Predicting the Crystal Structure of Beryl from the Chemical Composition

Abstract

Abstract Crystal-structure prediction is a challenging topic. Few models have been developed that use the chemical composition of a known compound to determine a complete crystal structure. A complete structural model should include all major bond lengths and angles, atomic coordinates, polyhedral volumes and distortions, and unit-cell parameters. The mineral beryl is used here to develop such a model. Beryl (Be3Al2Si6O18) is an ideal mineral to show that predicting the crystal structure using chemistry is possible: the framework structure is known, this structure has only two cation sites that experience substitutions, and these substitutions only minimally occur simultaneously. Vacant channel sites are involved in coupled substitutions, allowing alkali cations (typically Na+) to enter the structure, and the channel regularly contains molecular H2O correlated to Na content (Henry et al. 2022). The research employed single-crystal X-ray diffraction and electron probe microanalyses of 80 samples to create a model which was subsequently tested using 33 samples. Results show that the complete crystal structure of beryl can be accurately calculated using the Al-site average ionic radius (Al-SAIR) for octahedrally trending beryl, or the Be-site average ionic radius (Be-SAIR) for tetrahedrally trending beryl. Beryl for which Al-SAIR > (0.45 × Be-SAIR) + 0.414 is considered octahedrally trending and that for which Al-SAIR ≤ (0.45 × Be-SAIR) + 0.414 is considered tetrahedrally trending. Red beryl (differentiated by high Fe and Mn) exhibits a different trend, forming a subset of the octahedrally trending beryl. There is an upper limit to the predictable range of beryl structures of 0.604 Å Al-SAIR or 0.326 Å Be-SAIR. This model makes it possible to explore limitations on the crystal structure of beryl and the potential for unusual cation substitutions, or conversely, to compute the structure of a hypothetical pure endmember beryl. It is robust for true beryl (beryl for which Be and Al are the dominant non-Si cations) up to a high limit of cation substitutions, but not for other beryl-group minerals, including stoppaniite, bazzite, avdeevite, and johnkoivulaite. Future studies on beryl will be able to estimate basic crystal-structure features arising from standard chemical analyses as used in this research. It enables the creation of an extensive beryl database, aids comparisons of natural beryl to synthetics, and helps provide further guidance on provenance studies. It also invites future crystal-structure prediction research. This approach is applicable to broader fields, as crystal structures are linked to the physical characteristics of minerals and rocks in which they form.