Phasons modulate the atomic Debye–Waller factors in incommensurate structures: experimental evidence in ThBr₄ at 55 K

Abstract

The incommensurate displacive structure of fl-ThBr4 at 55 K has been determined from a neutron diffraction data set including main reflections and firstorder satellites. The superspace group is DI4damdJr-s-f sl.Final agreement factors are 0.0193, 0.0186 and 0.045 for all, main and satellite reflections, respectively. It is shown that the effect of phasons on the atomic Debye-Waller factors can be quantified by two additional structural parameters: the modulus Br fill.2 and the phase Br XI1.2 of a second harmonic that spatially modulates the temperature factors of Br atoms. Results are in good agreement, within the resolution of the experimental data, with the theoretically expected value for Br X IL2. Crystal data for the average structure: Mr=551.65, tetragonal, 141/amd, a= 8.919(1), c=7.902(1) A, V=628.6(2) A 3, Z=4,