The next technique works with solid pieces of material and thin films; however,
to really understand what pole figures can tell you, we need to take a step back and look at the
conditions for diffraction again. The diagram shown here is a more realistic representation
of diffraction. For polycrystalline samples, there are small regions called grains in which
all unit cells are aligned in the same way. These grains are outlined in red in the figure,
and neighboring grains have unit cells that are oriented differently. Let's pretend that
the lines within the grains shown here correspond to the (100) plane and that the X-ray source and
detector are at the proper angles for constructive interference to occur for the (100) planes,
normally producing a peak in the diffraction pattern. The diffraction vector as shown here
is the vector that bisects the angle between the X-ray source and detector. In this example,
the diffraction vector points straight up and is perpendicular to the diffraction plane. Here
are the normals for the (100) planes for each grain. The only grains that will contribute to
the appearance of the diffraction peak are those whose normals align with the diffraction vector.
In other words, this grain is the only grain shown here that will contribute to the diffraction
peak. Now let's look at a sample with preferred orientation. In this example, our diffraction
vector is the same as before but the (100) plane normals are different. For this sample,
there is a clear preference for the (100) normals to point up and to the left. Because none of the
normals are aligned with the diffraction vector, no grains will contribute to the diffraction peak,
so only background will be visible for this atomic plane even though the source and detector are at
angles that should produce a diffraction peak. When we collect pole figures, we align the source
and detector angles such that diffraction from a certain plane should occur. We then rotate the
sample around two axes to determine qualitatively how many grains are aligned with the diffraction
vector at each position. Let's go ahead and look at a real-life example. On the right, we see the
setup for collecting pole figures. Here's our sample, a square piece of cold-rolled copper.
X-rays strike the sample from this direction and diffract off in this direction to be picked up by
the detector off-screen. The system has been set up so that the source and detector are positioned
such that the (111) reflection should be detected. Once the measurement begins, the first thing that
will happen is that the sample will rotate 360 degrees in phi, which will be represented as
the appearance of data in a similar fashion on the left. The sample will then rotate back into
the screen in chi, which will be represented as a movement away from the origin in the pole figure.
As I said, we first rotate along phi, and we see almost no intensity on the plot, indicating that
there aren't any (111) planes oriented correctly for diffraction. We then rotate a bit back in chi
and rotate in phi again while collecting data. This time, we start to see some intensity appear,
so some (111) planes are oriented correctly. As we continue to rotate further in chi, more
intensity is seen at certain parts of the plot. We continue this until chi reaches approximately
70 to 80 degrees because it is at this point that the X-ray beam typically begins to fall off
of the sample. Because this type of experiment deals strictly with the intensity of the peak,
the entire X-ray beam must remain on the sample throughout the experiment. We see that at certain
orientations, the intensity is much stronger. This tells us how the (111) planes are preferentially
oriented in our sample. We are not limited to only investigating one type of plane. If we were to
rotate the source and detector to the angles that should produce other planes, we can do the same
experiment and determine each plane's preferred orientation. For this cold rolled copper example,
I also tested the (200) and (220) planes. Depending upon your material, you could get very
different looking pole figures. Here are some pole figures for an epitaxial thin film. An epitaxial
thin film is either a perfect or nearly perfect single crystal, meaning that the entire sample
is made up of a single grain, and all unit cells are oriented the same. Because of this, each type
of plane only diffracts constructively at very discrete orientations. That brings us to the end
of the video. If you would like more information about the JIAM Diffraction Facility or have any
questions, here is the address for our website and my email address. Thank you for watching!