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.     

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.     

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.     

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)     

X-Ray Studies of Some Europium Compounds at Elevated Temperatures

The temperature variation of the lattice constants of europium iron garnet (Eu₃Fe₅O₁₂), europium sulphide (EuS) and europium fluoride (EuF₂) has been studied using an X-ray powder diffractometer. The lattice constant of Eu₃Fe₅O₁₂ increases linearly upto 800 °C with an expansion coefficient of 10.4 × 10⁻⁶ °C⁻¹. In the case of EuS, the lattice constant increases non-linearly with temperature. At room temperature the expansion coefficient has a value of 14.3 × 10⁻⁶ °C⁻¹. In EuF₂ the lattice constant increases non-linearly upto 140 °C. At higher temperatures, the lattice constant decreases with increasing temperature with a negative expansion coefficient of −29 × 10⁻⁶ °C⁻¹ over the range 170–235 °C. The cause of the anomalous behaviour observed in EuF₂ is yet to be understood.     

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.     

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.     

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.     

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 determination of thermal lattice expansion of CuSi2 + xP3 (x = 1, 2) at elevated temperatures

CuSi₂P₃ is a semiconductor having sphalerite structure with the space group F3 3m with random distribution of the copper and silicon atoms on the cation sites. Silicon is soluble in CuSi₂P₃ upto 3 moles to form CuSi_{2 + x}P₃ (x = 1, 2, 3) compounds in single phase. In continuation of our work on thermal expansion of ternary semiconductors, CuSi₃P₃ crystals have been grown by a modified Bridgman method. Using a Unicam high temperature camera, the precision lattice parameter and the coefficient of thermal expansion (CTE) of CuSi₃P₃ at various high temperatures have been evaluated from X-ray diffraction data. It has been found that the lattice parameter increases non-linearly while the coefficient of thermal expansion increases linearly with temperature. The results on thermal expansion of various semiconductors have been discussed in terms of their ionicities.     

In‐situ investigation of the temperature dependent structural phase transition in CuInSe2 by synchrotron radiation

The temperature dependent structural phase transition from the tetragonal chalcopyrite like structure to the cubic sphalerite like structure in CuInSe₂ was investigated by in‐situ high temperature synchrotron radiation X‐ray diffraction. The data were collected in 1K steps during heating and cooling cycles (rate 38 K/h). The Rietveld analysis of the diffractograms led us to determine the temperature dependence of the lattice parameters, including the tetragonal deformation, |1‐η|, and distortion |u‐¼| (η=c/2a, a and c are the tetragonal lattice constant; u is the anion x‐coordinate). The thermal expansion coefficients α_a and α_c of the tetragonal lattice constant which are related to the linear thermal expansion coefficient α_L were obtained, as were α_a of the cubic lattice constant, also α_u and α_η. The transition temperature is clearly identified via a strong anomaly in α_L. The temperature dependence of the anion position parameter was found to be rather weak, nearly α_u∼0, whereas α_η increases slightly. However, both increase strongly when approaching to within 10 K of the transition temperature (the critical region) and |1‐η| as well as |u‐¼| go to zero with |T‐T_trans|^0.2 approaching the phase transition. The cation occupancy values, derived from the Rietveld analysis, remain constant below the critical region. Close to the transition temperature, the number of electrons at the Cu site increases with a dercrease in the number of electrons at the In site with increasing temperature, indicating a Cu‐In anti site occupancy, which is assumed to be the driving force of the phase transition. At the transition temperature 67% of Cu⁺ were found to occupy the Me1 site with a corresponding 67% of In³⁺ at the Me2 site. Although full disorder is reached with 50%, this level seems to be high enough that the phase transition takes place. The order parameter of the phase transition, goes with |T‐T_trans|^β to zero with the critical exponent β=0.35(7) which is in good agreement to the critical exponent β=0.332 calculated for order‐disorder transitions according to the Ising model. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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 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.     

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.     

Investigations of phase relations in the system CaO?Na2O?K2O?P2O5

The lattice constants of the compound Ca₂NaK(PO₄)₂ have been studied at room temperature using an X-ray powder diffractometer and also in the temperature range from 20 up to 1000 °C by Guinier-Lenné-technology. A hexagonal lattice with the parameters a₀ = 5.4367 Å and c₀ = 7.3125 Å and a cell volume of 187.18 ų has been determined for the high temperature phase, existing from 670 °C upward. At temperatures below 670 °C a superlattice structure is formed by tripling the axis a, a ′, and c so that it results in a hexagonal superlattice structure cell with the lattice constants of a₀ = 16.311 Å and c₀ = 21.939 Å and a cell volume of 5054 ų.     

High temperature x‐ray diffraction studies of zirconia thin films prepared by reactive pulsed laser deposition

Zirconium oxide thin films have been deposited on Si (100) substrates at room temperature at an optimized oxygen partial pressure of 3x10^‐2 mbar by reactive pulsed laser deposition. High temperature x‐ray diffraction (HTXRD) studies of the film in the temperature range room temperature‐1473 K revealed that the film contained only monoclinic phase at temperatures ≤ 673 K and both monoclinic and tetragonal phases were present at temperatures ≥ 773 K. The tetragonal phase content was significantly dominating over monoclinic phase with the increase of temperature. The phase evolution was accompanied with the increase in the crystallite size from 20 to 40 nm for the tetragonal phase. The mean thermal expansion coefficients for the tetragonal phase have been found to be 10.58x10^‐6 K^‐1 and 20.92x10^‐6K^‐1 along a and c‐axes, respectively. The mean volume thermal expansion coefficient is 42.34x10^‐6 K^‐1 in the temperature range 773‐1473 K. (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Contraction of amorphous CoP alloys during structural relaxation

The structural relaxation of amorphous alloys is accompanied by an increase of their mechanical density. This is shown by measurements of the thermal expansion of electrodeposited CoP alloys between room temperature and crystallization. Above 80°C, the temperature of preparation, the linear thermal expansion coefficient is apparently reduced as a consequence of a superimposed shrinkage, whereas the true thermal expansion coefficient is not affected by any preceding thermal treatment. The velocity of contraction increases with temperature when the material is continuously heated. But the value of the contraction per degree increase in temperature is constant above a certain temperature T₁. The higher the heating rate, the higher T₁. The mathematical treatment of these experimental results is difficult because the relaxation property, the contraction, depends not only on temperature but also on time and on the preceding thermal treatment.     

Glass transition and thermal expansivity in silica-polystyrene nanocomposites

The glass transition temperature T_g and the thermal expansion coefficient have been measured using the capacitive scanning dilatometry for silica-polystyrene (PS) nanocomposites with various silica volume fraction up to 50 vol.%. The glass transition temperatures for silica-PS nancomposites show a deviation from the bulk T_g together with a large scatter. Thermal expansivity decreases with increasing silica fraction both below and above T_g. A clear relaxation peak can be observed in the expansivity-temperature curve for silica-PS nanocomposites. The intensity of the peak decreases with increasing silica fraction. The decrement is larger than the value expected on the assumption that silica particles do not participate in the glass transition.     

Temperature variation of lattice parameter and thermal expansion of TmAl2

The lattice parameter of TmAl₂ has been measured from room temperature to 637 K using CuKα-radiation. The data have been used to evaluate the coefficient of thermal expansion at various temperatures. It was found that the lattice parameter increases while the coefficient of expansion remains constant throughout the range of temperature studied.