Weaire and Phelan's recent discovery of a clathrate structure (that of
beta-tungsten) as an ordered minimal froth (space-filling assembly of
polyhedral bubbles) with less surface per unit volume than Kelvin's b
,c.c. arrangement of truncated octahedra suggests searching among othe
r known tetrahedrally close-packed crystalline phases for a structure
with even less surface per unit volume. Two possible candidates are pr
oposed, the sigma-phase (beta-uranium) and the T phase of Bergman, Wau
gh and Pauling (1957, Acta crystallogr., 10, 254). A general expressio
n for the energy of tetrahedrally close-packed structures with equal b
ubble volume is given.