  A class of materials known as ``ferroelectric metals'' was discussed
theoretically by Anderson and Blount in 1965 [Phys. Rev. Lett. 14, 217 (1965)],
but to date no examples of this class have been reported. Here we present
measurements of the elastic moduli of Cd2Re2O7 through the 200 K
cubic-to-tetragonal phase transition. A Landau analysis of the moduli reveals
that the transition is consistent with Cd2Re2O7 being classified as a
``ferroelectric metal'' in the weaker sense described by Anderson and Blount
(loss of a center of symmetry). First-principles calculations of the lattice
instabilities indicate that the dominant lattice instability corresponds to a
two-fold degenerate mode with Eu symmetry, and that motions of the O ions
forming the O octahedra dominate the energetics of the transition.
