J. Phw
PII: SOO22-3697(%)00330-4
Pergamon
Chem Solids Vol 57. Nos 6-8. pp. 663-669. 1996 Copyright 0 1996 Eiwier Science Ltd Printed in Great Britain. All rights reserved 0022-3697196 $15.00 + 0.00
NOVEL FORMS OF LIGHT ELEMENT GUESTS IN MICROPORES GRAPHITIC SYSTEMS: STRUCTURES, ELECTRONIC STATES AND MAGNETISM TOSHIAKI
OF
ENOKI
Department of Chemistry, Tokyo Institute of Technology, Ookayama, Meguro-ku, Tokyo 152, Japan (Received 28 May 1995; accepted 31 May 1995)
Abstract-Carbon-based materials such as graphite and microporous carbon provide room for the accommodation of guest materials. In graphite, the galleries between graphitic sheets form a twodimensional space available for the guest materials, while guests are accommodated in the micropore network having a random structure in the microporous carbon systems. It is expected that the guest materials
in these micropore spaces, having restricted geometry and dimensionality, form different structures from the structures of the ordinary bulk states. Moreover, the guest materials, geometrically confined in the micropore state, provide novel solid state properties related to their peculiar structures. We designed novel forms of guest systems considering the structure, electronic properties and magnetism, employing light element guest materials such as He, HI and O2 in alkali metal-graphite intercalation compounds and microporous activated carbon fibers. In this paper, we review the four cases investigated in our group: the two-dimensional metallic hydrogen, the two-dimensional oxygen layer, helium atoms in ultra-micropores and the random magnetic system of condensed oxygen molecules. Keywords: A. inorganic compounds, A. microporous materials, A. nanostructures, D. electronic structures, D. magnetic properties
1. INTRODUCTION
Carbon-based materials such as graphite and microporous carbon have room for the accommodation of guest materials. In graphite, the stacking of graphene sheets provides two-dimensional space between the sheets, which is available for the accommodation of guest materials. Graphite intercalation compounds (GIC) are formed by introducing donor- or acceptor-type guest materials into the graphitic galleries through charge transfer between the host graphite and guest materials. Moreover, in alkali metal-GICs, gaseous materials such as H,, N2, Ar and CH4 are stabilized in the intercalate space through a chemisorption or physisorption process [l-3]. Meanwhile, microporous activated carbon fibers (ACF) are another form of carbon material that consists of a three-dimensional assembly of micro-graphitic domains, each of which comprises the stacking of three to four graphene sheets having dimensions of ca. 20 x 20a2 [4, 51. The gaps generated in the random network of the micro-graphitic domains form a micropore network having a random structure whose pore size ranges in the nanometer scale. Gaseous materials are adsorbed in the micropores of ACFs. In this paper, we focus on light element guest materials such as He, Hz, Nz, 02 and Ne,
accommodated in the micropore space of graphite intercalation compounds and microporous activated carbon fibers, which are introduced mainly through the gas adsorption process. It is expected that the condensed guest materials form novel structures confined in the geometrically restricted space, which give clues to the development of novel solid state properties of the guest systems different from those of the corresponding bulk states. Here, we present the novel structures, electronic states and magnetism of light element guest materials; He, Hz, O2 accommodated in alkali metal-GICs and microporous ACFs. Hydrogen accommodated in the intercalate space of alkali metal-GICs through the chemisorption process forms a two-dimensional metallic hydrogen system, while oxygen is stabilized as a two-dimensional double layer structure sandwiched between alkali metal sheets. In the ACF micropore network, helium atoms behave exceptionally among light element gaseous materials; that is, an extraordinarily large amount of helium is condensed even at room temperature, which is caused by the presence of ultramicropores. The condensed phase of oxygen molecules in the micropores shows the behavior of a random antiferromagnet which reflects the restricted geometry of the micropore network in ACFs. 663
664
T. ENOKI 2. HYDROGEN IN HYDROGEN-ALKALI METAL-GRAPHITE INTERCALATION COMPOUNDS
