A faster way to relax interfaces in supercells

• Published in: Journal of physics. Condensed matter Vol. 16; no. 27; pp. S2671 - S2678
• Main Author: Finnis, M W
• Format: Journal Article
• Language: English
• Published: Bristol IOP Publishing 14.07.2004; Institute of Physics
• Subjects: Condensed matter: structure, mechanical and thermal properties; Crystalline state (including molecular motions in solids); Exact sciences and technology; Physics; Structure of solids and liquids; crystallography; Theory of crystal structure, crystal symmetry; calculations and modeling; Interfaces; Total energy; Atomic position; Pair potentials; Crystals; Boundary conditions; Modelling; Structure relaxation
• ISSN: 0953-8984; 1361-648X
• DOI: 10.1088/0953-8984/16/27/006

The usual way of minimizing the total energy of a planar boundary between two crystals by relaxing the atomic positions is inefficient, because it does not exploit the physical insight that forces are localized near the interfaces or surfaces. I introduce a simple change of variables, which leads to much faster and more accurate relaxation in such systems. In general the method is formulated for three-dimensional monoclinic supercells with sides (a, b, c), subject to periodic boundary conditions. If the crystals fill space the method exploits the stress tensor in the supercell to adjust its side c, where the boundary lies in the (a, b) plane, but the stress tensor is not required for a slab of finite thickness, which would be simulated by including a vacuum layer in the supercell. In either case the number of conjugate gradient steps required to relax the atomic positions does not increase with the thickness of the system. The power of this method is demonstrated by calculations on one-dimensional chains, both finite and infinite, using a pair potential to calculate the energy, forces and stresses.