C A R B O N 4 7 ( 2 0 0 9 ) 2 5 0 1 – 2 5 1 0

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Density-functional theory calculations of the electronenergy-loss near-edge structure of Li-intercalated graphite

J.T. Titantaha,*, D. Lamoena, M. Schowalterb, A. Rosenauerb

aEMAT, Universiteit Antwerpen, Groenenborgerlaan 171, 2020 Antwerpen, BelgiumbInstitut fur Festkorperphysik, Universitat Bremen, D 28359 Bremen, Germany

A R T I C L E I N F O

Article history:

Received 12 March 2009

Accepted 5 May 2009

Available online 10 May 2009

0008-6223/$ - see front matter � 2009 Elsevidoi:10.1016/j.carbon.2009.05.002

* Corresponding author: Fax: +32 3265 3318.E-mail address: John.Titantah@ua.ac.be (J

A B S T R A C T

We have studied the structural and electronic properties of lithium-intercalated graphite

(LIG) for various Li content. Atomic relaxation shows that Li above the center of the carbon

hexagon in a AAAA stacked graphite is the only stable Li configuration in stage 1 interca-

lated graphite. Lithium and Carbon 1s energy-loss near-edge structure (ELNES) calculations

are performed on the Li-intercalated graphite using the core-excited density-functional

theory formulation. Several features of the Li 1s ELNES are correlated with reported exper-

imental features. The ELNES spectra of Li is found to be electron beam orientation sensitive

and this property is used to assign the origin of the various Li 1s ELNES features. Informa-

tion about core-hole screening by the valence electrons and charge transfer in the LIG sys-

tems is obtained from the C 1s ELNES and valence charge density difference calculations,

respectively.

� 2009 Elsevier Ltd. All rights reserved.

1. Introduction

From the search for alternative and clean energy sources to

the technology-driven surge in the mass of portable elec-

tronic devices, the need for energy storage devices keeps

increasing. This dramatic increase and the growing lobby

from environmental pressure groups encourage renewed

interest in battery technology for energy storage. Carbon

materials have been suggested and are now widely used as

anode materials for lithium–ion batteries [1–4]. For this,

graphite is one of the most promising anode materials owing

to its cheapness, inertness (health and safety) and its high

theoretical lithium intercalation capacity of 372 mAh/g. Alka-

li-doped pillared carbon materials have also been suggested

as possible vehicle for hydrogen storage [5]. A high pressure,

high Li capacity LiC2 compound has been found to have sev-

eral similar physical properties with ambient pressure LiC6

[6]. Numerous theoretical studies have been conducted in or-

der to elucidate the electronic, structural and energetic prop-

er Ltd. All rights reserved.T. Titantah).

erties of adsorbed metal atoms on graphene or their

intercalation into graphite [7–17] and carbon nanotubes [18–

20]. A study of the diffusion of Li atoms inside carbon nano-

tubes has also been undertaken [21].

Despite the extensive theoretical and experimental [6,22–

28] studies conducted on Li-intercalated graphite (LIG) a

unanimous understanding of the nature of charge transfer

in these materials is far fetched [21]. While some workers find

complete transfer [9,12,24,29,30] of the alkali metal’s s elec-

trons into graphite, others suggest a partial charge transfer

[11,13–15,25]. X-ray spectroscopy [9,25,31–33] and electron en-

ergy-loss spectroscopy (EELS) [24,34] have been used to probe

the nature of the charge transfer in LIG materials. It is still not

clear from these measurements what the status of the Li

charges is.

In this work, we perform density-functional theory (DFT)

calculations on LIG materials (LixC6) for Li content x ranging

from 0.167 to 1. Two possible Li arrangements were consid-

ered: (1) one in which all the interstitial spaces between the

.

Table 1 – The different LixC6 systems studied and thetype of Li arrangements considered: (1) one in which allinterlayer spaces between graphene sheets contain Liatoms and (2) one in which only one of the two interlayerspaces contain Li atoms.

System x Type

LiC36 1/6 2

LiC18 1/3 2

LiC18 1/3 1

LiC12 1/2 2

LiC9 2/3 1

LiC6 1 1

2502 C A R B O N 4 7 ( 2 0 0 9 ) 2 5 0 1 – 2 5 1 0

graphene layers contained Li atoms and (2) the case where

only one of every two interstitial spaces contained Li atoms.

In Table 1, the various systems investigated and the type of

Li arrangements (1 or 2) considered are listed. Detailed charge

transfer and energy-loss near-edge structure (ELNES) calcula-

tions are performed. We find that when Li atoms are arranged

such that one-dimensional Li chains running across the cen-

ter of the C hexagons of AAAA stacked graphite are formed

(type 1), lesser Li charge is given to the sea of interstitial con-

ducting charges than in systems whereby only alternating

layers do contain Li atoms. The sea of electrons run parallel

to and are somewhat closer to the graphene sheets than to

the Li planes. Orientation resolved ELNES calculations are

used to identify and assign the various ELNES features that

are often reported in the X-ray absorption near-edge structure

(XANES) and ELNES spectra of LIG materials. An important

fraction of the Li 1s ELNES spectrum is found to originate from

the dipole-forbidden 1s! 2s transition. A feature in this spec-

trum whose presence or absence can signal the absence or

presence of the linear Li chains in LIG systems is found at

an energy of about 13 eV above the Fermi level.

