Solving for B from this equation yields Furthermore, the value of A is determined from one of the previous equations, as follows: Thus, Equations 2.9 and 2.11 become Of course these expressions are valid for r and E in units of nanometers and electron volts, respectively. 2.21The net potential energy EN between two adjacent ions is sometimes represented by the expression (2.18) in r is the interionic separation and C, D, and are constants whose values depend on the specific material. ρ (a) Derive an expression for the bonding energy E0 in terms of the equilibrium interionic separation r0 and the constants D and using the following procedure: ρ (i) Differentiate EN with respect to r, and set the resulting expression to zero. (ii) Solve for C in terms of D, and r0. ρ, (iii) Determine the expression for E0 by substitution for C in Equation 2.18. (b) Derive another expression for E0 in terms of r0, C, and using a procedure analogous to the one ρ outlined in part (a). Solution (a) Differentiating Equation 2.18 with respect to r yields
Solving for B from this equation yields Furthermore, the value of A is determined from one of the previous equations, as follows: Thus, Equations 2.9 and 2.11 become Of course these expressions are valid for r and E in units of nanometers and electron volts, respectively. 2.21The net potential energy EN between two adjacent ions is sometimes represented by the expression (2.18) in r is the interionic separation and C, D, and ρ are constants whose values depend on the specific material. (a) Derive an expression for the bonding energy E0 in terms of the equilibrium interionic separation r0 and the constants D and ρ using the following procedure: (i) Differentiate EN with respect to r, and set the resulting expression to zero. (ii) Solve for C in terms of D, ρ, and r0. (iii) Determine the expression for E0 by substitution for C in Equation 2.18. (b) Derive another expression for E0 in terms of r0, C, and ρ using a procedure analogous to the one outlined in part (a). Solution (a) Differentiating Equation 2.18 with respect to r yields
Solution%20Manual%20for%20Materials%20Science%20and%20Engineering%20An%20Introduction%209th%20Edition%20Callister,%20Rethwisch.docx