A theoretical study of the electronic properties of intercalated graphite

Synthetic Metals, 1 (1979/80) 233 - 247

233

© ElsevierSequoia S.A., Lausanne-- Printed in the Netherlands

A THEORETICAL STUDY OF THE ELECTRONIC PROPERTIES OF INTERCALATED GRAPHITE*

INDER P. BATRAand L. SAMUELSON** IBM Research Laboratory, San Jose, CA 95193 (U.S.A..)

Summary We present the results of electronic structure calculations for first and second stages of lithium intercalated graphite (LiCe and LiC12). The various stages of Li intercalated graphite all have hexagonal symmetry, where different carbon layers are stacked with C-atoms directly on top of each other (AIAI...), as opposed to natural graphite where the C-layers are staggered (ABAB...). All our calculations have been performed within the framework of the extended tight binding method with Gaussian type basis sets. From the orbital and total densities of states, we conclude that Li-2s electrons are transferred into carbon n-bands. This results in shifting the Fermi level into the region of high density of states (compared with pure graphite) and, hence, to observed metallic behavior. The calculated density of states for LiCe and LiC12 is 0.25 and 0.12/(eV C-atom), respectively. Recall that for pure graphite the value is nearly zero and for copper it is 0.29. We also found it instructive to obtain the electronic structure of LiC e and LiC12 based on a rigid band model.

1. Introduction There is currently a high level of interest [ 1, 2] in various intercalation compounds of graphite due to their novel electronic properties. At the synthetic level, a large number of compounds have been prepared by diffusing intercalants into the relatively big voids between adjacent hexagonal carbon layers of pure graphite. The stage of a compound is usually defined by the number of carbon layers between nearest intercalant layers. For example, a stage-1 lithium intercalated compound has the composition LiC 6. Pure *Paper presented at the Symposium on the Structure and Properties of Highly Conducting Polymers and Graphite, San Jose, California, March 29 - 30, 1979. **Permanent address: Department of Solid State Physics, University of Lund, Box 725, S-22007 Lund 7, Sweden.

234

graphite has been extensively investigated both theoretically [3 - 13] and experimentally [14 - 23]. The electronic structure calculations [3 - 13] for various modifications of pure graphite have been done by essentially all the usual methods in the last thirty years. The band structure calculations for intercalated graphite have only started to appear recently [24 - 26]. The reason for the lack of such calculations lies in the fact that one is required to treat a large unit cell, consisting of seven atoms for LiCe and thirteen for LiC~. By contrast, the three dimensional calculation for pure graphite in which the carbon layers are arranged in an alternating stacking sequence (ABAB...) can be done by treating only four carbon atoms in the unit cell. The rhombohedral modification [4] (ABCABC...) can be described by only two carbon atoms in the unit cell. It is thus easy to understand why higher stages of intercalation have not been treated theoretically so far. One important structural consequence of intercalation [2] is that in stage-1 compounds all the hexagonal carbon layers are equivalent, corresponding to AIAI... stacking (A denotes carbon layers, I denotes intercalant layers). The carbon layers are stacked directly over each other making all layers equivalent to each other. This is to be contrasted with the ordinary ABAB... graphite sequence where each alternate layer is staggered. Off hand it appears that full, three dimensional calculations for graphite intercalation compounds (GIC's) should be simpler due to the AA... stacking, because this would then require only two carbon atoms per unit cell. Unfortunately, this is not so since only one third of the carbon hexagons have Li atoms directly above and below them (stage-l). One is then forced to include six carbon atoms from each layer, giving us the structure LiCe for the stage-1 compound. For the second stage compound, there are 13 atoms in the unit cell (LiC12). We have performed electronic structure calculations for stage-1 as well as stage-2 of lithium intercalated graphite. To understand the electronic structure in an intuitive manner, we have computed the electronic structure of a hypothetical layered structure (Ce) in which each layer contributes six atoms to the unit cell. The electronic structure of C6 can be compared and contrasted with the structure of aromatic molecules. Also, the electronic structure of LiCe can be anticipated from that of Ce by using rigid band model ideas. Our results for LiCe are compared with the recently published findings of Holzworth e t al. [ 25]. We have also calculated for the first time the electronic structure of a stage-2 compound, LiC12. Much understanding can be gained by again employing rigid band ideas. The present manuscript is arranged as follows. In the next Section, we briefly discuss the extended tight binding (ETB) method which has been used for performing all the calculations reported here. In Section 3, results for pure graphite are summarized. In Section 4, complete band structures for Ce, LiCe and LiC19 are given. Total, partial, and orbital densities of states are presented. Concluding remarks are given in Section 5.

