A Continuum Theory That Couples Creep and Self-Diffusion

2004 ◽  
Vol 71 (5) ◽  
pp. 646-651 ◽  
Author(s):  
Z. Suo
Keyword(s):  
Film Thickness ◽  
Chemical Potential ◽  
Relative Rate ◽  
Diffusion Flux ◽  
Stress Gradient ◽  
Continuum Theory ◽  
Potential Gradient ◽  
Self Diffusion ◽  
Component Material ◽  
Coupled Theory

In a single-component material, a chemical potential gradient or a wind force drives self-diffusion. If the self-diffusion flux has a divergence, the material deforms. We formulate a continuum theory to be consistent with this kinematic constraint. When the diffusion flux is divergence-free, the theory decouples into Stokes’s theory for creep and Herring’s theory for self-diffusion. A length emerges from the coupled theory to characterize the relative rate of self-diffusion and creep. For a flow in a film driven by a stress gradient, creep dominates in thick films, and self-diffusion dominates in thin films. Depending on the film thickness, either stress-driven creep or stress-driven diffusion prevails to counterbalance electromigration. The transition occurs when the film thickness is comparable to the characteristic length of the material.

scholarly journals Mechanics of Supercooled Liquids

2014 ◽  
Vol 81 (11) ◽  
Author(s):  
Jianguo Li ◽  
Qihan Liu ◽  
Laurence Brassart ◽  
Zhigang Suo
Keyword(s):  
Viscous Flow ◽  
Chemical Potential ◽  
Relative Rate ◽  
Diffusion Flux ◽  
Continuum Theory ◽  
Supercooled Liquid ◽  
Supercooled Liquids ◽  
Thermodynamic Consideration ◽  
Self Diffusion ◽  
Molecular Dimension

Pure substances can often be cooled below their melting points and still remain in the liquid state. For some supercooled liquids, a further cooling slows down viscous flow greatly, but does not slow down self-diffusion as much. We formulate a continuum theory that regards viscous flow and self-diffusion as concurrent, but distinct, processes. We generalize Newton's law of viscosity to relate stress, rate of deformation, and chemical potential. The self-diffusion flux is taken to be proportional to the gradient of chemical potential. The relative rate of viscous flow and self-diffusion defines a length, which, for some supercooled liquids, is much larger than the molecular dimension. A thermodynamic consideration leads to boundary conditions for a surface of liquid under the influence of applied traction and surface energy. We apply the theory to a cavity in a supercooled liquid and identify a transition. A large cavity shrinks by viscous flow, and a small cavity shrinks by self-diffusion.

Anionic and Cationic Diffusion in Ionic Conducting Oxides

2005 ◽  
Vol 237-240 ◽  
pp. 843-848 ◽  
Author(s):  
Georgette Petot-Ervas ◽  
C. Petot ◽  
Jean Marc Raulot ◽  
J. Kusinski
Keyword(s):  
Chemical Potential ◽  
Potential Gradient ◽  
Transport Processes ◽  
Electrical Field ◽  
Experimental Procedure ◽  
Conducting Oxides ◽  
Self Diffusion ◽  
Ionic Conducting ◽  
Applied Electrical Field

This paper concerns an analysis of the transport processes at high temperature in anionic conducting oxides subjected to a chemical potential gradient or an applied electrical field. The general equations are given. The principle of the cationic kinetic demixing under a “generalized“ thermodynamical potential gradient is reviewed. Experimental results obtained with yttria-doped zirconia are reported. An experimental procedure for the determination of the oxygen diffusion coefficient in ionic and semiconducting oxides is also described. The results obtained with yttriastabilized zirconia are compared to both self diffusion and conductivity data. This has allowed us to obtain information concerning the defect structure.

Solute Segregation Studied by Grain Boundary Diffusion

2005 ◽  
Vol 237-240 ◽  
pp. 499-501 ◽  
Author(s):  
Sergiy V. Divinski ◽  
Christian Herzig
Keyword(s):  
Grain Boundary ◽  
Boundary Diffusion ◽  
Chemical Potential ◽  
Diffusion Flux ◽  
Potential Gradient ◽  
Tracer Diffusion ◽  
Grain Boundary Diffusion ◽  
Cu Content ◽  
Component Systems ◽  
Order Of Magnitude

