  After summarizing the phenomenology of pressure amorphization (PA), we
present a theory of PA based on the notion that one or more branches of the
phonon spectrum soften and flatten with increasing pressure. The theory
expresses the anharmonic dynamics of the flat branches in terms of local modes,
represented by lattice Wannier functions, which are in turn used to construct
an effective Hamiltonian. When the low-pressure structure becomes metastable
with respect to the high-pressure equilibrium phase and the relevant branches
are sufficiently flat, transformation into an amorphous phase is shown to be
kinetically favored because of the exponentially large number of both amorphous
phases and reaction pathways. In effect, the critical-size nucleus for the
first-order phase transition is found to be reduced to a single unit cell, or
nearly so. Random nucleation into symmetrically equivalent local configurations
characteristic of the high-pressure structure is then shown to overwhelm any
possible domain growth, and an ``amorphous'' structure results.
