The b 0 precipitate phases formed in MgeY alloys, which exhibit characteristic periodic arrays of Y-rich zigzag-shaped atomic clusters at regular intervals of 1.1 nm, have attracted significant attention owing to their precipitation-hardening effect on the matrix. To investigate the formation mechanism of such cluster arrays, the interaction energies between Y clusters at various distances were quantitatively evaluated using first-principles calculations based on density functional theory. We found a weak but distinct interaction between the clusters caused by the interplay between attractive chemical interactions and repulsive relaxation energies. This interplay determines the energetically favorable structure of the cluster arrangements, and these structures are consistent with the experimental observations. We suggest that the long-range intercluster interactions dominate the alignment of Y clusters, which leads to the formation of b 0 precipitates in the Mg matrix, followed by the short-range clustering of Y atoms.