235 2. Calculational details

All of our calculations were p e r f o r m e d using the first principles e x t e n d e d tight binding (ETB) m e t h o d [27, 28] which is also known as the linear co mb in ation of atomic orbitals (LCAO) m et hod. Here, the one electron wave f u n ctio n for the system is expanded in terms of Bloch sums c o n s t r u c t e d o u t o f Gaussian t y p e [29] basis sets. F o r carbon atoms, we used [30] the 4-31 G basis set, in which each inner shell is represented by a single basis f u n c t i o n taken as a sum of four Gaussians and each valence orbital is split into inner and out er parts described by three and one Gaussian function, respectively. Th e 4-31 G basis set has been successfully used [30] in molecular orbital studies of organic molecules. F o r the lithium atom, we used the basis s et given by H e r m a nn and Bagus [31] but discarded the two long range exponents. Instead, we used a single Gaussian ( e x p o n e n t 0.15) of somewhat shorter range. We also examined the ef f ect o f using an e x p o n e n t 0.10 and f o u n d t h a t the filled valence bands were n o t affected at all. However, the e m p t y Li(2s) bands shifted lower in energy by a b o u t 1 eV. The e x p o n e n t s and c o n t r a c t i o n coefficients for both carbon and lithium atoms are given in Table 1. The crystal potential was generated by overlapping neutral at om potentials: TABLE 1 Exponents and contraction coefficients for carbon and lithium atoms

No.

Type

Carbon Exponent 486.966 9 73.371 09 16.413 46 4.344 98

Lithium Coefficient

Exponent

Coefficient

0.017 725 8 0.012 347 8 0.433 875 4 0.561 504 2

1 359.447 204.026 5 46.549 54 13.232 59 4.286 148 1.495 542

0.000 844 0.006 485 0.032 466 0.117 376 0.294 333 0.450 345

--1.213 837 --0.227 338 5 1.185 174

0.542 238

1.0

1

s

2

s

8.673 525 2.096 619 0.604 651

3

s

0.183 600

1.0

0.15

1.0

4

p

8.673 525 2.096 619 0.604 651

0.063 545 4 0.298 267 8 0.762 103 2

1.534 3 0.274 99

0.037 973 0.231 890

5

p

0.183 600

1.0

0.15

1.0

236

Very (r)

=

~

Va( r

u~),

(I)

where F~v = -~ r -- -* r -- ]~ and (the spherically symmetric) atomic potential,

Va(r) = _2Z+ 2 j~"~P(?') "3r' /3 \Z/3 r a --3a(~-) pZ/3(r).

(2)

The last term in the above expression is the effective exchange potential [32] in the Xa method. To generate the atomic potential we used selfconsistent Hartree-Fock charge densities obtained from the double zeta Slater functions [33]. The exchange parameter, a, was set equal to 2/3 according to the Kohn-Sham [32] prescription. The atomic configuration for carbon and lithium was taken to be ls22s12p 8 and ls22s 1, respectively. We typically retained 4th - 5th neighbor interaction depending upon the overlap tolerance which was set at 10 -7 .

3. Pure graphite In this Section, we discuss the backbone for the GIC's, i.e., the pure graphite. Band structure calculations for graphite [3 - 14] have been published frequently. Most of these authors have presented two-dimensional calculations, although, in some cases, the extension to three dimensions has been made. The two-dimensional approach has given a good understanding of the character of different bands (a-bands and r-bands), but to understand electronic properties determined by the Fermi surface, the interlayer interaction, i.e., the dispersion of bands perpendicular to the hexagonal plane must be taken into account. Pure graphite (in nature) occurs mainly in a form [34] where the planes of hexagonally ordered (two-dimensional) carbon atoms are staggered so that consecutive planes are shifted by one nearest-neighbor distance (Fig. l(a)). Thus, half the carbon atoms lie directly over one another in adjacent layers (black atoms in Fig. l(a)), while the other half lie over empty centers of the hexagons of neighboring planes (white atoms in Fig. l(a)). The planes follow the sequence ABAB .... where A and B denote the two alternating layer positions. The unit cell contains four carbon atoms. The atomic positions are given in Table 2 together with primitive lattice vectors. We calculated the electronic energy bands along various directions in the BZ (shown in Fig. l(b)). The complete band structure for graphite is shown in Fig. 2. The zero of energy is positioned at the Fermi energy. The bands originating from the inlayer 2s, 2px and 2py orbitals are drawn in full, while those arising from the 2pz orbitals directed perpendicular to the planes (q-bonds) are shown by dashed lines. Applying the notion of bonding and antibonding states, we can describe the orbital character of various bands. We will label the bands in numerically increasing order at F. The two lowest bands, Fz, F2 are formed from bonding combinations of s Bloch sums in plane. A slight splitting

