Volume 9 issue 1 Nuclear Future


a) ZrM2 C36 ZrM2 C14 ZrM2 C15 ZrM C36


b)


 Zr  Cr or Fe (Laves phases) Fe or Ni (Zr rich phase)


Figure 3: (a) Whole bi-material strip after heating to 100°C. Failed truss elements are shown in red and no longer carry load. The interface has already almost fully delaminated and the bending has initiated vertical cracks in the brittle top layer; (b) half the strip after heating to 200°C.


Figure 4: Unit cells of C36, C14 and C15 Laves and Zr2 intermetallic structures.


M SPP


the industry as their continuum counterparts; however, as the cost of powerful computational resources continues to decrease, their relevance will grow. In order to facilitate their continued adoption by industry,


nuclear engineers with knowledge of these methods are required. Given their widespread use within academia, the university sector is well placed to fi ll this skills gap. Already, the modelling component of the MSc in Nuclear Engineering at Imperial College contains sessions on atomic-scale simulation techniques using both classical pair potentials and quantum mechanical methods. To highlight potential applications of atomic modelling to nuclear materials some recent research performed within the Centre is presented here. One of the main concerns for failure in zirconium nuclear fuel


cladding is delayed hydride cracking. The mechanism through which hydrogen uptake occurs is not very well understood, but it is suspected that the second phase particles (SPPs) found in the alloys play a critical role. It was proposed by Hatano that Zr(Cr,Fe)2


of H through the oxide layer14


particles could act as bridges for the migration , while, conversely, Zr2


(Ni,Fe)-


type particles may trap the hydrogen until either dissolved or fully oxidised15


. Understanding these processes furthers a


more fundamental understa nding of nuclear fuel cladding and provides useful insight when developing or improving materials and processing routes for cladding materials. To this end, material behaviour can be predicted from the description of atomic interactions provided by quantum mechanics. In particular, Kohn and Sham’s Density Functional Theory (DFT) can be used to solve a system’s wave-function – and hence probe the local environment of atoms in a system including electronic effects 16


co-workers calculated the solution enthalpies of H in various binary intermetallic SPPs and compared these with the solution enthalpy for H in both α- and β-Zr metal phases17 Figure 4 shows the four crystal structures of the SPPs


.


considered: Cr forms three intermetallic Laves phases with Zr with the same formula of ZrCr2


. These include both cubic (C15)


and hexagonal forms (C14 and C36) and were all considered. In addition, a tetragonal Zr2


M structure, characteristic of SPPs in


the Zr-Fe and Zr-Ni system was simulated. The solution enthalpy for hydrogen in each of these structures is a measure of how favourable hydrogen incorporation is. By comparing enthalpies between SPPs, those phases likely to trap hydrogen become apparent. Furthermore, due to the atomistic nature of Burr’s simulations, different crystallographic sites can be compared to give a precise prediction of where hydrogen would sit within each structure. In order to achieve this, the following general procedure was employed. For each crystallographically distinct interstitial site within each crystal structure, a hydrogen atom was introduced. Through the use of the DFT the energy of a system can be calculated from its atomic positions and unit-cell dimensions. Using an iterative procedure, small adjustments to the atomic positions are made in order to lower the system energy until a local minimum is obtained. In this way, the relaxation of atoms around the hydrogen interstitial is obtained. From the energy of this relaxed system, the energy change on introducing the H atom is calculated and used to get an enthalpy of solution. Using this method, Burr and co-workers found that certain


. With relation to SPPs, DFT was employed to investigate the thermodynamic behaviour of H within these SPPs. Burr and


elements, such as V and Ni, form intermetallic phases with Zr that offer very favourable sites for H occupancy, whereas other elements, most notably Cr and Mo, form intermetallic SPPs that do not accommodate H readily when compared with pure Zr.


Materials modelling at Imperial 47


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