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.     

Thermal diffuse scattering in sub-angstrom quantitative electron microscopy-phenomenon,effects and approaches

This paper reviews the recent progress in the following areas. (1) In quantitative high-resolution transmission electron microscopy, the theoretically calculated images usually give better contrast than the experimentally observed ones although all of the factors have been accounted for. This discrepancy is suggested due to thermal diffusely scattered (TDS) electrons, which were not included in the image calculation. The contribution from TDS electrons is especially important if the image resolution is approaching 0.1 nm and beyond with the introduction of Cs corrected microscopes. A more rigorous multislice theory has been developed to account for this effect. (2) We proved that the off-axis holography is an ideal energy filter that even filters away the contribution made by TDS electrons in the electron wave function, but conventional high-resolution microscopy do contain the contribution made by phonon scattered electrons. (3) In electron scattering, most of the existing dynamical theories have been developed under the first order diffuse scattering approximation, thus, they are restricted to cases where the lattice distortion is small. A formal dynamical theory is presented for calculating diffuse scattering with the inclusion of multiple diffuse scattering. By inclusion of a complex potential in dynamical calculation, a rigorous proof is given to show that the high order diffuse scattering are fully recovered in the calculations using the equation derived under the distorted wave Born approximation, and more importantly, the statistical time and structure averages over the distorted crystal lattices are evaluated analytically prior numerical calculation. This conclusion establishes the basis for expanding the applications of the existing theories. (4) The 'frozen lattice' model is a semi-classical approach for calculating electron diffuse scattering in crystals arisen from thermal vibration of crystal atoms. Based on a rigorous quantum mechanical phonon excitation theory, we have proved that the frozen lattice mode is an excellent approximation and no detectable error would be possible under normal experimental conditions.     

The diffraction of electromagnetic waves by sound in conducting crystals

The diffraction of electromagnetic waves by sound in conducting crystals is investigated. It is shown that in such crystals a significant contribution to the scattering of electromagnetic waves can be made by electron waves which are generated by a sound wave and accompany it. An estimate shows that in the ‘hydrodynamic’ case ql 1 (where q is the wave number of the sound and l is the electron mean free path) the contribution from an electron density wave to the scattering of electromagnetic waves in the infrared and millimeter ranges in substances with a low electron effective mass (of the type of InSb) can be comparable to the contribution from the lattice deformation waves, or may even exceed it. The results of a concrete calculation of the first and second order intensities of Raman-Nath diffraction in a semiconductor are presented.     

杂质中心吸收宽带的电声子耦合问题(Ⅱ)

在这篇文章中,我们用一维晶格模型讨论了杂质中心中电声子耦合强度的问题。用场论方法严格地解得了含杂质晶格之运动方程的本征函数。由此得到了电声子耦合强度的解析表示式,它是用声子的波数k、表示相互作用范围的参量λ以及杂质参量P=γ′/γ解析地表示出来的。其中γ′和γ分别为杂质与近邻之间和一般近邻之间的力常数。对结果的分析表明,只改变质量的杂质不影响电声子耦合;导致力常数变化的杂质对电声子耦合有显著的影响。当有奇的局域模出现时,在离子晶体中它对带宽的贡献可以比带内模的贡献大很多。尤其是在离子晶体中有可能出现所谓“临界散射”,这时带内模的贡献可能变得很小,而主要的贡献几乎全来自于局域模。相反地,在非极化晶体中,局域模的贡献一般是很小的。文中最后讨论了由一维模型得到的结论对于三维晶体可能有的意义。     

Nuclear quadrupolar relaxation in ionic crystals

The nuclear quadrupolar relaxation time of alkali halide crystals is investigated by the Heitler-London approximation. We use the Slater determinant which is constructed by the Hartree-Fock wave functions of the free ions. The charge distribution around an ion is not spherically symmetrical because of mutual overlap of the atomic wave functions of nearest-neighbor ions. Moreover, the charge distribution around an ion changes its shape during thermal vibrations of the ions, because the degree of the overlap depends upon the distance apart of the ions. Therefore, the quadrupolar interaction in alkali halide lattices is the resultant of a combination of the thermal vibration with the charge overlap. As illustrations of the theory, we have computed the quadrupolar relaxation time of the ³⁹K and the ³⁵Cl nuclei in the KCl crystal, and the ²³Na nucleus in the NaCl crystal. The theoretical results are in good agreement with those of experiments. We have also computed the ratio of the quadrupolar relaxation time of the metal nucleus to that of the halogen nucleus for some alkali halide crystals. After computing the same ratio by the covalent model and the deformation model, we have compared these results with the available experimental data. Finally, by using the same overlap model as that mentioned previously, we have developed a formula which gives the chemical shift of ionic crystals.     

