Structural and Electronic Properties of Graphite and Graphite

Aug 1, 1994 - Block Copolymer Monolayer Structure Measured with Scanning Force Microscopy Moiré Patterns. Alexander Hexemer, Gila E. Stein, Edward J...
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J. Phys. Chem. 1994,98, 7602-7607

Structural and Electronic Properties of Graphite and Graphite Intercalation Compounds MCs (M = K, Rb, Cs) Governing Their Scanning Tunneling Microscopy Images M.-H. Whangbo,’ W. Liang, and J. Ren Department of Chemistry, North Carolina State University, Raleigh, North Carolina 27695-8204

S. N. Magonov’ and A. Wawkuschewski Materials Research Center, Albert-Ludwigs University, Stefan-Meier-Str. 31A, 0-79104 Freiburg, Germany Received: February 14, 1994; In Final Form: May 3, 1994’

Several puzzling observations in the scanning tunneling miucroscopy (STM) and atomic force microscopy (AFM) studies of highly oriented pyrolytic graphite (HOPG) and its intercalation compounds MCg ( M = K, Rb, Cs) were investigated on the basis of atom-atom potential and Coulombic interaction energy calculations. The charge or spin density wave state of a graphite monolayer is found inconsistent with an identical peak registry of the HOPG STM images obtained at plus and minus bias voltages. Simultaneous STM/AFM measurements of HOPG show the STM and AFM images to have an identical peak registry, which implies that the local hardness of the surface monolayer is larger at the B-site than at the A-site. We confirm this implication by estimating the local hardness in the surface monolayer of a graphite bilayer in terms of atomatom potential calculations. The essential characteristics of the Moire STM images of HOPG are correctly predicted by the local hardness map obtained for the surface monolayer of a graphite bilayer in terms of atom-atom potential calculations. This supports the notion that the tip-force-induced topography change in the surface monolayer is generally responsible for Moire STM patterns in layered materials. It is most likely that the surface charge density wave (CDW) of MCg (M = K, Rb, Cs) observed by STM is associated with the P band electrons of the surface graphite monolayer and is not caused either by a Fermi surface nesting driven electronic instability or by a possible topography change induced by the tip force. We calculate the Coulombic interaction energy of the surface KCg blayer for several different negative charge (transferred from K) distributions in the graphite monolayer. This energy is increasingly lowered when the charge distribution becomes more nonuniform, thereby suggesting that the surface CDW of MCg ( M = K, Rb, Cs) occurs most likely to lower the Coulombic interaction energy in the surface MCg bilayer.

Introduction Scanning tunneling microscopy (STM) and atomic force microscopy (AFM) have become important tools for surface analysis.’ Over the years, the (0001) surface of highly oriented pyrolytic graphite (HOPG) has been a subject of numerous STM and AFM investigations. Adjacent layers of HOPG are arranged in such a way that there occur two types of carbon atoms on the surface layer (Figure 1): the A-site carbon atoms lie directly above the carbon atoms of the underlying layer, and the B-site carbon atoms are located above the centers of the carbon hexagons of the underlying layer. Most STM images of HOPG show a hexagonal pattern of bright spots, which represent three nonadjacent carbon atoms for each carbon hexagon forming the surface graphite layer. This “three-for-hexagon” pattern is accounted for in terms of the interlayer interactions in HOPG, which make the P electron band levels around the Fermi level (ef) moreconcentrated on the B-site than the A-sitecarbon p,orbitals.* According to this explanation, theSTM images of stage-1 graphite intercalation compound (GIC), MCs (M = K, Rb, Cs), should show all the carbon atoms of the surface graphite monolayerZb because all of them are equivalent. However, the STM images of KC8 exhibit a three-for-hexagon att tern^.^ and so do the STM images of the graphite monolayer on Pt( 11l).5 This observation led to the suggestion6 that the three-for-hexagon STM pattern might originate from a charge density wave (CDW) or spin density wave (SDW) state of a graphite monolayer. To resolve which of the two explanations, one based on the CDW/SDW state of a monolayer and the other based on the Abstract published in Aduance ACS Abstracts, July 15, 1994.

