Study of commensurate and incommensurate phases in NaNO2 by 23Na NMR

The temperature dependence was determined of the ²³Na NMR spectrum of NaNO₂ with special emphasis on the small incommensurate phase and the surroundings of the phase transition points. Whereas far away from the transitions satellite lines of Gaussian shape with the natural line widths are observed near the transitions broad line distributions are detected showing distinct edge singularities. The results are related to the sinusoidally modulated and homogeneous order parameters of the incommensurate and ferroelectric phases.     

Transferred hyperfine field of Rb2CoCl4 single crystals in the ferroelectric-incommensurate-normal phase by Rb NMR

The molecular susceptibility and paramagnetic shift of Rb₂CoCl₄ single crystals grown using the slow evaporation method were measured, and from these experimental results we obtained the transferred hyperfine interaction due to the transfer of spin density from Co²⁺ ions to Rb⁺ ions. The transferred hyperfine field was obtained for the ferroelectric, incommensurate, and normal phases. In the case of Rb(I), the transferred hyperfine interaction decreases with increasing temperature in the incommensurate phase, and increases with increasing temperature in the normal phase. The value of H_hf in the incommensurate and normal phases increases abruptly with increasing temperature in the case of Rb(II). These results indicate that the effects due to the transfer of spin density from Co²⁺ ions to the Rb(I) and Rb(II) ions are large above T_i. In particular, the effect due to the transfer of spin density to Rb(II) ions in the normal phase is very large; the variations with temperature of the transferred hyperfine interactions of the Rb(I) and Rb(II) nuclei are more or less continuous in T_c1 and T_i, and are not affected by the ferroelectric-incommensurate-normal phase transitions.     

87Rb NMR study of the temperature and electric field dependence of the soliton density near the lock-in transition of incommensurate Rb2ZnCl4

The frequency distribution of the⁸⁷Rb NMR 1/2–1/2 central transition is measured in a detailed manner as a function of the temperature and the crystal orientation in the normal (N), incommensurate (IC), and commensurate (C) phases of high quality single crystals of Rb₂ZnCl₄ (RZC). Special emphasis is laid upon the region around the lock-in transition atT _c . While in the N and C phases discrete lines are observed, in the IC phase a continuous distribution of frequencies is detected. In a temperature interval not exceeding 15 K aboveT _c some centers of intensity termed C lines can be observed in the frequency distribution. They reflect the fact that in the IC phase close toT _c several nuclei feel a local surrounding very similar to that of the low temperature C phase. For the first time in the region aroundT _c the influence could be studied which an electric field favouring the ferroelectric C phase has on the NMR spectra. The experimental results are related to the temperature and electric field dependence of the soliton density near the lock-in transition. A general definition of the soliton density is developed whose validity is not limited to the very narrow soliton limit. The meaning of this definition is also discussed in terms of well known phenomenological theories of the three phases of RZC. The experimental NMR data can be well described by this general definition.Dedicated to Prof. Dr. H.E. Müser on the occasion of his 60th birthday     

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.     

Magnetic resonance investigations of phase transitions and modulation wave motions in incommensurate solids

We measured⁸⁷Rb nuclear magnetic resonance (NMR) and³⁵Cl nuclear quadrupole resonance (NQR) Hahn spin-echo magnetization decays in the incommensurate (I) phase of Rb₂ZnCl₄ and, in each case, obtained a Hahn echo decay that was shorter than the Carr-Purcell-Meiboom-Gill decay and one which decayed with a time constant proportional to the cube of the echo time. From these measurements we obtained from both the⁸⁷Rb NMR and³⁵Cl NQR measurements values for the diffusion coefficients that are comparable in magnitude, a fact that strongly supports the existence of slow modulation wave diffusionlike motions in the I phase, since such motions should affect both Rb and Cl ions similarly. In addition, we used⁸⁷Rb two-dimensional exchange-difference NMR to study atomic motions in the incommensurate (I) and paraelectric (P) phases to elucidate the nature of the I-P transition. We measured as a function of the mixing time the frequency shifts of the cross peaks from the main diagonal and observed a gradual increase towards an asymptotic value in the I phase but a sudden jump to the final value in the P phase. We interpreted the motions observed in the P phase as normal modes arising from simultaneous reorientations of ZnCl₄ tetrahedra and corresponding Rb ions displacements between two sites. These normal modes freeze out in the I phase and change to the diffusionlike motion of the modulation wave. We also performed³⁵Cl NQR lineshape andT ₁ measurements in K₂ZnCl₄ and obtained conclusive evidence for the presence of a narrow 1q (singly modulated) I phase between 146 and 149 K.     

