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Author King, R. B.
Source United States Department of Energy Office of Scientific and Technical Information
Content type Text
Language English
Subject Keyword MATERIALS SCIENCE ♦ MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS ♦ CARBON ♦ ALLOTROPY ♦ TOPOLOGY ♦ FULLERENES ♦ CRYSTAL STRUCTURE ♦ MOLECULAR STRUCTURE ♦ CALCULATION METHODS
Abstract The construction of graphite and fullerene structures from networks of trigonal sp{sup 2} carbon atoms of zero and positive curvature can be extended to a fourth form of carbon, provisionally called schwarzites, consisting of networks of trigonal sp{sup 2} carbon atoms decorating infinite periodic minimal surfaces (IPMS`s) of negative curvature and topological genus 3 such as the so-called D and P surfaces. The carbon networks of the simplest schwarzite structures contain only six- and seven-membered rings. The stable structures of both fullerenes and schwarzites contain enough six-membered rings so that no two five-membered rings in the fullerene structures or no two seven-membered rings in the schwarzite structures share edges leading to unstable pentalene and heptalene units, respectively. The smallest unit cell of a viable schwarzite structure of this type contains 168 carbon atoms and is constructed by applying a leapfrog transformation to a genus 3 figure containing 24 heptagons and 56 vertices. Although this C{sub 168} schwarzite unit cell has local O{sub h} point group symmetry based on the cubic lattice of the D or P surface, its larger permutational symmetry group is the PSL(2,7) group of order 168 analogous to the icosahedral pure rotation group, I, of order 60 of the C{sub 60} fullerene considered as the isomorphous PSL(2,5) group. The porosity of the IPMS`s on which the schwarzite structures are based leads to predictions of unusually low density for this type of carbon allotrope. 38 refs., 11 figs., 5 tabs.
ISSN 00223654
Educational Use Research
Learning Resource Type Article
Publisher Date 1996-09-12
Publisher Place United States
Journal Journal of Physical Chemistry
Volume Number 100
Issue Number 37


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