Influence of grain boundary diffusion

The process of combined surface diffusion and grain boundary diffusion was discussed in detail by Thouless (1993) who developed a plastic rate equation to describe the process. In the present notation, this rate equation has the form 

For columnar grain structure, the value of d t q)ically falls within the range 0.1 d/hj 10. Approximate solutions of the differential equation for stress history have been determined by numerical integration with initial stress (To = 2 X 10 N/m, film thickness of hf = 1/xm and grain sizes of d = 0.1 nm, 1/im and lOyum. The temperature history is again given by 

By combining continuum analysis of inelastic deformation, such as that described in Section 7.4, with the mechanistic models of the foregoing subsections, Shen and Suresh (1996) have identified the variation of equi-biaxial film stress through the thickness of the film during steady-state creep deformation. An appealing feature of such an approach is that the evolution of substrate curvature, spatial variation of residual stress and relative 

---

The difference in values of the diffusion coefficient of an element in the growing and non-growing layers of a chemical compound is often explained by the influence of grain-boundary diffusion. Such an explanation seems too universal in order to be valid in all cases. 

Polycrystalline diffusion couples can be studied in a similar way. Results show an increased transport and consequently an increase in the growth of the reaction product. However, the polycrystalline nature of the compacts makes it difficult to separate the influence of grain boundary diffusion and bulk diffusion. 

It has to be assumed that grain-boundary diffusion is not the only possible transport mechanism of ions in a bone, but that a significant amount of aqueous fluorine is transported through microfissures into a sample by capillary effects (Fig. 9). Diagenetic parameters influencing the uptake of fluorine into archaeological bone are discussed in detail by Reiche in this compendium. 

Khorunzhii and D in [7] investigated the influence of MnOj on the decompositions of K and Na perchlorates and chlorates and concluded that both surface and grain-boundary diffusion played an essential role in control of the decomposition rate. 

V.S. Stubican and J.W. Orenbach, Influence of anisotropy and doping on grain-boundary diffusion in oxide systems, Solid State Ionics 12, 375 (1984). 

The influence of confining boundaries on the effective diffusivity as reflected by Eqs. 15a,b has been repeatedly applied to determine the pore surface in rocks or beds of sand grains [106-115]. In [116], this concept has been for the first time successfully applied to beds of zeolites. Figure 9 shows the results of these studies, which have been performed with two different samples of Na-X, one loaded with n-hexane (two molecules per supercage), the other with n-hexane and hexafluoromethane (one molecule per supercage for either). In both samples, for the n-hexane measurements a temperature of 298 K was chosen, where the n-hexane molecules were found to be totally confined so that the data analysis could be based on Eq. 15a. The measure-... 

Fig. 5.10 Six distinct mechanisms can contribute to the sintering of a consolidated mass of crystalline particles 1 surface diffusion (5D), 2 lattice diffusion from the surface, 3 vapor transport, 4 grain boundary diffusion, 5 lattice diffusion from the grain boundary, and 6 plastic flow. Only mechanisms i to 5 lead to densification, but all cause the necks to grow and so influence the rate of densification. Reproduced with permission from [24]. Copyright 2007, Springer...

Figure 5.20 shows a model consisting of a row of cylinders with same radius, whose neck contours are shown in Fig. 5.21 [40]. Two situations are simulated for matter transport by (i) surface diffusion only and (ii) both surface diffusion and grain boundary diffusion, as shown in Fig. 5.21a, b, respectively. It is found that numerical simulation predicts undercutting and a continuous change in curvature of the neck surface, which is different from that given by the analytical models with the circle approximation. The region of the neck surface influenced by the matter transport also extends far beyond that predicted by the circle approximation. However, if both the surface diffusion and grain boundary diffusion are considered, the extension is less pronounced.

For polycrystalline solids, additional effects must be considCTed. The location of the pores will influence the gas diffusion path. When the pores are located within the grains, diffusion will depend on the gas solubility in the crystal lattice. For the more common case in which the pores are located at the grain boundaries, diffusion of the gas through the disordered grain boundary region provides an important additional path. 

---