Electron density distribution in Si and Ge using multipole, maximum entropy method and pair distribution function analysis

The local, average and electronic structure of the semiconducting materials Si and Ge has been studied using multipole, maximum entropy method (MEM) and pair distribution function (PDF) analyses, using X-ray powder data. The covalent nature of bonding and the interaction between the atoms are clearly revealed by the two-dimensional MEM maps plotted on (100) and (110) planes and one-dimensional density along [100], [110] and [111] directions. The mid-bond electron densities between the atoms are 0.554 e/?³ and 0.187 e/?³ for Si and Ge respectively. In this work, the local structural information has also been obtained by analyzing the atomic pair distribution function. An attempt has been made in the present work to utilize the X-ray powder data sets to refine the structure and electron density distribution using the currently available versatile methods, MEM, multipole analysis and determination of pair distribution function for these two systems.      

The principle of the maximum entropy method

Abstract

The theoretical background of the maximum entropy method (MEM) when it is applied to restore the electron or nuclear densities from diffraction data is described. In MEM, the concept of “entropy” is introduced to deal with any incompleteness in an observation in a proper way. An incompleteness causes some ambiguities in the results to some extent. The essence of the method is to find a solution which necessarily agrees with the observation, leaving the measure of ambiguities (entropy) maximum. A few results for simple structures with typical types of chemical bonding are also presented.     

Fluorescence lifetime characterization of bacteria using total lifetime distribution analysis with the maximum entropy method

Total lifetime distribution analysis was employed to obtain fluorescence lifetime profiles of the intrinsic fluorescence ofPseudomonas fluorescens, Escherichia coli, Bacillus subtilis, andStaphylococcus epidermidis. The lifetimes were measured using a multiharmonic Fourier transform phase-modulation fluorometer which can simultaneously measure the phase shift and demodulation at many modulation frequencies. The 364-nm line from an argon-ion laser and the 325- and 442-nm lines from a helium-cadmium laser were used for sample excitation. Broad emission windows were used to capture as much of the bacterial emission as possible for the lifetime measurements. The maximum entropy method was used to recover lifetime profiles from the multifrequency phasemodulation data. At all three excitation wavelengths, the bacteria exhibited three lifetime components, in the ranges of 0.5-1, 2–3, and 4–8 ns. Using 325-nm excitation, a fourth component, in the range of 9–14 ns, was recovered in all of the bacteria; using 364-nm excitation, the fourth component was resolved only in the two Gram-negative bacteria (P. fluorescens andE. coli). Excitation at 364 nm provided the most reproducible lifetime profiles and showed some differences among the four bacteria.     

最大熵法在风廓线雷达谱分析中的应用研究

为了解现代谱分析技术在风廓线雷达中应用的可行性,通过采用实测的和模拟的风廓线雷达回波信号,对比研究了FFT法与最大熵法的谱分析效果。结果表明:(1)当回波信号比较强时,两者都可以得到较好的谱分析效果;但是当回波信号较弱时,最大熵法分析效果优于FFT法,最大熵法对地杂波具有较好的抑制能力。(2)最大熵谱比较光滑,表明最大熵法对随机白噪声也有一定的抑制作用。(3)最大熵法的递推阶数对谱分析结果有一定影响,最终预测误差准则确定的递推阶数一般偏小,采用15阶的递推阶数进行最大熵法分析取得了较好结果。由于风廓线雷达回波通常都较弱,因此研究结果可望用于改善信号处理效果。     

High resolution electron density mapping for LiF and NaF by maximum entropy method (MEM)

High resolution maximum entropy method (MEM) electron density maps have been elucidated for LiF and NaF using reported X-ray structure factors. The ionic nature of the bonding between constituent atoms in both the systems is found to be well pronounced and clearly seen from the electron density maps. The resolution of the present MEM maps is 0.063 Å per pixel for LiF and 0.072 Å per pixel for NaF along the three crystallographic axes. The electron density at the middle of the bond along [111] is found to be 0.0673 e/ų for LiF and 0.003 e/ų for NaF showing the different ionic strengths of the bonding. The electron density along [100] and [110] has also been drawn and analyzed. The inequality in the ionicity for the individual atoms and the electron content for different ionic radii have also been analyzed and compared with already published results. The wR_MEM obtained from MEM analysis is 0.3% for LiF and 0.79% for NaF.     

Recovery of lifetime distributions from frequency-domain fluorometry data by means of the quantified maximum entropy method

The new quantified version of the maximum entropy method allows one to recover lifetime distributions with a precise statement of the accuracy of position, surface, and broadness of peaks in the distribution. Applications to real data (2,6-ANS in aqueous solutions of sodium dodecyl sulfate micelles of -cyclodextrin) are presented.Died on September 1, 1993.     