2. Computational details

The systems under study here consist of graphite supercells

made of two graphene layers containing 36 C atoms and 1

to 6 Li atoms. The Li atoms are inserted midpoint between

the two graphene sheets and directly above the center of

the C hexagons. For each Li content the out-of-plane super-

cell size is fixed at 7.1 A while the in-plane size is fixed at

7.43 A. DFT calculations are performed using the ab initio

all-electron Full-Potential-Linearized-Augmented-Plane-

Wave (FLAPW) package WIEN2k [35,36]. The exchange and

correlation energy is treated using the local density approxi-

mation [37] which is a fit to the Green’s-function Monte Carlo

calculations of Ceperley and Alder [38].

For the LiC6 system the out-of-plane supercell size was

systematically optimized and we found an equilibrium super-

cell size of 7.1 A. This value is smaller than the reported

experimental value of 7.4 A [7], which is in line with the ten-

dency of LDA to underestimate lattice parameters. It is how-

ever, higher than that of pure graphite. Throughout the rest

of this work and as already pointed out earlier, for all Li con-

tents, the out-of-plane supercell size was fixed at 7.1 A. It is

well known that, depending on the Li concentration, graphite

adopts a range of stacking orders when Li is intercalated into

it. We ignore the effect of this Li concentration dependent

stacking sequence and consider only AAAA stacked graphite

for all the systems investigated. Hartwigsen et al. [13] found

that the graphite stacking sequence in LIG systems is of min-

or importance especially for charge distribution.

For both carbon and lithium the 1s states are treated as

core states while the 2s and 2p states are the valence states.

Muffin-tin radii (RMT) are fixed at 1.3 (2.0) atomic units (a.u.)

for C (Li), while a RminMT � Kmax value of 5.5 is used

ðRminMT ¼ 1:3 a:u:Þ; Kmax being the plane wave cut-off. Up to

100 k-points are used to sample the full Brillouin zone (32 in

the irreducible Brillouin zone (IBZ)). For the ELNES calcula-

tions, the core-hole effect is introduced via the so-called ex-

cited-core method. In this method the occupancy of the

core state is reduced by 1 while a neutralizing charge of 1e

(e is the charge of an electron) is inserted as a background

charge. This method has been found to correctly model the

ELNES spectra of graphite [39], carbon nanotubes [40], dia-

mond and amorphous carbon [41]. The decomposition of

the ELNES spectrum into its various components is done

using the formulation of Nelhiebel et al. [42] which has been

implemented in the WIEN2k code [35] and applied to hexago-

nal boron nitride [43], carbon nanotubes [40] and graphite [39].

ELNES is a measure of the double differential scattering cross-

section for the excitation of an atom by fast electrons and is

given by the expression

o2roEoX

¼ 4c2

a20

kk0

1

Q4 SðQ;EÞ; ð1Þ

where a0 is the Bohr radius, c = (1 � b2)�1/2 is the relativistic

factor, k0 and k the fast electron wave vectors before and after

interaction, respectively, and Q = k0 � k is the momentum

transfer. The dynamic form factor S(Q,E) is defined as

SðQ;EÞ ¼X

i;f

i j eiQ�rjf� ��� ��2d Eþ Ei � Ef

� �ð2Þ

for excitations from states jii with eigenvalue Ei to state jfiwith eigenvalue Ef. For small Q the exponential can be ex-

panded as eiQÆr � 1 + iQ Æ r + . . .. The first term does not contrib-

ute to the scattering cross-section because the initial jii and

final jfi states are orthogonal. Only retaining the linear term

leads to the so-called dipole-approximation which is often

used in the analysis of ELNES and which implies that the ini-

tial and final states are related through Dl = ±1, where l is the

orbital angular momentum quantum number of the excited

atom. For K-edges this means transition from s! p. However,

since we retain the full exponential in Eq. (2) our results also

contain the non-dipole contributions. We shall show that the

latter are important for the Li K-edge.

Valence electron densities are calculated using the LAPW5

package of the WIEN2k code. The charge transfer in LIG is

studied by considering the charge density difference which

is defined by:

DnLIGðrÞ ¼ nLIGðrÞ � nGðrÞ � nLiðrÞ; ð3Þ

where nLIG(r) is the valence electron density of the LIG system

and nG(r) and nLi(r) those of graphite and lithium occupying

the same supercell, respectively.

Fig. 2 – The most stable AAAA stacked Li-intercalated LiC6

system as obtained by ab initio DFT relaxation.

