Abstract
The Gibbs phase rule relating the number of degrees of freedom f of a system to the number of components c and the number of coexisting phases p is a central, universally used relation, expressed by what is probably the simplest formula in the natural sciences, f = c − p + 2. Research into the behavior of small systems, notably atomic clusters, has shown in recent years that the phase rule is not as all-encompassing as is often assumed. Small systems can show coexistence of two or more phases in thermodynamic equilibrium over bands of temperature and pressure (with no other forces acting on them). The basis of this apparent violation of the phase rule, seeming almost like violation of a scientific law, is in reality entirely understandable, consistent with the laws of thermodynamics, and even allows one to estimate the upper size limit of any particular system for which such apparent violation could be observed.
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Acknowledgments
R.S.B. wishes to acknowledge the hospitality of the Aspen Center for Physics, which enabled the writing of this chapter. He also wishes to recognize with deep appreciation and very dear memories the companionship and stimulation of Carl Johan Ballhausen, from the time they were first together in the research group of William Moffitt at Harvard, in the 1950s until his passing.
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Berry, R.S., Smirnov, B.M. (2011). The Phase Rule: Beyond Myopia to Understanding. In: Mingos, D., Day, P., Dahl, J. (eds) Molecular Electronic Structures of Transition Metal Complexes II. Structure and Bonding, vol 143. Springer, Berlin, Heidelberg. https://doi.org/10.1007/430_2011_56
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DOI: https://doi.org/10.1007/430_2011_56
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