无箔二极管强流电子束空间密度分布初步研究

通过在强磁场条件下, 利用环形刀口石墨阴极（刀口尺寸38~39 mm）开展电子束轰击收集极内表面铜箔和垂直轰击金属靶片实验, 对无箔二极管中电子束的空间密度分布进行了初步研究, 并对其产生原因进行了分析。研究结果表明, 电子束径向分布在37.2~40.2 mm, 存在密度较高区域（38.8~39.4 mm）和密度最大值点（39.2 mm）, 且均偏向于阴极外侧。无箔二极管环形阴极爆炸发射产生电子束的径向密度分布可用偏态分布近似。     

无箔二极管强流电子束空间密度分布初步研究

通过在强磁场条件下,利用环形刀口石墨阴极(刀口尺寸38~39mm)开展电子束轰击收集极内表面铜箔和垂直轰击金属靶片实验,对无箔二极管中电子束的空间密度分布进行了初步研究,并对其产生原因进行了分析。研究结果表明,电子束径向分布在37.2~40.2mm,存在密度较高区域(38.8~39.4mm)和密度最大值点(39.2mm),且均偏向于阴极外侧。无箔二极管环形阴极爆炸发射产生电子束的径向密度分布可用偏态分布近似。     

Single-particle spectral density of the unitary Fermi gas: Novel approach based on the operator product expansion,sum rules and the maximum entropy method

Making use of the operator product expansion, we derive a general class of sum rules for the imaginary part of the single-particle self-energy of the unitary Fermi gas. The sum rules are analyzed numerically with the help of the maximum entropy method, which allows us to extract the single-particle spectral density as a function of both energy and momentum. These spectral densities contain basic information on the properties of the unitary Fermi gas, such as the dispersion relation and the superfluid pairing gap, for which we obtain reasonable agreement with the available results based on quantum Monte-Carlo simulations.     

悬浮型微波共振探针在电负性容性耦合等离子体中电子密度的测量

本文首先利用悬浮型微波共振探针测量了Ar等离子体的电子密度,并与朗缪尔双探针的测量结果进行了比较,表明了微波共振探针在低密度等离子体测量的可行性.对40.68 MHz单射频容性耦合Ar/SF₆和SF₆/O₂等离子体的测量结果表明:电负性气体SF₆掺入Ar等离子体显著降低了等离子体电子密度,但随着增加SF₆的流量,电子密度表现为缓慢下降;而O₂掺入SF₆等离子体中,电子密度则随着O₂流量的增加表现为持续的下降.另外,40.68 MHz/13.56 MHz双频激发的SF₆/O₂容性耦合离子体的电子密度并不随低频功率的变化而变化.本文对上述的实验现象进行了初步的解释.     

Local structure of the high-temperature thermoelectric material PbTe using the maximum entropy method (MEM) and pair distribution function (PDF)

The electron density distribution and the local structure of the high temperature thermoelectric material PbTe has been studied. Powder X-ray data set of PbTe is analyzed in terms of cell parameter, thermal vibration parameters, 1D, 2D and 3-dimensional electron density distributions. The bonding between the atoms using the maximum entropy method (MEM) and bond-length distribution using pair distribution function (PDF) have been analyzed. Both the pictorial and the numerical results of electron density and PDF studies show mixed ionic and covalent characters in PbTe.     

Development and application of the Fraunhofer-diffraction method for measurements of plasma density fluctuations using infrared lasers

This paper is concerned with systematic developments of the Fraunhofer-diffraction method for studies of plasma density fluctuations in high-temperature plasmas using infrared lasers, namely (i) development of the general theory of the Fraunhofer-diffraction method, (ii) measurements of fluctuations propagating in an azimuthal direction, (iii) measurements of fluctuation intensities, and (iv) application in measurements on high-temperature plasmas.     

Ab-initio study of phase transition and momentum density in PbTe

In this article, the high-pressure structural phase transition and electron momentum density in PbTe have been studied by means of first-principles total energy calculations which are based on the linear combination of atomic orbitals method within generalized gradient approximation. It is observed that the stable phase of PbTe is rocksalt (B1) type and it transforms to an orthorhombic Pnma (B27, FeB type) structure at 6.77?GPa. Further, structural phase transition from the Pnma phase to the cesium chloride (B2) phase has been observed at 13.04?GPa. The anisotropies in theoretical directional Compton profiles indicate larger occupied states along the [100] direction. On the basis of equal-valence-electron-density profiles, it is found that PbTe shows less ionicity as compared to PbS and PbSe.     

