Stress-driven diffusion

Cox RW and Cohen DS. A mathematical model for stress-driven diffusion in polymers. J. Polym. Set B Polym. Phys. 1989 27 589-602. 

Such a distance Lq is an inherent property of the material, along with other properties such as its density and viscosity. For water, L(, is about 1 nanometer, whereas for fused silica it seems to be 10 or 20 nanometers. Driving material to a new orientation is very like driving it to a new location whatever the means by which material travels, both operations are described in continuum terms as loss, gain or translation of infinitesimal wafers. Deformation occurs as if the transport distance were Lq, while stress-driven self-diffusion operates usually over greater distances. 

Of course, eventually, particles will reappear, through the equation = Po + RTln the existence of R depends on the existence of particles. But a theory of stress-driven deformation of a continuum does not require particles, even with stress-driven self-diffusion coefficients for viscosity and self-diffusion are the only things required. 

Similarly, the second stress term, or pair of terms, is for stress-driven diffusion in addition to the change of shape, some material diffuses along x away from the high-stress sites where incursion of B is a maximum. Again the two materials work jointly the effect depends on a weighted sum of their mobilities X. A difference is that this term, quite properly, increases if j... 

The picture from which K and emerge is the mixed compound (A, B)X, on which a stress fluctuation has two effects. Consider a site where the compressive stress is at a local maximum, with a local minimum or sink-region somewhere nearby. The two stress-driven diffusion effects are... 

Figure 19.2 Cross-sections through idealized inhomogeneous assemblies. Each assembly is built from long square-ended prisms that are joined to form a continuum. Large circles and small circles mark regions rich in one component or the othen unpattemed regions are of neutral composition. In (a) the stress state is hydrostatic in gross but nonhydrostatic locally on account of chemistry-driven diffusion. In (b) the chemistry is uniform in gross but nonuniform locally on account of stress-driven diffusion.

According to Nemst-Einstein equation, matter flux J caused due to the grainboundary diffusion is driven by stress and electromigration, which can be described... 

Stress-Driven Diffusion Stress and diffusion can be coupled in a number of ways. In a uniform stress field, the dijfusivity of the diffusing species can become directionally dependent. This is because the stress field can affect the amount work required for the species to move in different directions (e.g., parallel vs. perpendicular to the stress field). Movements in directions that cause the greatest distortions to the stress field will be penalized, while movements in directions that minimize the distortion to the stress field will be favored. 

Freund, L. B. (1995a), Evolution of waviness on the surface of a strained elastic solid due to stress-driven diffusion. International Journal of Solids and Structures 32, 911-923. 

Wu, C. H. (1996), The chemical potential for stress-driven surface diffusion. 

Considering the effect of stress-driven diffusion, the diffusion of Li-ions inside an electrode particle can be described as... 

EG. Yost, D.E. Amos, A.D. Romig Jr., Stress driven diffusion voiding of aluminum conductor lines. Proceedings of lEEE/IRPS (1989) p. 193. 

As in chronoamperograms, the fraction of the overall oxidation charge involved in relaxation processes is quite small in the absence of any external stress. The share of the overall current at every potential between electrochemical processes occurring under relaxation control and those driven by swelling-diffusion control can be observed in Fig. 66. I(r) has... 

In general, surface morphological instabilities driven by stresses are an important subject to investigate in connection with microelectronic applications. In particular, the degree of surface waviness in thin films as a consequence of surface and volume diffusion is a matter of pivotal importance. This topic has attracted considerable attention in the last two or so decades (11). Although surface diffusion is an important kinetic process, other kinetic processes may affect the evolution of stressed surfaces. Indeed, a possibility at high temperatures is the diffusion of atoms through the bulk. 

The validity of Eqs.(4.10)(4.12) probably extends well beyond the Rouse model itself [characterized by the specific set of rt values in Eq. (4.5)1 and it seems likely that they will apply, at least for small disturbances, whenever the elements supporting the stress are joined by sufficiently flexible connectors and configurational relaxation is driven by simple Brownian diffusion. One might speculate further that these same forms would apply even in concentrated systems, with Eq.(4.10) expressed in a somewhat more general form because of intermolecular interactions ... 

Mass diffusion between grain boundaries in a polycrystal can be driven by an applied shear stress. The result of the mass transfer is a high-temperature permanent (plastic) deformation called diffusional creep. If the mass flux between grain boundaries occurs via the crystalline matrix (as in Section 16.1.3), the process is called Nabarro-Herring creep. If the mass flux is along the grain boundaries themselves via triple and quadjunctions (as in Sections 16.1.1 and 16.1.2), the process is called Coble creep. 

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