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Diamond-graphite hybrids
CHEMICAL PHYSICS LETTERS
Volume 2 17, number 3
Diamond-graphite
hybrids
A.T. Balaban
and C.A. Folden
‘, D.J. Klein
14 January 1994
Department of Marine Sciences, Texas A and M University at Galveston, Galveston, TX 77553-1675. USA Received 17 September 1992; in final form 10 September 1993
The possibility of a general multifold class of novel allotropic forms of carbon is suggested. They consist of cubic or hexagonal diamond blocks or layers interconnected by blocks or layers of “graphitic” strips. Some simple consequences are noted with special attention to the possibility of electrical conduction along the “graphitic” strips.
1. Introduction There has long been an interest in novel three-dimensional carbon networks, with several theoretical proposals [ l-8 ] of possibilities. Like the finite buckminsterfullerene structure (which too was [ 91 first theoretically considered) most proposals for threedimensional networks have been based upon sp*-hybridized carbons, each with two single bonds and one double bond. Particular interest has focused on highdensity [ 5 ] and energetic [ 6 ] forms of carbon. Also recently [ 7,8 ] three-dimensional carbon networks with a mixture of sp*- and sp’-hybridized carbons have been considered. Here we propose a different multifold class of structures with both sp*- and sp3-hybridized carbons. The idea bears some analogy to that of blockcopolymers - one can conceive of fragments of the diamond lattice connected to fragments of the graphite lattice. The two forms of diamond (cubic and hexagonal, called henceforth for brevity diamond and isodiamond) have cleavage planes with rows of dangling coplanar bonds which may be attached to edges of graphite planes. Such edges may be of an scenic type or of a corrugated (or “tibonscenic” as for phenanthrene, chrysene, picene, etc.) type. With parallel cleavage planes from the diamond (or isodiamond) lattice one then obtains (iso ) diamond blocks or layers covalently interca’ Permanent address: Polytechnic Institute, Department of Organic Chemistry, Bucharest, Roumania. 266
lated between graphitic material. In turn blocks or layers of strips of the graphitic material are intercalated between the (iso)diamond layers. Two possibilities with diamond-layers of widths 1 and 2 are indicated in fig. 1, and two possibilities with the alternative isodiamond layers are indicated in fig. 2. Clearly the sp3-hybridized diamond or isodiamond layers may be increased to arbitrary widths, as may also the widths of the graphitic strips, and thereby still lead to plausible structures. Presumably these materials should be of high strength. The primary source of strain in our (iso)diamond-graphite hybrids arises from the fact that the distance between molecular planes of graphite is naturally x 335 pm, whereas the distance between the planes of attachment in diamond is only ~250 pm, or in isodiamond only slightly greater nearer 260 pm. Thence they might conceivably be high-density carbon candidates. However, in graphite the interplane van der Waals forces are weak, as indicated by the softness of graphite, so that the compressibility in the interplane direction is lo4 to lo5 times less than for the in-plane directions. A further possibility is that the diamond layers have only a limited extent in the direction normal to the graphite molecular planes. Then the severe interplane compression to = 250 pm need only occur in the region where the graphite strips are fastened to the ( iso ) diamond, with the strips spreading apart toward their centers. The loss of resonance energy due to bending should be small, especially for the scene-like strips of section 2 where it turns out that
0009-2614/94/S 07.00 0 1994 Elsevier Science B.V. All rights reserved. SSDI OOOOS-2614(93)E1379-U
Volume 2 17, number 3
CHEMICAL PHYSICS LETTERS
14 January 1994
Fig. 1. Diamond-graphite hybrids with width 1 and 2 diamond layers in (a) and (b ) . In (a) the bond lengths and angles in the vertically oriented diamond layer are slightly lengthened and distorted for convenience ofpresentation. In (b) the internal structure of the graphitic strips is suppressed for convenience of presentation, though there are different possibilities (in both (a) and (b) ) depending on the width of the strips.
[ 12 ] of “colloidal” diamond nucleation crucially entails a graphite-diamond boundary, though the theory is “thermodynamic” without reference to any explicit molecular structure. One might imagine too that alternating diamond and graphite layers could result from a suitable manner of epitaxial deposition. Here we consider the Htickel-theoretic x-band structure of the interconnecting graphitic strips. Section 2 considers the scene-like x-network strips of fig. 1 and the extension to widen such graphitic strips, with special attention to the band gap. Section 3 does the same for the corrugated-strip circumstance of fig. 2.
