The matlab scripts: madsum_iso.m (isotropic elasticity) madsum_aniso.m (general anisotropic elasticity) madsum_cubic.m (anisotropic medium with cubic symmetry) calculates the elastic energy of a dislocation dipole in a supercell under periodic boundary conditions Geometry: (x1,y1) A------------------------------------- \ \ \ P \ \ (-) (x2r,y2r) \ \ / \ \ / \ (+)-----------------------------------B (x0,0) Input: C0: C0(i,j,k,l) general elastic constant tensor (in eV/A^3, 1eV/A^3 = 160.22GPa ) b0 = [ bx, by, bz ] Burgers vector in unit cell frame (in Angstrom) e.g. b0 = [ 1 1 1 ]/2 * 3.1472 (for Molybdenum) M = [ e1, e2, e3 ] coordinate transformation matrix, e3 is parallel to dislocation line rc: cut-off radius coords = [ x0, x1, y1, x2r, y2r ] x0 x coord of B (0, infty) (in A) x1 x coord of A (-infty,infty) (in A) y1 y coord of A (0, infty) x2r reduced x coord of P (-0.5, 0.5] y2r reduced y coord of P (-0.5, 0.5] trunc = [ xcut, ycut ] truncation paramters -xcut:xcut times -ycut:ycut number of images will be added Output: Eel: total elastic energy, Eel = Eprm + Eimg Eprm: primary dipole energy Eimg: image energy ---------------------------------------------------------------------- Binary executables (compiled for Linux i386) maddiso (isotropic elasticity) maddaniso (anisotropic elasticity) are earlier versions with the same function (written in C, faster but less readable) For comparison, run matlab> testmadsumcubic ./maddaniso -cx=10 -cy=10 1 0.2 2 0 0.5 < phRI.dat matlab> testmadsumiso ./maddiso -cx=10 -cy=10 1 0.2 2 0 0.5 ---------------------------------------------------------------------- References: 1. Wei Cai, Atomistic and Mesoscale Modeling of Dislocation Mobility, Ph. D. Thesis, Massachusetts Institute of Technology, 2001. ( http://micro.stanford.edu/~caiwei/papers/CaiWeiThesis.pdf p. 296, for dislocation interaction energy in anisotropic medium. ) 2. Wei Cai, Vasily V. Bulatov, Jinpeng Chang, Ju Li and Sidney Yip, Periodic image effects in dislocation modelling, Philosophical Magazine A, 83, 539 (2003). ( for regularization of conditional convergence )