Zeolite LTA structure generation by Coordination Sequence and Vertex Symbol

Impact of Organic Templates on the Selective Formation of Zeolite Oligomers

“…On the other hand, TMA + and TEA + trigger the formation of branched 4‐rings (up to 37.7 % and 33.9 %, respectively in Figure S6), which may be likely precursors of larger key building blocks such as the double 4‐ring (D4R). D4R represents a common composite building unit (CBU) of about 39 known zeolite framework topologies, including synthetized structures (such as LTA, ACO and UFI)[40], as well as a large number of hypothetical structures [41–43] …”

“…D4R represents ac ommon composite building unit (CBU) of about 39 known zeolite framework topologies,i ncluding synthetized structures (such as LTA, ACOand UFI)[40],aswell as alarge number of hypothetical structures. [41][42][43]…”

On the growth of the wallpaper groups

“…The coordination sequence of this graph is an example of a topological property. In Baerlocher et al (2007), the first ten entries of the coordination sequence are used to document all known zeolites, while in Hu et al (2020), a program is created to construct new potential zeolite structures, given a vertex symbol and the first entries of the coordination sequence as input. Furthermore, similar to the classical notion of density as the weight of atoms per unit volume, the asymptotic behavior of the coordination sequence gives rise to the notion of topological density, which has been studied for zeolites by Brunner (1979) and for water by Herrero & Ramı ´rez (2013).…”

On the growth of the wallpaper groups

“…When Γ is an infinite graph, the growth rate of γ(n) when n → ∞ is an important characteristic of the graph. The function γ(n) is called the growth function or coordination sequence of Γ, and it appears in the study of lattices ( [10] and [20]), the study of crystallographic objects such as Zeolites in chemistry ( [5] and [17]), and also in geometric group theory [12].…”