[Background] [Live3D] [Puzzlers] [Storylines] [FAQ] [Links] [Downstream] [Acknowledgements]

Put on your Sherlock Holmes hat, and ask...

*Puzzler #1*: If the diameter of the disk is 3mm, what is
it's **thickness at the outer edge?** What is the
**diameter of the perforation?**

*Puzzler #2*: This is tougher: Estimate the
**radius of the spherical dimple** on one side of
the disk, as well as the **distance the dimpling
wheel protruded through the perforation** at the
end of the dimpling process. *Note*: One usually
stops dimpling before perforation, and perforates
by a gentler method e.g. argon ion milling, but
assume here (to be specific about geometry)
that the perforation was created by the spherical
dimple itself.

*Puzzler #3*: Perhaps equally tough, but
of more direct relevance to the microscopist:
Estimate the **wedge-angle between intersecting
specimen surfaces** at the perforation, and the
**length of perimeter** associated with each of the
32 sections which border the perforation.

*Puzzler #4*: Another practical
question for the microscopist: How
many **square microns of specimen**, whose thickness
is less than 0.5 microns, will the
microscopist find? If the objects of interest
occur 10^6 times per square centimeter of specimen,
**how many objects are you therefore likely to find** in
such thin areas of this specimen?

*Puzzler #5*: If the defects are
"bulk defects" much less than a micron in size,
the amount of "volume" of your specimen which
is thin becomes the important parameter.
How much **volume of this specimen (in
cubic microns)** is associated with parts
of this specimen which are less than 0.5
microns in thickness? If there are 10^10
of the interesting objects per cubic
centimeter, **how many would you expect to
find** in a survey of all such thin area
in this specimen.

*Puzzler #6*: What is the **spacing
between squares of the smaller "secondary grid"** that
you'll find somewhere near the edge of the perforation?
*Hint*: The distance is larger than the
wavelength of visible light, and perhaps 6 times
the feature width used in modern gigascale integrated
circuits.

*Puzzler #7*: As you zoom in, you may notice
a hierarchy of three more even smaller (e.g. call them
third, fourth, and fifth-level) grids at the
perforation's edge. These third, fourth, and fifth
level grids are not typically resolvable by light
microscopes, and hence constitute the primary domains
of electron and scanning probe microscopy. Most
scanning electron microscopes today can pick up
periodicities as small as those in the fourth-level
grid. Scanning tunneling and atomic force microscopes
(which mechanically scan a tip over the specimen)
under suitable conditions can pick up details smaller
than the fifth-level grid, as can conventional
transmission electron microscopes. **How many such
fifth-level grid squares would be needed to outline
the whole perimeter** of the perforation?
*Note*: Since mechanical
(scanning probe) microscopes use tips which are made
of atoms, sub-atomic lateral resolution is
difficult even though they can easily do sub-atomic
height profiling, but for decades transmission electron
microscopes have fallen into two categories:
the handful of atomic resolution scopes that can barely resolve
details smaller than the 2 Angstroms separation between
most atoms, and conventional scopes that cannot. This
is about to change with new aberration-correction
techniques, which will eventually allow us to see atomic
nuclei as little "points of light" in images, and force
us to add a sixth grid-level to illustrate their mapping
capabilities.

*Puzzler #8*: Note that the "shoreline"
around the perforation is irregular. Can you
tell us anything about **the frequency spectrum of
deviations from circularity**, either with a seat
of the pants estimate, or via quantitative
analysis? Does the character of these
deviations change as one goes to smaller and
smaller sizes, or **does the edge profile in
this specimen show signs of self-similarity?**

*Puzzler #9*: Note that the dimpled
side of the specimen shows more roughness than
the non-dimpled side. On what size scales **does
this roughness appear to caused by bumps, by
scratches, by pits, by random 1/f topography, or
by something else**? If you see bumps, what distribution
of widths and heights do they have, and how many per
square centimeter do your observations suggest are
present? Likewise for pits or scratches.
Can you put limits on the amount of root-mean-square
roughness per decade
of lateral frequency, on either side, between
one cycle per millimeter and one cycle per micron?
How about between one cycle per micron and
one cycle per nanometer?

*Puzzler #10*: Make note of the sizes
and shapes of the objects you find. For example,
**what are the dimensions of
the pollen particle, the red blood cells, the
tobacco mosaic virus particles, the nanotube,
and the buckyball**. Do the two tobacco mosaic
virus rods have the expected cross-sectional
shape? How many walls does the multi-walled
nanotube show? Is the
single-walled part of that nanotube of the
armchair, zig-zag, or chiral variety? Is there
anything which is atypical about it?
How many pentagons can be found on the surface
of the buckyball?

*Puzzler #11*: What are the distances between metal atoms in
those nearby arrays? Are the atom colors coordinated
with possible atom types? What is the largest
projected spacing between rows of atoms visible
in the arrays? What lattice direction allows
one to view two of these wide spacings at once?
How many such lattice directions are there?
**Capture a picture of the metal atom arrays viewed
down a three-fold symmetric projection.**

*Puzzler #12*: If the model had a moveable rotation
center randomly located, **could you find your way back to the
buckyball** on a second visit? How might you describe it's
location in terms of the superposed grid hierarchy? For example,
might one say it's located in perimeter cell 14.9.3.4.9, or
something similar, where perimeter-cell numbering starts
from that part of the perimeter nearest the pollen grain?
If the grid lines weren't drawn on the specimen, what landmarks and
facts about the grid hierarchy might you note so that (if need
be) you could redraw the gridlines yourself on images from
the next visit? Also, can you determine the number of buckyballs
in perimeter-cell 1.1.1.1.1, without moving the rotation center?

*Future Puzzlers*: Is there **anything yet to notice
about interfaces, or about point, line and extended
lattice defects?** How would you recognize an
extrinsic stacking fault in this model? How would you determine
a dislocation's Burger's vector? How would you measure
strain?

Storylines for Classroom Use:

Frequently Asked Questions:

Local links:

- Our first link page on variable size-scale adventures.
- More on research highlights and developing stories in our lab.
- Noom's notes on SPM
- For more scientific 3D
*in developmental stages*, check out our Adobe Atmosphere anyspeed motion and web-lab simulators.

Future objectives include abilities to:

- translate the rotation center in 3D, via the keyboard, where necessary with a dynamically-regenerated grid overlay to facilitate navigation, and to offer non-trivial atom-scale detail throughout the specimen.
- pass observation parameters back into a calculation engine that can provide the explorer with HREM images, diffraction patterns, X-ray or roughness spectra, etc. of the field of view.

This page is http://www.umsl.edu/~fraundor/nanowrld/dtemspec.html. Acknowledgement is due particularly to Martin Kraus for his robust Live3D applet. A background image from the Takanishi Lab webpage on robot expressions has been put up temporarily because we don't have a "first specimen" background showing curious students looking at an object in the lab.