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Figure 1. (a, top) Schematic projection view of two adjacent layers of HOPG.The C-C bonds of the top and underlying layers are represented by solid and dashed lines,respectively, and the B-site atoms are represented by filled circles. (b, bottom) Schematic side projection view of three consecutive graphite layers of HOPG.

interlayer interactions, is appropriate for HOPG, it is necessary to ask whether the two explanations give rise to different predictions that can be tested by experiment. Despite extensive studies, several important STM/AFM results of HOPG and GIC‘s have not yet been well understood. The STM image of stage-1 GIC MC8 (M = K, Rb, Cs) reveals a 2 X 2 superstructure superposed onto a three-for-hexagon pattern.3.4 That the 2 X 2 superstructure cannot correspond to a direct view of alkali metal Q - 1994 American Chemical Societv

Graphite and Graphite Intercalation Compounds sites was shown by Kelty and Lieber,sa+ who first suggested that the 2 X 2 superstructure may correspond to a CDW state of the surface graphite monolayer. This possibility was also discussed in the studies of Anselmetti et al." It has been speculated3b that the CDW state may be associated with the nondispersive states near er observed for KCs7 and CSCs8 by the angle-resolved photoelectron spectroscopy (ARPES) studies. Nevertheless,why such a CDW state should occur remains unclear. Simultaneous STM/AFM measurements9 of HOPG carried out with constantcurrent mode at ambient condition show that the AFM and STM images have a three-for-hexagon pattern with an identical peak registry. Implications of this important observation have not been fully explored. Occasionally,STM images of HOPG present a superstructure of hexagonal symmetry,1° which has been explained by referring to the Moire patterns generated when two adjacent graphite monolayer are rotated with respect to each other. The mechanism of how such geometrical arrangements cause the Moire patterns in the observed STM images is not well understood. In the present work, we attempt to answer these questions by analyzing relevant experimental STM/AFM results in the literature and also by performing Coulombic interaction energy and atom-atom potential calculations for appropriate model layer systems. The important basis of our discussion is that, to a first approximation, the STM image of a surface is well described by the partial density plot p(r0,er) of the surface" and the AFM image by the total density plot p(ro), where ro is the tipsurface distance. The p(rber) plot is associated with only those electron levelsin theimmediatevicinityofef,and thep(r0) plot isassociated with all the occupied electron levels. In interpreting the STM and AFM images of various layered materials,l*-l4 the p(ro,ef) and p(r0) plots calculated by the extended Hiickel tight binding (EHTB) electronic band structure method15 have been indispensable. However, what these density plots represent are "ideal" images. Tip-surface interactions might bring about a delicate change in the observed STM and AFM image patterns, because the tip can exert a strong mechanical force to the surface, thereby altering the surface topography.9 Indeed, for the interpretation of the STM and A M images of layered transition metal tellurides MA,Te2 (M = Nb, Ta; A = Si, Ge), the analysis based on p(ro,er) and p(r0) plots is insufficient, and it is necessary to take the local hardness of the surface layer into consideration.16 Consequently, as pointed out earlier,17a comprehensiveimage analysis requires the considerationof both the electronic and local hardness effects.

Three-for-Hexagon STM Pattern of HOPG The s electron band levels of HOPG in the vicinity of er are more concentrated on the p,, orbitals of the B-site than the A-site carbons,2becausethe p,orbitalsof the A-sites have u interactions through the interlayer C-C contacts while those of the B-sites experience no such interactions. Consequently, the p(er,ro) plot for HOPG has a greater density on the B-site carbons not only for the surface-to-tip but also for the tipto-surface tunneling.2 Thus, according to the interlayer interactions, the three-forhexagon patterns obtained for plus and minus bias voltages (Vbias) are predicted to have an identical peak registry, as confirmed by Tomanek et al.2 A CDW or SDW state of a low-dimensional metal typically arises from the electronic instability associated with its nested Fermi surface.'* A graphite monolayer does not have such an electronicinstability, because its Fermi surface is given by a single k-point. For the metallic state of a graphite monolayer,all atoms are equivalent, but it is still convenient to refer to the two sets of nonadjacent carbon atoms as A- and B-site carbon atoms. Tchougreeff and Hoffmann considered6 the CDW and SDW states of a graphite monolayer by treating the ?r electrons with a Hubbard Hamiltonian. In general, the occupied orbitals of the CDW or SDW state of a low-dimensional system have an out-