C A R B O N 4 7 ( 2 0 0 9 ) 2 5 0 1 – 2 5 1 0 2503

3. Results

3.1. Relaxation of internal coordinates in LiC6

Six Li atoms were inserted randomly in between the graphene

sheets of a 36 atom supercell ABAB stacked graphite and all

the atomic positions were relaxed using the MINI package

of the WIEN2k code. In order to understand the changes that

take place during the relaxation of the LIG systems, we have

also considered the relaxation of another system. This system

consists of 3 Li atoms adsorbed on a 18 atom graphene sheet

(to maintain the LiC6 stoichiometry) in a supercell of sides

7.43 · 7.43 · 10 A3. The changes in total energy per Li atom

during the course of the relaxation of the two systems are

shown in Fig. 1, respectively. For the Li-on-graphene system

(Li on isolated graphene sheet), the Li atoms attained their

most stable positions (above and at the center of the C hexa-

gons) within the first few relaxation moves. For the case of

LIG, two plateaus can be seen in the energy profile. The first,

occurring within roughly the first 50 DFT steps, results when

all the Li atoms are directly above the center of the carbon

hexagons of one graphene layer and directly below the C

atoms (atop position) of the other layer. This point in which

graphite maintains its ABAB stacking, is followed by a process

accompanied by a steep energy decline whereby the graphite

layer whose C atoms are directly above the Li atoms undergo

a glide along the (�110) direction until its C hexagons are di-

rectly centered above the Li atoms. It is at this point that

graphite undergoes the transformation from ABAB to AAAA

stacking which is well known for Li intercalation into graphite

to form LiC6.

The final structure of LiC6 is shown in Fig. 2. The structure

clearly shows the AAAA stacked graphite with Li atoms form-

ing linear chains that run across the center of the C hexagons.

During the relaxation of the Li-adsorption on graphene and

-70

-60

-50

-40

-30

-20

-10

0

0 50 100 150 200 250 300

Ener

gy p

er L

iC6 (

KJ/m

ol)

Relaxation steps

ABAB stacked

ABAB-AAAA transition

Single layer LiC 6

Double layer LiC 6

AAAA stacked

Fig. 1 – DFT relaxation of the atomic positions of Li adsorbed

on graphene and Li intercalated into graphite to form LIG

LiC6. In the latter case the transformation from ABAB to

AAAA graphite stacking is clearly seen.

intercalation into graphite no Li atom crossed from one inter-

layer to the next. This can be understood by noting that stud-

ies of Li adsorption on graphene [17] and carbon nanotubes

[19] both show a high energy barrier of more than 7 eV to

cross the C hexagon.

3.2. Density of states

The electronic density of states (DOS) has been calculated for

all Li concentrations and it is found that for all the Li contents

investigated in this work the LIG systems are metallic. The

metallic character arises from the filling of the graphite states

that are unoccupied in pure graphite thereby shifting the Fer-

mi level to higher energies. Typical DOS plots are shown in

Fig. 3 for graphite, LiC36, LiC12 and LiC6. An important aspect

of the DOS is the presence of Li 2s states around the Fermi le-

vel as the inset in Fig. 3 shows. This means that not all the Li

2s electrons have been transferred to graphite, thereby sup-

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

-4 -2 0 2 4 6 8

DO

S (s

tate

s/eV

/ato

m)

E-EFermi

(eV)

Li 2s DOS

GraphiteLiC36LiC12LiC6

0

0.005

0.01

0.015

-2 0 2

LiC12

LiC36

Fig. 3 – Density of states per C atom of graphite, LiC36, LiC12

and LiC6 showing the metallic nature of all the LIG systems.

The inset shows the Li 2s partial DOS of LiC36 and LiC12.

2504 C A R B O N 4 7 ( 2 0 0 9 ) 2 5 0 1 – 2 5 1 0

porting a partial charge transfer of the Li electrons. However,

the weak nature of this DOS is consistent with a net charge of

less than 0.05e.

3.3. Energy-loss near-edge structure

Within the excited-core approximation, C and Li 1s ELNES

spectra have been calculated. For both edges we adopted a

microscope convergence angle a and collection angle b of

1.9 and 3.0 mrad, respectively. The C 1s ELNES spectra are

shown in Fig. 4 for LiC18 and LiC6. The LiC18 system is con-

structed by inserting a Li atom in each interstitial region be-

tween the two graphene layers of a 36 atom bilayer AAAA

stacked graphite. For this stoichiometry and with respect to

each Li atom, three inequivalent carbon positions are possi-

ble: C atoms of the C hexagons above and below the Li atom

(� 2.3 A from the Li atoms), next neighbors located at

� 3.4 A and � 4.2 A away from the Li atoms, respectively. In

order to check the range of Li perturbation on the electronic

structure of graphite for this system we have calculated the

ELNES spectra of C atoms in these three positions. For LiC6

all C atoms are equidistant (� 2.3 A) from the Li atom. The

spectra of C in LiC6 and the 3 carbon positions of LiC18 are

shown in Fig. 4. Two major changes are seen in the C 1s ELNES

spectra of all LIG systems with respect to that of graphite. The

p* feature (appearing at the Fermi level) is greatly suppressed

upon Li insertion and the r* onset (showing up more than 5 eV

beyond the Fermi level) is shifted to lower energies. A visible

difference between the ELNES of the various carbon positions

in LiC18 is the size of the shift of the r* onset which is seen to

decrease with increasing distance from the Li atom as the ob-

lique line in the right panel of Fig. 4 shows.

