A quantitative study of diffracted X-ray intensities from type I natural diamond crystals by high resolution X-ray diffractometry and comparison with nearly perfect silicon single crystals

Results of accurate measurements of peak and integrated intensities of , 111 and 333 reflections of natural diamonds of type I and nearly perfect silicon single crystals are reported. Highly monochromated and collimated MoK _{α 1} exploring beam was used. A quadrupole crystal X-ray diffractometer was employed in (+, −, +) and (+, −, +, −) settings. (111) platelets of diamond and silicon crystals with thicknesses of about 1 mm were selected. High resolution diffraction curves, stationary and traverse topographs were recorded. Diffraction curve half widths of diamond and silicon crystals were in the range: 45–200 arc sec and a few arc sec respectively. The experimental values of integrated intensitiesρ for diamond crystals were found to lie between the theoretical values for ideally perfect and ideally imperfect crystals. Experimental values ofρ for silicon were closer to the “perfect crystal” values. This is consistent with the results of diffractometric and topographic evaluation. The peak intensities of all reflections were higher for diamond crystals in comparison to the silicon crystals. The ratioI _C/I _Si lies in the range 1.3 (111 reflection) to 10.5 and (333) reflections. This is anomalous and cannot be accounted for by considering the degree of perfection, structure factor and difference in absorption coefficient.     

The use of perfect crystals in high-resolution X-ray spectroscopy

The possibility of improving the resolution and angular dispersion in the X-ray wavelength region through the use of asymmetric crystals in parallel beams is demonstrated.     

Dynamic theory of resonant X-ray Bragg diffraction in perfect crystals

An exact solution is found to the problem of mirror reflection and resonant Bragg diffraction of X rays in a perfect crystal. An anomalous transmission of radiation with the energy close to the K-edge absorption of the atoms is shown to be feasible.     

X-ray determination of the mean Debye-Waller factors,amplitudes of vibration and Debye temperatures of six crystals with CsCl structure

From the integrated intensities of Bragg reflections measured at room temperature with an x-ray powder diffractometer, the mean Debye-Waller factorB, the average r.m.s. amplitude of vibration (ū ²)^1/2 and the Debye temperatureθ, have been determined for six crystals with the CsCl structure. The energy of formation of a Schottky pair in these crystals has been estimated from an empirical relation between the x-ray Debye temperature and the energy of formation.     

Features of X-ray diffraction in thick perfect crystals with deformed subsurface layers

Diffraction of X-rays in thick perfect crystals with deformed subsurface layers has been investigated. It is shown that in deformed layers kinematic scattering occurs, while in the bulk of perfect part dynamic scattering takes place. It is revealed that in the beams diffracted on surface defects, an essential role plays the second harmonic of the employed characteristic MoK_α1 radiation.     

All-order transition amplitudes in many-electron atoms

All-order expressions for transition amplitudes are obtained from the exact re-summation of three-operator perturbation series. They are formulated in terms of continued fractions where the role played by the non-central part of the many-electron atom potential is shown explicitly.     

Magnetogyrotropy in twisted CdS crystals

In this paper the optical activity (gyrotropy) induced by a simultaneous action of a magnetic field and a torsion in hexagonal CdS crystals has been investigated. The crystal having undergone to both external influences is placed between two crossed polarizers. The spectral course of transmittance of this system near the isotropic point of CdS (the wavelength where the birefringence changes its sign) is studied in the experiment. An explanation of the experimental results is given by using the model of elliptical birefringence in anisotropic gyrotropic crystals. Taking into account the superposition of both external influences, it has been proved that the torsion generates gyrotropy whose parameter changes its sign in the isotropic point.     

X-ray determination of the mean amplitudes of vibration and debye temperatures of some rare earth monochalcogenides

The x-ray diffraction intensities of Bragg reflections have been measured at room temperature for thulium selenide, samarium sulphide, samarium selenide and samarium telluride. On the basis of a common amplitude approximation, the Debye-Waller factor, the mean amplitude of vibration and the Debye temperature have been evaluated. The values of the Debye temperatures and mean amplitudes of vibration are 176±16°K, 0·185 ± 0·017 Å (TmSe), 155 ± 7°K, 0·244 ± 0·012 Å (SmS), 153 ± 14°K, 0·221 ± 0·020 Å (SmSe) and 151 ± 20°K, 0·204 ± 0·027 Å (SmTe).     

