Pressure Dependence of the Electromechanical and Vibrational Properties of Pentaerythritol

The elastic, piezoelectric and dielectric constants of pentaerythritol, C (CH₂OH)₄, (PET) have been computed as a function of pressure employing the structural data of KATRUSIAK and the lattice dynamical model of RAMAMOORTHY and KRISHNAMURTHY. Using these electromechanical constants, the Young's modulus, the linear compressibility, the bulk modulus and the acoustic wave velocities are computed for various high pressures. The pressure dependence of the vibration spectrum of PET using rigid and non‐rigid lattice models is also obtained. The anomalous variation of these electromechanical and other physical quantities predict the most probable pressure for phase transition in PET to be around 280 MPa. The mechanism of the transition and the variation in the physical behaviour accompanying the transition are discussed.     

Growth and Properties of Trigonal Aluminium Gallium Orthophosphate Single Crystals Al1-xGaxPO4

The new piezoelectric solid solution aluminium gallium orthophosphate single crystals have been successfully developed for the first time in our laboratory by hydrothermal method. It has been demonstrated that these crystals are homogeneous, and isomorphous with AIPO₄ and GaPO₄. The solid solution crystals Al_1-xGa_xPO₄ are easy to grown and have better optical quality than those of AlPO₄ crystals under the same conditions. A phase transition temperature T_α-β is 587 ± 3 °C for x = 0.12. Cell parameters, and elastic, piezoelectric, and dielectric constants are given.     

Crystal growth and characterization of Rb0.3K0.7TiOPO4

Single crystal growth and characterization of Rb_0.3K_0.7TiOPO₄ are reported. After improving the technological procedures of crystal growth, high-quality large single crystals were obtained. The refractive indices, pyroelectric coefficient, dielectric, piezoelectric, elastic, thermoelastic and elastooptic constants, SHG efficiency and damage threshold were measured.     

Physical properties of single crystals of KTiPO4, KxRb1−xTiOPO4 (x = 0.85; 0.75), KGeOPO4 and KTiOAsO4

Single crystals of the title compounds of optical quality and dimensions up to 30 × 25 × 25 mm were grown by the flux method. During the growth process the formation of twins consisting of bicrystals was observed, even in the case of single-crystalline seeds. The twinning boundaries could be detected by etching with hot KOH solutions. The following physical properties were investigated: refractive indices, dielectric constants, thermal expansion, piezoelectric, and electrooptic effects, elastic and thermoelastic constants. The crystals exhibit a quite similar behaviour. The anisotropy of all properties is quasi-tetragonal. In respect to polar properties only small differences within the mixed crystals K_xRb_1–xTiOPO₄ are found. Replacement of P by As does only slightly affect the polar properties, whereas the replacement of Ti by Ge leads to a drastic reduction of polar effects.     

Piezoelectric and Elastic Properties of Orthorhombic LiH2PO3 and LiH2PO4

Single crystals of LiH₂PO₃ and LiH₂PO₄, both of space group symmetry Pna2₁, with dimensions up to 40 mm were grown from aqueous solutions by controlled evaporation. Pyroelectric, dielectric, piezoelectric, elastic and thermoelastic properties were studied by standard methods. The static piezoelectric constants d₃₃₃ exceed d₁₁₁ of α-quartz by only a factor 2. The pyroectric effects reach 3 times and 7 times, respectively, that of tourmaline. The mean elastic stiffness of the phosphite is 13% smaller than that of the phosphate, a phenomenon also observed in the corresponding sodium and potassium salts.     

Growth,thermophysical and electrical properties of the nonlinear optical crystal BPO4

Bulk BPO₄ crystals have been successfully grown from high temperature solution of BPO₄, Li₂O, and MoO₃ in the molar ratio of 2.3:1:1.3 by the top‐seeded solution growth (TSSG) method using [101]^c orientation seeds. There are no visible scattering centers and impurity of Mo in the as‐grown BPO₄ crystals, whose optical homogeneity reaches up to 1.6×10^–5/cm. BPO₄ possesses a specific heat of 0.50–1.00 J·g^–1·K^–1 in the temperature range from 298 to 698 K and exhibits strong anisotropic thermal expansion behavior with α_a = 14.2 × 10^–6 K^–1 and α_c = ‐4.0 × 10^–7 K^–1. Moreover, the thermal conductivity coefficients are calculated to be κ_a = 62.4 W·m^–1·K^–1 and κ_c = 51.5 W·m^–1·K^–1, which are remarkably larger than those of some commonly used borates. The measured dielectric constants, ε_a and ε_c, are 4.8 and 6.1, respectively, and the ionic conductivity coefficients, σ_a = 4.3 × 10^–8 S/cm and σ_c = 9.5 × 10^–8 S/cm, are several orders of magnitude lower than that of LiB₃O₅ (LBO). (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elastic Properties of the Triclinic Pseudo-Trigonal Room-Temperature Phase of KIO3