Several groups have measured the C 1s ELNES spectra

[24,34], hard X-ray scattering spectra [25], inelastic X-ray scat-

0

5

10

0 5 10 15 20 25

ELN

ES In

tens

ity (a

rb. u

nits

)

E−EFermi (eV)

LiC 6

Graphite

sσπ

Total

0

5

10

15

20

25

0 5 10 15 20 25E−EFermi (eV)

LiC18

d=2.3 Å

d=3.4 Å

d=4.2 Å

Graphite

Fig. 4 – Carbon 1s ELNES spectra of LiC18 and LiC6 compared

with that of graphite. For LiC6 all C positions are equivalent.

The distances d = 2.3, 3.4 and 4.2 A in the right panel denote

the distances of the three inequivalent C positions from the

Li atom.

tering spectra (IXSS) [29] and soft X-ray emission spectra [9] of

LIG systems. While Hightower et al. [24] found that the p* peak

of graphite was greatly suppressed in LiC6, they did not find a

shift in the r* onset with respect to that of graphite. Schulke

et al. [29] also did not find this shift. However, a careful look

at their IXSS measurement reveals that the slope of the r* on-

set is stronger for graphite than LiC6. This is indicative of a de-

gree of shift of the r* feature to lower energies. A more recent

measurement by Balasubramanian et al. [25] found a shift of

0.6 eV. They attributed this shift to lengthened C–C bonds in

LiC6. The C–C bond lengths in our LiC6 were barely 0.01 A

longer than that of graphite, yet the shift of the r* onset

was found to be 0.9 eV. Shifts of this magnitude cannot be ex-

plained by such bond length changes [44] only. We will show

that the shift is a consequence of the screening of the cou-

lomb potential by the accumulation of Li 2s conduction elec-

trons around the carbon atoms. Such a screening should

decrease as the distance from the Li atom increases. This

trend is supported by the weakened shift in the r* onset as

the distance from the Li atom increases. Charge transfer anal-

ysis supports this trend. For example, in Figs. 5 and 6, we

show the charge transfer landscape near the graphene layer

and in the interstitial region between the C and Li layer of

the LiC18 system, respectively. Within the interlayer region

between the C and Li layers and directly above the carbon

hexagons surrounding the Li atom there are more charges

than above carbon rings further away. Another finding that

supports the idea that screening is the cause of the shift of

the r* onset is the C core-level shift. We have calculated the

core-level energies (following the procedure of ref. [45]) of

the carbon atoms located at 2.3 and 4.2 A away from the Li

atom and we find that the core-level energy of the nearest C

atom is larger than that of the farthest atom by 0.5 eV.

Fig. 5 – Charge transfer landscape at about 0.1 A above the

graphene layer on a plane parallel to the graphene layer of

LiC18. The scales show the charge transfer (in e/A3) as

obtained using Eq. (3). Negative (positive) numbers indicate

charge depletion (accumulation).

Fig. 6 – Charge transfer landscape on a plane running

through the center of the interlayer region between a

graphene layer and a Li layer and parallel to the graphene

plane of LiC18. The scales show the charge transfer (in e/A3)

as obtained using Eq. (3). Negative (positive) numbers

indicate charge depletion (accumulation).

C A R B O N 4 7 ( 2 0 0 9 ) 2 5 0 1 – 2 5 1 0 2505

A decomposition of the C 1s spectra into p* (out-of-plane)

and r* (in-plane) components reveals that a non-negligible

amount of r* features appear at energies that are convention-

ally attributed to p* scattering (0–5 eV above Fermi level).

0

50

100

150

200

250

300

55 60 65 70 75 80 85 90 95 100

ELN

ES In

tens

ity (a

rb. u

nits

)

Eloss (eV)

A

BC

D

EF

G

Li1/6 C6

Li1/3 C6

Li 1/2 C6

LiC 6

q⊥cq ⁄⁄ c

66 68 70

pxypz

2s

Fig. 7 – Lithium 1s ELNES spectra of LIG systems for

momentum transfer perpendicular and parallel to the

c-axis. The inset shows the decomposition of the spectrum

of LiC36 into the 2s, pz and pxy components around F feature

at � 69 eV for q?c.

There is therefore, a Li-mediated modification of the hybrid-

ization of the carbon atoms of graphite.

