# Modelling the Defect Processes of Materials for Energy Applications
## 3 Advanced Materials for Energy Applications  
In this section, we will briefly consider the requirements of key energy sectors and their need for advanced materials, with a focus on solid solutions. This is not an exhaustive account but rather aims to introduce the issues. Solid solutions are relevant and under investigation in solid oxide fuel cells, batteries, nuclear fuel, semiconductors, catalysts and superconductors [64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80]. Considering nuclear energy, there is significant research effort for the future generation reactors as nuclear energy is deemed to be an important component of the energy mix aiming to lower CO\({}_{2}\) emissions. These advanced nuclear reactors will be required to be safer, more economic and proliferation-resistant. To meet these targets, the community is working on mixed oxide fuels that will be thorium-based due to the abundance of thorium compared to uranium and its highest proliferation resistance [91; 92; 93; 94; 95]. There are numerous applications of the SQS and \(cB\Omega\) model methodologies in the literature [64; 65; 66; 67; 68; 69; 70; 71; 72; 73; 74; 75; 76; 77; 78; 79; 80; 81; 82; 83]. This is driven by the introduction of new material systems and the requirement for easy and inexpensive screening in an effort to lead to application as soon as possible. In that respect, the cB\(\Omega\) model has been employed to expand our understanding of the defect chemistry of novel microelectronic and nuclear fuel systems. As expected, most of the studies on nuclear fuel materials from a theoretical perspective focus UO\({}_{2}\), but given the requirement for proliferation-resistant fuels (for example, ThO\({}_{2}\) and mixed oxides), there are numerous systems and conditions that need to be investigated. Interestingly, in recent studies [40; 43; 70], there was a combination of molecular dynamics simulations and thermodynamic calculations based on the cB\(\Omega\) model to consider a wide range of pressures (0-10 GPa), PuO\({}_{2}\) and mixed oxide fuels. These studies can serve as a paradigm and a first step for the understanding of these systems, which can be expensive, time-consuming and difficult to study experimentally. More recently, density functional theory calculations were used in conjunction with the SQS approach to predict the formation of MAX phase solid solutions [90]. MAX phases have a range of ceramic and metallic properties and are thus important candidate materials for numerous applications, including aerospace and nuclear engineering [28; 29; 75; 76; 77; 78; 79; 80]. Figure 1 illustrates typical 128-atom SQS structures to mimic the (Zr\({}_{1-\rm{x}}\)M\({}_{\rm{x}}\))\({}_{2}\)AlC and Zr\({}_{2}\)(Al\({}_{1-\rm{x}}\)A\({}_{\rm{x}}\))C MAX phases for x = 0.25 and 0.5 [90]. The results are confirmed by the available experimental data and by employing chemical bonding analysis (crystal-orbital Hamilton population) predict that (Zr\({}_{1-\rm{x}}\)M\({}_{\rm{x}}\))\({}_{2}\)AlC (M = Nb, Ta) and Zr\({}_{2}\)(Al\({}_{1-\rm{x}}\)A\({}_{\rm{x}}\))C (A = Bi, Pb, Sn) MAX phases can be synthesised [90]. In a further, very significant advancement, [PERSON] and [PERSON] [75] performed an extensive (2702 compositions) theoretical study (employing SQS) of MAX phase alloys. This investigation identified as thermodynamically stable 92 i-MAX (in-plane chemical ordering) and 291 solid solution MAX phases [75]. In essence, the study by [PERSON] and [PERSON] [75] resulted in a very significant expansion of the MAX phase family and provides promising routes for more focused experimental work. This is illustrated in Figure 2.  
The advent of new materials (post-silicon) systems for the new era of nanoelectronics and radiation-tolerant electronic devices has regenerated the interest in the dopant-defect properties and interactions of semiconductor materials (for example, references [26; 32; 33; 34] and references therein).