Key Parameters for Piezo Ceramic Materials

The piezoelectric charge constant, d, describes the electric polarization generated per unit of applied mechanical stress. It can also describe the mechanical strain produced per unit of applied electric field.

The first subscript indicates the direction of the generated polarization or applied electric field. The second subscript indicates the direction of applied stress or induced strain.

Because the induced strain is directly related to the applied electric field and the value of d, this constant is especially important when evaluating piezo ceramic materials for actuator applications.

Common examples include:

• d33: polarization or strain in direction 3, parallel to the polarization direction
• d31: polarization in direction 3 caused by stress in direction 1, or strain in direction 1 caused by an electric field in direction 3
• d15: shear-related piezoelectric response, commonly used for shear-mode applications

The piezoelectric voltage constant, g, represents the electric field generated by a piezoelectric material per unit of applied mechanical stress. It can also represent the mechanical strain generated per unit of applied electric displacement.

This constant is particularly important for sensor applications, where the material must efficiently convert mechanical pressure, vibration, or force into an electrical signal.

Typical examples include:

• g33: electric field generated in direction 3 under stress in direction 3
• g31: electric field generated in direction 3 under stress in direction 1
• g15: shear-mode voltage response

In general, a higher g value indicates better sensitivity for sensing applications.

Permittivity, also known as the dielectric constant, describes the ability of a piezo ceramic material to store electrical energy in response to an electric field.

Two common forms are used:

• εT: permittivity under constant stress
• εS: permittivity under constant strain

The relative dielectric constant, K, compares the charge storage capability of the ceramic material with that of free space. This parameter is important for transducer design, capacitance calculation, impedance matching, and electrical performance evaluation.

Elastic compliance, s, describes the strain produced in a piezoelectric material per unit of applied stress. In the 11 and 33 directions, it is the reciprocal of Young’s modulus.

Common forms include:

• sE: compliance under constant electric field
• sD: compliance under constant electric displacement

Elastic compliance is important when evaluating mechanical deformation, resonance behavior, and vibration characteristics of piezo ceramic components.

Young’s modulus, Y, indicates the stiffness of a ceramic material. It is calculated as the ratio of applied stress to resulting strain in the same direction.

A higher Young’s modulus means the material is stiffer, while a lower value indicates greater elasticity. This parameter is widely used in the design of piezo ceramic rings, discs, plates, tubes, and ultrasonic transducer elements.

The electromechanical coupling factor, k, measures how effectively a piezoelectric material converts electrical energy into mechanical energy, or mechanical energy into electrical energy.

A high k value is generally desirable for efficient energy conversion. However, k alone does not represent total system efficiency, because dielectric loss, mechanical loss, and unrecovered energy must also be considered.

Common coupling factors include:

• k33: longitudinal coupling along the polarization direction
• k31: transverse coupling between direction 3 and direction 1
• kp: planar or radial coupling, commonly used for thin discs
• kt: thickness coupling, commonly used for plates and discs where thickness vibration is dominant

For ultrasonic transducers, the coupling factor is one of the key parameters affecting power conversion, vibration amplitude, and overall acoustic output.

The dielectric dissipation factor, usually expressed as tan δ, represents dielectric loss in a piezo ceramic material. It is the tangent of the dielectric loss angle and is typically measured at 1 kHz.

A lower tan δ value generally indicates lower dielectric loss and better electrical efficiency, which is important for high-power ultrasonic applications.

When a piezo ceramic element is driven by a high-frequency alternating electric field, it reaches resonance at specific frequencies depending on its geometry and vibration mode.

Important frequency constants include:

• NP: radial mode frequency constant, related to disc diameter
• NT: thickness mode frequency constant, related to element thickness
• NL: longitudinal mode frequency constant, related to element length

These constants are useful for estimating the resonance frequency of piezo ceramic components during transducer and ultrasonic system design.

• d: piezoelectric charge constant
• g: piezoelectric voltage constant
• ε: permittivity
• K: relative dielectric constant
• s: elastic compliance
• Y: Young’s modulus
• k: electromechanical coupling factor
• Qm: mechanical quality factor
• tan δ: dielectric dissipation factor
• fs: series resonance frequency
• fp: parallel resonance frequency
• fm: minimum impedance frequency
• fn: maximum impedance frequency
• Tc: Curie temperature