We know since the works of Landau that the natural language to deal with the static frozen distortions present in displacively distorted structures is the one of modes. Modes are collective correlated atomic displacements fulfilling certain symmetry properties. Structural distortions in distorted structures can be decomposed into contributions of modes with different symmetries given by irreducible representations of the parent space group. One can then distinguish primary and secondary (induced) distortions, which will have in general quite different weights in the structure, and will respond differently to external perturbations. In general, the use of symmetry-adapted modes in the description of distorted structures introduces a natural physical hierarchy among the structural parameters. This can be useful not only for investigating the physical mechanisms that stabilize these phases, but also for pure crystallographic purposes. The set of structural parameters used in a mode description of a distorted phase will in general be better adapted for a controlled refinement of the structure, or for instance for comparative studies between different materials or for ab-initio calculations.

AMPLIMODES is a computer program available on the Bilbao Crystallographic Server that can perform the symmetry-mode analysis of any distorted structure of displacive type. The analysis consists in decomposing the symmetry-breaking distortion present in the distorted structure into contributions from different symmetry-adapted modes. Given the high- and the low-symmetry structures, AMPLIMODES determines the atomic displacements that relate them, defines a basis of symmetry adapted modes, and calculates the amplitudes and polarization vectors of the distortion modes of different symmetry frozen in the structure. The program uses a mode parameterization that is as close as possible to the crystallographic conventions, using the asymmetric unit of the low-symmetry structure for describing modes and distortions.

After a brief introduction to the general problem, the program will be presented by means of some examples. This will be completed with an extensive practical session with exercises where the program should be used online.

Supplementary Material