Abstract
We discuss the filling of three-dimensional Euclidean space with tetrahedra having two possible kinds of vertex atoms and three kinds of edge lengths (interatomic distances) as described by K. Y. Szeto and J. Villain [Phys. Rev. B 36, 4715 (1987)]. We identify certain periodic structures corresponding to the authors' third solution with members of the family of tetrahedrally close-packed (tcp) alloy structures [including Frank-Kasper (FK) phases] and discuss factors limiting the generation of additional tcp alloy structure types with the procedure described.
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