Exploring Group 14 Structures: 1D to 2D to 3D

Various one-, two- and three-dimensional Group 14 (C, Si, Ge, Sn, and Pb) element structures at P = 1 atm are studied in this work. As expected, coordination number (CN)-not an unambiguous concept for extended structures-plays an important part in the stability of structures. Carbon not only favors four-coordination, but also is quite happy with pi-bonding, allowing three- and even two-coordination to compete. Highly coordinated (CN > 4) discrete carbon molecules are rare; that "saturation of valence" is reflected in the instability of C extended structures with CN > 4. Si and Ge are quite similar to each other in their preferences. They are less biased in their coordination than C, allowing (as their molecular structures do) CN = 5 and 6, but tending towards four-coordination. Sn and Pb 3D structures are very flexible in their bonding, so that in these elements four- to twelve-coordinate structures are close in energy. This lack of discrimination among ordered structures also points to an approach to the liquid state, consistent with the low melting point of Sn and Pb. The Group 14 liquid structures we simulate in molecular dynamics calculations show the expected, effective, first coordination number increase from 5.1 for Si to 10.4 for Pb. A special point of interest emerging from our study is the instability of potential multilayer graphene structures down Group 14. Only for C will these be stable; for all the other Group 14 elements pristine, unprotected, bi- and multilayer graphenes should collapse, forming "vertical" bonds as short as the in-plane ones.