Virial Stress

Virial stress is a measure of mechanical stress on an atomic scale. It is given by

where

• and are atoms in the domain,
• is the volume of the domain,
• is the mass of atom k,
• is the ith component of the velocity of atom k,
• is the jth component of the average velocity of atoms in the volume,
• is the ith component of the position of atom k, and
• is the ith component of the force applied on atom by atom .

At zero kelvin, all velocities are zero so we have

.

This can be thought of as follows. The τ₁₁ component of stress is the force in the x₁-direction divided by the area of a plane perpendicular to that direction. Consider two adjacent volumes separated by such a plane. The 11-component of stress on that interface is the sum of all pairwise forces between atoms on the two sides.