Busca global em LEED usando algorítmo genético

Abstract

The atomic structure determination of solid surfaces by LEED (Low Energy Electron Diffraction) is a problem that requires an extensive search in the parameters space that usually includes structural parameters, the Debye temperatures of the first layers and the optical potential, in order to get the theoretical I(V ) curves well fit to the experimental one. Therefore the use of algorithms that can find the global minimum more efficiently is very useful in the LEED analysis. This work presents the results of an application of the Genetic Algorithm method (GA) in the parameters optimization in the LEED analysis. As this is a computational method based on the species evolution it is implemented in a such way that starting from a random chosen initial population of solutions, the GA algorithm search for the best solution through evolution devices such as cloning, recombination and mutation. In the particular case of surface structural determination each individual (solution) is a structural and non-structural parameters set, that are coded in binary strings (chromosomes). In the present implementation the reliability of the solution is obtained by the SATLEED (Symmetric Automated Tensor LEED) code, which calculates the I(V ) curves from structures generated by the GA and does the comparison with experimental I(V ) curves. This comparison is carried out by using the so-called reability factor (R-factor) that quantifies the agreement between curves. The GA uses the R-factor to calculate probabilities of cloning and recombination. Preliminary results of the application of the GA to the structural determination of (111) face of the Ag crystal - where the optimization of three structural parameters plus the Debye temperature of the first layer and the optical potential were performed - showed a good performance. In addition, a second test was carried out using the (110) face of Cu, where four structural parameters plus the Debye temperature of the two first layers and the optical potential were optimized. Finally, the code was used for the Ni(111)(p3 £ p3)R30o ¡ Sn system. Here the optimization problem considered the search on six structural parameters plus the Debye temperature of the first and second layers and the optical potential, a total of nine parameters. Again, we got very good agreement among the obtained through GA and the results obtainedpreviously through other methods of minimization.