The length scales accessible to experimental techniques for analysis of the three-dimensional chemistry of solids and feasible for atomistic simulation have converged. The three-dimensional atom probe is capable of reconstructing the chemistry of solids atom-by-atom with subnanometer resolution, while atomistic simulation techniques can calculate similar quantities for ensembles of hundreds of thousands of particles. We present recent progress in the calculation of the interfacial excess of a segregating species by both simulation and experiment.

The proximity histogram (or proxigram for short) is used for analyzing data collected by a three‐dimensional atom probe microscope. The interfacial excess of Re (2.41 ± 0.68 atoms nm −2 ) is calculated by employing a proxigram in a completely geometrically independent way for γ/γ′ interfaces in René N6, a third‐generation single‐crystal Ni‐based superalloy. A possible dependence of interfacial excess on the variation of the threshold value of an isoconcentration surface is investigated using the data collected for René N6 alloy. It is demonstrated that the dependence of the interfacial excess value on the threshold value of the isoconcentration surface is weak. Copyright © 2004 John Wiley & Sons, Ltd.

The best calculation of concentration profiles, isoconcentration surfaces or Gibbsian interfacial excesses from three-dimensional atom-probe microscopy data requires a compromise between spatial positioning error and statistical sampling error. For example, sampling from larger spatial regions decreases the statistical error, but increases the error in spatial positioning. Finding the appropriate balance for a particular calculation can be tricky, especially when the three-dimensional nature of the data presents an infinite number of degrees of freedom in defining surfaces, and when the statistical error is changing from one region of a sample to another due to differences in collection efficiency or atomic density. We present some strategies for approaching these problems, focusing on efficient algorithms for generating different spatial samplings. We present a unique double-splat algorithm, in which an initial, fine-grained sampling is taken to convert the data to a regular grid, followed by a second, variable width splat, to spread the effective sampling distance to any value desired. The first sampling is time consuming for a large dataset, but needs only be performed once. The second splat is done on a regular grid, so it is efficient, and can be repeated as many times as necessary to find the correct balance of statistical and positioning error. The net effect is equivalent to a Gaussian spreading of each data point, without the necessity of calculating Gaussian coefficients for millions of data points. We show examples of isoconcentration surfaces calculated under different circumstances from the same dataset.

We present a custom MacOS-based application, adam, for analysis of data collected by a three-dimensional atom probe (3DAP). The application is designed to carry out a common set of analysis tasks, to be customizable, to provide easy export and import of data, and to be simple enough for novice users to understand quickly. The integration of both graphical (GUI) and scripting (SUI) user interfaces and the functionality accessible from both is discussed. Different types of visualization can be used for best presentation of 3DAP data.

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.

A new method for the calibration of three-dimensional atom-probe (3DAP) microscopy mass spectra has been developed. This method is based on a linear regression procedure that takes full advantage of the large number of data points collected during a typical 3DAP analysis. The data analysis procedures involved in the method are direct, relying only on simple scripting routines written in a spreadsheet program. When performed properly, the calibration ensures that all of the peaks in a mass spectrum lie at their expected positions, making subsequent peak identification and mass window determination procedures relatively unambiguous. One of the distinct advantages of the method is that mass windows determined for one 3DAP spectrum can be applied directly to subsequent spectra from similar specimens, avoiding the need to re-examine the individual peaks in each spectrum. The example of the calibration of a tungsten 3DAP mass spectrum is presented. With minor modifications, the method can be applied to the calibration of spectra from other techniques that utilize time-of-flight mass spectrometry.

A Mo-rich precipitate in an Fe-rich matrix and the heterophase interface bounding the precipitate have been examined on an atomic scale by three-dimensional atom-probe (3DAP) microscopy and transmission electron microscopy (TEM). The Mo-rich precipitate was generated by isothermal solid-state decomposition at 500 degreesC of an Fe-15 at.% Mo-5 at.% V alloy. After this heat treatment, TEM reveals a characteristic modulated strain contrast structure. The precipitate has a composition of Mo-13.0 at.% Fe-4.9 at.% V as measured by 3DAP microscopy. The alloy decomposes at a nearly constant 5 at.% V, constituting a metastable tie-line between Fe-rich and Mo-rich bcc solid solutions. The formation of the equilibrium intermetallic phases is kinetically impeded. A local vanadium enrichment of 21 at.% is detected at the interface of the precipitate in a matrix region about 0.27 nm or 1-2 atomic layers in thickness. The corresponding value of the Gibbsian inter-facial excess of vanadium is 3.3 +/- 1.3 nm(-2).

