Here we've eliminated some of the introductory material on our general goniometer page, as the focus here is on indexing two experimental diffraction and/or power-spectrum spots, and their interspot angle, against one or more candidate crystal structures.

The basic strategy is to move past the 3D-goniometer window below (which will soon show a "nano-sized" version of your lattice). Instead you may type the lattice parameters into the boxes at top of the crystal structure & orientation worksheet, leaving space group # set to zero so that centering disallowances are ignored. Then hit the "upload to goniometer" button.

The next step is to hit the update button associated with the Table 1 section down a bit
further on the page. **Just above that update button you will now find buttons which will
load in specific candidate phases from scratch.** In some cases, these buttons will set up
consideration of cell-centering disallowances as well. Either of these actions should fill
Table 1 with a set of 3D coordinates for g-vectors to compare with your measured data.

Note that only select spacegroup numbers are currently supported. In particular, we're using fcc space-group #225 for SiC even though it should be #216 since centering-extinctions should be the same, and the only hexagonal space groups already programmed in are #194 (hcp) and #186 (graphite). We do not yet address centering disallowances for hexagonal lattice structures WC (#187), ZrB2 (#191), B4C (#166), B2O3 (#144). Likewise for tetragonal ZrO2 (#137). This means that proposed indexings for these will still have to be checked against possible centering-disallowances, although NO will still mean NO.

Just below Table 1 you may then type in any two measured spacings and their interspot angle, as well as what you believe are your uncertainties in spacings and angles. Hitting the button to index should let you know if that structure might explain your spots.

Uses lattice parameters and atom positions within each unit cell.

Groups reflections onto one entry when spacings and structure factors are similar, so that the entry's Miller index may or may not be representative.

Note that intensities are only qualitatively relative and without scattering-angle falloff, and that extinction distances are not yet estimated at all.

Only about 20 entries from the Miller index range between -6 and 6.

What follows is a list of practical analytical tasks, addressable with these developing tools, that we plan to illustrate with lattice images and/or diffraction data from past and ongoing nanodetective challenges.

Real soon now...

* Note that [uvw] is normally used to denote a
*specific* (contravariant) lattice vector or crystallographic zone-axis,
<uvw> a *class* of such directions
or zones, (hkl) is the Miller index of a *specific* reciprocal-lattice
point, covariant "g-vector", or set of crystallographic planes,
and {hkl} denotes a *class* of
symmetrically equivalent reciprocal-lattice points.

What's next here? More
input/output and calculation options, illustrations,
class exercises, puzzlers, data, and theory.
We just added an *ActiveWidgets* spreadsheet
to list g-vectors from a specific crystal.
Only a few space-groups and simple crystal
sizes/shapes are available now, but this will
expand in days ahead, likely to include
special structures like n-wall nanotubes
and quasicrystal approximates, as well as
arbitrary (even aperiodic) lists of atom positions. Tools
(like SXTL)
to match and index observed spacings and interfringe/spot
angles may be next, along with buttons to record
single-crystal/powder diffraction patterns and
lattice images in 2D for closer examination.
Eventually, we hope to offer, for example, independent variation of cluster
size and shape, centering and extinction information
lookup from any spacegroup (look for A, B and C centering
soon, as it makes the single crystal indexing routine useful
for any structure), Wycoff-format atom-coordinate
entry tools,
fringe-visibility
maps, fringe probability/thickness plots, Kikuchi
maps and other stereo-projections,
strong-phase-object
through-focus series,
Cliff-Lorimer prediction of characteristic X-ray peak
heights from elemental ratios and vice-versa,
Debye-scattering
profiles, formatted
spiral
powder overlays, some simple plasmon/dielectric and
characteristic-edge energy calculations, select defect models including
SPM topography and surface reconstruction predictions, and
possibly even
digital-darkfield
analysis of images.

More importantly, tools for fitting
*data you've
taken* to specific candidate phases, and in some cases
to directly-determined structural models, are
planned as well. This experimental data might include
observed fringe and diffraction spot spacings/angles taken
at one or more specimen orientations,
azimuthally-averaged diffraction/power-spectrum profiles,
and eventually selected analyses of direct-space
images. Data on widely-interesting phases will be
programmed in locally, but we are also in discussion
with developers and patent holders of searchable
databases to facilitate more systematic comparison
of data to known structures downstream.

On the nanoeducation side, empirical observation exercises with in-class peer-review are already under development here for a range of introductory science classes. The nano-goniometer above, when viewed from the side in "dual space" mode already offers an excellent interactive illustration of Ewald-sphere mediated diffraction. With sufficient refinement it is hoped that empirical-observation exercises like this, patterned on evolving real-world challenges, can work their way into classrooms, onto timed tests, and perhaps (if sufficiently robust) even into the larger culture of social competition and educational video-gaming. This page also provides possibilities to this end. For example, all crystals in the goniometer so far are in "c-axis" orientation, but a set of adjustable Euler angles will be added in days ahead to allow creation of "true unknowns" for analysis. What better challenge for prospective nano-detectives than to be given a device capable of performing quantitative experiments (of their choosing) on an unknown, and then showing how they can make the most of it?

As far as implementation is
concerned, look for other applets
(e.g. *webMathematica*, *Jmol*, and *JavaView*)
to be put to use in the days ahead as well, and perhaps even a
more interesting "room" in which to put the nanogoniometer. In all
cases, we hope to make these tools available reliably and seamlessly
(free where possible without the download of plugins) for use
at many application levels, across
the planet, in years ahead.

- Our lattice fringe practicals page.
- Notes on the shadowy reciprocal lattice, and molecule spatial harmonics.
- Sample data from UM-StL Scanned Tip and Electron Image Lab outreach.
- Other Live3D and Jmol models.
- Other nano-microscopy web resources.
- Our powers of ten explorer.
- A 2005 intro-chem nanoquest.

This page is
http://www.umsl.edu/~fraundor/nanowrld/newlive/crystal9.html.
Acknowledgement
is due particularly to Peter Möck at Portland State University for
his energy in exploring these matters, and
Martin Kraus
for his robust
Live3D
applet. Thanks also to Noom Pongkrapan for the
nano-goniometer border. Although there are many
contributors, the person responsible for errors is P. Fraundorf.
There are likely to be many.
Reports about bugs, ways to correct them, algorithms that might be
fun to implement, and interest/energy/time in helping out,
are most welcome via e-mail to "`staff`

" at
newton.umsl.edu.
Putting "`nanocluster`

" in the subject line might improve its
chances of getting through.
This site is hosted by the *Department of Physics
and Astronomy* at UM-StL.
MindQuilts
site page requests ~2000/day approaching a million per year.
Requests for
a "stat-counter linked subset of pages" since 4/7/2005:
.