X-ray scattering factors for ionic crystals with complete electron shells

Scattering factors for ionic crystals with complete electron shells were considered by employing radially deformed atomic wave functions for “crystal ions”. The deformation was taken into account by the scaling method introduced by Mansikka in his earlier work. The correction due to the overlap between the deformed ions in crystals were evaluated by means of the formulae presented in our previous papers. Scattering factors for LiF and NaF crystals were computed and compared with experimental data. The effect of deformation is comparable in magnitude with the overlap ones.     

X-ray scattering factors for ionic crystals with complete electron shells

X-ray scattering factors for the NaF, NaCl, LiCl, LiBr, and KBr crystals were computed using the Hartree-Fock wave functions of the free ions given by Clementi [3]. The corrections, due to the overlap between the free ions in crystals, were evaluated by means of the formulae presented in our previous paper. The results show that these overlap corrections are small and, in practice, independent on direction for all alkali halides with the NaCl structure. The theoretical values obtained agree well with recent experimental data.     

X-ray and electron atomic scattering factors,allowing for hybridization of the states

The x-ray and electron scattering form factor is presented as a function of the vector s. Using the Slater approximation for the radial part of the wave function, an analytical expression is derived for the form factor. Particular expressions are given for the form factor in the presence of sp, sp², and sp³ hybrid states.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii Fizika, No. 9, pp. 50–55, September, 1971.     

A theoretical model for electron scattering in crystals

A theory for the scattering of electrons by impurities in crystals is presented. It makes use of multiple scattering theory and the Bloch representation for crystal wave-functions, and thus has a straightforward relationship with the partial-wave analysis familiar from elementary quantum mechanics. Some discussion is then given of the problems of first principles calculations, and some mention made of the practical problems of fitting to experimental data.     

X-ray scattering from polymer nematic liquid crystals

X-ray scattering from main chain polymer nematics is discussed from the point of view of its use in studying the ordering and fluctuations of the polymer chains that make up the nematic phase. An example of data from poly-γ-benzyl glutamate is given, with a discussion of the important features of the data, in terms of the current understanding of the nature of nematic ordering in main chain polymer systems. This includes analyses of the angular distribution function for the polymer segments, long wavelength fluctuations dictated by elastic phenomena, the effects of finite chain lengths, and effects due to the short range interactions and packing of the chains.     

Anomalous elastic scattering of X-ray emission by an atom with open shells

In the nonrelativistic approximation for one-electron wave functions, the differential cross section for anomalous scattering of linearly polarized X-ray emission by a sodium atom near the ionization threshold of the 1s ² shell is studied. The analysis takes into account the many-body effects of relaxation of atomic shells in the field of a deep vacancy, multiplet splitting, and the double excitation/ionization processes. The theoretical results obtained for the anomalous-dispersion scattering region are predictive.     

Comparing electron and X-ray scattering in metals

The cross sections for inelastic scattering of electrons and X-rays in metals for fixed momentum transfer are proportional according to the Born approximation. This contradicts the experiments. For electrons multiple scattering is essential. This can be included in a weak coupling limit, which depends on the usual dynamic structure factor only.     

Electron atomic scattering factors and scattering potentials of crystals

The concepts of complex electron atomic scattering factors and principles for evaluating these factors are discussed and their applicability is examined. Numerical procedures and routines for calculating these factors are described, and for 98 neutron atoms and 109 ions the real part of the electron atomic scattering factors were parameterized using 10 and eight parameters, respectively. Procedures for constructing two and three dimensional scattering potentials using the complex atomic scattering factors are illustrated with examples; effects of thermal vibrations of the crystal lattice are discussed.     

Characterization of Na precipitates in electron irradiated NaCl crystals by wide angle X-ray scattering (WAXS)

Samples of synthetic NaCl crystals have been exposed to different doses of electron irradiation up to 1500 MGy (150 Grad) at elevated temperatures, and studied subsequently by X-ray diffraction. Our experimental results clearly show that there is a close correspondence between the geometrical properties (such as lattice distances and the crystal orientation) of the host crystal and the radiation-induced Na precipitates, which is referred to as the Kurdjumov-Sachs orientation relationship (K-S OR). The size of the precipitates has been estimated.     

