J.M. Hyde

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 sensitivity analysis of the maximum separation method for the characterisation of solute clusters.

Variants of the maximum separation method have become the de-facto methodologies for the characterisation of nanometre scale clusters in atom probe tomography (APT) data obtained from dilute solid solutions. All variants rely on a number of parameters and it is well known that the precise values for these parameters strongly influence estimates of cluster size and number density. Quantitative analyses require an improved understanding of the inter-relationship between user-defined parameters, experimental parameters such as detection efficiency and the resultant parameterisation of the microstructure. A series of simulations has been performed to generate clusters with a range of compositions (50-100%) and diameters (1.5-2.5 nm) in a dilute solid solution. The data were degraded to simulate the effects of the finite detection efficiencies and positioning uncertainties associated with the ECOPoSAP and LEAP-3000X HR. An extensive analysis of each resultant dataset, using a range of values for the maximum separation parameters was then performed. Optimum values for each material condition were identified and it is shown that it is possible to characterise cluster size, number density and matrix chemistry. However, accurate estimates of cluster compositions are more difficult and absolute measurements must be treated with caution. Furthermore, it is shown that D(MAX) must increase with decreasing detection efficiency and consequently clusters of a specific size will appear slightly larger in atom probes with a lower detection efficiency.

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.

Nuclear reactor materials at the atomic scale

With the renewed interest in nuclear energy, developing new materials able to respond to the stringent requirements of the next-generation fission and future fusion reactors has become a priority. An efficient search for such materials requires detailed knowledge of material behaviour under irradiation, high temperatures and corrosive environments. Minimizing the rates of materials degradation will be possible only if the mechanisms by which it occurs are understood. Atomic-scale experimental probing as well as modelling can provide some answers and help predict in-service behaviour. This article illustrates how this approach has already improved our understanding of precipitation under irradiation, corrosion behaviour, and stress corrosion cracking. It is also now beginning to provide guidance for the development of new alloys.

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.

Improvements in three-dimensional atom probe design

Abstract An improved position-sensitive atom probe has been designed which uses a combination of a parallel timing system and a silicon photodiode array camera. The use of two separate data acquisition systems allows the two functions of accurate positioning and flight time determination to be divorced, thus removing the compromises which must be made when these functions are carried out with only a single detector. The resulting instrument is able to determine flight times and positions of impacts straightforwardly, even when multiple ions are evaporated on a single pulse, and should be capable of operating at evaporation rates close to that of a conventional probe-hole atom probe.

Lateral and depth scale calibration of the position sensitive atom probe

Abstract In this paper a method is outlined to calibrate both the lateral and depth scales using a combination of FIM and PoSAP microanalysis. Results are given for the following alloy systems: Fe-45at%Cr, Cu-1at%Co, Al-3at%Zn-3 at%Mg-1at%Cu and Fe-1.3wt%Cu-1.4wt%Ni. For each system a direct relationship between the applied voltage and tip radius was found from indexed FIM images and estimates of the image compression factor. The reconstructed PoSAP data was divided into a series of frames in which each represented a fraction of an atomic layer evaporated. Individual rings were seen to collapse inwards when the frames were displayed in succession. The visual effect is similar to watching ring collapse in a FIM image when DC field evaporation occurs. A depth scale calibration was determined directly from the number of ions detected per plane evaporated. The lateral resolution of the wedge and strip anode was analysed by placing a thin mask, consisting of a series of small circular apertures, arranged in a concentric ring pattern, in front of the double channel plate assembly. A series of FIM images was generated and compared with a simulation of the expected distribution of ion impacts. In order to simulate a uniform detector resolution a Gaussian scatter was added to each coordinate in the x and y directions of the simulated impact positions. A comparison between the observed impact positions and simulations showed that approximately 96% of observations would be located to within one atomic spacing during a typical PoSAP experiment.

Statistical analysis of atom probe data: Detecting the early stages of solute clustering and/or co-segregation

Statistical analysis of atom probe data has improved dramatically in the last decade and it is now possible to determine the size, the number density and the composition of individual clusters or precipitates such as those formed in reactor pressure vessel (RPV) steels during irradiation. However, the characterisation of the onset of clustering or co-segregation is more difficult and has traditionally focused on the use of composition frequency distributions (for detecting clustering) and contingency tables (for detecting co-segregation). In this work, the authors investigate the possibility of directly examining the neighbourhood of each individual solute atom as a means of identifying the onset of solute clustering and/or co-segregation. The methodology involves comparing the mean observed composition around a particular type of solute with that expected from the overall composition of the material. The methodology has been applied to atom probe data obtained from several irradiated RPV steels. The results show that the new approach is more sensitive to fine scale clustering and co-segregation than that achievable using composition frequency distribution and contingency table analyses.

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.