title: Crystallography of ordered colloids using optical microscopy. 2. Divergent-beam technique.
abstract: A technique has been developed to extract quantitative crystallographic data from randomly oriented colloidal crystals using a divergent-beam approach. This technique was tested on a series of diverse experimental images of colloidal crystals formed from monodisperse suspensions of sterically stabilized poly-(methyl methacrylate) spheres suspended in organic index-matching solvents. Complete sets of reciprocal lattice basis vectors were extracted in all but one case. When data extraction was successful, results appeared to be accurate to about 1% for lattice parameters and to within approximately 2 degrees for orientation. This approach is easier to implement than a previously developed parallel-beam approach with the drawback that the divergent-beam approach is not as robust in certain situations with random hexagonal close-packed crystals. The two techniques are therefore complimentary to each other, and between them it should be possible to extract quantitative crystallographic data with a conventional optical microscope from any closely index-matched colloidal crystal whose lattice parameters are compatible with visible wavelengths.
authors.affiliation: Department of Materials Science and Engineering, Case Western Reserve University, 10900 Euclid Avenue, Cleveland, Ohio 44106, USA. richard.b.rogers@nasa.gov
authors.forename: Richard B
authors.initials: RB
authors.lastname: Rogers
authors.forename: K Peter D
authors.initials: KP
authors.lastname: Lagerlöf
mesh_terms: D000465:Algorithms; D003102:Colloids / Q000737:chemistry*; D003461:Crystallography / Q000379:methods*; D007090:Image Interpretation, Computer-Assisted / Q000379:methods*; D008853:Microscopy / Q000379:methods*; D008968:Molecular Conformation; D055095:Optics and Photonics; D012031:Refractometry / Q000379:methods*
chemical_list: D003102:Colloids