
The standard way of studying the structures of crystals on atomic lengthscales, is X-ray diffraction. We fire X-rays at a sample and then detect the X-rays that bounce off the sample, as a function of the angle X-rays come out. This gives us what is called a structure factor, S(k), where k is called the wavector, which has dimensions of inverse length, i.e., m-1.

Understanding how crystals start to form is tricky. We can’t see how it happens as crystals start off microscopic, it is very sensitive to pretty much every aspect of the experimental set up, and the standard theory (called classical nucleation theory) has basically zero ability to predict anything. So we are a bit stuck. But we don’t have the toughest job around, arguably the most complex, and hardest to understand, thing around is the human body, so perhaps the toughest job belongs to medics and biomedical scientists studying diseases.
Steel is not pure iron, it contains a small fraction of carbon that transforms the soft pure iron into the much tougher steel. I guess I have known that for a long time. But I have not really thought about how the carbon is incorporated into the crystalline iron. Dissolving salt in liquid water is straightforward. The ions of sodium and chloride just diffuse around in the liquid surrounded by the diffusing molecules of water. This is a liquid solution, a solution of salt in liquid water. Steel is a solid solution, it is carbon dissolved in solid iron.