Axial crystals – macroscopic symmetry and tensor properties

ABSTRACT

Axial crystals have axial symmetry which keeps invariant straight line with a fixed point. Axial symmetry groups include 27 non-cubic crystallographic point groups and 5 limit groups describing symmetry of textures and liquid crystals. We show that, except for four cases, each axial symmetry belongs to one of five axial types: polar, chiral, pseudopolar (three basic axial types), directional (possessing none of characteristic properties of basic types) or rotational (exhibiting characteristic properties of all basic types). Each basic type can appear in two structurally different variants with the same symmetry. These variants can coexist and form a mesoscopic structure (antiparallel ferroelectric or chiral domain structure, mixture of enantiomers). We examine macroscopic properties of axial types and variants, and experimental accessivity of their characteristic features.     

Domain structure of triglycine sulfate family crystals according to the data of piezoresponse force microscopy and their macroscopic dielectric properties

The domain structure of triglycine sulfate (TGS) crystals, specifically nominally pure crystals and those with impurities (LADTGS+ADP, DTSG, and TGS:Cr), is studied by piezoresponse force microscopy (PFM). The measured macroscopic dielectric characteristics are compared with microscopic data on the domain structure of these crystals. The values of the spontaneous polarization, bias voltage, and dielectric permeability as a function of temperature ?(T) are shown to be in agreement with the PFM data. The anomalous behavior of the dependence ?(T) was observed for LADTGS+ADP crystals.     

Electric quadrupole interactions measured by nuclear orientation and NMR on oriented nuclei

A review is given of the situations in which low temperature nuclear orientation and NMR of oriented nuclei have been applied in recent years to the measurement of electric quadrupole interactions in metals and in dielectric crystals. The review is concerned with the variety of methods by which quadrupole interactions have been measured. Illustrative examples are given for each technique, but no attempt is made to give a full bibliography of work. As regards nuclear orientation, pure quadrupole algnment is discussed (although in non-cubic metals rather than in dielectric crystals), followed by outlines of work on mixed magnetic dipole and electric quadrupole hfi when these interactions are (a) co-axial and (b) mutually perpendicular. The sensitivity of nuclear orientation to small quadrupole interactions is shown to be improved in the second case.For NMR on oriented nuclei the review centres upon the small quadrupole effects detected in dilute ferromagnetic alloys both by direct observation of resonance line structure and by interpretation of signals following adiabatic fast passage.Republished from the XVIIth Winter School on Physics (Hyperfine Interactions) held from February 19-March 3, 1979 in Bielsko Biala (Poland), with the kind permission of the Editors.     

Acoustic properties of glycine phosphite crystals with an admixture of glycine phosphate

Acoustic and dielectric anomalies in the region of the ferroelectric phase transition in crystals of glycine phosphite (GPI) with a 2 mol % admixture of glycine phosphate (GP) are studied. The acoustic anomalies were found to differ strongly from those observed in nominally pure glycine phosphite crystals. A theoretical analysis of the acoustic and dielectric properties of the crystals was carried out within the model of a pseudoproper ferroelectric phase transition. It is shown that the acoustic anomalies, as well as the temperature dependences of the dielectric constant (for various external electric fields) and pyroelectric current observed in the vicinity of the phase transition in GPI-GP crystals, can be adequately described when the macroscopic polarization present in these crystals above the phase transition temperature is taken into account. The thermodynamic-potential parameters describing electrostriction and the biquadratic relation between the polarization and strain turned out to be close to those characterizing a nominally pure GPI crystal. An irreversible phase transition was observed to occur in GPI-GP crystals at T = 240 K, i.e., above the ferroelectric phase transition temperature.     

Effective charges in binary and ternary oxide compounds

Effective charges in non-cubic binary oxide crystals are evaluated on the basis of their transverse and longitudinal optical phonon frequencies. The temperature dependence of the effective charge is reported in quartz, rutile and corundum. Three procedures which allow the determination of effective charges in ternary compounds are presented and applied to halogenate, silicate, aluminate and ABO_n-type crystals, where A is an alkali or alkaline earth and B is a transition-metal element. Results are compared with Phillips's ionicities.     

