Photoelectron diffraction from random surface alloys: critique of calculational methods

For random single crystal alloys, the lack of periodicity parallel to the surface, which is consequence of the substitutional disorder, complicates the calculation of photoelectron diffraction (PD) patterns. One way to calculate PD spectra from random surface alloys is to evaluate the spectra for each member of the complete ensemble of configurations and then to sum appropriately to generate the PD spectra from the alloy. The number of different configurations is very large, which makes this approach very time consuming computationally. A computationally efficient approximation, which has had success in applications to low energy electron diffraction from random alloys, is the average t-matrix approximation (ATA), where the scattering properties are described by an effective t-matrix. In this work we compare the ATA with the average over configuration within the context of the cluster-based PD theory and compare the results of both methods with experimental data from a random surface alloy, namely Pd on Cu(1 1 1). The results of this study indicate that the ATA is efficient in extracting structural and concentration information. Cluster details can be obtained from the configuration average method. Furthermore, the ATA is useful in determining the best parameters (energy, angles, etc.) to be used in an experiment.