J . Phys. Chem. 1990, 94. 4346-4351
4346
in the phenothiazine crystal, 0.07 cm-' between 250 and 350 K, but seems slightly larger. Therefore, the strength of the hydrogen bond is not considered to be changed simply by the linear thermal expansion, It has been suggested that a change in the molecular orientation occurs in the low-temperature phase.2 This change is considered to be the tilt of the molecule against the mirror plane of the high-temperature phase. If this is the case, the tilt weakens the hydrogen bond which is formed on the mirror plane, causing the shift of uN-H to the high-frequency side. It should be noted that uN-H shows a small maximum just below T, (Figure 2). This is considered to be due to the competition of the effect of the thermal contraction which strengthens the hydrogen bond and the opposite effect of the molecular tilt. Actually, the temperature region (220 K-T,) where vN-H shows the anomaly corresponds to the region where the extinction angle, which reflects the molecular orientation, shows a large temperature dependence.] Raman bands related to the vibrations involved in hydrogen bonds are usually broad. This is understood since such vibrations easily couple with the lattice vibrations. The steep increase in the N-H bandwidth of the phenothiazine crystal just below T, (Figure 2) is attributable to the coupling of the N-H vibration with the librational lattice mode which shows a partial softening as the temperature approaching T, in the low-temperature phase.2 The amplitude of this libration may become larger as its frequency is softened. Therefore, the coupling between these vibrations is considered to increase in this temperature region, giving rise to
the acceleration of the relaxation of the excited states of the N-H vibration and to the observed increase in the Raman bandwidths. Conclusion Anomalous temperature dependences observed for the frequency and width of the Raman band arising from the N-H stretching vibration in the phenothiazine crystal were discussed from the viewpoints of the changes in the dihedral angle 0 of the molecule or in the hydrogen-bond state. It was shown by the CNDO/2 calculation that the N-H stretching frequency YN-H increases with 0. However, this mechanism cannot explain the large difference of uN-H in the crystal, neat liquid, solution, and vapor states. To explain the above difference, the existence of hydrogen bonds in the crystal was proposed. It was shown that the crystallographic data do not exclude the existence of the weak hydrogen bonds. The competing effects of the reorientation of the molecule and the thermal expansion of the crystal on the hydrogen-bond strength were shown to cause the anomalous temperature dependence of u ~ - ~The . anomaly in the bandwidth was, on the other hand, explained by the coupling with the lattice mode. In conclusion, there are weak hydrogen bonds in the phenothiazine crystal. The anomalous behaviors of the N-H stretching Raman band are due to the change in the hydrogen-bond state. Although there is a possibility that the change in the dihedral angle of the molecule contributes to the change in the frequency of the above Raman band, its contribution is considered to be small. Registry No. Phenothiazine, 92-84-2
Electronic Band Structure of Graphite-Boron Nitride Alloys John P. LaFemina Pacific Northwest Laboratory,t P.O.Box 999, Richland, Washington 99352 (Receioed: August 7 , 1989: In Final Form: October 27, 1989)
Extended-Huckel crystal orbital band calculations, frontier crystal orbital analysis, and degenerate-level perturbation theory are used to explore the electronic structure of several graphite-boron nitride alloys: BC3, C3N, BC2N, and their structural isomers. These materials are treated as two-dimensional solids, and the effect of crystal relaxation on the bandgap is considered. Similarities and differences between the band diagrams of these structurally similar materials are discussed and understood in a simple crystal orbital framework.
