1 Problem 4: The energy difference between "hard" (centered at H) and "easy" (centered at and E2 ) core structures of screw dislocations in BCC Mo has been estimated to be 0.08 eV/b by density functional theory (DFT) calculations (Here b is the magnitude of its Burgers vector). Assuming that the screw dislocation must go through the "hard" core structure as it moves from one "easy" core structure centered at E to the next at E2, estimate the critical stress required to move the screw dislocation at zero temperature (i.e. the Peierls stress). Assume the core energy varies with the dislocation center position as a simple sinusoidal function, and the lattice constant of Mo is a =3.147 . The distance between two "easy" core centers E 6 and E is [112]| = == a. A2 E2 | | 3 A3 C3 C2 H S E2 Hint: you can regard the energy difference between "easy" and "hard" core results from the variation of the misfit energy described on Page 19 in Chapter3_3_Dislocation_Crystals.pdf. How does the misfit energy change when the center of dislocation core changes from E to E2 along the x coordinate || [112]? You can also ignore the core position variation along the y coordinate || [110]. For simplicity, you do not need to consider the kink formation-migration mechanism here. [110]|| y [112] || x [111]