Statics and dynamics of the modulation in incommensurate Rb2ZnBr4 as detected by NMR

The dynamics of the incommensurate modulation of Rb₂ZnBr₄ is investigated near the transition to the normal high-temperature phase using first-order quadrupole effects in nuclear magnetic resonance (NMR).⁸⁷Rb NMR spectra and two-dimensional⁸⁷Rb NMR exchange spectra are reported. All results can be described consistently in terms of a static modulation in the incommensurate phase without any indication for “floating” or large-scale fluctuations of the modulation wave. The spectra taken about 135 K below T_i in the lower incommensurate phase well above the soliton regime show no indication for the existence of a higher-order commensurate modulation in Rb₂ZnBr₄.     

The incommensurate - commensurate phase transition in Rb2ZnCl4: confrontation of permittivity and birefringence data

Permittivity ϵ and birefringence Δn of the c-plates of Rb₂ZnCl₄ crystals have been measured simultaneously in the vicinity of the incommensurate (IC) - commensurate phase transition. Samples used are characterized by the maximum value ϵ = 150 occuring at a temperature T_m. Since ϵ in the IC phase is determined by the phase of the order parameter while Δn is sensitive to its modulus, confrontation of these data provides some insight into the transition process. The data show that i) the transition is essentially 1st order; ii) T_m marks the beginning of the transition process on cooling and its end on heating. Below T_m, both phases coexist within an interval ΔT_tr = 1.5K on cooling and 0.6K on heating. iii) There is no indication of any significant phase coexistence above T_m. An indirect conclusion is drawn that within ΔT_tr, the anomalous dielectric tail is due both to surviving solitons and to true domain wall contribution; below T_m−ΔT_tr domain walls take over.     

Thermodynamic properties of successive phase transitions in Rb2ZnBr4

Heat capacity measurements have given the following transition temperatures and entropies: 0.027 J K^?1mol^?1 at 76.5 K, 0.47 J K^?1mol^?1 at 111.7 K, and 0.048 J K^?1mol^?1 at 193.6 K. These are interpreted as “lock-in”, soft-mode, and “lock-in” transitions, respectively, from comparison with analogous results for Rb₂ZnCl₄ and K₂SeO₄. The N-IC transition was located at 347 K by DTA.     

Study of Mn2+ EPR spectra in the incommensurate phase of Rb2ZnCl4

An EPR study of Mn²⁺ centers in the incommensurate phase of rubidium tetrachlorozincate crystals is reported. It is shown that the temperature dependence of the high-field hyperfine line group M _S=3/2↔5/2 can be described in terms of a simple “local” model. The data obtained support the nonclassical type of critical behavior in Rb₂ZnCl₄ crystals corresponding to the three-dimensional Heisenberg model for a two-component order parameter. Fiz. Tverd. Tela (St. Petersburg) 41, 691–694 (April 1999)     

Effect of γ irradiation on the hysteresis phenomena at the incommensurate-commensurate phase transition in Rb2ZnBr4

The effect of γ irradiation on the temperature hysteresis in dielectric permittivity ɛ and loss tangent tan δ of crystalline Rb₂ZnBr₄ has been studied in the vicinity of the incommensurate-commensurate phase transition. The ɛ(T) and tan δ(T) curves were found to exhibit anomalies in the form of maxima. Hysteresis was observed in the measured properties, including the transition temperature T _c (ΔT=T _c ^h −T _c ^c ), in both unirradiated and irradiated samples. It is shown that, as the radiation dose increases the extent of the hysteresis ΔT increases, the values of ɛ _max and tan δ _max at the transition point decrease, and the anomalies wash out. Fiz. Tverd. Tela (St. Petersburg) 40, 1911–1914 (October 1998)     

Influence of crystal synthesis on the incommensurate phase and lock-in transition of Rb2ZnCl4 crystals

A comparative study of several crystals of Rb₂ZnCl₄, obtained by different crystal growing methods, has allowed us to determine the influence of growth defects on the incommensurate phase and on the lock-in transition of these samples. X-ray diffraction has allowed us to complete previous dielectric measurements realized on the same samples and to relate the crystalline quality to the evolution of the modulation as a function of the temperature. The principal influence of an increasing defect density seems to be a stronger pinning of the modulated phase and this induces a lower lock-in temperature and a wider hysteresis.     

Commensurate and incommensurate modulated structures of Rb2ZnCl4

The commensurate and incommensurate structures of Rb₂ZnCl₄ have been refined using the four-dimensional formalism for modulated structures. They are characterized by a rigid body modulated rotation of the ZnCl₄ tetrahedra and by a translation motion of the Rb atoms.     

Effect of γ irradiation on the heat capacity of Rb2ZnBr4 in the vicinity of phase transitions

Heat capacity of Rb₂ZnBr₄ as a function of γ irradiation dose has been measured within the 85–300 K range by the adiabatic calorimeter technique. It is shown that, as the irradiation dose increases, the heat capacity peak in the vicinity of the incommensurate-commensurate first-order phase transition (PT) decreases, and the transition temperature T _c increases. The heat capacity peak in the region of the second-order PT at T ₃=112 K does not depend on γ irradiation, both in magnitude and in position, just as the heat capacity throughout the remainder of the temperature range studied. Fiz. Tverd. Tela (St. Petersburg) 40, 1106–1108 (June 1998)     

Fluctuation-induced broadening of Mn2+ EPR lines in the incommensurate phase of Rb2ZnCl4 crystals