Three-dimensional atom-probe (3DAP) microscopy has been applied to the study of segregation at ceramic/metal (C/M) interfaces. In this article, results on the MgO/Cu(X) (where X = Ag or Sb) systems are summarized. Nanometer-size MgO precipitates with atomically clean and atomically sharp interfaces were prepared in these systems by internal oxidation. Segregation of the ternary component (Ag or Sb) at the MgO/Cu heterophase interface was enhanced by extended low-temperature anneals. Magnesia precipitates in the 3DAP reconstructions were delineated as isoconcentration surfaces, and segregation of each ternary component at the C/M interfaces was analyzed with the proximity histogram method developed at Northwestern University. This method allows the direct extraction of the Gibbsian interfacial excess of solute at the C/M interfaces from the experimental data. A value of (3.2+/-2.0) x 10(17)m(-2) at 500 degrees C is obtained for the segregation of Ag at a MgO/Cu(Ag) interface, while a value of (2.9+/-0.9) x 10(18) m(-2) at 500 degrees C is obtained for the segregation of Sb at a MgO/Cu(Sb) interface. The larger Gibbsian excess for Sb segregation at this ceramic/metal heterophase interface is most likely due to the so-called pdeltaV effect.

The constraint of a coherent interface between a homogeneously precipitating phase and its matrix is known to have a strong influence on the decomposition trajectory and microstructure. The selection of the phase, shape, and composition of the precipitates, as well as their spatial distribution, depend on the volume strain and interfacial free energy associated with the coherent interface. These effects have been studied predominantly by transmission electron microscopy (TEM) (1,2) and by computer simulations based on various models and numerical approaches (3,4,5). The three-dimensional nature of straininfluenced microstructures, however, makes an experimental characterization extremely difficult. The present work investigates the strain dominated precipitate microstructure in an Fe–20 at.% Mo alloy, aged at 500°C for 20 h, resolved in three dimensions (3D), on an atomic scale, by 3D-atom-probe microscopy (3D-APM). The Fe-Mo system has a difference in atomic volume of about 27% between the elements; Thus, coherency strains are expected to have significant effects. References (6–8) report on the development of a tweed-like modulated strain-contrast in TEM images after annealing an Fe–20 at.% Mo alloy, indicating a periodic decomposition microstructure. Previous investigations by atom-probe field-ion microscopy (APFIM) in combination with high resolution electron microscopy (HREM) (7,8) revealed that homogeneous decomposition of this alloy proceeds during the initial stages via the formation of metastable and coherent Mo-rich bcc precipitates. The four intermetallic phases of the Fe-Mo equilibrium phase diagram (9) are bypassed during the initial stages of the decomposition due to the kinetic constraint of a coherent interface (8). The Fe-Mo system thus constitutes an example of a kinetically determined metastable phase with a composition very different from the phase predicted by the equilibrium phase diagram. The coherency during the initial stages and the large lattice parameter misfit of 7.15% between the Mo-rich precipitate and Fe-rich matrix result in large strain energy effects on the decomposition microstructure. The present work investigates the 3D alignment of the decomposition microstructure in Fe–20 at.% Mo by 3D-APM. This experimental technique reconstructs in three Scripta mater. 42 (2000) 645–651

The three-dimensional (3D) atom-probe technique produces a reconstruction of the elemental chemical identities and three-dimensional positions of atoms field evaporated from a sharply pointed metal specimen, with a local radius of curvature of less than 50 nm. The number of atoms collected can be on the order of one million, representing an analysis volume of approximately 20 nm x 20 nm x 200 nm (80,000 nm(3)). This large amount of data allows for the identification of microstructural features in a sample, such as grain or heterophase boundaries, if the feature density is large enough. Correlation of the measured atomic positions with these identified features results in an atom-by-atom description of the chemical environment of crystallographic defects. This article outlines a data compilation technique for the generation of composition profiles in the vicinity of interfaces in a geometrically independent way. This approach is applied to quantitative determination of interfacial segregation of silver at a MgO/Cu(Ag) heterophase interface.

The results of a three-dimensional atom probe (3DAP) analysis, on a subnanometer scale, of a ceramic/metal heterophase interface, MgO/Cu, are presented. Segregation of Ag, from the Cu (Ag) matrix, at MgO/Cu interfaces is investigated and the Gibbsian interfacial excess of silver is determined; the range is 2.33 x 10(18) to 5.81 x 10(18) m(-2). Also, silver segregation at the same MgO/Cu interfaces is analyzed employing a new approach that utilizes a proximity histogram or proxigram.

