# Piezoelectric Tube Scanners

Piezoelectric tube scanners are thin cylinders of radially poled piezoelectric material with four external electrodes and a solid or quadrant internal electrode. When a voltage is applied to one of the external electrodes, the actuator wall expands which causes a vertical contraction and a large lateral deflection of the tube tip. A circumferential electrode can be used for vertical or radial extension and contraction.

Piezoelectric tube scanners are used extensively in scanning probe microscopes and applications such as fibre stretching and beam scanning. Customised dimensions and/or specifications are available on request.

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### Specifications

Order
Code
Length Diameter Thickness Max.
Voltage
Scan
Range
Extension
Range
Capacitance
$AU Buy Now TB1005 10.00 mm 5.0 mm 0.66 mm $\pm$ 264 V 3.8 um 2.1 um 3 nF$AU 74 Buy Now
TB1206 12.7 mm 6.35 mm 0.635 mm $\pm$ 254 V 4.8 um 2.7 um 4 nF $AU 174 Buy Now TB2005 20.00 mm 5.0 mm 0.66 mm $\pm$ 264 V 15 um 4.2 um 6 nF$AU 130 Buy Now
TB3306 33.00 mm 5.0 mm 0.508 mm $\pm$ 203 V 32 um 7 um 8 nF $AU 234 Buy Now TB3507 35.00 mm 7.0 mm 0.66 mm $\pm$ 264 V 39 um 7.4 um 10 nF$AU 209 Buy Now
TB5009 50.8 mm 9.5 mm 0.66 mm $\pm$ 264 V 52 um 10 um 17 nF $AU 290 Buy Now TB7312 73.66 mm 12.62 mm 0.89 mm $\pm$ 356 V 82 um 15 um 28 nF$AU 405 Buy Now

When the base of the tube is fixed, the tip translations $\Delta x$ and $\Delta y$ are approximately $$\Delta x = V_x \frac{2 \sqrt{2} d_{31} L^2}{\pi D h} ~~~~~~~ \Delta y = V_y \frac{2 \sqrt{2} d_{31} L^2}{\pi D h}$$ where $\Delta x$ and $\Delta y$ are the $x$ and $y$ axis deflection, $d_{31}$ is the piezoelectric strain constant, $L$ is the length of the tube, $D$ is the outside diameter, $h$ is the tube thickness, and $V_x$ and $V_y$ are the electrode voltages which are applied oppositely to either side of the tube.

Vertical elongation due to a voltage applied on all four quadrants or the internal electrode is approximately $$\Delta L = V \times \frac{d_{31} L}{h}.$$

The diameter expansion due to a voltage applied on all four quadrants or the internal electrode is approximately $$\Delta D = V \times 2 d_{33}$$

The expansion range in the vertical and radial directions can be doubled by driving the internal and external electrodes with opposite voltages.

### Driving Piezoelectric Tubes with the TD250 Amplifier

The TD250 is an ultra-low noise, six-channel 250V amplifier optimized for driving piezoelectric tube scanners. Although many configurations are possible, the driven internal electrode configuration shown below is simple and provides the maximum X, Y and Z travel range.

Driving piezoelectric tubes with the TD250

In the driven internal electrode configuration, the X and Y electrodes are driven in the standard way with equal and opposite voltages. By applying the full-scale negative voltage to the internal electrode, a contraction equal to half the vertical scan range is obtained. This method exploits the higher positive electric field strength of the piezoelectric material, which is usually five times the negative electric field strength. Care must be taken not to apply positive voltages to the internal electrode since this can lead to depolarisation.

### Driving Piezoelectric Tubes with PDm200B Modules

The PDm200B can be configured in the $\pm$200V range to drive piezoelectric tubes. The connection diagram for a typical positioning application is illustrated below. Two amplifiers are required for the $x$ and $y$ axis.The centre electrode can be grounded or driven if vertical deflection is required.

Driving piezoelectric tubes with the PDm200B

### Mounting

The most common mounting configuration is the cantilever arrangement with a fixed base and free end. The base can be bonded directly to an insulating surface with a two part epoxy such as Araldite, or a high viscosity Cyanoacrylate such as Loctite Super Glue Gel. Piezoelectric Tubes can also be bonded to a conductive surface by removing a small amount of electrode as described in “Electrodes” below.

### Electrodes

The tubes are supplied with a Nickel thin film electrode. The internal electrode is continuous and the external electrodes are quartered. Electrode area can be removed by etching with dilute Nitric Acid. Custom electrode configurations are available on request.

In applications that require high magnetic fields, the Nickel electrodes can be replaced with Copper or Gold. Copper is an economical choice but Gold provides excellent corrosion resistance and electrical conductivity.

### Electrical Current Requirements

Calculate Power Bandwidth

The required current is $I = C~dV/dt$ where $I$ is the current, $C$ is the effective capacitance, and $dV/dt$ is the voltage rate of change. For a sine-wave, the required peak current is equal to:
$$I_p = 2 \pi f V_{p-p}$$ where $V_{p-p}$ is the peak-to-peak voltage. For a triangle wave, the required peak current is equal to: $$I_p = 2 C f V_{p-p}$$

### Connecting Wires

Wires can be attached using conductive epoxy (Circuitworks CW2400) or standard solder and Rosin flux. After flux application, a one second contact with a 300C iron is recommended.

Piezoelectric tubes can also be supplied with attached wires. A number of options are available:

• 10cm AWG36 wires (-W10)
• 10cm AWG36 wires connected to a TD250 compatible male panel-mount DSUB9 connector (-DCon)
• Specified length shielded multi-conductor cable (-CableX, X is the length in cm)

### Vacuum Compatibility

Piezoelectric tubes do not contain any outgassing materials and are fully vacuum compatible.

### Cryogenic Compatibility

The material PZT-5H works well at cryogenic temperatures. As a guide, the sensitivity reduces by a factor of four. However, at cryogenic temperatures the applied voltage can be increased to +/-2 kV/mm, which can regain or exceed the room temperature deflection but requires a high voltage.

For example, the predicted deflection of the TB6309 tube is +/-10 um with an applied voltage of +/-250 V. However, the full +/-40 um range can be recovered by increasing the voltage to +/-1 kV.

### Options / OEM Customization

• Custom dimensions and thickness
• Custom electrode configurations
• Custom wiring arrangements / connectors
• Mounting platform design and fabrication

### Piezoelectric Properties

The piezoelectric material is similar to PZT-5H and Navy Type VI.

Property Symbol Value Unit
Piezoelectric constants d33 600 10-12 m/V
d31 -270 10-12 m/V
g33 19.4 10-3 Vm/N
g31 -9.2 10-3 Vm/N
Electro-mechanical
coupling coefficients
Kp 0.65 NA
Kt 0.37 NA
K31 0.38 NA
Frequency constant Np 1980 Hz-m
Nt 1950 Hz-m
N31 1450 Hz-m
Elastic constant Y33 5.3 1010 N/m2
Y11 7.2 1010 N/m2
Q Factor Qm 80 NA
Dielectric constant e33 ⁄ e0 3500 @1 kHz
Dissipation factor tan δ 2.5 % @ 1 kHz
Currie Temperature Tc 220 C
Density ρ 7.8 g/cm3