TABLE 4 lectric Piezoelectric, and Electrostrictive materials Type Material Class Example Applications Electret Electret Organic Fluorine based Ferroelectric No known Ferroelectric PZT thin film Organic PVF2 PLZT Single cry LiNbO Electrostrictive Ceramic PMN 49.2 Mechanical characteristics Materials are acted on by forces(stresses)and the resulting deformations are called strains. An example of a strain due to a force to the material is the change of dimension parallel and perpendicular to the applied force. It is useful to introduce the coordinate system and the numbering conventions which are used when discussing these materials. Subscripts 1, 2, and 3 refer to the x, y, and z directions, respectively. Displacements have single indices associated with their direction. If the material has a preferred axis, such as the poling direction in PZT, the axis is designated the z or 3 axis Stresses and strains require double indices such as xx or xy. To make the notation less cluttered and confusing, contracted notation has been defined. The following mnemonic rule is used to reduce the double index to a single index 165 This rule can be thought of as a matrix with the diagonal elements having repeated indices in the expected order, then continuing the count in a counterclockwise direction. Note that xy yx, etc so that subscript 6 applies equally to xy and yx. Any mechanical object is governed by the well-known relationship between stress and strain, S=ST (49.1) where S is the strain(relative elongation), T is the stress(force per unit area), and s contains the coefficients <s nnecting the two. All quantities are tensors; S and T are second rank, and s is fourth rank. Note, however, that usually contracted notation is used so that the full complement of subscripts is not visible PZT converts electrical fields into mechanical displacements and vice versa. The connection between the two is via the d and g coefficients. The d coefficients give the displacement when a field is applied(transmitter), while the g coefficients give the field across the device when a stress is applied (receiver ). The electrical effects are added to the basic Eq (49.1)such that s=st +dE (49.2) where E is the electric field and d is the tensor which contains the coupling coefficients. The latter parameters are reported in Table 49.2 for representative materials. One can write the matrix equation [Eq (49.2)1 c 2000 by CRC Press LLC© 2000 by CRC Press LLC 49.2 Mechanical Characteristics Materials are acted on by forces (stresses) and the resulting deformations are called strains. An example of a strain due to a force to the material is the change of dimension parallel and perpendicular to the applied force. It is useful to introduce the coordinate system and the numbering conventions which are used when discussing these materials. Subscripts 1, 2, and 3 refer to the x, y, and z directions, respectively. Displacements have single indices associated with their direction. If the material has a preferred axis, such as the poling direction in PZT, the axis is designated the z or 3 axis. Stresses and strains require double indices such as xx or xy. To make the notation less cluttered and confusing, contracted notation has been defined. The following mnemonic rule is used to reduce the double index to a single index: 165 xx xy xz 2 4 yy yz 3 zz This rule can be thought of as a matrix with the diagonal elements having repeated indices in the expected order, then continuing the count in a counterclockwise direction. Note that xy = yx, etc. so that subscript 6 applies equally to xy and yx. Any mechanical object is governed by the well-known relationship between stress and strain, S = sT (49.1) where S is the strain (relative elongation), T is the stress (force per unit area), and s contains the coefficients connecting the two. All quantities are tensors; S and T are second rank, and s is fourth rank. Note, however, that usually contracted notation is used so that the full complement of subscripts is not visible. PZT converts electrical fields into mechanical displacements and vice versa. The connection between the two is via the d and g coefficients. The d coefficients give the displacement when a field is applied (transmitter), while the g coefficients give the field across the device when a stress is applied (receiver). The electrical effects are added to the basic Eq. (49.1) such that S = sT + dE (49.2) where E is the electric field and d is the tensor which contains the coupling coefficients. The latter parameters are reported in Table 49.2 for representative materials. One can write the matrix equation [Eq. (49.2)], TABLE 49.1 Ferroelectric, Piezoelectric, and Electrostrictive Materials Type Material Class Example Applications Electret Organic Waxes No recent Electret Organic Fluorine based Microphones Ferroelectric Organic PVF2 No known Ferroelectric Organic Liquid crystals Displays Ferroelectric Ceramic PZT thin film NV-memory Piezoelectric Organic PVF2 Transducer Piezoelectric Ceramic PZT Transducer Piezoelectric Ceramic PLZT Optical Piezoelectric Single crystal Quartz Freq. control Piezoelectric Single crystal LiNbO3 SAW devices Electrostrictive Ceramic PMN Actuators