Given the interatomic bonding energy, EN between adjacent ions in solid materials is a function of interionic distance r as follows: EN=rA+rnB where A,B, and n are constants for the particular ion pair. (a) Derive an expression for the bonding energy E0 in terms of the equilibrium interionic separation r0 using the following procedure: 1. Differentiate EN with respect to r and set the resulting expression equal to zero. 2. Solve for r0 in the form of A,B,n. 3. Determine the expression for E0 by substitution for r0. (b) The modulus of elasticity E is proportional to the slope of the interionic force-separation curve at the equilibrium interionic separation; that is, E(drdF)r0 Derive an expression for the dependence of the modulus of elasticity on these A,B, and n parameters (for the two-ion system) using the following procedure: 1. Establish a relationship for the force F as a function of r, realizing that F=drdEN 2. Now take the derivative dF/dr. 3. Develop an expression for r0, the equilibrium separation. Because r0 corresponds to the value of r at the minimum of the EN-versus-r curve (Figure 2.10b), take the derivative dEN/dr, set it equal to zero, and solve for r, which corresponds to r0. 4. Finally, substitute this expression for r0 into the relationship obtained by taking dF/dr. (c)Given the appropriate A, B, and n parameters for these brass and steel are tabulated below and the proportion coefficient are 0.2GPa(E=200(dF/dr)r0), determine the elastic modulus of Brass and steel. (c)Given the appropriate A, B, and n parameters for these brass and steel are tabulated below and the proportion coefficient are 0.2GPa(E=200(dF/dr)r0), determine the elastic modulus of Brass and steel