lattice fringe visibility
Lattice fringe-visibility models, which can be shown for a given specimen thickness as interactive 3D models like the sapphire Kikuchi map above right, might help you to:
determine the 3D lattice of a single particle given lattice images at two or more tilts,
measure the thickness of a specimen given images over a small range of tilts,
statistically distinguish between epitaxial, columnar & randomly-oriented particle assemblies e.g. on nanotube surfaces,
statistically identify icosahedral twinning in a population of randomly-oriented nano-particles,
estimate fraction-crystalline given a population of randomly-oriented particles in an amorphous matrix,
and what else?
Some related references:
P. Fraundorf (1987) " Determining the 3D lattice parameters of nanometer-sized single crystals from images" Ultramicroscopy 22:225.
Wentao Qin and P. Fraundorf (2003) "Lattice parameters from direct-space images at two tilts", Ultramicroscopy 94:3-4, 246-262 pdf.
P. Fraundorf, Wentao Qin, P. Moeck and Eric Mandell (2005) "Making sense of nanocrystal lattice fringes", Journal of Applied Physics 98:114308 pdf.
W. Qin and P. Fraundorf (2005) "Cross-fringe versus single-fringe probabilities" Microscopy & Microanalysis 11:S2, pp. 1960-1961 pdf.
Eric Mandell, P. Fraundorf, and W. Qin (2005) "Measuring local thickness through small-tilt fringe visibility" Microscopy & Microanalysis 11:S2, pp. 562-563 pdf.
P. Wang, A. L. Bleloch, U. Falke and P. J. Goodhew (2006) "Geometric aspects of lattice contrast visibility in nanocrystalline materials using HAADF STEM", Ultramicroscopy 106:277-283.
Jinfeng Wang, P. Fraundorf and Yangchuan Xing (2006) "Lattice fringe signatures of epitaxy on nanotubes", arXiv:cond-mat/0603312.
Jinfeng Wang and P. Fraundorf (2006) "Lattice fringe signatures of epitaxy on nanotubes", Microscopy and Microanalysis, 12:Supplement 2, 664-665 pdf.
cf. P. Moeck and P. Fraundorf (2007) "Structural fingerprinting in the transmission electron microscope: Overview and opportunities to implement enhanced strategies for nanocrystal identification", Zeitschrift fuer Kristallographie 222, 634-645.
Mukherjee S, Ramalingam B, Griggs L, Hamm S, Baker GA, Fraundorf P, Sengupta S, Gangopadhyay S. (2012) "Ultrafine sputter-deposited Pt nanoparticles for triiodide reduction in dye-sensitized solar cells: impact of nanoparticle size, crystallinity and surface coverage on catalytic activity", Nanotechnology 23(48):485405.
Shane Meyer and P. Fraundorf (2013) "Geometry versus paint models of FCC lattice-fringe visibility", Microscopy and MicroAnalysis19:s2, 804-805 pdf.
P. Fraundorf and Somik Mukherjee (2013) "Lattice-image estimates of nano-particle fraction crystalline", Microscopy and MicroAnalysis 19:s2, 1590-1591pdf.
P. Fraundorf and Chris Bishop (2013) "Efficient lattice-image detection of icosahedral twins", Microscopy and MicroAnalysis 19:s2, 1804-1805 pdf.
Although more than one contrast mechanism can create them, lattice fringes are often made visible by electron-phase-contrast in a conventional high resolution electron microscope (HRTEM). This type of contrast maps high-energy electron deBroglie phase shifts at the exit surface of the specimen by recording intensity variations that result from wave interference downstream of the specimen e.g. at "Scherzer defocus". The phenomenon is made even more remarkable since beam currents are so low that to pull this off individual electrons must interfere with themselves.
As the availability and quality of lattice-imaging by both electron-phase-contrast and scanning-transmission microscopy increases, understanding the effect of specimen orientation, specimen thickness, and diffuse scattering from a disordered matrix, on the visibility of these fringes will become increasing important. Work on quantifying these effects, and applying to a variety of problems, are the subject of this page.
