Preparation,structure and thermal properties of CuGa5Se8

The structural parameters, the axial thermal expansion coefficients and the characteristic Debye temperatures for the order vacancy compound CuGa₅Se₈ with the chalcopyrite‐related structure, prepared by the Bridgman technique, were determined at different temperatures between 90 and 650 K by the X‐ray diffraction method. The melting point of this compound was defined from the differential thermal analysis data. The anisotropy of thermal expansion in CuGa₅Se₈ is shown to exist with the coefficients along a ‐axis being larger than those along the c ‐axis throughout the temperature range studied.     

Thermal expansion in the AgGa(S1−xSex)2 solid solutions from X-ray diffraction data

The lattice parameters a and c as well as the axial thermal expansion coefficients in the AgGa(S_1-xSe_x)₂ solid solutions with chalcopyrite-type structure were determined as a function of temperature in the range from 80 to 700 K and composition x using an X-ray powder diffractometry technique. It is found that the thermal expansion coefficients were anisotropic and for all the solid solutions the thermal expansion coefficients along the tetragonal c-axis were negative whereas those along the a-axis and the volume coefficients were positive. The directions in which the crystal thickness does not change as temperature varies, were found. The composition dependences of these coefficients were non-linear.     

Temperature dependence of lattice parameters of langasite single crystals

To determine the coefficient of thermal expansion of trigonal langasite (La₃Ga₅SiO₁₄) the two independent lattice parameters a and c are measured over a temperature range of 800 °C using X‐ray diffraction on single crystal samples. From the given nonlinear temperature dependence the linear and quadratic thermal coefficients of expansion α₁₁, β₁₁ and α₃₃, β₃₃ for the two lattice parameters a and c could be deduced. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Lattice Thermal Expansion in CuGaT2 and CuInTe2 Compounds over the Temperature Range 80 to 650 K from X-ray Diffracion Data

The lattice parameters a and c as well as the thermal expansion coefficients α⟂ and α∥ in the two principal direction for CuGaTe2 and CuInTe 2 chalcopyrite-type compounds have been determined as a function of temperature in the range from 80 to 650 K by the X-ray diffraction method. It is found for both the compounds the coefficient of expansion along the α axis (α⟂) is larger than that along the c axis (α∥) over the whole investigated tem-perature range. When comparing the results for a series of the CuB^IIIC compounds (B Ga, In; C S, Se, Te) it is shown that the thermal expansion anisotropy increases strongly when the Ga atom replaces the In atom while it changes a little when the Te atom replaces the Se atom or the S atom.     

Trends in the thermal expansion coefficients of the AIBIIIC2VI and AIIBIVC2V chalcopyrite compounds

Empirical relations are derived for the average linear thermal expansion coefficient α_L and the linear thermal expansion coefficients α_a and α_c of the lattice parameters a and c, respectively, of the A^IB^IIIC₂^IV and A^IIB^IVC₂^V compounds. It is shown that the thermal expansion coefficients of all tetrahedrally coordinated compounds can be described within the same model. The anisotropy of the thermal expansion coefficients depends essentially on the lattice constant ratio c/a. There exists a critical c/a value below of which α_c becomes negative.     

Thermal expansion in CuAlTe2 compound

The lattice parameters a and c as well as the axial thermal expansion coefficients α ⟂ and α ∥ in the CuAlTe₂ chalcopyrite-type compound are determined as a function of temperature in the range from 80 to 650 K by a X-ray diffractometry technique. The data obtained are used to evaluate the axial ratio c/a, the tetragonal distortion δ = 2 — c/a, the interatomic distances for Cu Te and Al Te bonds and their temperature coefficients. It is found that the thermal expansion behaviour of CuAlTe₂ is similar to that of other CuB^IIIC^VI₂ compounds in having a relatively small expansivity along the c-axis and a large one in the perpendicular direction. When comparing the results for a series of the CuB^IIIC^VI₂ compounds (B Al, Ga, In; C S, Se, Te) it is shown that the correlations between the thermal expansion coefficients α ⟂, α ∥, α_m, dδ/dT and the tetragonal distortion δ, as well as the molar mass of the compound take place.     

Unusual Thermal Behaviour of Mercurous Chloride

A precise determination of the lattice parameters and the coefficients of thermal expansion of mercurous chloride has been made at different temperatures ranging from 30 °C to 260 °C with a Unicam 19 cm high-temperature powder camera and FeKα radiation. The ‘a’ parameter increases non-linearly, whereas the ‘c’ parameter decreases linearly with temperature. Both the c/a value and the unit-cell volume are found to decrease with increasing temperature. The coefficient of thermal expansion along the ‘c’ axis, α∥, is found to have a constant negative value throughout the range of temperature studied. The positive value of α⊥ increases while the negative value of volume coefficient (β) decreases linearly with increasing temperature indicating an unusual and interesting thermal behaviour.     

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)     

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.     

