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.     

Interatomic force constants in AIIBIVCV2 chalcopyrite compounds

Force constants of the A^II C^V and B^IV C^V bonds in the A^IIB^IVC^V₂ compounds with chalcopyrite structure are estimated from experimental lattice vibration data using a simplified version of the Keating model. It is shown that the force constants depend exponentially on the bond length. The parameters of this relation are practically the same as those found for the A^IV A^IV, A^III B^V and A^II B^VI bonds in the elemental semiconductors and binary compounds and for the B^III C^VI bond in the A^IB^IIIC^VI₂ semiconductors.     

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.     

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 anisotropy and individual bond expansion coefficients in ternary chalcopyrite compounds

The individual bond expansion coefficients of the A^IIB^IVC and A^IB^IIIC₂^VI chalcopyrite compounds are calculated from the principal linear thermal expansion coefficients of the lattice parameters using the regular B C tetrahedron model and a model with a temperature independent free parameter of the lattice. It is shown that the bond expansion coefficients derived from the latter model are in better agreement with the trends found for the interatomic forces in the chalcopyrite compounds and observed for the thermal expansion coefficients in the binary AC, A^IIC and BC compounds.     

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.     

Heat capacity of LiInS2, LiInSe2 and LiInTe2 between 200 and 550 K

The molar heat capacity at constant pressure of LiInS₂, LiInSe₂ and LiInTe₂ was measured in the temperature range from about 200 K to 550 K. An analysis of the experimental data showed that the anharmonic contribution to the heat capacity can be described by a polynomial of fourth order in the temperature. A comparison of the results for the LiInC₂^VI compounds with those for the AgB^IIIC₂^VI and A^IIB^IVC₂^V chalcopyrite compounds showed that the lattice anharmonicity effects are essentially influenced by the specific nature of the Li C^VI bond.     

Heat capacity and lattice anharmonicity in CdBIVC chalcopyrite compounds

The heat capacity at constant pressure of CdSiP₂, CdGeP₂, CdSnP₂ and CdGeAs₂ is measured in the temperature range from 300 to 500 K. The anharmonic contribution to the heat capacity is evaluated and it is shown that the degree of lattice anharmonicity decreases with increasing atomic weight of the constituent atoms of the compounds. Comparing the temperature variation of the heat capacity and of the thermal expansion coefficient some conclusions are made regarding the interatomic potential in the A^IIB^IVC compounds.     

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.     

Intra- vs intermolecular hydrogen bonding. The crystal structure of 5-methyl-2-hydroxyacetophenone thiosemicarbazone monohydrate and salicylaldehyde-2-methylthiosemicarbazone monohydrate

The crystal structure of 5-methyl-acetophenonethiosemicarbazone monohydrate,A, and salicylaldehyde-2-methylthiosemicarbazone monohydrate,B, were determined using single crystal X-ray diffraction.A crystallizes in the monoclinic space groupC2/c, with lattice parametersa=14.161(2),b=15.753(1) ?,c=11.084(1) ?, β=112.59(1)° andZ=4, yielding a calculated density ofD _calc=1.352 mg/m³.B crystallizes in the triclinic space groupP1, witha=7.233(2) ?,b=7.371(2) ?,c=11.841(2) ?, α=82.77(2)°, β=78.33(2)°, γ=63.06(2)° andD _calc=1.371 mg/m³ forZ=2,. In bothA andB the immine nitrogen and the sulfur atom areanti with respect to N2-C8. WhileA presents the usual intramolecular six membered hydrogen bond ring,B has instead an intermolecular hydrogen bond between the hydroxy moiety of the salicyladehyde and a water molecule. AM1 calculations agree with the experimental conformations observed in both compounds. Contribution No. 1619 of the Instituto de Química, UNAM.     

Über die röntgenographische Analyse der mittleren quadratischen Atomverschiebungen in einigen Halbleiterkristallen

X-ray measurements of the Debye-Waller factor were performed with single crystals of Ge and of semiconducting compounds A^IIIB^V, A^IIB^VI, A^IVB^VI in the temperature range 100 K — 1000 K. From the results the mean square atomic displacements 〈u²〉 and the Debye characteristic temperatures θ of the materials were calculated. Both parameters are discussed with respect to the influence of the temperature, the influence of point defects and, in the case of the compounds, deviations from the stoichiometric composition on the thermal lattice vibrations. Finally, considerations are presented, concerning the relationship between the parameters 〈u²〉 and θ_M, respectively, and the activation energies of vacancy formation and diffusion in the materials.     

