Here, we will define and discuss grain boundaries. Grain boundaries play an impor­tant role in strengthening in that finer grain sizes lead to higher strength and vice versa, also popularly known as Hall-Petch strengthening. Their presence may lower the thermal/electrical conductivity of the material. They may act as the pre­ferred sites for corrosion (intergranular corrosion), for precipitation of new phases to occur, or may contribute to the plastic deformation or failure at higher tempera­tures (grain boundary sliding) and many other phenomena. A grain boundary can be defined as the interface boundary between two neighboring grains. In a poly­crystalline material, each grain is a single crystal with a particular orientation (Figure 2.35a).

The grain boundaries are the regions of misfit where the atoms are confused. When the misorientation angle (0) between the grains is small (~10°), the bound­ary is called a low-angle boundary. Low-angle boundaries can be described as an array of dislocations and are of two types: tilt and twist. Tilt boundaries can be gen­erated by bending a single crystal with the rotation axis being parallel to the bound­ary plane (Figure 2.36a), while the twist boundary is created when the rotation axis is normal to the boundary plane (Figure 2.36b). Tilt boundaries can be described as an array of parallel edge dislocations, as illustrated in Figure 2.37. The tilt angle (0) is given by

tan(0) — 0 — b/h, (2.16)

where b is the Burgers vector of the dislocation and h is the vertical distance of separation between two neighboring edge dislocations at the boundary. The tilt boundaries are generated during a metallurgical process known as recovery when excess dislocations of the same type arrange themselves one below the other. The

twist boundaries refer to similar low-angle boundaries formed by arrays of screw dislocations.

High-angle boundaries (0 > 10-15°) can be extrapolated from the simple the­ory of low-angle grain boundaries. But the dislocation model becomes invalid when there are too many dislocations at the boundary such that the adjacent dislocation cores start overlapping. To overcome this difficulty, grain boundaries are often described by the coincident site lattice model; however, a complete dis­cussion is outside the scope of the chapter. The high-angle boundaries generally have a “free space” or “free volume,” whereby solutes can collect and a solute — drag effect can be generated. The energy of high-angle grain boundary varies from 0.5 to 1.0 J m~2 for most metals. Migration of high-angle boundaries occurs due to atom jumps across the boundary during the grain growth, which can be influenced by the grain boundary crystallography, presence of impurities, and temperature.