Specific Surface Energy and Surface Stress

2. Specific Surface Energy and Surface Stress

The specific surface energy γ (J/m²) can be defined as the energy required to create a new surface by cleaving a crystal. More generally, it represents the work needed to increase the surface area of a material.

If the surface area increases by an amount dA, the work done is given by:

dW = γ dA

Here, γ is the specific surface energy. The increase in surface area can occur by moving atoms from the bulk to the surface. Alternatively, the area can be increased by stretching the surface while keeping the number of surface atoms constant.

In the case of stretching, the work done is:

dW = g_ij dA

where g_ij represents the surface stress (J/m²). It is a tensor quantity because it depends on crystallographic directions.

Surface stress is related to elastic stresses generated due to deformation (strain) at the surface.

The relation between surface stress and specific surface energy is:

g_ij = δ_ij γ + ∂γ / ∂u_ij

where:

• u_ij = strain tensor
• δ_ij = Kronecker delta

For liquids, there is no strain tensor, and therefore:

g_ij = γ

This is because when the surface area of a liquid increases, atoms from the bulk move to the surface to maintain constant density.