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.     

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.     

Crystal Growth and Properties of the Compounds CuGa3Se5 and CuIn3Se5

CuIn₃Se₅ and CuGa₃Se₅ uniform single crystals 12 mm in diameter and 40 mm in length with the chalcopyrite‐related structure were prepared by directed crystallization of the melt. The melting points of these compounds were defined by means of the differential thermal analysis (DTA). The lattice parameters a and c as well as the axial thermal expansion coefficients α_a and α_c were determined as a function of temperature in the range from 90 to 650 K by the X‐ray diffraction method (XRD). It is found that for both the compounds the coefficients of expansion along the a ‐axis are larger than those along the c ‐axis over the entire temperature range studied.     

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.     

X-Ray Study of the Structure and Thermal Properties of Ba1–xKxBiO3 at Different Temperatures

The crystal structure as well as the temperature and composition dependences of the lattice parameters, the thermal expansion coefficients in the high-temperature superconducting Ba_1–xBiO₃ system were determined by an X-ray powder diffraction method at temperatures between 80 and 650 K. The character of variation of intensity, profiles, and line widths of the diffraction lines for different perovskite structures as a function of the content x and temperatures was found. The correlation between the behaviour of the thermal expansion coefficients and potassium content was revealed at different temperatures. It is shown that the thermal expansion coefficients vary inversely with rising x at any temperature in the range from 80 to 400 K.     

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.     

Effect of Lithium Doping in the Bi-2212 Superconducting System

Samples with the nominal composition Bi₂Sr₂Ca_1–xLi_xCu₂O_y (x = 0.2,0.4, and 0.6) and Bi₂Sr₂CaCu_2−x L1_xO_z (x = 0.4, 0.6, and 1.0) were prepared by the solid state reaction method. The role of L1 at both Ca and Cu sites in the Bi-2212 composition were studied. From the X-ray diffraction data it was found that the L1-doped at the Ca site increases the c-axis and that doped at the Cu site decreases the c-axis. From the D.C. four-probe resistivity data it was found that Li-doped at the Ca site reduces the T_c and the L1-doped at the Cu site gives T_c(0) above the liquid nitrogen temperature. It was observed that the L1 doping reduces the melting point of Bi-2212 composition. The presence of Lithium was confirmed by inductive the coupled plasma method.     

Compressibility in the Tetragonal Phase of AgInS2 From the X-ray Diffraction Data under High Pressure

The lattice parameters a and c as well as the compressibilities for different directions in the AgInS₂ chalopyrite-type compound are determined as a function of pressure up to 5 GPa using a powder X-ray technique under high pressure. It is found that the compressibility is anisotropic, with compressibility along the tetragonal c-axis (𝓏_c) being smaller than that along the a-axis (𝓏_a). It is shown that as pressure rises the axial ratio c/a increases and as a result the tetragonal distortion δ = 2 - c/a reduces.     

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.     

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.     

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.     

Controllable thermal expansion properties of In2 − xCrxMo3O12

Solid solutions In_{2 − x}Cr_xMo₃O₁₂ have been prepared via the solid state reaction method. The structural and thermal expansion properties have been characterized using X‐ray diffraction. All compounds exhibit monoclinic structure with space group P2₁/a at room temperature, and transform to orthorhombic structure at higher temperature. Compounds In_{2 − x}Cr_xMo₃O₁₂ (x = 0.7, 1.0 and 1.3) possess strong positive thermal expansion in the monoclinic structure, while their thermal expansion coefficients of orthorhombic structure vary from negative to positive with increasing Cr content. It is worthwhile to note that In_1.3Cr_0.7Mo₃O₁₂ and InCrMo₃O₁₂ have near zero thermal expansion properties.     

Debye characteristic temperatures from X-ray diffraction data and some thermal properties for AgGa1−xInxS2 solid solutions

Investigations of the Debye characteristic temperature for the AgGa_1−xIn_xSe₂ solid solutions, calculation of some thermodynamic properties and analysis of its variation during substitution of Ga by In showed the increase of the molar volume, density, heat capacity, enthalpy, and decrease of the melting temperature, microhardness, thermal expansion coefficients, intrinsic energy with zero-point energy, this giving evidence for a decrease of the forces of the interatomic interaction.     

