Open AccessStructure of incommensurate ammonium tetrafluoroberyllate studied by structure refinements and the maximum entropy method
Author(s) -
Palatinus Lukás,
Amami Mongi,
Van Smaalen Sander
Publication year - 2004
Publication title -
acta crystallographica section b
Language(s) - English
Resource type - Journals
eISSN - 1600-5740
pISSN - 0108-7681
DOI - 10.1107/s0108768104000874
Subject(s) - ferroelectricity , superspace , crystal structure , crystallography , condensed matter physics , phase transition , space group , chemistry , physics , diffraction , materials science , dielectric , x ray crystallography , optics , quantum mechanics , supersymmetry
Incommensurately modulated ammonium tetrafluoroberyllate (AFB) occurs in a narrow temperature interval between the paraelectric room‐temperature phase with space group Pnma ( T i = 178 K) and the ferroelectric low‐temperature phase with space group Pna 2 1 ( T c = 173 K). The structure is determined from accurate single‐crystal X‐ray diffraction data collected with synchrotron radiation at 175 K. The superspace group of the structure is Pnma (α00)0 ss with α = 0.4796 (4). Both structure refinements and the maximum entropy method lead to the same structure model, which involves only single harmonic modulations. The building units of the structure are BeF and NH complex ions with approximately tetrahedral point symmetry. They are relatively rigid and the modulations consist mainly of translations of the tetrahedra and their rotations around a fixed axis. The modulation is related to changes in the network of the hydrogen bonds. The low‐temperature superstructure can be described as a commensurately modulated structure with the same superspace symmetry. The first harmonic modulations of the low‐temperature and incommensurate phases are related by a scale factor with a value of approximately two. In addition, the low‐temperature phase exhibits a second harmonic modulation that is responsible for shifts along c and the ferroelectricity in this phase. The experimental data of the incommensurate phase do not contain any evidence for the presence of a second harmonic in the modulation functions. This suggests that the development of the second harmonic, i.e. the development of the spontaneous polarization, is responsible for the lock‐in transition.