The lithium 1s spectra of the LIG systems are shown in

Fig. 7. That of LiC6 is reproduced in Fig. 8 for momentum

transfer perpendicular and parallel to the c-axis. We have

shifted these spectra by 56 eV for easy comparison with mea-

surements. Within the first 15 eV above the Fermi level (about

15 eV above edge onset) we have identified seven features:

feature A at �57 eV, B at � 59 eV, C at � 62 eV, D at � 65 eV,

E at � 67 eV, F at � 69 eV and G at � 71 eV. As Fig. 7 shows, fea-

ture C is very sensitive to the orientation of the electron

beam; it vanishes as the momentum transfer becomes per-

pendicular to the c-axis. Features A, B, C and D have been

commonly reported for LIG systems [25,28,29,34]. In addition

to these features Schulke et al. [29] and Hightower et al. [24]

measured features at �70 and �71 eV, respectively. Both fea-

tures correspond to the G feature in this work. Due to energy

resolution limitations, feature E may only show up as a weak

feature in the measurements. Feature F has been consistently

absent in all available measurements apart from the mea-

surement of Hightower et al. [24] which revealed a weak fea-

ture at about 69 eV (�13 eV above the edge-onset). In our

calculations this feature is only present in LiC36 and LiC12.

The common characteristic of these two systems is that while

an interstitial layer contains Li atoms, the next does not (type

2 arrangement). All the layers of the other systems contain Li

atoms (type 1 arrangement). In order to understand the origin

of this feature we have plotted in the inset of Fig. 7 the 2s, 2pz

and 2pxy components around this feature. It results from in-

plane bonding of the Li atom. This feature demonstrate that

more pxy charge is depleted. The presence of this feature in

the spectrum of Ref. [24] and the lack of a shift in the r*

edge-onset of the C 1s spectrum reported therein may suggest

that the Li concentration in that sample was lower than that

in LiC6. The presence of Li in all the layers of LIG systems im-

ply the formation of linear chains of Li running across the C

hexagons of graphite. Therefore, the presence of feature F in

0

10

20

30

40

50

60

70

80

90

50 55 60 65 70 75 80 85 90

Inte

nsity

(arb

. uni

ts)

Energy loss (eV)

A B C D E G

q ⁄⁄ c-axis

q ⊥ c-axis

Fig. 8 – Lithium 1s ELNES spectra of LiC6 for momentum

transfer perpendicular and parallel to the c-axis.

2506 C A R B O N 4 7 ( 2 0 0 9 ) 2 5 0 1 – 2 5 1 0

any Li 1s spectrum of a LIG system may signal the absence of

these linear Li chains. The staging of LIG systems is character-

ized by the presence (stage 1) and absence (stages 2 and 3) of

these chains. Feature F can thus be used to characterize the

various stages of LIG systems.

Recently, Balasubramanian et al. [25] performed multiple

scattering calculations of the near-edge X-ray absorption fine

structure (NEXAFS) of LiC6. Their calculations reproduced fea-

ture B, C, D and G. However, for momentum transfer parallel

to the c-axis, only feature D showed up in their calculations,

even though their measurement for that orientation revealed

more than one feature.

The assignment of features A, B, C and D is still lacking or

not accurate. In order to resolve this we decomposed the

spectra of Li in Fig. 9. Our analysis shows that the dipole-for-

bidden 1s! 2s transition is very important for energy losses

lower than 75 eV. Most assignments overlook this component

which can become dominant, depending on the microscope

setting. For almost parallel illumination (small collection

and convergence angles) this component dominates as the in-

set in Fig. 10 shows. We propose the following assignment:

the dipole-forbidden 1s! 2s transition contributes to all fea-

tures A–D. Grunes et al. [34] only assigned feature B to this

transition although they pointed out that it should be weak.

They assigned feature A to the transition 1s! Fermi level.

We can confidently state that the 1s! 2pz transition does

not contribute to feature B but contributes strongly to C and

D, and this is further evidenced by its weak nature when

the momentum transfer is perpendicular to this orbital (see

Fig. 7). Once more, these two features were generally assigned

to the 1s! 2p transitions in Ref. [34].

0 5

10 15 20 25 30

50 55 60 65 70 75 80 85 90

Inte

nsity

(a.u

.) (a) pz: q⊥q ⁄⁄

0 5

10 15 20 25 30 35 40

50 55 60 65 70 75 80 85 90

Inte

nsity

(a.u

.) (b) pxy : q ⊥q ⁄⁄

0 2 4 6 8

10 12 14 16

50 55 60 65 70 75 80 85 90

Inte

nsity

(a.u

.)

Energy loss (eV)

(c) s: q ⊥q ⁄⁄

Fig. 9 – The 2s, pxy and pz components of the Li 1s ELNES

spectrum of LiC6 for momentum transfer q parallel and

perpendicular to the c-axis. Note that the dipole-forbidden

1s! 2s transition is not weak.

