Thermoelastische und elastische Eigenschaften des tetragonalen Quecksilberdijodids

All elastic constants c_ij and thermoelastic constants T_ij = d log c_ij/dT (T temperature) of tetragonal HgI₂ have been measured by ultrasonic methods on single crystals which had been grown from the vapour phase by the method of dynamical gradient reversal. HgI₂ exhibits strong anisotropic elastic properties which are qualitatively explained by structural details. The temperature dependence of the elastic constants is smaller than expected. Only the very small shear constant c₆₆ is strongly decreasing with increasing temperature. This behaviour might be seen in connection with the known phase transition at about 126°C.     

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.     

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.     

Crystal growth and physical properties of monoclinic L-arginine hydrochloride monohydrate,C6H14O2N4HCl · H2O,and L-arginine hydrobromide monohydrate,C6H14O2N4HBr · H2O

Single crystals of optical quality of L-arginine HCl · H₂O and L-arginine HBr · H₂O with dimensions up to 80 × 60 × 30 mm have been grown from aqueous solutions by controlled evaporation at about 310 K. The isotypic crystals exhibit a quite similar behaviour with respect to morphological, pyroelectric, dielectric, optical, thermal expansion, electrostrictive, electrooptic, elastic, thermoelastic and non-linear optical properties. A distinct anisotropy of the longitudinal elastic stiffness is observed with a maximum along the direction of the alignment of the arginine ions. Nearly in the same direction a minimum of thermal expansion, dielectric constant and index of refraction is found. The pyroelectric, electrostrictive, electrooptic and non-linear-optical effects are of only mediocre magnitude except the electrostrictive constant d₂₁₁ which surmounts the longitudinal electrostrictive constant d₁₁₁ of alpha-quartz by a factor three.     

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)     

Phase transitions in Cs5(HSO4)2(H2PO4)3 crystal

The symmetry (sp. gr.I $\bar 4$ 3d) and lattice parameters have been determined for the first time for Cs₅(H₂SO₄)₂(H₂PO₄)₃ crystals in the temperature range from 172 to 390 K. The thermal and optical properties of crystals, as well as their conductivity, have been investigated at elevated temperatures. It is shown that a crystal heated to T = 365 K undergoes a phase transition with symmetry lowering to the tetragonal phase (with the parameters a = 4.965(1) Å and c = 5.016(1) Å), while at T ≈ 390 K a phase transition to the cubic phase is presumably observed. With a decrease in temperature, a phase transition without a change in symmetry occurs at T = 240 K.     

Elastic properties of the dithionates Na2S2O6 · 2 H2O,K2S2O6, Rb2S2O6, CaS2O6 · 4H2O and SrS2O6 · 4 H2O

Single crystals of the title compounds having optical quality and dimensions of several cm were grown from aqueous solutions. The elastic and thermoelastic constants were determined from ultrasonic resonance frequencies of thick plates. The true point symmetry of K₂S₂O₆ and Rb₂S₂O₆, which is screened by a hexagonal hypermorphy, could be clearly revealed to be trigonal (32) by the existence of the elastic constant c₁₄. In the case of CaS₂O₆ · 4H₂O and SrS₂O₆ · 4H₂O the constant c₁₄ of the specimens appeared too small to confirm the trigonal symmetry group required from electrooptic and non-linear optic effects unambiguously. The isotypy of K₂S₂O₂ and Rb₂S₂O₆ as well as that of CaS₂O₆ · 4H₂O and SrS₂O₆ · 4H₂O is confirmed by their elastic behaviour. The mean elastic stiffness of dithionates is closely related to that of the corresponding sulphates. In the vicinity of the second-order phase transition of K₂S₂O₆ near 235 K weak anomalies of the temperature derivatives of the longitudinal elastic stiffnesses are observed.     

