Dielectric Lattice Research Articles

Relaxor properties of compositionally disordered perovskites: Ba- and Bi-substitutedPb(Zr1−xTix)O3

Dielectric spectroscopy, lattice structure, and thermal properties have revealed the relaxor dielectric response of Ba-substituted lead zirconate/titanate (PZT) having the composition $({\mathrm{Pb}}_{0.71}{\mathrm{Ba}}_{0.29})$ $({\mathrm{Zr}}_{0.71}{\mathrm{Ti}}_{0.29}){\mathrm{O}}_{3}$ and containing $2\phantom{\rule{0.3em}{0ex}}\mathrm{at.}\phantom{\rule{0.2em}{0ex}}%$ Bi as an additive. The relaxor behavior is attributed to the compositional disorder introduced by the substitution of ${\mathrm{Ba}}^{2+}$ at the A site and ${\mathrm{Bi}}^{3+∕5+}$ at the B site (and possibly A site) of the $\mathrm{AB}{\mathrm{O}}_{3}$ PZT host lattice. Analysis of the results gives clear evidence for the nucleation of polar nanodomains at a temperature much higher than the peak $({T}_{m})$ in the dielectric susceptibility. These nanodomains grow in size as their correlation length increases with decreasing temperature, and ultimately their dipolar fluctuations slow down below ${T}_{m}$ leading to the formation of the relaxor state. The influences of hydrostatic pressure on the dielectric susceptibility and the dynamics of the relaxation of the polar nanodomains were investigated and can be understood in terms of the decrease in the size of the nanodomains with pressure. The influence of dc electrical bias on the susceptibility was also investigated. Physical models of the relaxor response of this material are discussed.

Dielectric Properties and Lattice Distortion in Rhombohedral Phase Region and Phase Coexistence Region of PZT Ceramics

In this paper, the relation between the dielectric properties and thelattice distortion in the phase coexistence region is discussed using a phasestatistical distribution model, and in the rhombohedral phase region the two connectionequations on the dielectric properties and the lattice distortion areestablished. Particularly, the relation between the dielectric propertiesand the lattice distortion is investigated in the phase coexistence regionof PZT ceramics, and the fitting value of the volume fraction ofthe tetragonal phase VT to composition x in the equation is determined.Further, the fitting results are well consistent with the relatedexperimental data. It involves more profound physical process thanrelation between the dielectric properties and composition x.

Densification Behavior and Electrical Properties of K3Li2(Nb1 - xTax)5O15 Ceramics

Tetragonal tungsten bronze structured K3Li2(Nb1 - xTax)5O15(KLNT) (0.0≤x≤1.0) ceramics was synthesized by the solid state reaction method. The sintering behavior, phase development and dielectric characteristics of KLNT ceramics as a function of x (Nb/Ta ratio) were examined. When the content of Ta increased the temperature where the highest sintered density obtained increased. More Ta increased the degree of ionic character in the KLNT ceramics which enabled a formation of KLT single phase, even though KLN single phase was not obtained. On the basis of dielectric analysis and lattice parameter it was found that a morphotropic phase boundary (MPB) region exists around x = 0.4.

Silica photonic crystals: synthesis and optical properties

Dielectric crystal-like lattices, termed photonic crystals, attract growing interest due to their unique and useful optical properties. Natural and artificial opals composed of three-dimensional (3D)-ordered lattices of submicron silica microspheres are highly interesting model objects for the study of photonic crystals. Synthetic opals based on monodisperse 270-nm-diameter silica microspheres were obtained. Optical measurements demonstrated the presence of different optical pseudogaps appeared due to reflection from different planes in the face-centered cubic (fcc) structure of opal; the positions of pseudogaps were estimated using the modified Bragg law.