Solid-State Rb NMR Study in Powdered RbMnCl3

Structural phase transition at 290 K and the implication on the intermediate phase above 290 K in powdered RbMnCl₃ are observed by using a solid-state ⁸⁷Rb NMR spectroscopy. Quadrupole coupling constants (e²qQ/h), the asymmetry parameters (η), and the relative peak intensities for two physically nonequivalent Rb sites, Rb(I) and Rb(II), are determined from nonlinear least-squares fits to the ⁸⁷Rb NMR powder patterns in the temperature range from 260 to 330 K. Quadrupole coupling constants and the asymmetry parameters are examined for the detection of the phase transition resulting in a significant structural change in the Rb(II) site. In addition, changes in the relative peak intensity between the Rb(I) and Rb(II) sites seem to suggest the existence of an anomalous intermediate phase, which is complemented by the differential scanning calorimetry and X-ray diffraction studies.     

23Na nuclear magnetic resonance study of the phase transition in ammonium rochelle salt,NaNH4C4H4O6 • 4H2O

The satellite NMR spectrum of ²³Na in ammonium Rochelle salt (NaNH₄C₄H₄O₆ ? 4H₂O) is investigated near the transition temperature. Each line in the paraelectric phase splits discontinuously into four lines at the transition temperature; this fact is compatible with the first-order phase transition and reveals the existence of the superstructure in the ferroelectric phase.     

Electronic absorption spectrum of Cs<Subscript>2</Subscript>ZnI<Subscript>4</Subscript> thin films

The absorption spectrum of Cs₂ZnI₄ thin films in the energy range 3–6 eV at temperatures from 90 to 340 K has been investigated. It is established that this compound belongs to direct-gap insulators. Low-frequency exciton excitations are localized in ZnI₄ structural elements of the lattice. Phase transitions at 280 K (paraelectric phase ? incommensurate phase), 135 K (incommensurate phase ? monoclinic ferroelastic phase), and 96 K (monoclinic phase ? triclinic ferroelastic phase) have been found from the temperature dependences of the spectral position and halfwidth of the low-frequency exciton band. Additional broadening of the exciton band is observed for ferroelastic phases; it is likely to be due to exciton scattering from strain fluctuations near domain walls.     

Investigating the dielectric properties of potassium iodate polycrystals

Linear and nonlinear dielectric properties of KIO₃ polycrystalline samples are investigated. It is shown that linear dielectric permittivity ε' displays four anomalies corresponding to phase transitions in KIO₃. Anomalies of third-harmonic coefficient γ_3ω are observed at temperatures of 113, 263, and 345 K, corresponding to phase transitions between KIO₃ ferroelectric phases. It is established that the third-harmonic coefficient responsible for the nonlinearity of dielectric properties displays no anomalies during the transition to the paraelectric phase of KIO₃ at approximately 485 K. Possible reasons for there being no such anomaly are discussed.     

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)     

Kinetics of phase transitions in modulated ferroelectrics: Time-resolved neutron diffraction from Rb2ZnCl4

The kinetics of the ferroelectric phase transition between modulated phases in Rb₂ZnCl₄ at about 190K has been investigated by time-resolved neutron scattering. Observing the time dependence of satellite spectra, it is found that the structural changes associated with the field-induced transformation proceed on a millisecond time scale. Under the influence of fast cycling strong electric fields unusual non-equilibrium states are obtained which are modulated in space as well as in time and characterised by the presence of internal mechanical strains.     