Alkali metal-GICs have catalytic activities for hydrogen, which result in hydrogen adsorption in graphitic galleries through chemisorption or physisorption process [l, 21. Thus, the introduction of hydrogen results in hydrogen-alkali metal ternary GICs. On the basis of the hydrogen chemisorption, we find a novel structure for the hydrogen condensed phase confined in the two-dimensional graphitic galleries [3, 6-91. X-ray diffraction analysis and transmission electron microscopic observation of hydrogen-alkali metal-GICs, which have the compositions of Cd,MH, (M = Na, K; stage number n = 1,2. . , x = 0.8-l), reveal the presence of a two-dimensional hydrogen lattice sandwiched by two alkali metal layers in the graphitic galleries, as shown in Fig. 1. The charge transfer from the alkali metal-graphite host to hydrogen makes the hydrogen species negatively charged, H-, which is stabilized by the presence of positively charged alkali metal ion layers through ionic attractive force. The electronic nature of the hydrogen depends on the type of alkali metal species. In this regard, c-axis resistivity values, pc, give information on the electronic structure of the hydrogen layers, since the hydrogen layer makes a bridge between the two adjacent graphitic sheets in the c-axis conduction process. In the case of hydrogen-sodium-GIC, pc is relatively high (1 Rem), indicating the non-conducting nature of the hydrogen sheet. Shubnikov-de Haas [7] and thermoelectric power experiments [S] prove that the charges transferred from sodium layers to graphite are considerably smaller compared with the isostructural hydrogenpotassium graphite system. This means that the ionic structure consisting of Na+ and H- is almost completed in the graphitic galleries, taking into account the charge neutrality rule. Therefore, the two-dimensional hydrogen layer is characterized as an ionic layer of H- anions. Meanwhile, the hydrogen lattice in the hydrogen-potassium-graphite system has a different nature from that of the hydrogen-sodium-graphite system. Figure 2 shows the temperature dependence of C K’ H-
K’ C Fig. 1. The structure of the hydrogen-potassium_GIC
lo-38 1
10
r (lo
102
103
Fig. 2. Temperature dependence of the spin-lattice relaxation rate r;’ for proton NMR of stage-l hydrogen-potassiumGIC. the spin-lattice relaxation rate T;' in proton NMR of the hydrogen-potassium-GIC [9]. There is a linear temperature dependence of T;'in the T;'vs.Tplot, which indicates the metallic nature of the hydrogen species in the hydrogen-potassium-GIG; namely, the two-dimensional metallic hydrogen lattice is realized in the graphitic galleries in the hydrogen-potasiumGIC. This is a unique example of a novel metallic hydrogen realized without the application of ultrahigh pressure. Next, we consider the origin of the metallic nature of the hydrogen lattice in the hydrogen-potassiumgraphite system. A H- ion has a large ionic diameter D of 3.08 A due to the Coulomb repulsion between two electrons in the hydrogen 1s orbital, which is larger than that of a potassium ion K+ (2.66 A). According to the results of the in-plane X-ray diffraction, showing the intercalate superlattice with the periodicity of 2& x 5 [lo], the nearest hydrogenhydrogen distance is 2.9& which is about the same or smaller than the diameter of a H- ion. This makes the wave functions of adjacent hydrogen anions overlap with each other, resulting in an extended electronic structure in the two-dimensional hydrogen sheet. The presence of the two-dimensional metallic hydrogen state observed experimentally is also proved by band calculations [I I]. Now, we can give a simple scenario for the generation of the two-dimensional metallic hydrogen state. The hydrogen adsorption process in potassium-GIC is considered to be equivalent to the insertion of potassium hydride in graphitic galleries, since the intercalate lattice consists of Kt and H- ions. Therefore, the structural rearrangement of the intercalate by hydrogen uptake is explained by the fact that the ionic K’H- lattice is
Guests in micropores of graphitic systems inserted between weakly negative-charged metallic graphitic layers having 7r-conduction carriers. The pristine potassium hydride has the rock salt structure with a lattice constant of 5.700& where the nearest H-H distance is 4.04A. When the K+H- is inserted in a graphitic gallery, negatively charged graphitic sheets attract positive K+ ions, while negative H- ions are pushed away from the negative graphitic sheets on both sides, resulting in the condensation of hydrogen ions on a single sheet in the center of the gallery, where the H-H distance becomes as short as the distance of metallic hydrogen. Thus, the field of graphitic sheets works to realize the two-dimensional condensation of hydrogen ions, which easily induces a metallic state without the application of ultra-high pressure.
