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Towards the Development of a Universal Expression for the Configurational Entropy of Mixing
1  Comisión Nacional de Energía Atómica, Argentina

Abstract: Several decades ago, the development of analytical expressions for the configurational entropy of mixing was an active field of research. Empirical or theoretical expressions and methods were deduced in each field of the condensed matter. Several examples can be found in the literature, as: i) the expressions of Flory and Huggins for linear polymer solutions, ii) Cluster Variation Method (CVM) and Cluster Site Approximation (CSA) for studying order-disorder and phase equilibrium in alloys, and iii) the expression of Gibbs and Di Marzio for glasses, just to cite the most well known expressions in each field. Each model has its own area of research and applications. For example, CVM can not be applied to polymer solutions and Flory's expression is not suitable to study order-disorder in alloys. However, the traditional methodology, based on the calculation of the number of configurations, found severe restrictions in the development of accurate and general expressions in complex systems, like interstitial solid solutions or liquids and amorphous materials. The development of a common model for all previously cited methods just counting the number of configurations is an impractical idea. However, a recent formalism to compute the configurational entropy, based on the identification of energetically independent complexes within the mixture and the calculation of their respective probabilities, opens new possibilities to consider seriously such proposal. The importance of such idea is not only academic in nature, i.e., the development of a unified description for all states of the matter. It has its origin in the need of developing general expressions with the same level of accuracy for each state of the matter. Indeed, it would be desirable to describe liquids, glasses and solid states with the same model and level of accuracy to get a precise description of their physical properties and phase diagrams. This work shows that it is possible to develop such a model but a major theoretical and computational effort will be required. The main requirement to achieve this goal is to find a complex (clustering of atoms) suitable to describe, simultaneously, the structural features of liquids, glasses and solids. The first step towards such formulation are discussed in this work based on several inspiring previous works related to hard sphere systems, metallic glasses, CVM method and a recently deduced analytical expression for interstitial solutions. The methodology presented in this work is based on the identification, through a careful analysis of the main physical features of the system, of the energy independent complexes in the mixture and the calculation of their corresponding probabilities. The examples presented in this work show that accurate and general expressions for the configurational entropy of mixing can be developed, even in systems with no translational symmetry.
Keywords: Configurational entropy; analytical expressions; interstitial solutions; glasses