The Journal of Physical Chemistry, Vol. 98, No. 31, 1994 7603 of-phase relationship with theunoccupied orbitals in thevariation of their orbital amplitudes in real space.'* Thus, provided that the CDW state of a graphite monolayer has a greater electron density on the A-sites, the occupied levels have a greter weight on the A-site p,, orbitals, but the unoccupied levels on the B-site p,, orbitals. Consequently, the p(r0,er) plot of the CDW state for the surfaceto-tip tunneling ( Vbiaa < 0) should have a higher density on the A-sites, but that for the tip-to-surface tunneling (Vbi, > 0) must havea higher densityon theB-sites. Thesameconclusion is also reached for the SDW state of a graphite monolayer (in terms of spin orbitals). Thus, according to the CDW or SDW state of a graphite monolayer,the three-for-hexagonSTM patterns of HOPG obtained for plus and minus Vbm must not have an identical peak registry. This prediction does not agree with experiment. As a result, the three-for-hexagon pattern of HOPG is not caused by a CDW or SDW state of a graphite monolayer but by the interlayer interactions.

Identical Peak Registry in Simultaneous STM/AFM Measurements SimultaneousSTM/AFM measurementsgof HOPG show that, under typical ambient tunneling conditions, significant repulsive forces acting in the compression modes are more the rule than theexception. (Incidentally, the study of Mate et ala+ motivated in part to understand the "giant corrugations" observed by STM, strongly suggests that a large apparent corrugation of -20 A is probably caused by a weak spring element such as a whisker on the end of the tip.) As the tip initially approaches the surface, the tip experiences repulsive forces before detecting a tunneling current,ga and the repulsive force the tip experiences is in the range 10-6-10-7 N.7 The latter is at least 1 order of magnitude greater than the repulsive force typically employed in contactmade AFM measurements. The STM and AFM images of HOPG obtained from simultaneous STM/AFM measurementsg have a three-for-hexagon pattern with an identical peak registry. Consequently, the bright spots of the AFM images, where the tipsurface repulsive interaction is strong, coincidewith the highdensity spots of thep(ro,ef) plot of HOPG (Le., the B-sites), where the bright spots of the STM images are found.2 The three-forhexagon AFM pattern in these simultaneousSTM/AFM experiments (with a constant-current mode) can be accounted for by taking into consideration the mechanical force the tip exerts to the surface,9J9provided that the surface topography is modified according to the local hardness variation by the mechanical force transmitted through the contamination layer. This reasoning leads us to conclude that the B-site is depressed less than the A-site by the tip force; Le., the B-site is harder than the A-site. Tipsurface interactions for HOPG have been the subject of several first-principleelectronicstructure calculations." The force responsesof theatomicand the hollow (Le., thecarbon-ring center) sites of the surface graphite monolayer, when an atomic tip is placed over them, have been studied in terms of an A1 atom tip2h These studies reveal that the repulsive and an Pd atom force the tip atom feels is stronger over the atomic sites than over the hollow sites. The topography change of the HOPG surface under the tip force has been examined in terms of empirical potential functions.21 In those studies, however, the difference in the force responses of the A- and B-sites was not examined. Let us now estimate the local hardness of the A- and B-sites in the HOPG on the basis of the atom-atom potential,22E = -A+ B exp(-Cr), for a nonbonded C-C contact of distance r. (E is in kcal/mol with r in angstroms, A = 568,B = 83 630, and C = 3.60.) The interlayer distance of 3.35 A in bulk HOPG is well reproduced by this potential. For simplicity, we estimate the local hardness of the A- and B-sites in the surface graphite monolayer on the basis of a graphite bilayer. What matters eventually for the STM and AFM imaging is the topography change in the surface layer induced by the tip force. Thus, we

+

7604 The Journal of Physical Chemistry, Vol. 98, No. 31, 1994

Whangbo et al.

TABLE 1: A&('), AEB(O),Ar, and A& Values Calculated as a Function of Azo (for Azl = 0) 0

