Purpose, Approach, Limitations 1001



LEEDpat is designed to help interpret experimentally observed LEED spot patterns for ordered periodic surfaces especially in the presence of superlattices, originating from reconstruction or adsorbate layers. In particular, LEEDpat allows one to tell which 2-dimensional (2D) surface lattices are compatible with an observed LEED pattern. Rotational domains and glide plane extinction of spots are taken into account (the latter at normal incidence only).


LEEDpat also provides extensive 2D symmetry information, showing all rotational, mirror and glide symmetries that are compatible with the observed pattern. This allows the user to narrow down possible structural models of the surface and to propose atomic positions in the actual structure. However, LEEDpat does not itself predict structural models or atomic coordinates. It does not calculate spot intensities, which would be needed to determine atomic positions.


Version 4.2 of LEEDpat includes many bug fixes, improvements, and new features. In particular, version 4.2 offers


         Analyses of incommensurate periodic overlayers.

         Analyses of periodic overlayers with higher-order coincidence (HOC) lattices

         PostScript print output for documentation purposes.

         Output/Input of structures on/from external (LEEDpat format) ASCII files

         Output on a structure file stack for quick comparisons.

         Improved visualization of the structure / pattern graphics (bottom left and right).

         Improved handling of symmetry domains, selection of domains from matrix representations

         improved handling of hexagonal geometries, allowing both acute and obtuse lattice vector sets.

         simulation of channel plate geometry in pattern output.





The user can select any basic 2D substrate lattice (oblique, rectangular (primitive and centered), square, or hexagonal (both acute and obtuse representation)), including any possible symmetries (i.e. any of the 17 two-dimensional space groups). The user can also specify any commensurate superlattice, again with any possible symmetries. LEEDpat then draws both a real-space lattice and a LEED pattern (representing a superposition of corresponding reciprocal lattices), including the option of symmetry-related domain orientations (of equal weight). The user can thus, by trial and error, find the pattern that best matches the experiment.


In addition, incommensurate periodic overlayers, resulting in 1D- or non-periodic LEED patterns, can be specified. This includes continuous adjustments of overlayer lattice vectors by mouse dragging to achieve best fits. Further, symmetry-related domain orientations (of equal weight) can be evaluated and selected where the symmetry is taken from the basic 2D lattice. This allows the analysis of LEED spot behavior when small deviations of the superlattice periodicity from a commensurate case are introduced.


Further, overlayers forming higher-order coincidence (HOC) lattices can be analyzed and resulting LEED pattern drawn. The analysis allows conversions between different representations of HOC lattices and the evaluation of HOC supercells.





A direct conversion from observed pattern to real-space lattice is not possible, due to complications, such as: multiple and thermal diffuse scattering, mixed structures, defects, two- and three-dimensional disorder, faceting, ordered steps, differently oriented terraces, in addition to the ambiguities due to symmetry-related domains of different orientation and unequal weights.


Commensurate, higher-order coincidence (HOC), and incommensurate superlattices are allowed in LEEDpat, i.e. the matrices defining superlattices can have integer, fractional, and real valued elements. For incommensurate superlattices symmetry considerations are taken into account only with respect to the basic 2D lattice (domain formation). The less user-friendly and program SARCH allows also incommensurate domains. This program is freely available at http://www.fhi-berlin.mpg.de/KHsoftware/SLP/. (SARCH is outdated computationally and will run only inside a DOS window on modern MS Windows personal computers.) Supercells and transformations of HOC lattices can be evaluated with LEEDpat. In some cases, resulting supercells may not be primitive but can be resized. Conversions between incommensurate and nearby HOC lattices are restricted to transformations with fractional values pij/qij where denominators qij are defaulted not to exceed 20 where the upper limit can be reset.


Case of steps: Stepped ("vicinal") surfaces produce well-known "spot splittings". The apparent spot splitting is an intensity effect: only a few of many spots are intense enough to be visible. LEEDpat will simulate such a pattern, but will treat all spots as being of equal intensity, thus not giving the appearance of "split spots". The program SARCH, available at http://www.fhi-berlin.mpg.de/KHsoftware/SLP/, does include kinematic LEED intensities and can be used to simulate this "spot splitting" effect, see above.


Despite these limitations, LEEDpat can simulate a large fraction of observed patterns, and thus should be useful in most cases.