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

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