E

I

0.1 0.2 0.3 0.4 0.5

0.13 0.40 0.87 1.61 2.77

0.09 0.29 0.65 1.23 2.13

0.004 0.014 0.03 1 0.055 0.086

0.005 0.075 0.37 1.16 2.78

are not concerned with the "macroscopic" bending of the HOPG sample*' under the pressure of the tip and its contamination layer but rather with the relative depression in the surface monolayer, so that the geometry of the bottom layer of the graphite bilayer can be assumed to be frozen. Interesting quantities to calculate are the energy needed to depress one A-site carbon atom, and also needed to depress one B-site carbon atom, of the surface layer vertically by AZOtoward the underlying layer while keeping all the remainingcarbon atom positionsfured. The AE.t,(O) and values calculated as a function of Azo are summarized in Table 1, which reveals that, for a given amount of energy supplied, the B-site carbon can be depressed more than the A-site carbon, and the difference in their depressions is smaller than 0.05 A. To achieve the same extent of depression, the A-site requires more energy, and is therefore harder, than the B-site. Apparently, this finding based on the AE.t,(O) and A E B ( O ) values contradicts the conclusion derived from the simultaneous STM/ AFM measurements. All carbon atoms are linked by the C-C bond network, and the stretching of the C-C bond raises its energy. Thus, the depression of one carbon atom (A- or B-site) directly under the tip atom by AZOwill induce that of its three first-nearest-neighbor (FNN) carbon atoms by Azl, that of its six second-nearestneighbor (SNN) carbon atoms by Azz, and so on, eventually forming a circular region of depression under the tip atom. The C-C bond length (- 1.42 A) of the graphite layer is not large compared with the atomic radii of the metal atoms Pt and Ir (1.39 and 1.36 A, respe~tively)~~ constituting the tip. Therefore, for the ideal case when the tip end is given by a single atom, the depression effect of the tip force must be strongly felt by the four adjacent carbon atoms, i.e., the carbon atom lying directly under the tip atom plus its three FNN carbon atoms (Le., AZO Azl > Az2 > On the basis of a graphite bilayer, we calculate the energy AEA(l) needed to depress one A-site atom of the surface monolayer by Azo and its three FNN B-site atoms by &I, with the positions of all other atoms frozen, for several values of the ratio Azl/Azo. Likewise, we calculate AEg(l) needed to depress one B-site atom of the surface monolayer by AZO and its three F" A-site atoms by Azl. Figure 2 plots the hardness of the B-siterelative to that ofthe A-site (Le., AE#)-AEA(I)) calculated as a function of Azl/AZo for Azo = 0.3 A. Now the B-site is calculated to be harder than the A-site (Le,, P A H I ) > 0), in agreement with experiment, since the Azl/Azo is expected to be close to unity because the C-C bond length and the tip atom radius are comparable in magnitude. For a Csp2-Cspzbond, the bond stretch by Ar (angstroms) is estimated to increase the bond energy by AE,,,= 379.8(ArI2 (kcal/mol).24 For AZl = 0, the Ar value of the graphite C-C bond varies with the AZO value as listed in Table 1. The AE,,, valuescalculated (for AZl= 0) as a function of Azo are summarized in Table 1. When AZO< -0.2 A, Us,, is negligible compared with AEA(l)and AEg(l), because Ar is very small. When Azo > -0.3 A, AE,,,becomes close to, and eventually becomes larger than, AEA(l)and AE#). Thus, for AZO> -0.3 A, the depression of one carbon should induce that of its three FNN atoms, that of its six SNN atoms, and so on, even if it is imagined that only the carbon atom right underneath the most protruded tip atom is depressed. The experimental finding that the B-site is harder than the A-site on the surface of HOPG is understandable if the

-

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0

u

Y

Y

r

w a a

A2(IAZo

Figure 2. Relative repulsive energy, ANI(') = A&(') calculated as a function of A . q / A z o for b o = 0.3 A. Positve A M ( ' ) values mean that the B-site is harder than the A-site.

most protruded tipatomexerts force to thesurfacemainly through the carbon atom lying directly underneath plus its three F" carbon atoms so that Azo Az1 > Azz > -.

