Some crystals, when squeezed in certain directions, will develop a momentary electric current. This effect is known as piezoelectricity. When a crystal is subject to stress it may deform elastically. Ions will move. If opposite charges move away from or toward each other, a current is developed. If both charges move in the same direction no net current will develop. The current lasts only as long as the ions are in motion. In order for a crystal to show the piezoelectric property it must have a polar axis. In order to have a polar axis the crystal must belong to a non-centrosymmetric crystal class. Non-centrosymmetric means the class does not have a center of symmetry. A polar axis is an axis that possesses different forms at opposite ends of the axis. Twenty-one crystal classes are non-centrosymmetric. One class, the gyroidal class 432, has no polar axis. The remaining twenty classes do have at least one polar axis and therefore are capable of showing the piezoelectric effect.
When a piezoelectric crystal is subjected to an electric current the crystal will physically deform. This effect is known as the converse piezoelectric effect or the electrostriction effect. The piezoelectric effect was discovered by Pierre and Jacques Curie in 1881 in quartz. The converse piezoelectric effect was first used in 1921 to control radio frequencies. When a plate of quartz is subjected to an alternating electric current the plate vibrates. The thinner the slice the greater the frequency of vibration. If the quartz plate is in a radio circuit, the frequency of the circuit is stabilized at the resonant frequency of the plate. Quartz oscillators greatly improved radio transmission and reception. The same phenomenon has been used in recent years in quartz watches which use a circuit to count the vibrations of the plate and use the number of counts to determine time.
Quartz crystals have also been used in piezometers, which detect pressure waves. Such devices can sense the sound waves produced by submarines. Tourmaline piezometers are less sensitive than quartz and can be used to detect large pressure changes such as those produced in atomic bomb blasts. Other common minerals which show a measurable piezoelectric effect are sphalerite, topaz, and low boracite.
Piezoelectricity is a directional property. It is described mathematically as a third-order tensor. Scalers are numbers. Vectors, or first-order tensors, given direction and magnitude. A vector has three components. A second-order tensor, such as the stress tensor, has nine components. Third-order tensors have twenty-seven components, while fourth-order tensors, such as the electrostriction effect, have eighty-one components. The polarization produced by the piezoelectric effect may be described as shown in equation 1,
where Pi is the polarization vector,
dijk is the piezoelectric modulus, and
σjk is the stress tensor.
NOTE: In some versions of Netscape, the Greek letter sigma is not represented correctly. For &sigma, read the lowercase "sigma".
© 2005 by David L. Warburton
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Last updated: June 29, 2005