3. ALKALI METAL-SUPEROXIDE-GRAPHITE INTERCALATION COMPOUNDS The introduction of paramagnetic oxygen molecules in two-dimensional graphitic galleries is an interesting subject to develop novel magnetic GICs where the interaction between the graphitic conduction r-electron and the localized magnetic moment of an oxygen molecule plays an important role in realization of a graphite version of metal magnet. For this purpose, we tried to develop oxygen-potassium-GICs [12, 131.The preparation of the compounds is carried out with the reaction between potassium, potassium superoxide (K02) and graphite at 360°C. The compositions of the products are given as C4K02 and CsKO* for stage-l and -2 compounds which have the c-axis repeat distances of 8.21 and 11.62& respectively. As shown in Fig. 3, the electron density profile obtained from the intensity analysis of (001) X-ray diffraction peaks suggests that oxygen species form a two-dimensional
c-axis f
665
double layer structure between two potassium cation layers, different from the triple atomic layer intercalate of alkali metal/hydrogen/alkali metal in hydrogenalkali metal-GICs. Detailed in-plane X-ray diffractions give in-plane carbon-carbon bond distances of 1.426 and 1.4306 a for stage-l and -2 oxygen-potassiumGICs, respectively, which are larger than the C-C distance, 1.4216,&, of pristine graphite. Taking into account the relation between the C-C distance and the charge transfer from/to graphite [14], the elongation of the C-C distance indicates the donor character of the potassium-oxygen intercalate having the partial valence state of Oe6(6 N 0.3) which is determined on the basis of the balance between donor-type potassium and acceptor-type oxygen species. The electronic properties investigated by magnetic susceptibility reveal the large density of states at the Fermi energy, &, which is about six times as large as the density of states expected for the graphitic r-electrons in the stage-l compound if the graphitic r-electrons are the unique carriers in the system. Moreover, magnetic susceptibility suggests the absence of localized magnetic moments, showing non-magnetic properties of the oxygen species. The band calculation of the systems was carried out on the basis of the local density functional formalisms in order to clarify the electronic nature of oxygen included in the graphitic galleries [ 151.The results of the calculation prove the existence of narrow bands at EF ascribed to the oxygen 2s and 2p levels with mixing of a small fraction of the potassium 4s state, which is superimposed upon the graphitic conduction r*-band. This is consistent with the experimental results showing the large density of states at EF. The absence of magnetism in the oxygen species is associated with the location of the oxygen bands having narrow band widths at EF, indicating the weakly delocalized nature of the electronic state of the oxygen species. The c-axis conductivity where the oxygen makes a bridge in the c-axis transport process is considerably large (about 10 Q-’ cm-‘) for a stage-l compound. This is evidence of the weakly delocalized nature of the oxygen electronic states.
4. HELIUM IN MICROPOROUS ACTIVATED
CARBON FIBERS
Fig. 3. The electron density profile along the c-axis obtained from the intensity analysis of (001) X-ray diffraction for stage 2 potassium-oxygen-GIC. The solid and dotted lines denote the experimental and calculated results, respectively.
Activated carbon fibers. which are microporous carbon having huge specific surface areas (SSA), ranging from 1000 to 3000mZg-‘, consist of a threedimensional random network of micro-graphitic domains composed of stacks of three to four graphene m sheets with dimensions of 20-30A, where the micrographitic domains are linked to each other through bridging groups [4, 51. The micro-graphite network provides a microporous network with an average unit
666
T. ENOKI
pore size of about lo-20 A, leading to the huge specific surface areas. The micropore space is available for the accommodation of light element guest materials. Here, we investigate the adsorption of light element gaseous materials He, Ne, At-, HZ, Nz and O2 into the micropores of pitch-based ACF3000 having SSA = 3000m2g-’ [16-191. Figure 4 shows the applied pressure dependence of the effective pressure P,R of the investigated gases inside the micropores at room temperature. In the case of Ar and Nz, which have almost identical behavior, the effective pressure increases rapidly at low applied pressures, below about 20 Torr, as the pressure increases, then the increase tends to be slow at higher applied pressures. Oxygen has a linear relation between the effective pressure and the applied pressure, different from the former two cases. Compared with the above cases, helium has exceptional properties as shown in Fig. 4(a). The effective pressure of helium increases remarkably at low helium pressures, below about 5 Torr, and tends to saturate at higher pressures. The effective pressure reaches 80 atm at the applied pressure of only 10 Torr. The condensation rate defined with the ratio of the effective pressure to the applied pressure becomes about 6000 at the applied pressure of 10 Torr, which is one or two orders of magnitude larger than that 100
80 f
60
a,g
40
!
