39K NMR study of the low temperature phase transitions in KLiSO4

The³⁹K NMR spectra, spin-spin (T ₂) and spin-lattice (T ₁) relaxation times of KLiSO₄ have been measured in the temperature range from 300 K to 90 K. The temperature dependence of the³⁹K (I=3/2) NMR spectra demonstrates the occurrence of a first order phase transition atT _c1=217 K which occurs without a change in the K⁺ site symmetry and another first order transition atT _c2=190 K which is connected with a lowering of the K⁺ site symmetry and the formation of three kinds of ferroelastic domains. From the angular dependence of the second order quadrupole shifts of the³⁹K NMR 1/2–1/2 transitions the electric-field gradient (EFG) tensors at the potassium sites were determined at 290 K, 204 K and 180 K. The symmetry of the ferroelastic phase is monoclinic and not orthorhombic as the K⁺ EFG tensors are tilted away from thec-axis belowT _c2. TheT ₁ data further show the freezing in of the slow reorientational motion 10^–8 s with decreasing temperature from 300 to 90 K.On leave from: J. Stefan Institute, E. Kardelj University of Ljubljana, Ljubljana, Yugoslavia     

Applications of optical activity to studies of phase transitions

This article reviews at an introductory level the physics of optical activity and its recent applications to studies of phase transitions of ferroelectrics. Optical activity is a kind of internal perturbation of the refractive index, and accordingly induces a resonating effect on the eigenstates of the susceptibility. This is the reason why optical activity provides us with unreplaceable information concerning the chirality of the structure and specific bonding nature of constituent atoms. The principles of our high accuracy universal polarimeter (defined as HAUP) method are described, which realized for the first time simultaneous measurements of birefringence, optical activity, and rotation angles of the indicatrices of any crystals, even those belonging to monoclinic and triclinic systems. The utility of the HAUP method is exemplified by our recent experiments. The origin of the occurrence of incommensurate states in some A₂BX₄ crystals was theoretically explained from the fact that they showed optical activity. It is of particular interest that the origin is also resonance of eigenstates of the dynamical matrix. The merits of the HAUP method have been extended to the evaluation of the soliton density in the incommensurate phase, discrimination of the twin mechanism of the ferroelectric domains, and search for the origin of ferroelectricity of Rochelle salt.     

Elastic studies of phase transitions

We report some results on acoustic studies of phase transitions in which the order parameter is coupled to the elastic wave strain, when direct behaviour observation is not possible. First by Brillouin scattering it was possible to observe the softening of C₅₅ of ammonium oxalate hemihydrate and it was concluded that the order parameter is not the deformation. In the case of members of A₂MX₄ family a softening of C₆₆ related to a shear wave near the lock-in transition was observed for [N(CH₃)₄]₂ZnCl₄, as previously found for C ₅₅ of K₂SeO₄. Such a behaviour did not occur for (NH₄)₂BeF₄ in which a strong hysteresis effect appeared.     

Crystal imperfections and structural phase transitions in perovskites

High‐resolution X-ray scattering measurements of the antiferrodistortive phase transitions in the perovskites SrTiO₃, RbCaF₃ and KMnF₃ have recently revealed the existence of two length scales in the critical scattering above T_e . Here we review these observations and discuss how they might be related to the well known existence of two time scales (the "central peak" problem) in the critical dynamic response function above T_e . We reach the tentative conclusion that within a few degrees of T_e both the time and length scales of the fluctuations are strongly influenced by defects and that the intrinsic critical behaviour is swamped by these effects in most crystals.     

Crystal field parameters and phase transitions in ErSb

The crystal field levels of the Er ($\text{J =}\text{15}\text{2}$) ion in a single crystal of ErSb have been measured by inelastic neutron scattering. The crystal field parameters obtained by a least squares fit to the spectra at several temperatures are: B₄ = (0·473 ± 0·005) × 10^?2°K and B₆ = (0·59 ± 0·06) × 10^?5°K, which differ considerably from the values o by interpolation from measurements on other compounds. In addition the temperature dependence of the magnetic scattering in the vicinity of the Néel temperature (T_N = 3·55°K) clearly demonstrates that the transition is second order in contrast to the first order behavior suggested by specific heat measurements. Also, any lattice distortion accompanying the magnetic ordering is less than 0.1 per cent, the resolution of the present experiment.     

