Introducing the use of artificial intelligence in materials science

It is well known that nuclear reactor pressure Vessel steels (RPVS) become brittle under neutron irradiation. Copper precipitation is considered as one of the major causes of this phenomenon and is, therefore, the subject of interest of a research project started a few years ago at SCK•CEN (Research Centre for Nuclear Energy, Mol, Belgium).

An accurate prediction of the kinetics of copper precipitation in RPVS containing 0.1-0.3%Cu is important to assess the lifetime of existing nuclear power plants. The concepts developed in this project can, however, be applied to other binary alloys, such as iron-chromium, the base for high-Cr ferritic/martensitic steels. These are expected to play an important role in fusion and in new generation fission plants.

The concept of Atomistic Kinetic Monte Carlo (AKMC) simulations was introduced many years ago in scientific literature and is particularly well-suited to studying problems of solute segregation and precipitation in alloys for two major reasons. The first is that, contrary to other Monte Carlo schemes, the kinetics of the process is explicitly modeled allowing, for example, for the time required to reach a certain average radius of copper precipitates to be predicted under a given set of experimental conditions: temperature, vacancy concentration (neutron flux), copper concentration… The second is that the process is modeled at the atomic level, i.e. by explicitly accounting for the fundamental physical mechanism of solute diffusion in alloys. The approach used in this project has an additional advantage: the only required input is a reliable inter-atomic potential for the alloy interesting question. In the present case such a potential had been constructed to fit a number of key features of the Fe-Cu system, in particular the experimental copper solubility limit in iron.

At the moment, AKMC methods are limited to relatively small simulation boxes, containing less than 1 million atoms. Moreover, a rigid bcc crystallographic lattice is imposed, and the presence of interstitials is not yet taken into consideration. However, the main drawback of AKMC simulations is that they require the evaluation of defect migration energies at each steps of the calculation. This energy is a complex function of the local atomic configuration (LAC). It can be accurately calculated, without any simplification, with the aid of molecular dynamics (MD). MD techniques are however extremely computational time costly, making their systematic use in the course of an AKMC simulation totally impossible to envisage.

In this project it is proposed to replace the use of MD techniques by a fast artificial neural network (ANN). The objective was, accordingly, to construct a fast, optimized energy barrier calculation system composed of the ANN program, a fuzzy logic (FL) system to feedback its predictions and a data base module that records every MD calculation done.

A software coupling the ANN-FL-MD-Tables modules has been developed and prepared to be used with the LAKIMOKA software (the AKMC code developed by EdF, France). The concept of evolutionary strategy, allowing the MD calculations to be focused on the most problematic LAC’s, has been defined and proposed as a future guideline to treat the real problem of copper precipitation in iron under neutron irradiation.

Applications to the study of copper precipitation in iron under thermal ageing, with the presence of one single vacancy in the simulation box, have been performed to study the evolution with temperature of the copper solubility limit in iron. Although no fully satisfactory correlation with experimental measurements has been obtained so far, the results are however highly encouraging, because it has been shown that they are consistent with reference equilibrium conditions previously reached with other Monte Carlo simulations. On the basis of these studies, guidelines to achieve better compatibility with experimental data in future simulations could, therefore, be identified.

The originality of this project resides in the use of advanced computational tools in material sciences: an ANN is used as a correlation function to avoid the use of a costly but accurate technique and a genetic algorithm is used to prepare a fuzzy logic system to feedback the ANN predictions and, thus, improve the system’s performance. The project is, consequently, the application of known modern tools to solve a problem never addressed before with their use, or, conversely, it is the development of a new method to solve a well-known but not yet completely solved problem. The ultimate goal of this field of research is to simulate years of irradiation under large neutron fluxes. The use of artificial intelligence is an elegant and very promising tool for this purpose.

The project is led by Dr. L. Malerba, with the collaboration of Dr. R. Domingos and Dr. F. Djurabekova. It has been the subject of a Masters thesis presented by N. Castin for the degree of Master of Sciences in Nuclear Engineering (Belgian Nuclear higher Education Network, BNEN), which has been awarded by SCK•CEN the title of “the best university thesis for the academic year 2005-2006.”

Editor’s note: N. Castin has recently also received recognition from the Belgian Nuclear Society as the “Best nuclear science university thesis for 2006.”