Grain Boundaries. In the last four lectures, we dealt with point defects (e.g. vacancy, interstitials, etc.) and line defects (dislocations). There is another class of defects called interfacial or planar defects : They occupy an area or surface and are therefore bidimensional.
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Figure 16.1. Grains in a metal or ceramic; the cube depicted in each grain indicates the crystallographic orientation of the grain in schematic fashion
grains having a common  axis and angular difference in
orientation of (b) two grains joined together to form a
low-angle grain boundary made up of an array of edge
where b is the Burgers vector.
(for q very small) (16-1)
decrease in the boundary misorientation.
1. At low temperature (T<0.5Tm, where Tm is the melting point in K), the grain boundaries act as strong obstacles to dislocation motion. Mobile dislocations can pile up against the grain boundaries and thus give rise to stress concentrations that can be relaxed by initiating locally multiple slip.
4. Grain boundaries can act as sources and sinks for vacancies at high temperatures, leading to diffusion currents as, for example, in the Nabarro Herring creep mechanism.
5. In polycrystalline materials, the individual grains usually have a random orientation with respect to one another.
Grain structure is usually specified by giving the average diameter. Grain size can be measured by two methods.
(a) Lineal Intercept Technique: This is very easy and may be the preferred method for measuring grain size.
(b) ASTM Procedure: This method of measuring grain size is common in engineering applications.
In this technique, lines are drawn in the photomicrograph, and the number of grain-boundary intercepts, Nl, along a line is counted.
where L is the length of the line and M is the magnification in the photomicrograph of the material.
magnification M = 1,300. Thus,
In a grain size measurement of an aluminum sample, it was found that there were 56 full grains in the area, and 48 grains were cut by the circumference of the circle of area 1 in2. Calculate ASTM grain size number n for this sample.
The grains cut by the circumference of the circle are taken as one-half the number. Therefore,