Problem 3 Interfaces and dislocations (5 + 7 + 13) a) Draw atomic level schematics of (a) coherent, (b) semi-coherent and (c) incoherent interfaces. b) Let us say we are depositing a very thin Ge film (bulk lattice constant 0.566 nm) on Si (001) substrate (lattice constant 0.543 nm). Assume that all the misfit strain is accommodated by 60 dislocations with burgers vector 1/2. Estimate the dislocation density assuming uniform distribution of these dislocations, without any dislocation reaction. c) The assumption in a) that "all the misfit strains is accommodated by "60 dislocations", is generally not valid. Why? Use suitable schematic diagrams and simple analytical expressions (qualitative trends are sufficient, don't worry about exact pre-factors for your equations) to establish your argument