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.     

Determination of lattice parameters and thermal expansion of CuGe2P3 + 0.2 Ge3P4 at elevated temperatures

CuGe₂P₃ is a p‐type semiconductor with zincblende structure. Ge₃P₄ is soluble up to 35 mole% in CuGe₂P₃. Lattice parameters of CuGe₂P₃ + 0.2 Ge₃P₄ have been determined at elevated temperatures from room temperature to 873 K using the x‐ray diffraction profiles (111), (200), (220), (311), (222), (400), (331), (420), (422) and (511) obtained from high temperature diffractometer. It is found that the lattice parameter increases linearly from 0.53856 nm at RT to 0.54025 nm at 873 K. The data on lattice parameter is used and coefficient of lattice thermal expansion of CuGe₂P₃ +0.2 Ge₃P₄ was determined at different temperatures. It is found that the coefficient of thermal expansion of CuGe₂P₃ +0.2 Ge₃P₄ is 5.48 x 10^‐6 K^‐1 and is independent of temperature. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Effect of In and Sb Vacancies on Temperature Dependence of InSb Lattice Parameter at High Temperatures

The temperature dependence of the thermal expansion coefficient for InSb has been determined in the range 25–515 °C by precision measurements of the lattice parameter of InSb single crystals. It is shown that beginning from 460 °C the temperature dependence of the lattice parameter for InSb single crystals grown from melts of different compositions is essentially affected by vacancies in the indium and antimony sublattices. The vacancy concentration and possible deviation of InSb from the stoichiometric composition are estimated from a relative decrease in the lattice parameter.     

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.     

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.     

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.     

Thermal Expansion of SrF2 at Elevated Temperatures

The X-ray method was used to determine the linear thermal expansion coefficient of SrF₂ in the temperature range from 301 to 1173 K. A comparison of the thermal expansion coefficients of CaF₂, SrF₂ and BaF₂ at T > 300 K shows that the degree of lattice an–harmonicity in the alkaline earth fluorides decreases with increasing mass of the alkaline earth atom. The results for the thermal expansion of SrF₂ are used to discuss the temperature dependence of the lattice mismatch in the SrF₂/InP film–substrate system.     

Low temperature neutron diffraction and magnetization of Fe25Cu75 solid solutions

Metastable Fe₂₅Cu₇₅ solid solution obtained by high-energy ball milling has been studied by means of neutron thermo-diffraction and magnetization measurements. This material, which crystallizes in a face centered cubic (FCC) crystal structure, is ferromagnetic, with a value for the Curie temperature, around 190 K. The linear thermal expansion coefficient, α_T, has been estimated from the temperature dependence of the lattice parameter in the temperature range 5–300 K. An increase in the value of α_T following the normal trend observed in other metallic compounds is observed below 150 K, however, above this temperature α_T remains almost constant indicating a slight magneto-volume effect in this material.     

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)     

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 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.     

Growth,composition, ferroelectric and magnetic properties of new multiferroic Pb3.3Mn4.8Ni1.1Ti0.56O15.3 single crystals

Multiferroic single crystals in the novel system Pb‐Mn‐Ni‐Ti‐O have been grown by the high temperature solution growth method. At room temperature the crystals are indexed in the hexagonal space group P6₃cm. The dielectric and magnetic properties along with the temperature dependence of the c‐lattice parameter have been studied in the temperature range 2 K ‐ 500 К. The magnetic measurements reveal a paramagnetic to antiferromagnetic phase transition around 48 K. The dielectric permittivity exhibits a maximum at 430 K, indicating ferroelectric to paraelectric phase transition. The temperature dependent Raman and XRD measurements around 430 K reveal an anomaly and abrupt change of the lattice parameter along the z‐axis respectively, thus confirming the ferroelectric‐to‐paraelectric phase transition.     

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)     

Influence of the real structure on the linear thermal expansion coefficient of A15-type intermetallic compounds from room temperature to 10K

The temperature dependence of the thermal expansion coefficient of a number of A15-compounds was investigated by X-ray diffraction experiments. The expansion coefficient of the high-temperature superconductors with the A15-structure is highly temperature dependent and has negative values below 100K. Deviations from the stoichiometric composition, substitution of foreign atoms and lattice distortions prevent negative values of the expansion coefficient. The results are discussed in connection with other physical properties of these compounds.     

