Larger grain sizes in ceramics lead to reduced grain-boundary contributions to diffusivity due to fewer grain boundaries and decreased grain boundary surface area. The linear intercept method is a common technique for measuring grain size in polycrystalline materials by counting intercepted grain boundaries. Grain boundaries exhibit higher entropy because they consist of a mixture of different types of atoms. This higher entropy at grain boundaries can influence diffusivity characteristics. Understanding these relationships is crucial for optimizing the properties of ceramic materials.