PRINCEPS: A Computer-Based Approach to the Structural Description and Recognition of Trends within Structural Databases, and Its Application to the Ce-Ni-Si System

Intermetallic crystal structures offer an enormous structural diversity, with an endless array of structural motifs whose connection to stability and physical properties are often mysterious. Making sense of the often complex crystal structures that arise here, developing a clear structural description, and identifying connections to other phases can be laborious and require an encyclopedic knowledge of structure types. In this Article, we present PRINCEPS, an algorithm based on a new coordination environment projection scheme that facilitates the structural analysis and comparison of such crystal structures. We demonstrate the potential of this approach by applying it to the complex Ce-Ni-Si ternary system, whose 17 binary and 21 ternary phases would present a daunting challenge to one seeking to understand the system by manual inspection (but has nonetheless been well-described through the heroic efforts of previous researchers). With the help of PRINCEPS, most of the ternary phases in this system can be rationalized as intergrowths of simple structural fragments, and grouped into a handful of structural series (with some outliers). These results illustrate how the PRINCEPS approach can be used to organize a vast collection of crystal structures into structurally meaningful families, and guide the description of complex atomic arrangements.