  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.
