1.1 Piezoelectricity
Piezoelectricity is the ability of certain crystals to produce a voltage when subjected to mechanical stress. The word is derived from the Greek
“piezo”, which means to squeeze or press. Piezoelectricity is a linear effect that is related to the microscopic structure of the solid. Some ceramic materials become electrically polarized when they are strained. This linear and reversible phenomenon is referred to as the direct piezoelectric effect.
Piezoelectric materials also show the opposite effect, called the converse piezoelectricity. Figure 1.1 demonstrates the connection between electrical and mechanical domains. An electrical field creates mechanical stress (distortion) in the crystal structure because the charges inside the crystal are separated. The applied voltage affects different points within the crystal differently, resulting in the distortion. The microscopic origin of the piezoelectric effect is the displacement of ionic charges within a crystal structure. In the absence of external strain, the charge distribution within the crystal is symmetric and the net electric dipole moment is zero. However, when an external stress is applied, the charges are displaced and the charge distribution is no longer symmetric. A net polarization develops and results in an internal electric field. A material can only be piezoelectric if the unit cell has no center of inversion. The effect is of the order of nanometers, but nevertheless finds useful applications such as the production and detection of sound, generation of high voltages, electronic frequency generation, and
ultrafine focusing of optical assemblies.
1.2 History
In 1880, the brothers Pierre Curie and Jacques Curie predicted and demonstrated piezoelectricity using tinfoil, glue, wire, magnets, and a jeweler's saw. They showed that crystals of tourmaline, quartz, topaz, cane sugar, and Rochelle salt (sodium potassium tartrate tetrahydrate) generate electrical polarization from mechanical stress. Quartz and Rochelle salt exhibited the most piezoelectricity. Twenty natural crystal classes exhibit direct piezoelectricity. In 1881, the term "piezoelectricity" was first suggested by W. Hankel, and the converse piezoelectricity was mathematically deduced by Lipmann from fundamental thermodynamic principles. The Curies immediately confirmed the existence of the "converse effect," and went on to obtain quantitative proof of the complete reversibility of electro-elasto-mechanical deformations in piezoelectric crystals.
In the next three decades, collaborations within the European scientific community established the field of piezoelectricity; and by 1910, Voigt’s
“Lerbuch der Kristallphysic” was published and became a standard reference work detailing the complex electromechanical relationships in piezoelectric crystals. However, the complexity of the science of piezoelectricity made it difficult for it to mature to an application until a few years later. The first practical application for piezoelectric devices was sonar, first developed during World War I. In France in 1917, Langevin et al. developed an ultrasonic submarine detector. The detector consisted of a transducer, made of
thin quartz crystals carefully glued between two steel plates, and a hydrophone to detect the returned echo. By emitting a high-frequency chirp from the transducer, and measuring the amount of time it takes to hear an echo from the sound waves bouncing off an object, one can calculate the distance to that object. Their success opened up opportunities for intense development interest in piezoelectric devices. Over the next few decades, new piezoelectric materials and new applications for those materials were explored and developed. In 1935, Busch and Scherrer discovered piezoelectricity in potassium dihydrogen phosphate (KDP). The KDP family was the first major family of piezoelectrics and ferroelectrics to be discovered.
During World War II, research in piezoelectric materials expanded to the U.S., the Soviet Union and Japan. Up until then, limited performance by these materials inhibited commercialization but that changed when a major breakthrough came with the discovery of barium titanate and lead zirconate titanate (PZT) in the 1940s and 1950s respectively. These families of materials exhibited very high dielectric and piezoelectric properties.
Furthermore, they offered the possibility of tailoring their behavior to specific responses and applications by the use of dopants. Starting around 1965, several Japanese companies focused on developing new processes and applications, and opening new commercial markets for piezoelectric devices.
The success of the Japanese effort attracted other nations.
Today, PZT is one of the most widely used piezoelectric materials. It is noted that most commercially available ceramics (such as barium titanate and PZT) are based on the perovskite structure shown in Figure 1.2. The perovskite structure (ABO3) is the simplest arrangement where the corner-sharing oxygen octahedra are linked together in a regular cubic array
with smaller cations (Ti, Zr, Sn, Nb etc.) occupying the central octahedral B-site, and larger cations (Pb, Ba, Sr, Ca, Na etc.) filling the interstices between octahedra in the larger A-site. Compounds such as BaTiO3, PbTiO3, PbZrO3, NaNbO3 and KNbO3 have been studied at length and their high temperature ferroelectric and antiferroelectric phases have been extensively exploited. This structure also allows for multiple substitutions on the A-site and B-site resulting in a number of useful though more complex compounds such as (Ba,Sr)TiO3, (Pb,Sr)(Zr,Ti)O3, Pb(Fe,Ta)O3, (KBi)TiO3 etc.
1.3 Motive
To date, the needs and uses of piezoelectric devices extend from medical applications to the communications field to military applications and the automotive field. Piezoelectric materials are well known for great rigidity, low power consumption, rapid response, and ultra-high resolution. As very high voltages correspond to only tiny changes in the width of the crystal, this width can be changed with better-than-micrometer precision, making piezo crystals the most important tool for positioning objects with extreme accuracy.
Due to the piezoelectric effect and these excellent features, piezoelectric ceramics are commercially available devices for measuring displacements in the range of 10pm to 100um. These applications include optical fiber alignment, mask alignment, scanning electron microscope, focusing and tracking of a hard disk drive, etc. Thus, we look forward to construct a new design of the micro-stepping mechanism with piezoelectric actuators to achieve the accuracy of positioning.
1.4 Research Orientation
First, the non-linearity of piezoelectric actuators is introduced. The non-linear effects between the input voltage waveform and the output deformation cause undesirable inaccuracy especially hysteresis. It brings about a rate-independent lag phenomenon and residual displacement near zero input. These phenomena reduce the accuracy of the actuators and result in poor performance in the piezoelectric actuator which is operated in open-loop mode.
The main purpose is to design a mechanism of the piezoelectric actuator in precise positioning with long traveling displacement. We choose the piezoelectric impact drive mechanism (IDM) which belongs to stick-slip actuators of the pulse type for experiment. To expand the working range of stroke with high resolution, a voltage amplifier is necessarily needed. IDM is one type of micro-stepping device that can achieve nanometer resolution. The operating principle of the impact drive mechanism is explained. Applying an asymmetric voltage waveform to piezoelectric elements which is connected to the slider and the counter-mass of IDM causes a series of motions on the guide way. The piezoelectric elements used to excite each stepping motion of IDM are considered to be a linear and rigid device that can provide a fast displacement response. A mass-damper-spring model is constructed to investigate the dynamics of the mechanism.
An experimental environment, based on the laser interferometer, is set up for managing the displacement of the piezoelectric actuator. After data converting reference and measurement signals from laser head and
measurement receiver, the information is processed by DSP which provides fast digital input read operation. The DSP module can also produce driving waveforms needed in the experiment at the same time. With experimental results, we can observe the relation between the input voltage waveform and the output deformation then make a conclusion.