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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<\/jats:italic> (a metallic element X<\/jats:italic>) in the B$$_h$$<\/jats:tex-math>\n \n \n h<\/mml:mi>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and L1$$_1$$<\/jats:tex-math>\n \n \n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> structures constructed from the buckled honeycomb (BHC) structure and in the B2 and L1$$_0$$<\/jats:tex-math>\n \n \n 0<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> structures constructed from the buckled square (BSQ) structure. We demonstrate that (i) if CuX<\/jats:italic> in the BHC structure is dynamically stable, those in the B$$_h$$<\/jats:tex-math>\n \n \n h<\/mml:mi>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and L1$$_1$$<\/jats:tex-math>\n \n \n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> structures are also stable. Using molecular dynamics simulations, we particularly show that CuAu in the B$$_h$$<\/jats:tex-math>\n \n \n h<\/mml:mi>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> and L1$$_1$$<\/jats:tex-math>\n \n \n 1<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> structures withstand temperatures as high as 1000\u00a0K. Although the interrelationship of the metastability between the BSQ and the 3D structures (B2 and L1$$_0$$<\/jats:tex-math>\n \n \n 0<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>) is not clear, we find that (ii) if CuX<\/jats:italic> in the B2 (L1$$_0$$<\/jats:tex-math>\n \n \n 0<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula>) structure is dynamically stable, that in the L1$$_0$$<\/jats:tex-math>\n \n \n 0<\/mml:mn>\n <\/mml:msub>\n <\/mml:math><\/jats:alternatives><\/jats:inline-formula> (B2) is unstable. This is rationalized by the tetragonal Bain path calculations.<\/jats:p>","DOI":"10.1038\/s41598-021-94034-6","type":"journal-article","created":{"date-parts":[[2021,7,16]],"date-time":"2021-07-16T10:03:33Z","timestamp":1626429813000},"update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Metastability relationship between two- and three-dimensional crystal structures: a case study of the Cu-based compounds"],"prefix":"10.1038","volume":"11","author":[{"given":"Shota","family":"Ono","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"297","published-online":{"date-parts":[[2021,7,16]]},"reference":[{"key":"94034_CR1","doi-asserted-by":"publisher","first-page":"106101","DOI":"10.1103\/PhysRevLett.118.106101","volume":"118","author":"M Ashton","year":"2017","unstructured":"Ashton, M., Paul, J., Sinnott, S. B. & Hennig, R. G. 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