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We model the quasicrystal-related structure CaCd$_6$, a bcc packing oficosahedral clusters containing tetrahedra which undergo orientationalorderings at T<100 K. We use general schemes to evaluate an effectiveHamltonian for inter-tetrahedron orientations, based on all-atom relaxations,either in terms of discrete cluster orientations, or of continuous rotationangles. The effective Hamiltonian is used in Monte Carlo simulations to findthe (complex) ground state ordering pattern as a function of pressure. Apreliminary investigation of thermal transitions found (in part of the pressurerange) two different first-order transitions occurring below 100 K.

Orientational interaction and ordering of Cd_4 tetrahedra in a quasicrystal approximant