EPR evidence for a weak first order behavior of the ferroelectric transition in (NH4)2SO4

EPR line-broadening effects have been analyzed for the low (∼ 10¹⁰ Hz) rotational fluctuations of NH₃ ⁺ radicals in (NH₄)₂SO₄ crystals near their ferroelectric transition. Critical fluctuations together with coexistence of the paraelectric and ferroelectric phases have been observed and interpreted in terms of a weak first order, Landau-type model for the phase transition.     

Pseudocritical NMR frequency shift above the normal-incommensurate phase transition

The NMR satellite frequencies were measured as a function of temperature in the normal high-temperature phase for ⁸⁷Rb in Rb₂ZnBr₄ and Rb₂ZnCl₄ and for ³⁵Cl in betaine calciumchloride dihydrate. Approaching the respective normal-incommensurate phase transition an anomalous shift of the NMR frequency is observed for the first two cases. This effect is ascribed to the increasing order parameter fluctuations. The experimental data are compared to calculations which relate the observed behaviour of the NMR frequencies to the non-classical critical behaviour of the substances under investigation. Received 6 August 1998     

The non-isotropic character of electric and dielectric properties of ammonium zinc chloride crystal

The dielectric constant, ε, and the d.c. conductivity, σ, were measured along the a-, b- and c-axes of (NH₄)₂ZnCl₄ (AZC) crystal in the 300-450 K temperature range. Crystals of AZC grown from aqueous solutions containing excess of ZnCl₂ were used. The value of the dielectric permittivity of AZC is extremely small compared to other ferroelectric crystals. Pronounced broad or step-like peaks at the phase transition temperatures were detected along the a- and b-axes, while ε along the c-axis is temperature independent up to the end of the measuring range. Reciprocal of the dielectric permittivity in the range of the commensurate to incommensurate phase transition obeys a relation similar to the Curie-Weiss law that is valid for second order ferroelectric/paraelectric phase transitions. The constants of the proposed relationship applied to the cooling run are given. The J-E characteristics along the three crystallographic axes were measured in the normal, incommensurate, commensurate and antiferroelectric phases. Hence, the type of conduction mechanism has been estimated. Parameters of Poole-Frenkel and Richardson-Schottky types of conduction mechanism have been determined. The effect of applied electric field on the conductivity measurement was also tested. Conductivity anomalies with different character were observed at the phase transition temperatures. The lnσ−1000/T dependence revealed thermal activation energy of conduction along the a-, b- and c-axes with different values in different phases of AZC.     

Anomalous states of the structure of (NH4)2SO4 crystals in the temperature range 4.2–300 K

Crystals of the (NH₄)₂SO₄ ammonium sulfate are studied using x-ray diffractometry. It is revealed that the temperature dependence of the lattice parameters exhibits an anomalous behavior, namely, a global hysteresis, and an anomalous increase in the lattice parameter a and the unit cell volume at temperatures below the ferroelectric phase transition point (T _c=223 K). The series of superstructure reflections observed corresponds to an incommensurate composite structure. Analysis of the temperature behavior of the mismatch parameters for the matrix (host) and superstructure (guest) lattices demonstrates that the (NH₄)₂SO₄ compound undergoes a number of phase transitions, including a transition to a three-dimensionally incommensurate composite phase and transitions to commensurate (along one of the crystallographic directions) composite phases.     

