Views from aSmall: Specimen #1

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 31 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.

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. Is the surface topography self-similar on some or all size scales? On what size scales does the roughness appear to associated with bumps, scratches, pits, random 1/f topography, or 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 clusters? Are the atom colors coordinated with possible atom, or different unit cell, types? What features make the various cluster types preferable, for those atoms which adopt them? Capture an image of each of the metal atom arrays viewed down a three-fold symmetric projection. How many three-fold directions does each of these arrays have? Five-fold? Four-fold? Can you name the polyhedron associated with each of these nearest neighbor cluster types? How might you describe the structure and crystallographic orientation of atoms which make up the specimen disc itself, in the sections where they are visible. Does this structure suggest values for the atomic number of these atoms (and hence the chemical composition of this part of the specimen)? If these are typical interatom spacings, how many atoms are contained in the specimen as a whole? What is the largest projected spacing between rows of atoms visible in these disc atoms? What lattice direction allows one to view two of these wide spacings at once? How many such lattice directions are there? If the term "dimer row" is familiar to you, can you tell which direction the dimer rows are running on the flat (non-dimpled) underside of this region of the disc? Can you explain how changes in this direction are often associated with surface steps, easily seen by scanning probe microscopes, which are less than an inter-atom spacing in height?

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?

This is one of several web-based "active mnemonics", designed: (i) to offer complementary perspectives and resources for achieving present day teaching goals among students with a wide range of learning styles; (ii) to do this in the context of emergent topics in modern day science (e.g. nanoscale exploration, information physics, allpaths/action/aging and metric-based anyspeed dynamics), many of which have only begun to work their way into textbooks and curriculum goals; and (iii) to be reliably available for use by individual teachers in class and by students out of class. Nanoworld exploration is especially interesting in this regard since it can offer an open-ended challenge to one's skills at empirical observation and reporting, allowing students to "participate in scientific investigations based on real-life questions that progressively approximate good science". This is, for example, a primary goal of the K-12 Show-Me Standards on scientific inquiry, the basis for Missouri Assessment Program tests. Most classroom challenges instead focus on factual knowledge and skills at theoretical prediction, perhaps since robust empirical challenges have been more difficult to set up.

• The generic storyline for probing student skills and biases for empirical observation might go something like this: "Someone has just prepared a specimen for a closer look in your web microscope. You see it spinning in front of the robot's image when you move your mouse over the picture containing it. By dragging your mouse with a button down, you can rotate or even spin the specimen. By dragging the mouse vertically with the shift key pressed you can move in toward the rotation center for a closer look. Check out the specimen, and report back on what you are able to find out." This of course will not be specific enough for most students, or in fact most teachers. By that same token, with added specifics it might prove useful for students at various levels in topic areas ranging from materials microscopy to gestalt psychology. Revisiting the same model, with a new assignment in a different class, would also reinforce students' corollary awareness of the challenges faced in doing detective work at the nanoscale.
• Thermal physics and uncertainty: Fleas on fleas on fleas... (e.g. in a general studies course on the physical principles underlying "how things work"): "In this exercise at empirical discovery, you will be assessed on your ability to describe what you found and did not find, as well as on the quality of the data you managed to come back with. Basically, so far in this course we've talked of baseballs and tables and other macroscopic objects as just that: Individual objects. In fact, they are composed of tiny building blocks. A key parameter in thermal physics (e.g. the way temperature works) turns out to be uncertainty about the microscopic state of those building blocks. Since detective work on these nanoscales is increasingly important in fields ranging from engineering to medicine, this exercise gives you a feel for detective work on the state of atoms making up a small 3mm disk." Assignment: "Zoom in and around on the tiny disk that you'll find in this web microscope. Feel free to assume the disk diameter is 3mm, and to use the superposed grid to help estimate sizes of smaller things. The field-width estimator can also be used, although this might add additional uncertainty to your measurement. Then do the best you can to determine the spacing between gray atoms in the specimen's disk, a few of which are visible if you zoom in enough to see them. In the panel below then report: (i) your measured value, (ii) an estimate of your uncertainty in your measured value, and (iii) a description of the method you used to come up with it."
• Measuring Size Scales and Densities: Powers of 10... (e.g. as supplement to the opening "measurement" chapter of a standard introductory physics textbook): "Zoom down for a closer look at this 3mm diameter web specimen, to see if you can determine the distance between atoms in it, and/or the number of atoms it contains per cubic centimeter." You might be inclined to let them determine spacings on the superposed grids on their own. Alternatively, you might tell them to assume that the level 2 grid squares are about a micron across, and the level 5 squares about a nanometer across. Advantages to this exercise: It is an experimental challenge (something students often don't get outside of a lab), it offers a visceral feel for the large number of intervening worlds between that of humans and that of atoms, and it facilitates self-discovery about the nature of these concepts in a cutting-edge but practical setting frequented by today's nanoscale explorer.