Rozhdestvenski hooks in two-photon parametric light scattering

The interference of spontaneous parametric radiation was observed from two nonlinear crystals separated by a macroscopic layer of a linear substance and excited by a common pump beam. In the presence of strong dielectric dispersion in the layer, the frequency-angular spectra display features analogous to the Rozhdestvenski hooks. The hook wavelength corresponds to the compensation of group velocity dispersions in the nonlinear crystals and the layer.     

Evidence for non-cubic magnetostriction in epitaxial bubble garnets

Epitaxial bubble garnet films grown on non-magnetic garnet substrates exhibit a dominant growth or stress induced uniaxial anisotropy, which is responsible for the stripe and bubble domain structures, and the intrinsic cubic magnetocrystalline anisotropy which can affect bubble device performance. The anisotropy constants have been deduced from measurements of stripe domain nucleation in the garnet films. We extend this measurement technique and its interpretation so that it also yields values of the magnetoelastic interactions.The measurement is based on observing the details of the topography of the nucleating domain structure, specifically the orientation of the nucleating stripe domains as a function of the orientation and magnitude of the applied magnetic field.The interpretation is based on a micromagnetic analysis of the conditions for homogeneous second order stripe domain nucleation. The contributions to the phenomena of the cubic anisotropy and of the magnetostriction are included in the analysis as perturbations.The theory produces predictions which are compatible with qualitative earlier experiments reported in the literature. It provides a satisfactory quantitative account of systematic new observations we have made on a GdTmY bubble garnet film with the specific objective of measuring magnetostriction.Analysis of the experimental data yields strong evidence for a non-cubic component of the magnetostriction possibly associated with the same growth-kinetic mechanism that gives rise to the non-cubic anisotropy. The sign and magnitude of the macroscopic non-cubic magnetoelastic constant is estimated from the experimental results.     

Optical Bloch oscillation and resonant Zener tunneling in one-dimensional quasi-period structures containing single negative materials

We studied the optical Bloch oscillation and resonant Zener tunneling in macroscopic quasi-period structures of alternatively stratified single negative and dielectric slabs. By a decrease in the thicknesses of the dielectric slabs, the electronic potential of crystals subjected to external dc electric fields is mimicked and the optical Wannier-Stark ladder (WSL) is realized. Both scattering states and the time-resolved transmission of a short pulse are provided to show the existence of the optical analogue of electronic Bloch oscillation. At a critical gradient, the resonant photon Zener tunneling is demonstrated both from the amplitude and the time delay in the transmitted signal of a short pulse.     

Effects of spin ordering on phonon and plasmon spectra,and dielectric properties in magnetic semiconductors

Effects of spin ordering on the phonons, plasmons, and dielectric properties have been investigated for many magnetic crystals, such as Cr-spinels, EuX (X = O, S, Se, Te), and fluorite-type compounds. Of these phenomena, the static dielectric constant and Raman scattering have been extensively discussed. However, the dielectric parameters obtained from infrared spectra have not been discussed in spite of observed various phenomena arising from the direct coupling of spin system with phonons or electrons. Furthermore, these microscopic phenomena can be combined with the macroscopic dielectric values with respect to the spin ordering effect. It will ascertain the mechanism of the spin ordering effect on the values. From this point of view, we review the spin-dependent phenomena on the frequencies of TO and LO phonon modes, phonon damping, optical and static dielectric constants, effective charge, and also on plasmon parameters in the spinel type magnetic semiconductors.     

Orientation dependence of the interfacial energies of chromium and α-iron crystals at boundaries with nonpolar organic liquids

Interfacial energies of chromium and α-iron at boundaries with nonpolar organic liquids are calculated within the modified variant of the statistical electron method. Calculations are performed with allowance for dispersion, oscillatory, polarization corrections and the contribution from temperature. The dependence of the interfacial energy on the orientation of metallic crystals, and on the macroscopic dielectric permeability of the organic liquid, is established. The profiles of the potential and electron density at the boundary of the phase separation are considered.     

