The calculation of electrostatic energies of metals by plane-wise summation

The Madelung method of plane-wise and line-wise evaluation of lattice sums is used to calculate the electrostatic energies of metals consisting of point charges at the lattice sites and a uniform negative compensating background charge. The resulting expression is rapidly convergent and provides a simpler and more natural approach than the Ewald method in some problems.

It has been conjectured that the electrostatic energy of the hexagonal closepacked structure has a minimum at the ideal axial ratio (8/3)^1/2. It is shown that this is not true and that the minimum occurs at an axial ratio of 1.6356 ((8/3)^1/2 = 1.6330). The difference in energy, however, is very small.

Plane-wise summation is used to calculate the electrostatic energy of growth and deformation stacking faults in hexagonal metals. This approach is simpler and yields more physical insight than the Ewald method, and can be readily generalized to any form of ion-ion potential and to more than one stacking fault.