Principle of maximal simplicity for modular inorganic crystal structures

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Marco E. Ciriotti
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Principle of maximal simplicity for modular inorganic crystal structures

Messaggio da Marco E. Ciriotti » mar 30 nov, 2021 10:24

Referenza:
▪ Krivovichev, S.V. (2021): The Principle of Maximal Simplicity for Modular Inorganic Crystal Structures. Crystals, 11, 1472.

Abstract:
Modularity is an important construction principle of many inorganic crystal structures that has been used for the analysis of structural relations, classification, structure description and structure prediction. The principle of maximal simplicity for modular inorganic crystal structures can be formulated as follows: in a modular series of inorganic crystal structures, the most common and abundant in nature and experiments are those arrangements that possess maximal simplicity and minimal structural information. The latter can be quantitatively estimated using information-based structural complexity parameters. The principle is applied for the modular series based upon 0D (lovozerite family), 1D (biopyriboles) and 2D (spinelloids and kurchatovite family) modules. This principle is empirical and is valid for those cases only, where there are no factors that may lead to the destabilization of simplest structural arrangements. The physical basis of the principle is in the relations between structural complexity and configurational entropy sensu stricto (which should be distinguished from the entropy of mixing). It can also be seen as an analogy of the principle of least action in physics.
Marco E. Ciriotti

«Things are interesting only in so far as they relate themselves to other things»

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Marco E. Ciriotti
Messaggi: 31675
Iscritto il: ven 25 giu, 2004 11:31
Località: via San Pietro, 55 I-10073 Devesi/Cirié TO - Italy
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Re: Principle of maximal simplicity for modular inorganic crystal structures

Messaggio da Marco E. Ciriotti » dom 20 mar, 2022 10:43

In a modular series of inorganic crystal structures, those that are most common and abundant in nature and experiments are those arrangements that possess maximal simplicity and minimal structural information. This principle is empirical and is valid for those cases only where there are no structuredestabilizing factors, such as one observed for the (1, 1) spinelloid (poirierite). The influence of such factors depends upon the scale of the modules; for atomic-scale modules, it is of high importance (in fact, single atoms may hypothetically be considered as modules as well), but, for modules of larger size, the relevance of structural destabilization decreases and the principle of maximal simplicity plays the primary role. The physical basis of the principle is in the relations between structural complexity and configurational entropy sensu stricto (which should be distinguished from the entropy of mixing). In turn, configurational entropy, in general, correlates positively with vibrational entropy, and the sum of the two kinds of entropy constitutes the major contribution to this thermodynamic quantity. Thus, the principle can be re-phrased in favor of the abundance of highly entropic and less complex structures. It can also be seen as an analogy of the principle of least action in physics that had always been considered as a principle of economy in (or of) nature, expressed by Pierre Louis Maupertuis (1748) as: ‘Nature is thrifty in all its actions’. In his Principia, Isaac Newton noted that ‘Nature does nothing in vain, and more is in vain when less will serve; for Nature is pleased with simplicity, and affects not the pomp of superfluous causes’ (1687). The principle of minimal action corresponds to the group of variational principles in physics that are usually expressed analytically through the minimization of some function (e.g., energy or distance). It is rather doubtful that the principle of maximal simplicity in modular series may have a universal analytical expression since the crystal structures are complex systems that involve a whole range of atomic species and their interactions.
Marco E. Ciriotti

«Things are interesting only in so far as they relate themselves to other things»

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