Informed modeling of disorder

Understanding structure is paramount in developing structure-property relationships in all categories of materials, from hard to soft matter. Developing this understanding becomes particularly challenging in the realm of disorder, where the notion of periodicity breaks down. For systems of increasing disorder, the experimental probes of canonical crystallography contain diminishing information content, and traditional methods prove insufficient for structural solution. This thesis uses the methodology of informed modeling to gain insight into the structures of disordered materials, and investigate the limits of using reciprocal space information to derive meaningful real space structures. Informed modeling procedures are data-driven approaches to extracting structural solutions from the total scattering pattern, that incorporate some instance of prior information. This inclusion of priors — which can from complementary experiments or from first principles — is an inherently Bayesian approach to modeling structure. To establish this methodology, I investigate a series of three distinct systems with increasingly severe levels of disorder, that also possess increasingly powerful prior information. This thesis is comprised of a series of monographs on structural modeling, tied together by a central inquiry, and spanning crystalline, amorphous, and solution phase materials. The anomalous hydration behavior of ZrW2O8 is modeled using a set of local rules derived from experimental scattering and ab initio calculations. The propagation of deformations associated with these local rules throughout the structure is described by a series of spaghetti states which map onto the population of many negative thermal expansion phonons. The developed mixed modeling procedures effectively incorporate prior information from first principles, and cast a meaningful structure solution that is validated by total scattering and lattice dynamics. Next, a system of unique topological disorder is considered. Total scattering data are combined with rigid local constraints to develop the first ever squareplanar continuous random network (CRN), which is subsequently used to model an amorphous Pd/Pt(im)2 phase. This model is refined against the total scattering data using reverse Monte Carlo (RMC). Finally, an explicitly Bayesian approach is developed for refining solution phase protein structures against the pair distribution function (PDF). Although the protein PDF has very few features and limited information content, continuous prior probability distributions of local conformations are implemented in a Bayesian RMC. This proof of concept study vindicates the utility of the PDF in structure prediction, so long as a set of robust prior information is available. The three systems are considered in concert to demonstrate when structure solution is tractable: as the data becomes less discriminating, more judicious prior information is necessary in order to approach a meaningful structural solution.