Three-dimensional magnetophotonic crystals based on artificial opals

We fabricated and experimentally investigated three-dimensional magnetophotonic crystals (3D MPCs) based on artificial opals. Opal samples with three-dimensional dielectric lattices were impregnated with different types of magnetic material. Magnetic and structural properties of 3D MPCs were studied by field emission scanning electron microscopy, x-ray diffraction analysis, and vibrating sample magnetometer. We have shown that magnetic materials synthesized in voids of opal lattices and the composites obtained have typical magnetic properties.

Theory of ferroelectric phase transition inSrTiO3induced by isotope replacement

A theory to describe the dielectric anomalies and the ferroelectric phase transition induced by oxygen isotope replacement in ${\mathrm{SrTiO}}_{3}$ is developed. The proposed model gives consistent explanation between apparently contradictory experimental results on macroscopic dielectric measurements and microscopic lattice dynamical measurements by neutron-scattering studies. The essential feature is described by a three-state quantum order-disorder system characterizing the degenerated excited states in addition to the ground state of ${\mathrm{TiO}}_{6}$ cluster. The effect of isotope replacement is taken into account through the tunneling frequency between the excited states. The dielectric properties are analyzed by the mean-field approximation (MFA), which gives qualitative agreements with the experimental results throughout full range of the isotope concentration. The phase diagram in the temperature-tunneling frequency coordinate is studied by a quantum Monte Carlo method to confirm the qualitative validity of the MFA analysis.

Band Gap Modification of Diamond Photonic Crystals by Changing the Volume Fraction of the Dielectric Lattice

Photonic crystals with a diamond structure of epoxy lattices in which TiO2‐based ceramic particles are dispersed were fabricated by stereolithography. The periodicity of the lattice was designed to reflect electromagnetic waves in the gigahertz range. The volume fraction (β) of the dielectric lattice medium was modified from 14% to 33% by changing the rod diameter of the lattice. The photonic band gap was observed along Γ‐L 〈111〉, Γ‐X 〈100〉, and Γ‐K 〈110〉 directions and the complete photonic band gap was formed at over β= 20%. The width of the forbidden gap increased gradually when the β increased over 14%, and reached 2.4 GHz at β= 33%. These results agreed with the band calculation using the plane wave expansion method.

Free Energy Functional of Disordered Dielectrics - Random Field Approach

We derive the free energy functional of disordered dielectrics with dipole impurities. These dipoles, being randomly positioned and oriented, create in the host dielectric lattice random electric field E in the points where other impurity dipoles are situated. The distribution function f(E) of this random field, defined as an average (over spatial and orientational disorder) value of Dirac delta contributions of each dipole, enables us to obtain equations for order parameters. Latter equations permit to derive the free energy functional which substitutes (within limitations of the proposed model) the initial Hamiltonian of disordered system.

Destabilization of olivine by 30-keV electron irradiation: a possible mechanism of space weathering affecting interplanetary dust particles and planetary surfaces

Electron irradiation experiments were performed using a 30-keV electron beam on single crystals of olivine in a scanning electron microscope (SEM) and in an electron microprobe (EMP). We determined that, under certain conditions, structural damage is caused to the irradiated surface of iron-bearing olivines. The irradiated areas comprise spherules with sizes of hundreds of nanometers and micrometer-sized holes. In the immediate vicinities of the irradiated areas, droplets with sizes of tens of nanometers and branching tracks are observed. With increasing total charge, the hundreds of nanometer-sized spherules become larger and more irregular in shape. The size and shape of the nanometer-sized droplets remain almost constant, but their surface density increases (in m −2). Chemical fractionations compared to the initial olivine were found: the irradiated areas are slightly enriched in MgO, whereas the deposits are enriched in SiO 2. Destabilization of olivine is not due to the dissipation of the implanted energy as heat, but results most probably from electrostatic discharges leading to the breakdown of the dielectric lattice. The possibility that such processes could be responsible for significant space weathering of interplanetary dust particles and regoliths of planetary surfaces should be taken into account. In the interplanetary medium, 10-keV range electrons are carried by the solar wind, whereas at 1 AU from the Sun, the lifetime of cometary dust and the exposure time of lunar regolith are, at least, 10 to 100 times greater than the duration required to accumulate the damaging electronic doses applied in this study. Moreover, the comparison of the microstructures of samples irradiated in the present study with features of lunar regolith grains reveals several chemical and structural similarities.

