A novel algorithm for characterization of order in materials

Abstract

In this work, we present a simple approach for devising order parameters (OPs) for atomic systems based on pattern recognition techniques. It exploits the fact that all crystalline substances are characterized by a unique “signature” cell (SC) which is constructed using a central atom and its nearest NSC neighbors in a given crystal. The algorithm measures the local degree of similarity between a SC and the system to be analyzed. The best fit of a SC to NSC atoms surrounding a given atom in the system is determined by maximizing a fictitious energy of binding among those atoms and the SC atoms. The fictitious potential energy is designed to give maximum attractive energy for maximum overlap. The maximum binding energy of interaction attained in this process is used as a measure of similarity between the crystal structure and the system (i.e., as an OP). The proposed method provides a unified and intuitive approach for constructing relevant OPs for a given system. We used these OPs to characterize the order of different phases in the Lennard-Jones system and in a model silicon system. It is shown that these novel OPs give a more complete description and a better understanding of the structural order in amorphous silicon than conventional OPs.

Atomistic computer simulation of explosive crystallization in pure silicon and germanium

“…The properties of the amorphous material were consistent with those described in Ref. 18. Experimentally, the sample is initially all amorphous, with explosive crystallization typically initiated by a laser.…”

“…Monitoring the order of the system on a per-atom or a slicewise basis is the most natural way to determine this. Many order parameters for tetrahedrally coordinated atoms are available, [18][19][20][21][22] and there is little to choose among them in terms of effectiveness. We chose to use the angular criterion of Uttormark and Clancy, 19 which we had employed previously for studies of Si.…”

Assessing Local Structure Motifs Using Order Parameters for Motif Recognition, Interstitial Identification, and Diffusion Path Characterization

“…Hence, there is a need to more reliably identify structural motifs with order parameters. Peters (2009) and Zimmermann et al (2015) have introduced order parameters based on pattern-matching ideas put forward by Shetty et al (2002). The OPs specifically recognize body-centered cubic-like (Peters, 2009) as well as tetrahedral and octahedral environments (Zimmermann et al, 2015).…”

“…Neighbors can be found on the basis of interatomic distances-possibly in combination with typical bond lengths (Brunner, 1977;Hoppe, 1979;O'Keeffe and Brese, 1991)-or by a topology-based approach (Dirichlet, 1850;Voronoi, 1908;Mickel et al, 2013). For pattern matching, there exist two popular conceptual approaches: (i) using Monte Carlo (MC) moves (Shetty et al, 2002) and (ii) using order parameters (Steinhardt et al, 1983;Peters, 2009;Zimmermann et al, 2015). In the MC approach, an ideal structure motif is placed onto a central atom and its neighbors, and the ideal motif 's position and size are varied to yield a small root mean square deviation between the positions of the ideal motif and the neighbors of the central atom.…”

Competing nucleation pathways in a mixture of oppositely charged colloids: Out-of-equilibrium nucleation revisited

“…Our procedure is similar to the template based order parameters of Shetty et al 57 Atoms in a CsCl environment are surrounded by a cube of oppositely charged nearest neighbors, as shown in Fig. Our procedure is similar to the template based order parameters of Shetty et al 57 Atoms in a CsCl environment are surrounded by a cube of oppositely charged nearest neighbors, as shown in Fig.…”