High-Order Diffraction Satellites and Temperature Variation of the Modulation in the Incommensurate Phase of Rb2ZnCl4

Temperature Dependence of the Static Distortion in Incommensurate Displacive Phases and its Effect on the Diffraction Pattern. II. Satellite Reflections

“…As, for x << 1, Jn(x)~_ x ~, it is expected that these satellites would show unexpectedly strong intensities in comparison to the rest, including satellites of lower order. This is what happens with third-order satellites in thiourea (r = 2) (Zfifiiga et al, 1989) or fifth-and seventh-order satellites in Rb2ZnCI 4 (r ---6) (Andrews & Mashiyama, 1983;Aramburu, Madariaga, Grebille, P6rez-Mato & Breczewski, 1997).…”

“…As the atomic displacements increase and new terms become significant in (2), the relation between the effective exponents (/3elf,n) of the nth-order satellites and the effective exponent (13) of the order parameter [p(t)= po ts] becomes quite complex. The expression /3elf,,, "~ 2n/3 obtained in the limit of small displacements is no longer valid, as observed experimentally in Rb2ZnCI4 (Andrews & Mashiyama, 1983;Aramburu, Madariaga, Grebille et al, 1997).…”

“…In order to verify all these qualitative results, the temperature dependence of the diffraction diagram of RbEZnCl 4 in its IC phase has been simulated. Owing to the high value of r (6) in this compound, relatively simple expressions for g~'(H) are expected, while the detection of high-order satellites (fifth and seventh) (Andrews & Mashiyama, 1983;Aramburu, Madariaga, Grebille et al, 1997) indicates the presence of a strong soliton regime in the structural modulation. The approximated temperature dependence of the structural distortion in this compound, including the soliton density, has been recently determined (Aramburu, Madariaga, Grebille et al, 1997).…”

“…Although this primary distortion is expected to be the most important in the structural modulation, harmonics of other symmetries compatible with the superspace group of the IC phase will also be present and, in general, will not be negligible compared with the primary distortion. This is the case of the second-harmonic modulation determined in the IC phase of thiourea (Zfifiiga et al, 1989) or the thirdharmonic modulation in Rb2ZnC14 (Aramburu, Madariaga, Grebille et al, 1997). The presence of this secondary distortion involves an additional complication of the functional form of g"(H).…”

Temperature Dependence of the Static Distortion in Incommensurate Displacive Phases and its Effect on the Diffraction Pattern. I. Main Reflections

“…As polarization vectors for the primary distortion P {ui~ ' tp~' }, those experimentally determined by Hedoux et al (1989) and Zffiiga et al (1989) were, respectively, considered. In the case of RbzZnCI 4, the functions {p(T),ns(T)} deduced from experimental data (Aramburu, Madariaga, Grebille, P6rez-Mato & Breczewski, 1997) were used. In the case of thiourea, as the temperature dependence of these parameters has not been yet determined, the relation p(ns) obtained from the minimization process of the free energy (Golovko, 1980;Aramburu, Madariaga & P~rez-Mato, 1994) has been assumed.…”