Structure maps for A ^I ₄ A ^II ₆(BO ₄) ₆X ₂ 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 ^I ₄ A ^II ₆(BO ₄) ₆X ₂ apatites is used as the basis for the study where each A ^I ₄ A ^II ₆(BO ₄) ₆X ₂ 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 - O ₁ 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.