a previous theoretical work,10 it was shown that the migration barrier of the Li interstitiality mechanism is higher than that of the vacancy mechanism. This is supported by more recent experimental investigations on the Li+ migration in Li2O,17 in which a vacancy mechanism was proposed. Therefore, we concentrated on the vacancy mechanism in our present investigation. A 4 × 4 supercell with six atomic layers was employed for the investigation of Li+ migration in the Li2O(111) surface. In the previous section, it was observed that basis set has a very small effect on both cation vacancy and Frenkel defect formation energy values. Therefore, to avoid the high expense of CPU time, only the smaller BS A was applied for the Li+ migration investigation. As a first step, a single neutral Li atom was removed from the Li2O slab. This is a simplification of the real situation in which Li remains in the lattice and may affect the movement of other Li atoms. But in the present investigation, we are interested in only the activation barriers for hopping processes between regular lattice sites. Li migration may then occur from a tetrahedral third-layer site to a cation vacancy at the topmost layer, which is only 3-fold coordinated to oxygen atoms or vice versa. Another possibility is a hopping process between an occupied and an unoccupied 3-fold coordinated site of the first layer. In both cases, one or two oxygen atoms are shared by the migrating Li+ and the cation vacancy as shown in Figure 3.
Figure 3. Schematic representation of possible Li hopping processes. (a, b) A 4-fold coordinated Li+ ion (third-layer) migrates to a 3-fold coordinated vacancy site. (c, d) A 3-fold coordinated Li+ ion (firstlayer) migrates to a 3-fold coordinated vacancy site.
In the present study, we assume that the transition state is located in the middle of the path between the initial position of the migrating atom and the vacancy. This represents an approximation of the real transition state that might deviate from the central position due to the reduced symmetry at the surface. Unfortunately, a full transition state search is not possible with CRYSTAL06. Similar approximations were made for diffusion paths of Li in TiO2.38,39 The possibility of a different migration path, such as Li+ ion movement in a two-dimensional curve rotation, was investigated in a previous study.14 There, it was observed that for the Li+ ion migration in crystalline Li2O, the activation energy ∆E in the curve rotation is almost identical to that obtained in the straight line path. Therefore, we are convinced that the conclusions of our study are not affected by the limited accuracy of the transition state geometries. In the following, we describe the possible pathways for the Li+ migration in the Li2O surface. We have studied various possible pathways for the Li+ migration in the Li2O-B2O3 nanocomposite.23 In the present investigation, we present only the representative pathways for the Li+ ion migration in the Li2O(111) surface. In Figure 2, selected lithium atoms are denoted to represent the possible migration pathways for the Li+ ion movement. A1 and E are nearest neighbors in the first atomic Li layer, B1 and C are in the third atomic layer, and D belongs to the next Li row of the first layer. The migration of Li+ ion can occur in a zigzag pathway, such as the migration of lithium type A1 to B1 or A1 to C. Alternatively, migration can occur in a straight line, either along the [1-10] direction via A1 f D or along the [-110] direction (A1 f E). Spin polarization plays an important role for the Li+ migration. It was observed that the unpaired electron, created due to the cation vacancy, is localized on the 2p orbital of one of the surrounding