Population inversion and IR amplification induced by intersubband electron transitions and resonant Auger processes in quantum wells

A mechanism for electron population inversion and mid-IR amplification is proposed for the case of the current or optical injection of electron-hole pairs into the undoped region of a heterojunction with quantum wells. The presence of an upper long-lived size-quantization level and resonant Auger recombination in the well are crucial features of the mechanism. A long electron lifetime at the upper level or a relatively low probability of electron scattering to the other subbands is achieved by choosing the shape of the well and its parameters in such a way as to provide weak overlap between the upper level and two lower level electronic wave functions. Resonant Auger recombination plays a positive role. It stabilizes the electron and hole concentrations at lower levels and makes a substantial contribution to the excitation of the upper electronic level and the population inversion. The degree of population inversion and the gain coefficient are estimated.     

Free carrier absorption in n-type CdTe

Experimental results for free carrier absorption at room temperature in lightly doped samples of n-type CdTe, including the λ³ dependence of the absorption coefficient on the photon wavelength, can be satisfactorily accounted for in terms of polar optical mode scattering with a very small contribution by impurity scattering. Use is made of the quantum theory of free carrier absorption initially developed for direct gap III–V semiconducting compounds, which utilizes the Kane band structure and includes nonparabolicity, arbitrary spin-orbit splitting values, overlap wave function factors, and intermediate states in other bands.     

About forbidden and weak reflections

Reflections forbidden under the single scattering approximation are not expected to remain extinct for crystal thicknesses for which multiple scattering becomes important, except for reflections of the Gj?nnes-Moodie type. However, it has been observed that in many crystals with the incident beam along a zone axis, such as diamond-like crystals along the [110] zone, reflections forbidden under the single scattering approximation remain very weak up to large thicknesses. This is hard to explain in terms of many-beam dynamical scattering in Fourier space. The picture becomes clear if one describes the scattering in real space in terms of the channelling of the electrons along the atom columns parallel to the zone axis. In that case the exit wave of each atom column can be described by the S-state model, which is radially symmetric around the centre of the atom column. As a consequence the exit wave shows the same symmetry as the projected potential, so that the reflections forbidden under the single scattering approximation remain extinct. This condition only breaks down when the crystal thickness becomes so large that the S-state model becomes invalid, which is a function of the distance between neighbouring atom columns and/or the tilt from the exact zone axis. The sensitivity for small tilts is also in agreement with very old observations that have not been explained thus far.     

Fine structure of the diffraction image of an edge dislocation in high-resolution section topography

The propagation of an x-ray wave field in an elastic field of an edge dislocation crossing a scattering triangle exactly along the bisector of the scattering angle has been considered. The scattering of the x-ray wave field by a complex elastic field of the edge dislocation has been analyzed using the methods of geometrical optics. It has been established that the fine structure of a diffraction image of defects in thick crystals is determined by the differences in scattering of the normal and anomalous modes of the x-ray wave field in the vicinity of the Bragg reflection. In the case of thick crystals, the x-ray diffraction image of defects can have a symmetry different from the symmetry of the function of local misorientations of the crystal lattice. X-ray wave scattering by local distortions of the crystal lattice can occur according to two different mechanisms depending on the gradient of space changes in the deformation field. In the crystal regions where the elastic field varies slowly with a change in the distance, the x-ray wave field has had time to adjust itself to follow the course of deviations of the crystal lattice from the exact Bragg condition. In the crystal region where the elastic field changes significantly at distances of the order of the extinction length, this region leaves the reflecting position and interference scattering occurs at the interface of the region. It is important that the form of the deformation field in this case is of no significance.     

Anharmonic processes of scattering and relaxation of slow quasi-transverse phonons in cubic crystals

Relaxation of slow quasi-transverse phonons in anharmonic processes of scattering in cubic crystals with positive (Ge, Si, diamond) and negative (KCl, NaCl) anisotropies of the second-order elastic moduli has been considered. The dependences of the relaxation rates on the direction of the wave vector of phonons in scattering processes with the participation of three quasi-transverse phonons (the TTT relaxation mechanisms) are analyzed within the anisotropic continuum model. It is shown that the TTT relaxation mechanisms in crystals are associated with their cubic anisotropy, which is responsible for the interaction between noncollinear phonons. The dominant contribution to the phonon relaxation comes from large-angle scattering. For crystals with significant anisotropy of the elastic energy (Ge, Si, KCl, NaCl), the total contribution of the TTT relaxation mechanisms to the total relaxation rate exceeds the contribution of the Landau-Rumer mechanism either by several factors or by one to two orders of magnitude depending on the direction. The dominant role of the TTT relaxation mechanisms as compared to the Landau-Rumer mechanism is governed, to a considerable extent, by the second-order elastic moduli. The total relaxation rates of slow quasi-transverse phonons are determined. It is demonstrated that, when the anharmonic processes of scattering play the dominant role, the inclusion of one of the relaxation mechanisms (the Landau-Rumer mechanism or the mechanisms of relaxation of the slow quasi-transverse mode by two slow or two fast modes) is insufficient for describing the anisotropy of the total relaxation rates in cubic crystals.     

