STRESS-INDUCED DIFFUSION

There is a local (Fickian transport) and a non-local (stress induced) term in this flux equation. In the local term, the stress acts in the same way as an activity coefficient does. It always increases local diffusion since V] is positive and independent of the sign of the partial molar volume of /. 

Eqn. (14.22) can be neglected compared to the Fickian transport term in a zeroth order approach. The reason is that the gradient of ct at = 0 is high at the beginning of the diffusion process, whereas the integral over the concentration in the nonlocal term is still small. Therefore, q c° erf ( /2(Djt)1/2). The stress induced part of the flux can now be calculated for short times in a first order approach and yields... 

The Kirkendall effect alters the structure of the diffusion zone in crystalline materials. In many cases, the small supersaturation of vacancies on the side losing mass by fast diffusion causes the excess vacancies to precipitate out in the form of small voids, and the region becomes porous [11], Also, the plastic flow maintains a constant cross section in the diffusion zone because of compatibility stresses. These stresses induce dislocation multiplication and the formation of cellular dislocation structures in the diffusion zone. Similar dislocation structures are associated with high-temperature plastic deformation in the absence of diffusion [12-14]. 

An analysis of the rate of elongation of a wire possessing a bamboo-type grain structure is given in Section 16.1.3. An essential aspect of the analysis is the assumption that the stress-induced atomic transport producing the elongation is diffusion-limited. Now, construct the main framework of a model for the same system in which the atomic transport is source-limited, as indicated below, and explain how the model works. 

Figure 16.12 Idealized array of edge dislocations subjected to applied stress, a. Arrows show stress-induced diffusion current around each climbing dislocation.

Three theories were proposed to explain wall-slip (a) adhesive failure at the wall, (b) cohesive failure within the material as a result of disentanglement of chains in the bulk and chains absorbed on the wall, and (c) the creation of a lubricating surface layer at the wall either by a stress-induced transition, or by a lubricating additive. If the polymer contains low molecular weight components or slip-additives, their diffusion to the wall will create a thin lubricating layer at the wall, generating apparent slip. 

Boron fibers, like any CVD fiber, have inherent residual stresses which originate in the process of chemical vapor deposition. Growth stresses in the nodules of boron, stresses induced due to diffusion of boron into the W core, and stresses generated due to the difference in the coefficient of expansion of the deposited boron and the tungsten boride core, all contribute to the residual stresses, and thus can have a considerable influence on the fiber mechanical properties. 

SIMS has also been used to determine the As concentration profile after liquid state diffusion from laser melted spin-on arsenic glass. In this case laser diffusion was desireable because It avoided the thermal stress-induced damage to large thinned wafers that could occur during heating In a furnace. (41). 

P. Tripodi, V. Violante, Stress-induced diffusion of hydrogen in metallic membranes Cylindrical vs. Planar formula-... 

Figure 7.4 Stress-induced lattice diffusion in a single crystal a) Crystal under the action of tensile and compressive stresses (the arrows in the crystal show directions of vacancy motion) b) Strains produced by the stress-assisted diffusion process.

Various types of coupled non-linear Fickian diffusion processes were numerically simulated using the free-volume approach given by equation [12.8], as well as non-Fickian transport. The non-Fickian transport was modeled as a stress-induced mass flux that typically occurs in the presence of non-uniform stress fields normally present in complex structures. The coupled diffusion and viscoelasticity boundary value problems were solved numerically using the finite element code NOVA-3D. Details of the non-hnear and non-Fickian diffusion model have been described elsewhere [14]. A benchmark verification of the linear Fickian diffusion model defined by equations [12.3]-[12.5] under a complex hygrothermal loading is presented in Section 12.6. 

Cold drawing of PET amorphous samples (at temperatures lower than the glass transition temperature, Tg) induce formation of a highly disordered metastable mesomorphic form, which transforms into the normal crystalline (triclinic) form by heating above Tg [18-20], This form was early identified by Bonart [18], studying the stress induced crystallization of amorphous PET samples by X-ray diffraction techniques. The diffuse nature of X-ray diffraction patterns of samples obtained by stretching at room temperature... 

Many connections have been established between microscopic MD simulations and macroscopic experimental properties of polymers, such as seen in conformational disorder and heat capacities [1], molecular motion and the vibrational spectrum- [2], stress-induced frequency shifts and conformational changes [3], twist motion and the dielectric a-relaxation [4], molecular diffusion... 

Using sorption-desorption kinetics, the extent of non-Fickian behavior decreases as the thickness of the film increases. Presumably, as the ratio of the time scale for diffusion to the time scale for stress-induced relaxation I ID) becomes large, the time-dependent relaxation occurs so rapidly (relatively) that it has a small effect on the diffusion process. In other words, in the limit where molecular-scale responses to swelling stresses are rapid compared to the rate of diffusion, the process appears to be Fickian. This is the case for totally amorphous rubbery polymers that behave as high molecular weight liquids. 

The relaxation of stress-induced dichroism of the 9000nm O infra-red absorption band was investigated in samples of Czochralski material which had been annealed in H plasma at 225 to 350C. It was found that the in-diffusion of H enhanced the rate of O diffusion, so that dichroism disappeared gradually from the external surfaces. Other measurements indicated that O diffusion jumps were catalyzed by collisions with diffusing H atoms. It was deduced that the H diffusivity was described by ... 

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