3.4. Charge transfer

As it was pointed out in the introduction, there are two view

points regarding the nature of the charge transfer in LIG sys-

tems. One holds that Li atom gives away only a fraction of its

2s electron [13–15,25] and the other argues that the entire 2s

electrons are transferred to graphite [9,12,24,29,30]. Both argu-

ments presuppose that the Li charges can only be transferred

to the C atoms of graphite. It is well known that interlayer

states exist in graphite [10]. When Li is intercalated into

graphite what becomes of these interlayer states? In order

words, to which atoms should they be assigned? How much

Li charge goes into these states? We will not answer these

questions, rather we will begin by limiting the charge transfer

analysis to the charge given up by Li and we will not go into

the specifics of how much charge carbon has received. Based

on this we will find that Li in all the LIG systems gives away

almost its entire 2s electron.

The electron density of states has been used to perform

charge transfer quantification [15]. We follow the same proce-

dure for our LIG systems. The total DOS was integrated over

an energy interval DEF up to the Fermi level, where DEF is

the difference between the Fermi energy and the Dirac point

(defined as the point where the density of states vanishes).

We find that DEF varies from 0.75 eV for Li1/6C6 (LiC36) to

1.75 eV for LiC6. For all the LIG systems a charge transfer of

(1.0 ± 0.08)e/LiC6 was found. This value should be compared

with the value of 0.90e obtained in Ref. [15] using similar

method for Li on graphene. Note that we have used the total

DOS for this calculation, implying that the interlayer state

DOS was included. Since the shift in the Dirac point is a con-

sequence of the filling of the previously unoccupied states by

Li valence electrons, this charge of (1.0 ± 0.08)e is thought to

be the charge transfer from Li. Thus this methods demon-

strates an almost total charge transfer from Li.

0

20

40

60

80

100

120

140

55 60 65 70 75 80 85

ELN

ES In

tens

ity (a

rb. u

nits

)

Eloss (eV)

0.5mrad

1.0

2.03.04.0

5.0

0.5

q ⊥ c-axis

q ⁄⁄ c-axis

5.0

0

20

40

60

80

60 70

0.5mrad

3.0mrad 2s

2p

Fig. 10 – The effect of microscope collection angle b on the Li

1s ELNES spectrum. The convergence angle a is set at 1.87

mrad. The inset shows how the 1s! 2s transition becomes

dominant for small b.

C A R B O N 4 7 ( 2 0 0 9 ) 2 5 0 1 – 2 5 1 0 2507

Spectroscopic methods have been suggested and used for

charge transfer quantification of these materials, yet the re-

sults are conflicting [24,25,28,46]. An early Auger electron

spectroscopy study on LiC6 and CsC8 [46] has been conducted

in order to study charge transfer in these materials. The find-

ing of that measurement was that the screening of the core-

electron renders inadequate the use of such methods for

charge transfer analysis as the intensity of the p* peak was

consistent with a transfer of four electrons from each Li atom

into the pz orbitals of carbon. Core-hole screening was sug-

gested to be responsible for this discrepancy. This can easily

be checked by performing ELNES calculations with and with-

out core-hole effect taken into account. We know that if

charges are transferred into the pz orbitals of graphite we ex-

pect a decrease in the scattering cross-section corresponding

to the transition into this orbital. The C 1s ELNES spectra on

Fig. 4 show a dramatic decrease in the p* ELNES feature of

both LiC6 and LiC18. By assuming that the pz orbital of pure

graphite is empty and denoting the ratio of the integrated p*

differential cross-section of pure graphite to the total inte-

grated differential cross-section by R0(DE) and the corre-

sponding ratio for LIG system as R(DE), we evaluate the

charge transfer (in e) into the pz orbital by the expression

DQpzðDEÞ ¼ R0ðDEÞ � RðDEÞ

R0ðDEÞ 1� RðDEÞð Þ : ð4Þ

Each integration is over the same energy window DE which is

measured from the Fermi level. Fig. 11 shows the dependence

of DQpzðDEÞ on DE for LiC6 and LiC18. For LiC6, both core-hole

and non-core-hole calculations are considered. We see almost

no dependence on DE for this quantity especially when core-

hole effects are not accounted for. For LiC18 core-hole calcula-

−0.1

0

0.1

0.2

0.3

0.4

0.5

0.6

8 10 12 14 16 18 20

ΔQ

pz (e

/C)

Energy Window ΔE (eV)

LiC 6: core−hole

LiC 6: non−core−hole

LiC 18: d=3.4 Å

LiC 18: d=2.3 Å

LiC 18: d=4.2 Å

Fig. 11 – Charge transfer from ELNES quantitative analysis of

LiC6 and LiC18. Non-core-hole and core-hole ELNES spectra

are considered for LiC6. For LiC18 core-hole calculations are

performed and the three inequivalent carbon positions are

reported showing that charge transfer to graphite occurs

within the first two carbon shells.