2. Graphite strips between cubic diamond layers Fig. 2. Isodiamond-graphite hybrids with width 1 and 2 isodiamond layers in (a) and (b). The isodiamond structure is the wurtzite structure with altemant sites taken identical.
the benzenoid structure involved tends to ameliorate resonance near the strip edges. Our models for boundaries between graphitic and diamond phases may also already be realized in experimental fact, where commercially melt-grown (see, e.g., ref. [ lo] ) diamond commonly has many graphitic inclusions, and vapor phase deposited (see, e.g., ref. [ 111) diamond is often treated with etching cycles to remove graphitic growths. In such experiments the graphitic phase has typically been sought to be minimized, and the graphitic impurities are presumed to occur in a random fashion. One theory
Strips of different possible widths are indicated in fig. 3. Both structures of fig. 1 involve the strips of width w=2, but clearly any are conceivable. The question naturally arises as to whether the graphitic strips might admit electrical conduction (along the length of the strips). Thence the n: network of these strips is considered, as in fact has been done in the accompanying article [ 13 1. There an analysis of the band structure reveals that (for the isolated x-network structures) a nonzero band gap occurs for arbitrary strip width w. The band gap A located near wavevector k= f-21~13 appears to be little effected by a Hartree-Fock (spin polarization) instability which splits apart other bonding-antibonding or267
Volume 2 17, number 3
CHEMICAL PHYSICS LETTERS
Fig. 3. The first four members of a sequence of possible graphitic strips suitable for the diamond-graphite hybrid case. The dashed lines identify the strip outline in fig. 1, while the present solid lines identify the 6 network of sp2-hybridized carbon atoms.
bital pairs which would otherwise be closer. The band gaps so estimated are A/~j?~~2.0,
1.2,0.9and0.7
atw=l,2,3and4,
(1)
where 8% - 3 eV is the usual Hiickel “resonance integral”. Beyond w= 5 the band gap is argued to scale as ~27r/(2w+l), so that for w~6 we have (semi)conduction which is slowly enhanced as the width w increases. Of course the x networks of the graphitic strips are not isolated but interact to some extent with the adjoining diamond layers. In particular the diamondlayer carbon located where two dashed lines meet in fig. 3 each have two symmetrically out-of-plane sp3 orbitals angled away from the polymer strip, such that in + and - combinations they form a o’ and R’ orbitals. Having partial s character this x’ orbital has a lower diagonal (“Coulomb”) matrix element, say [ 14,15 ] Aa = 3 eV, and since the sp3 components of K’ are angled away from the graphitic strip, the associated “resonance integral” is less, say [ 14 ] /3’ x J/l. Thence the effect on frontier (and antibonding) orbitals might reasonably be estimated by perturbation theory, the consequent second-order energy shift being
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where ( 11E ) is the energy e “unit-cellular” eigenorbital coefficient on a side spicule of the graphitic polymer strip. By “unit-cellular” we mean that ]e) is normalized over a single unit cell, as in ref. [ 13 1, so that usually one expects I( 11E) I ‘z 1/w. Further the quantities I( 1 I E) I ’ are identical for the (HOMO and LUMO) orbitals on either side of the band gap. Therefore though the energies near the band gap should shift slightly (upward), the direct band gap (for the uncoupled x system) is anticipated to remain substantially unchanged. There is an interesting feature which occurs for the graphitic strips, and which is intimately related to the coupling of the sp2-hybridized x network to the sp3-hybridized o network. Especially for larger width w, unpaired (at least locally) spin density (of opposing signs) develops in edge-localized orbitals on the two sides of the strips. From a resonating VB viewpoint locally unpaired electrons pile up near the edges so that a greater variety of pairing patterns (KekulC structures) occur in the strips’ interior and thereby give rise to resonance stabilization. The edgelocalized orbitals naturally have I ( 1 I 6) I ’ x 1, so that more pronounced n interaction with the adjoining diamond carbons is expected. These exceptional band orbitals are not too far in energy from the HOMO and LUMO, so that the energy shift is z w times that of the HOMO and LUMO. Thus the bonding edgelocalized orbital might be shifted to become the HOMO for wider strips, whence also that band gap could be dramatically reduced. Of course the band gap is indirect, between the upward shifted localized band orbital (near k=O) and the LUMOs (near k= z!z2x/3). If the shift is sufficient an overlap in energies of these two bands can occur so that the gap falls to 0. Indeed such a circumstance is consistent with the resonating VB picture where the introduction of additional (conductive) electrons or holes on the edges would have the same resonance enhancing effect as the introduction of (locally) unpaired electrons there. Thence for the possibility of semimetallic or even metallic conduction (along the strip direction) arises, though more precise prediction seems to us to be best left to a detailed (all electron) computation.
