  We discuss the first infrared reflectivity measurement on a BiFeO3 single
crystal between 5 K and room temperature. The 9 predicted ab-plane E phonon
modes are fully and unambiguously determined. The frequencies of the 4 A1
c-axis phonons are found. These results settle issues between theory and data
on ceramics. Our findings show that the softening of the lowest frequency E
mode is responsible for the temperature dependence of the dielectric constant,
indicating that the ferroelectric transition in BiFeO3 is soft-mode driven.
