Archaeo-Acoustics : Chichen Itza
Archaeo-Acoustics : Epidaurus
phononic crystals - transduction
ultrasonic diffraction - isotropic materials
ultrasonic diffraction - anisotropic materials
room acoustics : Alvar Aalto's discussion room
fiber reinforced composites
acousto-optic crystals
piezo-electric crystals
Minimum variance guided wave imaging
polar scans
Electrets for Ultrasonic Transducers
piezo-electric crystals

Ultrasound in Piezoelectric Media

A crystal is a solid material whose atoms are arranged in a definite pattern and whose surface regularity reflects its internal symmetry. Each of a crystal's millions of individual structural units contains all the substance's atoms, molecules, or ions in the same proportions as in its chemical formula. The cells are repeated in all directions to form a geometric pattern, manifested by the number and orientation of external planes (crystal faces). Crystals are classified into seven main crystallographic systems based on their symmetry: isotropic, trigonal, hexagonal, tetragonal, orthotropic, monoclinic, and triclinic. The picture on the right is a Quartz crystal. This crystal is one example of crystals whose mechanical behavior is connected to its electrical behavior and vice versa. The coupling effect is called ‘the piezoelectric effect’. It was first observed by Paul-Jacques and Pierre Curie in 1880.
Piezoelectricity is the appearance of an electric field in certain nonconducting crystals as a result of the application of mechanical pressure. Pressure polarizes some crystals, such as quartz, by slightly separating the centers of positive and negative charge. The resultant electric field is detectable as a voltage. The converse effect also occurs: an applied electric field produces mechanical deformation in the crystal. Using this effect, a high-frequency alternating electric current can be converted to an ultrasonic wave of the same frequency, while a mechanical vibration, such as sound, can be converted into a corresponding electrical signal. Piezoelectricity is utilized in microphones, phonograph pickups, and telephone communications systems.
In ultrasonics, the device that transforms an electric signal into a sonic signal (and vice versa), is called ‘a transducer’. Transducers were first applied for sonar systems, initially by the military, later by ocean liners, fishing vessels, cargo ships and submarines for underwater archeology.
For sound waves, anisotropy of a certain media, means that its velocity and polarization depend on the direction of propagation. It also means that for most directions of propagation, the direction of phase propagation differs from that of energy propagation. To some extent, this is comparable to a sailing boat, steering in one direction, but being drifted in another course. Also, for a given direction in an anisotropic media, there are in general three sound velocities possible, comparable to the effect of birefringence in optics.
A thourough study is performed on the influence of piezoelectricity on the different modes of wave propagation, inlcuding inhomogeneous waves in piezoelectric crystals. Piezoelectric crystals are also often applied in acousto-optics.


Stiffening of crystals due to piezoelectricity

The effect of stiffening of crystals due to piezoelectricity, is well known and is shown graphically, by plotting the difference of the slowness surfaces with and without piezoelectricity. Furthermore, arrows can be added to the graphics, that denote the change of polarization or the change of energy flux.


Inhomogeneous waves in piezoelectric crystals

Inhomogeneous waves in piezoelectric materials are better susceptible to the presence of piezoelectricity in crystals than homogeneous plane waves.


Enhanced anisotropy in Paratellurite

Enhanced anisotropy in Paratellurite for inhomogeneous waves is possibly important in the future development of Acousto-optic devices. The strong anisotropy in paratellurite is very important for the fabrication of acousto-optic cells. Here, it is shown that the effect of anisotropy on inhomogeneous waves in this crystal, is much more outspoken than the effect on homogeneous plane waves. This makes it reasonable to consider fabricating acousto-optic cells, based on inhomogeneous waves instead of homogeneous waves.


Sound in biased piezoelectric materials

A generalized form of the Christoffel equation was formulated for biased piezoelectric crystals of general anisotropy. This is done by considering a linear acoustic regime in a crystal that is biased by nonlinear effects. An expression is given of the energy flux for the considered situation of biased piezoelectric crystals. Numerical results are reported for Lithium Niobate. The influence is calculated of an initial pressure, in the piezoelectric case and in the non-piezoelectric case, for homogeneous plane waves and also for inhomogeneous plane waves. Furthermore, the influence of the magnitude and the direction of the considered pressure, on the change in the acoustic wave velocity, is studied as well.



[NFD-J-27] Nico F. Declercq, Joris Degrieck, Oswald Leroy, "Sound in Biased Piezoelectric Materials of General Anisotropy", Annalen der Physik (Ann. Phys. - Berlin) 14 (11-12), 705-722, 2005
[NFD-J-33] Nico F. Declercq, Nataliya V. Polikarpova, Vitaly B. Voloshinov, Oswald Leroy, Joris Degrieck, "Enhanced anisotropy in Paratellurite for inhomogeneous waves and its possible importance in the future development of acousto-optic devices", Ultrasonics 44 (1), 833-837,2006

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