Weakly twinned triclinic crystals of the room temperature γ-phase of KIO₃, grown from aqueous solutions, exhibit a quasi-trigonal behaviour of point symmetry group 3m in respect to thermal expansion, piezoelectric effects, and elastic properties. The elastic tensor and its temperature derivative were determined from ultrasonic resonance frequencies of thick plane-parallel plates and their shift upon variation of temperature, respectively. The static piezoelectric constants d₂₂₂ and d₂₁₁ are about fifty times larger than d₁₁₁ of α-quartz resulting in strong piezoelectric coupling coefficients of elastic waves (k₁ = 0.42; k₆₆ = 0.60). Approaching the γ-β transition at 345.6 K from lower temperatures, the shear stiffness c^E₆₆ shows a drastic softening. The transition appears to be of second-order ferroelastic.     

Contribution to the study of elastic properties of KGd(WO4)2:Er3+ single crystals by Brillouin spectroscopy

In this paper we present the study of the acoustic phonons propagating in Er³⁺‐doped KGd(WO₄)₂ single crystals by Brillouin spectroscopy. For the investigated crystals the velocities of the longitudinal and transverse acoustic phonons [100], [010], [001], [101] and [110] have been determined. Moreover, the values of the elastic constants: C₂₂, C₄₄ and C₆₆ of Er³⁺‐doped KGd(WO₄)₂ single crystals have been estimated. It was revealed that the presence of the Er³⁺‐ions in KGd(WO₄)₂ crystals, for the used doping concentration 1 at% does not influence their elastic properties. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elastic properties of KGd(WO4)2:Ho3+ single crystals studied by Brillouin spectroscopy

The analysis some of the acoustic phonons propagating in pure and Ho³⁺‐doped KGd(WO₄)₂ single crystals in the GHz frequency range by Brillouin scattering method has been presented. For investigated crystals the velocities of the longitudinal and transverse acoustic phonons [100], [010], [001], [101], [101] and [110] have been determined. Moreover, the value of elastic constants C₂₂, C₄₄ and C₆₆ of pure and Ho³⁺‐doped KGd(WO₄)₂ single crystals have been estimated. It was revealed that the presence of the Ho³⁺‐ions in KGd(WO₄)₂ crystals, for the used doping concentration 1 at% and 8 at%, does not influence their elastic properties. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Physical Properties of K2ZnCl4

Large single crystals of orthorhombic K₂ZnCl₄ with optical quality have been grown by the Czochralski method. The elastic constants and their temperature and pressure derivatives have been determined from ultrasonic resonance frequencies of thick plates of different orientation and the shift of these frequencies induced by temperature and pressure changes, respectively. K₂ZnCl₄ shows a small elastic anisotropy. Measurement of the dielectric constant was made along the ferroelectric axis ε_a in the temperature from 303 K to 573 K. ε_a of K₂ZnCI₄ grown by the Czochralski-method shows a smaller thermal hysteresis at the incommensurate-commensurate transition point (403 K) than that of crystals grown from an aqueous solution. It explains that crystals grown by the Czochralski-method are more purified, the pinning effect is weakened. The thermal hysteresis occurs with the same width at 10 KHz, 100KHz, 1 MHz and 10 MHz.     

Piezoelektrische und elastische Eigenschaften von Triglycinselenatkristallen im Bereich des Phasenüberganges

The piezoelectric constants d₂₁, d₂₃, d₂₅ and the elastic constants S₁₁, S₁₅, S₃₃ and S₃₅ of triglycine selenate are measured by the resonance method in the region of phase transformation. The elastic and piezoelectric constants are shown to have sharp maxima in the Curie point. The influence of a constant electric field on the temperature dependence of the piezoelectric constant d₂₃ and of the elastic constant S₃₃ is studied as well as the dependence of the mentioned constants on the intensity of a constant electric field at temperatures below and above the Curie temperature. A considerable increase of the elastic constant S₃₃ is found in weak electric fields of the ferroelectric phase. The electrostrictional coefficients Q₂₁, Q₂₃ and Q₂₅ are determined by means of the piezoelectric constants, spontane polarisation and dielectric receptivity. The found experimental dependences are explained on the base of the character of the domain structure of this crystal.     

