For a precipitate and matrix of equal molar volumes, the interfacial strain energy will be smallest for which of the following conditions: A coherent boundary? A semi-coherent boundary? An incoherent boundary? None of the above? or Not enough information to answer? Which option is correct?
To determine the condition that will result in the smallest interfacial strain energy for a precipitate and matrix of equal molar volumes, let's break down each type of boundary:
1. Coherent boundary: In this case, the lattice structures of the precipitate and matrix exactly match each other. There is no misfit or dislocation between them. Hence, the interfacial strain energy is minimized due to the absence of lattice distortion.
2. Semi-coherent boundary: In this scenario, there is some degree of lattice mismatch or misfit between the precipitate and the matrix. However, the misfit is accommodated with a periodic array of misfit dislocations at the interface. Though there is still some strain energy associated with these dislocations, it is generally smaller than in the case of an incoherent boundary.
3. Incoherent boundary: Here, there is a significant lattice mismatch or misfit between the precipitate and matrix, which leads to high strain energy. The misfit cannot be accommodated through dislocations, resulting in a strained and distorted interface.
Considering the given options, the condition that will result in the smallest interfacial strain energy is a coherent boundary, as it provides a perfect lattice match between the precipitate and matrix, minimizing strain energy. Therefore, the correct option is "A coherent boundary."