In Section 2.6, it was noted that the net bonding energy

QUESTION:

In Section 2.6, it was noted that the net bonding energy EN between two isolated positive and negative ions is a function of interionic distance r as follows: EN = -A r + B rn (6.31) where A, B, and n are constants for the particular ion pair. Equation 6.31 is also valid for the bonding energy between adjacent ions in solid materials. The modulus of elasticity E is proportional to the slope of the interionic forceseparation curve at the equilibrium interionic separation; that is, E a dF dr b r0 Derive an expression for the dependence of themodulus of elasticity on these A, B, and n parameters(for the two-ion system), using the followingprocedure: 1. Establish a relationship for the force F as afunction of r, realizing thatF = dENdr 2. Now take the derivative dF/dr. 3. Develop an expression for r0, the equilibriumseparation. Because r0 corresponds to the valueof r at the minimum of the EN-versus-r curve(Figure 2.10b), take the derivative dEN/dr, set itequal to zero, and solve for r, which correspondsto r0. 4. Finally, substitute this expression for r0 into therelationship obtained by taking dF/dr.