Two-Dimensional Frank-Kasper Z Phase with One Unit-Cell Thickness

Z phase is one of the three basic units by which the Frank-Kasper (F-K) phases are generally assembled. Compared to the other two basic units, that is, A₁₅ and C₁₅ structures, the Z structure is rarely experimentally observed because of a relatively large volume ratio among the constituents to inhibit its formation. Moreover, the discovered Z structures are generally the three-dimensional ordered Gibbs bulk phases to conform to their thermodynamic stability. Here, we confirmed the existence of a metastable two-dimensional F-K Z phase that has only one unit-cell height in the crystallography in a model Mg-Sm-Zn system, using atomic-scale scanning transmission electron microscopy combined with the first-principles calculations. Self-adapted atomic shuffling can convert the simple hexagonal close-packed structure to the topologically close-packed F-K Z phase. This finding provides new insight into understanding the formation mechanism and clustering behavior of the F-K phases and even quasicrystals in general condensed matters.