Volume 2 17, number 3
CHEMICAL. PHYSICS LETTERS
3. Graphite strips between hexagonal diamond layers
Strips of different possible widths are indicated in fig. 4. Both structures of fig. 2 involve strips of width w=4, but clearly any are conceivable. Again the question of electrical conductivity naturally arises, and again band structures for the isolated n networks are available, with the even- and odd-width strips having been treated in ref. [ 16,17 1. In fact a Hiickel band gap of 0 is obtained for one out of three of the strip widths: it occurs for w= 3r+ 2 with r> 0 an integer. In these cases there are no modifications due to edge-localization or “spin polarization”: the nonbonding band orbitals are delocalized across the width of the strip. Now these cases of Hiickel band gaps of 0 occur at wavevector k= f x, so that there should occur a Peierls dimerization [ 181 along the strip length, with a consequent band-splitting and the possibility for solitonic [ 19 ] semiconduction. The strips of widths other than w= 3r+ 2 have quite wide band gaps so long as they are not too wide: A> 2 eV for these other wd 7. Ultimately of course the band gap does scale AZ 1/w. Actually for the case of isodiamond there are two possibilities. The layers may be cut from hexagonal diamond as in fig. 2, whence the appropriate graphite strips are the corrugated ones of this section, or else the layers may be cut in a direction normal to this, whence the appropriate graphite strips are of the scene-like type. That is, in this second case the pattern of fastening bonds at the edge is the same as
14 January 1994
for the (cubic) diamond layers, and the considerations of section 2 apply to the graphitic strips.
4. Conclusion Evidently there is a possibility of novel layered graphite- ( iso )diamond hybrids which in some cases may even be (solitonicly) conducting along strips in the graphite layers. The sp3-hybridized layers are of cubic or hexagonal diamond connected covalently with layers of graphite strips having either scenic or zig-zag fibonacenic edges. The former type of edge is compatible with both forms of diamond (depending in the isodiamond case which type of face is exposed at the surface of the layer), whereas the latter edge type is compatible with only (one of the surfaces possible in) isodiamond. Novel edge states are revealed as likely playing a key role for the scene-like graphite edges, whence there is some altemant spin polarization to altemant edges. The considered boundaries between graphitic and diamond phases may also serve as models for those involved [ 12 ] in high-pressure melt-grown diamond. Particularly this last interest would require much more extensive computations to look at rearrangement pathways allowing the boundary to move. A different approach to layered diamond-graphite hybrids has also been recently reported [ 201.
Acknowledgement Support of this research is acknowledged to The Welch Foundation of Houston, Texas, and to the Donors of the Petroleum Research Fund, administered by the American Chemical Society.
References [ 1lA.T.
Fig. 4. The first five members of a sequence of possible graphitic strips suitable for the isodiamond-graphite hybrid case. The dashed lines indicate the strip outline of tig. 2, while the present solid lines identify the x network of sp* carbons.
Balaban, Comput. Math. Applic. 17 (1987) 397 (reprinted in I. Hargittai, ed., Symmetry II (Pergamon Press, Oxford, 1989) pp. 397-416); A.T. Balaban, C.C. Rentia and E. Ciupitu, Rev. Roum. Chim. 13 (1968) 231; 13 (1968) 1233 (E). [2] V. Stankevich, M.V. Nikerov and D.A. Bochvar, Russ. Chem. Rev. 53 (1987) 670.
