A technique for characterizing spatial distributions of particles based on Nth-nearest neighbor statistics

Excerpt

Spatial heterogeneity in secondary phase particle distributions can strongly influence failure processes. In developing models that capture the stochastic nature of failure, the fact that real particle distributions rarely exhibit the “true” randomness of an equilibrium ensemble (as may be generated computationally using a Metropolis algorithm [1]) presents a challenge. In modeling investigations, some form of “random” state has typically been assumed. Representative volume element models are often employed in which particles are added via Random Sequential Addition (RSA) [2‐5]. Microstructures that deviate from equilibrium have been modeled by distributing particles within randomly dispersed spherical clusters [6], or by adopting a cellular automata approach [7‐9]; in each case, the model microstructures were arbitrarily constructed. …