Clamped Dielectric Constant Research Articles

Elastic and Dielectric Studies on the Phase Transition of Ferroelectric LiTlC4H4O6·H2O

Elastic and dielectric properties of ferroelectric LiTlC 4 H 4 O 6 ·H 2 O (LTT) were studied in the paraelectric phase. The Curie-Weiss type anomalies were observed in the elastic stiffness constant at constant electric field, the free dielectric constant and the clamped dielectric constant, while no definite anomaly was found in the elastic stiffness constant at constant electric displacement. The phase transition of LTT is proper ferroelectric, in contrast to the case of isomorphic LiNH 4 C 4 H 4 O 6 ·H 2 O (LAT) known as proper ferroelastic. The dielectric instability in LTT is consistently explained by the low-lying soft TO mode reported previously.

Experimental determination of the three-port impedance matrix for an array of transflexural elements.

A transducer has been built that consists of an array of transflexural piezoelectric disks embedded in a soft potting material. This transducer can be configured as a thin layer yet exhibits significant low-frequency (audio band) sensitivity. It has been modeled as a general three-port transducer, and an experimental determination of the three-port impedance matrix over a range of frequencies for a prototype transducer has been made. The matrix is expressed in terms of effective constants (the electromechanical coupling constant, the clamped dielectric constant, and the elasticity constant) of a thickness mode piezoelectric transducer. Predictions of the frequency response of the transducer and its performance as an active surface have been made using the measured impedance matrix. These predictions have been compared to its actual performance as an active surface.

Determination of the dielectric, piezoelectric, and elastic constants of crystals in class 32.

A new approach employing only two differently oriented crystal plates to determine all the dielectric, piezoelectric, and elastic constants of crystals in class 32 has been put forward. Meanwhile, a method to improve the determination accuracy of the clamped dielectric constants of crystals in class 32 also has been suggested. For example, all the constants of \ensuremath{\alpha}-quartz have been measured by the approach. The experimental results of \ensuremath{\alpha}-quartz have shown that the approach is very efficient.

Dielectric relaxation of mixed crystals of Rb1-x(NH4)xH2PO4 at microwave frequencies

Measurements of the clamped dielectric constant on mixed single crystals of Rb1-x(NH4)xH2PO4,x=0.35, are reported up to 11 GHz. Between 24 and 60 K, the dielectric dispersion can be fitted to a Cole-Cole relaxation, the parameters of which indicate a temperature-dependent distribution of relaxation times consistent with Vogel-Fulcher freezing. Both the audio and the microwave measurements can be scaled up to ≊ 100 MHz, with a freezing temperature ofT o≅8.4 K. In the GHz range, a relaxation process in addition to the low-frequency freezing mode contributes to the dielectric response.

Low frequency phonon polaritons in several ferroelectrics

Abstract Near-forward Raman scattering measurements have been made to determine the dispersion relations of low frequency phonon polaritons. The experimental results are given for BaTiO3, BNN, LiTaO3 and LiNbO3. The clamped dielectric constants and the propagation lengths are estimated.

Stokes and anti‐stokes scattering of light by low‐frequency polaritons in LiIO3

AbstractResults are presented on near‐forward Raman scattering from low‐frequency polaritons in LiIO3 obtained by the photographic method using an iodine filter for attenuation of the laser light before it enters a spectrograph. Our experiment shows that the value of dielectric transition strength of the 238 cm−1 phonon mode measured by Otaguro et al. must be corrected. The clamped dielectric constant (ϵz = 5.9) was determined from polariton measurements at frequencies below the lowest transverse mode. This value is compared with those published elsewhere.

Dielectric properties of single crystals of Pb(zr,til - x) O3 solid solutions (x∼0.5)

The dielectric constants and spontaneous polarisations of Pb(ZrxTi1-x)O3 single crystals (x = 0.4 ∼ 0.5) were measured. On the tetragonal side, the low frequency (1 kHz) free and high frequency (50 MHz) clamped dielectric constants along the a-axis, ∊T11, ∊S11, increase remarkably on approaching the tetragonal-trigonal morphotropic phase boundary. At this phase boundary, an increase of the low frequency free dielectric constant along the c-axis, eT33, is observed, but the high frequency clamped dielectric constant along the c-axis, ∊S33 is independent of the composition. The temperature dependence of the free and the clamped dielectric constants were measured for x = 0.5 and 0.51 single crystals. Above the Curie temperature, equality between ∊S33 and ∊11 was not observed. The temperature dependence of the spontaneous polarisation Ps(x = 0.4) was measured by the Sawyer-Tower method. The room temperature value of Ps is 50 ∼ 55 μC/cm2 for x = 0.4 ∼ 0.5 single crystals.