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CHEMICAL PHYSICS LETTERS
[3] R. Hoffmann, T. Hughbanks, M. Kertesz and P.H. Bird, J. Am. Chem. Sot. 105 (1983) 7831; R.H. Baughman, H. Eckherdt and M. Kertesz, J. Chem. Phys. 87 (1987) 6687. [4] K.M. Men Jr., R. Hoffmann and A.T. Balaban, J. Am. Chem. Sot. 109 (1987) 6772. [ 5 ] R. Biswas, R.M. Martin, R.J. Needs and O.H. Nielsen, Phys. Rev. B 30 (1984) 3210; R.L. Johnston and R. Hoffmann, J. Am. Chem. Sot. 111 (1989) 810; G. Laqua, H. Musso, W. Boland and R. Ahlrichs, J. Am. Chem. Sot. 112 (1990) 7391; D. Boercker, Phys. Rev. B 44 ( 1991) 11592. [ 6 ] A.Y. Liu, M.L. Cohen, K.C. Hass and M.A. Tamon, Phys. Rev, B 43 ( 199 1) 6742; C. Mailhot and A.K. McMahan, Phys. Rev. B 44 ( 199 1) 11578. [7] J. Robertson and E.P. G’Reilly, Phys. Rev. B 35 (1987) 2946; H.R. Karfunkel and T. Dressler, J. Am. Chem. Sot. 114 (1992) 2285. [8] S.E. Stein and R.L. Brown, J. Am. Chem. Sot. 109 (1987) 3721; in: Molecular structure and energetics, eds. J.F. Liebman and A. Greenberg (VCH Publishers, Berlin, 1987) ch. 2, pp. 37-66.
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[9] D.A. Bochvar and E.G. Galpem, Dokl. Akad. Nauk SSSR 209 (1973) 612; R.A. Davidson, Theoret. Chim. Acta 58 ( 198 1) 193. [lo] J.C. Angus and C.C. Hayman, Science 241 (1988) 913. [ 111 W.A. Yarbrough and R. Messier, Science 247 ( 1990) 688; P.K. Bachmann and R. Messier, Chem. Eng. News May 15, (1989) 24. [ 121 L.F. Vereshchagin, Y.A. Kalashinikov and M.D. Shalimov, High Temp. High Pres. 7 (1975) 41; V.P. Vamin and L.L. Builov, Zh. Fiz. Khim. 35 (1990) 235. [ 131 D.J. Klein, Chem. Phys. Letters 217 (1993) 261. [ 141 EA. Matsen, J. Am. Chem. Sot. 72 (1950) 5243. [ 151 R. Hoffmann, J. Chem. Phys. 39 (1963) 1397. [ 161 M. Bradbum, C.A. Coulson and G.S. Rushbrooke, Proc. Roy. Sot. Edinburgh A 62 (1948) 336. [ 171 D.J. Klein, Rep. Mol. Theory 1 (1990) 91. [ 181 R.E. Peierls, Quantum Theory of Solids (Oxford Univ. Press, 1955); H.C. Longuet-Higgins and L. Salem, Proc. Roy. Sot. (London) A251 (1959) 172. [ 191 W.P. Su, J.R. Schrieffer and A.J. Heeger, Phys. Rev. B 22 (1980) 2099; M.J. Rice, Phys. Letters A 71 (1979) 152. [20] G.T. Visscher, D.C. Nesting, J.V. Badding and P.A. Bianconci, Science 260 (1993) 1496.
Volume 2 17, number 3
Diamond-graphite
hybrids
A.T. Balaban
and C.A. Folden
‘, D.J. Klein
14 January 1994
Department of Marine Sciences, Texas A and M University at Galveston, Galveston, TX 77553-1675. USA Received 17 September 1992; in final form 10 September 1993
The possibility of a general multifold class of novel allotropic forms of carbon is suggested. They consist of cubic or hexagonal diamond blocks or layers interconnected by blocks or layers of “graphitic” strips. Some simple consequences are noted with special attention to the possibility of electrical conduction along the “graphitic” strips.