Cd‐Doping Effects on The Properties of Polycrystalline α‐In2Se3 Thin Films

The X‐ray diffraction has revealed that the polycrystalline hexagonal structured α‐In₂Se₃ thin films grown at substrate temperature of 200 °C with the unit cell parameters a = 4.03 Å and c = 19.23 Å becomes polycrystalline hexagonal structured InSe with a unit cell parameters of a = 4.00 Å and c = 16.63 Å by Cd‐doping. The analysis of the conductivity temperature dependence in the range 300‐40 K revealed that the thermionic emission of charged carriers and the variable range hopping are the predominant conduction mechanism above and below 100 K, respectively. Hall measurements revealed that the mobility is limited by the scattering of charged carriers through the grain boundaries above 200 K and 120 K for the undoped and Cd‐doped samples, respectively. The photocurrent (I_ph) increases with increasing illumination intensity (F) and decreasing temperature up to a maximum temperature of ∼100 K, below which I_ph is temperature invariant. It is found to have the monomolecular and bimolecular recombination characters at low and high illumination intensities, respectively. The Cd‐doping increases the density of trapping states that changes the position of the dark Fermi level leading to the deviation from linearity in the dependence of I_ph on F at low illumination intensities.     

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)     

Low-temperature X-ray studies of crystal-lattice parameters and thermal expansion of KTiOPO4 crystals

The unit-cell parameters a, b, and c of KTiOPO₄ crystals have been measured by the X-ray diffraction method in the temperature range 80–320 K. The parameters obtained were used to determine the thermal expansion coefficients α_[100], α_[010], and α_[001] along the principal crystallographic axes. It was established that thermal expansion in the crystals is essentially anisotropic and that α_[010] > α _[100], whereas α_[001] is close to zero.     

Crystal Data,Electrical Resisitivity and Mobility in Cu3In5Se9 and Cu3In5Te9 Single Crystals

X-ray powder diffraction data were obtained for Cu₃In₅Se₉ and Cu₃Te₉, which were found to crystallize in orthorhombic and tetragonal systems, respectively. The electrical resistivities and Hall mobilities of these compounds were investigated in the temperature range 35–475 K. Cu₃In₅Se₉, was identified to be n-type with a room temperature resistivity of 3 × 10³ Ω·cm which decreases with increasing temperature. For T < 65 K impurity activation energy of 0.03 eV and for T > 350 K onset of intrinsic conduction yielding a band gap energy of 0.99eV were detected. The neutral impurity scattering was found to dominate at low temperatures, while in the high temperature region thermally activated mobility was observed. Cu₃In₅Te₉ exhibits p-type conduction with a room temperature resistivity of 8.5 × 10⁻³ Ω·cm decreasing sharply above 400 K and yielding an impurity ionization energy of 0.13 eV. The temperature dependence of mobility indicates the presence of lattice and ionized impuritiy scattering mechanisms above and below 160 K, respectively.     

X-ray diffraction study of (TlInSe<Subscript>2</Subscript>)<Subscript>1−<Emphasis Type="Italic">x</Emphasis></Subscript>(TlGaTe<Subscript>2</Subscript>)<Subscript><Emphasis Type="Italic">x</Emphasis></Subscript> crystal system

The crystallographic and dynamic characteristics of TlInSe₂ and TlGaTe₂ crystals have been studied by X-ray diffraction in the temperature range of 85–320 K. The temperature dependences of the unit-cell parameters a of TlInSe₂ and TlGaTe₂ crystals, as well as their coefficients of thermal expansion along the [100] direction, are determined. The concentration dependences of the unit-cell parameters a and c for (TlInSe₂)_{1 − x} (TlGaTe₂) _x crystals are measured. Anomalies are found in the temperature dependences of the unit-cell parameters a and, correspondingly, the coefficient of thermal expansion, indicating the existence of phase transitions in TlInSe₂ and TlGaTe₂ crystals.     

Thermoelectric properties of Tl‐doped Bi2Se3 single crystals

The single crystals of the ternary system based on Bi_2‐xTl_xSe₃ (nominaly x = 0.0‐0.1) were prepared using the Bridgman technique. Samples with varying content of Tl were characterized by the measurement of lattice parameters, electrical conductivity σ_⊥c , Hall coefficient R_H (B∥c), and Seebeck coefficient S (ΔT ⊥c). The measurements indicate that by incorporating Tl in Bi₂Se₃ one lowers the concentration of free electrons and enhances their mobility. This effect is explained in terms of the point defects in the crystal lattice – formation of substitutional defects thallium on the site of bismuth Tl_Bi and the decrease of concentration of selenium vacancies V_Se⁺². We also discuss the temperature dependence of the power factor σS² of the samples. Upon the thallium doping we observe a significant increase of the power factor compare to the parental Bi₂Se₃. (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Anomalous thermal expansion of osmium dioxide

The precision lattice parameters of osmium dioxide have been determined at different temperatures, in the temperature range 30–444 °C, using a Unicam high temperature powder camera 19 cm in diameter and CuKα radiation. The data have been used to evaluate the coefficients of thermal expansion at various temperatures by a graphical method. The ‘a’ parameter increases non-linearly with increasing temperature while the ‘c’ parameter remains constant throughout the range of temperature studied indicating a zero coefficient of expansion along the c-direction. The abnormal thermal behaviour of this compound is explained in terms of the electronic configuration of the d-shell of the cation.     

