Most existing thermal barrier coating (TBC) studies do not account for the depletion of Al in the BC and growth of mixed oxides (MOs). In this complementary study, we modify and extend our earlier (Lim and Meguid in Mater Des, 2019. https://doi.org/10.1016/j.matdes.2018.107543) coupled finite volume (FV)–finite element (FE) formulations to incorporate diffusion reactions of Al and Cr in the BC. The modified/expanded FV–FE formulations are supported by the introduction of appropriate diffusion–reaction equations and high temperature oxidation model. Three aspects of the work were accordingly examined. Firstly, the FV model is used to describe the diffusion and reaction of Al and O₂ in the formation of α-Al₂O₃. The β-phase rate of depletion predicted by the model agrees well with experimental findings. Secondly, the diffusion of Cr through the TGO that leads to the formation of an external layer of MOs is simulated using the FV model. Our simulations reveal that MOs form in the early stage of thermal exposure, although there are sufficient Al in the BC to sustain the growth of α-Al₂O₃ phase. We reasoned this to the formation of internal oxides and diffusion cell in the BC. Lastly, we studied the effect of roughness on β-phase depletion and growth of TGO (α-Al₂O₃ + MOs). We show that β-phase in the peak of undulation depletes faster and the interface between the β + γ phase and γ phase in the BC straightens over time. Furthermore, our results reveal that MOs tend to form in the valley of undulation due to the shorter diffusion path.

大多数现有的热障涂层（TBC）研究都无法说明BC中Al的耗竭和混合氧化物（MOs）的生长。在这项补充研究中，我们修改并扩展了之前的方法（Lim和Meguid in Mater Des，2019. https://doi.org/10.1016/j.matdes.2018.107543）耦合有限体积（FV）-有限元（FE）公式在铝中掺入铝和铬的扩散反应。通过引入适当的扩散反应方程式和高温氧化模型，可以支持改进/扩展的FV-FE配方。因此，对工作的三个方面进行了审查。首先，FV模型用于描述的扩散及Al和O的反应₂中的形成的α-Al ₂ ö ₃。该模型预测的β相耗竭率与实验结果非常吻合。其次，使用FV模型模拟了Cr通过TGO扩散导致MOs外层形成的过程。我们的模拟显示，在MO中的热暴露的早期阶段形成，虽然有足够的Al在BC维持的α-Al的生长₂ Ó ₃相。我们将其推论为BC中内部氧化物和扩散池的形成。最后，我们研究了粗糙度对β相耗尽和TGO的生长的影响（α-Al系₂ ö ₃ + MOs）。我们发现，起伏峰中的β相会更快耗尽，并且BC中β+γ相和γ相之间的界面会随着时间的推移而变直。此外，我们的结果表明，由于较短的扩散路径，MO倾向于在起伏的山谷中形成。