1. Introduction There has long been an interest in novel three-dimensional carbon networks, with several theoretical proposals [ l-8 ] of possibilities. Like the finite buckminsterfullerene structure (which too was [ 91 first theoretically considered) most proposals for threedimensional networks have been based upon sp*-hybridized carbons, each with two single bonds and one double bond. Particular interest has focused on highdensity [ 5 ] and energetic [ 6 ] forms of carbon. Also recently [ 7,8 ] three-dimensional carbon networks with a mixture of sp*- and sp’-hybridized carbons have been considered. Here we propose a different multifold class of structures with both sp*- and sp3-hybridized carbons. The idea bears some analogy to that of blockcopolymers - one can conceive of fragments of the diamond lattice connected to fragments of the graphite lattice. The two forms of diamond (cubic and hexagonal, called henceforth for brevity diamond and isodiamond) have cleavage planes with rows of dangling coplanar bonds which may be attached to edges of graphite planes. Such edges may be of an scenic type or of a corrugated (or “tibonscenic” as for phenanthrene, chrysene, picene, etc.) type. With parallel cleavage planes from the diamond (or isodiamond) lattice one then obtains (iso ) diamond blocks or layers covalently interca’ Permanent address: Polytechnic Institute, Department of Organic Chemistry, Bucharest, Roumania. 266
lated between graphitic material. In turn blocks or layers of strips of the graphitic material are intercalated between the (iso)diamond layers. Two possibilities with diamond-layers of widths 1 and 2 are indicated in fig. 1, and two possibilities with the alternative isodiamond layers are indicated in fig. 2. Clearly the sp3-hybridized diamond or isodiamond layers may be increased to arbitrary widths, as may also the widths of the graphitic strips, and thereby still lead to plausible structures. Presumably these materials should be of high strength. The primary source of strain in our (iso)diamond-graphite hybrids arises from the fact that the distance between molecular planes of graphite is naturally x 335 pm, whereas the distance between the planes of attachment in diamond is only ~250 pm, or in isodiamond only slightly greater nearer 260 pm. Thence they might conceivably be high-density carbon candidates. However, in graphite the interplane van der Waals forces are weak, as indicated by the softness of graphite, so that the compressibility in the interplane direction is lo4 to lo5 times less than for the in-plane directions. A further possibility is that the diamond layers have only a limited extent in the direction normal to the graphite molecular planes. Then the severe interplane compression to = 250 pm need only occur in the region where the graphite strips are fastened to the ( iso ) diamond, with the strips spreading apart toward their centers. The loss of resonance energy due to bending should be small, especially for the scene-like strips of section 2 where it turns out that
0009-2614/94/S 07.00 0 1994 Elsevier Science B.V. All rights reserved. SSDI OOOOS-2614(93)E1379-U
Volume 2 17, number 3
CHEMICAL PHYSICS LETTERS
14 January 1994
Fig. 1. Diamond-graphite hybrids with width 1 and 2 diamond layers in (a) and (b ) . In (a) the bond lengths and angles in the vertically oriented diamond layer are slightly lengthened and distorted for convenience ofpresentation. In (b) the internal structure of the graphitic strips is suppressed for convenience of presentation, though there are different possibilities (in both (a) and (b) ) depending on the width of the strips.
[ 12 ] of “colloidal” diamond nucleation crucially entails a graphite-diamond boundary, though the theory is “thermodynamic” without reference to any explicit molecular structure. One might imagine too that alternating diamond and graphite layers could result from a suitable manner of epitaxial deposition. Here we consider the Htickel-theoretic x-band structure of the interconnecting graphitic strips. Section 2 considers the scene-like x-network strips of fig. 1 and the extension to widen such graphitic strips, with special attention to the band gap. Section 3 does the same for the corrugated-strip circumstance of fig. 2.
2. Graphite strips between cubic diamond layers Fig. 2. Isodiamond-graphite hybrids with width 1 and 2 isodiamond layers in (a) and (b). The isodiamond structure is the wurtzite structure with altemant sites taken identical.
the benzenoid structure involved tends to ameliorate resonance near the strip edges. Our models for boundaries between graphitic and diamond phases may also already be realized in experimental fact, where commercially melt-grown (see, e.g., ref. [ lo] ) diamond commonly has many graphitic inclusions, and vapor phase deposited (see, e.g., ref. [ 111) diamond is often treated with etching cycles to remove graphitic growths. In such experiments the graphitic phase has typically been sought to be minimized, and the graphitic impurities are presumed to occur in a random fashion. One theory
Strips of different possible widths are indicated in fig. 3. Both structures of fig. 1 involve the strips of width w=2, but clearly any are conceivable. The question naturally arises as to whether the graphitic strips might admit electrical conduction (along the length of the strips). Thence the n: network of these strips is considered, as in fact has been done in the accompanying article [ 13 1. There an analysis of the band structure reveals that (for the isolated x-network structures) a nonzero band gap occurs for arbitrary strip width w. The band gap A located near wavevector k= f-21~13 appears to be little effected by a Hartree-Fock (spin polarization) instability which splits apart other bonding-antibonding or267
Volume 2 17, number 3
CHEMICAL PHYSICS LETTERS
Fig. 3. The first four members of a sequence of possible graphitic strips suitable for the diamond-graphite hybrid case. The dashed lines identify the strip outline in fig. 1, while the present solid lines identify the 6 network of sp2-hybridized carbon atoms.
