We present a simple analytical formalism based on the Lorentz-Scherrer equation and Bernoulli statistics for estimating the fraction of crystallites (and the associated uncertainty parameters) contributing to all finite Bragg peaks of a typical powder pattern obtained from a static polycrystalline sample. We test and validate this formalism using numerical simulations, and show that they can be applied to experiments using monochromatic or polychromatic (pink-beam) radiation. Our results show that enhancing the sampling efficiency of a given powder diffraction experiment for such samples requires optimizing the sum of the multiplicities of reflections included in the pattern along with the wavelength used in acquiring the pattern. Utilizing these equations in planning powder diffraction experiments for sampling efficiency is also discussed.
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Both because of the shortcomings of existing risk assessment methodologies, as well as newly available tools to predict hazard and risk with machine learning approaches, there has been an emerging emphasis on probabilistic risk assessment. Increasingly sophisticated AI models can be applied to a plethora of exposure and hazard data to obtain not only predictions for particular endpoints but also to estimate the uncertainty of the risk assessment outcome. This provides the basis for a shift from deterministic to more probabilistic approaches but comes at the cost of an increased complexity of the process as it requires more resources and human expertise. There are still challenges to overcome before a probabilistic paradigm is fully embraced by regulators. Based on an earlier white paper (Maertens et al., 2022), a workshop discussed the prospects, challenges and path forward for implementing such AI-based probabilistic hazard assessment. Moving forward, we will see the transition from categorized into probabilistic and dose-dependent hazard outcomes, the application of internal thresholds of toxicological concern for data-poor substances, the acknowledgement of user-friendly open-source software, a rise in the expertise of toxicologists required to understand and interpret artificial intelligence models, and the honest communication of uncertainty in risk assessment to the public.
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