Diffusion of 64Cu, 59Fe, and 63Ni radiotracers has been measured in Cu–Fe–Ni alloys of different compositions at 1271 K. The measured penetration profiles reveal grain boundary-induced part along with the volume diffusion one. Correction on grain boundary diffusion was taken into account when determining the volume diffusivities of the components. When the Cu content in the alloys increases, the diffusivities increase by order of magnitude. This behaviour correlates well with decreasing of the melting temperature of corresponding alloys, as the Cu content increases. Modelling of interdiffusion in the Cu–Fe–Ni system based on Danielewski-Holly model of interdiffusion is presented. In this model (extended Darken method for multi-component systems) a postulate that the total mass flow is a sum of the diffusion and the drift flows was applied for the description of interdiffusion in the closed system. Nernst-Planck’s flux formula assuming a chemical potential gradient as a driving force for the mass transport was used for computing the diffusion flux in non-ideal multi-component systems. In computations of the diffusion profiles the measured tracer diffusion coefficients of Cu, Fe and Ni as well as the literature data on thermodynamic activities for the Cu–Fe–Ni system were used. The calculated interdiffusion concentration profiles (diffusion paths) reveal satisfactory agreement with the experimental results.

Optoelectronic Properties of Plasma CVD a-Si:H Modified by Filament-Generated Atomic H

1992 ◽  
Vol 258 ◽  
Author(s):  
Y.M. Li ◽  
I. An ◽  
M. Gunes ◽  
R.M. Dawson ◽  
R.W. Collins ◽  
...  
Keyword(s):  
Film Thickness ◽  
Real Time ◽  
Chemical Potential ◽  
Defect Density ◽  
Plasma Deposition ◽  
Plasma Cvd ◽  
Near Surface ◽  
Optical Gap ◽  
New Material ◽  
Control Samples

ABSTRACTWe have studied a-Si:H prepared by alternating plasma deposition with atomic H treatments performed with a heated W filament. Real time spectroscopie ellipsometry provides the evolution of film thickness, optical gap, and a measure of the fraction of Si-Si bonds broken in the near-surface (200 Å) during H-exposure of single films. This information guided us to the desired parameters for the H-treatments. Here, we concentrate on a weak hydrogenation regime characterized by minimal etching, a higher H content by 2 at.%, and a larger optical gap by 0.02 eV for the growth/hydrogenation structures in comparison to continuously deposited control samples. This new material has shown an improvement in the defect density in the light-soaked state in comparison to the control samples. This may result from stabilization of the Si structure due to an increase in the H chemical potential in the a-Si:H.

scholarly journals The influence of elastic deformations in high-strength structural materials on the hydrogen transport

2021 ◽  
Vol 225 ◽  
pp. 01010
Author(s):  
Polina Grigoreva ◽  
Elena Vilchevskaya ◽  
Vladimir Polyanskiy
Keyword(s):  
Chemical Potential ◽  
Potential Gradient ◽  
Elastic Solid ◽  
High Strength ◽  
Ideal Gas ◽  
Linear Elastic ◽  
Coupled Diffusion ◽  
Elastic Boundary ◽  
Linear Effects ◽  
Solid System

In this work, the diffusion equation for the gas-solid system is revised to describe the non-uniform distribution of hydrogen in steels. The first attempt to build a theoretical and general model and to describe the diffusion process as driven by a chemical potential gradient is made. A linear elastic solid body and ideal gas, diffusing into it, are considered. At this stage, we neglect any traps and non-linear effects. The coupled diffusion-elastic boundary problem is solved for the case of the cylinder under the tensile loads. The obtained results correspond to the experimental ones. Based on them, the assumptions about the correctness of the model and its further improvement are suggested.

Change of Shape and Change of Volume

1993 ◽  
Author(s):  
Brian Bayly
Keyword(s):  
Isotropic Material ◽  
Chemical Potential ◽  
Stress Gradient ◽  
Small Length ◽  
Large Sphere ◽  
Point Of Interest ◽  
Principal Axes ◽  
Principal Directions ◽  
Point To Point ◽  
Spatial Stress

