Nearest-neighbor distances between particles of finite size in three-dimensional uniform random microstructures

Nearest-neighbor distances (first and higher order) are an important class of spatial descriptors useful in materials science and other disciplines. These descriptors play a dominant role in microstructural evolution during recrystallization, coarsening, sintering and numerous other materials processes. In the present article, nearest-neighbor distances for mono-sized hard-core spheres in three-dimensional space are studied using computer simulations by two popular algorithms (random sequential adsorption (RSA) and equilibrium Monte Carlo method) and a simple expression (given below) is proposed for the mean values of first-, second-, and higher-order (up to sixth) nearest-neighbor distances: 〈 H n 〉 〈 P n 〉 = 1 + 2 − 1 / 6 ( n − 1 ) ! [ ( 4 / 3 ) π ] − 1 / 3 Γ [ ( 3 n + 1 ) / 3 ] − 1 f f 0 2 n / ( 2 n + 1 ) where 〈Hn〉 is the mean nth nearest-neighbor distance, f is volume fraction, 〈Pn〉 is corresponding mean nearest-neighbor distance for a point process and f0 is the volume fraction for the close-packed structure (i.e., π / 18 or ∼0.74). The predictions of this equation are in good agreement with the simulated results. This expression is applicable over the complete volume fraction range of 0 to π / 18 (i.e., ∼0.74).