237 ~z I

--[

i

33~AI

-

I

~

,l

I

', ]

I 11

t

.L~L,..-~'"

C1

~

(a)

(b) Fig. 1. (a) Geometrical arrangements of atoms in three-dimensional AB graphite and (b) the corresponding Brillouin zone. TABLE 2 Unit cell geometry* for pure graphite (ABAB stacking) Center name

x

y

z

C1

C2

0

0

0

a /,,/-~

0 o

C3 c4

0

a/,/~

c/2

o

2a/,/-~

c/2

~1 ~,2 T3

a/2 --a/2

a,4~/2 a,J3"/2

0

0

0 0 c

*a = 2 . 4 6 A , c ffi 6 : 7 0 A .

between the bands is due to interplanar interaction (bonding ( r l ) and antibonding (£2) along the interplanar direction) which is quite weak. Bands r s , 1"4 are formed from pz-orbitals bonding in plane b u t are, respectively, bonding and antibonding along the interplanar direction. These bands are split by a b o u t 1 eV because of the considerable overlap between pz-orbitals pointing

238 12

--

F"', EFffiO

I

-

-8 -10 -12 -14 --16 -18 -20

-22

.8

.8

.4

.2

k

M

K

F

M

K'--*H

States/eV Unit cell

Fig. 2. Energy bands for three-dimensional AB... graphite. Bands derived from Pz atomic orbitals are shown by dotted lines. Total and partial densities of states are shown in the left panel.

in a direction perpendicular to the planes. Bands F(5) - r(8) are bonding Px,Py orbitals on four atoms, and F(9) - F(12) are antibonding px,py orbitals on four atoms. Each is a nearly four-fold degenerate set because p~,py orbitals lie in a plane and experience almost no interplanar interaction. Bands r(13), F(14) are antibonding (pz-type) corresponding to r(3) and r(4). The total and partial densities of states are shown in the left hand panel of Fig. 2. As expected the bands in the vicinity of EF have their origin in C(pz) orbitals (r-bands in the two-dimensional structure). The density of states at EF was estimated to be 0.01 states/(eV C-atom) making pure graphite a semimetal. The total valence band width is calculated to be 21.5 eV which agrees well with the recent photoemission data [23]. We also computed various populations using Mulliken's population analysis [35] and found each carbon to be in the configuration 2s 0.s22px, _2.18o_1.0 y ~p~ • This is very close to our starting (assumed) configuration and thus we do not expect selfconsistency corrections to play any major role. Also, the population analysis (2p 1"°) shows clearly that graphite can be treated as a r-electron system (the sp2, y hybrids form typical a-bonds). For the understanding of the electronic properties of pure graphite as well as of dilute intercalated graphites, much emphasis has been placed on the energy bands in the vicinity of the Fermi energy E F. Experiments suggest that E F cuts a relatively fiat band along the z-direction (K - H), leaving an electron pocket around the K-point and hole-pockets centered around the H-points(see Fig. 3). This model, the Slonczewski-Weiss [5] model, explains

239 H

K

K

h

H

Fig. 3. Detailed band structure along the K - H direction for AB graphite. Also shown are electron and hole pockets (schematic).