oxygen atoms. For the migration of A1 to B1 and A1 to C, spin is localized on the oxygen atom nearer to the migrating lithium in the transition states, whereas in the case of A1 to D and A1 to E migrations, the unpaired electron is localized on the oxygen atom nearer to the defect in the transition states. A similar situation was observed for the Li+ diffusion in crystalline Li2O,14 Li2O-B2O3 nanocomposite,23 and Li2B4O7.30 The calculated values for the migration energy ∆E for all considered migration pathways are presented in Table 7. Unlike in the case of bulk Li2O, the migration energy ∆E
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TABLE 7: Comparison of Calculated Li+ Migration Energies ∆E (eV) in the Li2O(111) Surface with Bulk Values a b ∆Eab ∆Eba
A1 B1 0.25 0.08
C 1.10 0.89
Li2O bulk D 1.16 1.11
E 1.02 1.02
exptl17 0.31
calcd14 0.33
for the Li ion migration in the Li2O surface is not symmetric because the sites are not energetically equivalent. We therefore distinguished between ∆Eab and ∆Eba, where the energy of the transition state refers to the structure with occupied site a (b) and empty site b (a). As in the case of Li2O-B2O3 nanocomposite,23 here, too, the zigzag migrations are more suitable than the migrations in the straight lines either along the [1-10] direction or the [-110] direction. The smallest activation barriers were found for the migration of lithium type A1 to B1 along the zigzag pathway. For the A1 f B1 direction, ∆E is 0.25 eV. Experimental values are 0.31 eV (Li2O bulk),17 0.34 ( 0.04 eV (Li2O-B2O3 nanocomposite)19 and 0.30 ( 0.02 eV (Li2O-Al2O3 nanocomposite).24 For the hopping process in the opposite direction, B1 f A1, ∆E is much smaller, 0.08 eV (Table 7), due to the higher energy of a Li vacancy at site B1 as compared to A1. In a macroscopic process in which Li vacancies migrate over distances corresponding to many lattice parameters, both barriers have to be overcome. The smaller barrier, corresponding to the fast step, will not be observed in the experiments. According to our present results, migration energy values in the bulk and surface of Li2O are not significantly different. The increased Li mobility near grain boundaries of nanocrystallites is therefore attributed mainly to the increased Li vacancy concentration due to their higher thermodynamical stability as compared to the bulk. 4. Summary and Conclusions The energetics, structural relaxation, and electronic properties of Li2O (111) and (110) surfaces were investigated theoretically. In accordance with previous quantum-chemical studies, it was found that the (111) surface is thermodynamically the most stable surface. Surface relaxation is more pronounced for the (110) surface, as compared to the (111) surface. The band gap for both surfaces is reduced with respect to the bulk due to the presence of surface excitons. An isolated cation vacancy and a cation Frenkel defect were studied for the most stable (111) surface. The calculated defect formation energy for the Li2O surface (539 kJ/mol) is significantly smaller than the corresponding value of the bulk (576 kJ/mol). The effect is even more pronounced for the cation Frenkel formation energy, which is 151 kJ/mol for the (111) surface and 244 kJ/mol in the bulk. We therefore conclude that the defect concentration in (111) surface is larger than in the bulk. The ion conductivity of the Li2O (111) surface was investigated by calculating the activation energy for local hopping processes. The most likely mechanism for Li+ migration is in a zigzag pathway rather than in a straight line along a direction parallel to the surface plane. The calculated activation energy for Li+ migration in the zigzag pathway is 0.25 eV. This is in good agreement with experimental values in bulk Li2O and in Li2O-B2O3 nanocomposites.
