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@@ -0,0 +1,73 @@ +# LatticeMatch + + +## Licence info: +Copyright (C) 2012 Andreas Grois + +This program is free software; you can redistribute it and/or +modify it under the terms of the GNU General Public License +as published by the Free Software Foundation; either version 2 +of the License, or (at your option) any later version. + +This program is distributed in the hope that it will be useful, +but WITHOUT ANY WARRANTY; without even the implied warranty of +MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the +GNU General Public License for more details. + +You should have received a copy of the GNU General Public License +along with this program; if not, write to the Free Software +Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA. + +## Description +This is a small script that calculates possible lattice matches as discussed in: + +Fritz, Torsten: Molecular Architecture in Heteroepitaxially Grown Organic Thin Films +Dresden: sfps - Wissenschaftlicher Fachverlag, 1999 +ISBN: 3-934264-50-6 + +The advantage of this script compared to the original work of T. Fritz is, that this +program does not use a brute-force approach, but instead determines ranges of possible +values for the angle between the first lattice vectors of the interface unit cell of +substrate and adlayer analytically. +To do this, the user has to enter the substrate interface unit cell, giving the length +of the lattice vectors a1 and a2, and also the angle between them, alpha. +For the interface unit cell of the adlayer the user has to input ranges in which the +magnitude of the lattice vectors b1 and b2 may lie, as well as a range for the angle +between them, beta. The program then uses these inequalities together with the +underdefined set of equations describing a coincident lattice match to determine ranges +in which the angle theta between a1 and b1 may lie. + +According to the work quoted above, a coincident lattice match occurs when both elements +in one of the columns of the epitaxy matrix are integer, while in case all entries are +integer, one is dealing with a commensurate lattice match. + +The epitaxy matrix, as given in the work quoted above, reads: + +( px, qy ) +( qx, py ) + +with: +px=b1*sin(alpha-theta)/(a1*sin(alpha)) +qx=b2*sin(alpha-theta-beta)/(a1*sin(alpha)) +qy=b1*sin(theta)/(a2*sin(alpha)) +py=b2*sin(theta+beta)/(a2*sin(alpha)) + +There are two reasons for the length of this program: +o) asin isn't unique. +o) ranges of angles are a pain to deal with. +Both points together made writing the correct conditions for upper and lower bounds +of the result ranges a pain, and I'm pretty certain there might still be the one or the other +bug hidden. + +##Usage +Using this program is quite easy: Just supply the input as command line parameters in this order: +a1, a2, alpha, b1min, b1max, b2min, b2max, betamin, betamax +Use degrees for the angles. + +The output consists of several ranges of possible values for theta, one range per line. + +##Contact +To contact the author either use electronic mail: Andreas Grois <andreas.grois@jku.at> +or write to: +Andreas Grois, Institute for Semiconductor and SolidState physics, Johannes Kepler University, +Altenbergerstraße 69, 4040 Linz, AUSTRIA |