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Unformatted text preview: PHZ 5156 Final project Conjugate-gradient relaxation One important problem in materials physics is to determine the energy associated with various structures, including the formation energy of a lattice vacancy and the energy of a free surface. To develop a model for these problems, some account of the atomic relaxations is required. For practical reasons, it is sometimes important to optimize the relaxation of atoms to a local minimum where ~ F i = 0 for each atom i . We will explore the approach of conjugate-gradient minimization for this problem. In the conjugate gradient approach, we want to first relax along some direction, and then choose the next direction conjugate to the preceding directions, so that subsequent relaxations do not interfere with the preceding ones. We explored this in lecture. Use as a starting point the molecular-dynamics code with the fcc starting structure. Do your calculations for a 4 4 non-primitive cell containing 255 atoms. In other words, consider a system with a 256 lattice sites and a single vacancy. Determine thewords, consider a system with a 256 lattice sites and a single vacancy....
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- Fall '08