Page "Metallic bond" Paragraph 3

With the advent of quantum mechanics this picture was given more formal interpretation in the form of the free electron model and its further extension, the nearly free electron model.

In both of these models the electrons are seen as a gas traveling through the lattice of the solid with an energy that is essentially isotropic in that it depends on the square of the magnitude, not the direction of the momentum vector k. In three-dimensional k-space, the set of points of the highest filled levels ( the Fermi surface ) should therefore be a sphere.

In the nearly free correction of the model, box-like Brillouin zones are added to k-space by the periodic potential experienced from the ( ionic ) lattice.