Structural,optical and dielectric studies on K1‐x(NH4)xH2PO4 mixed crystals grown from z‐cut seeds

Mixed crystals of K_1‐x(NH₄)_xH₂PO₄(KADP) were grown from KDP (KH₂PO₄) dominated mixed solutions with varying molar proportion of ADP (NH₄H₂PO₄) addition. It was found that, as the increase of ADP molar concentration, the growth rate along z‐axis of KADP crystal decreased rapidly. The structure of KADP crystals was investigated by powder XRD and the lattice parameter was calculated. The results showed that the lattice parameter c of KADP crystal increased with the molar concentration of ADP. The optical homogeneity of grown KADP crystals was determined with a differential phase‐shifting interferometry. Frequency dependences of the dielectric constant and dielectric loss of KADP crystals were measured at room temperature (290 K). The dielectric constants of KADP crystals were almost invariant with the increase of frequency. In the region of 10²∼10⁴Hz, the values of the dielectric loss reduced with the increase of frequency. The piezo‐resonance coupling effect still exists in KADP crystals at room temperature, but shifted to low frequency band. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Elastic and dielectric properties of A<Superscript>II</Superscript>B<Stack><Subscript>2</Subscript><Superscript>V</Superscript></Stack> (<Emphasis Type="Italic">A</Emphasis> = Cd or Zn, <Emphasis Type="Italic">B</Emphasis> = P or As) single crystals

Elastic and dielectric properties of CdP₂, ZnP₂, and ZnAs₂ single crystals are investigated at frequencies of 10², 10³, 10⁴, 10⁶, and 10⁷ Hz in the [00l], [h00], and [hk0] directions in the temperature range 78–400 K. The elastic constants, the Gruneisen parameters, and the force constants of the crystals are calculated from the measured ultrasonic velocities. The elastic constants C_ij decrease with an increase in temperature and anomalously change in narrow (ΔT = 10–20 K) temperature ranges. The permittivity sharply increases from ε ≈ 7–14 at 78–150 K to ε ≈ 10²–10³ in the temperature range 175–225 K without any signs of a structural phase transition. The behavior of the temperature-frequency dependences of the complex permittivity ε*(f, T) is typical of relaxation processes. The dielectric relaxation in A^IIB ₂ ^V is considered on the basis of the model of isolated defects. The conuctivity σ of the single crystals under study is a sum of the frequency-dependent (hopping) conductivity σ_h and the conductivity σ_s that is typical of semiconductors. The hopping conductivity increases with an increase in frequency according to the law σ _h ～f^α, where α < 1 at low temperatures and α > 1 at high temperatures.     

Elastic, piezoelectric, and dielectric properties of α-GeO2 single crystals

The elastic, piezoelectric, and dielectric characteristics of α-GeO₂ crystals are studied at room temperature. The measurements were performed by the resonance method on crystals grown on α-quartz seeds from solutions in the recirculating mode. In germanium dioxide crystals, the piezoelectric moduli have high values. The characteristic features of variations of the electromechanical and elastic properties in crystals with the quartzlike structure observed earlier are confirmed.     

Molecular Statistical Theory of the Frank Elastic Constants of Liquid Crystals

Abstract

The Frank elastic constants K ₁, K ₂, K ₃ are calculated in the mean field approximation by assuming that the intermolecular force is the sum of hard rod repulsion (length L and width D) and Maier-Saupe's type attraction. The main conclusions are as follows. (1) the inequlaities K ₃? K ₁ > K ₂ necessarily hold. (2) All the K'_is are nearly proportional to the square of the orientational order parameter S. (3) In thermotropic system, K ₁/S ², K ₁/K and K ₂/K(K: mean elastic constant) increase slowly and K _3/K, K ₃/K ₁ decreases with L/D, whereas K/kT _c is nearly constant for L/D = 3 ～ 5. These tendecies agree fairly well with the observations on liquid crystals with almost rigid structure. (4) In the lyotorpic system in which L/D ? 1, K ₁/3 = K ₂ = cLk _T/3π D ² and k ₁/K ₃ = 4D/5cL are obtained (c: packing fraction). The estimate for PBLG solution nearly agrees with recent experimental data.     

Optical properties of pure and metal ions doped ammonium sulfate single crystals

A study of the optical properties of pure‐and some metal ions doped ammonium sulfate crystals (AS) were made. Optical constants of AS crystals were calculated at room temperature. The optical absorption coefficient (α ) was analyzed and interpreted to be in the allowed direct transition. The introduction of Rb⁺ or Cs⁺ ions gives rise to an intense charge transfer band with a maximum at λ= 310 nm in the optical spectrum. In case of Cr³⁺ ‐doping, the absorption shows a shoulder just before the onset band to band transition. The values of the allowed direct energy gap E_g for undoped and doped crystals were calculated. It was found that E_g values were decreased with metal ions doping. The refractive index, the extinction coefficient and both the real and imaginary parts of the dielectric permittivity were calculated as a function of photon energy. The validity of Cauchy‐Sellimeier equation was checked in the wavelength range 4.9 ‐ 5.6 eV and its parameters were calculated. Applying the Single‐Effective‐Oscillator model, the moments of ε (E ) could be estimated. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Thermoelastic and Piezoelastic Properties of Hexagonal RbMnCl3

