Modeling of particle size evolution during mechanical milling

The process of mechanical alloying (MA) involves the repeated deformation, welding, and fracture of powder materials during grinding in high-energy mills. During MA, the size and size distribution of the particles change as a result of the particles’ different fracture and welding rates. The evolution of particle volume distributions during such a combined “fission-fusion” process can be described via a differential-integral equation. While analytical solutions are known for systems in which only fusion takes place, there is apparently no such solution for the fission-fusion problem. In this article, we describe a discretized form of the fission-fusion equation and apply it to modeling of particle size distributions during milling of elemental powders using previously determined fracture and welding rates appropriate to the global system of particles. Predicted particle size distributions mimic well those determined experimentally