Resonant scattering of X-ray radiation in magnetic crystals with non-cubic local anisotropy

Features of resonant diffraction of synchrotron radiation in magnetic crystals in which the local symmetry of resonant atom positions is lower than cubic are considered. It was shown that the simultaneous presence of two anisotropic factors can cause asymmetry of the azimuthal dependence of purely resonant reflections. The observed azimuthal dependence of the 002 reflection in the HoFe₂ crystal was numerically simulated.     

Bragg rods and multiple X-ray scattering in random-stacking colloidal crystals

Synchrotron small-angle x-ray diffraction images of random-stacking-induced Bragg scattering rods are obtained in a wide range of wave vectors from a single colloidal crystal. The results reveal a strong multiple scattering effect, which leads to new features in the diffraction pattern-secondary Bragg rods. We argue that dynamic x-ray diffraction is rather common for high-quality colloidal photonic crystals and should be taken into account.     

On the role of nonpolar optical scattering for a delocalized positronium in ionic crystals

The role of optical deformation-potential scattering is studied for the delocalized positronium atoms in ionic crystals. At high temperatures, when the scattering becomes substantial, it (unless forbidden by the selection rules) renormalizes the positronium-acoustic phonon coupling constant. Such a renormalization was experimentally justified by measuring the momentum distribution for a delocalized positronium in the MgF₂ crystal. A similar effect is predicted for a positronium in crystalline quartz at temperatures above the transition from α-to β-quartz (846 K).     

Lyotropic bicontinuous cubic phase single crystals investigated using high-resolved X-ray scattering

Single crystals of an Ia d bicontinuous direct cubic phase formed by a non-ionic surfactant in water are investigated using high-resolved X-ray diffraction. The shape of the Bragg peaks confirms the existence of a 3D long-range order inside the cubic phase. A weak diffuse scattered intensity signal is measured very near the Bragg peaks. We attribute this signal to thermal diffuse scattering (TDS) and we give an estimation of the contribution of elastic waves to this TDS. Received 4 May 2000     

Quadrupole deformation of electron shells in the lattice dynamics of compressed rare-gas crystals

The lattice dynamics of rare-gas crystals has been constructed taking into account the deformation of electron shells of the atoms of the dipole and quadrupole types, depending on the displacement of the nuclei. The obtained equations of lattice vibrations have been investigated in the long-wavelength approximation. The role played by the three-body interaction and the deformation of the electron shells in the violation of the Cauchy relation has been discussed. The calculated Birch elastic moduli for Xe and deviations from the Cauchy relation are in good agreement with the available experimental data over a wide range of pressures.     

The distribution of the valence electron density in predominantly ionic crystals with different Bravais sublattices

Based on the theory of the local-density functional, self-consistent valence electron densities are calculated for CaO with a rock-salt lattice, CaF₂ with a fluorite lattice, K₂O with an antifluorite lattice, and for their constituent sublattices. It is shown that in the crystals with different Bravais sublattices, the anionic sublattice is a framework with covalent bonds containing a metal sublattice inside of them. The coupling between the sublattices is characterized by the density difference, which is deflned as the difference between the total electron density and the densities of the individual sublattices. The density difference is found to be an order of magnitude smaller than the crystal and sublattice densities, which is evidence of weak hybridization of the sublattices and of the predominately ionic character of the bonding between them.     

Conductivity of ionic crystals when they are irradiated by picosecond electron beams

This paper discusses the pulsed electron conductivity σ of KCl, KBr, and NaCl crystals when they are excited by an electron beam (0.2 MeV, 50 ps) with current densities in the interval j=(30–10⁴) A/cm². It is shown that the lifetime of the electrons in the conduction band is τ≪100 ps. To explain the experimental σ(j) dependences, a model is proposed that includes electron capture by structural defects and stable radiation defects at low excitation densities and electron capture predominantly by unstable radiation defects generated by the excitation pulse at high excitation densities. Fiz. Tverd. Tela (St. Petersburg) 41, 1200–1203 (July 1999)