This chapter shows that there is good agreement between the experimental and theoretical studies in MgO for the defect properties, although there is significant differences between the formation energy of Schottky defects. The computational simulations are also able to give an answer to conflicting experimental results, such as the Mg vacancies. The vast amount of experimental results in the literature means that the computational models are able to check accuracy and therefore make useful and accurate predictions.
ited computational results in agreement with the behaviour of the bulk under irradiation. The coordination changes of the titanium polyhedra are the most prominent changes in the bulk due to an irradiation event, observed both experimental and theoretically, as well as the ease in formation of the Ca defects, seen in the leaching studies and the cascade simulations.
Chapter 4
Point defects in MgO
4.1
Introduction
Radiation events, such as the decay of encapsulated radio-nuclides, produce high energy particles, such as alpha particles, and recoil nuclei with energies of the order of several tens of keV. The high velocity nuclei and particles exchange energy with the host atoms and create regions of local dynamic disorder in the lattice. The disordered system recrystallises over a period of a few tens of picoseconds but residual defects remain and it is the long timescale evolution of these residual defects that will eventually modify the microstructure of the material.[116, 117] The initial radiation event can be successfully modelled by molecular dynamics cascade simulations but long timescale methods, such as kinetic Monte Carlo[92] and rate theory,[118] are required to investigate microstructure evolution.
The interaction of the alpha particle with the host matrix results in the loss of energy via two mechanisms, elastic and inelastic collisions (figure 4.1). The energy loss due to the elastic collisions with atoms is known as nuclear stopping, Sn. The dissipation of energy into the atomic system causes the dynamic disorder associated
with radiation damage. The energy loss due to inelastic collisions with electrons is known as electronic stopping, Se. The Seresults in the excitation of electrons as the energy is absorbed from the alpha particle. This results
in the formation of excited electrons, holes and excitons, which are able to diffuse through the material and become localised in the lattice (self-trapping) or at defect/impurity sites (trapping). The energy of an alpha particle ejected from an actinide is around 5 MeV,[15] at these energies there is an average of three orders of magnitude difference between Seand Snfor a ceramic material. Therefore, more energy will be dissipated into
the electronic system before sufficient energy has been removed from the alpha particle for Snto dominate. This
is shown by the alpha particle causing about 100 atomic displacements in zircon compared to the 1000 created by the recoil particle.[15]
Radiation damage simulations have traditionally employed classical methodologies because the length and timescales required are orders of magnitude higher than those feasible for ab initio methods. The cascade simulations that are usually performed give a good description of Snbut take no account of Se and therefore
they neglect the contribution to radiation damage from electronic excitations. There has been a recent revival of interest in attempting to understand and include these effects, with notable progress in metallic materials.[119, 120, 121] Electronic excitations in insulating materials are more complex than those in metals as the band gap results in a range of additional processes, including the trapping and self-trapping of electrons, holes and excitons.[122] The trapping of electrons and holes at defects in ionic crystals is particularly relevant to radiation damage,[123] as the trapped carriers will effectively change the net defect charge and this will have a strong effect on defect migration energies, and hence the microstructure evolution. Such effects cannot be reliably
Figure 4.1: A comparison of the nuclear and electronic stopping power in silicon. The vertical dashed line shows the average energy of an α particle emitted from an actinide element. Graph calculated by SRIM.[4]
studied using classical methods. Trapped electrons and holes will also affect the defect formation energies in ionic crystals.
MgO has been studied because it is considered to be a model oxide because it is a binary oxide with the simple face centred cubic crystal structure. MgO has also received a large amount of attention, both experimen- tally and theoretically, allowing a comparison of the results to the literature. The comparison with the literature is important as it will allow the confidence in the modelling of the different charge states, meaning the obtained results are not an artifact of inaccurate models. The doubly charged ions in MgO make it more suitable for this research than another model oxide, NaCl, as it allows more charge states to be studied and thus allows a wider set of conclusions to be drawn on the effect of charge localisation on defect properties.
Electrons are known to localise on O vacancies in MgO and holes can localise on O interstitials. We focus on oxygen defects because of the stronger charge localisation. We investigate the effect of charge localisation on oxygen vacancy and interstitial formation energies in MgO. We calculate defect formation energies for O vacancies with zero (F2+), one (F+), and two (F0), trapped electrons and O2− interstitials with zero, one and
two trapped holes. These energies are used to calculate Frenkel defect energies for neutral, singly charged and doubly charged defect pairs along with the corresponding migration barrier energies for the vacancies and interstitials. Frenkel pairs are created by radiation events in crystals and it is the creation and migration of these defects that dominate the long timescale evolution of the microstructure.