The EPR spectra of Mn²⁺ ions in Rb₂ZnCl₄ crystals is investigated in the vicinity of the transition from the paraelectric phase to an incommensurate modulated phase. When these crystals are cooled below the transition temperature T _i =304 K, a splitting of the resonance lines is observed in the singular spectrum. A one-harmonic model is used to discuss the contributions that fluctuations in the amplitude and phase of the incommensurate displacement wave make to the local width of the singular spectra. It is shown that anomalies in the local width of the low-temperature singular peaks observed in the vicinity of T _i are caused by amplitude fluctuations. Fiz. Tverd. Tela (St. Petersburg) 41, 1668–1674 (September 1999)     

A priori theory of incommensurate behavior in Rb2ZnCl4

We have performed a study of the potential energy, normal modes, static relaxation, and molecular dynamics of Rb₂ZnCl₄ using ab initio Gordon-Kim interionic potentials for intermolecular and interionic potentials. We find that the Pnam–Pna2₁ transition in this, and almost certainly many isomorphous systems, is entropy driven and shows no soft mode behavior. This is shown to arise from the presence in this system of a large equipotential volume of phase space between the Pnam and the tripled Pna2₁ low temperature structure. This region arises from a major lattice instability involving large rotations and displacements and having approximately six-fold screw symmetry along the a axis. This concealed imperfect symmetry which we call latent symmetry is the basic cause of the existence of a near-tripled incommensurate phase over a range of 113 K (302 K–189 K) between the Pnam and Pna2₁ phases. In this region the helicity is incommensurate with the lattice, being largely determined by the relief of intrahelical stresses. In addition, we have demonstrated by molecular dynamics that the ZnCl₄ ^2- tetrahedra are orientationally disorderd, but, despite this, the helical instability remains. These findings are also related to anomalies in the observed Raman spectra and to X-ray data which confirm the presence of dynamically correlated disorder.     

Observation of87Rb NMR satellite transitions in the commensurate and incommensurate phases of Rb2ZnCl4

It is shown that the first order quadrupole split NMR satellite transition frequencies of the⁸⁷Rb nucleus can be detected in the paraelectric, incommensurate and ferroelectric phases of Rb₂ZnCl₄. From rotation patterns the electric field gradient tensor at the Rb sites is determined for the paraelectric phase. The data demonstrate a considerable influence of the structural changes in the incommensurate and ferroelectric phases on the observed NMR transition frequencies. For some crystal orientations the satellite transitions are followed through the incommensurate into the ferroelectric phase. Whereas in the former typical quasi continuous spectra are observed in the latter several sharp lines appear. The results are discussed in relation to the structural changes at the phase transitions.     

Propagation of light in Rb2ZnCl4-type crystals with incommensurate modulation

Wave equation for optical waves in the incommensurate phase of Rb₂ZnCl₄-type crystals is solved taking into account spatial dependence of optical permittivities due to incommensurate modulation of the lattice. Using the procedure originally proposed by Golovko and Levanyuk it is shown that for the wave vectors parallel to the orthorhombic axes: a) the waves are not purely transverse, b) their amplitudes are spatially modulated and c) their velocities are changed so that corrections to refractive indices exist due to permittivity modulation. Data on birefringence of Rb₂ZnCl₄ are analysed and it is shown that these corrections are responsible for the jump-like changes of refractive indices at the incommensurate-ferroelectric phase transition, together with the quasi-discontinuous change of the order parameter modulus. The spatial variance of the wave amplitudes may be responsible for the possibility of SHG in the incommensurate phase whose averaged point group is centrosymmetric.The authors gratefully acknowledge helpful discussions with Dr. V. Dvoák.     

Linear birefringence studies of incommensurate systems: II. KFeF4

Abstract

The temperature dependence of the linear birefringence (LB), Δn _c , is measured in the range 5 K ? T ? 500 K on samples of KFeF₄, which originate from hydrothermal, flux and Bridgman growth techniques. Pronounced anomalies are found at the orthorhombic-orthorhomic phase transition at T _c ∽ 400 K. It is weakly discontinuous with a near-tricritical exponent β ∽ 0.2. Weak anomalies near T _i ∽ T _c + (25 … 40 K) seem to indicate a transition into an intermediate incommensurate phase. Its XY-model character is reflected by the critical LB exponent β = 0.8 ± 0.1. A smooth LB anomaly below 200 K is due to 2-dimensional ferromagnetic spin-order.     

On the structural phase transitions in the incommensurate Cs2CdBr4

Abstract

In the series of incommensurate A₂BX₄ halides with the β-K₂SO₄ type structure, Cs₂CdBr₄ exhibits an unusual behaviour since the “lock-in” phase transition occurs at the centre of the Brillouin zone. The observed phase sequence is the following: Pnma (Z = 4)?INC(k₀ ≈ 1/6a*)?P2_1/n(Z = 4)?P1 (Z = 4). These phase transitions have been studied by means of Raman scattering and ultrasonic measurements. It is shown that the Pnma?INC?P2_1/n sequence is governed by order-disorder processes due to CdB2-₄ tetrahedra reorientations coupled with translations of the Cs⁺ cations, and that the low-temperature P2_1/n?P1 transition is of a displacive nature, governed by a soft optical mode. The “pseudo-proper” ferroelastic character of these transformations is clearly established. A model potential developed in the framework of Landau theory is proposed; this model is able to reproduce the general trends observed in the temperature dependence of the soft-modes and of the elastic constants in the different phases.