VORONOI POLYHEDRA AND DELAUNAY SIMPLEXES IN THE STRUCTURAL-ANALYSIS OF MOLECULAR-DYNAMICS-SIMULATED MATERIALS

Voronoi and Delaunay tessellations are applied to pattern recognition of atomic environments and to investigation of the nonlocal order in m olecular-dynamics (MD)-simulated materials. The method is applicable a lso to materials generated using other computer techniques such as Mon te Carlo. The pattern recognition is based on an analysis of the shape s of the Voronoi polyhedron (VP). A procedure for contraction of short edges and small faces of the polyhedron is presented. It involves con traction to vertices of all edges shorter than a certain fraction x of the average edge length, with concomitant contraction of the associat ed faces. Thus, effects of fluctuations are eliminated, providing ''tr ue'' values of the geometric coordination numbers f, both local and av eraged over the material. Nonlocal order analysis involves geometric r elations 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 I ntermolecular 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. Taka da, A. Osaka, Y. Minura, and I. Yosui, J. Non-Cryst. Solids 177, 131 ( 1994)]. For Pb the contraction results are independent of x. For the o pen structure of GeO2, there is an x dependence of the contracted stru cture, so that using several values of x is preferable. In addition to removing effects of thermal perturbation, in open structures the proc edure also cleans the resulting VP from faces contributed by the secon d neighbors. The analysis can be combined with that in terms of the ra dial distribution g(R), making possible comparison of geometric coordi nation numbers with structural ones.