The availability of group theory tools like AMPLIMODES, within the Bilbao Crystallographic Server (www.cryst.ehu.es), and the automatic generation of input files for FullProf allow the treatment of experimental data in a new way that captures the physics of structural phase transitions. It is supposed that the crystal structure under hand (space group L) derives from a high symmetry phase (space group H, L⊂H). In practice the program AMPLIMODES calculates all the possible symmetry modes (irreducible representations of H) participating in the complete group-subgroups chain relating L with H as well as the list of all expected polarization vectors (basis functions) of the atomic modes normalized in such a way as their components are referred to the unitary basis {a/a, b/b, c/c} of the L phase. Within FullProf the calculation of the fractional coordinates of atom positions in the asymmetric unit of the L phase is done as:

r_j(L)=r_j(H)+Σ_mQ_me(j|m)

Where r_j(H) are the ideal positions of the H phase referred to the L basis (fixed data), Q and e are the amplitudes and polarization vectors of the modes. The method is especially useful for treating pseudo symmetric structures (even in cases a real phase transition does not occur) in which a great number of atomic positions are, in principle, free parameters. Once the decomposition of the proposed structure in terms of symmetry modes is done, the free parameters become amplitudes of collective modes instead of individual atom positions. A natural hierarchy can be established from the refined values of such amplitudes and more stable and robust refinements can be performed when the data are insufficient or of low quality (e.g. powders or twinned crystals).

The implementation of the method within FullProf will be described and the key points that are needed in the input control file (PCR file) will be discussed in detail. A series of examples will be presented in which we will treat single crystals and powder data. The use of simulated annealing when the structure is not yet completely known will be illustrated in simple cases. Troubleshooting and eventual problems will also be discussed.

Practical session:

Use of AMPLIMODES for FullProf in different cases (eventually cases proposed by the participants) in order to simulate powder diffraction patterns.

Steps for using AMPLIMODES + FullProf for treating real cases. Examples: LaMnO₃, high temperature phase of YBaMn₂O₆, etc.

Supplementary Material