ArticleActa crystallographica. Section A, Foundations and advances2023
Site-occupancy factors in the Debye scattering equation. A theoretical discussion on significance and correctness.
Article in Acta crystallographica. Section A, Foundations and advances, 2023. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Cited by 4 papers.
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4 citing papers in PubMed.
- Tracking Out-Of-Equilibrium Growth of Bimetallic Nanoalloys Using Deep Learning and X-ray Scattering.ACS nano · 2026Article
- Ligand-Engineered Methylammonium Lead Bromide Nanoplatelets: Single-Photon Emission and Strong Light-Matter Coupling.ACS nano · 2026Article
- Article
- Atomistic Insights into Halide Double Perovskite Nanocrystals obtained by Multistep Synthesis and Efficient Compositional Engineering.ACS nano · 2025Article
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7 authors.
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Abstract
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).
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