scholarly journals On a Conjecture about Diffusion of Gaseous Ions

1973 ◽  
Vol 26 (6) ◽  
pp. 897 ◽  
Author(s):  
Gregory H Wannier
Keyword(s):  
Diffusion Coefficient ◽  
Einstein Relation

A previous conjecture by the author about the diffusion coefficient of gaseous ions is restated more precisely, thereby eliminating, in particular, an error of a factor of two which seemed to be contained in it in certain cases. The conjecture, which is essentially an extension of the Nernst-Einstein relation to situations not close to equilibrium, is made plausible by a Langevin-type derivation.

Electrical conductivity and Einstein relation modeling in phosphorene

2019 ◽  
Vol 33 (06) ◽  
pp. 1950033
Author(s):  
E. Mansouri ◽  
J. Karamdel ◽  
M. T. Ahmadi ◽  
M. Berahman
Keyword(s):  
Diffusion Coefficient ◽  
Fermi Energy ◽  
Carrier Mobility ◽  
2D Materials ◽  
Einstein Relation ◽  
Fundamental Parameters ◽  
Electron Diffusion Coefficient ◽  
Energy Formula ◽  
Higher Carrier Mobility ◽  
And Diffusion

Investigation on (2-dimensional) (2D) materials is growing significantly due to the fundamental electronic properties in the direct inherent bandgap, higher carrier mobility, and easier exfoliation. Phosphorene as a new 2D configuration has presented excellent potential in electronic and optoelectronic applications. In this study, the conductivity of monolayer phosphorene and Einstein’s relations as fundamental parameters in semiconductor manufacturing are analytically modeled. In addition, dependency of conductivity on normalized Fermi energy ([Formula: see text]) is demonstrated. According to the simulation results, conductivity and Einstein’s relation are completely dependent on temperature, therefore, rising up the temperature leads to conductivity and diffusion coefficient (Dn) growth. Indeed, conductivity is saturated when the normalized Fermi energy exceeds than 6. Also, the conductivity and Einstein’s relation dependency to voltage are studied. Results show that carrier conductivity and the electron diffusion coefficient (Dn) increase by amplifying the voltage.

Fractional Exponent of the Modified Stokes-Einstein Relation in the Metallic Glass-Forming Melt Pd43Cu27Ni10P20

2010 ◽  
Vol 146-147 ◽  
pp. 1463-1468
Author(s):  
Masahiro Ikeda ◽  
Masaru Aniya
Keyword(s):  
Diffusion Coefficient ◽  
Glass Transition ◽  
Transition Temperature ◽  
Glass Transition Temperature ◽  
Metallic Glass ◽  
Bond Strength ◽  
Coordination Number ◽  
Einstein Relation ◽  
Glass Forming ◽  
Highly Correlated

The diffusion coefficient in the metallic glass-forming systems such as Pd-Cu-Ni-P exhibits a marked deviation from the Stokes-Einstein (SE) relation in the proximity of the glass transition temperature. Such a deviation is characterized by the fractional exponent p of the modified SE expression. For the material Pd43Cu27Ni10P20, it has been reported that it takes the value p = 0.75. In this work, it is shown that the value of p is highly correlated with the ratio ED / ENB, where ED and ENB are the activation energies for diffusion coefficient D and cooperativity NB defined by the Bond Strength-Coordination Number Fluctuation (BSCNF) model. The present paper reports that for the metallic glass-forming melt Pd43Cu27Ni10P20, the fractional exponent p can be calculated accurately within the framework of the BSCNF model.

The influence of diffusion on the current-voltage curve in a flame ionization detector. II

1992 ◽  
Vol 438 (1903) ◽  
pp. 361-370 ◽  
Keyword(s):  
Diffusion Coefficient ◽  
Applied Voltage ◽  
Flame Ionization Detector ◽  
Three Dimensions ◽  
Einstein Relation ◽  
Ionization Detector ◽  
Flame Ionization ◽  
Voltage Curve ◽  
Current Voltage ◽  
Current Voltage Curve

