Lead titanate,

PHYSICS · Subjective · Fermi University Physics · Electricity, Magnetism & Electromagnetism · Condensed Matter, Materials & Soft Matter · Electric fields in matter

Solid State Physics, Ch Dielectric response, local fields and ferroelectricity

Problem

Lead titanate,

\mathrm{PbTiO_3}

, is tetragonal at room temperature with

a=3.90\,\mathrm{\AA}

c=4.15\,\mathrm{\AA}

and one formula unit per primitive perovskite cell of volume

V=a^2c

. Structural refinement finds the

\mathrm{Ti}

ion displaced by

\delta=0.30\,\mathrm{\AA}

from the centre of its oxygen octahedron, along

c

. Treating this as a single point dipole per cell carrying the nominal ionic charge of

\mathrm{Ti^{4+}}

(

q=4e

), estimate the spontaneous polarisation

P_s

and compare it with the measured room-temperature value,

P_s=0.75\,\mathrm{C\,m^{-2}}

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