jMol series: Easier? unknown #3

Evaluating data from tools which extend our senses to the nano-scale is going to be increasingly important in a wide range of technical fields in the days ahead. These fields include product support of all sorts, clinical medicine, and crime scene investigation as well as the traditional but growing application areas of materials and biological science, metallurgy, catalyst design/application, geology, and the laboratory study of extraterrestrial materials.

When someone tells a good microscopist (or a good crime scene investigator) what might be present in a specimen, they will try to determine what is actually going on for themselves. With aberration-corrected electron microscopes of the future, one will be able to see nano-particle lattices almost as clearly as that seen in the model below. But even with such views of the specimen, combined with tools that allow quantitative measurement of angles and distances and atom-type in 3D (these are available here, and in development for real microscopes), the job of lattice determination is far from trivial!

In this exercise, you are encouraged to imagine, rotate, zoom, measure, analyze, and perhaps even do image capture and Fourier transforms, but in the end should address this question: How would you quantitatively describe the crystal lattice illustrated below? For example, what is the particle diameter and aspect ratio? (Hint: Double-clicking on two atoms in sequence will draw a scale-bar between them.) Is the lattice cubic, hexagonal, or something else? How about a set of approximate lattice parameters that describe its periodicity? What is its likely space group, and its "conventional" unit cell? Caution: The structure of this particular nano-particle may, or may not, have ever been previously imagined.

A curious detective could go further as well. For example, what is your favorite direction for viewing this particle? What atoms is the nanocrystal made up of? What's its stoichiometry? Approximately what is its density in grams per cubic centimeter (or in other words, will it float)? What kind of nearest neighbor environments do the carbon atoms experience? Is there any sign of faceting, or surface reconstruction? Any bulk defects, like dislocations or precipitates? Is this stuff a likely absorber of light in the visible or infrared? Will a single crystal of it be harder, or softer, than diamond?

Ok, so how does one figure all this stuff out from 3D sub-Angstrom resolution data on a single nano-crystal? Let's go through some of the questions:

• Particle dimensions: As mentioned above, double-clicking on two atoms in sequence draws a scalebar between them. Thus choosing atoms on opposite sides of the structure will give you an idea of the structure's width in the direction defined by the vector between those two atoms. The aspect ratio might be defined as the ratio between the longest such dimension, and the shortest.
• A unit cell: This is a bit trickier. One approach is to try looking for a three-dimensional "tile" inside the structure that repeats itself in all directions. This tile will have the form of a parallelepiped (six sides in parallel pairs). If you draw scale bars from a starting point along three non-parallel edges of this tile, they will tell you the lengths of a set of unit cell axes. These axis lengths are commonly called a, b and c. Double-clicking on the far end of axis a, single-clicking on the axes' origin, and then double-clicking on the far end of axis b will now label the angle between a and b (commonly called gamma). Similarly measuring alpha (the angle between b and c) and beta (the angle between c and a) will then give you the full set of lattice parameters {a, b, c, alpha, beta, gamma} for your unit cell.

• Primitivity: The good news is that the lattice is unambiguously described by your unit cell. The bad news, however, is that the unit cell you find by this method is not unique, and hence won't necessarily be the conventional one. The first thing to check: Is your unit cell primitive? It is primitive if it cannot be further subdivided into a set of identical but smaller unit cells. The Figure at right is that of a marked-up unit-cell which is not primitive, but has the advantage of a cubic symmetry. For now let's be content with finding the lattice parameters for a primitive unit-cell, conventional or not.
• Atom types: You can identify atom types by simply holding the mouse pointer over an atom for a while, until a label appears which tells the element abbreviation (sometimes with an atom index number as well).
• Stoichiometry: This gets tricky again. If you've previously labeled a unit cell, as described above, try counting the number of each type of atom inside it. Caution: Atoms on unit-cell faces each only contribute half an atom to the total, atoms on unit-cell edges only contribute one fourth of an atom to the total, and atoms on unit-cell corners only contribute one eighth of an atom to the total.