Influence of paramagnetic chromium ions in crystalline YAG at microwave frequencies

The microwave properties of chromium-doped mono-crystalline yttrium aluminium garnet (Y3Al5O12 : YAG) were determined between 6 K and room temperature. It exhibited very strong microwave losses near 15.5 GHz. The mechanism producing the losses was found to follow standard Curie law behaviour below 30 K. In combination with the thermal expansion of the material, the magnetic characteristics produced turning points in the mode frequency-temperature dependence at 60 K. Analysis showed that the Cr3+ doping into the dielectric lattice resulted in an anisotropic paramagnetic susceptibility, which was resolvable at temperatures below 77 K. Room temperature data also indicated anisotropic susceptibility due to Cr3+ ions with the addition of another species with a loss peak near 20 GHz. Zero field splitting of the ground state energy level equivalent to 0.76 K and an excited state energy level 29 K above the ground state of the Cr3+ ions was confirmed. The lifetime of the excited state was found to be very temperature dependent and below 100 K was dominated by the Raman two-phonon scattering process.

Derivation of the basic system of kinetic equations governing superparamagnetic relaxation by the use of the adjoint Fokker-Planck operator

The basic equations governing the kinetics of superparamagnets (and dielectric lattices in the Debye approximation) are derived by taking advantage of the properties of the adjoint Fokker-Planck operator. The equations obtained, which duly reduce to those derived by direct averaging of the corresponding stochastic Landau-Lifshitz-type equations, are expressed in terms of the coefficients determining the action of the angular momentum operator and the spin variables on the spherical harmonics. The structure of the equations so obtained directly reflects that of the adjoint Fokker-Planck operator, which permits to trace back easily the origin of the different contributions (precession and relaxation). This makes the method specially suitable for generalization to more elaborate descriptions of rotational relaxation.

Computation of Static Effective Permittivity for a Multiphase Lattice of Cylinders

A methodology is described to calculate the static effective permittivity for a two-dimensional multiphase lattice composed of dielectric and/or conducting circular cylinders. This methodology uses an accurate T-matrix method to determine the dipole moments of the cylinders immersed in a uniform electric field, and then computes the effective permittivity by relating the lattice to a macroscopic model. With this methodology, the multiple scattering solution for the infinite lattice is presented in a succinct matrix-vector notation and is valid for any lattice type. The static effective permittivity equation described in this work allows us to account for the effect of all mutual interactions between the cylinders. This methodology is used to calculate the static effective permittivity for a two-phase lattice of metallic inclusions. These results are compared with the Maxwell Garnett formula and another formula presented by Kharadly and Jackson. Three additional examples are presented including two-phase dielectric lattices, multiphase lattices, and clusters. The static effective permittivity in all three situations deviates from the Maxwell Garnett result at high-volume fractions, as expected. This deviation is the most obvious for the cluster lattice because of the significant mutual coupling between the cylinders, even at relatively low-volume fraction.

Diffuse phase transition in (Na,Bi)-doped PbSnxTi[formula omitted]O3 ferroelectric ceramics

The temperature dependence of the dielectric behavior of Pb0.85(Na0.5Bi0.5)0.15SnxTi1−xO3 (PSNB) with x=0.40,0.45,0.50,0.55,0.60 has been investigated. A careful analysis of the dielectric properties reveals a relaxor behavior near Tc where the diffuseness parameter (δ) increases as the content of Sn4+. It is observed that the temperature of the permittivity maximum shifts toward lower temperatures and the permittivity maximum decreases with the increase of Sn content in the PSNB solid solutions. The diffuseness (δ) and deformation structure (γ) parameters were determined for each composition using the results of the dielectric measurements and experimental lattice constant values.