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 structure,thermal and compositional deformations of β‐CsB5O8

The crystal structure of β‐CsB₅O₈ has been determined from X‐ray powder diffraction data using synchrotron radiation: Pbca, a = 7.8131(3) Å, b = 12.0652(4) Å, c = 14.9582(4) Å, Z = 8, ρ_calc = 2.967 g/cm³, R‐p = 0.076, R‐wp = 0.094. β‐CsB₅O₈ was found to be isostructural with β‐KB₅O₈ and β‐RbB₅O₈. The crystal structure consists of a double interlocking framework built up from B‐O pentaborate groups. The crystal structure exhibits a highly anisotropic thermal expansion: α_a = 53, α_b = 16, α_c = 14 · 10^‐6/K; the anisotropy may be caused by partial straightening of the screw chains of the pentaborate groups. The similarity of the thermal and compositional (Cs‐Rb‐K substitution) deformations of CsB₅O₈ is revealed: increasing the radius of the metal by 0.01 Å leads to the same deformations of the crystal structure as increasing the temperature by 35°C. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Growth and ionic conductivity of γ-Li<Subscript>3</Subscript>PO<Subscript>4</Subscript>

Single crystals of γ-Li₃PO₄ have been grown from flux. The 4 × 8 × 9-mm crystals have the cleavage along the [010] and [120] directions. The anisotropy in ionic conductivity in the grown crystals, ((σ ‖ a)/(σ ‖ b) = 2.5 and (σ ‖ a)/(σ ‖ c) = 1.3), is explained by specific features of the γ-Li₃PO₄ structure.     

Low-temperature X-ray studies of a [(CH3)2NH2]2 · CuCl4 crystal

The a, b, c lattice parameters of a [(CH₃)₂NH₂]₂ · CuCl₄ crystal have been measured by the X-ray diffraction method within the temperature range of 100–300 K. The temperature dependences of thermal expansion coefficients α_a = f(T), α_b = f(T), and α_c = f(T) along the principal crystallographic axes and thermal expansion coefficient of the unit-cell volume αV = f(T) are determined. It is found that all the three parameters, a, b, and c, vary with temperature in a complicated way and show jumplike anomalies in the a = f(T), b = f(T), and c = f(T) curves at phase-transition temperatures T _c1 = 255 K and T _c2 = 279 K. An incommensurate phase with the modulation wave vector q _i = (1/2 + δ)(a* + c*) is revealed in the temperature range 279–296 K. It is shown that the incommensurability parameter δ increases with an increase in temperature.     

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.     

Structure refinement with X-ray powder diffraction data for synthetic calcium hydroxyapatite by Rietveld method

Ca₅(PO₄)₃OH, M_r = 502.3, hexagonal, P 6₃/m, a = 9.4207(3), c = 6.8780(2) Å, V = 528.67 ų, Z = 2, D_x = 3.156 Mg · m⁻³, CuKα, λKα₁ = 1.54051, λKα₂ = 1.54433 Å, μ = 26.25 mm⁻¹, F(000) = 500, T = 294 K. The powder diffraction pattern was analysed by the Rietveld method. The parameters were refined by the program PFSR (DBW2.9) to final R-factors R_p = 0.079, R_wp = 0.081 and R_B = 0.015.     

Me2O-P2O5-H2O solubility phase diagrams and growth of MeH2PO4 single crystals (Me = Li, Na, K, Rb, Cs, NH4)

The Me ₂O-P₂O₅-H₂O solubility phase diagrams are used to determine the optimum compositions and the temperatures for growing crystals of MeH₂PO₄ solid phases (Me = Li, Na, K, Rb, Cs, NH₄). The optimum conditions for dynamic growth of dihydrophosphates of the elements of the first group and ammonium are determined. LiH₂PO₄, NaH₂PO₄, NaH₂PO₄ · 2H₂O, NaH₂PO₄ · H₂O, KH₂PO₄, K(H,D)₂PO₄, RbH₂PO₄, CsH₂PO₄, and (NH₄)H₂PO₄ single crystals are grown on seed from aqueous solutions by the methods of temperature lowering and isothermal evaporation. __________ Translated from Kristallografiya, Vol. 49, No. 4, 2004, pp. 773–777. Original Russian Text Copyright ? 2004 by Soboleva, Voloshin.     

