25.1 Piezoelectric Effect and Ultrasonic Waves

Piezoelectric Effect

The piezoelectric effect is the phenomenon in which certain crystalline materials generate an electric potential difference across their faces when subjected to mechanical stress (compression or tension). Conversely, when an electric voltage is applied across such a crystal, it undergoes mechanical deformation (expansion or contraction). This reverse process is called the inverse piezoelectric effect.

Key Materials

Mechanism

In a piezoelectric crystal, the positive and negative charge centres do not coincide when the crystal is deformed. This asymmetry creates an electric dipole moment, resulting in a measurable voltage across the crystal faces.

• Direct piezoelectric effect: Mechanical stress → Electric voltage
• Inverse piezoelectric effect: Applied voltage → Mechanical vibration

Medical Application

In medical science, piezoelectric transducers serve as both transmitters and receivers of ultrasonic waves:

1. Transmission: A high-frequency alternating voltage (AC) is applied to the crystal. By the inverse piezoelectric effect, the crystal vibrates at the same frequency, generating ultrasonic pressure waves that travel into the body.
2. Reception: Reflected ultrasonic waves returning from internal structures cause the crystal to vibrate, generating a voltage signal (direct piezoelectric effect) that is processed to form an image.

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Ultrasonic Waves

Ultrasonic waves (ultrasound) are longitudinal mechanical waves with frequencies above the upper limit of human hearing, i.e., above $20,000\text{ Hz}$ ($20\text{ kHz}$). Medical ultrasound typically operates in the range of $1\text{ MHz}$ to $20\text{ MHz}$.

Properties Relevant to Medical Imaging

• Short wavelength: High-frequency waves have short wavelengths ($\lambda =v/f$), allowing them to resolve fine structural details and detect small features.
• Non-ionizing: Unlike X-rays, ultrasound does not carry enough energy to ionize atoms, making it safe for repeated use and for imaging sensitive patients such as pregnant women.
• Reflection at boundaries: Ultrasound is partially reflected at interfaces between tissues of different acoustic impedance. These echoes are used to construct images.
• Real-time imaging: Ultrasound provides dynamic, real-time images of moving structures (e.g., a beating heart or a moving foetus).

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Generating Ultrasound: The Ultrasonic Transducer

An ultrasonic transducer exploits the inverse piezoelectric effect:

1. A high-frequency AC voltage (e.g., $5\text{ MHz}$) is applied across a piezoelectric crystal (typically PZT).
2. The crystal alternately expands and contracts at the same frequency.
3. This mechanical vibration launches longitudinal (compression) waves into the surrounding medium.

The same transducer then switches to receive mode: reflected echoes cause the crystal to vibrate, producing a voltage that is amplified and processed.

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Ultrasound Diagnostics

Pulse-Echo Technique

In medical ultrasound imaging, short pulses of ultrasound are transmitted into the body. At each tissue boundary, a fraction of the pulse is reflected (echo) and the rest is transmitted deeper. The time delay $t$ between transmission and reception of an echo is used to calculate the depth $d$ of the reflecting surface:

$d=\frac{v\cdot t}{2}$

where $v$ is the speed of ultrasound in tissue (approximately $1500{\text{ m s}}^{-1}$) and the factor of 2 accounts for the round trip.

A-Scan and B-Scan

Acoustic Impedance and Coupling Gel

The fraction of ultrasound reflected at a boundary depends on the acoustic impedance $Z=\rho v$ of the two media (where $\rho$ is density). A large impedance mismatch (e.g., between air and skin) causes almost total reflection. To prevent this, a coupling gel is applied between the transducer and the skin, eliminating the air gap.

Advantages of Ultrasound over X-rays

• Non-ionizing — safe for foetuses and repeated examinations.
• Real-time — can image moving structures dynamically.
• Distinguishes soft tissues — X-rays show poor contrast between soft tissues; ultrasound detects density differences well.
• Portable and relatively inexpensive.

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SONAR — An Application of Ultrasound

SONAR (Sound Navigation And Ranging) uses the same pulse-echo principle to measure the depth of the ocean floor or detect underwater objects:

$d=\frac{v\cdot t}{2}$

where $v\approx 1500{\text{ m s}}^{-1}$ in seawater and $t$ is the time between pulse transmission and echo reception.