The Real Alcazar de Seville is beautiful. And the reason it is beautiful is the marvellous use of symmetry in the many tilings decorating the inside walls, floors and ceilings. But nothing is perfect (except in Plato’s World of Ideas) so the patterns tend to contain a mistake, an imperfection, an example of broken symmetry.
In crystallography, we also work with symmetry and enjoy the beauty of our structures, but it is often the cases where symmetry is broken that are the most interesting. For many applications, high symmetry is not desirable, despite its aesthetic appeal. For example, a lot of research is focused on ferroelectric material: compounds which may develop an electric polarisation that switches direction if the electric field reverses. But for a polarisation to be possible, the structure must have at least one axis with no perpendicular mirror planes or 2-fold rotation axes. If a material scientist wants to construct a ferroelectric material, he/she must be able to design a compound subject to these symmetry constraints.
A useful example is the highly symmetrical structure known as the perovskite structure. It consists of corner-sharing octahedral units in a cubic arrangement and has no less than 48 symmetry operations, making it one of the most symmetrical structures possible. However, just like there are many symmetry elements of the parent structure, there are many ways of removing these elements to give a phase transition into a structure of lower symmetry (child structures). The possible structural distortions have been well studied and their effects on the symmetry are, in many cases, well documented. One way for the material scientist to come up with the desired ferroelectric compound, is then to try to combine different distortions, in order to achieve the appropriate symmetry.
Now, in recent years, molecular perovskites have gained increasing amounts of research attention. Here, the octahedra are not joined at the corners, but instead tied together by a molecular linker. This increases the number of distortions available for the material scientist. For example, the individual columns and layers of connected octahedra can slide relative to each other, something which is not possible in an ordinary perovskite. We call this “columnar shifts” and explain its significance in a recent paper. Shifts lower the symmetry and when combined with rotations of the octahedral units, it may lead to space groups capable of sustaining a polarisation.
Another interesting feature of distorted child structures is that they mirror the dynamic distortions present in the high-symmetry parent structure. Many structural distortions are present as vibrations in the parent structure, but below a transition temperature, they freeze in, i.e., become static. We show that shifts may be present as vibrations in seemingly unshifted molecular perovskites and that they may cause negative thermal expansion, where compounds counterintuitively shrink when heated. Molecular perovskites, such as the family of Prussian blue analogues, show negative thermal expansion, and maybe this is caused by the columnar shifts? Whatever the answer, we should be lucky that we do not live in Plato’s World of Ideas, since lack of imperfection would lead to lack of useful materials.
Columnar Shifts as Symmetry-Breaking Degrees of Freedom in Molecular Perovskites
H L B Boström, J A Hill, and A L Goodwin
Physical Chemistry Chemical Physics 18, 31881-31894 (2016)