the measured extremal orbit properties as studied by the de Hass-van Alphen effect and other methods [6]. For dilute donor GIC's this picture has also been used [ 1] where a slight increase of the Fermi level position results in a larger electron p o c k e t around K and a smaller or vanishing hole pocket around H. As we show below, this picture is somewhat misleading for certain GIC's which do not show ABAB-stacking. Figure 3 shows the details of our band structure (drawn on a magnified scale) around E F along the K - H direction. We get the expected three bands K1, K2, K 3 between K and H, with a t o t a l splitting at the K-point of ~ 0 . 8 eV, which is a b o u t half of what ix data suggest. The same trend, i.e., less dispersive bands along K - H than suggested by experiments, is observed in the almost fiat K 8 band. We find the total width of this band to be ~ 0 . 0 0 5 eV. The r e a s o n K 3 bands (doubly degenerate) are dispersionless is that they arise from bonding and antibonding combinations of the pz-orbitals located on atoms C1 and C4 (Fig. l(a)) which are not overlapping. The pz-orbitals on atoms C2 and C3 give rise to K1 (bonding) and K 2 (antibonding) bands which are split due to the interplanar interaction. An important difference between the two- and three-dimensional treatments occurs at this point. In twodimensional calculations, all eigenvalues at the K-point are degenerate and there is no dispersion along the K - H direction. The three-dimensional interaction removes the degeneracies and causes graphite to become a semimetal. The weakly dispersive band that governs the electronic properties of AB-graphite simply does n o t exist for AA-- stacking of the graphite layers. Consequently, the discussion of the changes of the electron and hole pockets with dilute doping does n o t apply to Li intercalated graphite, where the stacking sequence AA... is found. Hence, we predict drastically different extremal orbit properties for dilute LiC, and for, e.g., dilute KC, in which case AB-- stacking is observed. 4. Results for Li-intercalated graphite We n o w present results for a high concentration of Li intercalation, where we have c o m p u t e d band structure and properties for the first stage

240

compound, LiC e and for the second stage, LiC12. The insertion of planes of Li atoms, occupying one third of the positions between the hexagonal carbon atom planes, gives but a minor increase (~ 10%) of the distance between these carbon planes. This fact suggests that, basically, graphite bands should maintain their characteristic properties even when the planes of the Li superlattice are introduced between every carbon layer, i.e., even up to first stage LiCe.

A. Electronic structure of LiCs To understand the electronic structure of LiC6 and to test the applicability of the rigid band model, we proceed systematically. We first calculate the band structure of C2 (two atoms per unit cell) which represent the AA... stacking sequence of graphite (Fig. 4(a)) and follow it with the calculation for Cs (six atoms/unit cell) which has the same structure as LiCe but the planes of Li atoms have been removed. The geometrical structure of C6 is clearly identical to the AA... stacking (see Fig. 4(b)). But the calculation is being done with larger primitive translation vectors. Thus, we will expect the electronic structure of Ce to be obtainable from that of C2 by appropriate zone foldings. From the electronic structure of Ce the band structure for LiCe will be predicted on the basis of rigid bands. This will then be compared with the actual calculation for LiC e. The positions of Li atoms are indicated in Fig. 4(b). The basal planes (k2 = 0) o f t h e BZ's for C2 and Ce (LiCe) are shown in Fig. 4(c). The symbols in parentheses denote the symmetry labels for C2. The BZ for Cs (LiCe) is hexagonal in the kx,ky plane like graphite, but its size is reduced corresponding to the larger unit cell that contains six atoms in

(a)

(b)

i

\

(c) Fig. 4. (a) Direct unit cell for C2 suitable for studying AA... graphite. (b) Direct unit cell for Ce and LiCe. Filled dots at the center o f the hexagon denote Li atoms above the plane. (c) Brillouin zones for C2 (heavy lines) and C6 (light lines). The symbols in parentheses denote the symmetry labels for C2.

241 one C-layer instead of 2 as for the graphite structure. The K point for C 2 maps into F for the Ce (LiCe) and the M point maps into the M point for the Ce (LiCe) structure. The M2/s point, which lies 2/3 of the way along the F - M direction for C2 maps into the K-point for the Ce (LiCe) structure. Following this prescription we have obtained the C(2pz) derived bands for C6 shown in Fig. 5. The entire family of bands originating from C(2s,2px, y,2pz) are shown in Fig. 6 for completeness. It is instructive to study the eigenvectors of the pz-derived bands in the vicinity of EF at the F-point. As is well known in benzene or other six membered rings compounds, we get the following six eigenvectors for C6, obtained from linear combinations of pz-orbitals (~1 through ~e are Pzorbitals localized on carbon atoms in the unit cell):

1 2

0 1

1

1

2

2

1

1

0

2

1

@8

¢3

1

1

1

1

1

1

@4

1

1

At F, all)1 is a completely bonding combination (rl-band) and @6 is antibonding (re-band) and the bands originating from them are separated by about 16.5 eV (see Fig. 5). The other four orbitals give rise to a four-fold degenerate level at F about 7 eV above the most bonding combination. In isolated benzene, one gets two sets of doubly degenerate levels (@ 2,@ s and @ 4,@ 5), but in the present case, due to translationalsymmetry, these levels have collapsed into a four-fold level at r. As we move away from the high symmetry point, F, towards the K-direction, the expected degeneracies (1,2,2,1) are observed. Along r - M, all these levelssplitapart. To anticipate the band structure for LiC6, let us assume that Li donates its 2s electron into carbon r-bands. O n the basis of the rigid band model, the Fermi level would move up to accommodate an extra electron. This picture is not far from the truth, as can be seen from the calculated band structure for LiC e shown in Fig. 7. This is based on the atomic positions and primitive translation vectors given in Table 3. The major departure from the rigid band model occurs at various zone boundaries where band gaps appear due to