Characterisation of Bi2Se3 Crystals Highly Doped with Pb

Pb-doped Bi₂Se₃ crystals were prepared from starting elements Bi, Se and Pb of 5N purity in the concentration interval c_pb = 0 – 4 × 10²⁵ Pb atoms m⁻³ by a modified Bridgman method. The measured values of the transmittance and reflectance were used to determine the dependence of the absorption coefficient K on the photon energy for crystals with various values of cpb and to prove the shift of the short-wavelength absorption edge with cpb. On the basis of the assumption of the validity of the “single valley” model, which can describe the lowest conductivity band of Bi₂Se₃, and using the values of the freecarrier effective mass in the directions perpendicular and parallel to the trigonal axis c we determined the value of the reduced Fermi energy η 300 K for crystals with various values of cpb. Using the value of η, we calculated the dependence of the Seebeck coefficient on cpb and compared it with the experimentally determined values. The comparison has shown that the increasing content of Pb atoms in the Bi₂Se₃ lattice leads to a suppression of the role of the mechanism of scattering by ionised impurities; at higher concentrations of Pb in the crystal the mechanism of scattering of free carriers by acoustic phonons becomes dominant. Further, the ideas on the nature of the point defects in the Bi₂Se₃(Pb) crystals are presented and the “anomalous” dependence of the free-electron concentration on cpb is qualitatively accounted for.     

Structural and Electrical Characterization of Ag3Ga5Te9 and Ag3In5Se9 Crystals

X-ray powder diffraction studies revealed that Ag₃Ga₅Te₉ and Ag₃In₅Se₉ crystallize in orthorhombic and tetragonal systems, respectively. The temperature dependent conductivity and Hall effect measurements have been carried out between 65—480 K. Ag₃Ga₅Te₉ exhibits p-type conduction with a room temperature conductivity of 4.3 × 10^—4 (Ω · cm)^—1 and mobility less than 1 cm²/V · s. Ag₃In₅Se₉ was identified to be n-type with room temperature conductivity 7.2 × 10^—5 (Ω · cm)^—1 and mobility 20 cm²/V · s. From temperature dependence of the conductivity three different impurity ionization energies were obtained for both compounds. The anomalous behavior observed in the temperature dependence of mobility was attributed to the different features of the microstructure.     

Lattice thermal expansion of potassium lithium sulphate

Unit-cell parameters and coefficients of thermal expansion of potassium lithium sulphate have been determined accurately, as a function of temperature, by the X-ray powder diffraction method. Both the parameters ‘a’ and ‘c’ increase non-linearly with increasing temperature, the change in the ‘a’ parameter being more than that in the ‘c’ parameter. As a result, the average expansion coefficient along the c-axis is found to be very small when compared to that along the a-axis. The lattice thermal behaviour of this compound is explained in terms of the strength of the bonds along the respective directions. The diffraction pattern obtained at 435 °C was completely different from those taken at other lower temperatures, suggesting a structural change contrary to the earlier reports.     

Synthesis and structures of Na4P2Se6, Cs3PSe4, and Rb4P2Se9

Na₄P₂Se₆ (1) crystallizes in the orthorhombic space group Cmca (No. 64) with a = 11.836(3) ?, b = 13.311(4) ?, c = 8.061(2) ?, V = 1270.0(6) ?³, Z = 4, and, D _c = 3.283 g/cm³. Na₄P₂Se₆ belongs to the family of compounds with the general formula where A = Na⁺ and Q = Se²⁻. The crystal structure consists of isolated ethane-like P₂Se anions surrounded by Na⁺ cations. Cs₃PSe₄ (2) crystallizes in the orthorhombic space group Pnma (No. 62) with a = 10.0146(9) ?, b = 11.9899(10) ?, c = 9.9286(9) ?, V = 1192.17(18) ?3, Z = 4, and, Dc = 4.154 g/cm³. Cs₃PSe₄ belongs to the family of compounds with the general formula [(A^{+ x} ) _{z / x} (P ^v Q₄)^{− z} ] where A = Cs⁺ and Q = Se²⁻. The crystal structure consists of isolated methane-like PSe anions surrounded by Cs⁺ cations. Rb₄P₂Se₉ (3) crystallizes in the monoclinic space group C2/c (No. 15), a = 9.725(2) ?, b = 10.468(3) ?, c = 19.155(5) ?, β = 93.627(5)°, V = 1946.1(8) ?³, Z = 4, D _c = 3.804 g/cm³. Rb₄P₂Se₉ belongs to the family of compounds with the general formula [(A^{+ x} )_{(2 z −2)/ x} (Q₃PQ′—Q″—Q′PQ₃)^{−(2 z −2)}] where A = Cs⁺ and Q = Se²⁻, Q′ = Se¹⁻, Q″ = Se⁰. The crystal structure consists of isolated P₂Se anions surrounded by Rb⁺ cations.