Materials Science and Engineering A327 (2002) 24 – 28 Measurement of the Gibbsian interfacial excess of solute at an interface of arbitrary geometry using three-dimensional atom probe microscopy Olof C. Hellman, David N. Seidman * Department of Materials Science and Engineering, Northwestern Uniersity, 2225 N. Campus Dr., Eanston, IL 60208 -3108, USA Abstract We show how the Gibbsian interfacial excess of solute can be calculated from three-dimensional atom probe data, even in the case of irregularly shaped interfaces. Standard treatments of interfacial thermodynamics implicitly define a one-dimensional geometry for an interface by assuming a planar interface. Of course, many real systems exhibit non-planar interfaces, and these treatments are difficult to apply. We show how our treatment derives from Gibbs’ original approach and how it is used to derive real thermodynamic quantities. The technique can be applied to any interfacial excess quantity. © 2002 Elsevier Science B.V. All rights reserved. Keywords: Gibbsian excess; Segregation; Interface; Atom probe microscopy www.elsevier.com/locate/msea 1. Introduction One of the applications of three-dimensional atom probe (3DAP) microscopy [1,2] is the measurement of the chemical compositions of interfaces, such as grain boundaries [3] or heterophase interfaces [4]. The segre- gation of a solute species to such a boundary is quantified by the Gibbsian interfacial excess of solute,  s , a rigorously defined thermodynamic property [5]. Atom probe microscopy produces a discrete count of the atoms in the vicinity of an interface thus allowing for a direct measurement of  s . Gibbs outlined an approach for quantifying the inter- facial excess, which assumed an interface in a medium with a continuous concentration profile, and involved the definition of a dividing surface [6]. Cahn refined this treatment to avoid the necessity of choosing a dividing surface, and in the process allowed for the composition at an interface to be expressed in numbers of atoms of each species, rather than a particular concentration [5]. Cahn’s treatment is not only more elegant, but allows for more direct application to 1D atom probe field ion microscopy, where the raw data is in the form of individual atoms: i.e. the local densities in the material need not be considered. Both of these treatments, how- ever, assume that the interface is planar, and that linear profiles of composition across the interface can be expressed in 1D form. 3DAP produces data for which this assumption is invalid. We present a straightforward treatment that extracts the interfacial excess from a region of analysis that includes an interface of any arbitrary geometry, maxi- mizes the statistical accuracy, and is insensitive to deci- sions made during the analysis concerning the placement of the interface. At no point in the analysis is the measurement of the area of the interface ever required, and thus there is no error associated with its measurement. In addition, the method can accumulate data from more than one interface as measured by 3DAP, thus allowing for improved statistics to be ac- quired from multiple samples or multiple regions of a single sample. 2. From 1D to 3D There are a number of subtleties in the extraction of the interfacial excess when the interface is not planar. * Corresponding author. Tel.: +1-847-491-4391; fax: +1-847-467- 2269. E-mail address: d-seidman@northwestern.edu (D.N. Seidman). 0921-5093/02/$ - see front matter © 2002 Elsevier Science B.V. All rights reserved. PII:S0921-5093(01)01885-8