On the satellite extinction in incommensurate phase

For ZnP₂ and CdP₂ crystals in incommensurate phase selective superstructure X-ray reflections are observed. As shown a phason and amplitudon excitation modes do not result in this selective extinction of satellites. Apparently, it is associated with a modulation wave form in the incommensurate phase. The X-ray spectrum peculiarity of incommensurate crystals is discussed taking into consideration systematic and selective extinction of satellites.     

The relaxation of the structure of RADP in an electric field

X-ray scattering measurements have been made to study the behaviour of the ferroelectric glass of Rb_1–x(NH₄)_xH₂PO₄ withx0.22 in the presence of an electric field. The results showed that the system has very long relaxation times, characteristic of competing interactions. The change in the intensity of the x-ray scattering from the incommensurate modulation and the ferroelectric phase have a roughly linear relationship with time.     

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.     

Second Harmonic Generation in TlInS2 Crystals

The temperature dependence of the generation of the second optical harmonic in TlInS₂ crystals in the vicinity of the phase transitions high–temperature–incommensurate–polar phases is investigated. It is shown that radiation in the incommensurate phase occurs only when the fundamental wave propagates along the axis of the superstructure of a crystal and the presence of radiation for certain geometries of the experiment confirms the symmetry group C ₂ ³ of the low–temperature polar phase. The dependence of the spectra on the periodic temperature change is attributed to the occurrence of long–lived metastable states.     

Far infrared and millimetre dielectric response of incommensurate and ferroelectric K2SeO4

Dielectric response of K₂SeO₄ in the spectral region 5–460cm^–1 was determined using transmissivity and reflectivity measurements as a function of temperature between 80 and 300K. The spectral features above 20cm^–1 are interpreted using results of lattice vibrational analysis in three known commensurate phases. The low-frequency dielectric anomaly in the incommensurate phase can be roughly described by critical slowing-down of a Debye relaxation given rise to by the overdamped infrared active phason mode which softens at the incommensurate-commensurate transition.     

Model of periodic superstructure formation induced by mobile defects on a semiconductor surface

A model for forming a periodic superstructure on a semiconductor surface with mobile defects is proposed. It is shown that a self-organized system of such defects could lead to considerable modulation of incommensurate phase parameters in near-surface layers under the conditions of defect interaction with an incommensurate displacement wave. This type of defect system could induce a substantial energy decrease for the incommensurate phase and its additional stabilization on the one hand, and an increase in modulation amplitude that might be accompanied by a soliton-like nonsinusoidal incommensurate displacement wave on the other. The model allows us to explain the experimental results regarding the periodic superstructure discovered by G.V. Benemanskaya et al. on the surface of a GaN semiconductor. In particular, the model enables us to explain the nature of such superstructures based on the self-organization of mobile neutral triad-type defects, composed of negatively charged (3−) vacancies of the host lattice centers of Ga³⁺ and surface impurity ions of Cs⁺ and Ba²⁺, under conditions of triad interaction with an incommensurate displacement wave.     

EPR lineshape study of the incommensurate phase in γ-irradiated K2SeO4

The temperature dependence of the SeO^4-₄ EPR frequencies and the asymmetric broadening of the EPR lines in the incommensurate phase of K₂SeO₄ can be explained by an incommensurate spatial modulation of the g tensors which corresponds to the “broad” phase soliton limit. A comparison between the experimental and calculated lineshape shows a ≈1% volume fraction of commensurate regions in the middle of the incommensurate phase at 110 K.     

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.     

Nonlinear phenomena in A2MX4 type crystals with incommensurate phases

Investigations of the nonlinear phenomena in A₂MX₄ type crystals (A, organic cation or alkaline metal ion; M, metal ion; X, halogen ion) with incommensurate phases are very interesting from both a scientific and a practical point of view. In the crystals many interesting nonlinear phenomena are observed, e.g., thermal hysteresis of birefringence and absorption coefficient, piezooptic effect, electrooptic effect. Different anomalies (e.g., a discontinuity or change of sign of the briefringence coefficient, a distinct increase of the value of piezooptic and electrooptic coefficients) exist in the phase transition regions. They are especially distinct for a transition from the incommensurate phase to the commensurate phase. Some possibilities of detection and recognition of the existence of incommensurate phases by optical methods are suggested.     

High-pressure polymorphic transformation of rutile to alpha-PbO2-type TiO2 at {011}R twin boundaries

The presence of nano-scale lamellae of the α-PbO₂-type polymorph of TiO₂ sandwiched between twinned rutile inclusions in jadeite has been confirmed by electron diffraction and high-resolution transmission electron microscopy, backed up by image simulation techniques, from ultrahigh-pressure jadeite quartzite at Shuanghe in the Dabie Mountains, China. The crystal structure is orthorhombic with lattice parameters a = 4.58 Å, b = 5.42 Å, c = 5.02 Å and space group Pbcn. A three-dimensional structural model has been constructed for the rutile to α-PbO₂-type TiO₂ phase transformation based on high-resolution electron microscopic images. Computer image simulation and structural model analysis reveal that rutile {0 1 1}_R twin interface is a basic structural unit of α-PbO₂-type TiO₂. Nucleation of α-PbO₂-type TiO₂ lamellae 1–2 nm thick is caused by the displacement of one half of the titanium cations within the {0 1 1}_R twin slab. This displacement reduces the Ti–O–Ti distance and is favored by high pressure.