质子束尾波场中利用密度跃变实现电子捕获及加速的粒子模拟

用2D3V粒子模拟程序研究了高能质子束驱动的尾波场加速电子的方案,及其在此方案中应用背景等离子体密度的跃变致使等离子体电子自注入加速相区的可能性。粒子模拟结果显示:密度跃变实现了电子的自注入,并且捕获的电子束处于加速相位,等离子体尾波场纵向电场对捕获的电子束起箍缩作用;捕获的电子束随着传输,表现为窄能谱分布;同时随着密度跃变大小的增大,可以增加等离子体电子的捕获。     

利用介质阻挡探针法测量大气压氦等离子体射流电子密度

分别利用电子的漂移速度和等离子体的传播速度计算了大气压下氦等离子体射流的电子密度。     

质子束尾波场中利用密度跃变实现电子捕获及加速的粒子模拟

 用2D3V粒子模拟程序研究了高能质子束驱动的尾波场加速电子的方案,及其在此方案中应用背景等离子体密度的跃变致使等离子体电子自注入加速相区的可能性。粒子模拟结果显示:密度跃变实现了电子的自注入,并且捕获的电子束处于加速相位,等离子体尾波场纵向电场对捕获的电子束起箍缩作用;捕获的电子束随着传输,表现为窄能谱分布;同时随着密度跃变大小的增大,可以增加等离子体电子的捕获。     

Assessment of the nature of interactions of cations with cycloheptatriene derivatives using change in the aromaticity: Comparison with electron density and NBO results

ABSTRACT

Interactions of cycloheptatriene derivatives, C₇H₆X, (X?=?NH, PH, AsH, O, S, Se) with the cations H⁺, CH₃⁺, Cu⁺, Al⁺, Li⁺, Na⁺, and K⁺ are studied using B3LYP functional and 6-311++G(d,p) basis set. The calculated gas-phase cation affinities (CA) and cation basicities (CB) for all molecules decrease as H⁺ > CH₃⁺ > Cu⁺ > Al⁺ > Li⁺ > Na⁺ > K⁺. We used the induced aromaticity in the 7-membered ring of C₇H₆X upon interaction with the cations, M⁺, as a measure of C₇H₆X/M⁺ interaction. Nucleus-independent chemical shift (NICS) and harmonic oscillator model of aromaticity (HOMA) were used as two indices of aromaticity. The highest and lowest induced aromaticities were observed for interactions of H⁺ and K⁺, respectively. Also, the aromaticity induced by interaction with a cation in C₇H₆AsH and C₇H₆PH was larger than that in C₇H₆NH and C₇H₆O. Hence, the aromaticity was considered as a measure of covalency for the C₇H₆X/M⁺ interactions showing a rational dependence on both the molecule and cation. The nature of the interactions was also assessed using electron density, charge distribution analysis and NBO calculations. The results of the aromaticity indices, NICS and HOMA, were compared with the electron density and NBO results.     

等离子体中X射线激光传输与电子密度诊断的理论及数值比较

通过数值模拟描述X射线激光在等离子体介质中传输的傍轴偏微分方程,分析了等离子体电子密度诊断中折射率测量法(如Abel变换方法)的成立条件及适用范围.同时分析了由Schrdinger形式理论得到的电子密度诊断的修正项的效果,并给出了修正后的电子密度诊断算法. 关键词： 等离子体 电子密度 X射线激光 Abel变换     

Non-nuclear maxima (NNM), symmetric and asymmetric charge distribution in solar grade Si and n-GaAs, using X-ray powder data

The symmetric and asymmetric charge distribution of bonding electrons in silicon and gallium arsenide has been studied using experimental powder X-ray data sets. The mid-bond electron densities from the origin are found to be 0.787 and 1.725 e/ų at 1.175 and 1.222 Å, respectively, for Si and n-GaAs. The effectiveness of powder data sets in precise bonding studies has been verified. Multipole analysis of the valence charge distribution has also been done. The thermal vibration parameters have been studied and presented for both these systems. The magnitudes of the non-nuclear maxima of both these systems are consistent with those obtained using single-crystal studies.     

Inequalities of the electron density at the nucleus and radial expectation values of the ground state for the lithium isoelectronic sequence

The electron density at the nucleus, ρ(0), and the radial expectation values, (-2≤n≤10), of the ground state for the lithium isoelectronic sequence are calculated with a full core plus correlation (FCPC) wavefunctions. By using these obtained expectation values, the accurate inequalities of the electron density at the nucleus and the radial expectation values derived by Gálvez and Porras for these systems are examined and verified. The final results show that FCPC wavefunctions used in this work can give satisfactory results in full configuration space.