This lecture covers the concept of coherent interfaces in materials science, focusing on the Cahn Hillard model. The instructor, Francesco Stellacci, discusses topics such as heterophase grain boundaries, antiphase domain boundaries, and the energetics of semi-coherent grain boundaries. The lecture delves into the nomenclature of special grain boundaries and the key factors affecting their behavior. Various diagrams and equations are used to illustrate the energetics and behavior of these interfaces.