STRUCTURAL HIERARCHY AND STRUCTURAL COMPLEXITY OF MINERALS: QUANTITATIVE ASSESSMENT

One of the major contributions of Frank Hawthorne to theoretical mineralogy and crystallography is the development of structural hierarchies for large and different groups of minerals. In his 1983 paper "Graphical enumeration of polyhedral clusters" (Acta Cryst. A39:724-736), he proposed to classify structures on the basis of coordination polyhedra of higher bond-valences. This established a quantitative basis for dealing with hierarchical organization of crystal structures of minerals. In our contribution, we will try to correlate hierarchical depth of mineral structures with their complexity understood in terms of structural information amount. According to this approach (Miner. Mag. 77:275-326, 2013), crystal structure is considered as a message consisting of atoms classified into equivalence classes according to their distribution over crystallographic orbits (Wyckoff sites). The proposed complexity measures combine both size- and symmetry-sensitive aspects of crystal structures. According to the proposed quantitative approach to structural complexity, the crystal structures of minerals can be viewed as resevoirs of information encoded in their atomic arrangement. Complex structures store more information than simple ones. Since erasure of information is always associated with dissipation of energy, information stored in crystal structures of minerals must have an important influence upon natural processes. It might be demonstrated that explosions of complexity (=information) are associated with the inputs of energy released in some specific chemical reactions, e.g. oxidation of ions in oxidation zones of mineral deposits.