Ultrasonic studies of phase transitions in stage-4 antimony pentachloride intercalated graphite

The c-axis shear elastic constant C₄₄ and transverse sound attenuation α_T for stage-4 SbCl₅ intercalated graphite from 4 to 300 K are studied with ultrasonic pulse-echo techniques. No transverse sound echo is observable above 230 K. At constant temperatures between 230 and 200 K, both C₄₄ and α_T drift spontaneously toward lower bounds over a period of hours. A decrease in C₄₄ by a factor of ～ 2 is observed. Below 195 K, the sample becomes metastable. From 195 to 4 K, C₄₄ increases by 60% for the quenched sample, and by 30% for the annealed sample. This abnormal behavior of the elastic property can be interpreted by a disordered-liquid to incommensurate-solid phase transition of the intercalant layer at 230 K. The time-dependence of C₄₄ and α_T is attributed to the growth of islands with a slightly incommensurate solid structure.     

Optical studies of the ferroelastic phase transitions in KFe(MoO4)2

ABSTRACT

The ferroelastic phase transitions in KFe(MoO₄)₂ have been studied by means of polarized light microscopy. The crystal undergoes a sequence of ferroelastic phase transitions. It has been found that the second transition consists of two transitions separated by the temperature interval of about 0.4 K. Both these transitions are of the first order and are evidenced through a phase front passing, without the domain structure rebuilding. The disposition of optical indicatrix axes n_g, n_m has been established, and the birefringence has been measured in the plane (0001) in the temperature range covering all ferroelastic phases. From temperature studies of the morphic birefringence, a critical exponent of the order parameter has been estimated.     

Magnetostriction studies of magnetic phase transitions in the copper metaborate CuB2O4

The field dependences of the longitudinal and transversal magnetostriction of the copper metaborate CuB₂O₄ were measured at various temperatures below the Néel point in magnetic fields directed along the tetragonal axis or in the basal plane. Magnetostriction was found to exhibit jumps at magnetic-field-induced phase transitions to a commensurate weak ferromagnetic state, as well as to grow smoothly in fields above and below the critical level. The magnetostriction observed in a magnetic field directed along the tetragonal axis is shown to be primarily caused by volume dilatation of the crystal. The experimental data obtained were used to construct the magnetic phase diagram of copper metaborate magnetized along the tetragonal axis.     

NMR-NQR studies of structural phase transitions

Moving dislocations in II–VI semiconductors carry a large electric charge. This charge is not in thermal equilibrium, but is due to the sweeping up of electrons from point defects. Its movement produces a dislocation current during plastic deformation, and conversely, the application of an external field changes the flow stress. This paper reviews the structure and properties of these dislocations, the theory of their charge and the phenomena which are a consequence of the strong mutual interactions of the dislocation and electronic sub-systems in these crystals. The materials show a large photoplastic effect (a change in flow stress under illumination), and related effects due to the injection of electrons at an electrode. Deformation produces reversible changes in the conductivity, pulsed and continuous luminescence and the emission of electrons from the surface.     

One-dimensional phase transitions in a two-dimensional optical lattice

A phase transition for bosonic atoms in a two-dimensional anisotropic optical lattice is considered. If the tunnelling rates in two directions are different, the system can undergo a transition between a two-dimensional superfluid and a one-dimensional Mott insulating array of strongly coupled tubes. The connection to other lattice models is exploited in order to better understand the phase transition. Critical properties are obtained using quantum Monte Carlo calculations. These critical properties are related to correlation properties of the bosons and a criterion for commensurate filling is established.     

