The piezoelectric effect

The piezoelectric effect is the appearance of a potential difference (voltage) across certain crystals when they are squeezed, stretched or bent. One face becomes positive and the opposite face negative. It also works the other way round: applying a potential difference makes the crystal change shape, which is called the converse (or inverse) piezoelectric effect. Quartz is the best known piezoelectric material, and the effect is used in ultrasound scanners, quartz clocks and microphones.

What is the piezoelectric effect?

The word comes from the Greek piezein, to press: piezoelectricity is electricity from pressure. It was discovered in 1880 by the brothers Pierre and Paul-Jacques Curie. They found that compressing certain crystals, including quartz, tourmaline and Rochelle salt, along particular directions produced a voltage on the crystal's surface. A year later they observed the converse effect.

Reverse the force, from squeezing to stretching, and the p.d. reverses too. Reverse the applied p.d. and the crystal changes shape the other way. So an alternating p.d. makes a piezoelectric crystal vibrate, and a vibrating crystal produces an alternating p.d.

Why some crystals are piezoelectric

A crystal is a regular lattice of positive and negative ions. In most crystals the arrangement is symmetrical, so squeezing it moves the charges without separating them overall. Piezoelectric materials have no centre of symmetry. When a stress is applied, the centres of the positive and negative charge shift relative to each other, forming tiny electric dipoles. Inside the material neighbouring dipoles cancel, but at the surfaces they do not, so one face is left positive and the other negative.

In the converse effect, an electric field pushes the positive and negative ions in opposite directions, which slightly stretches or compresses the lattice. The change in size is very small, but it happens very quickly, which is why piezoelectric crystals are good at making high-frequency vibrations.

Piezoelectric materials

Uses of the piezoelectric effect

Ultrasound transducers

In medical ultrasound, the probe held against the patient is a transducer containing a piezoelectric crystal, and it is both the transmitter and the receiver:

1. Generating ultrasound (converse effect). An alternating p.d. at ultrasonic frequency is applied to the crystal, so it vibrates and sends ultrasound into the body. It is driven in short bursts, called pulses.
2. Echoes. Some of each pulse reflects at every boundary between tissues, for example between muscle and bone.
3. Detecting ultrasound (direct effect). Between pulses, returning echoes make the crystal vibrate, which produces a small alternating p.d. that the scanner measures.
4. Building the picture. The time each echo takes to return gives the depth of the boundary, and its strength tells you about the boundary. One line of echoes is an A-scan; sweeping the beam builds a 2D B-scan image.

Both AQA (3.10.4.1, in the Medical physics option) and OCR (6.5.3) ask you to explain how a piezoelectric transducer generates and detects ultrasound pulses.

Quartz clocks and watches

A quartz watch contains a tiny quartz crystal in an electronic circuit. The converse effect makes it vibrate, the direct effect turns the vibration back into an electrical signal, and the crystal resonates at a very steady frequency. NIST explains that a watch crystal is designed to run at 32,768 Hz: when it has oscillated 32,768 times, the watch records that one second has passed.

Microphones, pickups and sensors

Sound waves pressing on a piezoelectric material produce a matching alternating p.d., so it can act as a microphone or as a pickup on an acoustic guitar. The same idea gives pressure sensors and accelerometers. Run the other way, a piezoelectric disc driven by an alternating p.d. works as an earphone, and a sharp squeeze of PZT can produce a high enough p.d. to make a spark.

Worked examples

Example 1: depth from an echo

Ultrasound moves at 1540 m/s in soft tissue. The echo of one pulse from a boundary returns to the transducer 130 μs after the pulse was sent. How deep is the boundary?

1. Distance travelled by the pulse = speed × time = 1540 × 130 × 10⁻⁶ = 0.200 m.
2. The pulse goes there and back, so the depth is half of that: 0.200 ÷ 2 = 0.100 m, or 10.0 cm.

Example 2: wavelength in tissue

A transducer drives its crystal at 4.0 MHz. How long is each wave once it is inside the body, where sound moves at 1540 m/s?

• λ = v ÷ f = 1540 ÷ (4.0 × 10⁶) = 3.85 × 10⁻⁴ m, about 0.39 mm.
• Higher frequencies give shorter wavelengths and finer detail, but they do not travel as deep. The wave speed calculator checks v = fλ.

Example 3: why ultrasound gel is used

The fraction of ultrasound intensity reflected at a boundary between materials of acoustic impedance Z₁ and Z₂ is:

OpenStax gives acoustic impedances of about 429 kg m⁻² s⁻¹ for air and 1.70 × 10⁶ kg m⁻² s⁻¹ for muscle. For an air gap between the probe and the skin:

• I_r ÷ I_i = ((1.70 × 10⁶ − 429) ÷ (1.70 × 10⁶ + 429))² = 0.999.
• About 99.9% of the ultrasound would reflect straight back and almost none would enter the body.
• Gel has an impedance close to that of tissue, so it removes the air gap and lets most of the ultrasound through. OCR calls this impedance matching.

Common mistakes

• Mixing up the two effects. Force in, p.d. out is the direct effect; p.d. in, change of shape out is the converse effect.
• Saying the crystal produces a current on its own. It produces a p.d.; a current only flows if there is a complete circuit.
• Saying any crystal is piezoelectric. Only crystals without a centre of symmetry are.
• Forgetting to halve the echo distance. The pulse travels to the boundary and back.
• Saying the transducer sends ultrasound continuously. It sends short pulses and listens for echoes in between.

Practise with a short timed paper

Ultrasound and the piezoelectric transducer are in the second year of A-level Physics: OCR covers them in module 6, and AQA in the Medical physics option. The daily A-level Physics: Year 2 paper is a short timed paper of 8 questions, with a new one every day. For the waves behind ultrasound, see sound waves.

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