bital pairs which would otherwise be closer. The band gaps so estimated are A/~j?~~2.0,
1.2,0.9and0.7
atw=l,2,3and4,
(1)
where 8% - 3 eV is the usual Hiickel “resonance integral”. Beyond w= 5 the band gap is argued to scale as ~27r/(2w+l), so that for w~6 we have (semi)conduction which is slowly enhanced as the width w increases. Of course the x networks of the graphitic strips are not isolated but interact to some extent with the adjoining diamond layers. In particular the diamondlayer carbon located where two dashed lines meet in fig. 3 each have two symmetrically out-of-plane sp3 orbitals angled away from the polymer strip, such that in + and - combinations they form a o’ and R’ orbitals. Having partial s character this x’ orbital has a lower diagonal (“Coulomb”) matrix element, say [ 14,15 ] Aa = 3 eV, and since the sp3 components of K’ are angled away from the graphitic strip, the associated “resonance integral” is less, say [ 14 ] /3’ x J/l. Thence the effect on frontier (and antibonding) orbitals might reasonably be estimated by perturbation theory, the consequent second-order energy shift being
268
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where ( 11E ) is the energy e “unit-cellular” eigenorbital coefficient on a side spicule of the graphitic polymer strip. By “unit-cellular” we mean that ]e) is normalized over a single unit cell, as in ref. [ 13 1, so that usually one expects I( 11E) I ‘z 1/w. Further the quantities I( 1 I E) I ’ are identical for the (HOMO and LUMO) orbitals on either side of the band gap. Therefore though the energies near the band gap should shift slightly (upward), the direct band gap (for the uncoupled x system) is anticipated to remain substantially unchanged. There is an interesting feature which occurs for the graphitic strips, and which is intimately related to the coupling of the sp2-hybridized x network to the sp3-hybridized o network. Especially for larger width w, unpaired (at least locally) spin density (of opposing signs) develops in edge-localized orbitals on the two sides of the strips. From a resonating VB viewpoint locally unpaired electrons pile up near the edges so that a greater variety of pairing patterns (KekulC structures) occur in the strips’ interior and thereby give rise to resonance stabilization. The edgelocalized orbitals naturally have I ( 1 I 6) I ’ x 1, so that more pronounced n interaction with the adjoining diamond carbons is expected. These exceptional band orbitals are not too far in energy from the HOMO and LUMO, so that the energy shift is z w times that of the HOMO and LUMO. Thus the bonding edgelocalized orbital might be shifted to become the HOMO for wider strips, whence also that band gap could be dramatically reduced. Of course the band gap is indirect, between the upward shifted localized band orbital (near k=O) and the LUMOs (near k= z!z2x/3). If the shift is sufficient an overlap in energies of these two bands can occur so that the gap falls to 0. Indeed such a circumstance is consistent with the resonating VB picture where the introduction of additional (conductive) electrons or holes on the edges would have the same resonance enhancing effect as the introduction of (locally) unpaired electrons there. Thence for the possibility of semimetallic or even metallic conduction (along the strip direction) arises, though more precise prediction seems to us to be best left to a detailed (all electron) computation.