Temperature and pressure derivatives of the elastic constants, indices of refraction, dielectric constants, Faraday effect and thermal expansion of RbMnCl₃ near T_c = 278 K confirm the existence of a second-order phase transition. A strongly anomalous behaviour is observed with the elastic shear stiffness c₄₄ which possesses a positive temperature derivative and a negative pressure derivative. These properties and also the pressure derivative of the transition temperature, dT_c/dp = 6.2 K kbar⁻¹ closely resemble the anomalous behaviour of two other ferroelectric species, betaine borate and betaine hydrogen maleinate.     

Acoustical properties of single crystals of mercurous halides

Velocities of propagation of elastic waves along principal crystallographic directions in Hg₂Br₂ and Hg₂J₂ single crystals were measured using the pulse and phase-pulse techniques. The values obtained were used to calculate the components of the elastic tensors c_ik and s_ik, as well as the phase and group velocities of propagation of longitudinal and transverse waves in the (100) and (001) planes, and the angular deviation of acoustic energy flux from the direction of the corresponding wave normal. Knowledge of the anisotropy of the elastic properties of Hg₂X₂ crystals and of their change with the anion (X = Cl, Br, J) leads to deeper understanding of the character of bonds in the crystal lattice and points the way to a better utilization of technical properties of the crystals. — Minimum velocity of propagation of an elastic wave falls in the case of Hg₂J₂ to a value v [100] [11 10] = 0,25 · 10⁵ cm/s, what is the lowest value known among all crystals. Maximum angular deviation of acoustic energy flux — nearly 50° — is exhibited by the quasi-longitudinal wave in Hg₂J₂ crystals. On substituting the Cl⁻ ions with Br⁻ and J⁻ ions, the anisotropy of elastic moduli C₃₃/C₁₁ increases by nearly 80%. Different mechanisms contribute to vectorial dependence of the elastic properties along different crystallographic directions.     

Electron irradiation‐induced effects on optical spectra of (NH4)2ZnCl4: x Sr2+ single crystals

The effect of electron‐beam irradiation with different doses on optical constants of (NH₄)₂ZnCl₄: x Sr²⁺ crystals with x=0.000, 0.020, 0.039, 0.087 or 0.144 wt% has been studied. The optical transmission in the energy range 3.4‐6.4 eV was measured hence the absorption coefficient was computed as a frequency function. The absorption coefficient was also calculated as a function of electron‐beam dose. Irradiation with e‐beam did not affect the allowed indirect type of transition responsible for interband transitions of (NH₄)₂ZnCl₄: x Sr²⁺ crystals. Values of the optical energy gap E_g and optical moment E_p for electronic interband transition of unexposed and (NH₄)₂ZnCl₄: x Sr²⁺ crystals after e‐beam exposure were deduced. The area under the absorption band at 5.30 eV was used to evaluate the effect of e‐irradiation on optical parameters of samples with x=0.00, 0.020 or 0.039. A shift in the position and a nonmonotonic change in the intensity of this band with increasing e‐beam dose was observed. Changes in the E_g value were used to evaluate the effect of e‐beam exposure dose on (NH₄)₂ZnCl₄: x Sr²⁺ samples with x=0.087 or 0.144. The obtained results were compared with those obtained for the same crystals after irradiation with different γ‐doses.     

Crystal Growth and Elastic Properties of Hopeite,Zn3(PO4) · 4 H2O

Single crystals of orthorhombic Zn₃(PO₄)₃ · 4 H₂O of optical quality with dimensions up to 12 × 10 × 8 mm were grown from aqueous solutions of ZnSO₄ and NaH₂PO₄ by controlled diffusion of NH₃ into the solution. The elastic constants c_ij and the thermoelastic constants T_ij = dc_ij/dT, T temperature, were determined from ultrasonic resonance frequencies of thick plates in the range between 5 and 40 MHz and between 250 and 320 K. In respect to the longitudinal elastic stiffness hopeite behaves quasi isotropically, however, the elastic shear stiffness shows a large anisotropy of about a factor 2.5. Above 260 K the shear stiffness c₆₆ possesses a quite anomalous temperature dependence (T₆₆ > 0). Further, the linear thermal expansion reveals a strong anisotropy (α₁₁ = −3.3, α₂₂ = 3.4, α₃₃ = 33 · 10⁻⁶/K).