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.



  • [Snapshot]
  • [Snapshot]
  • [Snapshot]


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
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.

Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2018 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+