# The Evolution of Solid Oxide Fuel Cell Materials
## 1 Introduction  
SOFCs have been considered for decades and have a vast number of applications including mobile (cars and buses) and industrial uses. In the past years, there has been a trend to introduce more efficient systems for energy conversion and storage and this includes SOFCs, batteries, supercapacitors, solar cells, etc. [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. The main interest in SOFC technology is because of its very efficient energy conversion in conjunction with reduced emission of the so-called greenhouse gases as compared with the typical power generation routes [1; 3]. Typically, SOFCs operate efficiently at high temperatures (up to 1000 \({}^{\circ}\)C), with hydrogen and fossil fuels converting chemical energy to electricity; however, they can also be used in combined heat and power applications [26; 27]. A consequence of the high temperatures in which SOFCs operate is the high materials costs (materials issues include thermal cycling, chemical degradation, etc.) due to expensive interconnects and heat exchangers [28]. The impact of high temperature can be mitigated by lowering the operating temperatures to 500-700 \({}^{\circ}\)C (known as the intermediate temperature range). Nevertheless, SOFC thermal-activated processes (i.e., diffusion) are affected by the reduction in temperature, and this is particularly problematic for the cathode and electrolyte. This leads to the requirement of advanced materials with high rates of oxygen self-diffusion at these reduced temperatures. In particular, it is necessary to accelerate the oxygen diffusion in the cathode and electrolyte of the SOFC.  
It should be stressed that the more conventional cathodes, for example, La\({}_{1-\lambda}\)Sr\({}_{x}\)MnO\({}_{3-\delta}\), that are considered to be competent electronic conductors are not appropriate because of their low bulk ionic conductivity ([10] and references therein). This has led to the use of another group of materials called mixed ionic-electronic conductors (MIECs) as the oxygen reduction reaction (ORR) in MIEC electrodes is ruled by the oxygen surface exchange andoxygen diffusion [10]. Similarly to cathodes, electrolytes for SOFCs also need to possess high ionic conductivity but with low electronic conductivity [10].  
Oxygen diffusion is therefore fundamentally and technologically important for the cathode and electrolyte materials of SOFC [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13; 14; 15; 16; 17; 18; 19; 20; 21; 22; 23; 24; 25]. Oxygen self-diffusion in these systems is a complicated phenomenon that is influenced by the composition, crystal structure, oxygen stoichiometry, doping and elastic strain ([10] and references therein). In that respect, predictive computational modelling can be used synergistically with experimental work to ensure an efficient design route for fast oxygen ion diffusion in SOFCs. Essentially, the complexities constitute the determination of the defect processes and the impact of various factors on these difficulties when using experiments and simulations at the atomic scale can offer detailed insights.  
In this review, the focus is on the oxygen diffusion mechanisms of SOFC materials moving from more common materials (perovskite-related materials) to novel concepts, considering the latter emphasis is given on recent theoretical (refer to Section 2.2) and associated experimental results highlighting the importance of strain, interfaces and architectures on the enhancement of the diffusion properties of oxide materials for SOFC applications.