Evaluation of Defect Concentrations in Crystalline Systems Via Molecular Simulation

Point defects – particularly vacancies and substitutions – are thermodynamically stable features of crystals, and consequently they should be expected in some concentration when using any self-assembly synthesis method. Such defects have a disproportionate impact on the electronic and photonic properties and mechanical performance of the material. Thus, it is important to assess defect concentration and distribution in the equilibrium crystal, and this is done through reference to the free energy. Calculation of defect free energies is significantly complicated by the need to match the lattice-site concentration, which is determined by thermodynamic equilibrium, to the size of the simulation cell. If this is not done carefully, then one results with behavior that appears to be thermodynamically inconsistent.^1,2

We have developed several approaches to address this problem efficiently in molecular simulations. Each method may be most appropriate for different molecular systems and modeling goals. We evaluate defect behavior the demonstrate various cases, and show how these features affect the system properties. We also consider the behavior of point defects in relation to other types of defects, such as stacking faults.

(1) Swope, W. C. and Andersen, H. C. Thermodynamics, statistical thermodynamics, and computer simulation of crystals with vacancies and interstitials, Phys. Rev. A 1992, 46, 4539-4548.

(2) Pronk, S. and Frenkel, D. Point defects in hard-sphere crystals, J. Phys. Chem. B 2001, 105, 6722-6727.