Cutting Materials in Half: A Graph Theory Approach for Generating Crystal Surfaces and Its Prediction of 2D Zeolites

Abstract

Scientific interest in two-dimensional (2D) materials, ranging from graphene and other single layer materials to atomically thin crystals, is quickly increasing for a large variety of technological applications. While in silico design approaches have made a large impact in the study of 3D crystals, algorithms designed to discover atomically thin 2D materials from their parent 3D materials are by comparison more sparse. We hypothesize that determining how to cut a 3D material in half (i.e., which Miller surface is formed) by severing a minimal number of bonds or a minimal amount of total bond energy per unit area can yield insight into preferred crystal faces. We answer this question by implementing a graph theory technique to mathematically formalize the enumeration of minimum cut surfaces of crystals. While the algorithm is generally applicable to different classes of materials, we focus on zeolitic materials due to their diverse structural topology and because 2D zeolites have promising catalytic and separation performance compared to their 3D counterparts. We report here a simple descriptor based only on structural information that predicts whether a zeolite is likely to be synthesizable in the 2D form and correctly identifies the expressed surface in known layered 2D zeolites. The discovery of this descriptor allows us to highlight other zeolites that may also be synthesized in the 2D form that have not been experimentally realized yet. Finally, our method is general since the mathematical formalism can be applied to find the minimum cut surfaces of other crystallographic materials such as metal–organic frameworks, covalent-organic frameworks, zeolitic-imidazolate frameworks, metal oxides, etc.

Graph similarity drives zeolite diffusionless transformations and intergrowth

“…We propose that descriptors based on topology and structure can achieve improved explanatory and predictive power for some classes of experimental relations. Graphs are well-known representations to encode the topology of zeolites [16][17][18][19] . capture periodic boundary conditions ( Fig.…”

Bridging the Gap between Structurally Distinct 2D Lamellar Zeolitic Precursors through a 3D Germanosilicate Intermediate

“…[9a] Thep air distribution function has been used experimentally for estimating the similarity between zeolites. [10] Interestingly,t he similarity score (1/D) was extraordinarily high for the fer layer versus the pcr layer (Figure 1a), which indicates as trong topological relationship between them. [10] Interestingly,t he similarity score (1/D) was extraordinarily high for the fer layer versus the pcr layer (Figure 1a), which indicates as trong topological relationship between them.…”

“…[9b] Thec urrent study employs the pcr layer from the disassembly of the UTL phase as ar eference to evaluate its structural similarity with other 2D zeolites,w hich were cleaved from their corresponding 3D zeolites (Scheme S1). [10] Interestingly,t he similarity score (1/D) was extraordinarily high for the fer layer versus the pcr layer ( Figure 1a), which indicates as trong topological relationship between them. Indeed, the fer and pcr layer exhibit asimilar projection along their crystallographic c directions (Figure 1b, c).…”

Using graphs to quantify energetic and structural order in semicrystalline oligothiophene thin films

“…Although morphology has been previously represented as graphs, the quantification has been focused on either meso scale 13,14 or atomistic level 15 . The work reported in this paper in an interesting step towards convergence of representation in multiscale modeling, as graphs have been mostly used to represent molecular structure [16][17][18] .…”