242

8/r\A~7

12

[

10 -

/ 6-

I t1 # 7r5~ ,

4-

/ ,/ I

2/

I

\\

,,,

\\10 -8 -

\

~r4

EF =0~- . . . . . . %\ -2- \\

-~x\ \

k\%\

////

\

9/1

',\ ?

A //

/

2

//

ll/I //

3

-18 /

3

-,o--

3

-22

--8"' K(r)

//

-I0 ~- l i e

//

\\\ / ~ ' 2

--6-

\%%

!

/

2- F;'~"~,,/

I

/,.-.

/ %

6 i -~.~~ 16~'~%`~'~-~, 41}\ ,%1 ',14 //

M(M) r(r) M2/3(K) M(M) K(F)

K M

F

(a) C6

K

r M2/3 M (b) C2

_2 K

Fig. 5. Carbon (2pz) derived bands for C 2 (dotted lines) and C6 (solid lines). The latter are obtained by folding C2 bands into the C6 Brillouin zone. The solid lines with open circles are bands which are obtained from C2 bands not shown in the Figure. Fig. 6. Carbon (2s, 2Px.y, 2Pz) bands for (a) C6 and (b) C2 obtained by zone foldings as discussed in Fig. 5. hybridization with Li. At I~, K, M this interaction results in band gaps ~ 0 . 5 eV. Holzwarth e t al. [25] have given an excellent account of LiCe band structure using a modified KKR method. They go beyond the usual muffintin approximation'for the crystal potential by computing correction terms with numerical quadrature techniques. Our results for LiCe are in good overall agreement with their calculation. However, we get a gap at P in ~-bands due to Li interaction, which is absent in the Holzwarth e t al. calculation. Also, the unoccupied Li(2s) bands in our calculation appear at about 5 eV higher than those reported by Holzwarth e t al. [25]. This is perhaps due to an inadequate description of Li conduction bands in our calculation. At P, we have gone over to the (1,2,2,1) degeneracy order for the ~-bands, whereas Holzwarth et al. obtain (1,4,1). The Fermi level is located at about 2 eV above the value found in Ce. In Fig. 8 is shown the total, local, and orbital densities of states. We note that there is very little Li(2s) character below E F. In fact, the population analysis shows that Li has lost its 2s electron and each C has gained 1/6 o f an electron. This has caused the Fermi level to move from near the minim u m of graphite rigid bands to a maximum. The density of states at EF is f o u n d to be 0.25 states/(C-atom eV), which is consistent with the value

243

I w

I 1

H

KM

F LiC6

KM

L

Fig. 7. Band structure for LiCe along various symmetry directions.

TABLE 3 Unit cell geometry* of LiC6 Center name

x

y

z

c1 C2 C3 C4 C5 C6 Li

0 a/2 a/2 0 --a/2 --a/2 0

~1

3a12

~/J-~ a/2~/~ --a12~"3 --a/~ ---a/2~/-3 a/2x/f'3 0 a~/-312 J--3~ 0

0 0 0 0 0 0 d/2 0 0 d

~2

0

r3

0

*a = 2.485 A, d = 3.76 A. o b t a i n e d b y H o l z w a r t h (0.24) a n d t h e e x p e r i m e n t a l value [ 3 6 ] (0.21) d e r i v e d f r o m specific h e a t m e a s u r e m e n t s . Recall t h a t m e a s u r e d [37] N(EF) f o r p u r e g r a p h i t e is 0 . 0 0 6 a n d f o r Cu [ 3 7 ] it is 0 . 2 9 s t a t e s / ( e V - a t o m ) . We m a y m e n t i o n t h a t t h o u g h t h e c a l c u l a t i o n was p e r f o r m e d n o n - s e l f - c o n s i s t e n t l y we did e x a m i n e t h e e f f e c t o f altering t h e starting o c c u p a n c i e s f o r g e n e r a t i n g t h e

244 4 N(E)

3 2 ~

A

(a) Densityof States i---I LiC6 S~OD L for Lii

I/

l

EIF li

I/

^A^ ,',

1 0 4 (b) ODOS C (2s, 2Px,v)

2

1

(c) ODOSC(2pz)

/ . ~

/~_

-22 0 -;~0-18-16 -14-112-110-8-6-4-2 0 2 4 6 8 10 12 14 16 Energy(eV) Fig. 8. Total, local, and partial densities of states for LiC 6.

crystal potential. We found no qualitative differences in the calculated band structures whether we used ionic or neutral configurations.