The Three Dimensional Atom Probe produces a real space map of the elemental identities and positions of atoms field-evaporated from a sharply pointed specimen. The analyzed volume is on the order of 20 nm × 20 nm × 100 nm. This is large enough to enclose microstructural features such as grain- or heterophase boundaries. Correlation of the measured atomic positions with such features results in an atom-by-atom description of the chemical environment of these crystallographic defects. We describe here a method for identifying these interfaces and profiling the composition in the vicinity of the interfaces without any assumptions about the interface geometry. This approach is applied to quantitative determination of interfacial segregation of Ag at a MgO/Cu(Ag) heterophase interface. We discuss the implications of our technique with respect to classical treatments of segregation at interfaces.

Three-dimensional atom-probe (3DAP) microscopy permits the atom-by-atom reconstruction of a small volume (typically 10 nm × 10 nm × 100 nm) of a material with respect to both the positions and chemical identities of individual atoms. It is, therefore, ideally suited for the study of solute segregation at internal heterophase interfaces. We present recent results of a 3DAP microscopy study of solute segregation at ceramic/metal (C/M) heterophase interfaces prepared by internal oxidation. In particular, results on the CdO/Ag(Au) (where Au is the segregating species) system are presented. In the 3DAP atomicreconstructions, the interfaces of nanometer-size CdO ceramic particles are delineated as Cd isoconcentration surfaces. The distribution of the segregating species as a function of distance to the isoconcentration surfaces is determined with the proximity histogram (or proxigram) method. Two interfaces are investigated in detail. The first shows no appreciable Au segregation, while the second exhibits segregation with a Gibbsianinterfacial excess of 1.65 nm -2 at 650°°C.

Segregation of a solute species to a grain boundary is known to be dependent on many factors, including strain, chemistry and crystal structure. We attempt to make general statements about the relationship of segregation to the stress calculated on an atomic scale. We find a relationship between local stress and segregation, but also show that the traditional definition for stress at an atomic site is only part of the influence of stress on segregation phenomena.

Surface stress and energy are concepts which are often misunderstood. In this work, we will clarify the difference between the two. We describe the use of transmission electron microscopy to measure surface stress by quantitative analysis of strain contrast images. We find that images of surface-stress-induced strain fields can be used to measure quantitative differences in surface stress provided the imaging parameters are accurately determined. We have applied this method to measure the stress difference between the 7×7 and high temperature "1×1" phases of the Si(111) surface at the phase coexistence temperature and between metastable phase boundaries on the Si(111) and amorphous-Ge interface. We discuss the significance of these measurements and pitfalls to be avoided in image simulations.

We study the crystallization of a thin film of amorphous Ge deposited at room temperature on Si (111). Features of the silicon surface buried beneath the Ge film are shown to affect the rate of crystallization. In particular, solid phase epitaxy is observed to be enhanced at surface steps and defects in the surface reconstruction. It is further shown that one-dimensional crystallization patterns can be caused by impurity-mediated crystallization. Precipitates of an impurity rich phase migrate in the plane of the film, leaving behind a crystalline trail. The migration path of these precipitates is also dependent on the buried surface structure.

The preparation of amorphous insulating films containing nanometer-scaled structures of semiconductors has attracted increased attention since the observation of room temperature emission of light from films containing indirect-bandgap semiconductors such as Ge and Si. While most experimental reports on these Si and Ge nano-scale structures have been based on thin films created using sputter-deposition, in this study we have used conventional ion implantation of Ge to create the non-equilibrium mixture of materials that, upon annealing, develops a nano-crystallite phase embedded in the amorphous matrix. The presence of clusters that are difficult to image in TEM, in addition to microcrystallites, is an issue of interest since the source of light emission is still controversial. The second phase is formed from excess amounts of the semiconductor, in this case added by implantation. In this paper the formation and size distribution of the Ge nano-structures was characterized using Raman scattering and transmission electron microscopy (TEM). Similarly to reported sputtered film results, Raman spectra suggest Ge clusters that are not well formed crystallites may be present for anneals at low temperatures and in unannealed films. For annealing temperatures exceeding 600°C, a mixture of amorphous-like clustering and nano-crystallites may result, depending on the volume fraction of Ge. For low dose samples it was found that temperature and time of annealing could be used to manipulate the nucleation behavior of the nano-crystallites.