This article is a continuation of an earlier article with the same title which extended the analysis of the current-voltage curve of the flame ionization detector near the origin of the curve, in terms of both mobility and diffusion of the flame ions oxonium hydrates. It is shown here that diffusion dominates the current only when the value of the applied voltage is much less than 1 V. The theory of the instrument using only diffusion is given in one, two and three dimensions. Experiments have been performed on a flame ionization detector using applied voltages up to 5 V and the current extrapolated to zero applied voltage. From this value of the current the ionic diffusion coefficient was obtained which agrees with that deduced from the Einstein relation and the measured value of the mobility. The theory also yields a method of obtaining the diffusion coefficient from the slope of the current-voltage curve at the origin but the coefficient so obtained is incorrect because the voltage interval of 1 V is too large and to use the theory successfully would need the region of the current-voltage curve much closer to the origin.

Unipolar Flow of Charge Carriers in a Dense Gas with and without Consideration of Diffusion

1970 ◽  
Vol 25 (10) ◽  
pp. 1447-1452
Author(s):  
W. Dällenbach
Keyword(s):  
Diffusion Coefficient ◽  
Electric Field ◽  
Cross Section ◽  
Current Density ◽  
Charge Carriers ◽  
Einstein Relation ◽  
Dense Gas ◽  
Modified Equations ◽  
Basic Equations ◽  
And Diffusion

Abstract The basic equations for the unipolar, stationary, one-dimensional flow of charge carriers in a dense gas, characterized by mobility and diffusion coefficient, can be integrated numerically. The discharge gap generally has a finite length; as far as in the end cross-section either density of particles and intensity of electric field tend towards infinity, or the density of particles becomes zero. Which of these two cases occurs depends on the current density of the discharge and on the intensity of the electric field in the initial cross-section. The notions mobility and diffusion coefficient will lose their applicability close to a pole like singularity as well as in a "dilution to zero", so that from a certain cross-section onwards the continuation of discharge is determined by modified equations.It is shown that in case the diffusion component of the current density is neglected, the integrals of the basic equations change fundamentally. Neglecting the diffusion is inadmissible. This is finally a consequence of the relationship between mobility and diffusion coefficient, as expressed by the Einstein-relation.

On the diffusion theory of rectification

1952 ◽  
Vol 213 (1113) ◽  
pp. 226-237 ◽  
Keyword(s):  
Diffusion Coefficient ◽  
Diffusion Equation ◽  
Einstein Equation ◽  
Concentration Distribution ◽  
Diffusion Theory ◽  
Slight Modification ◽  
Formal Theory ◽  
Einstein Relation ◽  
Conduction Electrons ◽  
A Current

It is pointed out that the Einstein relation eD = vkT between the mobility ( v ) and the diffusion coefficient ( D ) of current carriers has not so far been established theoretically or experimentally for the case of rectifying junctions which are carrying a current. It is shown that the theory can be developed without appealing to this relation, so that experimental characteristics can be utilized to test for the validity of the Einstein equation. When this is done experiment suggests different values of v , D and v/D for forward characteristics from those it does for reverse characteristics. This result has been discussed, taking into account Fermi-Dirac statistics, in the light of the formal theory of conduction. This has been shown to lead ( a ) to the diffusion equation and ( b ) to a slight modification of Einstein’s relation, provided v and D are regarded as averages for the barrier. Strictly, v and D depend on the concentration distribution of conduction electrons in the barrier. The shapes of the experimental curves are in agreement with theory.

QUANTUM THEORY OF THE SEEBECK COEFFICIENT IN METALS

2000 ◽  
Vol 14 (21) ◽  
pp. 2231-2240 ◽  
Author(s):  
S. FUJITA ◽  
H.-C. HO ◽  
Y. OKAMURA
Keyword(s):  
Diffusion Coefficient ◽  
Quantum Theory ◽  
Seebeck Coefficient ◽  
Carrier Density ◽  
Noble Metals ◽  
Einstein Relation ◽  
Charge Carrier Density ◽  
Thermal Emf ◽  
Different Temperatures ◽  
New Formula

Based on the idea that different temperatures generate different carrier densities and the resulting diffusion causes the thermal emf, a new formula for the Seebeck coefficient S is obtained: [Formula: see text], where q, n, εF, [Formula: see text]. and [Formula: see text]. are respectively charge, carrier density, Fermi energy, density of states at ∊F and volume. Ohmic and Seebeck currents are fundamentally different in nature. This difference can cause significantly different transport behaviors. For a multi-carrier metal the Einstein relation between the conductivity and the diffusion coefficient does not hold in general. Seebeck (S) and Hall (RH) coefficients in noble metals have opposite signs. This is shown to arise from the Fermi surface having "necks" at the Brillouin boundary.

