  Recent high-pressure x-ray diffraction studies of alkali metals revealed
unusual complex structures that follow the body-centered and face-centered
cubic structures on compression. The structural sequence of potassium under
compression to 1 Megabar is as follows: bcc - fcc - h-g (tI19*), hP4 - oP8 -
tI4 - oC16. We consider configurations of Brillouin-Jones zones and the Fermi
surface within a nearly-free-electron model in order to analyze the importance
of these configurations for the crystal structure energy that contains two main
contributions: electrostatic (Ewald) and electronic (band structure) energies.
The latter can be lowered due to a formation of Brillouin zone planes close to
the Fermi surface opening an energy gap at these planes. Under pressure, the
band structure energy term becomes more important leading to a formation of
complex low-symmetry structures. The stability of the post-fcc phases in K is
attributed to the changes in the valence electron configuration implying the
overlap of valence band with the upper core electrons. This effect offers an
understanding of structural complexity of alkali metals under strong
compression.
