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How do ferroelectric domains affect polarization in barium titanate ceramics?

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Figure 1: Ferroelectric properties of barium titanate (BaTiO3). (Left) Above 120° C the structure of the BaTiO3 crystal is cubic, and there is no net polarization of charge; (right) below 120° C the structure changes to tetragonal, shifting the relative positions of the ions and causing a concentration of positive and negative charges toward opposite ends of the crystal. — capacitor dielectric and piezoelectric ceramics Figure 1: Ferroelectric properties of barium titanate (BaTiO₃). (Left) Above 120° C the structure of the BaTiO₃ crystal is cubic, and there is no net polarization of charge; (right) below 120° C the structure changes to tetragonal, shifting the relative positions of the ions and causing a concentration of positive and negative charges toward opposite ends of the crystal.

In barium titanate (BaTiO $_{3}$ ) ceramics, ferroelectric domains are regions where the internal electric dipoles are aligned in the same direction. These domains significantly influence the material's polarization and its effectiveness as a dielectric:12

Spontaneous Polarization: Below the Curie point, the crystal structure shifts from cubic to tetragonal, creating permanent dipoles that cluster into these domains.13
Net Polarization: In a typical ceramic, these domains are randomly oriented, leading to an overall cancellation of polarization.1
Field Response: When an external electric field is applied, the boundaries between domains can move. Domains already aligned with the field grow at the expense of those that are not, producing a large net polarization.13
Capacitance: This susceptibility to polarization allows the material to store significant electric charge, resulting in the high dielectric constants that make barium titanate essential for capacitor technology.12