Fig 1 A cluster of Kelvin tetrakaidecahedron shaped grains. This grain shape minimizes grain boundary curvature.

Grain growth is a vague term used in the context of recrystallization, "normal" grain growth and secondary recrystallization. In each case, a difference in chemical free energy produces the diffusion of atoms into the growing grain. The chemical free-energy difference associated with recrystallization is easy to understand because the new grain is relatively free of the defects produced by cold working. During recrystallization, the new grain consumes the surrounding material and grows until impinging another recrystallized grain. Both subsequent normal grain growth and secondary recrystallization are associated with surface energy and are the focus of this discussion.

The term normal grain growth is used to describe the phenomenon associated with an increase in average grain size during the annealing process. The driving force for normal grain growth often is related to the net decrease in surface area as the average grain size increases. However, this logic cannot explain the unusual stability of nanophase materials or the effect of particle pinning on normal grain growth. For a discussion on particle pinning, see March 2000 Engineering Concepts. Normal grain growth is driven by grain curvature, which then is combined with surface energy to create the driving force. In a mixed grain structure, there are both smaller and larger than average grains. Larger grains have a larger than average number of grain faces, which have a center of curvature that lies outside the grain. In contact, smaller grains have centers of curvature within the grain. Like a soap bubble, surface tension produces a higher pressure within the smaller grains. Consequently, atoms within the smaller grains diffuse out in an attempt to equalize the pressure in each grain; the diffusion produces normal grain growth. The pressure difference also can be expressed as a change in chemical free energy. If all grains were the same size and shaped like Kelvin tetrakaidecahedrons (Fig. 1), there would be no grain curvature and the grain structure would be stable regardless of grain size.

Fig 2 A ball and stick model of the {110} and {100} in a body centered cubic crystal. The planar packing density is calculated as the number of atoms per unit area, which, in this case, is 2 atoms per Ã2a^2 for {110} and 1 atom per a^2 for the {100}. The ratio of the surface energies of the two planes is calculated as (equation)

Growth of grains during secondary and tertiary recrystallization usually is associated with thin sheet materials where the surface grains represent a large fraction of the total number of grains. The transformation is again driven by surface energy, but it is not entirely curvature driven. The grains that grow are those having a crystal orientation where the free surface has an atomic plane parallel to the surface that minimizes surface energy. Typically, this is a plane of high atomic packing density; i.e., a close-packed plane. A general rule for metals is that surface energy is inversely proportional to the planar packing density. Figure 2 shows a sample calculation of the {110} and {100} planar packing density for a body-centered-cubic (bcc) crystal. The {110} also is the closest packed plane in the bcc metals. Silicon steels used for transformers have a Goss, or cube-on-edge, texture, where <100> is parallel to the rolling direction and {110} is parallel to the rolling plane (sheet surface). Annealing in dry hydrogen helps stabilize this crystallography, which makes sense in the context of surface energy because {110} is parallel to the surface. However, the {100} planes are stabilized in the presence of oxygen and the Goss texture can be replaced with grains having {100} parallel to the sheet surface. The new {100} oriented crystals have planar isotropy; i.e., the in plane <010> are random with respect to the rolling direction. This process is reversible; a Goss texture can be regained by annealing in hydrogen-an example of tertiary recrystallization.