20
of other gases whose values are estimated at 100-300 at the same applied pressure. This experimental finding proves an exceptionally large condensation of helium atoms in the micropores. The properties of helium atoms accommodated in the micropores are investigated by means of dangling bond spins attached around the periphery of micro-graphitic domains. Figure 5 shows the ESR signal intensity I of the dangling bond spins plotted as a function of the square root of the microwave power, q, for ACFs adsorbing the gaseous materials He, Ne, Ar, HZ, N2, O2 of 10 Torr at room temperature. The evacuated sample with no guest gas shows a deviation from a linear I vs. J;? relation above 1 mW, suggesting the beginning of saturation. For all the samples with gases, the magnitudes of the microwave powers needed to make saturation are large compared with the magnitude of the evacuated sample. In particular, the sample with 10 Torr helium gas does not show any saturation up to 200 mW which is the maximum power of the ESR machine. The experimental results of the saturation curves (I vs. fi plot) clearly show that foreign gases govern the spinlattice relaxation mechanism of the dangling bond spins. In particular, helium gas gives an exceptionally strong effect on the spin-lattice relaxation rate, which seems to be related to the remarkable condensation of helium atoms in the micropores mentioned above. Actually, analysis of the saturation curves suggests that the spin-lattice relaxation rate, l/T,, is enhanced by more than one order of magnitude from IO5s-’ to IO6ss’ when we introduce 10 Torr helium gas in the evacuated sample. Now, we discuss the role of helium gas in the mechanism of the spin-lattice relaxation process. Taking into account that helium gas atoms are accommodated in the micropores having dangling
0 0
2
6
4
8
IO
12
P (Torr)
14,
He 1OTorr
o
4
10 -
0
Ar 1OTorr
8-
l
N, 1OTorr
0
Vacuum
12 -
I417
I
I n
I .-
1OTorr
. .
64-
00
01 0 20
40
60
80 100 120140
160
P (Torr) Fig. 4. The effective pressure Pes inside the micropores as a function of the applied pressure P, obtained from the gas adsorption isotherms for (a) He and (b) N2, Ar, O2 inpitchbased ACF3000 at room temperature.
/ 5 &
I
1
10
15
(mW"*)
Fig. 5. The saturation curves of the ESR intensity I of dangling bond spins as a function of the square root of microwave power q under the presence of 10 Torr guest gaseous materials He, Oz. Ar, N2 in pitch-based ACF3000 at room temperature. The behavior of the sample with Hz or Ne is almost identical to that with Nz or Ar.
Guests in micropores
bond spins, we can expect the participation of collisional process between a helium atom and a dangling bond in the spin-lattice relaxation. The interaction between a dangling bond and a helium atom is described in terms of the van der Waals interaction. Thus, the spin-lattice relaxation calculated on the basis of the electric dipole-dipole interaction is expressed in the following equation [20];
(1) where Mand R. are the mass of a helium atom and the minimum distance of helium atom approach to a dangling bond, respectively. I and J are the parameters for a helium atom given as follows;
QdG%,l Wr, J = %(Mhpl (r)dr, (2) where @‘I,(r)rQ2s(r) and Qr,(r) are the wave functions for the Is, 2s and 2p, states for a helium atom. AE is the energy difference between ‘P and ’ S states of a helium atom. For the carbon dangling bond, p is given by x/A where X is the spin-orbit coupling constant of the carbon p state and A is the energy difference between the ground and the excited states of a carbon dangling bond electron. At 10 Torr of helium gas, where the effective pressure becomes about 80 atm inside the micropore, the density of helium is estimated to be n N 1.85 x 102’mp3. Taking into account the values of the parameters [20]; M = 6.7 x 10e2’ kg, AE = 21 eV, T = 2OOK, p = 4 x 10m3, ZJ = 0.52ai (aa = Bohr radius), Ro = 3A, w = 0.2, the spin-lattice relaxation rate is calculated at 8.4 x 10’s_’ from eqn (I), which is in good agreement with the experimental results. Thus, the experimental findings related to the exceptionally large helium condensation and the remarkable acceleration of the spin-lattice relaxation rate by the helium collisional process prove the presence of a large number of ultra-micropores which can accommodate only small diameter helium atoms in activated carbon fibers.