Introduction Recent interest in the electronic properties of layer-type crystals has been sparked by the synthesis of several alloys of graphite and boron nitride,'-' materials in which some of the carbon atoms have been replaced by boron atoms (BC3),2,3nitrogen atoms (C3N), or a combination of both boron and nitrogen atoms (BC2N).1,4 Electron and X-rav diffraction studies of these materials indicate graphite-like layer structures with sp2bonding in-plane, and a large distance between layers (>3 A).3,4 In this paper the electronic band structure of the structural isomers of single-layer BC,, C,N, and BC2N (see Figure 1) are examined via extended-Huckel crystal orbital (EHCO) band c a l ~ u l a t i o n s . Since ~ these band diagrams can be thought of in terms of the perturbation of graphite via boron and nitrogen substitution, the degeneracy lifting near the Fermi energy6 (and hence the energy gaps) can be understood in a simple crystal orbital (CO) context by using first-order perturbation theory, the ideas of qualitative crystal orbital theory (QCOT),' and the concept of transferability.a Furthermore, these same principles can be used to qualitatively evaluate the effect of crystal relaxation
on the bandgap by examining the leading frontier COS of the system.6 Band Diagrams The weak interlayer interactions permit these materials to be treated as two-dimensional solids in the computation of their electronic band structure and allow for a qualitative understanding
'Operated for the US. Department of Energy by Battelle Memorial Institute under Contract DE-AC06-76RLO 1830.
6602. (8) Lowe, J . P.: Kafafi, S. A. J . Am. Chem. Soc. 1984, 106, 5837.
0022-3654/90/2094-4346$02.50/0
(1) (a) Badzian, A. R.; Niemyski, T.; Appenheimer, S.; Olkusnik, E. In Proceedings of the International Conference on Chemical Vapor Deposition; Glaski, F. A,, Ed.; American Nuclear Society: Hinsdale, IL, 1972; Vol. 3. (b) Kosolapova, T. Ya.: Makarenko, 9 . N.; Serebryakova, T. I.; Prilutskii, E. V.; Khorpyakov, 0. T.; Chernsheva, 0. 1. Poroshk. Mefall. (Kieu) 1971, I , 27. (2) Kouvetakis, J.; Kaner, R. 9 . ; Sattler, P.: Bartlett, N. J , Chem. SOC., Chem. Commun. 1968, 1758. (3) Kaner, R. B.; Kouvetakis, J.; Warble, C. E.; Sattler, M. L.; Bartlett, N.Mater. Res. Bull. 1987, 22, 399. (4) Sasaki, T.; Bartlett, N., unpublished, referenced in: Liu, A. Y.: Wentzcovitch, R. M.; Cohen, M. L. Phys. Rev. B 1989, 39, 1760. (5) (a) Whangbo, M. H.; Hoffmann, R.; Woodward, R. 8.Proc. R. SOC. London, Ser. A 1979,366, 23. (b) Whangbo, M. H.; Hoffmann, R. J . A m . Chem. SOC.1978, 100, 6093. ( 6 ) (a) LaFemina, J. P.; Lowe, J. P. In?. J . Quantum Chem. 1986.30.769. (b) LaFemina, J . P.; Lowe, J. P. J. A m . Chem. SOC.1986, 108, 2527. (7) Lowe, J. P.; Kafafi, S. A,; LaFemina, J . P. J . Phys. Chem. 1986, 90,
e 1990 American Chemical Society
The Journal of Physical Chemistry, Vol. 94, No. 10, 1990 4347
Graphite-Boron Nitride Alloys
M
K‘
n
Figure 2. First Brillouin zone and symmetry points where the bands were computed, along with the eight-atom unit cell used in the computations.