‘Dirty’ displacive ferroelectrics

Using the powder Raman technique we have measured most of the lattice vibrational modes in the Pb 1− x La x Ti 1− x/4 O 3 perovskite solid solution series. From the data for these disordered systems the clamped dielectric constant at zero frequency, ϵ m , was determined and compared with the clamped dielectric constant, ϵ cap, measured by standard capitance techniques. We find that ϵ cap/ϵ m exceeds one, and increases as the transition temperature is approached from below. Strikingly, we also find similar behavior for the ‘classical’ ferroelectrics BaTiO 3, LiNbO 3 and LiTaO 3, as well as for ferroelectrics with the tungsten bronze crystal structure.

Lattice Modes in Ferroelectric Perovskites: PbTiO3

A complete study of the lattice-dynamical behavior of the ferroelectric tetragonal perovskite PbTi${\mathrm{O}}_{3}$ has been carried out using Raman spectroscopy. The temperature dependence of all the long-wavelength mode frequencies are determined. We show that a damped-harmonic-oscillator model with a frequency-independent damping coefficient is sufficient to explain the observed shape of the soft $E(1\mathrm{TO})$ mode in the ferroelectric phase at all temperatures below ${T}_{c}=493$ \ifmmode^\circ\else\textdegree\fi{}C. Moreover, by combining our experimental mode-frequency data with pyroelectric measurements of the change in spontaneous polarization ${P}_{s}$ with temperature, we obtain values of ${P}_{s}(25 ^{\ensuremath{\circ}}\mathrm{C})=81$ \ensuremath{\mu}C/${\mathrm{cm}}^{2}$ and ${P}_{s}({T}_{c})=42$ \ensuremath{\mu}C/${\mathrm{cm}}^{2}$. This is in excellent agreement with a recent direct experimental measurement. The temperature dependence of all the mode strengths has also been determined to ${T}_{c}$. These results are used to extract the temperature dependence of the clamped dielectric constants. In PbTi${\mathrm{O}}_{3}$ the dielectric constant along the ferroelectric axis ${\ensuremath{\epsilon}}_{c}$ is determined primarily by the lowest frequency ${A}_{1}(1\mathrm{TO})$ mode at all temperatures to ${T}_{c}$, in contrast to BaTi${\mathrm{O}}_{3}$ where in the ferroelectric phase the lowest mode determines only $\ensuremath{\approx}25%$ of ${\ensuremath{\epsilon}}_{c}$. In PbTi${\mathrm{O}}_{3}$ the dielectric constant perpendicular to the $c$ axis ${\ensuremath{\epsilon}}_{a}$ is also determined by the lowest $E(1\mathrm{TO})$ mode at all temperatures. The possibility of observing critical effects near ${T}_{c}$ in the soft-mode data of PbTi${\mathrm{O}}_{3}$ has been examined. These effects are not observed. Also, it is shown that very careful fitting of the soft-mode temperature dependence to a functional form containing a minimum number of separately determined parameters is required before critical effects can be invoked in first-order phase transitions of the displacive type.

Temperature dependent polariton measurements in BaTiO 3

Polariton techniques are used to determine the temperature dependence of all three A 1 modes between room temperature and T c = 134°C in the ferroelectric phase of BaTiO 3. The results shows that there is a large difference between the clamped dielectric constant, ϵ(0), determined from these results and ϵ(0) determined from microwave capacitance techniques. It is argued that, while soft modes in displacive ferroelectrics are the driving force for the transition, other oscillators play an important role in low frequency dielectric behavior.

Dielectric, mechanical and optical properties of orthorhombic KNbO3

Dielectric, piezoelectric and elastic constants have been measured in single domain KNbO3, and electrooptic r-coefficients are estimated. Results allow a thorough verification of Devonshire's theory for the orthorhornbic phase. Good agreement is found for the dielectric and piezoelectric properties whereas fitting the elastic behaviour requires inclusion of terms coupling stiffness to spontaneous strain. The temperature dependence of clamped dielectric constants and elastic stiffness points to the importance of piezoelectric coupling for the low temperature phase transitions. Absorption measurements reveal a nearly isotropic polarization-induced band edge shift of 200 meV. Large anisotropy is observed in the polarized UV reflectance spectra measured up to 10 eV. Comparison of reflectivity in ferroelectric KNbO3 with electroreflectance in cubic KTaO3 gives further evidence for the unified nature of electro-optic effects in oxygen-octahedra compounds. Differences in ε''-spectra derived from Kramers-Kronig analysis account quantitatively for the birefringence and reveal the spectral origin of the electrooptic effect.

Infrared Study of the Lattice Vibrations in LiTaO3

Polarized infrared reflectivity measurements have been made on single-crystal LiTa${\mathrm{O}}_{3}$ in the frequency range 20 - 10 000 ${\mathrm{cm}}^{\ensuremath{-}1}$ at 300 \ifmmode^\circ\else\textdegree\fi{}K. Kramers-Kronig and classical-oscillator dispersion-theory analyses of these data have yielded values for the frequency, strength, and linewidth of the infrared-active transverse optic modes and longitudinal optic modes. Analysis of the far-infrared interference spectrum yields values of 41 and 40 for the ordinary and extra-ordinary clamped dielectric constants, as well as values for their temperature dependence and dispersion. A calculation is made of the spontaneous polarization in LiTa${\mathrm{O}}_{3}$ and LiNb${\mathrm{O}}_{3}$ using the x-ray ion displacements.

