Time dependence of X-ray polarizability of a crystal induced by an intense femtosecond X-ray pulse.

The time evolution of the electron density and the resulting time dependence of Fourier components of the X-ray polarizability of a crystal irradiated by highly intense femtosecond pulses of an X-ray free-electron laser (XFEL) is investigated theoretically on the basis of rate equations for bound electrons and the Boltzmann equation for the kinetics of the unbound electron gas. The photoionization, Auger process, electron-impact ionization, electron-electron scattering and three-body recombination have been implemented in the system of rate equations. An algorithm for the numerical solution of the rate equations was simplified by incorporating analytical expressions for the cross sections of all the electron configurations in ions within the framework of the effective charge model. Using this approach, the time dependence of the inner shell populations during the time of XFEL pulse propagation through the crystal was evaluated for photon energies between 4 and 12 keV and a pulse width of 40 fs considering a flux of 10(12) photons pulse(-1) (focusing on a spot size of ∼1 µm). This flux corresponds to a fluence ranging between 0.8 and 2.4 mJ µm(-2). The time evolution of the X-ray polarizability caused by the change of the atomic scattering factor during the pulse propagation is numerically analyzed for the case of a silicon crystal. The time-integrated polarizability drops dramatically if the fluence of the X-ray pulse exceeds 1.6 mJ µm(-2).

Covariant description of X-ray diffraction from anisotropically relaxed epitaxial structures.

A general theoretical approach to the description of epitaxial layers with essentially different cell parameters and in-plane relaxation anisotropy has been developed. A covariant description of relaxation in such structures has been introduced. An iteration method for evaluation of these parameters on the basis of the diffraction data set has been worked out together with error analysis and reliability checking. The validity of the presented theoretical approaches has been proved with a-ZnO on r-sapphire samples grown in the temperature range from 573 K up to 1073 K. A covariant description of relaxation anisotropy for these samples has been estimated with data measured for different directions of the diffraction plane relative to the sample surface.

Anomalous scattering method in crystallography on the basis of parametric X-radiation.

Spectra of parametric X-radiation (PXR) in the range of anomalous dispersion of atoms of a crystallographic unit cell are theoretically analyzed. Characteristics of PXR are calculated for both ultrarelativistic (E > or = 50 MeV) and non-relativistic (E approximately 100 keV) electrons interacting with complex organic crystals. The analysis of the PXR angular distribution is shown to permit the realization of the anomalous scattering method for the direct measurement of structure amplitude phases.

A new method for calculation of crystal susceptibilities for X-ray diffraction at arbitrary wavelength.

A novel method for the calculation of the X-ray susceptibility of a crystal in a wide range of radiation wavelengths is described. An analytical interpolation of one-electron wave functions is built to approximate the solution to Hartree-Fock equations for all atoms and ions of the periodic system of elements with high accuracy. These functions allow the calculation of the atomic form factors in the entire range of a transmitted momentum as well as the description of their anisotropy taking into account external and intracrystalline fields. Also, an analytical approximation for the force matrix of an arbitrary crystal is obtained and the microscopic calculation of the Debye-Waller factor for crystals with a complicated unit cell is presented.

Interference of parametric X-ray and coherent Bremsstrahlung radiation from nonrelativistic electrons: application to the phase analysis in crystallography.

The intensity of coherent X-radiation (CXR) from a relativistic electron beam interacting with the crystal [Feranchuk, Ulyanenkov, Harada & Spence (2000). Phys. Rev. E, 62, 4225-4234] is studied in view of its application to the phase determination problem. The analysis of CXR spectra is shown to permit an independent measurement of unit-cell structure factors, defined by both the electron-density distribution and the nucleus positions. In relation to these structure factors, two new types of Patterson function are introduced that can simplify the solution of crystal structure.