Moment reconstruction of grain size distributions from nucleation and growth

The grain size distribution of a polycrystalline material is an important determinant of the material’s properties – for example, thermal stability, strength, and ductility. Typically this distribution depends on the nucleation and growth process at the beginning of the material’s formation. Therefore, modeling this processing-structure relation, in conjunction with a structure-property relation, has important applications for the prediction and optimization of material properties. An efficient model exploits the reconstruction of a grain size distribution from the distribution’s moments, which may be computed for a given nucleation and growth schedule. A caveat of the method is the sensitivity of the reconstruction to the choice of a basis distribution, and the lack of fundamental principles favoring one basis distribution over another. Presently, the question of which basis distribution to use remains open, hindering direct application of the method. We therefore propose an answer to this question, via comparative study of reconstructions using different basis distributions. These basis distributions will be evaluated based on identifiability of basis parameters, speed of identification of basis parameters, and fidelity of reconstructions to analytic distributions. We consider a large class of relevant distributions, so our results may extend to arbitrary grain distributions from general nucleation and growth schedules.