Statistical comparison of the geometry of second-phase particles

In microscopic studies of materials, there is often a need to provide a statistical test as to whether two microstructures are different or not. Typically, there are some random objects (particles, grains, pores) and the comparison concerns their density, individual geometrical parameters and their spatial distribution. The problem is that neighbouring objects observed in a single window cannot be assumed to be stochastically independent, therefore classical statistical testing based on random sampling is not applicable. The aim of the present paper is to develop a test based on N-distances in probability theory. Using the measurements from a few independent windows, we consider a two-sample test, which involves a large amount of information collected from each window. An application is presented consisting in a comparison of metallographic samples of aluminium alloys, and the results are interpreted.