Acknowledgment. This work was supported by the State of Lower Saxony, Germany, by a Georg Christoph Lichtenberg fellowship (M. M. Islam). References and Notes (1) Minami, T.; Tatsumisago, M.; Wakihara, W.; Iwakura, C.; Kohjiya, S.; Tanaka, I., Eds. Solid State Ionics for Batteries; Springer: Tokyo, 2005. (2) Wakihara, W.; Yamamoto, O., Eds. Lithium Ion Batteries; WileyVCH: Weinheim, 1998. (3) Keen, D. A. J. Phys.: Condens. Matter. 2002, 14, R819. (4) Noda, K.; Ishii, Y.; Ohno, H.; Watanabe, H.; Matsui, H. AdV. Ceram. Mater. 1989, 25, 155. (5) Johnson, C. E.; Kummerer, K. R.; Roth, E. J. Nucl. Mater. 1988, 155-157, 188. (6) Tanifuji, T.; Yamaki, D.; Jitsukawa, S. Fusion Eng. Des. 2006, 81, 595. (7) Itoh, M.; Murakami, J.; Ishi, Y. Phys. Status Solidi B 1999, 213, 243. (8) Masaki, N. M.; Noda, K.; Watanabe, H.; Clemmer, R. G.; Hollenberg, G. W. J. Nucl. Mater. 1994, 212-215, 908. (9) Chadwick, A. V.; Flack, K. W.; Strange, J. H.; Harding, J. Solid State Ionics 1988, 28-30, 185. (10) De Vita, A.; Gillan, M. J.; Lin, J. S.; Payne, M. C.; Stich, I.; Clarke, L. J. Phys. ReV. Lett. 1992, 68, 3319. (11) Tanigawa, H.; Tanaka, S. J. Nucl. Mater. 2002, 307-311, 1446. (12) Mackrodt, W. C. J. Mol. Liq. 1988, 39, 121. (13) Noda, K.; Uchida, K.; Tanifuji, T.; Nasu, S. Phys. ReV. B 1981, 24, 3736. (14) Islam, M. M.; Bredow, T.; Minot, C. J. Phys. Chem. B 2006, 110, 9413. (15) Koyama, Y.; Yamada, Y.; Tanaka, I.; Nishitani, S. R.; Adachi, H.; Murayama, M.; Kanno, R. Mater. Trans. 2002, 43, 1460. (16) Hayoun, M.; Meyer, M.; Denieport, A. Acta Mater. 2005, 53, 2867. (17) Heitjans, P.; Indris, S. J. Phys.: Condens. Matter 2003, 15, R1257. (18) Indris, S.; Heitjans, P.; Roman, H.; Bunde, A. Phys. ReV. Lett. 2000, 84, 2889. (19) Indris, S.; Heitjans, P. J. Non-Cryst. Solids 2002, 307-310, 555. (20) Pfeiffer, H.; Sanchez-Sanchez, J.; Alvarez, L. J. J. Nucl. Mater. 2000, 280, 295. (21) Goel, P.; Choudhury, N.; Chaplot, S. L. Phys. ReV. B 2004, 70, 174307. (22) Fracchia, R. M.; Barrera, G. D.; Allan, N. L.; Barron, T. H. K.; Mackrodt, W. C. J. Phys. Chem. Solids 1998, 59, 435. (23) Islam, M. M.; Bredow, T.; Indris, S.; Heitjans, P. Phys. ReV. Lett. 2007, 99, 145502. (24) Wilkening, M.; Indris, S.; Heitjans, P. Phys. Chem. Chem. Phys. 2003, 5, 2225. (25) Mackrodt, W. C.; Tasker, P. W. Chem. Ber. 1985, 21, 366. (26) Lichanot, A.; Gelize, M.; Larrieu, C.; Pisani, C. J. Phys. Chem. Solids 1991, 52, 1155. (27) Bredow, T.; Gerson, A. R. Phys. ReV. B 2000, 61, 5194. (28) Perdew, J. P.; Wang, Y. Phys. ReV. B 1992, 45, 13244. (29) Perdew, J. P.; Chevary, J. A.; Vosko, S. H.; Jackson, K. A.; Penderson, M. R.; Singh, D. J.; Fiolhais, C. Phys. ReV. B 1992, 46, 6671. (30) Islam, M. M.; Maslyuk, V. V.; Bredow, T.; Minot, C. J. Phys. Chem. B 2005, 109, 13597. (31) Islam, M. M.; Bredow, T.; Minot, C. Chem. Phys. Lett. 2006, 418, 565. (32) Maslyuk, V. V.; Islam, M. M.; Bredow, T. Phys. ReV. B 2005, 72, 125101. (33) Islam, M. M.; Bredow, T.; Minot, C. J. Phys. Chem. B 2006, 110, 17518. (34) Bredow, T.; Islam, M. M. Surf. Sci. 2008, 602, 2217. (35) Saunders, V. R.; Dovesi, R.; Roetti, C.; Orlando, R.; ZicovichWilson, C. M.; Harrison, N. M.; Doll, K.; Civalleri, B.; Bush, I.; D’Arco, Ph.; Llunell, M. CRYSTAL2003 User’s Manual; University of Torino: Torino, Italy, 2003. (36) Ishii, Y.; Murakami, J.; Itoh, M. J. Phys. Soc. Jpn. 1999, 68, 2236. (37) Liu, L.; Henrich, V. E.; Ellis, W. P.; Shindo, I. Phys. ReV. B 1996, 54, 2236. (38) Stashans, A.; Lunell, S.; Bergstro¨m, R. Phys. ReV. B 1996, 53, 159. (39) Tielens, F.; Calatayud, M.; Beltra´n, A.; Minot, C.; Andre´s, J. J. Electroanal. Chem. 2005, 581, 216.
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