Which Inorganic Structures are the Most Complex?

Abstract

The discovery of the diffraction of X-rays on crystals opened up a new era in our understanding of nature, leading to a multitude of striking discoveries about the structures and functions of matter on the atomic and molecular scales. Over the last hundred years, about 150,000 of inorganic crystal structures have been elucidated and visualized. The advent of new technologies, such as area detectors and synchrotron radiation, led to the solution of structures of unprecedented complexity. However, the very notion of structural complexity of crystals still lacks an unambiguous quantitative definition. In this Minireview we use information theory to characterize complexity of inorganic structures in terms of their information content.

High-temperature order–disorder phase transition in nacaphite, Na2CaPO4F

“…(Hawthorne 2013). The effect of temperature upon the structural complexity of nacaphite polymorphs can be estimated using Shannon information content per atom (I G ) and per unit cell (I G,total ) calculated according to the following formulae (Krivovichev 2012(Krivovichev , 2013(Krivovichev , 2014: where k is the number of different crystallographic orbits and p i is the random choice probability for an atom from the ith crystallographic orbit, that is:…”

Structural complexity and crystallization: the Ostwald sequence of phases in the Cu2(OH)3Cl system (botallackite–atacamite–clinoatacamite)

“…Thus, the crystallization in the Cu 2 (OH) 3 Cl system follows Ostwald step rule and corresponds to the sequence of phases botallackite-atacamite-clinoatacamite. Below, we analyze this sequence from the viewpoint of informationbased complexity parameters [9][10][11][12][13] and show that the system exactly obeys the Goldsmith's simplexity principle. We also provide structural description of the three phases in order to clarify the differences in their structural architecture in more details.…”

“…Recently, complexity of crystals has received a renewed attention from the various points of view, including its role in the interpretation of energy landscapes in solids [6], mathematical description of complex alloys [7], and analysis of disordered materials [8]. In a series of recent papers, Krivovichev [9][10][11][12] suggested estimation of structural complexity of crystals in terms of their Shannon information contents per atom and per unit cell and showed that the latter represents a negative contribution to the configurational entropy of crystalline solids [13].…”

Structural changes of synthetic paulingite (Na,H-ECR-18) upon dehydration and CO2 adsorption

“…The small pore zeolite paulingite (topology type PAU) [13][14][15][16][17] is one of the most complex zeolites [18] and has a remarkable framework structure that contains cages connected in some cases by 8Rs and in others by D8Rs. The body-centred structure (space group 3 Im m ) in its undistorted, maximum symmetry form, is built up from seven different tiling units: d8r, lta, pau, gis, oto, phi and plg ( Figure 2).…”