Electronic structures of PbTiO3:: II.: Properties of Pb ion displacement

Properties of lead ion displacement in PbTiO3 were studied in reference to the electronic structures. Appearance of lead ion displacement is not independent of the existence of the Madelung potential but is strongly dependent on the existence of titanium ion displacement. This result is in contrast with our previous calculated result that titanium ion displacement appears without lead ion displacement, but is consistent with the experimental result of the properties of displacements of Ti and Pb ions below the phase-transition temperature. Our calculated results suggest that the softening of the Slater mode occurs before the softening of the Last mode.