Infrared and ESR spectroscopy of KTaO3 : Er

Infrared reflection and ESR spectra of KTaO₃ : Er³⁺ single crystals have been investigated. The frequency of the lowest optical phonon mode TO₁ has been found to increase as compared to undoped KTaO₃ crystals, which indicates the suppression of the ferroelectric instability of the system. The ESR spectra have revealed the presence of two Er³⁺ centers of different (cubic and non-cubic) symmetries in KTaO₃ : Er³⁺.     

Phases and phase transitions of (NaCl)1−x(NaCN)x

(NaCl)_1–x(NaCN)_x mixed crystals with CN-concentrationsx of 0.87, 0.76, 0.71 and 0.65 have been investigated by X-ray powder diffraction. Apart from the cubic room temperature phase, a rhombohedral and an orthorhombic phase have been identified. In addition a glass state has been observed which is characterized by a strong broadening of the cubic powder lines. The phase diagram shows a wide coexistence gap between the non-cubic phases and the glass state.     

Macroscopic quadrupole moment of dielectric solids with structural phase transitions

The macroscopic quadrupole moment is the main electronic characteristic of structural transformations between nonpolar states of dielectric solids. Several experimental methods are suggested for measuring the different components of the quadrupole moment tensor as a function of external actions. We describe the observation of quadrupole pyro-and piezoelectric, inverse piezoelectric, and electrooptic effects in centrosymmetric crystals without phase transitions, some quadrupole effects in the regions of ferroelastic and nonferroelastic phase transitions, and effects arising due to plastic deformation. The influence of defects on the quadrupole moment of real crystals is considered. Special attention is paid to the observation and study of the anomalously large quadrupole effects related to a frozen polarization wave in incommensurate phases of ferroelectrics. The experimental and theoretical data published up to 1984 are reviewed and some new results are presented.     

Low frequency dielectric relaxation in lightly doped VO2 single crystals

The relative effects of intrinsic and extrinsic defects on the dielectric relaxation of VO₂ crystals have been investigated by measurement of the dielectric parameters of undoped crystals and crystals doped with Ti, Cr and Al. Measurements have been made in the temperature range 77–250 K and the frequency range 50–100 kHz. The dielectric data is described by a Cole-Cole distribution function with a distribution parameter α ? 0.45 which decreases with increasing temperature. However, the distribution of activation energies g(E) derived from α is almost independent of temperature. The overall dielectric relaxation behaviour is determined primarily by the intrinsic defect structure of VO₂, and the effect of impurities is observed only in changes in the low frequency limiting (static) value of the dielectric constant. The same transport mechanism is found to determine the dc conductivity and the dielectric relaxation and evidence is presented that the dielectric relaxation is of dipolar origin.     

Expansion of the Madelung parameter in terms of multipole moments and as a function of the ratio of two lattice parameters

A method is derived to expand the Madelung parameters of non-cubic crystals as a function of the ratio of two lattice parameters and in terms of multipole moments. Only one expansion of this kind is necessary to evaluate the Madelung constants for a series of compounds of one type of structure either containing polyatomic ions or spherical ions at positions slightly varying from one compound to the other. This method also allows the minimisation of the lattice energy with respect to one particular lattice parameter, leaving invariant all internal distances in the polyatomic ions.     

Microwave dielectric tangent losses in KDP and DKDP crystals

By adding cubic and quartic phonon anharmonic interactions in the pseudospin lattice coupled mode (PLCM) model for KDP-type crystals and using double-time temperature dependent Green's function method, expressions for soft mode frequency, dielectric constant and dielectric tangent loss are obtained. Using model parameters given by Ganguliet al [9] the dielectric losses are calculated for KDP and DKDP crystals. In the microwave frequency range an increase in frequency (1–35 GHz) is followed by an increase in dielectric tangent loss (1–35) at 98 K and (1–15) × 10⁻² at 333 K for KDP and DKDP crystals respectively. The dielectric tangent loss decreases from 0.052 to 0.042 for KDP crystals with increase in temperature from 130 to 170 K and for DKDP crystals it decreases from 0.0166 to 0.0074 with an increase in temperature from 230–343 K in their paraelectric phases at 10 GHz. This shows Curie-Weiss behavior of the dielectric tangent loss     

Temperature dependence of dielectric constant of crystals with fluorite structure

The experimental data on the temperature variation of dielectric constant of six crystals with fluorite structure are analysed using an approach proposed by Havinga and Bosman for ionic crystals. The temperature variation of dielectric constant is resolved in three components related to the thermal expansion, the pressure dependence of dielectric constant and the temperature variation of polarizability (theA, B, C terms). In the present work, theB term is calculated semiempirically, such that the analysis can be extended to crystals like EuF₂ for which high pressure dielectric constant data are not available. For the first time, such calculations have been made for EuF₂ and PbF₂ at elevated temperatures. TheC term, which is related to the temperature variation ofir polarizability is seen to play a dominant role in determining the temperature variation of dielectric constant.     

