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)     

Low-temperature X-ray studies of crystal-lattice parameters and thermal expansion of KTiOPO4 crystals

The unit-cell parameters a, b, and c of KTiOPO₄ crystals have been measured by the X-ray diffraction method in the temperature range 80–320 K. The parameters obtained were used to determine the thermal expansion coefficients α_[100], α_[010], and α_[001] along the principal crystallographic axes. It was established that thermal expansion in the crystals is essentially anisotropic and that α_[010] > α _[100], whereas α_[001] is close to zero.     

Algorithm and program for precise determination of unit-cell parameters of single crystal taking into account the sample eccentricity

Crystallography Reports - A technique has been developed to refine the unit-cell parameters of single crystals with minimization of the influence of instrumental errors on the result. The...     

Temperature dependence of lattice parameters of SBN single crystals in the vicinity of their structural phase transitions

Changes of lattice parameters of Sr_xBa_1‒xNb₂O₆ (0.35 < x < 0.72) solid solution single crystals were measured as a function of temperature. The X‐ray Bond’ method was used to carry out very precise measurements of the lattice parameters. Fine correlations between values of the lattice parameter and the Sr concentration in the solid solution of Sr_xBa_1‒xNb₂O₆ single crystals are found. A conventional analysis of lattice parameter data in terms of spontaneous strain and strain/order parameter coupling shows that a normal structural phase transition does occur. While the ferroelectric system (SBN26) displays a nearly tricritical behavior, β ≈ 0.20, the relaxor one (SBN61) complies with the two‐dimensional Ising‐model‐like criticality, β ≈ 0.17.     

Correlation between the lattice parameters of crystals with perovskite structure

The correlation \((\bar a_2 + \bar a_3 ) = (\bar a_1 + \bar a_4 )\) has been established for the mean parameters of the reduced perovskite unit cells, \(\bar a_1 ,\bar a_2 ,\bar a_3 \) and \(\bar a_4 \) of four arbitrary compounds with the perovskite structure having the compositions (1) ABX₃, (2) A′BX₃, (3) AB′X₃, and (4) A′B′X₃, where A, A′ and B, B′ are the pairs of metal atoms with equal valences and X is an oxygen or halogen atom. The above correlation is consistent with the model of harmonic quasi-elastic atomic interactions.     

X-ray two-crystal diffractometer for testing of plane analyser crystals

A two-crystal diffractometer (TCD) for testing the mosaic structure of LiF crystals is presented. Peculiarities are the adapted sensivity (angular minutes), short measuring times, large registered areas and the possibility of application for various kinds of surface treatment.     

X-ray crystal orientation determination for semiconductor single crystals

An improved method to measu reorientation angles of flat single crystals was developed taking Buerger precession technique. The method is described and compared with Laue- and goniometer techniques. Advantages are low costs and short measuring time. An easy evaluation of the records allows to take this method as a routine angle determination for semiconductor manufacturing.     

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.     

New method for calculating the intensities of X rays and thermal neutrons diffracted in single crystals with defects

A new method is proposed to calculate the intensities of X rays and thermal neutrons diffracted in single crystals with defects. This method is based on comparing the dynamic theory of the Bragg diffraction of X rays and thermal neutrons in perfect single crystals with the small-angle scattering theory.     

Adiabatic bond charge model for lattice dynamics of ternary chalcopyrite semiconductors

The adiabatic bond charge model of Rustagi and Weber is extended to study lattice dynamical properties of ternary chalcopyrite semiconductors AgGaS₂, AgGaSe₂, CuInS₂, CuInSe₂, CuGaS₂, CuGaSe₂, CuAlS₂ and CuAlSe₂. The new model calculations agree well with the results of Raman/IR and neutron measurements of Brillouin zone center phonon frequencies for both low and high frequency modes which was difficult for other phenomenological lattice dynamical models. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Atomic structure and high anisotropy of thermal expansion in NiSi single crystals. II. Temperature-induced structural changes

X-ray diffraction analysis of the atomic structure of NiSi crystals was performed by diffraction data obtained at 295 and 418 K. The temperature-induced changes in the bond lengths and valence angles were analyzed and the high anisotropy of thermal expansion of these single crystals was interpreted in terms of crystal chemistry.     

