DescriptionThe lack of chemical uniformity in a powder mixture, such as clustering of a minor component, can lead to deterioration of materials properties. A method to determine powder mixture quality is to correlate the chemical homogeneity of a multi-component mixture with its particle size distribution and mixing method. This is applicable to rare earth-doped ceramics, which require at least 1-2 nm dopant ion spacing to optimize optical properties. Mixedness simulations were conducted for random heterogeneous mixtures of Nd-doped LaF3 mixtures using the Concentric Shell Model of Mixedness (CSMM). Results indicate that when the host to dopant particle size ratio is 100, multi-scale concentration variance is optimized. In order to verify results from the model, experimental methods that probe a mixture at the micro, meso, and macro scales are needed. To directly compare CSMM results experimentally, an image processing method was developed to calculate variance profiles from electron images. An in-lens (IL) secondary electron image is subtracted from the corresponding Everhart-Thornley (ET) secondary electron image in a Field-Emission Scanning Electron Microscope (FESEM) to produce two phases and pores that can be quantified with 50 nm spatial resolution. A macro was developed to quickly analyze multi-scale compositional variance from these images. Results for a 50:50 mixture of NdF3 and LaF3 agree with the computational model. The method has proven to be applicable only for mixtures with major components and specific particle morphologies, but the macro is useful for any type of imaging that produces excellent phase contrast, such as confocal microscopy. Fluorescence spectroscopy was used as an indirect method to confirm computational results for Nd-doped LaF3 mixtures. Fluorescence lifetime can be used as a quantitative method to indirectly measure chemical homogeneity when the limits of electron microscopy have been reached. Fluorescence lifetime represents the compositional fluctuations of a dopant on the nanoscale while accounting for billions of particles in a fast, non-destructive manner. The significance of this study will show how small-scale fluctuations in homogeneity limit the optimization of optical properties, which can be improved by the proper selection of particle size and mixing method.