KELVINS CONJECTURE ON MINIMAL FROTHS AND THE COUNTEREXAMPLE OF WEAIREAND PHELAN

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.