B. Electronic structure o f LiC12 The electronic structure of the second stage of GIC's has n o t been calculated before because one needs to treat 13 atoms in the unit cell. For a double-zeta basis set for the valence states (see Table 1) this leads to a 117 × 117 secular matrix. The m e t h o d we are using enables us to perform these calculations rather rapidly because our integrals on the basis sets are done only once. This is to be contrasted with the work of Holzwarth et al. [25] where the basis sets are ]~-dependent. Once again, one can get an idea of the band structure from the rigid band model. In Fig. 9, we have shown schematically the F-bands of AA... sequence of graphite (done with four atoms/unit cell). Notice that pure AA graphite can actually be done with only two atoms in the unit cell; however, since LiC12 contains two layers of C-atoms, it will then be necessary to look at the bands of AA ~ a p h i t e using the larger direct unit cell. Since the kx,ky plane of the BZ for LiC12 is the same as that of LiCe, we have to do the same foldings as we did for LiCe. However, n o w we get twelve F-bands, which is consistent with there being twelve carbon atoms in the unit cell. These twelve bands can be rationalized in terms of bands of Ce by adding one extra degree o f freedom, namely, the bands can n o w have bonding or antibonding character with respect to the other carbon plane in the unit cell. The complete band structure for LiCz2 is shown in Fig. 10. The atomic positions of various atoms and the primitive translation vectors are given in Table 4. The effect of lithium hybridization is to open up gaps ~ 0 . 2 eV at some zone edges. The Fermi level again passes through ~-bands as it did for LiCe.

245

8 6

g

~o--

J/L

-o

-~K M

P

M

F

K

K H L LiC12

A

H F"--A

Fig. 9. Systematic ~-band of AA graphite folded into the Lie12 BZ. Fig. 10. Band structure for LiC12.

TABLE 4 Cell unit geometry* for LiC12 Center name

x

y

C1, C 7

0

a/x/-3

O, c]2

C2, Cs

a/2 a/2 0

a/2,q~ --a/2~/-3

O, c/2 O, cl2

"-aI,4"3

O, c12

"-a/2

---a121,/3" O, c12

---a/2 0

a/2x/"3 0

C3, C 9

C4, C10 C5, C11 C6, C12 Li

~l T3

z

O, c/2 c/4

3a/2

avf'3/2

0

o

,,/-~a

o

0

0

C

*a = 2.476 •, c = 7.065 A. Finally, in Fig. 11 we have shown the total, local, and partial density of states for LiC12. The Fermi level is located at about 1.5 eV, in a region where the density of states is 0.12 states/(C atom-eV). Thus, at higher stages, we would expect the E F to move in the direction of lower and lower densities of states. From the population analysis, we conclude that the Li(2s) electron

246 (a) Density of States

]

~ l a LDOS for Li

N(E)

it

EF

I \

r

(b) ODDS C (2s, 2Px.y)

t

(C) ODOS for C (2p z)

0 i J i J ] i J -22 -20 -18 -16 -14 -12 -10 -8 -6

-4 -2 0 Energy (eV)

2

4

6

8

,, t0

12 14 16

Fig. 11. Total, local, and partial densities of states for LiC12. has been d o n a t e d t o carbon ~-bands. Each C-atom has captured 1/12 of the e x t r a electron.

5. Concluding remarks We have presented a systematic study of the electronic structure o f the first two stages o f lithium intercalated graphite. We have f o u n d that the rigid band ideas are quite suitable f or understanding the electronic structure of these c o m p o u n d s if one uses the rigid bands for the AA... graphite. Lithium atoms th en simply donat e their 2s electrons t o the carbon ~-orbitals. This results in shifting the Fermi energy from the region of relatively low density o f states to a region where the density o f states is comparable t o Cu metal. Thus, strictly from the density of states considerations, we have p r o d u c e d a transition f r o m a semimetal t o a metal u p o n doping graphite.

References

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