correlation with improved cell performance. Additionally, however, the temperature dependence of oxygen vacancy concentration means that the CTE is not a linear property, which further complicates measurements and predictions. Just as thermal stresses increase as cell performance improves through improved ionic conductivity, the fracture toughness of the material also decreases as cell performance increases. This is because, to increase reaction sites, porous ceramics are preferable. However, as shown in the equation below, fracture toughness decreases as porosity increases. Where: = fracture toughness = fracture toughness of the non-porous structure = experimentally determined constant = porosity Thus, porosity must be carefully engineered to maximize reaction kinetics while maintaining an acceptable fracture toughness. Since fracture toughness represents the ability of pre-existing cracks or pores to propagate, a potentially more useful metric is the failure stress of a material, as this depends on sample dimensions instead of crack diameter. Failure stresses in SOFCs can also be evaluated using a ring-on ring biaxial stress test. This type of test is generally preferred, as sample edge quality does not significantly impact measurements. The determination of the sample's failure stress is shown in the equation below. Where: = failure stress of the small deformation = critical applied force = height of the sample = Poisson's ratio = diameter (sup = support ring, load = loading ring, s = sample) However, this equation is not valid for deflections exceeding 1/2h, making it less applicable for thin samples, which are of great interest in SOFCs. Therefore, while this method does not require knowledge of crack or pore size, it must be used with great caution and is more applicable to support layers in SOFCs than active layers. In addition to failure stresses and fracture toughness, modern fuel cell designs that favor mixed ionic electronic conductors (MIECs), Creep (deformation) pose another great problem, as MIEC electrodes often operate at temperatures exceeding half of the melting temperature. As a result, diffusion creep must also be considered. Where: = equivalent creep strain = Diffusion coefficient = temperature = kinetic constant = equivalent stress (e.g. von Mises) = creep stress exponential factor = particle size exponent (2 for Nabarro–Herring creep, 3 for Coble creep) To properly model creep strain rates, knowledge of Microstructure is therefore of significant importance. Due to the difficulty in mechanically testing SOFCs at high temperatures, and due to the microstructural evolution of SOFCs over the lifetime of operation