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### Modelling of solutes in ferritic reactor pressure vessel steels

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 Title: Modelling of solutes in ferritic reactor pressure vessel steels Authors: Whiting, Thomas M. Item Type: Thesis or dissertation Abstract: The lifetime of a steel reactor pressure vessel (RPV) is dictated by its toughness which is gradually reduced during operation due to the elevated temperature and high energy neutron flux leading to the formation of nanoscale defects in the form of matrix damage and solute-vacancy clusters composed primarily of Cu, Mn, Ni and Si. However, the mechanics governing clustering in the Fe-Cu-Mn-Ni-Si system are not currently well understood, and so kinetic Monte Carlo (KMC) methods parameterised by density functional theory (DFT) are often employed to model the time evolution of clusters. To build on existing DFT studies of the binding enthalpies of solute pairs, the binding enthalpies of triplet clusters of Mn, Ni, Cu, Si, and vacancies in \textit{bcc} Fe were explicitly calculated using 128 atom DFT supercells to show that the presence of vacancies, Si, or Cu stabilizes cluster formation and clusters exclusively containing Mn and/or Ni are not energetically stable. Comparisons of triplet binding enthalpies approximated as a sum of defect pair interactions with DFT calculated triplet binding enthalpies revealed that the three-body term can account for as much as 0.3 eV, especially for clusters containing vacancies, and should be considered significant in cluster formation. DFT calculations of Cu, Mn, Ni, Si, vacancies and dumbbells in a strained \textit{bcc} Fe lattice were performed. Experimental observations of Cu-Mn-Ni-Si clusters close to dislocation loops are attributed to the more favourable binding enthalpy of first nearest neighbour (1nn) solute-vacancy pairs (0.19 -- 0.34 eV) and the reduced vacancy formation enthalpy (1.13 eV) in regions of compressive strain. SIA-driven migration of Mn to regions of tensile strain associated with dislocation loops will also occur due to the favourable binding enthalpy of Mn-Fe dumbbells and reduced dumbbell formation enthalpy ($\sim2.5$ eV) in regions of tensile strain. Shear strain and hydrostatic strain acting on second nearest neighbour (2nn) defects were not found to have a significant effect on solute enthalpies. Regression analysis of the relationship between hydrostatic strains and point defects showed that determination of point defect enthalpies for arbitrary volumetric strain within the imposed strain limits of $-5\%<\varepsilon<+3\%$ were in good agreement with explicit DFT calculations. Both the $\Gamma_2$-phase and G-phase have been postulated to form in irradiated RPV steels. The $\Gamma_2$-phase has varying Si content and DFT studies of the $\Gamma_2$-phase found that formation was favoured by increased Si content, but that Si atoms prefer to maximise their separation within the structure. Further, if the chemistries of solute clusters are correct and the Fe content is reduced significantly ($\sim18$ at.\% for the G-phase and $\sim26$ at.\% for the $\Gamma_2$-phase), the G and $\Gamma_2$-phases will form under equilibrium conditions. Finally, it was found that vacancies enhance the formation of both phases and that Hf, Nb, Ta, Ti, Zr will favour the precipitation of the G and $\Gamma_2$-phases, and so these elements should not be considered for future RPV compositions or steels undergoing neutron irradiation without due consideration. Content Version: Open Access Issue Date: Mar-2020 Date Awarded: Aug-2020 URI: http://hdl.handle.net/10044/1/82297 DOI: https://doi.org/10.25560/82297 Copyright Statement: Creative Commons Attribution NonCommercial Licence Supervisor: Wenman, Mark Sponsor/Funder: Rolls-Royce LtdEngineering and Physical Sciences Research Council Funder's Grant Number: EP/L015900/1 Department: Materials Publisher: Imperial College London Qualification Level: Doctoral Qualification Name: Doctor of Philosophy (PhD) Appears in Collections: Materials PhD theses