B2c4
U
n
Figure 1. Substitution patterns in the eight-atom unit cell for the structural isomers of B2C, (A, B, and C), C,N, (A, B, and C), and B2C4N2( I , 11, and 111). of the electronic s t r ~ c t u r e . Band ~ calculations were performed on single layers of unrelaxed ( d = 1.40 A) material; the effects of bond-length relaxation are discussed qualitatively. The unit cell used in the computations is the eight-atom cell shown in Figure 2 . While this is not the primitive unit cell for all of the structures considered, it is useful since it is the smallest unit cell common t o all structures. Figure 2 also shows the irreducible part of the first Brillouin zone (FEZ) and the location of the symmetry points at which the band energies were computed. It is instructive to note that the states at both points M and M’ need to be considered, while the states at K and K’ are equivalent because of the symmetry (both translational and point symmetry) of the surface. (The point symmetry possessed by the substitution
patterns labeled A (Figure 1) result in the states at M and M’ being equivalent for these isomers as well.) At this point it is useful to discuss a problem with the use of E H C O theory in the computation of electronic band structures, in particular for B-, C-, and N-containing materials. And that is that the highest occupied a-bands (consisting of the nonbonding, in-plane atomic p orbitals) are calculated to be too high in energy ( > 5 eV in the case of graphite) relative to the *-system.lo Attempts at reparametrization of the EHCO method to improve this have proved unsuccessful.10 Hence, in examining the electronic structure of systems such as those considered here, the focus is on the mystem, and the band diagrams presented in the following sections contain only r-bands. The degeneracy lifting can be qualitatively understood by considering the nature of the PCOS involved. Because they are initially degenerate, an infinite number of representations are possible.” However, the introduction of a perturbation (in this case chemical substitution) will induce a unique proper zerothorder representation that must satisfy the condition prescribed by degenerate-level perturbation theory, viz. where +io)and +io) are the proper zeroth-order wave functions for the perturbation Vobtained from degenerate levels and $b.For a point perturbation, eq 1 requires that the proper zeroth-order orbitals be respectively symmetric and antisymmetric for reflection through the site of the perturbation. As a result, one member of the set will have maximum orbital density, while the other has zero orbital density, at the site of the perturbation. Consequently, the proper zeroth-order representation is the one that has the largest first-order energy difference as a result of the perturbation6-8,I 1 Finally, it is important to point out that while the arguments that will be made in the following sections are based on first-order perturbation theory, the band diagrams presented are those computed by using the EHCO method and hence contain higher (IO) Kertesz, M., private communication.
(9) LaFemina, J. P. Inr. J . Quontum Chem., in press
( 1 1) Lowe, J. P. Q u m f u m Chemistry; Academic Press: New York, 1978.
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The Journal of Physical Chemistry, Vol. 94, No. 10, 1990
LaFemina
t r
T
K
X I -
M
Figure 3. *-band diagram for the C Bunit cell of graphite.
Figure 5. Proper zeroth-order * - c o s for B,C,(B) and B2C6(C) at
r.
3
-2
1 0,
1,
-9
d
-13
I Figure 4. Proper zeroth-order *-COS for B & , ( A ) at
r
order effects. The practical effect of this is that in some instances orbitals predicted to be degenerate in first order will be split by higher order effects, and this splitting will be reflected in the computed band diagram. These instances will be explicitly noted as they occur. Boron-Substituted Graphite: BC3
r
~
~
r
K
Y
Figure 6. *-band diagram for B&(A). 3
>
2 -5 1 L 0,
The computed EHCO band diagrams for single-layer, unrelaxed C8 and the three isomers of B2C6 are presented in Figures 3 and 6-8, respectively, and detail the evolution of the r-band structure quite nicely. Figure 3 reveals, as expected, that unrelaxed graphite is semimetallic, the Fermi level occurring at point K where the highest occupied ~(x,,)and lowest unoccupied P * ( A ~ bands ) are degenerate. The substitution of two carbon atoms with boron atoms forms the alloy B2C6 (Figure 1). This substitution lifts the x-band degeneracies (as seen in Figure 6) throughout the FBZ. Because boron has a valence-state ionization potential (VSIP = -8.5 eV) higher than that of carbon (VSIP = -1 1.4 eV), any C O with orbital density at t h e substitution sites will be destabilized (raised in energy). There are three unique substitution patterns, shown in Figure 1 and labeled A, B, and C. It is interesting to note here that structure B has been suggested as a possible organic ferromagnet. I
g
-9
LL
- EF
- 3
-17
r T K l r l m K 8 r x r Figure 7. *-band diagram for B,C,(B).
3
-> 2
-5
1
m L
," -9 W
(12) Ovchinnikov, A. A. Theor. Chim. Acfa 1978, 47, 297. While this is an interesting possibility, it is one that cannot be explored with the one-electron EHCO method. ( I 3) LaFemina, J. P., unpublished. It is interesting to note that the inclusion of interlayer effects moves the LUCO from M to L and breaks the equivalence of points M and M' (L and L'). A quick look at the orbitals for the A isomer at these points (Figure 9) reveals that if neighboring layers interact, the LUCO at L (CO ?r3 of Figure 9a translated in the z direction with a phase factor of -1) will be stabilized, while the LUCO at M" (Figure 9b) is unaffected, being an interlayer nonbonding CO.
