Modelling radiation resistant low activation High Entropy Alloys

Lead Research Organisation: Loughborough University
Department Name: Mathematical Sciences


The UK Government policy is that nuclear energy has an important role to play in providing an energy future that is safe and low carbon with minimal waste production; for example, the Government's "Nuclear Sector Deal" paper published this summer has as a priority "a long-term vision of innovation-led growth that delivers successively lower generation costs and a 20% reduction in decommissioning costs to the taxpayer".
In 2018, the UK derived ~20% of its electrical power from nuclear reactors and it is likely that demand for electrical energy will only increase, e.g., through the electrification of transport. In the short term, small-modular reactors (SMR) and Gen-III technologies may be utilised to meet demand. The development of radiation-resistant alloys for use in next-generation nuclear reactors will help sustain and expand the UK's capacity to build advanced power plants, with the ability to deliver reliable low-carbon energy. With Materials science highlighted as the key challenge in the 2016 EPSRC Independent Review of Fission and Fusion, this project will aim at addressing the functional materials challenge using advanced computer modelling and simulation.

Therefore in this project, atomistic models High Entropy Alloys (HEAs) will be developed and the models used to investigate the mechanical and thermal properties of specific low activation (i.e. they do not become highly radioactive for long periods) HEAs. HEAs are novel alloys where no single metallic element dominates and four or more elements are used in near equal atomic ratios. HEAs are currently the subject of a significant international research effort due to their reported superior mechanical properties compared to conventional alloys, such as excellent hardness and high temperature strength and stability. They have therefore excellent potential for nuclear applications provided they do not become active under irradiation.

Various theoretical models based on ab initio techniques will be implemented to investigate mechanical and thermal properties and these will be compared to experiment. However the system sizes that can be studied using ab initio methods are necessarily small due to computing limitations and so a second aim of the project is to study larger systems through the use of multi scale modelling by linking the ab initio results with a classical potential formalism. This will allow the alloy behaviour under irradiation also to be investigated and the results compared with other more conventional materials.

The project will concentrate on the investigation of reduced activation HEAs specifically those comprising of TiVZrTa and VWMoCr and TiVCrMnFe, which will be considered in a related experimental programme but the techniques that will be developed and used will have a general application to other complex alloys and therefore potentially wide use outside the nuclear area.

Planned Impact

In 2018, the UK derived ~20% of its electrical power from nuclear reactors. The demand for electrical energy will only increase, e.g., through the electrification of transport. In the short term, small-modular reactors (SMR) and Gen-III technologies may be utilised to meet demand. However, in a future in where nuclear waste is minimised and fuels other than uranium utilised, new Gen-IV and fusion reactors need to be developed. Such reactors will only be built with the help of new materials that can operate in more extreme environments than currently.
One family of materials that is showing great promise are the High Entropy Alloys (HEAs). They are a relatively new class of materials and therefore there is a limited understanding of the electronic, elastic and thermodynamic stability properties.
In this project we aim to bring a range of advanced computational methods to develop a better understanding of the structure - property relationship of complex High Entropy Alloys. These HEAs are inherently complex in nature with 4 or more elements in the compilation e.g. VWMoCr or TiZrHfTa.

The main economic impact will occur in conjunction with the associated experimental programme, which will be involved in producing the low activation alloys. The ability to scale up the most successful alloys into commercial quantities has a large economic potential. The modelling proposed in the project will facilitate the development of these materials in the laboratory and therefore bring the objective of commercial alloy production closer.
The work is focussed towards understanding low activation materials with potential use in the nuclear industry so as a result the work will have impact with commercial organisations such as National Nuclear Laboratories, EDF, Rolls-Royce plc, AREVA who will benefit, not only from the results of the project in identifying new materials for nuclear applications but also through the skills acquired by the personnel working on the project. The work will have impact with the nuclear energy agency (NEA) of the OECD, who will benefit through the PI's interaction with the structural materials modelling group of the NEA. The work will also be publicised at the annual UK nuclear academics meeting.
Another direct output will be highly skilled researchers who have developed multidisciplinary skills in the nuclear modelling area. The appointed PDRA will directly help in the supervision of PhD students working in the area adding further impact through the training of new researchers.
Impact will be achieved not only through publication in top international journals, the usual presentations at important international meetings such as the US Materials Research Symposia, held in Boston each Fall, but also through the development of a web site, promotional materials, preprint archives and small intense workshops with leading international experts.


