Lower Bounds to Hammett σ Constants for meta and para Normal Substituents

1999 ◽  
Vol 64 (10) ◽  
pp. 1607-1616 ◽  
Author(s):  
João Carlos R. Reis ◽  
Manuel A. P. Segurado ◽  
Jaime D. Gomes de Oliveira
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Benzoic Acid ◽  
Lower Bounds ◽  
Lone Pair ◽  
Hyperbolic Model ◽  
Benzoic Acid Derivatives ◽  
Lower Bounding ◽  
Hammett Σ Constants ◽  
Electric Effect

Twenty-four pairs of meta and para Hammett σ constants recommended by IUPAC for normal substituents, i.e. dipolar groups without a lone pair of electrons (and with a full octet) in the atom next to the aromatic ring, were analysed with respect to their meta-para interrelationship. In terms of a previous hyperbolic model, the para/meta ratio of the universal electric effect is found to be 0.964 with a standard error of 0.028 estimated by Monte Carlo simulation. This value for benzoic acid derivatives supports the view that the universal electric effect, which is proposed to be termed the Electra effect, is transmitted through space. For normal substituents, it is demonstrated that the hyperbolic model predicts lower bounding values of σm and σp constants. It is proposed that organometallic substituents in which a metallic atom is bounded to the α carbon should not be considered as normal substituents. It is asserted that no normal substituent should exist for which either σm is less than -0.1 or σp is less than -0.3 in the Hammett σ scale.

Taylor series expansion for evaluating the bounds of electric potentials in an electrostatic system with interval parameters

2018 ◽  
Vol 37 (2) ◽  
pp. 832-848
Author(s):  
Pengbo Wang ◽  
Jingxuan Wang
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Lower Bounds ◽  
Taylor Series ◽  
Taylor Series Expansion ◽  
Upper And Lower Bounds ◽  
Content Type ◽  
Interval Parameters ◽  
Electric Potentials ◽  
Electrostatic System

PurposeUncertainty is ubiquitous in practical engineering and scientific research. The uncertainties in parameters can be treated as interval numbers. The prediction of upper and lower bounds of the response of a system including uncertain parameters is of immense significance in uncertainty analysis. This paper aims to evaluate the upper and lower bounds of electric potentials in an electrostatic system efficiently with interval parameters. Design/methodology/approachThe Taylor series expansion is proposed for evaluating the upper and lower bounds of electric potentials in an electrostatic system with interval parameters. The uncertain parameters of the electrostatic system are represented by interval notations. By performing Taylor series expansion on the electric potentials obtained using the equilibrium governing equation and by using the properties of interval mathematics, the upper and lower bounds of the electric potentials of an electrostatic system can be calculated. FindingsTo evaluate the accuracy and efficiency of the proposed method, the upper and lower bounds of the electric potentials and the computation time of the proposed method are compared with those obtained using the Monte Carlo simulation, which is referred to as a reference solution. Numerical examples illustrate that the bounds of electric potentials of this method are consistent with those obtained using the Monte Carlo simulation. Moreover, the proposed method is significantly more time-saving. Originality/valueThis paper provides a rapid computational method to estimate the upper and lower bounds of electric potentials in electrostatics analysis with interval parameters. The precision of the proposed method is acceptable for engineering applications, and the computation time of the proposed method is significantly less than that of the Monte Carlo simulation, which is the most widely used method related to uncertainties. The Monte Carlo simulation requires a large number of samplings, and this leads to significant runtime consumption.

Electron Scattering in Solids

1990 ◽  
Vol 48 (2) ◽  
pp. 4-5
Author(s):  
Ryuichi Shimizu ◽  
Ze-Jun Ding
Keyword(s):  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Angular Distribution ◽  
Elastic Scattering ◽  
Electron Scattering ◽  
Cross Sections ◽  
Expansion Method ◽  
Electron Excitation ◽  
Partial Wave Expansion ◽  
Backscattered Electrons

Monte Carlo simulation has been becoming most powerful tool to describe the electron scattering in solids, leading to more comprehensive understanding of the complicated mechanism of generation of various types of signals for microbeam analysis.The present paper proposes a practical model for the Monte Carlo simulation of scattering processes of a penetrating electron and the generation of the slow secondaries in solids. The model is based on the combined use of Gryzinski’s inner-shell electron excitation function and the dielectric function for taking into account the valence electron contribution in inelastic scattering processes, while the cross-sections derived by partial wave expansion method are used for describing elastic scattering processes. An improvement of the use of this elastic scattering cross-section can be seen in the success to describe the anisotropy of angular distribution of elastically backscattered electrons from Au in low energy region, shown in Fig.l. Fig.l(a) shows the elastic cross-sections of 600 eV electron for single Au-atom, clearly indicating that the angular distribution is no more smooth as expected from Rutherford scattering formula, but has the socalled lobes appearing at the large scattering angle.

Determination of Stoichiometry of GaAs Component in (Gaas)Ge Epitaxially Grown Thin Films by Electron Microprobe X-Ray Analysis

1990 ◽  
Vol 48 (2) ◽  
pp. 264-265
Author(s):  
D. R. Liu ◽  
S. S. Shinozaki ◽  
R. J. Baird
Keyword(s):  
Thin Film ◽  
Thin Films ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Compound Semiconductors ◽  
Energy Dispersive Analysis ◽  
X Ray ◽  
Metastable Alloys ◽  
Lower Voltage

The epitaxially grown (GaAs)Ge thin film has been arousing much interest because it is one of metastable alloys of III-V compound semiconductors with germanium and a possible candidate in optoelectronic applications. It is important to be able to accurately determine the composition of the film, particularly whether or not the GaAs component is in stoichiometry, but x-ray energy dispersive analysis (EDS) cannot meet this need. The thickness of the film is usually about 0.5-1.5 μm. If Kα peaks are used for quantification, the accelerating voltage must be more than 10 kV in order for these peaks to be excited. Under this voltage, the generation depth of x-ray photons approaches 1 μm, as evidenced by a Monte Carlo simulation and actual x-ray intensity measurement as discussed below. If a lower voltage is used to reduce the generation depth, their L peaks have to be used. But these L peaks actually are merged as one big hump simply because the atomic numbers of these three elements are relatively small and close together, and the EDS energy resolution is limited.

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