460 Final, 2005

Section 1: Basic Facts (1-2 paragraph answers and/or a short diagram, 5 pts each)

  1. In the microscope there is both elastic as well as inelastic scattering. Which of these is coherent, and which is incoherent?

Elastic is coherent, inelastic is incoherent. A little explanation of what these mean would be appropriate.

  1. If you have a grain boundary in the region you are looking at in bright field, does the position change if you tilt the sample by a fraction of a degree? What about the contrast?

There are several elements to the answer. One small element would be if you do not have the eucentric height set right, in which case the sample would move a lot. Even if you do it will move a little.

More relevant, if you only tilt by a fraction of a degree you are not going to change the apparent position of the grain boundary w.r.t. other features in the object by much (<1nm). However, you are going to change the contrast rather a lot since the tilt will not have the same effect on the two grains on either side of the boundary. There is typically strain around a grain boundary, so the change in sz will change the strain contrast.

  1. An fcc sample contains stacking faults (which lie on (111) planes). For an image taken along [110] what will be the angle between the different families of stacking faults which are perpendicular to the electron beam (a plane is defined by the vector normal).

If the beam is along [110], then stacking faults on (1 -1 1) and (1 -1 -1) are normal to the electron beam. Relevant therefore is the angle between these which you can get from the dot product,

Cos(theta) = 1/3 so theta=70.5 degrees

  1. What are the main processes which lead to the build up of contamination in the electron microscope in the region being viewed?

Contamination is the build up of carbon in the region you are looking at. In brief, hydrocarbons from various sources (the vaccum, fingers) diffuse to the region of interest and decompose (primarily losing hydrogen) in the beam to form an amorphous “blob”. The main mechanisms (best answer) are either direct excitation of bonding electrons to antibonding levels, or via the excitation of core electrons; I did not cover the last in great detail in the class.

  1. Is it always true that diffraction spots further out (i.e. |g| is larger) are weaker than those further in (briefly justifying your answer).

It is not true. The intensity of diffraction spots further out depends on two things:

a) The structure factor

b) The tilt

It’s easy to have cases where either a) or b) makes a larger |g| spot stronger, even when the beam is exactly on a zone axis.


Section 2: Research Strategy - 20 points

You are given a sample which has very small grains, about 3-4nm in diameter. Your customer believes that some of the grains are pure tungsten (Z=72, bcc lattice parameter 3.16 Angstroms) and some are copper (Z=29, fcc lattice parameter 3.61), and there are no alloy particles. Starting with same preparation how do you determine whether this is the case or not? (N.B. you can only use TEM)

Note: Time is money; points will be deducted for grossly inefficient approaches

There are many ways to answer this, and I will only sketch the key points.

1) Copper is ductile, tungsten less so but is still a metal. Therefore crushing is not viable. If you are lucky you might have some powder to look at, but it might be too thick. It will have to be the ion-beam milling route, perhaps embedding in an epoxy first to give some mechanical strength.

2) The grain size is going to make most standard TEM methods hard to use. Of course the first thing to do is still to take a look in BF!

3) Assuming that the grain size etc is correct, you can look at the diffraction pattern. For some of the lower angle g’s the real space spacings are:

Cu / W
2.084234 / 1 / 1 / 1 / 2.234457 / 1 / 1 / 0
1.805 / 2 / 0 / 0 / 1.58 / 2 / 0 / 0
1.276328 / 2 / 2 / 0 / 1.290065 / 2 / 1 / 1
1.088456 / 3 / 1 / 1 / 0.99928 / 3 / 1 / 0

So you should be able to tell if you have pure Cu and W.

4) EDX or EELS can be slightly helpful, but it will be hard to get spectra from single particles – with this grain size a bulk sample will have overlapping particles.

5) To really answer the questions, you will need to try and find some way to get very small clumps isolated so you can look at single particles. You could try an ultrasonic treatment in some inert solvent then dispersing the particles onto a carbon grid. You never know, it might work (and would be quick)

6) Z-contrast/HREM might help, but to find an alloy they are a bit marginal. Since HREM is easier (with a good microscope) it would be worth a shot, but only if there are regions which are thin enough. One problem is that with a nanocrystalline sample it will be hard to find particles oriented near a zone axis, which you need for HREM (or atomic-level Z-contrast microscopy).

7) CBED is not a good idea. For it to work, you need to be on a zone axis, and you want the probe to only be on a single particle. You could perhaps do microdiffraction (CBED in a STEM) but this will be hard and you would need to look at many particles to get anything useful – HREM is better for this.

Note: spending a lot of time on conventional TEM in this case is not a good idea.

Section 3: Micrograph - 20 points

For the attached micrograph from a cubic material, answer the following questions with a brief justification in each case:

a)  Is it bright-field, dark-field or what? 5 pts

This is not trivial. There is what looks like a Fresnel fringe at the bottome left, and you almost always do not get this (very strongly) in DF (although you can). More to the point, you don’t have the high contrast typical of DF. In addition, it is hard to explain what the white feature in the center would be if it was DF. There is a “black line” running through the center, so this is not a hole, it must be an area with a different thickness. Perhaps most telling, all the dislocations (later) appear black which is very unlikely in DF. Hence, most likely, BF.

b)  What is the three-dimensional shape of the sample? 5 pts

Not much in the way of thickness fringes or large contrast variations, so probably fairly thin. The region in the center is thinner.

c)  Suggest a source for the contrast from the black linear features, one of which is arrowed ? 5 pts

If you look carefully, in various places where the long lines terminate there are some contrast oscillations. This implies that they are dislocations which are primarily running in the plane of the sample.

d)  What zone axis might this image have been taken from? 5 pts

There is a very definite 4-fold general symmetry to everything, which strongly implies a [100] type orientation

For reference, this is a sample after nanoindentation – the dislocations have been punched out by the indenter.