title: Where macro meets micro.
abstract: Reconciling or somehow linking the macroscopic and microscopic approaches to chemical and physical processes has been a challenge unaddressed for many years. One approach, presented here, treats the issue by examining individual phenomena well described by a macro approach that fails when applied to small systems. The key to the approach is determining the approximate system size below which the breakdown of the macro description is observable. The most developed example is the failure of the Gibbs phase rule for sufficiently small atomic clusters. Other examples, such as the onset, at sufficient size, of the insulator-to-metal transition, are discussed, as are some still more challenging phenomena.
authors.affiliation: The University of Chicago, 929 East 57th Street, Chicago, Illinois, USA. berry@uchicago.edu.
authors.forename: R Stephen
authors.initials: RS
authors.lastname: Berry
authors.forename: Boris M
authors.initials: BM
authors.lastname: Smirnov