Grain boundary illustration

Figure C2.11.6. The classic two-particle sintering model illustrating material transport and neck growtli at tire particle contacts resulting in coarsening (left) and densification (right) during sintering. Surface diffusion (a), evaporation-condensation (b), and volume diffusion (c) contribute to coarsening, while volume diffusion (d), grain boundary diffusion (e), solution-precipitation (f), and dislocation motion (g) contribute to densification.

Figure C2.11.7. An illustration of tlie equilibrium dihedral angle, 0, fonned by tlie balance of interfacial energies at a pore-grain boundary intersection during solid-state sintering.

The PTCR effect is complex and not fully understood in terms of the grain boundary states and stmcture. Both the PTCR effect and room temperature resistivities are also highly dependent on dopant type and ionic radius. Figure 11 (32) illustrates this dependence where comparison of the PTCR behavior and resistivity are made for near optimum concentrations of La ", Nd ", and ions separately substituted into BaTiO. As seen, lowest dopant concentration and room temperature resistivity are obtained for the larger radius cation (La " ), but thePTCR effect was sharpest for the smallest radius cation (Y " ), reflecting dual site occupancy of the Y " ion. 

Nucleation in solids is very similar to nucleation in liquids. Because solids usually contain high-energy defects (like dislocations, grain boundaries and surfaces) new phases usually nucleate heterogeneously homogeneous nucleation, which occurs in defect-free regions, is rare. Figure 7.5 summarises the various ways in which nucleation can take place in a typical polycrystalline solid and Problems 7.2 and 7.3 illustrate how nucleation theory can be applied to a solid-state situation. 

Pseudomorphism received methodical study from about 1905. A micro-section taken across the interface between a substrate and an electrodeposit shows the grain boundaries of the former continue across the interface into the deposit (Fig. 12.5). As grain boundaries are internal faces of metal crystals, when they continue into the deposit the latter is displaying the form of the substrate. Hothersall s 1935 paper contains numerous excellent illustrations with substrates and deposits chosen from six different metals, crystallising in different lattice systems and with different equilibrium spacing. Grain boundary continuation and hence pseudomorphism is evident despite the differences. 

Figure 6.11 (a) Definition of the dihedral angle, , at a junction of three grain boundaries in a polycrystalline solid, (b) Schematic illustration of the shape of an inclusion phase for different dihedral angles. 

This grain boundary fraction is truly disordered, if not plainly amorphous. This is illustrated in Fig. 1.15. The fraction of atoms that counts into grain boundaries should increase with milling time however, in powder particulates below some... 

In this section we illustrate the effect of grain boundaries on the conductivity of thin hlms of the TTF-based molecular metals TTF-TCNQ and TTF[Ni(dmit)2]2-In general the existence of grain boundaries hinders the metallic behaviour, inducing semiconducting-like activated conduction (<7rt < 10 cm ) because... 

Figure 5.14 Illustration of grain boundaries acting as barriers to slip in polycrystalline materials. Reprinted, by permission, from W. Callister, Materials Science and Engineering An Introduction, p. 166, 5th ed. Copyright 2000 by John Wiley Sons, Inc.

As described in Section 9.2.2, grain-boundary diffusion rates in the Type-C diffusion regime can be measured by the surface-accumulation method illustrated in Fig. 9.12. Assume that the surface diffusion is much faster than the grain-boundary diffusion and that the rate at which atoms diffuse from the source surface to the accumulation surface is controlled by the diffusion rate along the transverse boundaries. If the diffusant, designated component 2, is initially present on the source surface and absent on the accumulation surface and the specimen is isothermally diffused, a quasi-steady rate of accumulation of the diffusant is observed on the accumulation surface after a short initial transient. Derive a relationship between the rate of accumulation... 

Microstructures are generally too complex for exact models. In a polycrystalline microstructure, grain-boundary tractions will be distributed with respect to an applied load. Microstructures of porous bodies include isolated pores as well as pores attached to grain boundaries and triple junctions. Nevertheless, there are several simple representative geometries that illustrate general coupled phenomena and serve as good models for subsets of more complex structures. 

Three conditions are required for a complete solution to the problems illustrated in Figs. 3.10 and 16.1. If the grain boundary remains planar, dL/dt in Eq. 16.2 must be spatially uniform—the Laplacian of the normal surface stress under quasisteady-state conditions must then be constant ... 

If surface diffusion or vapor transport is rapid enough, the pores will maintain their quasi-static equilibrium shape, illustrated in Fig. 16.1 in the form of four cylindrical sections of radius R.6 The dihedral angle at the four intersections with grain boundaries, ip, will obey Young s equation, ip is related to 6 by sin( /j/2) = cos 0. 

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