Intermetallic compounds of the NaCd₂ family perceived as assemblies of nanoclusters

“The geometry of nature never ceases to astound, nor does the ingenuity of human beings in discerning patterns.”

D. C. Fredrickson, S. Lee, R. Hoffmann

Abstract

In this work, we proceed with the concept of developing nanoclusters (fundamental configurations), which are the basic building blocks of certain crystal structures, allowed us to propose a universal algorithm for crystal self-assembly structure, and hence to elaborate a uniform approach to the analysis of the essentially hierarchic structure of natural objects under the nanoscale. It should be noted that we use the conception, where the configuration of points on the single sphere that minimize potential energy for broad class of potential functions (with the characteristic quadric function of potential versus distance between points) has been studied. The model is not connected both with the undefined isolated from structure nets (like diamond net) and polyhedra (like Friauf polyhedra), which are the basis of clusters, but is hierarchically constructed on local polyhedral structure’s searching according to universal algorithm. Crystal structure can explicitly store the information on the structure of the particles that formed it. These particles, geometrically distorted in some extent, can remain in parts of fundamental nanoclusters, coherently grow into them, and emerge as clusters-centaurs.