Diffraction efficiency and guided light control by two-dimensional photonic-bandgap lattices

We report on the measurement of the diffraction efficiency of two-dimensional photonic-bandgap lattices consisting of a triangular array of circular air holes etched in a semiconductor waveguide. We use the spontaneous emission of the material as an internal point source. Combined with previous reflectivity and transmission measurements, the diffraction data allow us to assess the total amount of out-of-plane losses experienced by a guided wave traversing the dielectric lattice, as a function of the lattice pitch. We found that these losses are particularly weak for some range of parameters, especially in the photonic bandgap of interest. We discuss the reasons why they can be substantial with other parameters.

Photonic band structure in the nearly plane wave approximation

For photons propagating in a periodic dielectric lattice, the dispersion curve forms photonic bands separated by forbidden gaps. When the dielectric lattice deviates only slightly from being homogenous, the photonic band structure resembles the linear dispersion relation for photons folded into the first Brillouin zone, i.e., the so-called empty lattice bands. Using group theoretical technique, we calculate the splitting of the accidental degeneracies in the empty lattice bands at symmetry points for a simple cubic dielectric lattice.

Boundary transfer matrices for light waves in a layered system of anisotropic dielectric lattices

Boundary transfer matrices for light waves in a layered system of anisotropic dielectric lattices

Observation of total omnidirectional reflection from a one-dimensional dielectric lattice

We show that under certain conditions one-dimensional dielectric lattice possesses total omnidirectional reflection of incident light. The predictions are verified experimentally using Na3AlF6/ZnSe multilayer structure developed by means of standard optical technology. The structure was found to exhibit reflection coefficient more then 99% in the range of incident angles 0-86 (degree) at the wavelength of 632.8 nm for s-polarization. The results are believed to stimulate new experiments on photonic crystals and controlled spontaneous emission.

Photonic band gaps of three-dimensional face-centred cubic lattices

We show that the photonic analogue of the Korringa-Kohn-Rostoker method is a viable alternative to the plane-wave method for analysing the spectrum of electromagnetic waves in a three-dimensional periodic dielectric lattice. Firstly, in the case of a fcc lattice of homogeneous dielectric spheres, we reproduce the main feature of the spectrum obtained by the plane-wave method, namely that for a sufficiently high dielectric contrast a full gap opens in the spectrum between the eighth and ninth bands if the dielectric constant of the spheres is lower than the dielectric constant of the background medium. If , no gap is found in the spectrum. The maximal value of the relative band-gap width approaches 14% in the close-packed case and decreases monotonically as the filling fraction decreases. The lowest dielectric contrast for which a full gap opens in the spectrum is determined to be 8.13. Eventually, in the case of a fcc lattice of coated spheres, we demonstrate that a suitable coating can enhance gap widths by as much as 50%.

Resonant Scattering and Spontaneous Emission in Dielectrics: Microscopic Derivation of Local-Field Effects

Resonant classical light scattering by impurity atoms inside dielectric cubic lattices is investigated in the point-dipole limit. Modifications to resonance frequencies and linewidths are shown to be different for substitutional and interstitial impurities. Spontaneous emission rates inside dielectrics exhibit the well-known empty-cavity and Lorentz local-field factors for substitutional and interstitial atoms, respectively. The results are generalized to disordered dielectrics, indicating that the substitutional case occurs prevalently for impurity atoms. [S0031-9007(98)06814-8]

Non-diffusive heat transport and chaos in non-linear dielectric lattices

Deviations from Fourier's law emerge from numerical simulations of various lattices modelling solids. Non-integrability and moreover chaotic motion are considered to be conditions of normal heat conduction. However, these are not sufficient conditions. Using a simple model as an example, we show that non-diffusive transport could occur even in the presence of disorder in the lattice and completely chaotic dynamics. We conclude that diffusive and non-diffusive transport can coexist, while the system is moving along a chaotic trajectory in the phase space.