EF
-13
-'7
r
T
K
i"i'
Y'
"1
c
r
~i~~~~ 8, *-band diagram for B,c,(c),
The first perturbation to consider for all of the substitution patterns is the removal of two valence electrons (one per boron
x
r
The Journal of Physical Chemistry, Vol. 94, No. 10, 1990
Graphite-Boron Nitride Alloys
Q
kXuL5.
Illl;es
n3
W
P
T
3
Figure 10. HOCOs (at M’) and LUCOs (at r) for C6N2(A), (B), and (C). These are the leading FCOs in the alloys.
atom), which empties the highest occupied band (7r4). moving the Fermi level to point r and the triply degenerate (but partially filled) 7r2/7r3/7r4 bands at -12.41 eV. However, the (now) highest occupied doubly degenerate COS at points M and M’ must also be considered because of their proximity (-12.57 eV) to the new Fermi level. The proper zeroth-order COS for the (now) highest occupied ??z/K3/Tq bands at r for substitution patterns A, B, and C are shown in Figures 4 and 5. These COS have mixed so as to maximize the effect of the perturbation. For substitution pattern A (Figure 4),orbital 7rq, having maximum orbital density at the substitution sites, is destabilized, while orbitals 7r2 and 7r3 remain unaffected, having zero orbital density at the sites of the perturbation. Moreover, the energy of these unaffected orbitals is quantitatiuely transferable from the unperturbed graphite system.* The destabilized orbital is now completely empty while the remaining degenerate pair ( ~ 2 / ~ 3is) completely filled. For substitution patterns B and C (Figure 5), orbital 1r2 remains unaffected (and its energy transferable), while both 7r3 and 7r4are destabilized, but by different amounts (the extent of destabilization proportional to the orbital coefficients at the substitution site). It is interesting to note that the additional point symmetry possessed by the A pattern allows the COS to mix in such a way so as to result in the destabilization of a single CO, rather than the
destabilization of two COS as in cases B and C. At points M and M’, the removal of two valence electrons leaves the doubly degenerate bands 7r3/7r4 half-filled. The correct zeroth-order COS for boron substitution are shown in Figure 9, parts a and b. It is clear from these COSthat for each substitution pattern at point M (Figure sa), one CO (a3)remains unaffected (and filled, its energy transferable) while the other (a4) is destabilized (and emptied). To first order, each of these orbitals are destabilized to the same extent. However, when they are allowed to mix variationally with other COS, the extent of destabilization varies as C > B = A. At point M’ (Figure 9b) the result for A, as previously stated, is the same as at point M. (Although the shape of the COS is different at M and M‘, their response to the perturbation and hence energies are equal.) However, the situation for conformers B and C is quite different; each C O being destabilized to the same extent, thereby preserving the degeneracy in the disubstituted alloys.15 As was the case at point M, inclusion on higher order effects split this degeneracy for conformer C (see Figure 8), while the degeneracy persists for isomer B (see Figure 7). An analysis of the orbital coefficients (Figures 4, 5, and 10) reveals that the destabilized COS at r are pushed further up in energy than the destabilized COS at either M or M’, with the COS at M’ being destabilized the least. Hence the lowest unoccupied CO (LUCO) for each isomer is located at M’. Furthermore, since the unaffected COS at r are higher in energy than those at either M or M’, the highest occupied CO (HOCO) for each isomer is located at r. From the above analysis and the E H C O band diagrams in Figures 6-8, BzC,(A) is an indirect-gap insulator, with a gap of 1.2 eV between the HOCO at r and the LUCO at M(M’). The orbital analysis indicates that both BzC6(B) and BzC6(C) are semimetallic with the HOCO/LUCO at M’ forming a half-filled doubly degenerate pair.15 However, when second order effects are included in the full variational computation, this degeneracy is split for the C isomer, resulting in an indirect bandgap of 0.3 eV between the HOCO at r and the LUCO at M’.I5 The B isomer remains metallic by virtue of the facts that the degeneracy at M‘ is preserved, as well as having its HOCO at r lie higher
(14) TomBnek, D.; Wentzcovitch, R. M.; Louie, S. G.;Cohen, M. L. Pbys. Reu. B 1988, 37, 3134.