5. MAGNETIC BEHAVIOR OF OXYGEN CONDENSED PHASE IN MICROPOROUS ACTIVATED CARBON FIBERS
An O2 molecule is a paramagnetic species with the spin state of S = 1. It has been known that the bulk condensed phase of oxygen molecules has a complex phase diagram with the coexistence of liquid-solid, solid-solid and magnetic transitions, which are
of graphitic
667
systems
related to the translational, rotational and magnetic degrees of freedom. At ambient pressure, oxygen forms a liquid state below 90K. The liquid-solid transition takes place at 7&, = 54.4K, with solid phase y where the rotational motions of oxygen molecules survive. For the solid state, there are three different phase regions with two transition points Tay = 43.8 K and Tfia = 23.9K in the two lower temperature phases of which the rotational motion is quenched. In relation to the complex structural changes, there is a variety of magnetic behavior. The transition from y to p modifies the structure to the two-dimensional arrangement of oxygen molecules, resulting in the development of two-dimensional, short-range magnetic ordering. The transition /3 to (Y stabilizes a three-dimensional, long-range magnetic order. It is expected that the condensed phase of oxygen molecules accommodated in the ACF micropore space has different magnetic properties from the bulk condensed phase mentioned above, since the micropores have a random structure network. We investigated the magnetic behavior of condensed oxygen molecules in phenol-based ACF2000 with SSA = 2000m2g-’ [16,21]. The investigation of the adsorption isotherm for oxygen taken at 60K shows that the amount of adsorbed oxygen increases steeply at low oxygen pressures below about 1 Torr, and above this pressure the micropores are saturated with oxygen molecules where cu. 260 oxygen molecules are filled in a micropore having an average radius of cu. 16A. Figure 6 shows the temperature dependence of magnetic susceptibility for the samples with different oxygen adsorption rates, c, which are defined as the ratio of the amount of oxygen to the saturated amount. At
0
40
20
60
TOO Fig. 6. Temperature dependence of the magnetic susceptibility for oxygen in phenol-based ACFZOOO with different adsorption rates c. The solid line displays susceptibility of bulk oxygen phases which have discontinuous changes at T,,,r = 54.4 K, T* = 43.8 K and Tj, = 23.9 K.
668
T. ENOKl
oxygen adsorption rates below c w 0.01, where weak chemisorption takes place [16], the magnetic susceptibility obeys the Curie-Weiss law in the investigated temperature range, where the Weiss temperature ranges around 20K irrespective of the oxygen concentrations. This suggests that the adsorbed oxygen molecules tend to form finite size clusters having a small number of oxygen molecules even at the very low concentrations, indicating an inhomogeneous distribution of oxygen molecules in the micropore network. The magnetic susceptibility deviates from the Curie-Weiss law above about 20% where oxygen molecules are physisorbed, suggesting the formation of large size clusters. According to the results in Fig. 6, in the high adsorption rate region, magnetic susceptibility is described in terms of two contributions: the Curie-Weiss contribution and the contribution which is expected to have a broad peak above about 60 K. The Curie-Weiss contribution is considered to be associated with the small size clusters with odd numbers of oxygen molecules, where the main contribution comes from isolated oxygen molecules taking into account the calculation of the probabilities of existence for small size clusters. Therefore, we can assume that the behavior of the Curie-type contribution is mainly governed by the isolated oxygen molecules. The second contribution having a broad peak above about 60 K is considered to be caused by the large size clusters including infinite size clusters. The contribution of the larger clusters increases at the expense of small size clusters as the oxygen concentration increases. We compare the magnetic susceptibility of the second contribution to the magnetic susceptibility of the bulk solid oxygen system having the regular crystal structure, the latter of which shows discontinuous changes at the phase transition points depending on the changes in the arrangements of oxygen molecules. In the case of the oxygen condensed phase in ACF, the magnetic susceptibility does not show any discontinuous changes, suggesting the absence of definite phase transitions. This means that the condensed phase of oxygen molecules has a disordered structure affected by the random micropore structure. On the basis of the disordered structure, the behavior of the observed magnetic susceptibility proves that the condensed oxygen molecules form a spin glass-like state at low temperatures. Next, we discuss the local structure of the adsorbed oxygen molecule system. Figure 7 shows the concentration of isolated oxygen molecules nIs obtained from the Curie-Weiss contribution as a function of the adsorption rate of oxygen molecules c. nIs decreases as c increases. We assume that an oxygen molecule is surrounded by the nearest neighbors of oxygen molecules with the coordination
