Abstract
This work discusses the development of analytical expressions for the configurational entropy of different states of matter using a method based on the identification of the energy-independent complexes (clustering of atoms) in the system and the calculation of their corresponding probabilities. The example of short-range order (SRO) in Nb-H interstitial solid solution is used to illustrate the choice of the atomic complexes and their structural changes with H concentration, providing an alternative methodology to describe critical properties. The calculated critical composition of the miscibility gap is xc = 0.307, in remarkable agreement with the experimental value of xc ~ 0.31. The same methodology is applied to deduce the equation of state (EOS) of a hard sphere system. The EOS is suitable to describe the percolation thresholds and fulfills both the low and random close packing limits. The model, based on the partition of the space into Voronoi cells, can be applied to any off-lattice system, thus introducing the possibility of computing the configurational entropy of gases, liquids and glasses with the same level of accuracy.
Highlights
The development of analytical expressions for the configurational entropy of mixing was an active field of research several decades ago
This work presents a formalism to calculate the configurational entropy of mixing as an alternative to the usual method of counting the number of atomic configurations
The traditional methodology encountered important restrictions to encode the physical information into compact methodology encountered important restrictions to encode the physical information into compact expressions in complex systems, such as interstitial solid solutions or liquids and amorphous materials
Summary
The development of analytical expressions for the configurational entropy of mixing was an active field of research several decades ago. There are several analytical expressions that can be used to compute the entropy of mixing in these systems, they are all approximated or limited to low or medium solute concentrations They all assume a random distribution of interstitial atoms in the interstitial sub-lattice, and the interaction between defects is not considered in previous models, i.e., no short-range order (SRO). The deduction of an analytical and parameter-free expression for the configurational entropy of mixing of multicomponent systems, valid for any non-crystalline states of matter, remains a largely unsolved problem The development of such a model, involving counting the number of configurations, is an impractical idea. The methodology is suitable for application to any system with no lattice periodicity, such as liquids, glasses and amorphous materials
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