An effective method to determine the probability density function of spherical second-phase particles

An effective computer numerical method is developed to determine the continuous numerical empirical probability density function (PDF) of the three-dimensional size distribution (3-DSD) of spherical second-phase particles. The method consists of a precise stereological equation and a numerical algorithm including a self-adaptive grouping technique. Finally, the errors between the estimated and actual parameters of the 3-DSD are analysed and discussed. The findings indicate that the method can simulate the PDF of the 3-DSD and predict the 3-DSD accurately.