tions are performed and the three inequivalent carbon posi-

tions are reported showing that charge transfer to graphite

occurs within the first two carbon shells. For small DE there

is an increase of about 0.1e for the core-hole calculation of

LiC6 which is due to the well-known redistribution of r* inten-

sities to lower energies because of the presence of the core-

hole [40]. This effect is different for p* and r* spectra because

of the strong anisotropy in graphite. However, we can safely

state that (0.45 ± 0.08)e and (0.12 ± 0.03)e should have been

transferred to each C pz orbital of LiC6 and LiC18, respectively,

in order to be able to explain the drop in the p* intensity re-

ported here. (The value of 0.12e has been obtained by averag-

ing over the three inequivalent C atom sites of LiC18.) This

analysis excludes any screening effect of the core state. The

value of (0.45 ± 0.08)e for LiC6 should be compared with early

Auger electron spectroscopy measurement which found a

charge of 0.6e [46] and soft X-ray emission spectroscopy mea-

surements which gave 0.26e [9]. Of course Li can only give a

maximum of 0.167e (0.056e) to each C atom of LiC6 (LiC18). If

we then assume that all the Li 2s electrons were transferred

into the C pz orbital we find that screening is the major cause

of spectral drop in LiC6. The higher the Li content is, the more

the C 1s state is screened in LIG systems. This is because

increasing the Li content increases the population of conduc-

tion charges which play a big role in screening the core state.

This analysis of charge transfer based on the relative

intensity of the p* ELNES spectrum does not account for

charge transfer on the C–C bonds of the LIG systems; it as-

sumes that the carbon r* intensity of LIG systems remains

unaltered after Li intercalation. In fact, we have found that

Li intercalation causes a charge depletion of the C–C bonds

(see left panel of Figs. 5 and 6). This latter charge transfer will

influence the r* intensities and this may also be a reason for

the inconsistency noted in ELNES-derived charge transfer.

A direct method of charge transfer quantification is by ex-

plicit calculation of electron charge densities. For this we cal-

culated the valence electron charge densities of three types of

systems: (1) pure graphite, obtained by removing all Li atoms

from the LIG supercell, (2) lithium charges, by removing all

carbon atoms from the LIG supercell and (3) the charge of

the LIG system. Fig. 12 shows the various valence charge den-

sities of these three scenarios as obtained by integrating the

charge density per unit volume on planes parallel to the

graphene sheets. The entire supercell was divided into 400

planes.

At a glance, the total valence charge densities of all the LIG

systems look very similar. However, the Li charges of the Li

subsystem (with all C atoms removed) are spread over the en-

tire supercell, almost forming uniform densities for LiC18 and

LiC6, respectively (top two insets of Fig. 12). For the Li in LiC6,

fluctuations around the uniform value of 0.141 e/A/Li has an

amplitude which is less than 0.01 e/A/Li. This is interesting

since it means that even without the presence of graphene

sheets a good fraction of Li 2s electrons tends to be delocal-

ized throughout the whole supercell. To estimate this fraction

we fitted the Li charges as a sum of a constant charge and

some localized charges that are modeled as Gaussians cen-

tered on the extremas of the charge density profile. The frac-

tion of charges still bound to Li nucleus is taken as the area

under the Gaussian functions. For LiC6 we find this charge

0

2

4

6

8

10

ρ (e

/Å/C

6) Li in LiC18

Li in LiC 6

GraphiteLiC18LiC 6

0.045

0.05

0 0.5 1

0.135 0.14

0.145

0 0.5 1

0

2

4

6

8

10

0 0.5 1

ρ (e

/Å/C

6)

z/c

Li in LiC 36

Li inLiC 12

LiC 36LiC 12

0

0.02

0.04

0.06

0 0.5 1 0

0.1

0.2

0 0.5 1

Fig. 12 – The valence charge density of LIG, Li- and graphite-

only systems for various Li contents per C6 ring. These

results are obtained by integrating the valence charge

density per unit volume over planes parallel to the graphene

sheets. The arrows indicate the positions of the Li atoms.

The horizontal lines on the Li-only systems’ charge plots

indicate the values that are expected if the Li 2s electrons

were uniformly distributed across the supercell.

2508 C A R B O N 4 7 ( 2 0 0 9 ) 2 5 0 1 – 2 5 1 0

to be 0.03 e/Li. Therefore, 97% of Li 2s electrons are delocal-

ized throughout the crystal as conduction charges. We sug-

gest that the notion of charge transfer in LIG systems

should only be limited to the part of Li 2s electrons that are

−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0 0.5 1

Δρ (e

/Å/C

6)

LiC18

−0.3−0.25

−0.2−0.15

−0.1−0.05

0 0.05

0.1 0.15

0 0.5 1

Δρ (e

/Å/C

6)

z/c

LiC6

Li5 C36LiC9

Fig. 13 – Valence charge density difference for various LIG syste

The entire distribution is fitted as a linear combination of Gaussi

(1) graphitic (2) interstitial and (3) lithium.

still bound to the Li nucleus and a subsequent charge redistri-

bution as a result of a change in effective atomic volumes on

bringing together Li and graphite to form a LIG system: the so-

called geometrical charge transfer [11]. In what follows we

will not distinguish between these two aspects of charge

transfer.

