MSE 421/521 Structural Characterization
MSE 421/521
Spring 2016
Dr. Rick Ubic
Homework assignment 4
Due 13 April 2016
1. According to the Rayleigh criterion alone, how would the resolution in a TEM change
with accelerating voltage (neglect aberrations and assume a constant convergence
angle)?
10
Explain how the contrast (from both mass-thickness and diffraction effects) might be
expected to change with voltage using the same assumptions.
5
2. Consult the web page:
http://www.matter.org.uk/tem/lenses/beam_convergence.htm then
(a) list the following imaging conditions in order of increasing convergence angle: in
focus, underfocus, overfocus.
6
(b) calculate the maximum convergence angle (in degrees and mrad) for a system
with a condenser aperture of 50 µm and a C2 - specimen distance of 20 mm. 10
MSE 421/521 Structural Characterization
3. At a magnification of one million times, how large is the area of the specimen (in cm2)
which can be seen at one time on the 100mm x 100mm screen of the TEM?
5
4. It is required to examine a fractured component in the SEM at a magnification of x1000
and to achieve a depth of field of 1mm. If the maximum working distance that can be
used is 50mm, what is the maximum sized objective aperture that can be used? 10
5. Calculate the natural contrast in a backscattered image between phases of mean
20
atomic numbers 24 and 23. Assume normal incidence.
Note: C =
η1 − η 2
and η = −0.0254 + 0.016 Z − 1.86 ×10 −4 Z 2 + 8.31× 10 −7 Z 3
η1
MSE 421/521 Structural Characterization
6. If the natural contrast in a sample imaged using secondary electrons is 0.1, what is
the best obtainable spatial resolution in a W-filament microscope operating with the
following parameters using a frame time of 100s?
30
q (detector efficiency) = 0.2
j (current density at filament surface) = 4 A/cm2
T (filament temperature) = 2800 K
Cs (spherical aberration coefficient) = 20 mm
V (accelerating voltage) = 20 kV
MSE 421/521 Structural Characterization
7. Forecast what the best characterization instruments will be able to measure in 10 - 20
years. Do you think it is important to keep current on such technological advances?
Why/why not?
2
8. With the passage of the FY15 Government Appropriations Act, the Department of
Energy, Office of Science, Basic Energy Sciences (BES) terminated its support of
the user program at the Lujan Center, Los Alamos Neutron Science Center
(LANSCE) effective 1 October 2014. In light of this closure, discuss the implications
of analyzing materials at ever increasing resolution (spatial or compositional) on cost
of instruments, laboratories, and education. Propose solutions to some of these
2
issues.
MSE 421/521 Structural Characterization
BONUS:
Correctly identify the modes of failure (e.g., evaporative failure, vacuum fault, or
overcurrent) of the tungsten tips shown below and explain your reasoning.
15