Defect dynamics in energy materials

Lead Research Organisation: University of Leeds
Department Name: Applied Mathematics

Abstract

Advanced materials form the cornerstone of many emerging technologies, from next-generation energy production, transport and defence, to prosthetics and targeted drug delivery. Some of these eg. fusion energy require materials that do not yet exist, because the operating environment is so ferocious: high temperatures, corrosive environments and intense radiation mean no currently available material can be used. Theoretical modelling and predictive computer simulations are crucial steps in the development of new materials, since they can provide deeper understanding of the complex processes at work, and reduce lead times in product development. All modelling and simulation techniques are based on approximations, which limit their range of applicability. Whilst they have served well in the past, the extreme conditions mentioned above mean that some of these simplifying approximations no longer apply, and new techniques are required. The aims of this project are to develop new modelling approaches and simulation methods that are capable of handling the conditions, and apply them to unsolved problems in nuclear materials science.

The most precise simulation methods currently available track every atom in the system. Although they can be very accurate, the computer power required to run them means they can only model a few cubic nanometres of material for a few nanoseconds. This cannot capture the large-scale, long-time processes that control material performance, and eventually decide, for example, how many years a nuclear reactor can be safely run before it needs to be replaced. At the other end of the scale, computer-aided design programs simulate reactor-sized components, but base this on simple rules on how materials behave. Ideally, these would be derived from microscopic simulations, but there is a huge gap in length and time-scales between them. The mesoscale simulations that this project will develop aim to bridge that gap.

Over the last 60 years, particle physicists have developed powerful mathematical tools to understand quantum fluctuations. These tools can be modified to treat thermal fluctuations instead, and this will form the foundations of the new simulation methods. Instead of following every atom in the system, the new techniques will identify only the degrees of freedom that play important roles in the evolution of the material over time. These are the defects: impurity atoms, vacancies and self-interstitials (formed when atoms are knocked out of place in the regular lattice of eg. a metal) and dislocations (defect lines whose motion controls deformation).

Though the new methods will be widely applicable, this project will focus on 3 case studies. This will answer technologically important questions, as well as testing the new techniques. The first case study concerns the clustering of Re atoms in W. Under the intense radiation of a fusion reactor, up to 5% of W atoms will transmute into Re. According to currently available modelling, the Re atoms should disperse through the W, yet experiments show clusters form. These clusters cause the material to become brittle, limiting its useful lifetime. The first case study will apply the new simulations to understand this. The second concerns the behaviour of dislocations under irradiation. This can be very different from their usual behaviour, and will strongly affect the mechanical properties of reactor materials. Current simulation methods ignore the single-atom defects, but these are crucial for understanding radiation effects. The new methods will track both kinds of defect, and help provide the understanding needed to mitigate and control them. The final case study will investigate the interaction of C atoms with dislocations. This is the process that makes iron into steel, and its importance can hardly be overstated. Although identified decades ago, important unanswered questions remain, and the new tools this project aims to develop will answer them.

Planned Impact

The research performed during this fellowship will deliver far-reaching impact across academic and industrial science and engineering.

Academic: The principal academic impacts will be twofold. Firstly, the project will deliver fully quantitative, predictive simulations of the complex, out-of-equilibrium processes that control microstructural evolution in materials under irradiation, and their effects on mechanical properties. This will represent a major increase in our fundamental understanding of the behaviour of structural and functional materials under nuclear reactor conditions. Secondly, the mathematical and computational tools that will be developed to enable the simulations will be applicable to a wide range of material systems beyond the nuclear-focussed case studies that will be investigated in detail. These innovative tools, and their implementation in hybrid simulations, have transformative potential for mesoscale materials simulations.

Industrial and societal: Reliable predictive modelling benefits industry by accelerating product development and reducing the time delay between fundamental science and technological implementation. Computer simulations allow for fast screening of alloy compositions, explanations of experimental data, and optimization of experimental campaigns to test new materials. The mesoscale tools developed during the fellowship will be particularly important, because they will bridge the gap in quantitative understanding between accurate yet limited atomistic methods, and large scale computer-aided design. Letters of support from Rolls Royce, Culham Centre for Fusion Energy, and Materials Design demonstrate that the proposed research is of great interest and relevance to a range of commercial and industrial science and engineering organizations.

The benefits to wider society of advanced nuclear energy generation are clear, and the innovative simulation techniques this project creates will form an important step on the road to its delivery. Furthermore, graphical outputs from the simulations, such as animations depicting microstructural processes, are a powerful tool for visualization and research communication.

Wider academic: The implementation of the new simulation methods first requires a number of conceptual and technical barriers to be surmounted. This will involve deriving new transition rate formulae which take into account system memory and inertia, optimizing numerical methods for handling diffusion through periodic crystals, and developing algorithms capable of accurately simulating the stochastic motion of extended objects. Though they will initially be applied to crystal defect motion relevant to materials for nuclear energy, these advances will eventually be applicable to a wide range of physical and biological systems.

Publications

10 25 50
 
Description So far in this award, two significant discoveries have been made about the behaviour of crystal defects in irradiated materials. Both have been published in high-impact scientific journals.