Crystal growth and investigation of CuAlxGa1−xTe2 solid solutions

Alloys of the CuGaTe₂‐CuAlTe₂ system have been synthesized by the one‐temperature method and homogenized by annealing. It was established for the first time by X‐ray and DTA methods that a continuous row of solid solutions is formed in the system. Large block crystals of CuAl_xGa_1−xTe₂ solid solutions have been grown by the Bridgman method (horizontal version). Measurements of density, microhardness and thermal expansion have been carried out on the grown crystals. It has been established, that the density and thermal expansion coefficients are changed linearly with composition, microhardness has a maximum at x = 0.6. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Thermal expansion and structural properties of (CuAlTe2)1–x(CuAlSe2)x solid solutions

Investigations of the thermal expansion of (CuAlTe₂)_1–x(CuAlSe₂)_x solid solutions in the temperature range from 100 to 800 K have been carried out for the first time. It has been demonstrated that the thermal expansion coefficient α_L grows considerably in the temperature range from 100 to 300 K, whereas the temperature dependence above 300 K is rather weak. The isotherms of composition dependence of the thermal expansion coefficient α_L for 100, 293, 500 and 800 K were constructed, and it was found that linear relations could express them. The Debye temperatures θ_D , the average mean‐square dynamic displacements , the average root‐mean‐square amplitudes of thermal vibration RMS , the anion position parameter u using S. C. Abrahams & J. L. Bernstein (u_AB ) and J. E. Jaffe & A. Zunger (u_JZ ) models were calculated. The composition dependence of microhardness H using the phenomenological theory was also calculated, and it was discovered that this dependence has a non‐linear character with a maximum of 383 kg/mm² at x=0.67. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Distribution of aluminum and indium impurities in crystals of Ge-Si solid solutions grown from the melt

The problem regarding the distribution of aluminum and indium impurities in bulk crystals of solid solutions with a variable composition Ge_1−x Si _x (0 ≤ x ≤ 0.3) is solved in order to establish regularities of the changes in the segregation coefficients of impurities with variations in the composition of the host lattice in the germanium-silicon system. Aluminum-and indium-doped crystals of Ge_1−x Si _x (0 ≤ x ≤ 0.3) solid solutions with a silicon content decreasing along the crystallization axis are grown by a modified Bridgman method with the use of a silicon seed. The concentration distribution of impurities over the length of the crystals is determined from Hall measurements. It is demonstrated that the experimental data on the concentration distribution of impurities in the crystals are in good agreement with the results obtained from the theory according to which the equilibrium segregation coefficients of impurities vary linearly with a change in the composition of Ge-Si solid solution crystals.

     

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.     

X-ray determination of thermal expansion of Na(ClO3)x(BrO3)1−x mixed crystals

Lattice constants of sodium chlorate and sodium bromate and their mixed crystals were determined over the temperature range from room temperature to 320 °C. The observed lattice constants for the various compositions show strong deviations from those expected from Vegard's rule. The lattice constants at various temperatures were fitted to polynomials of type a = a₀ + a₁t + a₂t². The linear coefficients of expansion for the Na(ClO₃)_x · (BrO₃)_1−x series varies non-linearly with composition showing negative deviations from linearity.     

Temperature variation of the structural and thermal characteristics of YBa2Cu3O7−x in the range from 90 to 400 K

The X-ray studies of the tetragonal YBa₂Cu₃O_7−x compound are performed at different temperatures from 400 to 90 K and the temperature variation of the thermal expansion coefficients and the Debye characteristic temperature is determined. The anisotropy of thermal expansion is investigated. It is found that the two dynamical characteristics monotonously decrease with temperature lowering whereas for the superconducting orthorhombic modification their temperature dependences are anomalous. The mean thermal expansion coefficient as well as the overall Debye temperature for the tetragonal phase are smaller than those for the orthorhombic one.