(15) (a) Lee, Y. S.; Kertesz, M. J . Cbem. SOC.,Chem. Commun. 1988, 75. (b) Lee, Y. S.; Kertesz, M., preprint.
Figure 9. (a) Proper zeroth-order n-COSfor B2C6(A), (B), and (C)at M. (b) Proper zeroth-order r-COS for B2C6(A), (B), and (C) at M’.
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The Journal of Physical Chemistry, Vol. 94, No. 10, 1990
in energy than its LUCO at M’ (see Figure 7.) If the crystal is allowed to relax through the lengthening of the B-C bonds, the effect on the bandgap can be qualitatively evaluated by examining the H O C 0 and LUCO. For B2C6(A), crystal relaxation has the effect of destabilizing the LUCO (Figure 9a) while leaving the HOCO (Figure 4) unaffected, thereby further opening the gap.14x’5For B&(C) relaxation closes the gap by causing the H O C O (Figure 5) to be destabilized while the LUCO (Figure 9b) remains unaffected. Finally, B2C6(B)has its HOCO (Figure 5 ) destabilized while the degenerate LUCOs at M’ (Figure 9b) are split. Yet the HOCO remains at a higher energy than the LUCO leaving B2C6(B) a metal. Conductivity measurements indicate a conductivity for BC, higher than that of graphite, and hence conformer B, predicted to be metallic, should be the most likely structure for this material. However, conformer C, predicted to have a gap C0.3 eV when the effects of crystal relaxation are accounted for, is a viable alternative s t r ~ c t u r e . ’Moreover, ~ it has been demonstrated for BC3(A)14that the presence of bulk layers (depending upon their stacking sequence) changes the semiconducting monolayer into a semimetallic bulk via the concomitant destabilization of the HOCO at r and stabilization of the LUCO at M, which causes the LUCO to lie lower in energy than the HOCO.I3 Therefore no definitive declaration on the conformation of this material can be made from a simple analysis of the band diagrams consistency with the measured conductivity. These results are in complete agreement with the local density functional computations of TomPnek et aI.l4 (who considered only the A isomer) as well as with the E H C O computations of Lee and Kertesz.ls I n fact, the HOCO for conformer A (Figure 4) reflects quite nicely one effect of the boron atom perturbation, first observed by Tomgnek et aLI4 in valence density plots, which is the localization of the valence charge density onto the c6 rings. This fact was used by those researchers to explain why the C-C bond distance is nearly the same in both graphite and boron carbide (A) and is a reflection of the fact that all of the B atoms valence electrons are tied up in the sp2 in-plane bonding orbitals and thus are not able to participate in the out-of-plane a-system.
