caa a22 4500 467892490 CHVBK 20180406152753.0 cr unu---uuuuu 170328e20060301xx s 000 0 eng 10.1007/s10955-005-8067-x doi (NATIONALLICENCE)springer-10.1007/s10955-005-8067-x Kaplan T. Department of Physics and Astronomy and Institute for Quantum Sciences, Michigan State University, 48824, East Lansing, Michigan aut The Chemical Potential [Elektronische Daten] [T. Kaplan] The definition of the fundamental quantity, the chemical potential, is badly confused in the literature: there are at least three distinct definitions in various books and papers. While they all give the same result in the thermodynamic limit, major differences between them can occur for finite systems, in anomalous cases even for finite systems as large as a cm3. We resolve the situation by arguing that the chemical potential defined as the symbol μ conventionally appearing in the grand canonical density operator is the uniquely correct definition valid for all finite systems, the grand canonical ensemble being the only one of the various ensembles usually discussed (microcanonical, canonical, Gibbs, grand canonical) that is appropriate for statistical thermodynamics, whenever the chemical potential is physically relevant. The zero-temperature limit of this μ was derived by Perdew et al. for finite systems involving electrons, generally allowing for electron-electron interactions; we extend this derivation and, for semiconductors, we also consider the zero-T limit taken after the thermodynamic limit. The enormous finite size corrections (in macroscopic samples, e.g. 1 cm3) for one rather common definition of the c.p., found recently by Shegelski within the standard effective mass model of an ideal intrinsic semiconductor, are discussed. Also, two very-small-system examples are given, including a quantum dot. Springer Science + Business Media, Inc., 2006 Statistical thermodynamics nationallicence Insulators nationallicence Thermodynamic limit nationallicence Quantum dots nationallicence Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1237-1260 0022-4715 122:6<1237 2006 122 10955 https://doi.org/10.1007/s10955-005-8067-x text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10955-005-8067-x text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Kaplan T. Department of Physics and Astronomy and Institute for Quantum Sciences, Michigan State University, 48824, East Lansing, Michigan aut NATIONALLICENCE 773 0- Journal of Statistical Physics Springer US; http://www.springer-ny.com 122/6(2006-03-01), 1237-1260 0022-4715 122:6<1237 2006 122 10955 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer