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.     

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.     

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)     

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.     

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.     

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.     

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)     

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.     

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.     

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.     

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.     

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 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.     

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.     

On the occurrence of polytypism in single crystal CdTe thin films

Cadmium telluride thin films have been found to exhibit polytypism. The polytypes are formed when the as grown amorphous CdTe thin films undergo amorphous to crystalline transformation. The transformed single crystal regions correspond to different polytypes. Besides the well known zinc blende type 3 C cubic phase and less often found wurtzite type 2 H phase, four new polytypes (5 H, 6 H, 6 R and 15 R) the only ones known to-date have been found in the present investigation. In addition to the new polytypes, a new structural variant has also been found. This has the same ‘c’ parameter as that of the 2 H phase but has its ‘a’ lattice parameter as ‘a₀ \documentclass{article}\pagestyle{empty}\begin{document}$ a_{\rm o} \sqrt {3} $\end{document}’ (a₀ being the common lattice parameter of the polytypes). A feasible mechanism making the formation of polytypes intelligible has been suggested.     

Probabilistic and thermodynamic approach on phase behavior of nematic liquid crystals: A comparative study

The systems chosen for the present investigation, p-n-alkylbenzoic acid (nBAC; n = 6, 7) exhibits nematic-isotropic transition. A comparative study based on quantum probabilistic and statistical thermodynamics has been carried out with respect to translational and orientational motions. The evaluation of net atomic charges and dipole moment at each atomic centre has been carried out through the complete neglect differential overlap (CNDO/2) method. The modified Rayleigh-Schrodinger perturbation theory along with multicentered-multipole expansion method has been employed to evaluate the long-range intermolecular interactions, while the ‘6-exp’ potential function has been assumed for short-range interactions. The total interaction energy values obtained through these computations have been used as input to calculate the probability of occurrence of a particular configuration using the Maxwell-Boltzmann formula. Further, thermodynamic parameters such as Helmholtz free energy, and entropy at room temperature (300 K), and nematic-isotropic transition temperatures have been computed. An attempt has been made to understand the structure-phase behaviour relationship at molecular level.     

The thermal expansion of microcracks and grain boundaries in crystals (I). A new mechanism of crack formation

Apart from known reasons for crack formation it may be effected by the spontaneous microcrack wall heating. This heating takes place because of crack widening and formation of relatively free surfaces (crack walls). These surfaces must have the effective temperature that is well above the temperature in the bulk of crystals, as it has been shown earlier by the author. Simple equations for the thermal expansion of microcracks had been suggested. It has been shown that at the temperature above of 0.9T_m (T_m is the melting point) for the pure metals the spontaneous, without external stresses, crack formation takes place that may cause creep and superplasticity proceeding by the diffusion mechanism. At T_m the spontaneous cracking results in the crystal crushing to the microcrystallites, that is the spontaneous cracking may be considered to be the melting mechanism. From this point of view the intensive thermal expansion of liquids in temperature range from T_m to the critical temperature involves mainly the enlargement of microcrystallite gaps. By using this supposition simple equations for thermal expansion of liquids have been proposed.     

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.     

Thermal properties of a Nd:LuVO4 crystal

A Nd‐doped lutetium orthovanadate Nd:LuVO₄ crystal has been grown using a modified Czochralski method. The thermal properties of this crystal have been studied by measuring the thermal expansion, specific heat and thermal diffusivity. The thermal expansion coefficients are α₁₁ = 1.7 × 10^‐6, α₂₂ = 1.5 × 10^‐6 and α₃₃ = 9.1 × 10^‐6/K in the temperature range of 298–573 K along the three respective crystallographic axes. The specific heat is almost linear and increases from 0.442 to 0.498 Jg^‐1K^‐1 in the measured temperature range. The thermal diffusivity is anisotropic and decreases with increasing temperature from 295 to 548 K. At room temperature the calculated thermal conductivities κ₁₁ and κ₃₃ are 7.96 and 9.77 Wm^‐1K^‐1, respectively. These thermal parameters of Nd:LuVO₄ crystal have indicated that it is an excellent candidate laser material. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)