CERAMICS, PIEZOELECTRIC AND ELECTROSTRICTIVE
ANDREI KHOLKIN BAHRAM JADIDIAN AHMAD SAFARI
Rutgers University Piscataway, NJ
INTRODUCTION In a rapidly developing world, the use of smart materials becomes increasingly important when executing sophisticated functions within a designed device. In a common deﬁnition (1), smart materials differ from ordinary materials because they can performtwo or several functions, sometimes with a useful correlation or feedback mechanism between them. For piezoelectric or electrostrictive materials, this means that the same component may be used for both sensor and actuator functions. Piezoelectric/electrostrictive sensors convert a mechanical variable (displacement or force) into a measurable electrical quantity by the piezoelectric/electrostrictiveeffect. Alternately, the actuator converts an electrical signal into a useful displacement or force. Typically, the term transducer is used to describe a component that serves actuator (transmitting) and sensor (receiving) functions. Because piezoelectrics and electrostrictors inherently possess both direct (sensor) and converse (actuator) effects, they can be considered smart materials. Thedegree of smartness can vary in piezoelectric/electrostrictive materials. A merely smart material (only sensor and actuator functions) can often be engineered into a “very smart” tunable device or further, into an “intelligent structure” whose sensor and actuator functions are intercorrelated with an integrated processing chip. Recent growth in the transducer market has been rapid and, it is predictedwill continue on its current pace through the turn of the century. The sensor market alone rose to $5 billion in 1990, and projections are $13 billion worldwide by the year 2000 and an 8% annual growth rate during the following decade (2). Piezoelectric/ electrostrictive sensors and actuators comprise a signiﬁcant portion of the transducer market. There is a growing trend due especially toautomobile production, active vibration damping, and medical imaging. In this article, the principles of piezoelectric/electrostrictive sensors and actuators are considered along with the properties of the most useful materials and examples of successful devices. PIEZOELECTRIC AND ELECTROSTRICTIVE EFFECTS IN CERAMIC MATERIALS Piezoelectricity, ﬁrst discovered in Rochelle salt by Jacques and PierreCurie, is the term used to describe the ability of certain crystals to develop an electric charge that is directly
proportional to an applied mechanical stress (Fig. 1a) (3). Piezoelectric crystals also show the converse effect: they deform (strain) proportionally to an applied electric ﬁeld (Fig. 1b). To exhibit piezoelectricity, a crystal should belong to one of the twenty noncentrosymmetriccrystallographic classes. An important subgroup of piezoelectric crystals is ferroelectrics, which possess a mean dipole moment per unit cell (spontaneous polarization) that can be reversed by an external electric ﬁeld. Above a certain temperature (Curie point), most ferroelectrics lose their ferroelectric and piezoelectric properties and become paraelectrics, that is, crystals that havecentrosymmetric crystallographic structures do not spontaneously polarize. Electrostriction is a second-order effect that refers to the ability of all materials to deform under an applied electrical ﬁeld. The phenomenological master equation (in tensor notation) that describes the deformations of an insulating crystal subjected to both an elastic stress and an electrical ﬁeld is xi j = si jkl Xkl + dmi jEm + Mmni j Em En, i, j, k, l, m, n = 1, 2, 3,
where xi j are the components of the elastic strain, si jkl is the elastic compliance tensor, Xkl are the stress components, dmi j are the piezoelectric tensor components, Mmni j are the electrostrictive moduli, and Em and En are the components of the external electrical ﬁeld. Here, the Einstein summation rule is used for repeating indexes....