Low temperature Raman spectra of KLiSO4

Raman experiments have been performed on KLiSO₄ below room temperature. In the intermediate temperature range (190 K < T < 265 K), the spectra are better understood on the basis of the C₃ rather than C₆ point group, but a lower symmetry cannot be rejected. In the low temperature region (T < 190 K) the occurrence of three ferroelastic domains should be taken into account to explain the corresponding Raman spectra.     

High-pressure neutron diffraction studies of KH2PO4-type phase transitions

Abstract

High-pressure neutron-diffraction studies have been carried out on KH₂PO₄, KD₂PO₄, H₂C₄O₄ and PbHPO₄, using single-crystal samples. The results show that changes in the H-ordering temperature, T_C, with pressure (or deuteration) in these systems can be largely attributed to the variation of the H-site separation, δ, with pressure (or deuteration).     

Thermodynamic studies of successive phase transitions in BaZnGeO4 and a new solid phase below 186.1 K

The successive phase transitions of BaZnGeO₄ have been studied on meltsolidified samples. A new solid phase (named phase VI) has been found below 186.1 K in samples of large particle size (diameter:D0.1 mm). The higher temperature crystalline phase V can be supercooled easily down to liquid helium temperature. On heating, however, it transforms into phase VI above 95 K in a slow exothermic process. Heat capacities have been measured by adiabatic calorimetry between 14 and 300 K. The enthalpy and entropy of the V–VI phase transition are 187.1 Jmol^–1 and 0.971 J K^–1 mol^–1, respectively. The corresponding data for the IV–V phase transition at 199.8 K are 229.3 J mol^–1 and 1.168 JK^–1 mol^–1. The phase VI does not appear in samples of smaller particle size (D0.1 mm).     

Optical study of the phase transitions in LiKSO4

The birefringence of LiKSO₄ has been measured over the range 27–700°C. The change in birefringence with heating and cooling is seen to be very different. Observations have been made on domains in (001) and (100) plates near the phase transitions.     

Crystal geometry and phenomenological models of reconstructive phase transitions

The basic concepts of the phenomenological theory of reconstructive phase transitions are presented. The nonlinear order parameter concept is introduced and the connection between the classical form of the Landau theory and a density wave approach to phase transitions is given. This new phenomenological approach is applied both to standard examples of reconstructive phase transformations (BCC-HCP, BCC-FCC, HCP-FCC, BCC-w) and to new problems like the formation of quasicrystals.     

Computer simulation studies of magnetic phase transitions

The advancements which have been made in the use of computer simulations to study magnetic-phase transitions and critical phenomena are reviewed. We describe how the use of a combination of sophisticated Monte Carlo simulation algorithms and reweighting (histogram) techniques have allowed the determination of the static critical behavior with unprecedented precision. The study of “dynamic” critical behavior in simple spin models by both Monte Carlo and spin dynamics methods is also reviewed. Recent estimates for dynamic critical exponents are given including those for true dynamics.     

On the theory of vapor — Liquid — Crystal phase transitions

An approach is discussed which allows one to describe within the framework of the single model the aggregative states of a system of atoms obeying the Fermi statistics. A phase diagram is obtained containing both the critical point where the distinctions between the liquid and vapor vanish and the triple point where the liquid, vapor, and crystal are in equilibrium.     

Structural phase transitions of vortex matter in an optical lattice

We consider the vortex structure of a rapidly rotating trapped atomic Bose-Einstein condensate in the presence of a corotating periodic optical lattice potential. We observe a rich variety of structural phases which reflect the interplay of the vortex-vortex and vortex-lattice interactions. The lattice structure is very sensitive to the ratio of vortices to pinning sites and we observe structural phase transitions and domain formation as this ratio is varied.     

Light scattering studies of phase transitions of (NH4)2SO4-type crystals

The mechanism of the ferroelectric transition of pure and rubidium-doped ammonium sulfate is investigated by means of Raman, Brillouin and dielectric measurements. The study contributes to spectroscopic evidences of temperature anomalies of lattice vibrations in the paraelectric and ferroelectric range. The different behaviour of rubidium-doped crystals with respect to their dielectric and elastic properties at the transition is interpreted as an indication that different order parameters might become active in this first order transformation.