  Modeling microstructures is an interesting problem not just in Materials
Science but also in Mathematics and Statistics. The most basic model for steel
microstructure is the Poisson-Voronoi diagram. It has mathematically attractive
properties and it has been used in the approximation of single phase steel
microstructures. The aim of this paper is to develop methods that can be used
to test whether a real steel microstructure can be approximated by such a
model. Therefore, a general framework for testing the Poisson-Voronoi
assumption based on images of 2D sections of real metals is set out. Following
two different approaches, according to the use or not of periodic boundary
conditions, three different model tests are proposed. The first two are based
on the coefficient of variation and the cumulative distribution function of the
cells area. The third exploits tools from to Topological Data Analysis, such as
persistence landscapes.
