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    Net potential energy between ions

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    The net potential energy EN between two adjacent ions is sometimes represented by the expression: EN = -(C/r) + D exp(-r/p)
    in which r is the interionic separation and C, D, and p are constants whose values depend on the specific material.

    (a) Derive an expression for the bounding energy Eo in terms of the equilibrium interionic separation ro and the constants D, and p using the following procedure:

    1. Differentiate EN with the respect to r and set the resulting expression equal to zero.
    2. Solve for C in terms of D, p, and ro.
    3. Determine the expression for Eo by substitution for C in the equation EN = -(C/r) + D exp(-r/p)

    (b) Derive another expression for Eo in terms of ro, C, and p using a procedure analogous to the one outlines in part (a).

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    Solution Preview

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    En = -(C/r) + D e^(-r/p) --- (1)
    (1) Differentiating (1) with respect to r, we get
    d(En)/dr = (C /r^2) + {D e^(-r/p)} * ...

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