Nitrogen-Substituted Graphite: C3N The analysis of the band diagram evolution for the nitrogensubstituted systems is qualitatively identical with that given above for the boron-substituted systems. The differences are that the lower VSIP of nitrogen (-13.4 eV versus carbon at -1 1.4 eV) causes COS with orbital density at the substitution sites to be stabilized rather than destabilized as for boron carbide, and there are two extra valence electrons per unit cell which reside in the lowest a * band. As for the boron carbides, this change in electron count moves the Fermi level, though in this case from K to M (and M’), with the COS at r needing to be considered because of their proximity to the new Fermi level. (This is the opposite of what occurred for boron carbide; see Figure 3.) The results are that C,N2(A) is an indirect gap insulator with a gap of 1.6 eV between the HOCO at M(M’) and the LUCO at r; C6N2(B) is metallic with the LUCO at I’ lying below the HOCO at M‘ (which, as for the boron carbide, forms a half-filled doubly degenerate pair); and C6N2(C)is an indirect gap semiconductor with gap of 0.3 eV between the HOCO at M’ and the LUCO at r. The localization of valence electron density onto the c6 rings seen in the A conformer of boron carbide is not present in C,N(A) (see the HOCO, Figure IO). This is a reflection of the fact that, unlike boron, nitrogen does have electrons that can participate in the delocalized *-system. Therefore it is expected that the C-C bond length in the C,N(A) will be affected by the substitutional perturbation. The energy gap results for the carbon nitrides are remarkably similar to those obtained for the boron carbide isomers, and for good reason. The change in electron count for both systems moves the Fermi level away from K in such a way that the COS at both r and M (M’) need to be considered. These COS are either (i) the triply degenerate (at r) and doubly degenerate (at M/M‘) a-bonding COSfor the boron carbides or (ii) the triply degenerate
LaFemina (at r) and doubly degenerate (at M/M‘) r-antibonding COS for the carbon nitrides. Since graphite is an alternant system, the COS at any given k point are paired.” This pairing is imperfect because the extended Hiickel (with its inclusion of overlap) rather than the simple Hiickel formalism is used, and this manifests itself in the facts that the antibonding levels are higher above the energy zero (in this case the Fermi energy) than their bonding pairs are below it and that they have larger orbital coefficients. This is the first important point. The second is that in moving away from K to either M/M’ or I’, the Fermi level now resides at a point at which the highest filled and lowest unfilled COS form a partially filled degenerate set. Hence, when this set is split as a result of the heteroatomic perturbation, that splitting will (approximately) be the energy gap. Now, the extent of the splitting is related to (i) the VSIP difference for a carbon atom and the heteroatom and (ii) the size of the orbital coefficients at the perturbation sites. For nitrogen the VSIP difference (factor i in the discussion above) is -2 eV and for boron -3 eV. Hence on this basis the a-bonding COS in boron carbide are split to a greater extent than the a-antibonding COS in carbon nitride. Yet the a-antibonding COS in carbon nitride have larger orbital coefficients (factor ii in the above discussion) than their (imperfectly) paired a-bonding COS in boron carbide and hence are more affected by the substitution perturbation. The net result is that these competing effects cause the gaps in boron carbide and carbon nitride to be approximately equivalent. For the carbon nitrides, ignoring any change in the C-C bond lengths, crystal relaxation results in the shortening of the C-N bonds. The H O / L U COS for each isomer are shown in Figure 10 and the effects of relaxation on the bandgaps are easily evaluated. The shortening of the C-N bonds partially closes the gap in C6N2(A) by destabilizing the H O C 0 while leaving the LUCO unaffected. The B isomer’s LUCO is destabilized, while the degenerate HOCOs at M’ are split. Hence, if the destabilization of the LUCO is sufficiently strong, relaxed C6N2(B) could be a semimetal with a negligible indirect gap between the HOCO at M’ and the LUCO at r or a direct-gap semiconductor with a small gap between the HOCO and LUCO at M’. Finally, for C6N2(C) relaxation causes the HOCO to be stabilized while the LUCO is destabilized, thereby opening the gap. Graphite-Boron Nitride Alloys: BC,N The analysis for these systems is, again, qualitatively the same as that presented for the single-atom-type substitutions considered above. However, in those systems the COS and energy bands moved in a single direction in response to the perturbing atoms VSIP. In these alloys some of the COS will be stabilized, while others are destabilized depending upon where the bulk of the orbital’s electron density is located (Le., the C O will be stabilized if the bulk of the electron density is on the N atom substitution sites and destabilized if on the B atom substitution sites). Furthermore, the electron count in these alloys is exactly the same as in the unperturbed graphite. The isomers chosen for consideration do not form a complete set of all unique two-atom (B/N) substitutions but are the isomers considered by Liu et a1.I6 on the basis that the synthesis process is unlikely to disturb the integrity of the C-C and B-N linkages in the starting materials.I6 The *-band diagrams for each of the B2C4N2isomers are shown in Figures 11-13 where it is seen that B2C4N2(I)is metallic, with the HO/LU *-bands crossing; B2C4N2(II)is a direct gap insulator with a gap of 1.8 eV at r; and B2C4N2(III)is a direct gap insulator with a gap of 2.9 eV at K. These results and the band diagrams in Figures 11-1 3 are in good agreement with the local-density functional pseudopotential computations of Liu et a1.,I6 with few exceptions. One difference between the two computations worthy of comment involves BC2N(III), which their computations show to be an indirect gap (16) Liu, A. Y . ;Wentzcovitch, R. M.; Cohen, M. L. Phys. Reo. B 1989, 39, 1760.