Soft modes and phonon interactions in studied by neutron scattering

The low frequency lattice dynamics and its relationship to the second order paraelectric-to-ferroelectric transition in Sn₂P₂S₆ is studied. The dispersion branches of the acoustic and lowest lying optical phonons in the a^*-c^* plane have been obtained in the ferroelectric phase, for x-polarized phonons. Close to the phase transition a considerable softening is found for the lowest optical mode (P_x), comparable to the behaviour observed in previous Raman investigations. As found previously in Sn₂P₂Se₆, a strong coupling between the TO(P_x) and TA(u_xz) phonons is observed, although, apparently, not strong enough to lead to an incommensurate phase. The soft TO(P_x) mode at the zone center is observed. The temperature dependence of its frequency and damping shows that the transition is not entirely displacive. At low temperatures an unusual apparent negative LO-TO splitting is observed which is shown to arise from the coupling of the x-polarized soft mode to the nearby z-polarized optical phonon. For comparison, the soft TO(P_x) dispersion in the a^*-b^* plane is measured in both the paraelectric and ferroelectric phases. Consistent frequency changes and LO-TO splitting are observed, revealing a significant interaction between the TA(u_yx) and LA(u_xx) acoustics branches and the TO and LO soft optic branches, respectively. In contrast, the nearby y-polarized optic branch shows almost no temperature dependence. Finally, the influence of piezoelectric effects on the limiting acoustic slopes in the ferroelectric phase is discussed. Received: 11 May 1998 / Revised and Accepted: 15 June 1998     

Study of phase transitions in the system A1B11PO4 with A1 = Li,Rb and B11 = Mg,Ca, Sr,Ba, Zn,Cd, Pb

The series of the title compounds were prepared by solid-state reactions. The phase transitions between room temperature and 1450 °C were investigated by DTA and X-ray diffraction. All compounds undergo at least one reversible phase transition in the solid state. The Rb containing compounds, with the exception of those with Cd and Zn, show no liquid phase up to 1450 °C. The phases formed crystallize with various structures which can be described partly as distorted olivine, LiKSO₄, CsZnPO₄ or glaserite. RbCdPO₄ shows an incommensurate structure with a one-dimensional modulation.     

Second harmonic generation in layered TunS2 in the vicinity of the low-temperature phase transitions

Second-harmonic generation in the ternary layered semiconductor TlInS₂ excited with the wavelength λ = 1.06 μm of YAG: Nd^{3 +} laser is investigated in the temperature range corresponding to the low-temperature phase transitions. It is shown that the intensity of the second-harmonic signal corresponding to the non-linear coefficients d_eff, d₂₁, d₂₂ reveals peculiarities close to the commensurate-incommensurate phase transitions. The temperature hysteresis of the second-harmonic signal in the low-temperature region (below and close to T_i2 = 206K) is explained assuming that an incomplete lock-in transition in TlInS₂ takes place at T_c1 =204K within the temperature range between a ferroelectric (T_c2 = 201K) and an incommensurate (T_i2 = 206 K) phases. It is shown that the monoclinic point group symmetry C₂ is preserved also at temperatures lower than the phase transition temperature Tc4 = 79K to a weak ferroelectric state.     

The thermodynamic functions of SbSBr crystal

Using density functional theory methods, the phonon density of states, Helmholtz free energy, internal energy, and entropy of ferroelectric and paraelectric phases are investigated. The temperature dependence of the free energy indicates that vibrational entropy contributes to the destabilization of the ferroelectric phase. The vibrational entropy of Sb, S, and Br atoms is attributed to the stabilization of ferroelectric SbSBr at the temperature T _c. Calculations indicated that SbSBr in ferroelectric phase become more stable than in paraelectric phase at temperatures lower than 22.8 K. The calculated temperature of ferroelectric phase transition is in good agreement with the experimental data.     

X-ray study of the phase transition in RbHSeO4

The ferroelectric phase transition in RbHSeO₄ has been examined by precise measurements of the temperature dependence of the unit-cell parameters using the Bond technique. The transition, at T_c = 370.6 K, is of first order and the triclinic unit cell of the ferroelectric phase transforms to an equitranslational monoclinic cell in the paraelectric phase. In a temperature region of several K below T_c reflections belonging to both phases have been observed.