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.     

Polarization studies of resonant forbidden reflections in liquid crystals

We report the results of resonant x-ray diffraction experiments performed on thick films of a biaxial liquid crystal made of achiral bent-core molecules. Polarization properties of forbidden reflections are observed as a function of the sample rotation angle phi about the scattering vector Q for the first time on a fluid material. The experimental data are successfully analyzed within a tensor structure factor model by taking the nonperfect alignment of the liquid crystal into account. The local structure of the B2 mesophase is hence determined to be SmC_{S}P_{A}.     

Thermal motion induced resonant forbidden reflections in wurtzite GaN

We report on an experimental study of forbidden reflections in GaN (wurtzite structure) by resonant X-ray scattering at the Gallium K edge. Resonant reflections are explained by the coherent sum of a Thermal Motion Induced (TMI) scattering amplitude and a temperature independent term. We show that the shape of the TMI energy spectrum is the same for a number of reflections that are exactly forbidden by spacegroup symmetry, as well as one that relies on approximate cancellation due to special atomic sites. In addition to demonstrating new selection rules, several non-trivial aspects of the theory of TMI scattering in wurtzite crystals are quantitatively verified, including dependence on temperature, energy, azimuthal angle and polarization. The temperature-dependent and temperature independent spectra of GaN are very similar to those found in ZnO, suggesting strong similarities in the anisotropy of their electronic states. This is also supported by the strong linear dichroism observed in GaN. TMI spectra are determined by the evolution of the electronic anisotropy with nuclear position, and are likely to be extremely valuable for developing theories of electronic properties at elevated temperatures.     

Ab initio simulation of resonant forbidden reflections in Ge crystals

Forbidden reflections are observed in the case of diffraction of synchrotron radiation with wave-lengths close to the absorption edges in crystals. A new method for calculating the intensity of thermal-motion-induced (TMI) forbidden reflections is proposed in this paper. It includes two stages: simulation of instantaneous thermal atomic displacements using ab initio molecular dynamics and subsequent quantum-mechanical calculations of the resonance scattering amplitude for various configurations. This procedure is used to calculate the temperature dependence of the 600 reflection intensity for Ge. The proposed method for simulating forbidden TMI reflections is suitable for any crystal structures and can explain many results so far obtained using synchrotron.     

Anisotropic resonant X-ray scattering: Beauty of forbidden reflections

Experimental results and their theoretical explanation are reviewed for fundamentals of anisotropic resonant X-ray scattering. Resonant scattering depends on X-ray polarization, i.e. the scattering reflects anisotropic environment of atoms in crystal. The polarization anisotropy in atomic scattering can excite the forbidden Bragg reflections. Studying this type of forbidden reflections we can distinguish electronic orbitals of specific symmetry. This method is very useful for studying local electronic states in crystal. We reveal detailed property of the anisotropic scattering, effect of quadrupole transition, thermal motion, magnetic scattering and so on. Especially successful examples are given in detail: observation of phase of the scattering factor, the hybridization of states with different parity, local chirality of atom in centrosymmetric crystals, thermal-motion-induced resonant reflections, etc.     

Resonant x-ray diffraction studies on the charge ordering in magnetite

Here we show that the low temperature phase of magnetite is associated with an effective, although fractional, ordering of the charge. Evidence and a quantitative evaluation of the atomic charges are achieved by using resonant x-ray diffraction (RXD) experiments whose results are further analyzed with the help of ab initio calculations of the scattering factors involved. By confirming the results obtained from x-ray crystallography we have shown that RXD is able to probe quantitatively the electronic structure in very complex oxides, whose importance covers a wide domain of applications.     

Defect cores investigated by x-ray scattering close to forbidden reflections in silicon

A new x-ray scattering method is presented making possible the detection of defects and the investigation of the structure of their cores. The method uses diffuse x-ray scattering measured close to a forbidden diffraction peak, in which the intensity scattered from the distorted crystal lattice around the defects is minimized. As a first example of this nondestructive method we demonstrate how the local compression of the extra {111} double planes in extrinsic stacking faults in Si can be probed and quantified using a continuum approach for the simulation of the displacements. The results of the theory developed are found to be in very good agreement with atomistic simulations and experiments.     