-

MoirC Pattern and Tip-Force-Induced Topography Change The contribution of an atom to a p(r0,er) plot, and hence the associated STM image, increases with decreasing its distance to the tipand with increasingits electroniccontribution to the energy levels around er. p(ro,et) plot calculations for a variety of layered compounds12-14 show that, when the subsurface atoms lie more than 1A below the surfaceatoms, theSTM patterns aredominated by the topmost surface atoms even when the energy levels around ef are dominated by the subsurface atoms, because an atomic orbital amplitude decreases exponentially with increasing distance from the nucleus. Therefore, in terms of electronic contributions directly affecting the tunneling current, the MoirC STM pattermlo of HOPG can only be associated with the surface graphite monolayer,and for the Moire pattern to occur,the surface graphite monolayer cannot remain flat as in bulk HOPG. For similar reasons, it has been suggested17for layered materials with Moire STM patterns that the mechanical force exerted by the tip alters the topography of the surface layer according to its local hardness variation, and the imaging of the altered surface layer is responsible for the Moire patterns. When the surface graphite monolayer is slightly rotated with respect to the underlying graphite lattice, the surface-layer carbon atoms, being under a number of different environments, must possess different hardness. Thus, the local hardness map of the surface monolayer is expected to have a Moirb pattern. The harder atomic site will be depressed less under the tip force, so that theimaging of a modified (dynamically during thescanning) surface will give rise to a Moird STM pattern, with the harder site appearing as a brighter spot. To examine this feasibility, we calculate the hardness map of the surface graphite monolayer on the basis of a graphite bilayer, in which the top layer is rotated by a small angle I9 with respect to the bottom layer. The period D of the Moire pattern is related to the period d (2.46 A) of the graphite layer and the rotation angle I9 by D = d/(2 sin 19/2).1& For our study, a graphite bilayer with the Moire pattern of 8 = 4.7O and D = 30.0 A was chosen (Figure 3a), and each graphite layer was represented by a graphite sheet of rhombus shape made up of 1536 carbon atoms. We obtain the map of the repulsive energies, AE(I),by calculating the values at all the carbon atoms of the surface layer (with AZO= 0.3 A and A Z l / A z o = 0.8) and also the map of the associated repulsive forces the tip feels when it compresses the surface (as defined by A z o = 0.3 A and AZI/AZo= 0.8). The force map of the surface monolayer thus obtained is shown in Figure 3b, where the large, medium, and small (dotlike) circles represent the atoms with small, medium, and large repulsive forces, respectively. The atom site with the

The Journal of Physical Chemistry, Vol. 98, No. 31, 1994 7605

Graphite and Graphite Intercalation Compounds

will diminish. This in turn will decrease the contrast difference of the local hardness map and hence that of the associated Moire STM image. Indeed, by increasing Rep from 12.9 to 95.5 MQ, Rong and Kuiper foundlb not only a substantial decrease in the contrast difference between the brightest and darkest regions but also the loss of a clear distinction between the darkest and intermediate brightness regions. All these results are in support of our earlier suggestion17 that, for the Occurrence of Moirt patterns in the STM images of layered materials and overlayers on different substrates, the tip-force-induced topography change of the surface monolayer is essential. Finally, we comment why the hexagonal Moirt STM images of HOPG have the three-for-hexagon pattern in the darker as well as in the brighter regions. This is explained if two or more top graphite layers are rotated with respect to the underlying graphite lattice, so that the top layers possess such interlayer interaction as found in HOPG.

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Figure 3. (a, top) MoirC pattern of 0 = 4.7O and D = 30.0 A generated by two adjacentgraphite layers of rhombusshape made up of 1536 carbon atoms. (b, bottom) Map of the repulsive forces for the Moird bilayer in (a). The large, medium, and small (dotlike) circlesrepresent the contour values of 1.71 X 10-10, 1.82 X and 2.09 X 1@*0 N, respectively. These forces are small in absolute value, because they are based only on the interlayer C--C interactions. For our discussion of the relative magnitudes of the local forces, the neglect of the C-C bond stretching effect on the forces, which accompanies the surface atom depression, is not significant. The MoirC pattern deviates slightly from a hexagonal symmetry because the graphite layers of limited size were used in our calculations.

greater repulsive force resists the compression effect of the tip force more strongly. Thus, the hardest region of the map (i.e., that composed of mostly the large repulsive force sites) has the interlayer arrangement in which the carbon rings of the adjacent layers are mostly eclipsed (cf. Figure 3a,b). The softest region (Le., that consisting of mostly the small repulsive force sites) has the interlayer arrangement resembling that of HOPG (cf. Figure 3a,b), and the region of intermediate hardness is found in between every two adjacent softest regions. Clearly, the variation of the local repulsive force, and hence that of the local hardness, in the surface graphite monolayer exhibits a hexagonal Moirt pattern. The harder region is less depressed under the tip force, represents the higher-lying zone of the corrugated surface induced by the tip force, and hence becomes the brighter domain of the Moire STM pattern. Consequently,the map of the local hardness in Figure 3b predicts a Moirt STM image containing three regions of different contrast: the brightest domains forming a hexagonal pattern, the darkest domains around each brightest ones forming honeycomb pattern, and the intermediate domains in between every two adjacent darkest domains also forming a honeycomb pattern. This prediction is in good agreement with the experimental result of Rong and Kuiper.*b The tipsurface distance ro decreases with decreasing the gap resistance Rep = Vbias/zwr where Zsctis the set-point current. The extent of the tip force exerted to the surface should increase with decreasing ro, Le., with decreasing Reap. Therefore, as Rep increases, the extent of the height corrugation in the modified surface topography by the tip force

