At a given temperature, clean and adatom covered silicon surfaces usually e
xhibit well-defined reconstruction patterns. Our finite temperature ab init
io molecular dynamics calculations show that the tellurium covered Si(001)
surface is an exception. Soft longitudinal modes of surface phonons, due to
the strongly anharmonic potential of the bridged tellurium atoms prevent t
he reconstruction structure from attaining any permanent, two-dimensional p
eriodic geometry. This explains why experiments attempting to find a defini
te model for the reconstruction have reached conflicting conclusions.