Orientational interaction and ordering of Cd₄ tetrahedra in a quasicrystal approximant

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