When can we trust structural models derived from pair distribution function measurements?

The pair distribution function (PDF) is an important metric for characterising structure in complex materials, but it is well known that meaningfully different structural models can sometimes give rise to equivalent PDFs. In this paper, we discuss the use of model likelihoods as a general approach for discriminating between such homometric structure solutions. Drawing on two main case studies-one concerning the structure of a small peptide and the other amorphous calcium carbonate-we show how consideration of model likelihood can help drive robust structure solution, even in cases where the PDF is particularly information-poor. The obvious thread of these individual case studies is the potential role for machine-learning approaches to help guide structure determination from the PDF, and our paper finishes with some forward-looking discussion along these lines.