The structural configurations of atoms constituting materials are one of the fundamental factors in the study of the physical properties of materials. Presented in this paper is a mathematical and computational methodology based on Euclidean Voronoi diagrams to efficiently classify a given atomic structure of an Al-Co composite material into groups of atoms with BCC, FCC, and HCP crystal structures. In this paper, the presented mathematical theory has been applied to analyze a multi-layer atomic structure with a geometric perspective so that the best conditions for thin film growth can be found.

Multi-component ceramic composites consisting of two, three and four phases, based on duplex microstructures of zirconia and alumina, were fabricated by a polymer complexation route employing polyethylene glycol (PEG) as a polymeric carrier. The polymer complexation route showed an unique exothermic reaction involving expansion of the powder structure and it provided highly sinterable powder by a simple ball milling process. In this study, the microstructures and flexural strengths of the multi-component (Al2O3-ZrO2-CeO2-SrO) ceramic composites were examined on the processing variations of the forming and sintering for close to nano-structures. A composite having four phases showed grain growth retardation and the microstructure and final phases were largely dependant on the sintering conditions. Needle-like grains from the addition of SrO improved the flexural strength of the multiphase composites.