Lattice-fringe practicals

You encounter an electron microscope image with lattice information in it. How do you make the most of the data in the image? In the years ahead this question will occur to an increasing number of people, in an increasing number of application areas. On this page we break down some of your options, and collect a few resources that you can put to work as well.

The first question may be, what tools do you need? Much of our work is on digitized images, although a lot can be done with image prints or negatives using only a ruler and protractor. Some of the tools we use in our lab are listed in the table below. Our web-based nano-goniometry lab is a developing resource for getting and analyzing data from nano-sized specimens, which connects to resources described here in a complementary way. We are also developing a set of ImageJ plugins for periodicity mapping, strain analysis, roughness spectroscopy, and more. Others from the set below of most useful resources are also available for nominal cost, or free, over the web.

Note: A database of crystal structure information is also of great help. Examples include: MinCryst, AMCSD, CLS, COD, rNet, IUCr, ICDD/JCPDS, and ICSD, which uses this web program" to visualize crystal models. For notes on quantitative analysis of fibers, and other standard strategies for quantifying observations, the CDC's National Institute of Occupational Safety and Health's (NIOSH) Manual of Analytical Methods can provide useful insight. For notes on light microscopy and forensic applications, the McCrone Group is an interesting place to look. Also check out the International Union of Crystallography Teaching Resources. Note that [uvw] is normally used to denote a specific lattice direction or crystallographic zone axis, <uvw> a class of such directions or zones, (hkl) is the Miller index of a specific reciprocal lattice point, "g-vector", or set of crystallographic planes, and {hkl} denotes a class of symmetrically equivalent reciprocal-lattice points. Some interesting space group notes are here, here, here, here, here and here. An even wider collection of crystallography related programs may be found in Collaborative Compututational Project #14.

Spacings only (powder data)

A common goal here (but not the only one) is to come up with a profile of intensity as a function of spatial frequency or scattering angle, and then to infer from it the nature of the structures involved. The data in this case might be an azimuthally-averaged electron diffraction pattern, a histogram of spacings measured on individual-crystal power spectra in a nanoparticle specimen, or the azimuthally-averaged radial profile from the power-spectrum of a HR-TEM image containing a large number of nanocrystals.

Related links:

• Our spiral overlay paper for Microscopy Today.
• Nathan's reports on analysis of diffraction from unlayered graphene in AGB starsmoke.
• The Debye scattering equation listed here.
• Powder patterns from lattice images for Microscopy & Microanalysis 2005.

Lattice spacings & angles from one negative (2D single crystal data)

A wide range of questions can be asked here, generally starting with "What is the crystallographic phase that I'm looking at, and how can I index the spacings in the image". Beyond this, questions include e.g. what the lattice parameter, the crystal shape, and/or the relationship between adjacent crystals has to say. We plan to walk you through some examples here shortly.

Related links:

• Our interactive visiblity map collection.
• Recent work on making sense of lattice fringes.
• Notes on the use of digital darkfield decompositions
• Fringe covariance "fingerprinting" [poster] for Microscopy and Microanalysis 2005
• Digital darkfield decompositions: Manfred Rühle Interfaces Symposium [slides]

Multi-tilt spacings & angles (3D single crystal data)

This is a very powerful strategy for identifying unknowns, and if necessary determining a nano-crystal's lattice parameters in three dimensions from scratch. More soon...

Related links:

• Wentao's paper on lattice parameters from two tilts.
• Those early "diffraction stereo analysis" papers.