Ab initio calculations of the forbidden Bragg reflections energy spectra in wurtzites versus temperature

Thermal-motion induced (TMI) scattering is caused by the influence of atomic displacements on electronic states in crystals and strongly depends on temperature. It corresponds to dipole-dipole resonant x-ray scattering, but is usually accompanied by dipole-quadrupole scattering. The phenomenological theory supposes the dipole-quadrupole term to be temperature independent (TI). As a result, the transformation of the energy spectra with temperature observed experimentally in ZnO and GaN corresponds to the interference between the TMI and TI terms. In the present paper the direct confirmation of this theoretical prediction is given. Ab initio molecular dynamics was used to simulate the sets of atomic sites at various temperatures followed by quantum mechanical calculation of resonant Bragg reflection energy spectra. The results of simulation are in excellent coincidence with experimental energy spectra of forbidden reflections and confirm the earlier phenomenological conjecture about the interference between the TI dipole-quadrupole and TMI dipole-dipole contributions to the resonant atomic factor.     

Determination of the position of impurity atoms in yttrium-aluminum garnet by means of forbidden reflections

The possibility of determining the position of terbium impurity atoms in yttrium-aluminum garnet lattice is analyzed. It is shown that in the presence of the impurity in both aluminum and yttrium positions the tensor factors of the nearest yttrium atoms change. To determine the position of impurity atoms in the yttrium-aluminum garnet unit cell, measurements should be carried out at energies near the L-absorption edges of terbium.     

“禁忌”3-磁振子相互作用哈密顿项的有效性分析

考察磁有序晶体中局部存在的动量守恒而能量不守恒的3-磁振子激励过程，通过幺正变换，把自旋波理论中不合理的3-磁振子产生与湮没过程的哈密顿项构造为有 效的4-磁振子相互作用哈密顿项. 关键词： 磁振子 哈密顿项 幺正变换     

氧化锌微米花的共振拉曼和“负热淬灭”效应

利用化学气相沉积(CVD)的方法通过热氧化高纯锌粉在硅衬底上得到氧化锌微米花. X射线衍射(XRD)结果表明，其具有六角纤锌矿晶体结构.场发射扫描电子显微镜(FE-SEM)图像表明，合成的样品是由很多长且直的ZnO亚微米棒组成的微米花， 具有六角棱柱端面，棒的长度在30μm到50μm之间.在背向共振拉曼散射光谱测量中，观测到ZnO A₁(LO)的五阶声子紫外共振拉曼散射，表明样品具有较高的晶体质量.在变温光致发光谱测量中，观察到明显的中性受主束缚激子(A⁰X)的 关键词： ZnO微米花 光致发光 共振拉曼 “负热淬灭”效应     

Lgft-Values of forbidden beta-transitions

In this paper the influence of the interference and nuclear charge on lgft-values is investigated. It is shown that interference by most of 1st and 2nd forbidden transitions is weak and, further, that the nuclear charge influence, compared theoretically, is in good agreement with experimental results.     

Vacancy diffusion in magnetite

The chemical diffusion coefficient in a single crystal of magnetite was measured by observing the relaxation of deviations from stoichiometry responding to a stepwise change in oxygen partial pressure between 1300 and 1450°C. The chemical diffusion coefficient was proportional to $\text{(?}\text{In}\text{δ}\text{?}\text{In}\text{p}{}_{\mathrm{o2}}\text{)}{}^{\mathrm{?1}}$. The vacancy diffusion coefficient was calculated with the help of nonstoichiometric data and was found to be independent of the vacancy composition. The value of D_v was

$\text{D}{}_{\mathrm{v}}\text{= (0.14 ± 0.08)}\text{exp}\text{(?}\text{(32,500 ± 1800)}\text{RT)}\text{cm}{}^2\text{s}{}^{\mathrm{?1}}$

.     

Spin-induced forbidden evanescent states in III-V semiconductors

Within the band gap of a semiconductor no electronic propagating states are allowed, but there exist evanescent states which govern charge transport such as tunneling. In this Letter, we address the issue of their spin dependence in III-V semiconductors. Taking into account the spin-orbit interaction, we treat the problem using a k . p 14 x 14 Hamiltonian that we numerically compute for GaAs. Our results show that the removed spin degeneracy in the band gap can lead to giant energy splittings and induces forbidden zones in space where evanescent states are suppressed.