Effect of charged dislocations on dielectric, piezoelectric and elastic properties

A generalized treatment of the effect of charged dislocations on dielectric, piezoelectric and elastic properties is developed by considering the displacement of a charged dislocation segment, bounded by immobile pinning points, under separate or combined application of electric and elastic fields. Expressions for contributions to the dielectric constants Δχ ij, piezoelectric constants Δd imn and elastic compliances ΔS klmn are then derived, and their significance is discussed. Combined application of static electric and elastic fields or alternating electric and elastic fields yields Δd imn directly, whereas application of either an alternating electric or elastic field and a static field of the other kind yields either Δχ ij or ΔS klmn diminished by a factor containing the static field to the second power. Second-order piezoelectric phenomena, represented by the difference between mechanically clamped and free dielectric constants or electrically clamped and free elastic constants, provide additional ways to determine the magnitude of Δd imn.

Dielectric and optical properties of melt-grown BaTiO 3

Dielectric constant, spontaneous polarization, optical absorption, refractive index, and birefringence data are reported for melt-grown single-domain crystals of BaTiO 3. The temperature dependences of the clamped and unclamped dielectric constants and the spontaneous polarization are found to be similar to results previously reported for flux-grown crystals. Differences in dielectric behavior are largely attributable to the higher transition temperatures in melt-grown crystals, i.e. the tetragonal phase is stable between 6–133†C in melt-grown crystals, and between 2–120°C in flux-grown crystals. The optical properties of melt and flux-grown crystals are, however, significantly different. Melt-grown crystals, in contrast to flux-grown crystals, exhibit an exponential Urbach absorption edge with negligible absorption (< 1 cm −1) for photon energies below approximately 3 eV. Refractive indices are somewhat higher in melt-grown crystals and the dispersion, which fits a Sellmeier relation, differs from that previously reported. The birefringence is shown to be a consequence of the quadratic electro-optic effect with the same electro-optic coefficient as measured in the paraelectric phase.

Theory of the Ferroelectric Effect and Clamped Dielectric Constant of Rochelle Salt

Using the crystal structure determination of rochelle salt made by Beevers and Hughes, a theory of the ferro-electric effect and clamped dielectric constant has been worked out using the displacement of the hydrogen nucleus in the 1-10 hydrogen bond as the ferroelectric dipole. This theory has only one disposable constant, $\ensuremath{\beta}$, the factor of proportionality between the polarization and the Lorentz internal field. Taking the oxygen separation found by x-rays, the dielectric constant for electrons and atoms found by experiment, and the number of molecules per cubic centimeter found from the x-ray cell determinations, the value of $\ensuremath{\beta}$ becomes 4.07 which agrees well with the theoretical value $\frac{4\ensuremath{\pi}}{3}$ for an isotropic substance. This theory accounts for the clamped dielectric constant at low field strengths, which as shown by measurements presented here, has maximum values at -18\ifmmode^\circ\else\textdegree\fi{}C and +24\ifmmode^\circ\else\textdegree\fi{}C, the Curie temperatures for the free crystal. This shows that the anomaly must lie in the clamped dielectric constant alone and not in the interaction of the clamped dielectric constant and the piezoelectric effect. This model also accounts for recent measurements of W. A. Yager which show that the dipole dielectric constant is relaxed at a frequency of about 5\ifmmode\times\else\texttimes\fi{}${10}^{9}$ cycles.

The Location of Hysteresis Phenomena in Rochelle Salt Crystals

Measurements of the elastic properties of an unplated crystal, the piezoelectric constant ${f}_{14}$, and the clamped dielectric constant of a Rochelle salt crystal show that practically all hysteresis and dissipation effects are associated with the clamped dielectric properties of the crystal. A theoretical formulation of the equations of a piezoelectric crystal has been made which takes account of the dissipation effects. The formulation is given for the polarization theory. The frequency variation of the clamped dielectric constant when interpreted by Debye's theory of dielectrics, modified to take account of hysteresis losses, indicates that there are two components, one of which has associated with it at high viscous resistance, whereas the other one does not. The nonviscous component has a dielectric constant of about 100 at 0\ifmmode^\circ\else\textdegree\fi{}C and is probably due to the displacement of the ions in the lattice structure. The viscous component has a dielectric constant of about 140 at 0\ifmmode^\circ\else\textdegree\fi{}C and is probably due to the dipoles of the Rochelle salt. Both components have higher dielectric constants and hysteresis between the Curie points indicating a cooperative action of the molecules for both components in this temperature region.