Abstract

This work reviews, expands upon, tests, and utilizes reciprocal space models of diffraction. In Chapter 2, reciprocal space models are reviewed, moving from strict assumptions of spatial unboundedness and three-dimensional periodicity to more relaxed assumptions of partial periodicity and finite crystals. Throughout the chapter, concepts are illustrated practically through examples of metallic nickel. New expressions are presented and a new approach is shown for approximating the diffraction effect of finite crystal size for a powder ensemble of one-dimensionally disordered crystals. A generalized shape function approach is demonstrated for the first time for the case of a spatially finite one-dimensionally disordered average crystal, without introducing any new definition to the layer electron density. It is explicitly pointed out that care must be taken in choosing models: there is a trade-off between computational expense, accuracy, and physicality. It is essential that the limitations (assumptions) of the models are kept in mind when adopting any specific approach. In Chapter 3, reciprocal space models are tested on synthetic powder diffraction data computed by applying the Debye scattering equation to several atomistic powder specimens. A process for creating atomistic powder ensembles is outlined, and a novel method is proposed for accurately approximating the ensemble-averaged powder diffraction pattern. The minimum library size is determined and compared for each ensemble considered, and it is found that libraries of less than 620 domains are generally sufficient to approximate the ensemble average. The ensemble-averaged powder diffraction data is fit where possible using several different models, and it is found that only the new model for finite, linearly disordered-crystals is successful both at reproducing the powder diffraction data and accurately retrieving the physical characteristics of the samples. It is seen that while a failure to satisfy model assumptions does not necessarily imply that the data fitting fails, it can necessitate that the fitted parameters do not reflect the true characteristics of the sample. In Chapter 4, different RS models are utilizing to fit powder diffraction data from nanostructured boron nitride samples to establish the most likely nanostructure. It is found that models incorporating the powder diffraction effects of stacking disorder and finite crystal size, while not significantly improving the agreement with the observed diffraction data, yielded more accurate and precise refined parameters, and are in better agreement with electron microscopy studies when compared to models assuming a sintered mixture of two nanocrystalline phases. With this result, it is possible to conclude that the most likely nanostructural model is that of sintered bodies composed of a single one-dimensionally disordered nanocrsytalline phase, rather than a two-phase or nanocomposite sintered body. Beyond this, by constructing simulated nanostructures through stochastically sampling refined sample characteristics, it is possible to further conclude that in the samples investigated, the primary manifestation of one-dimensional disorder is the presence of twin boundaries, leading to nanometer scale twin bands or “nanotwins” as proposed by those who synthesized the samples, and ruling out the presence of significantly large bands showing a wurtzite boron nitride structure.