Using Pattern Search Methods for Surface Structure Determinationof Nanomaterials
Zhengji Zhao, Juan C Meza, Michel A. Van Hove · OSTI OAI (U.S. Department of Energy Office of Scientific and Technical Information) · 2006
Atomic scale surface structure plays an important roleindescribing many properties of materials, especially in the case ofnanomaterials. One of the most effective techniques for surface structuredetermination is low-energy electron diffraction (LEED), which can beused in conjunction with optimization to fit simulated LEED intensitiesto experimental data. This optimization problem has a number ofcharacteristics that make it challenging: it has many local minima, theoptimization variables can be either continuous or categorical, theobjective function can be discontinuous, there are no exact analyticderivatives (and no derivatives at all for categorical variables), andfunction evaluations are expensive. In this study, we show how to apply aparticular class of optimization methods known as pattern search methodsto address these challenges. These methods donot explicitly usederivatives, and are particularly appropriate when categorical variablesare present, an important feature that has not been addressed in previousLEED studies. We have found that pattern search methods can produceexcellent results, compared to previously used methods, both in terms ofperformance and locating optimal results.