Kurchatovite and Clinokurchatovite, Ideally CaMgB2O5: An Example of Modular Polymorphism

Kurchatovite and clinokurchatovite, both of ideal composition CaMgB2O5, from the type localities (Solongo, Buryatia, Russia, and Sayak-IV, Kazakhstan, respectively) have been studied using electron microprobe and single-crystal X-ray diffraction methods. The empirical formulae of the samples are Ca1.01Mg0.87Mn0.11Fe0.022+B1.99O5 and Ca0.94Mg0.91Fe0.102+Mn0.04B2.01O5 for kurchatovite and clinokurchatovite, respectively. The crystal structures of the two minerals are similar and based upon two-dimensional blocks arranged parallel to the c axis in kurchatovite and parallel to the a axis in clinokurchatovite. The blocks are built up from diborate B2O5 groups, and Ca2+ and Mg2+ cations in seven- and six-fold coordination, respectively. Detailed analysis of geometrical parameters of the adjacent blocks reveals that symmetrically different diborate groups have different degrees of conformation in terms of the delta angles between the planes of two BO3 triangles sharing a common O atom, featuring two discrete sets of the delta values of ca. 55 degrees (B' blocks) and 34 degrees (B " blocks). The stacking of the blocks in clinokurchatovite can be presented as ...(+B')(+B ")(+B')(+B ")... or [(+B')(+B ")], whereas in kurchatovite it is more complex and corresponds to the sequence ...(+B')(+B ")(+B')(-B')(-B ")(-B')(+B')(+B ")(+B')(-B')(-B ")(-B')... or [(+B')(+B ")(+B')(-B')(-B ")(-B')]. The B':B " ratios for clinokurchatovite and kurchatovite are 1:1 and 2:1, respectively. According to this description, the two minerals cannot be considered as polytypes and their mutual relationship corresponds to the term modular polymorphs. From the viewpoint of information-based measures of structural complexity, clinokurchatovite (I-G = 4.170 bits/atom and I-G,I-total = 300.235 bits/cell) is structurally simpler than kurchatovite (I-G = 4.755 bits/atom and I-G,I-total = 1027.056 bits/cell). The high structural complexity of kurchatovite can be inferred from the modular character of its structure. The analysis of structural combinatorics in terms of the modular approach allows to construct the whole family of theoretically possible "kurchatovite"-type structures that bear the same structural features common for kurchatovite and clinokurchatovite. However, the crystal structures of the latter minerals are the simplest and are the only ones that have been observed in nature. The absence of other possible structures is remarkable and can be explained by either the maximum-entropy of the least-action fundamental principles.