Valence charge density differences were evaluated using

Eq. (3) and are presented in Fig. 13. The entire density profile

is fitted as a linear combination of Gaussian functions each

of which is assigned to one of three layers: (1) graphitic, (2)

interstitial and (3) lithium layers. This partitioning permits

us to quantify the charges within each of the three regions.

These regions correspond to those defined in Ref. [13]. Fig. 14

shows the charge transfer per C atom for the graphitic and

the interstitial regions between the graphene and Li layers

and that per Li atom for the Li layers. Charges deplete from

the graphitic and lithium layers and accumulate in the inters-

tial region. The amount of charge extracted from Li and the

graphene layers increases as the Li content increases and the

extraction from Li atoms is about five times higher when the

Li layers are distant apart (type 2 arrangement). We find that

0.036 e/C and 0.057 e/Li are extracted from C and Li, respec-

tively, and deposited into the interstitial region for LiC6. These

values compare well with the values of 0.03 e/C and 0.07 e/Li as

obtained by Hartwigsen et al. [13] for this system.

The latter method of charge transfer analysis is not able to

capture any changes that may occur within each plane paral-

lel to the graphene sheets. In fact, on inspection of Figs. 5 and

6 we notice that at about 0.1 A away from a graphene sheet of

LiC18, a complex charge transfer takes place. The C–C bonds

of the C6 rings located above and below the Li atoms experi-

ence a charge depletion of about �0.03 e/A3 while about

+0.02 e/A3 accumulates on these C atoms. A better insight

−0.04

−0.02

0

0.02

0.04

0 0.5 1

LiC36

−0.2

−0.15

−0.1

−0.05

0

0.05

0.1

0.15

0 0.5 1z/c

LiC12

ms. The vertical lines indicate the positions of the Li atoms.

an functions each of which is assigned to one of three layers:

−0.1

−0.08

−0.06

−0.04

−0.02

0

0.02

0.04

0.2 0.4 0.6 0.8 1

Δρ (e

/ato

m)

x in Lix C6

Fig. 14 – Net charge transfer in LIG (LixC6) systems as a

function of Li content x: interstitial (circles), graphitic

(squares) and lithium (triangle). Open triangles are for

systems in which Li linear chains are formed (type 1 Li

arrangement) and filled triangles when Li chains are not

present (type 2 Li arrangement). Negative (positive) numbers

mean charge depletion (accumulation).

C A R B O N 4 7 ( 2 0 0 9 ) 2 5 0 1 – 2 5 1 0 2509

into the charge transfer on the carbon atoms of these C6 rings

can be obtained by inspecting the charge density difference

along a line parallel to the c-axis and passing through one

of the carbon atoms of these rings. This charge density as a

function of distance from the atom and for various Li con-

tents is shown in Fig. 15 and clearly shows that charges accu-

−0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 0.2 0.4 0.6 0.8 1 1.2 1.4

ΔρC

(e/Å

3 )

Distance from C−plane (Å)

A B

Lix C6: x=1

x=2/3

x=1/2

x=1/3

x=1/6

Fig. 15 – Charge transfer on the C atoms of the C6 hexagon

below and above the Li atom of LIG (LixC6) systems as a

function of Li content x. Negative (positive) numbers mean

charge depletion (accumulation).

mulate on these C atoms. For type 1 intercalation, these

charges extend to distances of about 1 A above and below

the carbon atoms and pass through a maximum at a distance

of about 0.3 A, meanwhile for type 2 intercalation the charge

distribution passes through two maxima: one at �0.20 A and

a second broader one at �0.9 A.

4. Summary

Within the core-hole implementation, we have shown that

the main changes in the C and Li 1s ELNES spectra can be

accurately described. A feature showing up in the Li 1s spec-

trum at about 13 eV above threshold is found which can be

used to characterize the stagings in LIG systems. We have

found that, depending on the microscope settings, the di-

pole-forbidden 1s! 2s ELNES transitions in Li can be very

important compared to the dipole allowed 1s! 2p transi-

tions. Charge transfer quantification based on C 1s ELNES

spectroscopy is seen to be inaccurate if core-screening cannot

be explicitly quantified. Based on the density of states, we

have found that Li gives up its entire 2s electron when it is

intercalated into graphite.

Acknowledgements

We acknowledge financial support from the FWO-Vlaanderen

under contract G.0425.05 and the Deutsche Forschungemeins-

chaft under contract number RO2057/4-1. The authors also

acknowledge financial support from the European Union un-

der the Framework 6 program under a contract for an Inte-

grated Infrastructure Initiative, Reference 026019 ESTEEM.

Calculations have been performed on the Calcua supercom-

puter of the University of Antwerp.

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