The elastic constant of a material is determined by the ________________ of potential energy vs interatomic distance curve.

The elastic constant of a material is determined by the ________________ of potential energy vs interatomic distance curve. Correct Answer curvature

In an elastic solid bond energy is a continuous function of the displacement (from the mean position of interatomic distance) thus: Φ(u) = Φo+(∂Φ/∂u)o u+1/2((∂Φ/∂u)o2 u2+ …………. Where Φ(u) is total potential energy, u is the displacement and Φo is equilibrium potential energy when u=0. So, the first differentiation of energy will give force at equilibrium (∂Φ/∂u)o=0. Hence the final expression will be => P= (∂Φ/∂u)o2 u, where P= ∂Φ(u)/∂u This is equivalent to the raw form of Hooke’s law, and the elastic constant will be equal to (∂Φ/∂u)o2, i.e. curvature of the curve.