The lattice instabilities of perovskite structure oxides are responsib
le for many of their interesting properties, such as temperature-depen
dent ferroelectric phase transitions. First-principles calculations us
ing linear response theory provide an accurate means to determine the
lattice dynamics throughout the entire Brillouin zone (BZ), Using the
LAPW linear response method([1]), we have previously carried out such
a study on ferroelectric KNbO3[2]. We present here the results of a si
milar investigation for cubic SrTiO3. While KNbO3 has only ferroelectr
ic-type instabilities, SrTiO3 exhibits both ferroelectric (FE) and ant
iferrodistortive (AFD) instabilities. We correctly predict the known i
nstability at the R-point in the Brillouin zone, which is responsible
for the AFD phase transition to the tetragonal structure at about 105
K. Furthermore, the phase space of the ferroelectric instability is gr
eatly reduced compared to KNbO3. Antiferrodistortive instabilities exi
st in one-dimensional cylindrical tubes extending along the entire R-M
-R line in the Brillouin zone. The essentially 1-D character of these
tubes corresponds to real-space planar instabilities characterized by
rotations oi oxygen octahedra.