Effective Diffusion Energy Barriers with the Boltzmann Distribution Assumption

2019 ◽  
Vol 34 (1) ◽  
pp. 1-5
Author(s):  
Rui Tu ◽  
Zhu Wang
Keyword(s):  
Effective Diffusion ◽  
Boltzmann Distribution ◽  
Energy Barriers ◽  
Distribution Assumption

Brownian Simulation of Matrix Diffusion

2000 ◽  
Vol 663 ◽  
Author(s):  
Sofie Andersson ◽  
Allan T. Emrén
Keyword(s):  
Effective Diffusion ◽  
Diffusion Constant ◽  
Boltzmann Distribution ◽  
Matrix Diffusion ◽  
Rock Matrix ◽  
Dissolved Species ◽  
Apparent Diffusion ◽  
Wide Variability ◽  
Far From Equilibrium ◽  
Solid Piece

ABSTRACTThe commonly used approach in dealing with matrix diffusion is to assign an effective diffusion constant for the radionuclide in the rock matrix. The idea behind this approach is that, on a scale much larger than the pore size, the irregularities tend to cancel out. Although it might look plausible at first sight, this approach has been questioned both for theoretical and experimental reasons.Here, Brownian simulation has been used to investigate the transport of dissolved material in a rock matrix modeled as a system of pores with a wide variability in size and shape. The Boltzmann distribution is used locally, although the system globally is far from equilibrium.The simulation consists of two main parts. First, the model rock is formed by precipitation of irregular mineral grains from a liquid phase. As the grains grow, they tend to form a mostly solid piece of rock.In the second part of the simulation, a dissolved species is introduced at one side of the rock and allowed to diffuse through its pore system. It is found that no apparent diffusion constant, D, can explain the properties of the system. Rather, D is found to be a function of both distance and time.

scholarly journals The role of vibrationally excited nitrogen and oxygen in the ionosphere over Millstone Hill during 16-23 March, 1990

2000 ◽  
Vol 18 (8) ◽  
pp. 957-966
Author(s):  
A. V. Pavlov ◽  
K.-I. Oyama
Keyword(s):  
Electron Density ◽  
Boltzmann Distribution ◽  
Ion Chemistry ◽  
Vibrationally Excited ◽  
Model Calculations ◽  
Maximum Value ◽  
Vibrational Levels ◽  
Electron Density And Temperature ◽  
Excited Nitrogen ◽  
Distribution Assumption

Abstract. We present a comparison of the observed behavior of the F region ionosphere over Millstone Hill during the geomagnetically quiet and storm period on 16-23 March, 1990, with numerical model calculations from the time-dependent mathematical model of the Earth's ionosphere and plasmasphere. The effects of vibrationally excited N2(v) and O2(v) on the electron density and temperature are studied using the N2(v) and O2(v) Boltzmann and non-Boltzmann distribution assumptions. The deviations from the Boltzmann distribution for the first five vibrational levels of N2(v) and O2(v) were calculated. The present study suggests that these deviations are not significant at vibrational levels v = 1 and 2, and the calculated distributions of N2(v) and O2(v) are highly non-Boltzmann at vibrational levels v > 2. The N2(v) and O2(v) non-Boltzmann distribution assumption leads to the decrease of the calculated daytime NmF2 up to a factor of 1.44 (maximum value) in comparison with the N2(v) and O2(v) Boltzmann distribution assumption. The resulting effects of N2(v > 0) and O2(v > 0) on the NmF2 is the decrease of the calculated daytime NmF2 up to a factor of 2.8 (maximum value) for Boltzmann populations of N2(v) and O2(v) and up to a factor of 3.5 (maximum value) for non-Boltzmann populations of N2(v) and O2(v) . This decrease in electron density results in the increase of the calculated daytime electron temperature up to about 1040-1410 K (maximum value) at the F2 peak altitude giving closer agreement between the measured and modeled electron temperatures. Both the daytime and nighttime densities are not reproduced by the model without N2(v > 0) and O2(v > 0) , and inclusion of vibrationally excited N2 and O2 brings the model and data into better agreement. The effects of vibrationally excited O2 and N2 on the electron density and temperature are most pronounced during daytime.Key words: Ionosphere (ion chemistry and composition; ionosphere-atmosphere interactions; ionospheric disturbances)

