  The lattice instabilities of perovskite structure oxides are responsible for
many of their interesting properties, such as temperature-dependent
ferroelectric phase transitions. First-principles calculations using linear
response theory provide an accurate means to determine the lattice dynamics
throughout the entire Brillouin zone (BZ). Using the LAPW linear response
method, we have previously carried out such a study on ferroelectric KNbO3. We
present here the results of a similar investigation for cubic SrTiO3. While
KNbO3 has only ferroelectric-type instabilities, SrTiO3 exhibits both
ferroelectric (FE) and antiferrodistortive (AFD) instabilities. We correctly
predict the known instability at the R-point in the BZ, 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 greatly
reduced compared to KNbO3. Antiferrodistortive instabilities exist in
one-dimensional cylindrical tubes extending along the entire R-M-R line in the
BZ. The essentially 1-D character of these tubes corresponds to real space
planar instabilities characterized by rotations of oxygen octahedra.
