Stochastic generation of complex crystal structures combining group and graph theory with application to carbon

Abstract

A method is introduced to stochastically generate crystal structures with defined structural characteristics. Reasonable quotient graphs for symmetric crystals are constructed using a random strategy combined with space group and graph theory. Our algorithm enables the search for large-size and complex crystal structures with a specified connectivity, such as threefold sp 2 carbons, four-fold sp 3 carbons, as well as mixed sp 2-sp 3 carbons. To demonstrate the method we randomly construct initial structures adhering to space groups from No.75 to No.230 and a range of lattice constants, and we identify 281 new sp 3 carbon crystals. First-principles optimization of these structures show that most of them are dynamically and mechanically stable and are energetically comparable to those previously proposed. Some of the new structures can be considered as candidates to explain the experimental cold compression of graphite.

Azugraphene: a new graphene-like hexagonal carbon allotrope with Dirac cones

“…The rst principle symmetric search program were performed with 3-40 carbon atoms per unit cell. 18,19 At rst, ve 2D unit cells were dened by g ¼ 120 and a ¼ b ¼ 4, 6, 8, 10, and 12 A, respectively. Secondly, given a 2D groups P6, P6mm, P3, P3m1, or P31m, these predened cells were lled by randomly putting the nite-sized atoms and their symmetric equivalent atoms step-by-step.…”

Low‐Energy GeP Monolayers with Natural Type‐II Homojunctions for SunLight‐Driven Water Splitting

“…It is different from the situations of C and N atoms in graphitic C 3 N 4 , C 2 N, and C 3 N, which P and Ge atoms with larger radius and mass prefer sp 3 hybridization to form three‐ and four‐connected atomic configurations, respectively. The mixed three and fourfold atomic configurations were potentially low‐energy crystalline structures for GeP compounds, which could be effectively visited by RG 2 code . Herein, RG 2 code is employed to systematically generate, with connectivity constraints of threefold triangular P and fourfold tetrahedral Ge, possible GeP monolayers (only 1:1 GeP alloys without P—P bonds are considered) containing up to 24 atoms.…”

“…In this work, we propose two new kinds of 2D GeP allotropes, named as GeP‐2 and GeP‐4, based on our recently developed crystal structure prediction code RG 2 . Their structures can be decomposed into hypothetical (2,2) and (4,4) GeP nanotubes, which are very similar to the experimentally synthesized C2/m (GeP‐3 structurally relating to (3,3) GeP nanotube) phase .…”

Extreme Energy Density Confined inside a Transparent Crystal: Status and Perspectives of Solid-Plasma-Solid Transformations

“…Therefore relaxation to the ambient conditions occurs along the unknown paths going through the metastable intermediate equilibrium potential minima. The theoretical (computational, modified DFT-studies) during the last decade searched for the possible paths of material transformations under high pressure from the initially chaotic (stochastic) state [5]. These studies uncovered many physically allowed paths for formation of multiple novel phases (including incommensurable phases) from the initially chaotic state.…”