CIC MCS (M = IC, Rb, Cs)

The STM images of stage-1 GIC MCa (M = K, Rb, Cs) exhibit a 2 X 2 superstructure superposed onto a three-for-hexagon pattem.3~~ [In addition to the 2 X 2 superstructure, I / 3 X 4 and 4 3 X 1/13 superstructures are also found for stage-1 GIC MC8 (M = Rb, CS).~~."] However, the STM images of stage-2 potassium GIC, KC24, whose surface is given by a graphite bilayer, show the same three-for-hexagon pattern as found for HOPG.30 Consequently, the 2 X 2 superstructure STM images of MCs reflect the electron density distribution of its surface graphite monolayer;" i.e., the surface graphite monolayer of MC8 is in a certain CDW state responsible for the observed STM images, as suggested by Kelty and Lieber.3b Whether or not a complete charge transfer occurs from K atoms to the graphite layers in KC8 has been controversial in terms of both electronic band structure calculations25 and experimental results.8 The angle-resolved photoelectron spectroscopy (ARPES) studies of KCs7and CsCa8reveal the presence of the r band as well as nondispersive states near ef. It has been s p e c ~ l a t e d ~that ~ * ~the J nondispersive states may originate from the "interlayer" state of bulk KC8 found in some electronic structure calculations26and that the surface CDW state observed by STM may be associated with the nondispersive states.3b We now examine a probable origin of the surface CDW state of MC8 (M = K, Rb, Cs) by considering KCs as a prototype example. As already pointed out, an atomic orbital amplitude decreases exponentiallywith increasing distance from the atomic nucleus, and the K atoms of KC8 closest to the tip lie -2.68 A below the surface graphite m0nolayer.2~ Thus, the STM image of KC8 cannot be associated with the K 4s orbitals, nor with the 'interlayer" state, even if present around er for bulk KCs, because it cannot exist above the surface graphite monolayer. Therefore, the STM image of KCs must be associated with the pI orbitals of the surface graphite monolayer, and consequently, the STM image of KC8 means that the additional electrons in the surface graphite monolayer, transferred from K, is not uniformly distributed. The Fermi surface of bulk KC8 or a KCs bilayer does not possess a proper nesting, and hence the associated electronic instability, to explain the surface CDW pattern of KC8. The low-energy electron diffraction pattern of KCs does not show any contrastedsuperstructure,28so that thesurface graphite monolayer is probably almost flat. However, asdescribedearlier, the surface topography can change under the tip force. According to the crystal structure of bulk KC8, there are two kinds of carbon atoms in the surface graphite layer, Le., those of the carbon rings lying above the K+ ions and each carbon joining three such carbon rings ( F i g ~ r e 4 ) .Thus, ~ ~ the compression of the surfacemonolayer by the tip force can generate a 2 X 2 superstructure in which all six carbons of each ring above K+ are equally protruded out with

7606 The Journal of Physical Chemistry, Vol. 98, No. 31, 1994

Whangbo et al.

TABLE 2 Coulombic Energy ( k and) On-Site Repulsion Energy (E,,..,d of a KCa Bilayer Calculated for the Point Charge Distributions 1-5 in the Graphite Monolayer

1 2 3

Figure 4. Schematic representation of the 2 X 2 arrangement of the K+ ions in KC8.

ct.w? (2)

(3)

( 11

(4) (5) Figures. Model point chargedistributions1-5 in the graphite monolayer carbon atoms of a KCa bilayer. Only the unit cell carbon atoms are shown, and the K+ ions (not shown) is located underneath the center of the carbon hexagon. Only the carbon atoms with negative charge are

