Structure maps for A^I₄A^II₆(BO₄)₆X₂ apatite compounds via data mining

This paper describes a method to identify key crystallographic parameters that can serve as strong classifiers of crystal chemistries and hence define new structure maps. The selection of this pair of key parameters from a large set of potential classifiers is accomplished through a linear data-dimensionality reduction method. A multivariate data set of known A^I₄A^II₆(BO₄)₆X₂ apatites is used as the basis for the study where each A^I₄A^II₆(BO₄)₆X₂ compound is represented as a 29-dimensional vector, where the vector components are discrete scalar descriptors of electronic and crystal structure attributes. A new structure map, defined using the two distortion angles α_AII (rotation angle of A^II—A^II—A^II triangular units) and ψ^{AIz = 0}_AI—O1 (angle the A^I—O1 bond makes with the c axis when z = 0 for the A^I site), is shown to classify apatite crystal chemistries based on site occupancy on the A, B and X sites. The classification is accomplished using a K-means clustering analysis.