Crystallographic image processing (CIP) is a technique first used to aid in the structure determination of periodic organic complexes imaged with a high-resolution transmission electron microscope (TEM). The technique has subsequently been utilized for TEM images of inorganic crystals, scanning TEM images, and even scanning probe microscope (SPM) images of two-dimensional periodic arrays. We have written software specialized for use on such SPM images. A key step in the CIP process requires that an experimental image be classified as one of only 17 possible mathematical plane symmetry groups. The current methods used for making this symmetry determination are not entirely objective, and there is no generally accepted method for measuring or quantifying deviations from ideal symmetry. Here, we discuss the crystallographic symmetries present in real images and the general techniques of CIP, with emphasis on the current methods for symmetry determination in an experimental 2D periodic image. The geometric Akaike information criterion (AIC) is introduced as a viable statistical criterion for both quantifying deviations from ideal symmetry and determining which 2D Bravais lattice best fits the experimental data from an image being processed with CIP. By objectively determining the statistically favored 2D Bravais lattice, the determination of plane symmetry in the CIP procedure can be greatly improved. As examples, we examine scanning tunneling microscope images of 2D molecular arrays of the following compounds: cobalt phthalocyanine on Au (111) substrate; nominal cobalt phthalocyanine on Ag (111); tetraphenoxyphthalocyanine on highly oriented pyrolitic graphite; hexaazatriphenylene-hexacarbonitrile on Ag (111). We show that the geometric AIC procedure can unambiguously determine which 2D Bravais lattice fits the experimental data for a variety of different lattice types. In some cases, the geometric AIC procedure can be used to determine which plane symmetry group best fits the experimental data, when traditional CIP methods fail to do so.
| Identifer | oai:union.ndltd.org:pdx.edu/oai:pdxscholar.library.pdx.edu:open_access_etds-2114 |
| Date | 02 July 2013 |
| Creators | Bilyeu, Taylor Thomas |
| Publisher | PDXScholar |
| Source Sets | Portland State University |
| Detected Language | English |
| Type | text |
| Format | application/pdf |
| Source | Dissertations and Theses |
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