1: We have shown how radiation (e.g. in a nuclear reactor) can vastly increase the rate of dislocation climb. This was not previously understood, and it can explain why the superb structural performance of certain advanced steels in normal, unirradiated conditions is not repeated under realistic radiation conditions. In particular the, drop-off in strength that occurred at very high temperatures (and was hence not thought to be an issue for industrial applications) may actually happen at much lower temperatures, well within the operating temperature window for fission and fusion reactors.

2: Together with collaborators, we have shown that defect clusters created when a material is irradiated can move quantum-mechanically at low temperatures. This was previously thought to be impossible, and is important because it could lead to very different low-temperature mechanical behaviour from what would have been expected. In particular, defects that were assumed to be "frozen" below a certain temperature turn out to be highly mobile. This is important for any low-temperature application, e.g. cryogenic environments like space.

In addition to this, we have developed an alternative approach to modelling stochastic processes (such as chemical or material systems), using mathematical techniques borrowed from quantum mechanics and field theory. This has elucidated deep connections between two previously disparate branches of mathematics: stochastic processes and Hamiltonian dynamics.
Exploitation Route The new understanding of defect dynamics in energy materials mentioned above could be used by materials scientists and engineers to develop new materials that have the desired properties under the required conditions. In particular, the first outcome above has explained why particle-strengthening methods such as oxide dispersion may not work under irradiation. The second outcome shows that defect motion needs to be taken into account even at temperatures where defects were previously thought to be immobile.

The links between different areas of mathematics that we have investigated have provided a potential means to vastly accelerate computer simulations of stochastic systems (such as chemical processes or nuclear materials). These could be applied to a many different real-world problems, ranging in principle from nuclear materials to mathematical biology to climate science.
Sectors Chemicals

Energy

Manufacturing

including Industrial Biotechology

Other

 
Description Impact has been confined to academia thus far, since the work is mainly technical mathematics, and impact outside academia will take more time to appear. Within academia, several important advances directly attributable to this grant have been made. The understanding of interstitial-mediated irradiation climb we provided offers insights into the potential performance of ODS steels, and could impact future reactor material design. Our explanation of the long-standing mystery of void lattice formation in terms of the Turing instability was selected by science writer Philip Ball as the subject of his weekly Nature Materials column.
First Year Of Impact 2020
 
Description Leeds - Loughborough stochastic dynamics 
Organisation Loughborough University
Department Department of Mathematical Sciences
Country United Kingdom 
Sector Academic/University 
PI Contribution Instigated collaboration; developed and applied path-integral-based algorithm to determine reaction pathways with finite time constraints. Further funding to pursue this avenue of research has been jointly applied for.
Collaborator Contribution Provided conventional numerical modelling for verification. Further funding to pursue this avenue of research has been jointly applied for.
Impact DOI 10.1063/5.0135880
Start Year 2021
 
Description Leeds - Loughborough stochastic dynamics 
Organisation Loughborough University
Department Department of Mathematical Sciences
Country United Kingdom 
Sector Academic/University 
PI Contribution Instigated collaboration; developed and applied path-integral-based algorithm to determine reaction pathways with finite time constraints. Further funding to pursue this avenue of research has been jointly applied for.
Collaborator Contribution Provided conventional numerical modelling for verification. Further funding to pursue this avenue of research has been jointly applied for.
Impact DOI 10.1063/5.0135880
Start Year 2021
 
Description Leeds - Manchester tritium diffusion 
Organisation University of Manchester
Country United Kingdom 
Sector Academic/University 
PI Contribution The new simulation techniques developed over the course of the award will be applied to a technologically-important materials engineering problem: diffusion of tritium (and other gases) through the structural and functional materials of a fusion reactor. The collaboration is still in its early stages, and we envisage applying for further resources to develop a computational simulation package for the community. My contribution is in stochastic modelling and computer simulation, which will be benchmarked and parameterised using experimental data taken at Manchester.
Collaborator Contribution Prof Edmondson is a new appointee at Manchester. His expertise lies in experimental characterisation of nuclear materials. If we are successful in our application for the required resources, an experimental campaign will be pursued at Manchester. In particular, the diffusion properties of hydrogen, deuterium, and helium (as models for the harder-to-handle tritium) will be measured over a variety of pressure and temperature conditions, and used to parameterise and validate the computer simulations.
Impact No outputs as yet (new collaboration). Involved mathematics and materials science.
Start Year 2023
 
Description Leeds-CEA quantum defect motion 
Organisation CEA Saclay
Country France 
Sector Public 
PI Contribution Theoretical quantum-mechanical calculations
Collaborator Contribution Computer simulations
Impact https://doi.org/10.1038/s41563-019-0584-0
Start Year 2018
 
Description Leeds-UPenn statistical mechanics 
Organisation University of Pennsylvania
Country United States 
Sector Academic/University 
PI Contribution I instigated this partnership and designed the research. I also contributed to the mathematical and computational work involved.
Collaborator Contribution Prof Celia Reina and I collaborated on developing new statistical approaches to modelling materials out of equilibrium. UPenn also provided the effort of two doctoral students and the input of two further academics. The collaboration is ongoing and has resulted in one publication so far.
Impact https://doi.org/10.1016/j.jmps.2022.104779
Start Year 2020