Symbols & Notation
Symbols & Notation
The piezoelectric properties are described by a system of symbols and notations, identifying compliance, electromechanical coupling, etc.
The tables include the MKS units used in measuring each property.
Also see the later section on Units & Symbols for a complete listing.
Ceramic Property Definitions
| Property | Definition | MKS Units |
|---|---|---|
| Electro Mechanical Coupling Coefficient | ||
| k |  or... | - |
 | - | |
| Piezoelectric Constants | ||
| d |  | m / V |
 | C / N | |
| g |  | V / N |
 | m2 / C | |
| Relative Dielectric Constant | ||
| K |  | - |
| Modulus of Elasticity | ||
| Y |  | Nm-2 |
| Density | ||
 |  | kg/m3 |
| Frequency Constant | ||
| N | Controlling Dimension x Resonant Frequency | Hz m |
Superscript and subscript notations describe the characteristics of a property. The next table illustrates and explains several examples of annotated symbols. The superscripts describe external factors (physical mounting, electrical conditions, etc.) that effect the piezoelectric property. The subscripts describe the relationship of the property to the poling axis.
The characteristics of piezoelectric properties depend on their orientation to the poling axis. This orientation determines the direction of the action or response associated with the property. The subscript notations define the axes of a component in terms of orthogonal axes: 1 corresponds to the x-axis, 2 corresponds to the y-axis, and 3 corresponds to the z-axis. Conventionally, the direction of polarization is defined as the 3 axis. (See below)
(4, 5 and 6 refer to shear strains)
The first subscript position identifies the direction of the action; the second identifies the direction of the response. For example, refer to the piezoelectric "d " constant in the following table. The first subscript refers to the direction of the field and the second refers to the direction of the strain. For the converse piezoelectric constant "g", the first refers to the stress and the second to the voltage.
 | indicates that compliance is measured with electrode circuit open |
| indicates that stress or strain is in direction 1 | |
| indicates that strain or stress is in direction 1 | |
| Compliance = strain / stress |
 | indicates that compliance is measured with electrodes connected together |
| indicates that stress or strain is in shear around axis 3 | |
| indicates that strain or stress is in direction 3 | |
| Compliance = strain / stress |
 | indicates that all stresses on material are constant; for example zero external forces |
| indicates that electrodes are perpendicular to axis 1 | |
Relative dielectric constant =  |
 | indicates that all stresses on material are constant; for example material completely blocked preventing deformation in any direction |
| indicates that electrodes are perpendicular to axis 3 | |
Relative dielectric constant =  |
 | |
| indicates that stress or strain is in shear around axis 2 | |
| indicates that electrodes are perpendicular to axis 1 | |
| Electromechanical coupling |
 | Planar, used only for thin discs. It indicates electrodes perpendicular to axis 3 and stress or strain equal in all directions perpendicular to axis 3. |
| Electromechanical coupling |
 | |||
| indicates that the piezoelectric induced strain, or the applied stress, is in direction 3 | |||
| indicates that electrodes are perpendicular to axis 3 | |||
|
 | Indicates that stress is applied equally in 1, 2 and 3 directions (hydrostatic stress; and that electrodes are perpendicular to axis 3) |
| short circuit charge / electrode area applied stress |
 | |||
| indicates that the applied stress or piezoelectric induced strain is in direction 1 | |||
| indicates that electrodes are perpendicular to axis 3 | |||
|
 | |||
| indicates that the applied stress or piezoelectric induced strain is in shear form around axis 2 | |||
| indicates that electrodes are perpendicular to axis 1 | |||
|