The Journal of Physical Chemistry, Vol. 94, No. 10, 1990 4351
Graphite-Boron Nitride Alloys
kKU2.s
3
w
-1
-5
-9
E, -'3 -17
r T K M' K ' Figure 11. r-band diagram for B2C4N2(I).
M
c
r
3
->
E
9
-1
d
-5
x
Figure 14. HOCOs and LUCOs for the alloys B2C4N2(I) and (11).
L m
2
-9
These are the leading FCOs in the alloys and are located a t
E., -13
-'7
r T K M, K, Figure 12. r-band diagram for B2C4NZ(11).
M
z
r
c
r
3 -1 h
>
2
-5
1 L cn
g
I
-9
E, -i3
-17
r
T
K
M' K'
M
Figure 13. r-band diagram for B2C4N2(111). semiconductor with a gap of 0.5 eV. However, the HO band in their band diagram is a a-band, which, for reasons already discussed, is not included in our analysis. If only the a-bands are considered, the two calculations agree. Conductivity measurements4 and X-ray photoemission data" suggest that BCzN is either a semiconductor with a negligible gap' or metallic." On the basis of the band structures in Figures 11-13, the most likely structure is I, the only one to exhibit metallic behavior in the monolayer. Yet the effect of neighboring layers, needs to be acwhich was dramatic in the case of BC3(A),l3>l4 counted for. Liu et a1.,l6based on earlier computations on graphite (17) Carr, R., private communication, referenced in: Liu, A. Y.; Wentzcovitch, R. M.; Cohen, M. L. Phys. Reo. B 1989, 39, 1760.
r.
and hexagonal boron nitride,'* estimate that this effect will lower the gaps by approximately 1 eV. Assuming this (and using the gap computed in ref 14), BC2N(III) now becomes a viable alternative to structure I. To estimate the effect of crystal relaxation on the bandgaps, the H O / L U COS for alloys I and I1 are shown in Figure 14. Alloy I11 is omitted because of the presence of the H O a-band. The bond length changes to be considered are (i) the shortening of C-N bonds, (ii) the lengthening of C-B bonds, and (iii) the lengthening of the B-N bonds. The C - C bond length will remain unaffected. It is clear from the symmetry of the COS in Figure 14 that for alloy I only changes in the B-N linkages will have a net effect on the orbital energy: stabilizing the HOCO and destabilizing the LUCO, causing the gap to open further. An analogous situation exists for alloy I1 where only changes in the C-B linkages have a net effect on the C O energies: destabilizing both the H O C O and the LUCO, the latter to a greater extent, again causing a further opening of the gap.
Synopsis Extended-Huckel crystal orbital computations on the structural isomers of several graphite-boron nitride alloys have produced band structures and energy gaps comparable to previous computations. More importantly, the concepts of qualitative crystal orbital theory have allowed for an understanding of the band diagrams and bandgaps of these structurally similar materials in a simple crystal orbital framework, as well as providing for an qualitative evaluation of the effects of crystal relaxation. Acknowledgment. I am especially grateful to Dr. Miklos Kertesz for many helpful discussions and to Dr. Myung-Hwan Whangbo for generously allowing the use of his EHCO computer program. (18) Bassini, F.; Parravicini, G . P. Electronic States and Optical Transitions in Solids. In International Series of Monographs in the Science of Solid State; Pergamon Press: Oxford, 1975; Vol. 8.
