First-principles studies for structural transitions in ordered phase of cubic approximant Cd6Ca

Recently low-temperature structural transition has been reported for complex cubic compounds Cd6M (M=Ca, Yb, Y, rare earth) and it is believed that the transition is due to orientational ordering of an atomic shell in the icosahedral cluster in Cd6M. The first-principles electronic structure calculations and structural relaxations are carried out to investigate structures and orientational ordering of the innermost tetrahedral shell of the icosahedral cluster in Cd6Ca. The very short interatomic distances in the experimental average structures are relaxed and the innermost tetrahedral shell of an almost regular shape is obtained. Three types of orientation for the tetrahedral shell and eight different combinations of them for the clusters at a vertex and body-centre of a cubic cell are obtained. A possible model describing the orientational ordering at low temperatures or high pressures is discussed.