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Pure Appl. Chem., 2009, Vol. 81, No. 10, pp. 1921-1930

Published online 2009-09-26

Thermodynamics: Nano vs. macro

Michel Wautelet1* and Aram S. Shirinyan2

1 Physics of Condensed Matter, University of Mons-Hainaut, Place du Parc, 20, B-7000 Mons, Belgium
2 Department of Physics, Cherkasy B, Khmelnytsky National University, 81, Shevchenko Street, Cherkasy 18031, Ukraine

Abstract: Ordinary macroscopic thermodynamics is applied when the number of atoms in the studied systems is "large". Conditions where nanosystems are "large" with respect to thermodynamics definition are first discussed. In the thermodynamical regime, size and shape effects are known to be important. It has been known for a long time that the melting temperature of nanosystems decreases when their size decreases. A generalization of this leads to the conclusion that phase diagrams are also size- and shape-dependent. In nanosystems, the number of atoms is limited. This differs from classical thermodynamics, where the number of atoms is assumed to be unlimited. The consequences of this difference for the definition of phase diagrams are discussed. In particular, the liquidus and solidus lines have to be carefully defined. The structure of the two-phase nanoparticles also plays a role in the calculation of the phase diagrams.