Multilevel atomic structural model for interstratified opal materials

• Published in: Journal of applied crystallography 2023-12, Vol.56 (6), p.1813-1823
• Main Authors: Wang, Hsiu-Wen, Page, Katharine, Neder, Reinhard B., Stack, Andrew G., Bish, David L.
• Format: Article
• Language: English
• Subjects: Cristobalite; Diffraction; Diffraction patterns; Distribution functions; Layered materials; MATERIALS SCIENCE; Mathematical models; Modelling; Multilevel; Opal; Optimization; pair distribution functions; Parameters; powder diffraction; stacking disorder; Stacking faults; Structural models; Tetrahedra; Tridymite
• ISSN: 1600-5767; 0021-8898; 1600-5767
• DOI: 10.1107/S1600576723009913

The structure of opal has long fascinated scientists. It occurs in a number of structural states, ranging from amorphous to exhibiting features of stacking disorder. Opal‐CT, where C and T signify cristobalite‐ and tridymite‐like interstratification, represents an important link in the length scales between amorphous and crystalline states. However, details about local atomic (dis)order and arrangements extending to long‐range stacking faults in opal polymorphs remain incompletely understood. Here, a multilevel modeling approach is reported that considers stacking states in correlation with the abundance of C and T segments as a high‐level structural parameter (i.e. not each atom). Optimization accounting for inter‐tetrahedral bond lengths and angles and the regularity of the silicate tetrahedra is included as lower levels of structural parameters. Together, a set of parameters with both coarse‐grained and atomistic features for different levels of structural details is refined. Structural disorder at the ∼10–100 Å distance scale is evaluated using experimental pair distribution function and diffraction datasets, comparing peak intensities, widths and asymmetry. This work presents a complete multilevel structural description of natural opal‐CT and explains many of the unusual features observed in X‐ray powder diffraction patterns. This modeling approach can be adopted generally for analyzing layered materials and their assembly into 3D structures. The structure of opal represents a missing link in the length scale between amorphous and crystalline states. This work revisits a long‐standing debate about the intermediate‐range order in natural opal (opal‐CT) and presents a complete multilevel structural description for local distortions and interstratification features observed in powder diffraction and pair distribution function datasets.