Thermal Expansion of EuF<Subscript>2 + <Emphasis Type="Italic">x</Emphasis></Subscript> Single Crystals and Their Thermal Stability

Thermal expansion of an EuF_2.136 nonstoichiometric crystal with the fluorite structure type (Eu _0.864 ²⁺ Eu _0.136 ³⁺ F_2.136, lattice parameter 5.82171(5) Å) has been experimentally investigated in the temperature range of 9–500 K. The coefficient of thermal expansion is α = 15.8 × 10^–6 K^–1 at T = 300 K. The observed anomalies in the behavior of the coefficient of thermal expansion at T > 400 K are related to the oxidation processes with partition of Eu²⁺ ions. It is established by differential scanning calorimetry that the onset temperature of EuF_{2 + x} oxidation in air is 430 K and that this process occurs in three stages. X-ray diffraction analysis shows that the oxidation is accompanied by the formation of a phase mixture based on two modifications of the Eu _{1– y} ³⁺ Eu _y ²⁺ F_3–y solid solution with the structure types of tysonite (LaF₃), orthorhombic β-YF₃ phase, and europium oxyfluorides of variable composition EuO_1–xF_{1 + 2x}, with dominance of the latter.     

衬底用单晶金刚石晶格随温度变化的研究

本文对CVD(Chemical Vapour Deposition,CVD)外延生长中作为衬底的高温高压(HTHP)单晶金刚石进行拉曼光谱测试,利用谱峰半高宽(FWHM)判断了衬底的结晶质量.开展了升温(室温～1000℃)和降温(1000℃ ～室温)过程中衬底晶格变化的X射线原位测量研究.实验表明:衬底的晶格常数随温度...     

Crystal Structures and Phase Transformations of the Fluorinated Fullerenes

Abstract

In situ x-ray diffraction experiments of the fluorinated fullerenes, C₆₀F _x (x = 0, 36 and 48) at high temperatures have been undertaken. The structural phase transformation of C₆₀F₄₈ was observed at about 358 K. It was also found that the lattice parameters of the low temperature phase of C₆₀F₄₈ show anomalous change at about 310 K. The thermal expansion coefficients of the fluorinated fullerenes were determined by using the change of the lattice parameters with temperature.     

X-ray investigation on GaAlAs/GaAs epilayers bending at temperatures 77–750 K

The Bond method of precise lattice constants measurements and double crystal (+, −) (004) reflections were applied to measure lattice constants, lattice mismatch, thickness of the layers and samples bending in temperature 77–750 K. The results enabled to calculate the ratio of GaAs and Ga_1−xAl_xAs elastic constants as well as thermal expansion coefficients.     

To the new theory of crystal strength

The main conceptions of the non-dislocation theory of crystal strength have been proposed. These are the thermal stress, the temperature coefficient of thermal stress, and the initial microstrain ϵ_in at which the thermal stresses start. These conceptions made possible an explanation of the crystal lattice mechanical instability that is well known from strength tests. A new simple form of Morse potential, a relation for the thermal stress, and a way to find the temperature coefficient in this relation have been advanced. Some measurements of very high and of common practice strengths of crystals were compared with theoretical suppositions and calculations.     

Low expansion in [(Fe0.9Co0.1)0.72B0.24Nb0.04]95.5Y4.5 bulk metallic glass

The thermal expansion behavior of an iron-based bulk metallic glass (BMG) [(Fe_0.9Co_0.1)_0.72B_0.24Nb_0.04]_95.5Y_4.5 is studied. The expansion coefficient in the wide temperature range of 100–300 K keeps in a constant, which is close to that of the Kovar alloy. Furthermore, the expansion coefficient of the BMG can be tuned by annealing below glass transition temperature. The results have implication for understanding the origin of low expansion, and the BMG may have a potential for commercial low expansion material.