shown by filled circles, with the larger circle representing the greater negative charge. The negative charges in 1 4 are as follows: 1 (each carbon with -1/8), 2 (four carbons with -1/4), 3 (twocarbonswith-1/4 and one with -1/2), 4 (two carbons with -1/8 and one with -3/4), and S (one carbon with -1). respect to each carbon joining three such rings. Such a 2 X 2 superstructure is qualitatively different than the observed 2 X 2 superstructure superposed onto a three-for-hexagon pattern (see bel~w).~a-C Therefore, a possible tip-force-induced topography changecannot explain the surface CDW state of KC8. [However, the 4 3 X 4 and 43 X 13 superstructures observed3a." for stage- 1 GIC MC8 (M = Rb, Cs) are explained in terms of the onedimensional ordering of the alkali metal atoms suggested by Anselmetti et al.," provided that the surface graphite monolayer undergoes an appropriate tip-force-inducedtopography change.] To understand why the formation of the surface CDW is energetically favorable, it is important to examine the ionic interactions between the negatively charged surface graphite monolaye and the underlying potassium ions K+. (For simplicity, a complete charge transfer from K may be assumed.) Since KC8 is a normal metal, the charge distribution in the graphite layer should be nonmagnetic; i.e., the up-spin density n t and thedownspin density nl on each carbon site are the same. We calculate the Coulombic energies @coulomb) of a KC8 bilayer for several nonmagnetic charge distributions depicted in Figure 5 : 1 has the uniform charge distribution, 2 has the three-for-hexagon pattern, 3 and 4 have a three-for-hexagon pattern with a 2 X 2 superstructure, and 5 has a 2 X 2 superstructure with no threefor-hexagon pattern. As summarized in Table 2, the ,!?coulombvalue of a KC8 bilayer becomes more favorable for a more nonuniform charge distribution and is attractive only for the strongly nonuniform charge distributions 4 and 5. This reflects the fact that, in the surface KC8 bilayer, a nonuniform charge distribution in the graphite layer reduces the Coulomb repulsion within the graphite layer. Also, the Coulomb attraction between the graphite and the K+ ion layers is less favorable when the charge is placed on the carbon

1.I59 0.780 0.212

2.531 2.563 2.594

4

S

-0.689 -2.362

2.648 2.750

atoms outside the carbon hexagon lying directly above each K+. It should be noted that 4 resembles the charge distribution of the surface graphite monolayer expected from the STM image of KC8. One energy term disfavoring a nonuniform charge distribution is the on-site repulsion because, at a site with n t and nl electrons,it is given by ntnl U. Here Uis the repulsion expected when two electrons reside on the atom. Table 2 lists the total on-site repulsion (Eon-sitc) energies calculated for the graphite monolayer with the point charge distributions 1-5. Clearly, in terms of on-site repulsion, the more nonuniform charge distribution is less energetically favorable. In terms Of Eon-sitc and ,!?coulomb alone, 4 and 5 are predicted to be more stable than 1, because the U value for carbon is estimated to be smaller than 11 eV.2 According to the above discussion, the surface CDW state of KC8 observed by STM is associated with the T band electrons of the surface graphite monolayer, occurs to lower the Coulombic interaction energy associated the surface KC8 bilayer, and is not related to the fiat-band states near ef observed by the ARPES studies. The STM images of KC8 obtained for plus and minus Vbias have an identical peak registry.3b This is not surprising because the carbon atoms with different charge densities will have nonidentical effective potentials. Thus, their pr orbital coefficientsin the T bands will differ accordingly, and their relative contributions will not change in the vicinity of ef (either above or below ef).

Concluding Remarks The STM images of HOPG for plus and minus vbiu have an identical peak registry, which is not explained by the CDW or SDW state of a graphite monolayer but by the interlayer interactions. The STM and AFM images of HOPG obtained from simultaneous STM/AFM experiments have an identical peak registry, thereby suggesting that the local hardness of the surface monolayer is larger on the B-sites than on the A-sites. In terms of atom-atom potential calculations, this finding is reproduced provided that the most protruded tip atom primarily affects the carbon atom lying directly underneath plus its three F"carbon atoms. This assumption is reasonable, because the C-C. bond length of the graphite monolayer is comparable in magnitude with the radii of the atoms constituting the tip. In terms of electronic contributions affecting the tunneling current, the Moire patterns of HOPG can only be associated with the surface graphite monolayer. It is the tip-force-induced topography change of the surface monolayer that can give rise to the Moir6 patterns. The local hardness map of the surface monolayer, obtained on the basis of atom-atom potential calculations for a graphite bilayer with a model Moird pattern, correctly predicts all the essential characteristics of the observed hexagonal Moirt STM images of HOPG. What is essential for Moird STM patterns to occur in layered materials and mismatched layered systems is a tip-force-induced topography change in the surface layer according to its local hardness variation. The d3 X 4 and d3 X 4 1 3 superstructures of stage-1 GIC MC8 (M = Rb, Cs) are explained in terms of the one-dimensionalordering of the alkali metal atoms suggested by Anselmetti et ai.," if the surface graphite monolayer undergoes an appropriate tip-forceinduced topography change. The "wagon wheel" Moir6 patterns observed for MoSez layers grown on a MoSz substrate29 can be