In earlier chapters we first defined a material's chemical potential, and then went on to enquire how the material responds. And similarly with a state of nonhydrostatic stress: having reviewed what it is, we consider how a material might respond. For the sake of simplicity, we imagine an extensive sample, such as a cubic meter, and suppose that the stress state is the same in every cubic centimeter; that is to say, there are no gradients in stress from point to point. Thus we do not enquire yet how a material responds to a spatial stress gradient; that comes later. We first enquire how it responds to a homogeneous but nonhydrostatic stress. Inside the material, close to the point of interest, we define a small length l by means of the material particles at its two ends. If, at a later moment, we find the distance between the particles to be l — δl, then we envisage the limit of the ratio δl/l as l goes to zero, give the limit the symbol ε, and name it the linear strain at the point of interest in the direction of l, positive when δl is positive, i.e., for a shortening and negative for an elongation. Another mental operation that can be performed in the neighborhood of the point of interest is to define a small sphere by means of the material particles that form its surface. At a later moment the particles will form the surface of an ellipsoid. (For a large sphere and an inhomogeneous situation, the new shape can be something more complicated; but as the imagined original sphere approaches zero diameter, the shape of its deformed counter-part can only approach an ellipsoid). The axes of the ellipsoid are principal directions of strain, and the magnitudes of the strains along them are named ε1, ε2, and ε3, with ε1 the largest. In an isotropic material, the principal axes of stress and strain coincide, with ε1 lying along the direction of σ1 and correspondingly; see Figure 7.la. As with stresses, the three values of ε themselves define an ellipsoid if they are all positive—see Figure 7.1b.

Disequilibrium 3: Internal Variables

1993 ◽  
Author(s):  
Brian Bayly
Keyword(s):  
Vinyl Chloride ◽  
Chemical Potential ◽  
Potential Gradient ◽  
Material Behavior ◽  
Internal Variables ◽  
Starting State ◽  
Separate Point ◽  
Point To Point ◽  
New Location ◽  
Rate Of Response

In Chapters 2, 3, and 4, the usefulness of the concept chemical potential has been explored for describing and predicting movement of material from point to point in space—from a location where a component's potential is high to a location where its potential is lower. But chemical potential influences another type of material behavior as well, as in the example at the end of Chapter 2, the polymerization of vinyl chloride. The polymerization is a process that runs at a certain rate, like diffusion of salt, and the rate depends on the potential difference between the starting state and the end state; but unlike diffusion of salt, there is no overall movement from one location to a new location—the vinyl chloride simply polymerizes where it is. There are movements, of course, on the scale of the interatomic distances, but nothing corresponding to the 4 m of travel that appears in the discussion of the dike. If no travel is involved, it is not so easy to calculate a potential gradient along the travel path and go on to predict a rate of response. Yet there definitely is a rate of response, even with PVC polymerizing. The purpose of this chapter is to consider this matter; we shall then be equipped to begin considering nonhydrostatic conditions. The essential idea is to represent all possible degrees of polymerization along an axis, as in Figure 5.1. The figure is drawn to represent a condition where the chemical potential per kilogram is greater in the monomer form than in the dimer form, i.e., a condition where the material polymerizes spontaneously. Suppose we know the chemical potential per kilogram for all degrees of polymerization and also, at some temperature, the rates at which 2 forms from 1, 3 forms from 2, etc. (per kg of the starting form in a pure state). Then we arbitrarily pick a distance on the horizontal axis to separate point 1 from point 2.

Active sodium transport in toad bladder despite removal of serosal potassium

1965 ◽  
Vol 208 (2) ◽  
pp. 401-406 ◽  
Author(s):  
Alvin Essig
Keyword(s):  
Sodium Transport ◽  
Chemical Potential ◽  
Potential Gradient ◽  
Ringer Solution ◽  
Active Sodium ◽  
Chemical Potential Gradient ◽  
Control Value ◽  
Active Sodium Transport ◽  
Solution Bathing ◽  
Determining Factor

Previous studies have demonstrated that removal of potassium from sodium-Ringer solution bathing the serosal surface of the toad badder depressed net sodium transport to some 5% of control value, whereas with choline-Ringer solution as serosal medium removal of serosal potassium depressed net sodium transport only to some 55% of control value. Although transport is down a chemical potential gradient in the latter situation, it appears to be an active process, for it is depressed by anaerobiosis, and persists against an electrochemical potential gradient. The data suggest that the concentration of potassium at the serosal aspect of the sodium pump is not in itself the rate-determining factor for active sodium transport following removal of serosal potassium.

A continuum theory of stress gradient plasticity based on the dislocation pile-up model

2014 ◽  
Vol 80 ◽  
pp. 350-364 ◽  
Author(s):  
Dabiao Liu ◽  
Yuming He ◽  
Bo Zhang ◽  
Lei Shen
Keyword(s):  
Stress Gradient ◽  
Continuum Theory ◽  
Gradient Plasticity ◽  
Pile Up
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