Fracture qustions The potential energy U of two atoms, a distance r apart, with a covalent bond is given by: m?
U A B
=- + , m= 2 , n=10
(a) Indicate the physical significance of the two terms in the potential energy equation.
(b) If the atoms form a stable molecule at a separation of 0.5 nm with an energy of -3 eV,
calculate A and B. (1 nm=10-9 m, 1 eV =1.60´10-19 J )
(c) Calculate the force required to break the molecule, and the critical separation at
which the molecule breaks (dissociation radius and force).
(d) The bond stiffness, S, is given by:
S dF d U
and for small stretching, S is constant and equal to
S d U
æç ÷ö=ççç ÷÷÷ è ø
This is the physical origin of Hooke’s Law, from which the elastic modulus can be
(e) Using a software, plot U (potential energy),
(stiffness) as a
function of r. Identify characteristic values on these plots (Equilibrium distance,
dissociation distance, separation force etc.)