surface energy

Imagine slicing a crystal cleanly in two. To do it you must break every bond that crossed the cut, and breaking bonds costs energy. When you are done you have created two new surfaces, and the energy you spent is now stored in them. Surface energy is exactly that: the extra energy a material carries per unit area of surface, simply because the atoms there have broken, unsatisfied bonds compared with atoms in the bulk.

Surface energy is usually written with the Greek letter gamma and measured in joules per square metre (J/m^2), that is, energy per unit area. A rough estimate: if breaking one bond costs energy epsilon and a surface exposes n broken bonds per unit area, then gamma is about (1/2) times n times epsilon, where the half is because the energy of the two bonds is shared between the two new surfaces you make. For metals gamma is typically around 1 to 2 J/m^2; for a weakly bonded molecular crystal it can be far smaller. Surfaces made of close-packed planes, with the fewest broken bonds per atom, have the LOWEST energy, which is why crystals grow with those faces showing.

Surface energy is the driving force behind a huge range of behaviour: droplets become spheres (the shape with least surface area for a given volume), fine powders sinter, small particles melt at lower temperatures, and cracks either grow or heal. The same quantity for a solid-solid internal boundary is called grain-boundary energy, or more generally interfacial energy. Honest note: for a solid, surface energy (from broken bonds) and surface stress (from stretching an existing surface) are subtly different quantities that beginners often conflate; for a liquid they happen to be equal.