Masao Kuriyama

Quantum Theory of X-Ray Diffraction by a Crystal

A new formulation of the theory of X-ray diffraction by a crystal using techniques of quantum field theory has been developed. The classical field amplitudes of previous theories are replaced, in the present work, by scattering amplitudes for the transmitted and diffracted beams which are obtained from a photon Greens function. The case of a single-Bragg reflection for a parallel sided crystal has been treated in detail. The scattering amplitudes for this case give results which are essentially those of the semi-classical dynamical theory with absorption. The application of the theory to the diffraction of a beam of finite width for the Laue geometry provides an alternate demonstration that the beam emerges from the exit surface of the crystal at a point given by the direction of energy flow.

X-ray Measurement of Scattering Factors of Manganese and Oxygen Atoms in Manganous Oxide

The atomic scattering factors of manganese and oxygen atoms in manganous oxide (MnO) were determined by measuring the integrated x-ray intensities of reflections from powder sample at room temperature. The intensities measured on a relative scale for five differently colored samples within an experimental error of ±0.4 to 4% were transformed to the absolute values by experimental scaling factors. The atomic scattering factors obtained were compared with those calculated by Watson and Freeman and by Suzuki and proved that the atoms were in the state of divalent ions. The tabulated anomalous dispersion terms were found to be reliable for Cu and Cr Kα radiations. The effect of non-spherical charge distributions was discussed by a comparison between the experimental and the theoretical factors. The lattice constant at room temperature was determined to be 4.444±0.001 A and thermal expansion coefficient above the Neel point, 1.1×10 -5 deg -1 . The root mean square amplitudes of thermal vibration were determine...

Theory of X-Ray Diffraction by a Distorted Crystal

Based on the quantum theory of X-ray diffraction by a perfect crystal (M. Ashkin and M. Kuriyama, J. Phys. Soc. Japan 21 (1966) 1549), a diffraction theory for a distorted crystal has been developed. The scattering amplitude for the case of a single Bragg reflection has been obtained in terms of a lattice sum including the displacement of each atom. A basic assumption for this formulation is that there is no overlap of the electron wave functions of the displaced atoms. The existing basic assumption in the dynamical theory for a distorted crystal, that the local distortion in the crystal must change very slowly so that the local wave field can be described by the dynamical theory for a perfect crystal, has been successfully avoided in the present formulation. A criticism is also made of the so-called “Fourier” expansion of polarizability or electron distribution in the distorted crystal, which has been important for the dynamical theory.

On the Relationship between X-Ray Inelastic Scattering and Absorption Spectra

The cross section for X-ray inelastic scattering from crystals has been derived from first principles to explain the coexisting Compton and Raman scattering in solids. This derivation makes it possible to express the inelastic scattering cross section in terms of the current correlation of electrons in a crystal. The criterion for having a distinct Raman scattering is obtained through the dependence of the current correlation on the momentum transfer.

Ferromagnetic Resonance Absorption of Single-Crystal Thin Films of Nickel

Single-crystal thin films of nickel having the (100) and the (111) orientations were epitaxially grown by deposition in vaccum onto heated rock salt and zincblende. By electron diffraction, these films were examined to be 100 A to 500 A in size of crystallites without appreciable strain. By the experiment of ferromagnetic resonance absorption at room temperature, three magnetic quantities were measured at the same time: the saturation magnetization, the crystalline anisotropy and the Lande splitting factor. The first quantity was found to be almost independent of the thickness of films (100 A to 1000 A) and its magnitude was 350 or 400 in gauss, respectively for the (111) or the (100) orientation. This difference may be ascribed to the stress in films. The second one varied in the range between -2×10 4 and -5×10 4 erg/cm 3 and the third was 2.2 in average. The crystalline anisotropy causes the shift of resonance line as the film is rotated in its plane. Besides, it was found that the more perfect orientat...

Theory of X-Ray Diffraction by a Distorted Crystal. II. Scattering Amplitude for a Wave Packet of Finite Size

The X-ray scattering amplitude for a finite wave packet diffracted by a distorted crystal is calculated by the use of a previously formulated theory (M. Kuriyama: J. Phys. Soc. Japan 23 (1967) 1369). Only a limited portion of the crystal is responsible for scattering. The geometrical arrangement of this region is discussed in terms of an observation point on the crystal exit surface, an incident (glancing) angle and an observation (detector) angle. The accuracy of the results depends on the lateral size of the incident X-ray beam. The internal wave fields and paths of classical energy flow are also discussed from the viewpoint of the present formulation.

Absolute Measurement of X-Ray Scattering Factors of Manganese and Oxygen Atoms in Manganous Oxide

The atomic scattering factors of manganese and oxygen atoms in manganous oxide reported in the previous paper were confirmed by absolute intensity measurements with monochromated Fe K α radiation. The results were compared with those obtained by relative measurements in a previous study to obtain the anomalous dispersion correction to the scattering factor of a manganese atom.

X-ray Line Broadening from the Polished Surfaces of Silver and Gold

The linear relation (Halls formula) and the quadratic relation between the integral breadth and the scattering angle can be derived from the general formula for intensity distribution by the assumption of the appropriate distribution for both size and strain. The use of these two formulae (line breadth method) can give not only the magnitude but also the plausible distribution for strain and size. The advantage of this method consists in the point that the magnitude and the distribution for size and those for strain can be separately obtained, in contrast with the Fourier analysis of line profile (line profile analysis method). The line breadth method is applied to the polished surfaces of Ag and Au and the results obtained are confirmed to be correct by the line profile analysis. On the other hand, the line profile analysis is required to study the strain variation with the depth in specimens, as far as only one kind of radiation is used. This strain variation can be observed by the line breadth method ...

Electron Diffraction Study on Polish Layers of Gold I

Polish layer of gold was examined by means of the transmission method of electron diffraction. The diffraction pattern from the highly polished layer of gold (the Beilby layer) consists of three haloes, as reported in the previous paper (J. Phys. Soc. Japan 12 (1957) 151). The radial distribution function of atoms in the layer was calculated by Fourier transformation of the observed intensity. The observed intensity was compared with those calculated from appropriate models of atomic arrangement. It was found that the Beilby layer has an amorphous arrangement in which the first and the second coordination number are about 10 and 8, respectively.