# What is Radial and Thickness Mode Vibration in a Piezo Electric Ceramic Disc Transducer?

I am trying to use a Piezo Electric Ceramic Disc Transducer for ultrasonic sensing measurements for fluid levels. A Piezo Ceramic Disc with a Resonant frequency of 215 KHz or 1 MHz is under consideration. These devices specify a Radial and Thickness mode vibration configuration.

Primary Question: What is Radial and Thickness mode vibration configuration?

Secondary Question: Is Axial and Thickness mode vibration mean the same mode?

## Part Specifications

Piezo Ceramic Disc 1 MHz,Thickness mode vibration

• Dimensions: 15mm diameter x 2.1mm thickness
• Resonant frequency fr: 1 MHz±3 %
• Electromechanical coupling coefficient Kt:≥39%
• Resonant impedance Zm: ≤7.6 Ω
• Static capacitance Cs: 900pF±15%@1kHz
• Test Condition: 23±3 °C 40~70% R.H.
• fr, Zm, Kp => Thickness mode vibration
• Cs => LCR meter at 1KHz 1Vrms

Piezo Ceramic Disc R 215 KHz, Radial mode vibration

• Dimensions: 10mm diameter x 2mm thickness
• Resonant frequency fr: 215 KHz±5 KHz
• Electromechanical coupling coefficient Kp:≥60%
• Resonant impedance Zm: ≤6 Ω
• Static capacitance Cs: 450pF±15%@1kHz
• Test Condition: 23±3 °C 40~70% R.H.
• fr, Zm, Kp => Radial mode vibration
• Cs => LCR meter at 1KHz 1Vrms

References:

There is an excellent white paper from piezotechnologies.com which is probably worth a read if you are new to working with piezoelectric devices. Quoting from the section on resonance frequencies:

If an AC voltage is applied to a piezoceramic disc with a diameter several times its thickness, two series of resonances may be observed. The resonance at the lowest frequency corresponds to motion in the largest dimension of the ceramic, which in this case is in the radial direction. Often, several harmonics will also be seen at higher frequencies.

The first thickness resonance appears quite different from the radial harmonics that are found just below it. The impedance drops to a much lower value and the span in frequency is far wider. The thickness mode frequency often appears much “rougher” than the radial mode. This is because the harmonics of the radial mode are excited by the strong thickness mode.

So, the radial mode is lower in frequency because it has a larger dimension. Since it is also the lowest frequency resonance it is much cleaner because it does not coincide with any other harmonics. See the figure below.

The axial (thickness) mode on the other hand has a stronger resonance since the piezo-crystal is designed to be driven in that direction. In addition, it overlaps with some of the higher harmonics of the radial mode and therefore has a 'dirtier' appearance. See the figure below.

The full spectrum showing the narrower, weaker radial mode and its resonances together with the axial mode puts the relative broadness and strength of the axial mode in perspective.

• The white paper url referenced points to a dead link. Is this the link you are referencing. piezotechnologies.com/knowledge-desk/overview-piezo-materials Commented Jun 19, 2015 at 11:15
• @MahendraGunawardena That one is shorter than the original one from my link, but it seems to have much of the same information. I am unable to locate the original unfortunately, so it will have to do. Commented Jun 19, 2015 at 11:51
• @ChrisMueller, Per the broken link, Looks like this is the paper you are referencing. ultrasonic-resonators.org/misc/references/articles/… Commented Jan 14, 2021 at 15:34

Radial: Oscillatory waveform is between edge and centre.
Thickness: Oscillation is across disc faces so will be higher frequency all else being equal.

Axial and thickness are probably equivalent terms.

Interestingly, while the relationship does not have to be this close

• Your thickness mode disc resonates at 1 MHz and is 2.1mm thick.

• Dia / thickness = 10:2.1 = 4.76:1

• 1 MHz / 215 kHz = 4.65:1

Texas Instruments has extensive material on this Piezo Electric disc for applications of measurements fluid level. You can search their website for STEMINC and you will see two discs used on Thickness mode. Both discs have frequency 1MHz and are used with a couple of their controllers. The discs are SMD10T2R111WL and SMD15T21R111WL. STEMINC also has these same dimensions discs with Radial frequency but the Texas Instruments Controller TDC100 for liquid level measurement will work with the 1MHz version.