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The phonon spectra of calcium, strontium, barium, radium, cadmium, zinc,magnesium, germanium, tin, and lead titanates with the perovskite structure arecalculated from first principles within the density functional theory. Byanalyzing the unstable modes in the phonon spectra, the possible latticedistortions are determined and the energies of the corresponding phases arecalculated. From analyzing the phonon spectra, force constants, andeigenvectors of TO phonons, a conclusion is drawn on the origin of theferroelectricity in considered crystals. It is shown that the main factorsdetermining the possible off-centering of atoms in the A position are thegeometric size and electronic configuration of these atoms.

Ab initio calculations of phonon spectra in ATiO3 perovskite crystals (A = Ca, Sr, Ba, Ra, Cd, Zn, Mg, Ge, Sn, Pb)