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Entropy 2017, 19(6), 248; doi:10.3390/e19060248

On the Configurational Entropy of Nanoscale Solutions for More Accurate Surface and Bulk Nano-Thermodynamic Calculations

1
Department of Nanotechnology, University of Miskolc, Miskolc H-3515, Hungary
2
MTA-ME Research Group on Materials Science, University of Miskolc, Miskolc H-3515, Hungary
3
Bay Zoltan Ltd for Applied Research, Igloi 2, Miskolc H-3519, Hungary
*
Author to whom correspondence should be addressed.
Academic Editors: Leslie Glasser and H. Donald Brooke Jenkins
Received: 10 April 2017 / Revised: 10 May 2017 / Accepted: 11 May 2017 / Published: 27 May 2017
(This article belongs to the Special Issue Thermodynamics in Material Science)
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Abstract

The configurational entropy of nanoscale solutions is discussed in this paper. As follows from the comparison of the exact equation of Boltzmann and its Stirling approximation (widely used for both macroscale and nanoscale solutions today), the latter significantly over-estimates the former for nano-phases and surface regions. On the other hand, the exact Boltzmann equation cannot be used for practical calculations, as it requires the calculation of the factorial of the number of atoms in a phase, and those factorials are such large numbers that they cannot be handled by commonly used computer codes. Herewith, a correction term is introduced in this paper to replace the Stirling approximation by the so-called “de Moivre approximation”. This new approximation is a continuous function of the number of atoms/molecules and the composition of the nano-solution. This correction becomes negligible for phases larger than 15 nm in diameter. However, the correction term does not cause mathematical difficulties, even if it is used for macro-phases. Using this correction, future nano-thermodynamic calculations will become more precise. Equations are worked out for both integral and partial configurational entropies of multi-component nano-solutions. The equations are correct only for nano-solutions, which contain at least a single atom of each component (below this concentration, there is no sense to make any calculations). View Full-Text
Keywords: thermodynamics; nano; configurational entropy; Stirling approximation; de Moivre approximation thermodynamics; nano; configurational entropy; Stirling approximation; de Moivre approximation
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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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Dezso, A.; Kaptay, G. On the Configurational Entropy of Nanoscale Solutions for More Accurate Surface and Bulk Nano-Thermodynamic Calculations. Entropy 2017, 19, 248.

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