Pressure-dependent EXAFS mean-square relative displacements of germanium and silicon crystals

In this paper, the statistical moment method (SMM) has been developed to study the pressure dependence of thermodynamic quantities of germanium and silicon crystals. We have derived the analytical expressions of the pressure-dependent parallel mean-square relative displacement (MSRD) or extended X-ray absorption fine structure (EXAFS) Debye–Waller factor, mean-square displacement (MSD) as well as lattice constant and volume change of diamond-type crystals. Numerical calculations performed for these semiconductors up to 11 GPa are found to be in good and reasonable agreement with available experimental data as well as with previous theoretical studies. Our results indicate that the SMM can be efficiently used for determining the relative change of the pressure-dependent MSRDs of germanium and silicon semiconductors. The research also shows the advantage of SMM on studying other thermodynamic properties of materials under high pressures.     

Entangling atoms in photonic crystals

We propose a method for entangling a system of two-level atoms in photonic crystals. The atoms are assumed to move in void regions of a photonic crystal. The interaction between the atoms is mediated either via a defect mode or via a resonant dipole-dipole interaction. We show that these interactions can produce pure entangled atomic states. We analyze the problem with parameters typical for currently existing photonic crystals and Rydberg atoms and we show that the atoms can emerge from photonic crystals in entangled states. Depending on the linear dimensions of the crystal we estimate that a pair of atoms entangled in a photonic crystal can be separated by tens of centimeters. Receive 11 June 1999 and Received in final form 4 October 1999     

Building the pyramids: perfect bubble crystals

Abstract

The use of appropriate flat-sided pyramidal containers to grow ordered foams allows single crystals to be formed. In the case of face-centred cubic crystals, these have been prepared with up to 500 bubbles. Strained and deliberately defective crystals can also be grown. The growth of simple cubic and body-centred cubic crystals is limited by instability; preliminary results are presented for these, as well as ordered bidisperse foams.     

Normal vibrational modes in benzil crystals

A group-theoretical analysis of the vibrational spectrum of benzil crystals was carried out. The selection rules and normal coordinates were found. Raman scattering spectra of benzil single crystals were studied in polarized light within a broad temperature range from 100 K to the melting point (T _m=96°C). The experimental data were found to correlate with theory. The temperature dependences of the spectral-line half-widths were used to separate the observed vibrations into translational and librational modes, and the correspondence between the experimentally observed vibrations and their normal coordinates was established in some cases.     

X-ray determination of the mean Debye-Waller factors and Debye temperatures of KCl-RbCl mixed crystals

Integrated intensities of Bragg reflections have been measured for KCl-RbCl mixed crystals with various compositions and the data used to evaluate the mean Debye-Waller factors and the Debye temperatures. The composition dependence of the Debye-Waller factor is highly nonlinear with positive deviations from linearity while that of the Debye temperature is slightly nonlinear with negative deviations from linearity. Using an empirical relationship between the Debye temperature and the molar volume, the average values of the Gruneisen parameter for some mixed crystal systems are obtained.     

Effect of mean-square amplitude of atomic vibrations on the creep behaviour of cubic crystals

Correlation between the activation energyQ of high-temperature creep and the Debye-Waller thermal parameterB, which is proportional to the mean-square amplitude of atomic vibrations, has been examined in the case of 17 faced-centred cubic, body-centred cubic and diamond-structure cubic elements. It is observed thatQ is a function ofB, irrespective of the crystal structure;Q decreases asB increases. The correlation is governed by the power-lawQ=Q ₀(B/B ₀) ^M0 , whereQ ₀=0.095eV andM ₀=−0.62 are numerical constants determined by least-squares fit method, and the constantB ₀=1 nm².