The rest of the article is organized as follows. Details of the dataset generation, training of the CNN model, and topology optimization algorithm are provided in Section 2. The results pertaining to the predictive performance of the model, and its ability to discover optimal microstructures when integrated with a topology optimization algorithm, are presented in Section 3. By modifying the inputs to the CNN model, we provide a physical interpretation of its learning aspects in Section 4. We report on the correlation of physics-inspired structural descriptors with cation diffusivity using the data-driven approaches in Section 5. Section 6 concludes the paper with a summary of our findings and provides an outlook regarding the generality of our methodology to train CNN models for exploring structure-property relationship in two-phase composites doped with spherical nanoparticles.