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Characterisation of Materials (2011)
Assignment No 1
Question No 1
An electron beam is accelerated from rest through a potential difference of 200 V. Calculate the
wavelength associated with the electrons.
Question No 2
The highest achievable resolving power of the microscope is limited only the wavelength used;
that is the smallest detail that can be separated is about equal to the wavelength. Suppose we
wish to ‘see’ inside an atom. Assuming the atom to have a diameter of 1.0 Å, .i.e., we wish to
resolve separation about 0.1 Å. (a) If an electron microscope is used, what is the minimum
energy electrons needed? (b) If an optical microscope is used, what minimum energy of photons
is needed? (c) Which microscope seems more practical for this purpose? Explain.
Question No 3
A tungsten filament produces an electron beam with a diameter of 50 μm and brightness 105
A/(cm2 sr). This electron beam passes through a condenser lens with a focal length of 1 inch. The
distance between the beam crossover produced by the gun to the center of the condenser lens is
10 inches. After passing through the lens, the beam current, measured with a picoammeter, is 500
pA. Calculate the convergence angle of the probe produced by the electron gun and condenser
lens, ignoring all possible aberration effects that could be caused by lens defects.
Question No 4
You been given the profile of a sample which is reproduced below. Sketch the signal detected by
each (A & B) of the backscatter detector whose direction is indicated below. Then sketch the
topographic contrast, (A-B) and the compositional contrast (A+B). Assume the probe size is
much smaller than any feature size.
Question No 5
PS is a plural scattering Monte Carlo model (available in learning material folder) which is well
suited for studies of electron interactions in bulk specimens. In this model:
(a) Using 250 trajectories and a beam energy of 15keV plot the interaction volumes for carbon,
copper, silver and gold. How do the interaction volumes vary from one element to another?
(b) Using at least 500 trajectories compute the backscattering coefficient for copper at energies
of 1,3,5,10,20 and 30keV. Does it vary? How do these numbers compare with those for carbon
and gold at the same energies?