Solids: Thermodynamics and Bonding

· The sum has the form: Ln(1 + x) with x = 1, so that the total Coulomb energy of interaction between the reference ion and the lattice is:

U_c = - 2(e²/4πε₀R)[ 1 -1/2 + 1/3 - 1/4 + - - - - ] = - 2(e²/4πε₀R)[Ln2]

· This energy contribution is known as the Madelung energy and is dependent on the lattice geometry. For this one dimensional case
U_c = - (e²/4πε₀R)α
where a = Madelung Constant contains the effects of lattice geometry.
· The major repulsive contribution to the total binding energy is due to the Pauli Exclusion principle repulsion between the ion cores and is given by:
V_r(r) = (1/r¹²)
· This interaction potential is short-range and the sum can be made over nearest neighbors only