Surface recombination effects on minority carrier diffusion length measurements using electron beam-induced current

1990 ◽  
Vol 48 (4) ◽  
pp. 744-745
Author(s):  
D.P. Malta ◽  
M.L. Timmons
Keyword(s):  
Electron Beam ◽  
Beam Energy ◽  
Minority Carrier ◽  
Diffusion Length ◽  
Effective Diffusion ◽  
Surface Recombination ◽  
Surface Recombination Velocity ◽  
Logarithmic Scale ◽  
Minority Carrier Diffusion Length ◽  
Carrier Diffusion

Measurement of the minority carrier diffusion length (L) can be performed by measurement of the rate of decay of excess minority carriers with the distance (x) of an electron beam excitation source from a p-n junction or Schottky barrier junction perpendicular to the surface in an SEM. In an ideal case, the decay is exponential according to the equation, I = Ioexp(−x/L), where I is the current measured at x and Io is the maximum current measured at x=0. L can be obtained from the slope of the straight line when plotted on a semi-logarithmic scale. In reality, carriers recombine not only in the bulk but at the surface as well. The result is a non-exponential decay or a sublinear semi-logarithmic plot. The effective diffusion length (Leff) measured is shorter than the actual value. Some improvement in accuracy can be obtained by increasing the beam-energy, thereby increasing the penetration depth and reducing the percentage of carriers reaching the surface. For materials known to have a high surface recombination velocity s (cm/sec) such as GaAs and its alloys, increasing the beam energy is insufficient. Furthermore, one may find an upper limit on beam energy as the diameter of the signal generation volume approaches the device dimensions.

Calculation of the free energy barriers in the oligomerisation of Ab

10.2741/3104 ◽  
2008 ◽  
Vol Volume (13) ◽  
pp. 5614 ◽  
Author(s):  
Mookyung Cheon
Keyword(s):  
Free Energy ◽  
Energy Barriers

Modelling of impregnation of γ-alumina with cobalt and molybdenum salts. CoCl2-(NH4)2MoO4-γ-Al2O3 (aluminate type) system

1987 ◽  
Vol 52 (3) ◽  
pp. 663-671 ◽  
Author(s):  
Jiří Hanika ◽  
Vladimír Janoušek ◽  
Karel Sporka
Keyword(s):  
Effective Diffusion ◽  
Type System ◽  
Catalyst Particle ◽  
Ammonium Molybdate ◽  
Active Components ◽  
Model Set ◽  
Cobalt Dichloride ◽  
Set Up ◽  
Electron Microanalysis ◽  
Kinetics Of

Adsorption data for the impregnation of alumina with an aqueous solution of cobalt dichloride and ammonium molybdate were treated in terms of the Langmuir adsorption isotherm and compared with a mathematical model set up to describe the kinetics of simultaneous impregnation of a support by two components. The effective diffusion coefficients of the two components at 25 °C in a cylindrical particle of alumina were obtained. The validity of the model used was verified qualitatively by comparing the numerical results with the experimental time dependent concentration profiles of the active components in a catalyst particle, measured by electron microanalysis technique.

Introduction

2018 ◽  
Author(s):  
Niels Engholm Henriksen ◽  
Flemming Yssing Hansen
Keyword(s):  
Schrödinger Equation ◽  
Schrodinger Equation ◽  
Degrees Of Freedom ◽  
State Level ◽  
Boltzmann Distribution ◽  
Theoretical Description ◽  
Time Dependent ◽  
Nuclear Dynamics ◽  
Molecular Reaction ◽  
Oppenheimer Approximation

This introductory chapter considers first the relation between molecular reaction dynamics and the major branches of physical chemistry. The concept of elementary chemical reactions at the quantized state-to-state level is discussed. The theoretical description of these reactions based on the time-dependent Schrödinger equation and the Born–Oppenheimer approximation is introduced and the resulting time-dependent Schrödinger equation describing the nuclear dynamics is discussed. The chapter concludes with a brief discussion of matter at thermal equilibrium, focusing at the Boltzmann distribution. Thus, the Boltzmann distribution for vibrational, rotational, and translational degrees of freedom is discussed and illustrated.

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