Voronoi and Delaunay tessellations are applied to pattern recognition of atomic environments and to investigation of the nonlocal order in molecular-dynamics (MD)-simulated materials. The method is applicable also to materials generated using other computer techniques such as Monte Carlo. The pattern recognition is based on an analysis of the shapes of the Voronoi polyhedron (VP). A procedure for contraction of short edges and small faces of the polyhedron is presented. It involves contraction to vertices of all edges shorter than a certain fraction $x$ of the average edge length, with concomitant contraction of the associated faces. Thus, effects of fluctuations are eliminated, providing “true” values of the geometric coordination numbers $f,$ both local and averaged over the material. Nonlocal order analysis involves geometric relations between Delaunay simplexes. The methods proposed are used to analyze the structure of MD-simulated solid lead [J. Rybicki, W. Alda, S. Feliziani, and W. Sandowski, in Proceedings of the Conference on Intermolecular Interactions in Matter, edited by K. Sangwal, E. Jartych, and J. M. Olchowik (Technical University of Lublin, Lublin, 1995), p. 57; J. Rybicki, R. Laskowski, and S. Feliziani, Comput. Phys. Commun. 97, 185 (1997)] and germianium dioxide [T. Nanba, T. Miyaji, T. Takada, A. Osaka, Y. Minura, and I. Yosui, J. Non-Cryst. Solids 177, 131 (1994)]. For Pb the contraction results are independent of $x.\mathrm{}$ For the open structure of ${\mathrm{GeO}}_2$ there is an $x$ dependence of the contracted structure, so that using several values of $x$ is preferable. In addition to removing effects of thermal perturbation, in open structures the procedure also cleans the resulting VP from faces contributed by the second neighbors. The analysis can be combined with that in terms of the radial distribution $g\left(R\right),$ making possible comparison of geometric coordination numbers with structural ones [W. Brostow, Chem. Phys. Lett. 49, 285 (1977)].

• Received 9 May 1997

DOI:https://doi.org/10.1103/PhysRevB.57.13448