Site-occupancy factors in the Debye scattering equation. A theoretical discussion on significance and correctness.

The Debye scattering equation (DSE) [Debye (1915). Ann. Phys. 351, 809-823] is widely used for analyzing total scattering data of nanocrystalline materials in reciprocal space. In its modified form (MDSE) [Cervellino et al. (2010). J. Appl. Cryst. 43, 1543-1547], it includes contributions from uncorrelated thermal agitation terms and, for defective crystalline nanoparticles (NPs), average site-occupancy factors (s.o.f.'s). The s.o.f.'s were introduced heuristically and no theoretical demonstration was provided. This paper presents in detail such a demonstration, corrects a glitch present in the original MDSE, and discusses the s.o.f.'s physical significance. Three new MDSE expressions are given that refer to distinct defective NP ensembles characterized by: (i) vacant sites with uncorrelated constant site-occupancy probability; (ii) vacant sites with a fixed number of randomly distributed atoms; (iii) self-excluding (disordered) positional sites. For all these cases, beneficial aspects and shortcomings of introducing s.o.f.'s as free refinable parameters are demonstrated. The theoretical analysis is supported by numerical simulations performed by comparing the corrected MDSE profiles and the ones based on atomistic modeling of a large number of NPs, satisfying the structural conditions described in (i)-(iii).

Automated Phasor Segmentation of Fluorescence Lifetime Imaging Data for Discriminating Pigments and Binders Used in Artworks.

The non-invasive analysis of fluorescence from binders and pigments employed in mixtures in artworks is a major challenge in cultural heritage science due to the broad overlapping emission of different fluorescent species causing difficulties in the data interpretation. To improve the specificity of fluorescence measurements, we went beyond steady-state fluorescence measurements by resolving the fluorescence decay dynamics of the emitting species through time-resolved fluorescence imaging (TRFI). In particular, we acquired the fluorescence decay features of different pigments and binders using a portable and compact fibre-based imaging setup. Fluorescence time-resolved data were analysed using the phasor method followed by a Gaussian mixture model (GMM) to automatically identify the populations of fluorescent species within the fluorescence decay maps. Our results demonstrate that this approach allows distinguishing different binders when mixed with the same pigment as well as discriminating different pigments dispersed in a common binder. The results obtained could establish a framework for the analysis of a broader range of pigments and binders to be then extended to several other materials used in art production. The obtained results, together with the compactness and portability of the instrument, pave the way for future in situ applications of the technology on paintings.