Selection rules for Bloch wave scattering for HREM imaging of imperfect crystals along symmetry axes

A Bloch wave analysis is used to investigate high-resolution electron microscope (HREM) imaging of crystals containing atomic displacements due to strain. In the absence of interband scattering, the shifts of peaks and troughs in the image will correspond to the displacements of the atoms in the exit surface. Interband scattering will shift the image peaks away from the actual atom positions and modify the apparent magnitude of the displacement identified by the observed image peak positions. By considering the case of seven-beam imaging of a cubic crystal aligned along a ?111? axis, it is shown that the symmetry of the Bloch waves leads to selection rules for the interband scattering, similar to those seen for dipole electron excitations in atoms. It is also shown that, to first order, no intraband scattering can occur.     

Excitation of states of medium-mass nuclei in the region of giant resonances in inelastic deuteron scattering

Results are presented that were obtained by measuring a continuum in the inelastic scattering of 37-MeV deuterons on ¹²C, ⁴⁸Ti, and ^58,64Ni nuclei in the angular range 16° ≤ θ ≤ 61°. Broad excitation maxima are found for deuteron scattering angles in the range θ ≤ 21°. The region of a broad maximum includes giant resonances of target nuclei, whose levels are excited quite readily at E _d = 37 MeV. Summation of the inelastic-scattering cross sections over all final states of the excited| nucleus and the use of completeness of the wave functions for these states make it possible to express the total cross section for inelastic (incoherent) deuteron scattering only in terms of the wave functions for the ground state of the target nucleus. The corresponding quasielastic-scattering amplitude is taken in the diffraction approximation. Nucleon correlations in the target nucleus are disregarded. Upon disregarding a small contribution of multiple quasielastic scattering at small scattering angles, the cross section for incoherent deuteron scattering is represented approximately as the product of known factors—the square of the absolute value of the amplitude for diffractive quasielastic scattering and the effective number of target nucleons scattering deuterons. The results of these calculations agree qualitatively with experimental data.     

Helicity-dependent generalized parton distributions in constituent quark models

Helicity-dependent generalized parton distributions of the nucleon are derived from the overlap representation of generalized parton distributions using light-cone wave functions obtained in constituent quark models. Results from two different quark models are used also to study the angular momentum sum rule and the spin asymmetry in polarized electron scattering.     

Optimization of a Bonse–Hart instrument by suppressing surface parasitic scattering

An improved crystal design for a Bonse–Hart ultra‐small‐angle scattering instrument is presented. Defects at the diffracting surfaces of the conditioning crystals were found to be at the origin of diffuse scattering that enhances the intensity in the wings of the rocking curves by several orders of magnitude. In order to improve the performance of the instrument, the monolithic channel‐cut crystals were replaced by pairs of separate polished and deeply etched crystals. These crystals were mounted on a mechanical stage that allows very precise parallel alignment of the crystals to within a tiny fraction of the rocking curve width (sub‐µrad range). By using these double‐crystal set‐ups, the parasitic background scattering was reduced by more than an order of magnitude. The steps to achieve the optimum surface quality of the crystals as well as the precision mechanical design for their parallel alignment are described. Significant improvement of the signal‐to‐background ratio and the available wavevector range of the instrument make it suitable for studying the microstructure and dynamics of dilute and weakly scattering soft‐matter systems. This development also has potential applications in X‐ray optics such as low‐background and tunable monochromators and collimators.     

Guided acoustic wave Brillouin scattering in photonic crystal fibers

We experimentally investigate guided acoustic wave Brillouin scattering in several photonic crystal fibers by use of the so-called fiber loop mirror technique and show a completely different dynamics with respect to standard all-silica fibers. In addition to the suppression of most acoustic phonons, we show that forward Brillouin scattering in photonic crystal fibers is substantially enhanced only for the fundamental acoustic phonon because of efficient transverse acousto-optic field overlap. The results of our numerical simulations reveal that this high-frequency phonon is indeed trapped within the fiber core by the air-hole microstructure, in good agreement with experimental measurements.     

On the neutron diffraction in crystals in the field of a sound wave

Diffraction of neutrons in crystals under influence of a sound wave is considered. The probability of scattering of neutrons at the elastic interaction with the crystal is calculated. On the contrary, scattering of neutrons by an acoustical phonon has inelastic character. The possibility to control the Debye-Waller factor is shown.     

Transition probability functions for applications of inelastic electron scattering

In this work, the transition matrix elements for inelastic electron scattering are investigated which are the central quantity for interpreting experiments. The angular part is given by spherical harmonics. For the weighted radial wave function overlap, analytic expressions are derived in the Slater-type and the hydrogen-like orbital models. These expressions are shown to be composed of a finite sum of polynomials and elementary trigonometric functions. Hence, they are easy to use, require little computation time, and are significantly more accurate than commonly used approximations.