M.G. Hetherington

Spinodal decomposition in Fe-Cr alloys: Experimental study at the atomic level and comparison with computer models—I. Introduction and methodology

Abstract A three-part series of papers is presented concerning the atomic scale analysis of spinodal decomposition in Fe-Cr alloys. This first part deals with the experimental techniques and computer simulations, the second part discusses the dynamics of early stage phase separation, and the third part describes the morphological and structural characterization of spinodal microstructures. In this first paper, three-dimensional reconstructions of the atomic structure of a series of thermally aged Fe-Cr alloys are shown. Two methods for computer simulation of the decomposition process are described. The first is an atomistic simulation based on the Monte Carlo algorithm and the second is a numerical solution to the Cahn—Hilliard—Cook theory. The three-dimensional atomic scale structures resulting from decomposition within the low temperature miscibility gap are reconstructed. It is shown that both models generate microstructures which are qualitatively similar to those observed experimentally.

A study of the precipitation of copper particles in a ferrite matrix

Abstract The influence of small amounts of Cu on the neutron irradiation induced embrittlement of reactor pressure vessel steels is of considerable practical importance. Previous work has shown that the embrittlement is associated with the formation of copper rich precipitates but uncertainties remain regarding their composition and form. The present paper reports preliminary results from a study of such precipitates in solution treated and aged Fe-Cu alloys with additions of Ni and P, using a combination of atom probe analysis in a Field Ion Microscope (FIM) and Small Angle Neutron Scattering (SANS).

SPINODAL DECOMPOSITION IN Fe-Cr ALLOYS: EXPERIMENTAL STUDY AT THE ATOMIC LEVEL AND COMPARISON WITH COMPUTER MODELS--III. DEVELOPMENT OF MORPHOLOGY

Abstract The fine-scale three-dimensional microstructures formed during spinodal decomposition in Fe-Cr alloys are characterized using two novel methods. In the first, a fractal analysis is used to characterize the interface between the phases and, in the second, the interconnectivity of the structure is determined from topology. It is found that the interface between Fe-rich α and Cr-enriched α′ regions in the experimental data and Monte Carlo simulations exhibit fractal behaviour whereas the microstructures from the solution to the Cahn—Hilliard—Cook model do not. Topological methods are used to characterize the complex α′ microstructures in terms of the number of cavities and loops. The decrease in the number of large scale loops in the microstructure, during thermal ageing, is shown to correlate with the increasing microstructural scale. The number of small scale loops is found to correlate with the complexity of the interface between the α and α′ regions.

Spinodal decomposition in Fe-Cr alloys: Experimental study at the atomic level and comparison with computer models—II. Development of domain size and composition amplitude

Abstract The three-dimensional interconnected microstructures resulting from spinodal decomposition in a series of thermally aged Fe-Cr alloys have been analysed in terms of scale and composition amplitude. The development of the microstructure scale was found to fit a power law with a time exponent considerably smaller than that predicted by the LSW theory but in agreement with Monte Carlo simulations of the decomposition. Numerical solutions to the classical non-linear Cahn—Hilliard—Cook equation were found to fit the classical LSW theory. A model, based on the non-linear theory of spinodal decomposition by Langer et al. is used to quantify the composition amplitude at any stage of the phase separation. A detailed comparison between the atomic scale experimental results and computer simulations of spinodal decomposition is given.

Materials analysis with a position-sensitive atom probe

A position‐sensitive detector has been combined with time‐of‐flight mass spectrometry in the atom probe field‐ion microscope to yield a system in which both chemical identity and spatial information are obtained for individual ions field‐evaporated from the specimen surface. This allows the variations in composition originally present in the sample to be reconstructed in 3‐D with sub‐nanometre resolution. The prototype position‐sensitive atom probe is being used to study phase chemistry in a number of metallurgical alloys, including accurate composition determination of 1–2 nm Cu‐rich precipitates formed in Fe–1.3% Cu–1.4%Ni aged to peak hardness. Other applications of the position‐sensitive atom probe (POSAP) include the analysis of surface layers on superconductors and atom probe studies of semiconductor multiple quantum wells. These initial applications of the instrument are reported, and the limitations and intended improvements to the instrument are discussed.

Measurement of the amplitude of a spinodal

Abstract One of the strengths of the atom-probe is its ability to measure the amplitude of composition fluctuations on a very fine scale. In previous papers, calculation of the amplitude of a spinodal using a sinusoidal composition distribution has been reported. In this paper, a comparison is made between the fit of experimental data from the atom-probe to a sinusoidal distribution and also to the amplitude of the composition variations expected from non-linear theories of the spinodal decomposition. It is shown that, in general, the Langer, Bar-on and Miller (LBM) non-linear theory provides better fits to the data. In particular, the non-linear theory is able to describe the asymmetry of the distribution functions for mean compositions far from the critical composition.

Atom probe field-ion microscopy: A technique for microstructural characterization of irradiated materials on the atomic scale

Atom probe field-ion microscopy (APFIM) is well suited to the microstructural characterization of the ultrafine-scale features that are formed in materials during irradiation. The atomic spatial resolution of this technique permits a complete microstructural and chemical description of the ultrafine features that control the mechanical properties to be made. A description of the technique and the types of analyses that may be performed are presented.

Three-dimensional characterization and modelling of spinodally decomposed iron-chromium alloys

Abstract The iron-chromium system has a spinodal region within which a random solid solution is thermodynamically unstable with respect to small composition fluctuations. The resulting decomposition yields Cr-enriched α′ and Fe-rich α phases forming complex and often interconnected morphologies. The resultant physical properties of the alloy are dependent on the scale and morphology of the microstructure and the amplitude of composition fluctuations. In this paper, the results of a series of thermally aged Fe-Cr specimens that have been analyzed with the position sensitive atom probe (POSAP) are compared with the results from a Monte Carlo simulation of the decomposition process. The resulting microstructures have been analyzed in terms of scale, composition amplitude and morphology. The scale has been measured by an autocorrelation analysis and the composition amplitude calculated from an analysis of the frequency distribution of block compositions. New morphological analysis techniques based on the measurement of a fractal dimension, and counting the number of handles within the microstructure, have been applied to characterize the detailed morphology on a subnanometre scale.

A topological approach to materials characterisation

This paper reports that a principal aim of materials science is the correlation of microstructure with properties. An example of such a relationship is the dependence of yield strength on the pinning of dislocations. The theories which describe these processes are well established and generally successful for secondary phases which exist as discrete particles. In engineering materials, second phases do not necessarily exist as discrete particles, but they can also form a sponge-like interconnected (percolated) structures. Some suggestions on the quantification of these interconnected microstructures were made by Camus et al. Extending the theories of structure/property relationships to these materials requires a method of characterization which is the equivalent of counting the number of particles for unconnected structures. In topological characterization, two structures are considered identical if they can be transformed into one another without requiring any cuts. The coffee mug and doughnut are therefore topologically identical since they both have only one hole or handle. Moving a dislocation through a connected microstructure, such as a sponge, will require cutting through the handles of the structure, and therefore the handle density of a percolated structure is the analogue of the particle density for separate particles.

Visualisation of three-dimensional microstructures

Abstract A variety of techniques are now available which can yield three-dimensional data on the atomic scale microstructures of materials. These include sequences of field-ion micrographs, field evaporation microscopy and direct chemical measurements from three-dimensional atom probes such as the position-sensitive atom probe. Methods of computer reconstruction of the microstructures from the various forms of data are discussed, together with the problems associated with the different data types. Despite the different methods for the collection of microstructural data, a common format is produced which allows topological measurements to be performed.