RED HIDRICA Y RETIROS DE LA CUENCA DE LA QUEBRADA SANTA

To distinguish solid-like from liquid-like environments for a particular atom i, we used the centro-symmetry parameter, defined as [192, 221, 222]:

Φi= 1 6 1 a2₀ 6 X j=1 |d_j + d−j|2, (4.54)

where dj and d−j are vectors connecting atom i to its opposite nearest neighbours j, −j; a2₀

is the equilibrium lattice parameter. The values of the centro-symmetry parameter are hence dimensionless through a2₀normalisation. For an fcc lattice, sufficient sensitivity of the method is obtained when six such vector pairs (four for bcc), corresponding to the first nearest-neighbour (nn) shell, are chosen. In practice, a cutoff distance rcut is selected (which is larger than the

first nn shell distance) within which the six shortest vector pairs j and −j are selected. To reduce the thermal noise in the analysis one can average the values of Φiover a particular

time period, over the nn values, or use a velocity damping technique [192]. In the case of fcc Au we are averaging the Φi parameter over the twelve nn values.

The centro-symmetry parameter provides us with a quantitative measure of a degree of crystallinity; it is zero for atoms in perfect crystalline surroundings and sharply increases as the local atomistic environment become disordered. It can also be used to detect defects, dislocations and indicate free surfaces.

4.5

Summary

In this chapter we described the evolution of the atomistic simulation techniques from classical molecular dynamics (Sec. 4.1), through damped MD (Sec. 4.2) to the more sophisticated non- equilibrium two-temperature MD (Sec. 4.2). We looked at some of the post-processing analyses methods, which help to visualise the phase transitions (Sec. 4.4.4) and relate the MD data to the experimentally measurable quantities (Sec. 4.4.1).

The common thread in the MD “evolution” presented here is a step-by-step inclusion of the non-equilibrium electron-ion interactions. Damped MD includes the electronic stopping power, while the two-temperature MD adds an effective description of the electron-phonon coupling. Beyond that, three-temperature models include a temperature to account for the spin degree of freedom in magnetic materials. We envisage that further non-equilibrium effects will be successively added in the future, such as selective electronic excitations (with a separate temperature describing each), selective phonon excitations and most importantly Te-dependent

Chapter 5

Radiation damage cascades

 Attribution: The 200-500 keV pka cascade simulations were performed in collaboration with researchers at Queen Mary, University of London. Parts of the simulation setup, parameter selection, the subsequent defect statistics and clustering analysis were conducted by the present author. The second batch of the simulations, in the range of 50-100 keV pka, was designed, run and analysed independently by the present author.

The parallel two-temperature DL POLY code development was carried out by M. Seaton (Daresbury Laboratory) and was based on a serial version provided by the present author, which was in turn built from a provisional development by A. Rutherford. Extensive acceptance testing performed before the code was released to our collaborators, as well as the code documentation was the assumed responsibility of the present author.

Parts of the research presented here were published in [1, 5, 223].

5.1

Introduction

The aim of this chapter is to investigate the effects of the electronic stopping and electron- phonon coupling on the primary radiation damage formation in α-iron using the two-temperature molecular dynamics model (2T-MD). An extensive comparison to ‘standard’ cascades, which do not include the interactions between the ions and the electrons, as well as literature data, is made. A method to separate e-s and e-p processes at the simulation level is presented and the impacts of each of these energy transfer channels on the evolution of the damage cascade are quantified. The results summarised here are particularly timely, since the impact of the electronic effects (particularly the strength of the e-p coupling) in cascade simulations has re- cently been investigated for low energy pka impacts (10 keV) [81, 224] and the requirement to include these processes has been emphasised in recent reviews (see also Sec. 3.2). Nonetheless, a detailed and rigorous comparison of the impact of the e-p and e-s effects against ‘stand-

ard’ cascades is still missing. Furthermore, the results reported here provide detailed defect number statistics for higher, more representative and hence realistic, 50-500 keV pka impact simulations. Modelling of such high energies was enabled by the progress achieved in building a massively parallel 2T-MD code.

This chapter concentrates on the simulations performed for α-iron, as it is a candidate for primary components of steels and alloys for the future nuclear reactors. Furthermore, α-iron is, by far, the most commonly studied material through cascade simulations, which makes the comparison with the vast amount of literature data possible.

Secondary aims of the chapter include detailed characterisation of the Frenkel pair (FP) distribution, for 50 keV and 100 keV pka impacts, over a large number of cascade runs. This is to investigate the possibility of rare-events - infrequent generation of very large defects clusters or exceptionally high FP numbers in comparison to the mean FP expected at a particular cascade energy1. Local defect structures and defect cluster distribution along with remarks on global morphology trends for 50, 100, 200 and 500 keV cascades are presented and analysed in the context of previous research findings. We note that the 500 keV cascade results presented here represent the highest energy cascade simulation in iron published to date.