Grain boundary definition

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. 

Figure 4.8. Definition of the dihedral angles i/> and formed at grain-boundary grooves in the...

For a grain boundary diffusion coefficient which is not a function of position, we find the later equality. The Lapladan of the chemical potential can be rewritten Vg/u. = if the preceding definitions of... 

For various mechanisms of grain boundary migration, the mobility wQl have various definitions, as given in Table 16.8. The driving force for grain-boundary migration is assumed to be due to the difference in grain curvature ... 

Another type of scratch hardness which is a logical development of the Mohs scale consists of drawing a diamond stylus, under a definite load, across the surface to be examined. The hardness is determined by the width or depth of the resulting scratch the harder the material the smaller the scratch. This method has some value as a means of measuring the variation in hardness across a grain boundary. In general, however, the scratch sclerometer is a difficult instrument to operate. 

The definition of low-angle grain boundaries generally covers the range of misorientations from 0° to 10°. In this regime, the grain boundary plane can be considered to be a linear array of separated dislocation cores. For [001] tilt boundaries in YBCO, the boundary plane will be composed of [100] or [010] dislocations, as shown in Fig. 11.6 (for YBCO the small distortion between the a- and fi-axes needs to be incorporated for quantitative models, but structurally results in no observable differences in the dislocation cores). 

Fig. 14.14. (a) Schematic illustration of the geometry of a step-edge on a substrate and the definition of 9. (b) Low-magnification TEM micrograph of a YBCO film on a step-edge on a (001) LaAlOs substrate, (c) HREM micrograph of the upper grain boundary arrowed in (b). 

For polycrystalline metals, the dissolution rate of the various crystallographic orientations is different. Grain boundaries or precipitations will also show a different corrosion rate. There is no accepted definition for what constitutes uniform corrosion. A possible definition could be that the variation of thickness loss all over the surface should not he greater than 5%. 

With the definition of the pore mobility, it is possible to analyze the influence of the interactions between the pores and the grain boundaries on the kinetics of grain growth. There are two cases that can be considered (i) the pore becomes separated from the boundary and (ii) the pore remains attached to the boundary. 

Dissimilar Electrode Cells. Examples of dissimilar electrode cells include the dry cell (discussed at the beginning of this chapter), a metal containing electrically conducting impurities on the surface as a separate phase, a copper pipe connected to an iron pipe, and a bronze propeller in contact with the steel hull of a ship. Dissimilar electrode cells also include cold-worked metal in contact with the same metal annealed, grain-boundary metal in contact with grains, and a single metal crystal of definite orientation in contact with another crystal of different orientation. ... 

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