jMol
series:
Easier? unknown #2
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.
Hit reload to view the tilt sequence again, or
simply use the mouse to orient the specimen at will.
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.