Application of finite strain theory to non-cubic crystals

The application of finite strain theory to a crystal of orthorhombic or higher elastic symmetry, which is subjected to a purely extensional deformation parallel to the crystallographic axes, yields stress-strain relations and effective elastic constants for hydrostatic stresses. Alternative formulations of the theory are obtained when the free energy is written as Taylor series in E, the invariant analogue of the Eulerian strain tensor, or η, the Lagrangian strain tensor. In most cases, the formulation in terms of E provides a better approximation when the Taylor series are truncated at the second or third order. In the case of cubic crystals, the stress-strain relations reduce to the Birch equation. For non-cubic crystals, the P-V relations calculated using the non-cubic and Birch equations will differ due to the effects of elastic anisotropy. A comparison between the second-order approximations of the non-cubic stress-strain relations and the cubic Birch equation suggests that the difference in volume will be less than 1% for most materials. The difference in volume is reduced when the third-order approximations are used. When the third-order terms are retained, the stress-strain relations calculated using the Eulerian formulation agree with measured linear compression data for quartz to 150 kbar $\text{(}\text{P}\text{K}{}_0\text{= 0.4).}$ For zinc, the calculated pressure-volume relation agrees with the shock-wave Hugoniot up to 750 kbar $\text{(}\text{P}\text{K}{}_0\text{= 1.2),}$ although both calculated and Hugoniot P-V relations disagree with X-ray compression data. At pressures greater than 300 kbar, the calculated axial ratio of zinc approaches that for other hexagonal metals $\text{(}\text{c}\text{a}\text{? 1.63).}$     

Growth,structural, mechanical,spectral and dielectric characterization of NaCl-added Triglycine sulfate single crystals

Pure and sodium chloride (NaCl)-added Triglycine sulfate (TGS) crystals were grown from aqueous solutions by slow evaporation technique. The values of concentration of dopants in the mother solution were 0.2, 0.6 and 1 mol%. The solubility of the grown samples have been found out at various temperatures. The determination of unit cell parameters was carried out by single crystal XRD method and found that the grown crystals crystallize in monoclinic structure. The dielectric characterization for the pure and NaCl-doped TGS crystals was performed by measuring the dielectric parameters like dielectric constant and dielectric loss with various frequencies in the range 10²–10⁶ Hz and with the temperatures ranging from 30 to 70 °C and this study reveals an increase of dielectric constant and loss with the increase of NaCl concentration. Studies on mechanical properties like microhardness and density of the grown pure and NaCl-doped TGS crystals were carried out. UV–Visible transmittance studies were carried out for the grown samples. A sharp fall in the transmittance is observed at 228 nm for pure and NaCl-doped TGS crystals. Atomic absorption spectroscopic (AAS) study was done on the NaCl-doped TGS crystals to ascertain the presence of Na⁺ ions in the lattice.     

Decomposition of the total momentum in a linear dielectric into field and matter components

The long-standing resolution of the Abraham–Minkowski electromagnetic momentum controversy is predicated on a decomposition of the total momentum of a closed continuum electrodynamic system into separate field and matter components. Using a microscopic model of a simple linear dielectric, we derive Lagrangian equations of motion for the electric dipoles and show that the dielectric can be treated as a collection of stationary simple harmonic oscillators that are driven by the electric field and produce a polarization field in response. The macroscopic energy and momentum are defined in terms of the electric, magnetic, and polarization fields that travel through the dielectric together as a pulse of electromagnetic radiation. We conclude that both the macroscopic total energy and the macroscopic total momentum are entirely electromagnetic in nature for a simple linear dielectric in the absence of significant reflections.