text: The origin of surface stress is the difference between bonding in the bulk and at a surface. The bulk spacings set the values of the in-plane surface spacings, and consequently the in-plane distance between atoms. However, the atoms at the surface have a different bonding, so would prefer to be at a different spacing, often (but not always) closer together. If they want to be closer, then  will be positive—a tensile or expansive strain will increase the surface energy.
  For many metals the derivative is positive, but in other cases it is negative, for instance solid argon and some semiconductors. The sign can also strongly depend upon molecules adsorbed on the surface. If these want to be further apart that will introduce a negative component.