• How do I measure distances? You can assume that the diameter of the disc is 3mm, and extrapolate all other dimensions from that. The superposed grid lines may be of qualitative, and in some cases quantitative, help. Serious detectives might also try to propagate uncertainties through the extrapolation as well. On the other hand, your teacher may tell you to start with different assumptions, e.g. the distance between atoms in a certain object. The "Estimate Field Width" button may also come in handy, although you might want to avoid taking the manufacturer's estimate blindly at face value. Quantitative comparisons are probably best done between objects whose distance from your vantage point is the same, and thus to set up may require some rotation and zooming on your part.
• How do I measure angles? In some cases the superposed grid lines, or other aspects of the geometry of objects, can be used to determine angles. Another trick for angles at the rotation point might be to note that you can spin an object at a constant rate of speed. If the spin takes you through the two directions of interest, the angle between them is simply 360 degrees multiplied by the time_between_directions divided by the rotation_period. Given that the beta applet also allows you to move the rotation center, in principle any two angles can be measured with arbitrary precision (e.g. using slower rotations) by this means. Lastly, the viewing direction is also roughly specified by values accessible from the Tilt and Rotation angle buttons. For those who enjoy spherical trigonometry, the angle between two different viewing angles (e.g. T1,R1 and T2,R2) is ArcCos[Cos[T1]Cos[T2]+Sin[T1]Sin[T2]Cos[R2-R1]].
• How do I record observations for later analysis, and reports? Although movies of what you see may be difficult to record, still photos of what you see on the screen should be possible to print out using File/Print (some browsers will let you select and print only the applet window), or capture as digital images using any of a number of screen capture utilities (e.g. Paint Shop Pro under Windows) or even with a camera. When saving an image, it's good practice to save relevant data (like field width at the rotation center) along with it. For example, you might append "w6p67n" to the filename of the image if the field width is 6.67 nanometers. When recording images on film, microscopists generally record useful information (along with the number of each negative) in a logbook. This is also recommended here, since not all information corollary to an image can be recorded in its filename. Note: Unlike magnification, field width and scale bar labels are not changed when the image is portrayed on larger or smaller screens. They also allow one to easily determine magnification e.g. by dividing field width into the width of the viewed image.

• Nano-exercise for Intro Chemistry in Spring 2005.
• A sample nanoWorld webQuest rubric for self or peer review, and evaluation.
• Our first link page on variable size-scale adventures.
• More on research highlights and developing stories in our lab.
• Noom's notes on SPM and webQuest interfaces to this model.
• Notes on a modular web/lab course for future users of nanomicroscopy data.
• Our Adobe Atmosphere anyspeed motion and web-lab simulators.
• Our ancient HTML-based microscope focus and astigmatism simulator.

• Push buttons to estimate the field width (now available), goniometer angles, and working distance.
• A couple of adenovirus particles and perhaps some other stray molecules, hidden elsewhere on the specimen.
• Ability to translate the rotation center in 3D, if desired with a dynamically-regenerated grid overlay and specimen to facilitate navigation plus offer non-trivial atom-scale detail throughout the specimen. This may seem like a modest task until one realizes that this specimen contains something akin to 10^20 atoms, i.e. around 10^12 gigabytes of information encoded in atom positions alone.
• Ability to 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.

Live3D applet

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