The configurational entropy of nanoscale solutions is discussed in this paper. As follows\nfrom the comparison of the exact equation of Boltzmann and its Stirling approximation (widely used\nfor both macroscale and nanoscale solutions today), the latter significantly over-estimates the former\nfor nano-phases and surface regions. On the other hand, the exact Boltzmann equation cannot be\nused for practical calculations, as it requires the calculation of the factorial of the number of atoms\nin a phase, and those factorials are such large numbers that they cannot be handled by commonly\nused computer codes. Herewith, a correction term is introduced in this paper to replace the Stirling\napproximation by the so-called ââ?¬Å?de Moivre approximationââ?¬Â. This new approximation is a continuous\nfunction of the number of atoms/molecules and the composition of the nano-solution. This correction\nbecomes negligible for phases larger than 15 nm in diameter. However, the correction term does\nnot cause mathematical difficulties, even if it is used for macro-phases. Using this correction, future\nnano-thermodynamic calculations will become more precise. Equations are worked out for both\nintegral and partial configurational entropies of multi-component nano-solutions. The equations are\ncorrect only for nano-solutions, which contain at least a single atom of each component (below this\nconcentration, there is no sense to make any calculations).
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