Eon Jean Guillaume
Instituto de Química, Universidade Federal do Rio de Janeiro, Cidade Universitária, Brazil.
Acta Crystallogr A. 2013 Jan;69(Pt 1):119-21. doi: 10.1107/S0108767312042298. Epub 2012 Nov 14.
It was shown in a previous paper [Eon (2004). Acta Cryst. A60, 7-18] that the topological density of a periodic net can be calculated directly from its cycles figure, a polytope constructed from those cycles of the quotient graph of the net that are associated with its geodesic lines. It may happen that these lines generate a grid pattern forming a supercell, a phenomenon that was not considered in the former derivation of the formula but is common for lattice nets. An adjustment of the expression is proposed to this effect and applied to the square and hexagonal lattice nets as well as to the 13 families of cubic lattice nets.
在之前的一篇论文[Eon (2004). Acta Cryst. A60, 7 - 18]中表明，周期网络的拓扑密度可以直接从其圈图计算得出，圈图是一个多面体，由网络商图中与测地线相关的那些圈构建而成。可能会出现这些线生成形成超胞的网格图案的情况，这种现象在公式的先前推导中未被考虑，但对于晶格网络来说很常见。为此提出了对该表达式的调整，并将其应用于正方形和六边形晶格网络以及13个立方晶格网络族。