Volume 2 17, number 3
CHEMICAL. PHYSICS LETTERS
3. Graphite strips between hexagonal diamond layers
Strips of different possible widths are indicated in fig. 4. Both structures of fig. 2 involve strips of width w=4, but clearly any are conceivable. Again the question of electrical conductivity naturally arises, and again band structures for the isolated n networks are available, with the even- and odd-width strips having been treated in ref. [ 16,17 1. In fact a Hiickel band gap of 0 is obtained for one out of three of the strip widths: it occurs for w= 3r+ 2 with r> 0 an integer. In these cases there are no modifications due to edge-localization or “spin polarization”: the nonbonding band orbitals are delocalized across the width of the strip. Now these cases of Hiickel band gaps of 0 occur at wavevector k= f x, so that there should occur a Peierls dimerization [ 181 along the strip length, with a consequent band-splitting and the possibility for solitonic [ 19 ] semiconduction. The strips of widths other than w= 3r+ 2 have quite wide band gaps so long as they are not too wide: A> 2 eV for these other wd 7. Ultimately of course the band gap does scale AZ 1/w. Actually for the case of isodiamond there are two possibilities. The layers may be cut from hexagonal diamond as in fig. 2, whence the appropriate graphite strips are the corrugated ones of this section, or else the layers may be cut in a direction normal to this, whence the appropriate graphite strips are of the scene-like type. That is, in this second case the pattern of fastening bonds at the edge is the same as
14 January 1994
for the (cubic) diamond layers, and the considerations of section 2 apply to the graphitic strips.
4. Conclusion Evidently there is a possibility of novel layered graphite- ( iso )diamond hybrids which in some cases may even be (solitonicly) conducting along strips in the graphite layers. The sp3-hybridized layers are of cubic or hexagonal diamond connected covalently with layers of graphite strips having either scenic or zig-zag fibonacenic edges. The former type of edge is compatible with both forms of diamond (depending in the isodiamond case which type of face is exposed at the surface of the layer), whereas the latter edge type is compatible with only (one of the surfaces possible in) isodiamond. Novel edge states are revealed as likely playing a key role for the scene-like graphite edges, whence there is some altemant spin polarization to altemant edges. The considered boundaries between graphitic and diamond phases may also serve as models for those involved [ 12 ] in high-pressure melt-grown diamond. Particularly this last interest would require much more extensive computations to look at rearrangement pathways allowing the boundary to move. A different approach to layered diamond-graphite hybrids has also been recently reported [ 201.
Acknowledgement Support of this research is acknowledged to The Welch Foundation of Houston, Texas, and to the Donors of the Petroleum Research Fund, administered by the American Chemical Society.
References [ 1lA.T.
Fig. 4. The first five members of a sequence of possible graphitic strips suitable for the isodiamond-graphite hybrid case. The dashed lines indicate the strip outline of tig. 2, while the present solid lines identify the x network of sp* carbons.
Balaban, Comput. Math. Applic. 17 (1987) 397 (reprinted in I. Hargittai, ed., Symmetry II (Pergamon Press, Oxford, 1989) pp. 397-416); A.T. Balaban, C.C. Rentia and E. Ciupitu, Rev. Roum. Chim. 13 (1968) 231; 13 (1968) 1233 (E). [2] V. Stankevich, M.V. Nikerov and D.A. Bochvar, Russ. Chem. Rev. 53 (1987) 670.
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CHEMICAL PHYSICS LETTERS
[3] R. Hoffmann, T. Hughbanks, M. Kertesz and P.H. Bird, J. Am. Chem. Sot. 105 (1983) 7831; R.H. Baughman, H. Eckherdt and M. Kertesz, J. Chem. Phys. 87 (1987) 6687. [4] K.M. Men Jr., R. Hoffmann and A.T. Balaban, J. Am. Chem. Sot. 109 (1987) 6772. [ 5 ] R. Biswas, R.M. Martin, R.J. Needs and O.H. Nielsen, Phys. Rev. B 30 (1984) 3210; R.L. Johnston and R. Hoffmann, J. Am. Chem. Sot. 111 (1989) 810; G. Laqua, H. Musso, W. Boland and R. Ahlrichs, J. Am. Chem. Sot. 112 (1990) 7391; D. Boercker, Phys. Rev. B 44 ( 1991) 11592. [ 6 ] A.Y. Liu, M.L. Cohen, K.C. Hass and M.A. Tamon, Phys. Rev, B 43 ( 199 1) 6742; C. Mailhot and A.K. McMahan, Phys. Rev. B 44 ( 199 1) 11578. [7] J. Robertson and E.P. G’Reilly, Phys. Rev. B 35 (1987) 2946; H.R. Karfunkel and T. Dressler, J. Am. Chem. Sot. 114 (1992) 2285. [8] S.E. Stein and R.L. Brown, J. Am. Chem. Sot. 109 (1987) 3721; in: Molecular structure and energetics, eds. J.F. Liebman and A. Greenberg (VCH Publishers, Berlin, 1987) ch. 2, pp. 37-66.
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