Piezoelectricity in Barium Titanate

Piezoelectricity is the ability of some materials to generate an electric potential in response to applied mechanical stress. The ceramic mineral barium titanate is a classic example. The crystal is characterized as a perovskite structure. At temperatures greater than the Curie point (120 ºC) the unit cell has cubic symmetry. A ion, shown as a gray sphere, is located at the center of the cube. It is surrounded by ions (green spheres) at the eight corners of the cube and ions (red spheres) at the six centers of the cube faces. The electrical charges of cubic perovskite have a completely symmetrical arrangement.
At temperatures below the Curie point, the crystal distorts to tetragonal symmetry. The titanium ion moves away from the center of the unit cell (chosen as downward in the graphic), thus giving the unit cell a net dipole moment—with the positive end downward. In a single crystal, idealized as a cylindrical slab on the right side of the graphic, this creates a small voltage difference between the top and bottom faces. Even in the absence of external stress, the crystal exhibits a poling voltage, shown as the midpoint reading on the attached voltmeter. The voltage increases from this value if the crystal is compressed, thus increasing the distortion of the unit cell. It decreases as the crystal is stretched. Thus a piezoelectric crystal is a natural oscillator. This is exploited by quartz oscillators, for example, in battery-operated wristwatches.
This Demonstration is intended only as a qualitative description of piezoelectricity. The changes in the dimensions of the slab are greatly exaggerated; they are typically of the order of 0.1%. The piezoelectric constant of is in the range m/V.



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Snapshot 1: above the Curie point, cubic symmetry
Snapshot 2: below the Curie point, the crystal becomes ferroelectric
Snapshot 3: decrease below the poling voltage upon stretching the crystal
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