MSE 421/521 Structural Characterization
MSE 421/521
Spring 2016
Dr. Rick Ubic
Homework assignment 3
Due 14 March 2016
1. Why is the resolution attainable in the electron microscope so much better than that
of the optical microscope?
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2. Calculate the position of the image and its magnification when an object is held 10 cm
from a convex lens of focal length 8 cm.
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3. At room temperature TlCl has a cubic CsCl structure with a = 3.8421 Å. What is the
maximum observable limit of h in {h00} assuming a maximum diffraction angle (2θ)
of 4° in a TEM operating at 200 kV?
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MSE 421/521 Structural Characterization
4. In a light microscope, an object is placed 2 mm away from a lens of diameter 2 mm.
The object is in air (µ = 1) and the wavelength of the (green) light is 520 nm. What is
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the best possible lateral resolution of this microscope?
5. The Rayleigh resolution criterion assumes two point sources of light and implies
unlimited contrast in the image. What factors are likely to prevent the attainment of
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the Rayleigh resolution in reality?
MSE 421/521 Structural Characterization
6. Calculate the semi-angle of acceptance and depth of field for a resolving power of
1 µm in a microscope with a final aperture of diameter 1 mm and a working distance
of u = 1.6 mm. What is the depth of focus at a magnification of 100x?
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MSE 421/521 Structural Characterization
7. Deduce the approximate value of Cs for (a) an electron microscope capable of 0.1 nm
resolution at 100 kV (λ = 0.003701 nm) and (b) a light microscope capable of 0.5 µm
resolution for green light (λ = 500 nm).
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8. The better resolution obtained with a high-numerical-aperture objective is
accompanied by reduced contrast and depth of field. Why?
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MSE 421/521 Structural Characterization
9. Complete the indexing of the diffraction pattern below from a bcc crystal and
determine the zone axis direction.
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224
1 03
2 33
1 12
242
1 21 1 30
000
130
12 1 1 1 2
24 2
23 3
10 3
22 4
10. (a) Complete the indexing of the following diffraction pattern from rock-salt and
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determine the zone-axis direction.
(b) What is the reason for the different spot intensities?
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242 3 3 1
000
22 2
3 3 1 242
MSE 421/521 Structural Characterization
11. Index the diffraction patterns below which were obtained from either Al (fcc, a = 4.05 Å)
or Fe (bcc, a = 2.87 Å). Label at least three non-co-linear spots in each pattern and
calculate the zone axis in each case.
You may find a tool like dSpace
(http://coen.boisestate.edu/rickubic/files/2012/05/dSpace.exe) useful in checking
interplanar spacings and angles.
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HINT: Make a table of the interplanar spacings of the first several allowed reflections
in each case (each cell in the table should contain the ratio of the spacing at the top
of its column to the spacing labelling its row), then find matches for the ratios of
spacings found in the SADPs. See slide set 13.
MSE 421/521 Structural Characterization
BONUS
12. Are short-sighted individuals blessed with "better" resolution than those with
otherwise “healthy” eyes?
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