Carbon Schwarzites: Properties and Growth Simulation from Fullerene Fragments
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Abstract We investigated by tight-binding molecular dynamics the structure, the bulk modulus and the electronic properties of the smallest four-branched carbon schwarzites fcc-(C 28)2 , fcc-(C 36 ) 2 and fcc-(C 40 ) 2 having the shape of a D minimal periodic surface. They are found to have a stability comparable to that of fullerene C 60 and to exhibit alternative metallic and insulating characters, with an apparent relationship to their local geometry. We also studied the coalescence of fullerenic fragments and carbon clusters by following the evolution of the topological connectivity. Though different temperature variation protocols lead to irregular structures similar to random schwarzites, their connectivity is found to stabilize at values corresponding either to tubulene or three-branched schwarzites, indicating that long time evolution at constant connectivity is potentially able to yield regular shapes. Experiments on laser-induced transformations of fullerite occasionally yield branched tubular structures with a schwarzite shape.
Introduction One of the most challenging development in modern technology is represented by devices based on atomic-scale porous materials. The interesting features that such materials exhibit range from large specific area (that permit to intercalate a great deal of lighter atoms such as alkali) to a large stability and stiffness (to prevent induced stress during the intercalation, unlike graphite that is damaged when intercalated.) In this framework carbon schwarzites [1] are predicted to be very interesting and promising materials for technological applications, e.g. as lithium absorbers for various functions in ionic devices. In particular, conducting schwarzites could be employed in cathodes (or/and anodes, depending on the combination of chemical potentials), while insulating schwarzites may work as low-temperature ionic conductors or molecular sieves. Most of schwarzite intriguing features derive from their peculiar atomic structure. The topology of schwarzites can be constructed solving the Euler's theorem for surface polygonal tilings. The theorem has to be referred to a single element, since schwarzites are open and infinitely extended surfaces. Among all the possible minimal periodic surfaces we constructed the topology of the D-type minimal periodic surfaces where each element coordinates four identical elements in the tetrahedral (staggered) configuration. The resulting crystal is fcc and has, like diamond, two elements per unit cell. In order to find the connectivity of this kind of schwarzites we can imagine to close a unit cell on itself by joining three pairs of opposite branches and transforming the surface in the topological equivalent of a three-hole torus of connectivity 7. Therefore, the Euler's theorem can be recast in the following form: vel - eei + f,1 = 3 - K
----2(1
529 Mat. Res. Soc. Symp. Proc. Vol. 491 c 1998 Materials Research Society
where vel, ee, and fe1 are the numbers of vertices (atoms), edges (bonds) and polygonal faces (rings) per element
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