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.

Input Data\Format | From diffraction patterns | From lattice images | Data modeling tools |

Spacings only (powder data) | ImageJ, eDPcalc, Photoshop, Russ Family Plugins, JASC's PaintShopPro, Synoptics' Semper, Mathematica | ImageJ, LFPcalc, Photoshop, Reindeer Graphics' Plugins, PaintShopPro, Semper, Mathematica | Wycoff, Cell, Lattice, Molecule, qPowder, JCPDS Card Files, Debye Scattering Equation, Mathematica |

Lattice spacings & angles from one negative (2D single crystal data) | Sxtl, ImageJ, eDPcalc, Photoshop, Reindeer Graphics' Plugins, PaintShopPro, Semper, Mathematica | Sxtl, ImageJ, LFPcalc, Photoshop, Reindeer Graphics' Plugins, PaintShopPro, Semper, Mathematica | Wycoff, Cell, Lattice, Molecule, Jmol, Mathematica, and LiveGraphics3D |

Multi-tilt spacings & angles (3D single crystal data) | Sxtl, ImageJ, eDPcalc, Photoshop, Reindeer Graphics' Plugins, PaintShopPro, Semper, Mathematica | Sxtl, ImageJ, LFPcalc, Photoshop, Reindeer Graphics' Plugins, PaintShopPro, Semper, Mathematica | Wycoff, Cell, Lattice, Molecule, Jmol, Mathematica and LiveGraphics3D |

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.

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.

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]

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.