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Description Multi-principal-component alloys have attracted great interest as a novel paradigm in alloy design, with often unique properties and a vast compositional space auspicious for materials discovery. High entropy alloys (HEAs) belong to this class and are being investigated for prospective nuclear applications with reported superior mechanical properties including high temperature strength and stability compared to conventional alloys. Computational materials design has the potential to play a key role in screening such alloys, yet for high temperature properties, challenges remain in finding an appropriate balance between accuracy and computational cost. Here we develop an approach based on density-functional theory (DFT) and thermodynamic integration aided by machine learning based interatomic potential models to address this challenge. This enables material properties (lattice constant, heat capacity, bulk modulus) of multicomponent alloys to be predicted up to the melting point Calculations are performed on an equiatomic HEA, TaVCrW - a low-activation composition and therefore of potential interest for next generation fission and fusion reactors. In addition the methodology has been applied to alloys with non-equiatomic composition and some preliminary cascade simulations have been carried out to determine how single phase alloys would react to irradiation. The key point defect generated have been identified.
Exploitation Route In conjunction with experimental collaborators we will be testing the predictions of the model. In addition the machine learning potentials can be used to model radiation damage in the alloys. This latter point has led to suggestions for radiation resistant alloys and is the subject of a follow-up grant application.
Sectors Energy

Title Supplementary information files for Design principles of low-activation high entropy alloys 
Description Supplementary files for article Design principles of low-activation high entropy alloys.The present study combines density functional theory (DFT) based calculations and experimental techniques to investigate the formation of equiatomic quaternary "low-activation" high entropy alloys (HEAs) for nuclear fission/fusion applications. DFT based techniques are adopted to screen the formation of possible single-phase ternary and quaternary alloys in chemical space consisting of the low-activation elements (Ti, V, Cr, Mn, Fe, Ta and W). The results indicate that TaTiVW and CrFeMnV can be formed in a single body centred cubic phase (BCC). Based on the DFT based screening, HEAs are fabricated by a vacuum arc melting process. Further characterisation by X-ray diffraction, energy dispersive X-Ray analysis, X-ray fluorescence and scanning electron microscopy confirms the formation of TaTiVW in a BCC single phase. Microstructures of CrTiVW and CrTaVW in as-cast conditions, consist of two BCC phases with very similar lattice parameters. CrTaTiW and CrTaTiV showed evidence of C15 Laves formation comprising of TaCr2 and TiV2, respectively. 
Type Of Material Database/Collection of data 
Year Produced 2022 
Provided To Others? Yes  
Description techniques for determining high temperature properties of high entropy alloys 
Organisation Daresbury Laboratory
Country United Kingdom 
Sector Private 
PI Contribution This is an EPSRC grant part of which is held by Andrew Duff at STFC Daresbury. The PDRA at Loughborough is performing the calculations using techniques developed by Duff to calculate thermal properties of high entropy alloys
Collaborator Contribution We have regular meetings about the application of the TU-tild technique.
Impact None as yet
Start Year 2019
Description Application of computational methods for modelling of scientific and technological processes at STFC 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact The presentation included work carried out as part of the project but also a general description of other computational methods presenytated by Andrew Duff, project partner
Year(s) Of Engagement Activity 2020
Description Multi-scale modelling of alloys, high entropy alloys (HEAs) and molten salts using MEAMfit, and high temperature properties of refractory materials including HEAs from ab initio 
Form Of Engagement Activity A talk or presentation
Part Of Official Scheme? No
Geographic Reach National
Primary Audience Postgraduate students
Results and Impact Talk by Andrew Duff (collaborator) Abstract
The first part of my talk will focus on interatomic potentials, which play a crucial role in the modelling of materials where large length- or time-scales are necessary to capture the relevant phenomena or statistics. Here I will discuss the features and algorithms of the MEAMfit code, which facilitates the optimization of LAMMPS-ready potentials, taking input direct from widely used DFT codes (VASP and CASTEP). I will discuss applications of MEAMfit to explore the temperature- and strain-induced beta-gamma phase transformation in nickel titanium, and elucidate the role of point- and extended-defects on the characteristic transformation temperatures. Calculations in the field of high entropy alloys, as well as a potential to model molten NaCl- as a precursor to more complex molten salts -will also be discussed.

The second part of my talk will focus on the TU-TILD method. Density functional theory (DFT) is state of the art for a wide range of materials modelling applications, yet its application to model high temperature properties has proven challenging. TU-TILD makes possible DFT-accurate free energies and accurate thermodynamic properties up to the melting point, within a computationally amenable framework. Recent results of calculations on the high entropy alloy TaVCrW- with potential applications in next generation and fusion nuclear reactors -will be presented, with the heat capacity, thermal expansion and elastic properties calculated up to the melting point. Furthermore the properties of Frenkel defects in zirconium carbide and their effect on these thermodynamic properties will be discussed.
Year(s) Of Engagement Activity 2020