Kernmagnetische Messungen von Selbstdiffusions-Koeffizienten in Wasser und Benzol bis zum kritischen Punkt

1966 ◽  
Vol 21 (9) ◽  
pp. 1410-1415 ◽  
Author(s):  
R. Hausser ◽  
G. Maier ◽  
F. Noack
Keyword(s):  
Experimental Data ◽  
Activation Energy ◽  
Nuclear Magnetic Resonance ◽  
Diffusion Coefficient ◽  
Room Temperature ◽  
Strong Influence ◽  
Spin Echo ◽  
Einstein Relation ◽  
Rate Theory ◽  
Resonance Spin

The most commonly used nuclear magnetic resonance spin-echo methods for determining selfdiffusion coefficients D are described; some experimental data are presented for protons in water and in benzene from room temperature up to the critical point. The results are interpreted in terms of the free-volume rate theory of MACEDO and LITOVITZ. The D-value of benzene may be described by a single activation energy. Water, however, shows such behavior only at high temperatures, thus demonstrating the strong influence of hydrogen bonding. The STOKES-EINSTEIN relation between diffusion coefficient and viscosity is well satisfied over that part of the temperature range where viscosity values are available.

scholarly journals Summary of New Insight into Electron Transport in Metals

Crystals ◽  
2021 ◽  
Vol 11 (6) ◽  
pp. 622
Author(s):  
Vilius Palenskis ◽  
Evaras Žitkevičius
Keyword(s):  
Diffusion Coefficient ◽  
Electron Transport ◽  
Drift Mobility ◽  
Effective Density ◽  
Einstein Relation ◽  
Lattice Atom ◽  
Dirac Distribution ◽  
The Creation ◽  
Electronic Defects ◽  
Insight Into

This paper gives a summary of a new insight into basic electron transport characteristics in crystalline elemental metals. The general expressions based on the Fermi-Dirac distribution of the effective density of the randomly moving electrons, their diffusion coefficient, drift mobility, and other characteristics, including the Einstein relation between diffusion coefficient and drift mobility, are presented. It is shown that the creation of the randomly moving electrons due to lattice atom vibrations produces the same number of electronic defects, which cause scattering of the randomly moving electrons and related transport characteristics.

MOLECULAR-DYNAMICS STUDIES OF BIATOMIC SUPERCOOLED LIQUIDS: INTERMITTENCY, STICK-SLIP TRANSITION AND THE BREAKDOWN OF THE STOKES-EINSTEIN LAWS

Fractals ◽  
2003 ◽  
Vol 11 (supp01) ◽  
pp. 139-147 ◽  
Author(s):  
CHRISTIANO DE MICHELE ◽  
DINO LEPORINI
Keyword(s):  
Molecular Dynamics ◽  
Diffusion Coefficient ◽  
Rotational Diffusion ◽  
Power Laws ◽  
Supercooled Liquid ◽  
Rotational Correlation Time ◽  
Einstein Relation ◽  
Stick Slip ◽  
Molecular Dynamics Methods ◽  
Slip Transition

The transport and the relaxation properties of a biatomic supercooled liquid are studied by molecular-dynamics methods. Both translational and rotational jumps are evidenced. At lower temperatures their waiting-time distributions decay as a power law at short times. The Stokes-Einstein relation (SE) breaks down at a temperature which is close to the onset of the intermittency. A precursor effect of the SE breakdown is observed as an apparent stick-slip transition. The breakdown of Debye-Stokes-Einstein law for rotational motion is also observed. On cooling, the changes of the rotational correlation time τ1 and the translational diffusion coefficient at low temperatures are fitted by power laws over more than three and four orders of magnitude, respectively. A less impressive agreement is found for τl with l = 2 - 4 and the rotational diffusion coefficient.

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