<P> Grain - boundary strengthening (or Hall--Petch strengthening) is a method of strengthening materials by changing their average crystallite (grain) size . It is based on the observation that grain boundaries impede dislocation movement and that the number of dislocations within a grain have an effect on how easily dislocations can traverse grain boundaries and travel from grain to grain . So, by changing grain size one can influence dislocation movement and yield strength . For example, heat treatment after plastic deformation and changing the rate of solidification are ways to alter grain size . </P> <P> In grain - boundary strengthening, the grain boundaries act as pinning points impeding further dislocation propagation . Since the lattice structure of adjacent grains differs in orientation, it requires more energy for a dislocation to change directions and move into the adjacent grain . The grain boundary is also much more disordered than inside the grain, which also prevents the dislocations from moving in a continuous slip plane . Impeding this dislocation movement will hinder the onset of plasticity and hence increase the yield strength of the material . </P> <P> Under an applied stress, existing dislocations and dislocations generated by Frank--Read sources will move through a crystalline lattice until encountering a grain boundary, where the large atomic mismatch between different grains creates a repulsive stress field to oppose continued dislocation motion . As more dislocations propagate to this boundary, dislocation' pile up' occurs as a cluster of dislocations are unable to move past the boundary . As dislocations generate repulsive stress fields, each successive dislocation will apply a repulsive force to the dislocation incident with the grain boundary . These repulsive forces act as a driving force to reduce the energetic barrier for diffusion across the boundary, such that additional pile up causes dislocation diffusion across the grain boundary, allowing further deformation in the material . Decreasing grain size decreases the amount of possible pile up at the boundary, increasing the amount of applied stress necessary to move a dislocation across a grain boundary . The higher the applied stress needed to move the dislocation, the higher the yield strength . Thus, there is then an inverse relationship between grain size and yield strength, as demonstrated by the Hall--Petch equation . However, when there is a large direction change in the orientation of the two adjacent grains, the dislocation may not necessarily move from one grain to the other but instead create a new source of dislocation in the adjacent grain . The theory remains the same that more grain boundaries create more opposition to dislocation movement and in turn strengthens the material . </P> <P> Obviously, there is a limit to this mode of strengthening, as infinitely strong materials do not exist . Grain sizes can range from about 100 μm (0.0039 in) (large grains) to 1 μm (3.9 × 10 in) (small grains). Lower than this, the size of dislocations begins to approach the size of the grains . At a grain size of about 10 nm (3.9 × 10 in), only one or two dislocations can fit inside a grain (see Figure 1 above). This scheme prohibits dislocation pile - up and instead results in grain boundary diffusion . The lattice resolves the applied stress by grain boundary sliding, resulting in a decrease in the material's yield strength . </P>

How does the grain size effect the strength of a metal
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