High-throughput systematic topological generation of low-energy carbon allotropes

Abstract

The search for new materials requires effective methods for scanning the space of atomic configurations, in which the number is infinite. Here we present an extensive application of a topological network model of solid-state transformations, which enables one to reduce this infinite number to a countable number of the regions corresponding to topologically different crystalline phases. We have used this model to successfully generate carbon allotropes starting from a very restricted set of initial structures; the generation procedure has required only three steps to scan the configuration space around the parents. As a result, we have obtained all known carbon structures within the specified set of restrictions and discovered 224 allotropes with lattice energy ranging in 0.16–1.76 eV atom−1 above diamond including a phase, which is denser and probably harder than diamond. We have shown that this phase has a quite different topological structure compared to the hard allotropes from the diamond polytypic series. We have applied the tiling approach to explore the topology of the generated phases in more detail and found that many phases possessing high hardness are built from the tiles confined by six-membered rings. We have computed the mechanical properties for the generated allotropes and found simple dependences between their density, bulk, and shear moduli.

A triatomic carbon and derived pentacarbides with superstrong mechanical properties

“…The experimental verification for the Vickers hardness is needed in the future. It is also larger than those of all previous reported superhard materials and carbon allotropes ( Avery et al., 2019 ; Chen et al., 2011 ; Tian et al., 2012 ), as seen in Figure 4 and Table S2 , including V-carbon of 90 GPa ( Yang et al., 2017 ), M-carbon of 83.1 GPa ( Li et al., 2009 ), Cco-C 8 carbon of 95.1 GPa ( Zhao et al., 2011 ), 4 3 T16-CA carbon of 91.16 GPa ( Blatov et al, 2021 ), etc. In Table S1 , all the results derived from Tian’s model ( Tian et al., 2012 ), Mazhnik’s model ( Mazhnik and Oganov, 2019 , 2020 ), Chen’s model ( Chen et al., 2011 ), and Teter’s model ( Teter, 2013 ) showed that h-C 3 is harder than diamond, while Gao’s model ( Gao et al., 2003 ) shows that h-C 3 is softer than diamond.…”

Topological transformations in metal–organic frameworks: a prospective design route?

“…The formalism of 'supernet-subnet' relations was developed before, automated in ToposPro, and successfully applied to explore the configuration space of the carbon system. [60][61][62][63] In terms of this formalism, the whole configuration space of a chemical system can be split into network regions, where particular underlying topologies are stable. Thus, to search for new phases, one does not need to scan all possible geometrical configurations, but can consider only countable numbers of different underlying nets.…”

Towards Predictive Synthesis of Inorganic Materials Using Network Science

“…The reactants, traverse a complex chemical space along reaction pathways (links) that are governed by kinetics, through intermediates (nodes) breaking and forming bonds, before finally reaching the desired products. In contrast, in the crystalline network of a solid, the nodes represent atoms and the links (bonds) are undirected (Blatov et al, 2019(Blatov et al, , 2021. What makes networks useful is that their interaction structure (i.e., the network's topology) accounts for their systemic properties and, therefore, topological analysis can lead to applicable, impactful outcomes.…”