J. Phys. I France
Volume 2, Numéro 12, December 1992
Page(s) 2191 - 2205
DOI: 10.1051/jp1:1992276
J. Phys. I France 2 (1992) 2191-2205

The T and CLP families of triply periodic minimal surfaces. Part 2. The properties and computation of T surfaces

Djurdje Cvijovic and Jacek Klinowski

Department of Chemistry, University of Cambridge, Lensfield Road, Cambridge CB2 1EW, G.B.

(Received 7 May 1992, accepted in final form 4 August 1992)

The geometry of a tD minimal surface depends on the ratio c/a of tetragonal axes, and can be fully described in terms of a single free parameter. We offer a choice of three such parameters, all related to surface geometry, and derive analytical expressions for their relationships to the axes ratio and the normalization factor. The latter is crucial for the matching of specific surfaces to real structures. Parametric equations for normalized tD surfaces make it possible, for the first time, to find the surface corresponding to any given value of the c/a ratio, and to compare it with actual structural data. Straightforward physical applications of tD surfaces are therefore possible. We discuss the geometric consequences of this result and show that the z coordinate of any tD surface can be approximated using elementary functions. A rational approximation for the relationship between the free parameter and the c/a ratio is also found. We list exact coordinates of tD surfaces corresponding to several prescribed values of the c/a ratio.

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