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