Views from aSmall: Specimen #1

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Below find an interactive model representing a transmission electron microscope specimen similar in size to the grid shown on the right, next to an ordinary staple. The model is of a rigid self-supporting specimen like that sometimes used for the study of semiconductors and layered metal/ceramic devices, nominally prepared by cutting a 3-mm diameter disc, thinning via abrasion to 100 micron thickness, dimpling from one side with a specialized milling machine, and then perforation by argon ion milling. Using your mouse, you can rotate, spin, as well as zoom around on (or even inside) the structure. The 32 sections of the specimen nearest the perforation in the center taper down to zero thickness. These are the regions which are most interesting for transmission electron microscopy. We have plans to allow you to explore this specimen on the micron, nanometer, and even atomic scales in the days ahead, as well as to taylor stories for the use of such models in classrooms from kindergarten through grad school. One objective is to provide visitors with a visceral feel for scale changes that the nano-explorer experiences, in the process of "getting small".

How astute are your observational skills? What information would you bring back from a fantastic voyage into the nanoworld? Don't mind the robot in the background. If you look carefully, you may already be able to find a bit of pollen, a few red blood cells, a couple of tobacco mosaic virus particles, a carbon nanotube, and even a buckyball with a few metal atoms hanging around. Of course, unfamiliar contrast mechanisms are needed to observe objects smaller than the wavelength of light, so be prepared for a few surprises.
Note: The mouse allows you to re-orient and or spin the specimen, while the Shift key plus vertical mouse motion allows zooming in on the model for a closer look. Hitting the Home key allows you to return to the original point of view. If this version bogs down on zooming (e.g. with an older PC), try a 400x400 or 200x200 window. Try this model for less surface topography, and this model if you wish to rotate "the camera" rather than the specimen. If you want electron clouds instead of atomic nuclei, try the beta version.

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. Do possible causes for these features come to mind? 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, 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, 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: Suggestions invited.
Frequently Asked Questions: Suggestions invited.
Local links:
Future objectives include abilities to:
This page is 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. Yet. Although there are many contributors, the person responsible for errors is P. Fraundorf. This site is hosted by the Department of Physics and Astronomy (and Center for Molecular Electronics) at UM-StL. The number of visits here since last reset on 23 Aug 2003 is .