Atomic structure and enormous anisotropy of thermal expansion in NiSi single crystals. I. Refinement of structure models

The atomic structure of NiSi single crystals has been studied by the methods of X-ray diffraction analysis at 295 and 418 K. The refinement of the structure models with due regard for anharmonicity of atomic vibrations revealed the pronounced anisotropy of thermal vibrations and the considerable contribution of the fourth-order anharmonicity. The maps of the probability density function of atomic displacements and single-particle potentials of both atoms were constructed.     

Modeling of the shape of polyethylene oxide single crystals and determination of the kinetic crystallization parameters: Theoretical and experimental approaches

The curvature of faces of polymer single crystals is described by the system of Mansfield equations, which is based on the Frank-Seto growth model. This model assumes the velocity of nucleus steps to be the same for their propagation to the right and left and is valid only for symmetric crystallographic planes. To describe the shape of polyethylene oxide single crystals grown from melt and limited by the {100} and {120} folding planes, it is assumed that the layer velocities to the right and left are different on {120} faces. This approach allows modeling, with a high accuracy, of the observed shapes of polymer single crystals grown at different temperatures, which makes it possible to determine unambiguously the fundamental crystallization parameters: the dimensionless ratio of the secondary homogeneous nucleation rate to the average velocities of nuclei along the crystallization planes and the ratio of nucleus velocities to the right and left. In addition, it was found that a known macroscopic single-crystal growth rate can be used to determine the absolute values of the secondary homogeneous nucleation rate and the velocities of nuclei along the growth plane.     

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)     

X-ray double crystal diffractometer for testing of plane analyser crystals of LiF

A double crystal diffractometer (DCD) for testing LiF crystals is presented. It is possible to distinguish in a relatively short measuring time (nearly 10 minutes including change of sample and adjustment) between crystals with block desorientation angles >1′ and ≦ 1′ (1′ = 0.291 · 10⁻³ rad). The extention of area registered during a measurement depends on the kind of section of crystal and the kind of reflection; at the examination of {100}-cleavage faces of LiF an elliptical area of a height of 15 mm and a length of 115 mm is registered.     

Temperature dependence of the dielectric parameters of nonstoichiometric SrTiO3 single crystals

The results of experimental studies of the temperature dependence of the low-frequency permittivity ε ₀ and the loss tangent taδ of nominally undoped and doped single crystals of strontium titanate at T = 10–300 K are given. The samples were doped with ions of iron-group metals (V, Mn, Fe, Co) and/or ions of rare earth metals (Pr, Nd, Sm, Tm) with concentrations of 10^?3?5 × 10^?1 at %. Anomalous temperature dependences ε₀ T and tanδ(T) were found for a number of samples. The anomalies found were attributed to the violation of stoichiometry of the single crystals under study and the transition of some fraction of Ti⁴⁺ ions to the Ti³⁺ state.     

Photoelastic and X-ray topographic studies of residual stress and lattice deformation in GaAs single crystals

The GaAs crystals, grown with three different methods were simultaneously studied by means of photoelastic and X-ray topographic methods. The methods provide complementary information about lattice deformation. The correspondence between interplanar distance changes and photoelastically measured stress values and the connection between cellular structure and high stress values were also found.     

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.     

Investigation of crystal lattice defects of PbZrO3 single crystals by transmission electron microscopy

The investigation of PbZrO₃ single crystal structure was carried out by the method of transmission electron microscopy (TEM). It is shown that extended planar defects, slip lines, twins, and morié patterns are observed in PbZrO₃.