Thermal Expansion and Oxygen Nonstoichiometry in High-Tc YBa2Cu3Ox Superconductor

The lattice parameters as well as the axial thermal expansion coefficients for YBa₂Cu₃O_x superconducting oxide ceramics with different oxygen content ranging from × = 6.14 to × = 6.95 are determined as a function of temperature between 80 and 400 K using X-ray powder diffractometry technique. The effect of oxygen concentration on the thermal expansion behaviour is regarded. The values of α are found to decrease with the oxygen content reducing and depend on the condition of heat treatment. The essential anisotropy of thermal expansion is shown to exist, with α_c being larger than α_a and α_b. The relationship between α_a and α_b depends both on the sample preparation conditions and temperature.     

Crystallographic investigation of single crystals of the mesogen compound 4′-nitrophenyl-4-n-octyloxybenzoate

X-ray investigations of single crystals of 4′-nitrophenyl-4-n-octyloxybenzoate (NPOB) have been performed for the determination of the space group P2₁/c and the lattice constants (a₀ = 16.77 ± 0.02 Å, b₀ = 9.207 ± 0.005 Å, c₀ = 16.72 ± 0.01 Å, β = 128.0 ± 0.5°). Furthermore powder patterns after Debye-Scherrer method have been taken to estimate the d-values together with the indexing. On the basis of small Miller indices the crystal angles yielded a discrepancy between axis ratios determined from optical measurements and X-ray methods. It can be shown that these differences appear with many molecular crystals.     

Crystal structures of two modifications of sodium pentahydrogendiphosphate NaH5(PO4)2

Two crystalline modifications of NaH₅(PO₄)₂ are obtained by the reaction of Na₂CO₃ with an excess of orthophosphoric acid. The crystal structures of α-and β-NaH₅(PO₄)₂ are determined by X-ray diffraction analysis. The crystal data are a = 8.484(4) Å, b = 7.842(3) Å, c = 10.353(4) Å, β = 90.50(3)°, V = 689.3(3) ų, space group P2₁/c, Z = 4, and R ₁ = 0.0250 for the α modification and a = 7.127(2) Å, b = 13.346(4) Å, c = 7.177(2) Å, β = 95.5(2)°, V = 679.5(3) ų, space group P2₁/c, Z = 4, and R ₁ = 0.0232 for the β modification. Based of the hydrogen-bond system, the formulas of the α and β modifications can be represented as Na(H₂PO₄)(H₃PO₄) and Na[H(H₂PO₄)₂], respectively. They correspond to the stable and metastable forms of the compound.     

Investigation of zirconium phosphate Zr<Subscript>3</Subscript>(PO<Subscript>4</Subscript>)<Subscript>4</Subscript> during heating

Zirconium phosphate Zr₃(PO₄)₄ has been synthesized by the sol-gel technique and investigated using X-ray powder diffraction, IR spectroscopy, and differential scanning calorimetry. It has been established that the symmetry of the unit cell, R \(\bar 3\) c, which is characteristic of the NaZr₂(PO₄)₃ (NZP) family, is lowered to P \(\bar 3\) c. The behavior of the zirconium phosphate during heating has been examined using high-temperature X-ray diffraction at temperatures ranging from 25 to 575°C. It has been revealed that the structure of the zirconium phosphate is hardly subjected to expansion due to heating in the temperature ranges 25–125°C (α _a < 1 × 10^?6 K^?1, α _c < 1 × 10^?6 K^?1, Δα < 1 × 10^?6 K^?1) and 325–575°C (α _a = ?1.4 × 10^?6 K^?1, α _c < 1 × 10^?6 K^?1, Δα < ?2.4 × 10^?6 K^?1). In the temperature range 125–325°C, the synthesized compound undergoes a second-order phase transition (upon heating), which is accompanied by the contraction of the structure along all crystallographic directions. Upon cooling in the range from 75 to 25°C, the phase transition is accompanied by the expansion of the structure.