Ferritic steels are an important class ofnuclear mate­rials, which include reactor pressure vessel (RPV) steels and high chromium steels for elevated temper­ature structural and cladding materials in fast reactors and fusion reactors, see Chapter 4.03, Ferritic Steels and Advanced Ferritic-Martensitic Steels. From a basic science point of view, the modeling of these materials starts with that of pure iron, in the ferro­magnetic bcc structure. Iron presents several difficul­ties for DFT calculations. First, being a three dimensional (3D) metal, it requires rather large basis sets in plane wave calculations. Second, the calculations need to be spin polarized, to account for magnetism, and this at least doubles the calculation time. But most of all, it is a case where the choice of the exchange — correlation functional has a dramatic effect on bulk properties. The standard LDA incorrectly predicts the paramagnetic face-centered cubic (fcc) structure to be more stable than the ferromagnetic bcc structure. The correct ground state is recovered using gradient corrected functionals,39 as illustrated in Figure 1. Finally, it was pointed out that pseudopotentials tend to overestimate the magnetic energy in iron,40 and therefore, some pseudopotentials suffer from a lack of transferability for some properties. In practice, how­ever, in the large set of the results obtained over the last decade for defect calculations in iron, a quite remark­able agreement is obtained between the various computational approaches. With a few exceptions, they are indeed quite independent on the form of the GGA functional, the basis set (plane wave or localized), and the pseudopotential or the use ofPAW approaches.

1.08.4.1.1 Self-interstitials and self­interstitial clusters in Fe and other bcc metals

The structure and migration mechanism of self­interstitials in iron is a very good illustrative example of the impact of DFT calculations on radiation defect

studies. Progress in methods, codes, and computer performance made this archetype of radiation defects accessible to DFT calculations in the early 2000s, since total energy differences between simu­lation cells of 128+1 atoms could then be obtained with a sufficient accuracy. In 2001, Domain and Becquart reported that, in agreement with the experiment, the (110) dumbbell was the most stable structure.41 Quite unexpectedly, the (111) dumbbell was predicted to be ^0.7 eV higher in energy, at variance with empirical potential results that pre­dicted a much smaller energy difference. DFT cal­culations performed in other bcc metals revealed that this is a peculiarity of Fe,42 as illustrated in Figure 2, and magnetism was proposed to be the origin of the energy increase in the (111) dumb­bell in Fe. The important consequence of this result in Fe, which has been confirmed repeatedly since

Figure 2 Formation energies of several basic SIA configurations calculated for bcc transition metals of group 5B (left) and group 6B (right), taken from Nguyen-Manh et a/.42 Data for bcc Fe are taken from Fu et a/.43 Reproduced from Nguyen-Manh, D.; Horsfiels, A. P.; Dudarev, S. L. Phys. Rev. B 2006, 73, 020101.

then, is that it excludes the SIA migration to occur by long 1D glides of the (111) dumbbell followed by on-site rotations of the (110) dumbbell, as predicted previously from empirical potential MD simulations. Moreover, DFT investigation of the migration mechanism yielded a quantitative agreement with the experiment for the energy of the Johnson translation-rotation mechanism (see Figure 3), namely ^0.3 eV.43

These DFT calculations were followed by a very successful example of synergy between DFT and empirical potentials. The DFT values of interstitial formation energies in various configurations and interatomic forces in a liquid model have indeed been included in the database for a fit of EAM type potentials by Mendelev et a/.45 This approach has resulted in a new generation of improved empirical potentials, albeit still with some limitations. When considering SIA clusters made of parallel dumbbells, the Mendelev potential agrees with DFT for predict­ing a crossover as a function of cluster size from the (110) to the (111) orientation between 4 and 6 SIA
clusters.44 However, discrepancies are found when considering nonparallel configurations.46 More pre­cisely, new configurations of small SIA clusters were observed in MD simulations performed at high tem­perature with the Mendelev potential. The energy ofthe new di-interstitial cluster, made ofa triangle of atoms sharing one site (see Figure 4), is even lower than that of the parallel configuration within DFT but higher by 0.3 eV with the Mendelev potential (see also Section 1.08.4.3 on dislocations). The new tri — and quadri-interstitial clusters, with a ring structure (see Figure 4), are one ofthe few examples in which a significant discrepancy is found between various DFT approaches. Calculations with the most accu­rate description of the ionic cores predict that the new tri-interstitial configuration is slightly more sta­ble than the parallel configuration, whereas more approximate ones predict that it is 0.7 eV higher. The first category includes calculations in the PAW approach, performed using either the VASP code or the PWSCF code and also ultrasoft pseudopotential calculations. The second one includes calculations

with less transferable ultrasoft pseudopotentials with VASP and norm-conserving pseudopotentials with SIESTA.46 Such a discrepancy is not common in defect calculations in metals. Further investigations are required to understand more precisely its origin, in particular the possible role of magnetism.

The structures of the most stable SIA clusters in Fe, and more generally of their energy landscape, remain an open question. One would ideally need to combine DFT calculations with methods for ex­ploring the energy surface, such as the Dimer47 or ART4 methods. Such a combination is possible in principle, and it has indeed been used for defects in semiconductors,49 but due to computer limitations this is not the case yet in Fe. The alternative is to develop new empirical potentials in better agreement with

DFT energies in particular for these new structures, to perform the Dimer or ART calculations with these potentials, and to validate the main features of the energy landscape thus obtained by DFT calculations.

To summarize, the energy landscape of interstitial type defects has been revisited in the last decade driven by DFT calculations, in synergy with empiri­cal potential calculations.