**Piezo Terminology: A Glossary**

机电耦合系数 | 介电常数 | 介质损耗 | 压电常数 | 弹性柔顺常数 | 机械品质因数 | 声速（m/s） | 体积密度 | 居里温度 | 杨氏模量 | 泊松比 | |||||||||

Kp | K31 | K33 | Kt | ε ^{T}_{r3} |
Tg δ% | d31 (-10^{-12}m/v) |
d33(-10^{-12}m/v) |
g31(-10^{-3}m/v) |
g33(-10^{-3}vm/n) |
S^{e}_{11}(-10^{-12}m^{2}/n) |
Qm | Vd | V1 | V3 | Vt | ρ(10^{3}kg/m^{3}) |
Tc(℃) | Y^{E}11﹤10^{9}N/m^{3} |
σ E |

## What’s Aging rate C?

The aging rate indicates the relative change in a given property per unit time, over intervals expressed on a decimal ex-ponent basis (“decades”).

The following variables are used:

c_{ε}: capacitance aging rate

c_{f}: resonance frequency aging rate

c_{k}: aging rate of the electromechanical coupling factor

Thus, if the capacitance aging rate of He Shuai Ltd P4 ceramics is given as -4.5 %

per decade, the aging curve is as for example:

1 day after polarization: 100 nF

10 days after polarization:96.6 nF (-3.4 %)

100 days after polarization:93.3 nF (-3.4 %)

1000 days after polarization:90.1 nF (-3.4 %)

## What’s the piezoelectric ceramic **Capacitance C?**

The capacitance of a piezoelectric transducer, measured at a frequency far below its minimum resonance frequency (usually 1 kHz).

By using the relative dielectric permittivity, this parameter can be computed from the datasheet for a defined component geometry and material by means of the following formula:

- = ε
_{r}^{T}ε_{O}· (A/d) - electrode area
- d: electrode spacing
- A good approximation of the capacitance (in pF) of a piezoceramic body can be achieved by means of the following simplified equations: Round disk/cylinder: C= ε
_{r}^{T}ε_{O}· (A/d)

## What’s **Charge constant, piezoelectric d?**

Denotes the ratio between charge generated and the force applied, indicated in Coulomb per Newton (direct piezo effect), or the ratio between the strain produced and the electrical voltage applied, indicated in meters per volt (inverse piezo effect).

For a short-circuited piezoceramic ele-ment (E = 0), the following equation ap-plies: **Q = d · F**

Q: charge (generated)

F: force (applied)

For a mechanical no-load condition (T=0), the following equation can be ex-pressed: **S = d · U**

S: strain (generated)

U: electrical voltage (applied)

## What is **Compliance, elastics?**

The elastic compliance s reflects the ratio between the strain S and the mechanical stress T and is equal to the inverse of the modulus of elasticity (Young‘s modulus)

## What is the **Coupling factor, electromechanical k?**

Measures for the efficiency of the electrical-to-mechanical energy conversion.

For electrically “driven“ components, the following equation applies:

k^{2} =stored mechanical energy / total energy stored

Depending on the boundary conditions, there exist five different coupling factors reflecting the form factors and oscillation mode of the component. Where boundary conditions like a specific diameter/thickness ratio are not granted, the effective coupling factor is normally used as a standard.

## What is the **Curie Temperature, T**_{c?}

_{c?}

This is the temperature at which the di-electric permittivity of ferroelectric ceramics will reach its maximum.

At this temperature, a piezoelectric ceramic will lose its polarized state. For this reason, operating temperatures normally should not exceed half the Curie temperature.

## What is the **Dielectric permittivity, relative **ε_{r?}

_{r?}

Denotes the ratio between the absolute dielectric constant and the permittivity of free space (ε_{O}= 8.85 x 10^{-12} F/m).

## What is the **Dissipation factor, dielectric tan **δ?

Denotes the ratio between power loss and reactive power when the component is excited with a sine-wave signal at a frequency far below its lowest resonant frequency (usually measured at 1 kHz). For power conversion applications it is recommended to use piezoceramics with a suitably low dissipation factor.

## What is the **Frequency constant N?**

Product of the mechanical resonance frequency and the dimension determining that frequency. The index indicates the oscillation form.

N_{p}: Frequency constant for the planar oscillation of a circular disk

N_{t}: Frequency constant for the thick-ness-mode oscillation of a thin plate

N_{1}: Frequency constant for the longitudinal or transverse oscillation of a thin rectangular plate

N_{3}: Frequency constant for the longitudinal oscillation of a slender rod or cylinder polarized in that direction

Since geometrically induced coupled-mode vibrations may occur in all of the above oscillation forms, the geometrical configuration of the specific oscillating body must be taken into account when using the frequency constant for calculating resonance frequencies (refer also to the section “Basic Oscillation Modes of

Piezoelectric Resonators

Apart from N_{p}, the frequency constants indicated equal one-half the sound propagation velocity in the piezoceramic material.

## What are the piezoelectric ceramic indices?

In piezoelectric materials, the direction of positive polarization is usually made to coincide with the z-axis of a rectangular system of crystallographic axes. These coordinates are normally designated 1, 2, 3, with direction 3 indicating the polarization.

direction. Mechanical and electrical influences acting in any of these directions are identified with the corresponding index. Since piezoelectric components are already polarized in a given direction (i.e., 3) and will therefore show an anisotropic behavior, the coefficients given in the material property data charts are direction-related and will often comprise two subscripts (plus, occasionally, one superscript).

The superscript indicates the variable that remains constant, while the two subscripts identify the direction in which the different variables (electric field, electric displacement, mechanical stress, and strain) are linked.

## What is the piezo ceramic superscript?

T: at constant mechanical stress

S: at constant strain

E: at a constant electrical field strength

D: at constant dielectric displacement

## What are the PZT ceramic subscripts?

perpendicular to the direction of polarization – directions 1 and 2 are orthogonal to each other and equivalent (isotropic behavior of ceramics)

in the direction of polarization

Example: A piezoelectric charge constant d_{33} (refer also to the datasheet) indicates that the mechanical stress applied during the measurement acts in direction 3 (polarization direction), whereas the electric displacement produced will also occur in the direction

## What is the piezo ceramic q**uality factor, mechanical Q**_{m?}

_{m?}

Amplitude magnification of an oscillating piezoelectric component at resonance. Defined as the ratio of energy input per oscillation cycle over the amount of energy consumed (i.e., dissipated) per oscillation cycle. The mechanical quality factor can be computed.

the mechanical quality factor is a dimensionless measure for a component‘s mechanical losses in dynamic driving mode.

### What is the PZT ceramic temperature** coefficient **α_{k?}

_{k?}

Indicates the relative change of the electromechanical coupling factor per Kelvin of temperature change.

**What is the piezoelectric ceramic voltage constant, piezoelectric g?**

Denotes the ratio between the electric field strength produced and the mechanical stress applied, indicated in voltmeter/Newton (direct piezo effect), or the ratio between the strain produced and the charge density applied, indicated in square meters per Coulomb (inverse piezo effect).

The voltage constant and charge constant are interrelated via the capacitance of the component. This relationship is expressed by the following formula:

**d = **ε_{r}** · **ε_{o}** · g**

ε_{r}: relative permittivity

ε_{o}: permittivity of free space

The following examples illustrate how the voltage across the piezoelectric component can be calculated by means of the voltage constant.