grain-boundary energy

A grain boundary is a region where atoms are poorly fitted, squeezed here and stretched there, with strained, unhappy bonds. Just as a free surface carries extra energy because its atoms have broken bonds, a grain boundary carries extra energy because its atoms are mis-bonded. Grain-boundary energy is that extra energy per unit area of boundary, the price, in energy, of the mismatched seam between two grains.

It is written with gamma (like surface energy) and measured in J/m^2, but it is typically SMALLER than the free-surface energy of the same material, often roughly one third, because the atoms across a grain boundary still have neighbours on both sides (just badly aligned), whereas a free-surface atom has empty space on one side. The energy depends strongly on the misorientation: a low-angle boundary (small tilt) has low energy that grows with the tilt angle, while a special coincidence boundary (like a coherent twin) can be unusually low. You can literally see energy balance at work where three grains meet: the boundaries pull like soap films and, if all three energies are equal, meet at 120-degree angles.

Grain-boundary energy is the engine of grain growth: a polycrystal can lower its total energy by having fewer, larger grains (less total boundary area), so on heating, big grains eat small ones. The same energy sets whether a second phase or a crack will wet and spread along boundaries. Honest note: because low-energy special boundaries resist migration and cracking, engineers deliberately try to increase their fraction, a strategy called grain-boundary engineering.