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While it is widely appreciated that disorder is intricately related to observed sample-to-sample variation in property values, outside of very specialized cases, analysis is often qualitative in nature. One well-understood quantitative approach is based on the 1930s work of Bragg and Williams, who established an order parameter S, which ranges from unity in the case of a perfectly ordered structure to zero in the case of a completely randomized lattice. Here, we demonstrate that this order parameter is directly related to charge carrier mobility in undoped GaN. Extrapolating experimental points yields a value of 1640 cm2/Vs for the maximum room temperature mobility in stoichiometric material, with higher values potentially accessible for Ga-rich material. Additionally, we present a model for observed trends in carrier concentration based on the occurrence of distinct structural motifs, which underpin S. The result is an alternative perspective for the interplay between lattice structure and charge carriers that enables a predictive model for tuning mobility and carrier concentration in undoped material. 

Several hundred plasma-assisted molecular beam epitaxy synthesis experiments of GaN and ZnO thin film crystals were organized into data sets that correlate the operating parameters selected for growth to two figures of merit: a binary determination of surface morphology, and a continuous Bragg–Williams measure of lattice ordering (S2). Quantum as well as conventional supervised machine learning algorithms were optimized and trained on the data, enabling a comparison of their generalization performance. The models displaying the best generalization performance on each data set were subsequently used to predict each figure of merit across the ZnO and GaN processing spaces. 

Quantifying disorder in physical systems can provide unique opportunities to engineer-specific properties. Here, we apply a methodology based on the approach pioneered by Bragg and Williams for metal alloys to quantify the disorder characterizing polymer fibers including polyaniline (PANI), polyaniline-polycaprolactone (PANI-PCL), and polyvinylidene difluoride (PVDF). Both PANI and PVDF possess electrical properties such as conductivity and piezoelectric response that find a wide range of applications in energy storage and tissue engineering. On the other hand, the mechanical properties of polymer fibers can be tuned by varying the concentration of PANI and PCL during synthesis. Here, we demonstrate that it is possible to control the amount of disorder characterizing a fiber, which provides a route to engineering desired values for specific material properties. The resulting measure of disorder is shown to have a direct relationship to Young’s modulus, band gap, and specific capacitance values. 

Abstract We demonstrate a methodology for predicting particle removal efficiency of polypropylene-based filters used in personal protective equipment, based on quantification of disorder in the context of methyl group orientation as structural motifs in conjunction with an Ising model. The corresponding Bragg-Williams order parameter is extracted through either Raman spectro-scopy or scanning electron microscopy. Temperature-dependent analysis verifies the presence of an order-disorder transition, and the methodology is applied to published data for multiple samples. The result is a method for predicting the particle removal efficiency of filters used in masks based on a material-level property.