A mixed radial, angular, three-body distribution function as a tool for local structure characterization: Application to single-component structures

Abstract

A mixed radial, angular three-body distribution function g3(rBC, θABC) is introduced, which allows the local atomic order to be more easily characterized in a single graph than with conventional correlation functions. It can be defined to be proportional to the probability of finding an atom C at a distance rBC from atom B while making an angle θABC with atoms A and B, under the condition that atom A is the nearest neighbor of B. As such, our correlation function contains, for example, the likelihood of angles formed between the nearest and the next-nearest-neighbor bonds. To demonstrate its use and usefulness, a visual library for many one-component crystals is produced first and then employed to characterize the local order in a diverse body of elemental condensed-matter systems. Case studies include the analysis of a grain boundary, several liquids (argon, copper, and antimony), and polyamorphism in crystalline and amorphous silicon including that obtained in a tribological interface.

Stress Anisotropy Severely Affects Zinc Phosphate Network Formation

“…The recently proposed mixed radial, angular, three-body distribution function (RADF) [70], g(r ik , cos ijk ) , contains implicitly most information from RDFs and ADFs. However, it allows additional insight to be gained in a single graphical representation, such as, typical angles between nearestneighbor and next-nearest-neighbor "bonds".…”

“…However, it allows additional insight to be gained in a single graphical representation, such as, typical angles between nearestneighbor and next-nearest-neighbor "bonds". Specifically, g(r ik , cos ijk ) can be defined as the probability density of finding an atom k at a distance r ik from atom i when the angles between vectors ik and ij take the value jik under the condition that the atoms i and j are nearest neighbors [70]. While there is some ambiguity to the precise choice beyond what maximally allowed bond length d max ij two atoms i and j cease to be considered neighbors, the precise value for d max ij usually does not play a significant role when it is chosen with moderate care.…”

Stress Anisotropy Severely Affects Zinc-phosphate Network Formation

“…To gain further insight on the structure, we computed the mixed radial, angular, three-body distribution function [70] (RADF) introduced in Sect. 2.4.4.…”

“…The recently proposed mixed radial, angular, three-body distribution function (RADF) [70], g(r ik , cos ϑ i jk ), contains implicitly most information from RDFs and ADFs. However, it allows additional insight to be gained in a single graphical representation, such as, typical angles between nearest-neighbor and next-nearest-neighbor "bonds".…”

“…However, it allows additional insight to be gained in a single graphical representation, such as, typical angles between nearest-neighbor and next-nearest-neighbor "bonds". Specifically, g(r ik , cos ϑ i jk ) can be defined as the probability density of finding an atom k at a distance r ik from atom i when the angles between vectors r ik and r i j take the value ϑ jik under the condition that the atoms i and j are nearest neighbors [70]. While there is some ambiguity to the precise choice beyond what maximally allowed bond length d max i j two atoms i and j cease to be considered neighbors, the precise value for d max i j usually does not play a significant role when it is chosen with moderate care.…”