A fundamental problem in assigning the correct diameter to particles is the shape of the particles. If the particles are spherical there is only one diameter applicable but several population means exist. If the particles are non-spherical there are also a number of dimensions that can be used as the characteristic "diameter". The SD of the distribution is standard statistics provided that the distribution is normal and not, as often occurs bimodal. There are many good texts on particle size analysis as it is an old topic; the problem with these fine particles is "seeing them" to characterise them.