The perovskite structure can be considered one beginning of complexity in materials science. The cubic perovskite structure is a simple one, chemical formula ABO₃, with oxygen atoms on the faces of a cube, the "B" atom in the center and the "A" atom on the vertices. However, cubic perovskites are inherently unstable. For a binary cubic compound (such as NaCl) the lattice constant can be taken to be the sum of the atomic radii. However, for a ternary compound, one must either be very fortunate to have the three effective atomic sizes in the correct ratio to make a cube, or, more often, the crystal distorts, slightly, to a lower symmetry, and lower energy, structure. The slight distortions open the door to a range of complex and useful properties: one finds the perovskite structure in piezoelectrics, ferroelectrics, and multiferroics, even superconductors - and then in nearly every technological field. This tendency toward a distortion is often reflected in the microscopic motion of the atoms even before the distortion occurs, and can be inferred from observing the vibrational normal modes, or phonons, and may be linked to a “soft-mode” picture of a phase transition. In this practical, we will use x-ray scattering to investigate these atomic motions.

X-rays are now emerging as a uniquely powerful probe of atomic dynamics in materials. The small, ~ 0.001 eV, energy scale of atomic motions, as compared to the, typical, ~10,000 eV energy of hard x-rays, means that building a sufficiently high-resolution x-ray spectrometer is difficult. However, when completed, the advantages of the x-ray source and the method, make such a spectrometer an invaluable and highly sought-after tool. The practical will first include an introduction to the optics and optical concepts needed for such a spectrometer and then focus on measuring phonons in a relatively simple perovskite.