Mathematical modelling of mechanical alloying
This thesis applies Smoluchowski's coagulation-fragmentation equations to model the mechanical alloying process. Mechanisms operating during the milling process are reviewed. In the first instance, models are developed that predict the size distribution of a single milled powder while ignoring mixing phenomena. A methodology is developed that allows experimentally measured sieve-fractions to be converted into volumetric cluster size distributions. Model parameters describing the rate of aggregation and fragmentation are obtained by fitting the model's predicted average particle size data over time to that measured in experiments. Different size-dependent aggregation and fragmentation rates are tested in many milling scenarios and the most realistic size-dependence of rates is found. In the second part of the thesis, the best size-dependent rates are generalised and used with a two-component version of \Smol's system of equations. This model also includes binary mixing phenomena by considering clusters that have two types of component. The two-component models are applied to experimental situations using the methods developed for one-component models. Comparing these multi-component models to experimental measurements verifies the modelling method and gives reasonable agreement. An improved fragmentation rate is suggested to enhance the model's accuracy in the prediction of mixing rates.