It is the fermion property of the electrons which prevents normal matter from collapsing under the attractive Coulombic or gravitational forces. We start from the free electrons of stellar matter in white dwarfs and outline qualitatively how particle interactions get gradually important if the matter density is reduced.

As a tool of quantitative dicussion we present a scheme for calculating properties of equilibrium phases in two steps: (1) obtain the spectral properties of the electrons from the Green function which involves all the wave interference, (2) obtain the temperature-dependent electronic properties from both the spectral properties and the Fermi-Dirac distribution. Spectral curves of the state density and the conductivity may display various spectral features. We discuss possible origins.

Next we confine to weak electron-ion scattering (high-pressure phases, nearly-free electron phases at normal pressure). Hence, the above scheme shrinks to the so-called diffraction picture of phase stabilization. The interference of many weak scattered waves supports the formation of lattice planes (crystals, plane waves) or of equidistant neighbor shells (liquid and amorphous phases, spherical waves). Examples are discussed employing the mentioned structure-adapted waves.

Some covalent systems (e.g. silicon) allow for on-site hybridization of the sp³ type. Open network-like atomic arrangements are formed rather than close-packed shell structures. Structure-adapted waves for network analysis are the sp³ hybrides.