Density of the p2gg-4c1 packing of ellipses (II)

Abstract

Abstract As the second paper of the series, the first of which was published in 1997 (M. Tanemura, T. Matsumoto, Density of the p2gg-4c1 packing of ellipses (I). Z. Kristallogr. 1997, 212, 637), the p2gg-4c1(b) packing of identical ellipses where four ellipses are included in the rectangular unit cell and where every ellipse has six contacting neighbors, is discussed. It is shown here that the p2gg-4c1(b) packing of ellipses does not exceed the maximum density ρ   =   π / 12 $\rho \; = \;\pi /\sqrt {12} $ through numerical computations and series expansions. It is also shown that the p2gg-2a2 packing of ellipses has the similar properties and that it is considered as a special case of p2gg-4c1(b) packing. The method of computing the density for every parameter values of aspect ratio and tilt angle is given.