Development of SAXS models to elucidate particulate formation during detonations

Recent progress in the application of time resolved small angle x-ray scattering (TR-SAXS) has enabled the monitoring of nanosecond particulate growth in detonations. Particularly useful for monitoring formation of various carbon allotropes, TR-SAXS can differentiate between the phases of carbon (sp² vs. sp³) and characterize the average particulate size, morphology, and surface structure. Despite the use of SAXS to probe carbon particulate growth in detonations, usually as diamond or graphite, the possibility of other products is not generally considered in the analysis. Taking into account other species in the SAXS models may impact the morphological description of carbon particles. Here, various model dependent and model independent analysis methods are considered for the description of carbon particulate growth during detonations. Models which accept the possibility of additional products result in a different radius of gyration compared to a standard model considering only the formation of carbon agglomerates. Guinier-Porod equations, as well as the SAXS invariant, are used to identify the primary contribution to the scattering based off of the scattering length density contrast. Accurately defining the contrast allows models to be developed with fewer parameters and are expected to provide more accurate estimates of particle size. The same analysis model proposed here can be used for all detonation synthesis systems and has the potential to change the existing understanding of carbon particulate morphology.