Graphite and Graphite Intercalation Compounds explained in a similar manner. The MoSe6 trigonal prisms of an MoSe2 overlayer will be in a number of different environments due to the lattice mismatch (5%) with the underlyingMoS2 layer. In general, a tip-force-induced surface relaxation provides a natiral explanadon for Moirt patterns found in the STM images of various layered compound^.'^ Dueto theexponentialdecreaseoftheatomicorbital amplitude, the surface CDWstate of GIC MCg (M = K, Rb, Cs) represented by its STM image must originate from the r band of the surface graphite monolayer. This surface CDW cannot be caused by a Fermi surface nesting driven instability, nor by a possible t i p force-induced topography change in the surface graphite monolayer. The surface CDW state is most likely caused by the Coulombic interactions in the surface MCg bilayer, because the energy of these interactions is increasingly lowered when the distribution of the negative charge (transferred from M) in the surface graphite monolayer becomes more nonuniform. Except for the hexagonal Moirt pattern, the STM images of the graphite monolayer on Pt(ll1) are very similar to those of HOPG in their three-for-hexagonpatterns. It will be interesting to investigate whether the CDW or SDW state of a graphite monolayer is responsible for this observation. If so, the STM images for plus and minus VM,should not have an identical peak registry. Alternatively,the STM images may be due to a surface CDW state, which might be induced by a charge transfer between the graphite monolayer and the pt( 111) surface. Then, the STM images for plus and minus VM, are expected to have an identical peak registry. It is crucial to examine the peak registry of the STM images for plus and minus Vbbs.

Ackmwledgment. The workat North Carolina State University was supported by the Office of Basic Energy Sciences, Division of Materials Sciences, U S . Department of Energy, under Grant DE-FG05-86ER45259, M.-H.W thanks Dr. S. P. Kelty for invaluable discussion. References and Notes (1) For r a n t reviews, see: (a) Scunning Tunneling Microscopy, I; Wiesendanger, R., GUntherodt, H.-J., Eds.;Springer-Verlag: Heidelberg, 1992. (b) Scunning TunnelingMicroscopy,Ik Wiarendanger, R., GUntherodf H.-J. Eds.; Springer-Verlag: Heidelberg, 1992. (cj Scunning Tunneling Mlcrarcopy, Ilk Wiesendanger, R., GUntherodt, H.-J., Eds.; SpringerVerlag: Heidelberg, 1993. (2) (a) Tominek, D.; Louie, S.G.; Mamin, H. J.; Abraham, D. W.; Thompson, R. E.; Gram, E.; Clarke, J. Phys. Rev. B 1987,35, 7790. (b) Tomhek, D.; Louie, S . G. Phys. Rev. B 1988,37,8327. (3) (a) Kelty, S.P.; Lieber, C. M. Crit.Rev. Surf. Sci. 1992,1,217.(b) Kelty, S.P.; Lieber, C. M. 1.Phys. Chem. 1989,93,5983. (c) Kelty, S.P.; Licber, C. M. Phys. Rm. B 1989,40,5856. (d) Kelty, S.P.; Lieber, C. M. Phys. Rev. B 1991, 44,4064. (4) (a) Anselmetti, D.; Wiesendanger, R.; Geiser, V.; Hidber, H. R.; GUntherodt, H.-J. J. Microsc. 1988,152,509.(b) Anselmetti, D.; Witsendanger, R.; GUntherodt, H.-J. Phys. Reu. B 1989,39,11135. (c) Anselmetti, D.;Geiser, V.; Overney, G.; Witsendanger, R.;Giinthcrodt, H.-J. Phys. Rev. B 1990,42,1848.(d) Wiesendanger, R.;GUntherodt, H.-J. In ref la, p 131. ( 5 ) Land, T. A.; Michely, T.; Behm, R. J.; Hemminger, J. C.; Comsa, G. Surf. Sci. 1992,264,261.

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