0.8 \ I-\
s-
0.6
\
P
0'
0
\ z=3
I
0.2
,
0.4
I
I
I
0.6
0.8
1.0
c Fig. 7. The oxygen adsorption rate c dependence of the concentration of isolated oxygen molecules errs obtained from the Curie-Weiss contribution in the magnetic susceptibility of phenol-based ACF2000. The solid and dashed lines are calculated with the average coordination numbers z = 5 and 3, respectively. number z. The probability of existence for the isolated oxygen molecules, which is proportional to nIs, is given as (1 - c)’ according to the percolation theory. Thus, we can analyze the average coordination number from the adsorption rate dependence of the concentration of the isolated oxygen molecules, which is shown by the solid and dashed lines in Fig. 7. At adsorption rates below c N 0.2, the concentration of the isolated oxygen molecules is described with the average coordination number z = 5, and the average coordination number becomes z = 3 at higher adsorption rates. Oxygen molecules are reported to form a hexagonal layer on a graphitic surface, suggesting that the coordination number is z = 6 in the regular lattice [22]. Compared with the coordination number in the regular lattice, the present experimental findings reveal the decrease of the coordination number in the micropores whose surface consists of micro-graphitic domains, due to the random structure of the micropore network. Moreover, the average coordination number decreases with the increase in the adsorption rate c. Therefore, it is suggested that the development of the clusters which starts at a place having a rather regular structure is affected by the presence of disorders around the marginal regions due to the random network structure of micro-graphitic domains with the dimension of 30A in ACFs. This situation is favorable to the development of the spin glass state in the micropore space, as mentioned above. 6. SUMMARY Carbon-based
materials
such as graphite
and
669
Guests in micropores of graphitic systems
microporous carbon provide room for the accommodation of guest materials. It is expected that the guest materials, geometrically confined in the micropore space, have novel solid state properties related to the peculiar structures of the host. We design novel forms of guest systems from the point of structure, electronic properties and magnetism, employing light element guest materials such as He, Hz and O2 in alkali metal-GICs and microporous activated carbon fibers. In this paper, we have reviewed four cases investigated in our group. The hydrogen species introduced in alkali metalGICs form a two-dimensional sheet of H- anions sandwiched by two positive ion potassium layers in the graphitic galleries. The electronic properties of the two-dimensional hydrogen layer depend on alkali metal species. In the case of the sodium-hydrogen-graphite system, hydrogen forms an ionic two-dimensional lattice where the charge transfer is almost completed between H- and Na+ in the intercalate space. On the contrary, the potassium-hydrogen-graphite system has novel two-dimensional metallic hydrogen layers. For the introduction of oxygen in the alkali metalGICs, we prepared a potassium-oxygen-graphite system by reaction of graphite with potassium and potassium superoxide. The structure is found to consist of a quadruple atomic layer unit K+-O--O--K+, different from the K+-H--K’ in the potassiumhydrogen-graphite system. The magnetic and transport investigation reveals the presence of narrow energy bands of oxygen-origin around EF, suggesting that oxygen is in a weakly delocalized electronic state. In the gas adsorption in the ACF random micropore network, an exceptionally large amount of helium gas is found to be adsorbed in the micropores. The spin-lattice relaxation rate of the dangling bond spins attached around the periphery of micro-graphitic domains is extremely accelerated by the introduction of helium through the collisional process. These experimental findings reveal the presence of a large number of ultra-micropores which can accommodate only small diameter helium atoms. The condensed phase of oxygen molecules in the random micropore network is interesting from the point of view of magnetism. At low oxygen concentrations, oxygen molecules are distributed inhomogeneously in the micropore space, resulting in the formation of small size clusters of oxygen molecules. At high concentrations, oxygen molecules form a spin glass-like state which is related to the ACF disordered micropore structure.
Acknowledgements-The author acknowledgesH. Inokuchi, S. Miyajima, H. Yamamoto, K. Nakazawa, N. Sakamoto, K. Matsutsuji, K. Suzuki, T. Yamashita, V. Mordkovich, A. Nakayama, K. Sugihara,C. Ishii, K. Kaneko, M. Endo, N. Shindo and N. Kobayashi who made important contributions to the present work. This work is partly supported by the Grant-in-Aid for Scientific Research No. 07240212 from the Ministrv of Education. Science and Culture, Japan.
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