A Physically-informed Graph-based Order Parameter for the Universal Characterization of Atomic Structures

Abstract

A new graph-based order parameter is introduced for the characterization of atomistic structures. The order parameter is universal to any material/chemical system, and is transferable to all structural geometries. Three sets of data are used to validate both the generalizability and accuracy of the algorithm: (1) liquid lithium configurations spanning up to 300 GPa, (2) condensed phases of carbon along with nanotubes and buckyballs at ambient and high temperature, and (3) a diverse set of aluminum configurations including surfaces, compressed and expanded lattices, point defects, grain boundaries, liquids, nanoparticles, all at non-zero temperatures. The aluminum configurations are also compared to existing characterization methods for both speed and accuracy. Our order parameter uniquely classifies every configuration and outperforms all crystalline order parameters studied here, opening the door for its use in a multitude of complex application spaces that can require fine configurational characterization of materials.

Quantifying Free-volume Topology in Atomistic Structures Through a Combination of Voxelization and Graph Theory

“…At the node-level of the graph, the degree of each node is simply the number of voxel-voxel sphere overlaps. SGOP-V, which is a modification of a previous graph-based order parameter [23], is then defined as:…”

“…SGOP-V is then used to distinguish unique classes of free-volume topologies. Further information regarding the theory behind this methodology can be found in our previous work [23].…”

“…Atomistic symmetry functions, such as the Smooth Overlap of Atomic Positions (SOAP) [21] and the Behler-Parrinello fingerprints [22] lack long-range connectivity information, resulting in their inability to capture the shape and density of features such as voids, channels, clusters, etc. [23].…”

Efficient, Interpretable Graph Neural Network Representation for Angle-dependent Properties and its Application to Optical Spectroscopy

“…DimeNet [11] and paiNN [13] were designed for non-periodic molecular structures. ALIGNN [12], which explicitly represents bond angles with (edges of) line graphs, is a general formulation applicable to non-periodic molecular graphs, as well as crystal graphs that represent periodic/crystalline systems [4,15]. However, such encoding is still not guaranteed to capture a system's full structural information.…”