Modulated structure ofRb2ZnCl4in the soliton regime close to the lock-in phase transition

Abstract

The structure of the incommensurate phase of Rb 2 ZnCl 4 has been determined at 194 K ͑2 K above the lock-in transition͒ within the soliton regime using satellites up to fifth order. The rather anharmonic modulation functions agree with the expected steplike functions supported by theoretical arguments. In addition, the constancy of the ratio between the amplitudes of the fifth-order and first-order harmonics, a relation predicted by theory, indicate the correctness of the model and imply a value of 0.4 for the soliton density n s. A symmetry mode analysis shows that the incommensurate structure is consistent with the one of the lock-in phase in the sense that the displacement pattern of every symmetry mode remains unaltered in the transition except for a global change in the amplitudes.

Mode crystallography of distorted structures

“…To use AMPLIMODES we only need to introduce the Pnma (parent) and Pna2 1 structures, and the transformation relating both groups: (À3a; c; b; 0; 0; 0). Similarly, the additional GM4À distortion is the polar distortion responsible for the spontaneous polarization and ferroelectric properties in this commensurate phase, and can be identified with a third harmonic in the atomic modulations (Perez-Mato et al, 1986;Aramburu et al, 2006). As expected, we have a dominant component for the irrep SM2, with wavevector (1/3, 0, 0).…”

Modulated anharmonic ADPs are intrinsic to aperiodic crystals: a case study on incommensurate Rb2ZnCl4

“…Experimental data and crystallographic information are summarized in Table 1. 1 The observed volume of the unit cell is significantly smaller than reported by Aramburu et al (2006), who gave V cell = 844.04 Å 3 with a = 7.241 (3), b = 12.648 (5) and c = 9. 216 (3) Å .…”

“…The modulation of Rb 2 ZnCl 4 increasingly deviates from a sinusoidal shape on approaching the lock-in transition, as shown by the growth of the intensities of higher-order satellite reflections in the X-ray diffraction of this compound on cooling toward T lockÀin (Aramburu et al, 1997). The results of structure refinements of a model of displacive modulation functions with up to fifth-order Fourier coefficients have been reported by Aramburu et al (2006). The latter authors interpreted this structure model as providing evidence for a soliton shape of the incommensurate modulation wave.…”

“…216 (3) Å . Since lattice parameters from point-detector measurements are much more accurate than from area detectors, we have employed the lattice parameters from Aramburu et al (2006) in the present refinements.…”

“…Here we present a re-analysis of the incommensurate structure of Rb 2 ZnCl 4 close to the lock-in transition, employing a more extensive data set of Bragg reflections than has been used by Aramburu et al (2006). The purpose of this work is twofold.…”