Metastability relationship between two- and three-dimensional crystal structures: a case study of the Cu-based compounds

Some of the three-dimensional (3D) crystal structures are constructed by stacking two-dimensional (2D) layers. To study whether this geometric concept, i.e., using 2D layers as building blocks for 3D structures, can be applied to computational materials design, we theoretically investigate the dynamical stability of copper-based compounds CuX (a metallic element X) in the B[Formula: see text] and L1[Formula: see text] structures constructed from the buckled honeycomb (BHC) structure and in the B2 and L1[Formula: see text] structures constructed from the buckled square (BSQ) structure. We demonstrate that (i) if CuX in the BHC structure is dynamically stable, those in the B[Formula: see text] and L1[Formula: see text] structures are also stable. Using molecular dynamics simulations, we particularly show that CuAu in the B[Formula: see text] and L1[Formula: see text] structures withstand temperatures as high as 1000 K. Although the interrelationship of the metastability between the BSQ and the 3D structures (B2 and L1[Formula: see text] ) is not clear, we find that (ii) if CuX in the B2 (L1[Formula: see text] ) structure is dynamically stable, that in the L1[Formula: see text] (B2) is unstable. This is rationalized by the tetragonal Bain path calculations.