Intra- vs intermolecular hydrogen bonding. The crystal structure of 5-methyl-2-hydroxyacetophenone thiosemicarbazone monohydrate and salicylaldehyde-2-methylthiosemicarbazone monohydrate

The crystal structure of 5-methyl-acetophenonethiosemicarbazone monohydrate,A, and salicylaldehyde-2-methylthiosemicarbazone monohydrate,B, were determined using single crystal X-ray diffraction.A crystallizes in the monoclinic space groupC2/c, with lattice parametersa=14.161(2),b=15.753(1) Å,c=11.084(1) Å, β=112.59(1)° andZ=4, yielding a calculated density ofD _calc=1.352 mg/m³.B crystallizes in the triclinic space groupP1, witha=7.233(2) Å,b=7.371(2) Å,c=11.841(2) Å, α=82.77(2)°, β=78.33(2)°, γ=63.06(2)° andD _calc=1.371 mg/m³ forZ=2,. In bothA andB the immine nitrogen and the sulfur atom areanti with respect to N2-C8. WhileA presents the usual intramolecular six membered hydrogen bond ring,B has instead an intermolecular hydrogen bond between the hydroxy moiety of the salicyladehyde and a water molecule. AM1 calculations agree with the experimental conformations observed in both compounds.     

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)     

The Preparation and Crystal Structure of MgP4

In the systematical study of the A¹¹B^V semiconducting compounds the Mg-P system has been examined. Among the products of crystallization from Bi Pb Sn alloy the crystals of a new compound MgP₄ have been identified. It has been found that these crystals are isostructural with CdP₄. The crystal structure refinement from X-ray data has been performed. The lattice constants are: a = 5.141 Å, b = 5.079 Å, c = 7.518 Å, β = 98.64°; Z = 2; space group P2₁/c.     

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.     

Strukturchemische Charakterisierung eines durch Gasphasenabscheidung darstellbaren orthorhombischen Borcarbids der Zusammensetzung B8C

Pyrolysis of BJ₃ and CJ₄ under a reduced pressure and at substrate temperatures of between 900 and 950°C yielded an orthorhombic boron carbide of composition B₈C, with a carbon concentration of 12,5 to 13,0 wt.% and a density of 2,42 g/ml. The structure of B₈C is built up from stable (B₁₂)₄C₂ subunits, the structures of which are known from the tetragonal B₄₈B₂C₂ compound. The (B₁₂)₄C₂ subunits are themselves linked by single carbon atoms in the a–b plane. Owing to the strong disorder of the B₈C crystals we were unable to distinguish between two possible structures: a) The unit cell of B₈C is built up from eight (B₁₂)₄C₂ subunits with the lattice constants a = 35,909, b = 17,653, and c = 5,094 Å, or b) The larger cell is formed by twinning and the unit cell of B₈C contains only four (B₁₂)₄C₂ subunits with lattice parameters a = 17,955, b = 17,653, and c = 5,094 Å.     

Lattice Parameter Study in the Bi1–xSbx Solid-solution System

The lattice parameters of Bi_1–xSb_x single crystals were measured for 0 ≦ x ≦ 1 by a special X-ray diffractometer technique using reflections chosen so that minimum errors were achieved. Corrections for thermal expansion and refraction were applied. The antimony concentration was determined by means of electron microprobe analysis. The dependences of the lattice parameters on x (in nm) can be described with good approximation by a = 0.45469 – 0.02398x and c = 1.186294 – 0.058632 [1 + 1.26 (x⁻¹ – 1)]⁻¹, resp. The behaviour of the parameter a is in agreement with the earlier study by CUCKA and BARRETT , whereas their linear expression for c(x) (0 ≦ x ≦ 0.3) was not confirmed.     

Lattice Vibrations and Interatomic Forces in AIIB2IIIC4VI Defect-Chalcopyrite Compounds (I) Keating Model Considerations

The lattice vibrations of the A^IIB^III₂C^VI₄ semiconductors with defect-chalcopyrite structure are treated in a simplified version of the Keating model considering only interaction with nearest neighbours and assuming that all anions occupy their ideal lattice sites. It is found that in this model the frequencies of the nonpolar and polar modes with highest energy are determined by the properties of the B^III–C^VI sublattice alone. The frequencies of all the other optical modes depend not only on the A^II–C^VI and B^III–C^VI interactions but are also influenced by the presence of the ordered array of vacancies. The results obtained are compared with previous model considerations.     

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.