Z phase is one of the three basic units by which the Frank-Kasper phases are generally assembled.Compared to the other two basic units, i.e., A15 and C15 structures, the Z phase 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 (3D) ordered Gibbs bulk phases to conform to their thermodynamic stability. Herein, we con rmed the existence of a metastable two-dimensional (2D) Frank-Kasper Z phase with one unit-cell height in the crystallography in a model Mg-Sm-Zn system, by using aberration-corrected high-angle annular dark-eld scanning transmission electron microscopy (HAADF-STEM) combined with density functional theory (DFT) calculations. This nding is important for understanding the relationship between the traditional crystal structures and the quasicrystals, and it is also expected to provide a new insight to understand the clustering and stacking behavior of atoms in condensed matters.
Main TextFrank-Kasper phase is a class of ordered crystals composed of the topologically close-packed atomiclayers [1,2], in which the atoms with a smaller radius form as the close-packed planes and the atoms with a larger radius embed in the tetrahedral gaps. So far, there have 28 different types of Frank-Kasper phases found experimentally (in Supplemental Table S1), including in metal alloys [3,4], inorganic colloids [5, 6], and soft matters [7][8][9][10].Generally, the Frank-Kasper phases can be considered as ordered approximates of quasi-periodic crystals due to some shared construction rules from atomic clustering and stacking [11]. Since the Al-Mn icosahedral quasicrystal discovered in 1984 by Shechtman et al [12], the complex architectures of Frank-Kasper phases are considered as a link between the traditional simple periodic structures (such as the face-centered cubic, hexagonal close-packed, and body-centered cubic structures) and quasicrystals [10,13].From the viewpoint of crystallography characteristics, there are two types of Frank-Kasper structures which be constructed by three basic units of A 15 (representative alloy: Cr 3 Si), C 15 (representative alloy:MgCu 2 ), and Z (representative alloy: Zr 4 Al 3 ) fundamental structures frequently observed to date, i.e., the pentagonal Frank-Kasper phases and the hexagonal Frank-Kasper phases [14,15]. The pentagonal Frank-Kasper structure (see Supplemental Figure S1) can be considered as a periodic arrangement of icosahedron (coordination number (CN) = 12) columns along the pseudo 10-fold axis promoting the formation of C 15 (parallelogram) and Z (rectangle) plane tiling patterns, and the parallelogram and rectangular patterns self-assemble under some geometrical constraints to generate the present pentagonal phases. Similarly, the hexagonal Frank-Kasper phases (see Supplemental Figure S2) can be regarded as a structure formed by the icositetrahedron (CN = 14) columns arranged periodically along the pseudo 12-fold ax...