Standards form an integral part of the work we do as engineers, providing a common language for communicating complex information. But standards committees are not omnipotent and sometimes revised standards are not universally adopted. This has happened in the case of the standards for piezoelectric materials, particularly for quartz. This blog post explains the multiple standards used to describe piezoelectrics in literature. Although the particular focus of this post is on quartz, the standards described apply for any piezoelectric material.

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Piezoelectric Materials

Piezoelectric materials become electrically polarized when strained. From a microscopic perspective, the displacement of charged atoms within the crystal unit cell (when the solid is deformed) produces a net electric dipole moment within the medium. In certain crystal structures, this combines to give an average macroscopic dipole moment and a corresponding net electric polarization. This effect, known as the direct piezoelectric effect, is always accompanied by the inverse piezoelectric effect, in which the solid becomes strained when placed in an electric field.

Several material properties must be defined in order to fully characterize the piezoelectric effect within a given material. The relationship between the material polarization and its deformation can be defined in two ways: the strain-charge or the stress-charge form. Different sets of material properties are required for each of these equation forms.

To complicate things further, there are two standards used in the literature: the IEEE Standard and the IRE standard, and the material properties take different forms within the two standards. IEEE actually revised the standard in , but this version of the standard contained a number of errors and was subsequently withdrawn. Confused yet? I was when I first started reading the literature!

Today’s blog post describes in detail the different equation forms and standards, with a focus on the particular case of quartz — the material that causes the most confusion. In both academia and industry, the quartz material properties are commonly defined within the older IRE standard. Meanwhile, other materials are now almost always defined using the IEEE standard. To make matters worse, it is not common to indicate which standard is being employed when specifying the material properties.

Two Equation Forms: The Strain-Charge and the Stress-Charge Form

The coupling between the structural and electrical domains can be expressed in the form of a connection between the material stress and its permittivity at constant stress or as a coupling between the material strain and its permittivity at constant strain. The two forms are given below.

Strain-Charge Form

The strain-charge form is written as:

\begin{array}{l}
\bf{S}=s_E \bf{T}+d^T \bf{E} \\[3mm]
\bf{D}=d \bf{T}+\epsilon_0 \epsilon_{rT} \bf{E}
\end{array}

where S is the strain, T is the stress, E is the electric field, and D is the electric displacement field. The material parameters sE, d, and εrT correspond to the material compliance, coupling properties, and relative permittivity at constant stress. ε0 is the permittivity of free space. These quantities are tensors of rank 4, 3, and 2, respectively. The tensors, however, are highly symmetric for physical reasons. They can be represented as matrices within an abbreviated subscript notation, which is usually more convenient. In literature, the Voigt notation is almost always used.

Within this notation, the above two equations can be written as:

Stress-Charge Form

The stress-charge form is as follows:

\begin{array}{l}
\bf{T}=c_E \bf{S}-e^T \bf{E} \\[3mm]
\bf{D}=e \bf{S}+\epsilon_0 \epsilon_{rS} \bf{E}
\end{array}

The material parameters cE, e, and εrS correspond to the material stiffness, coupling properties, and relative permittivity at constant strain. ε0 is the permittivity of free space. Once again, these quantities are tensors of rank 4, 3, and 2 respectively, but can be represented using the abbreviated subscript notation.

Using the Voigt notation and writing out the components gives:

The matrices defined in the above equations are the key material properties that need to be defined for a piezoelectric material. Note that for many materials, a number of the elements in each of the matrices are zero and several others are related, as a result of the crystal symmetry.

Using the international notation for describing crystal symmetry, the symmetry group of quartz is Trigonal 32. The nonzero matrix elements take different values within different standards, which can result in confusion when specifying the material properties for a simulation, especially for quartz, where two different standards are commonly employed.

Finally, there is another complication in the case of quartz. Quartz crystals do not have symmetry planes parallel to the vertical axis. Correspondingly, they occur in two types: left- or right-handed (this is known as enantiomorphism). Each one of these enantiomorphic forms results in different signs for particular elements in the material property matrices.

The material property matrices appropriate for quartz and other Trigonal 32 materials are shown below. Note that the symmetry relationships between elements in the matrix hold irrespective of the standard used or whether the material is right- or left-handed.

Two Standards: IRE and IEEE

Having defined a set of material properties in terms of matrices that operate on the different components of the stress or the strain in the x,y,z axes system, all that remains is to define a consistent set of axes to use when writing down the material properties.

Correspondingly, all of the standards define a consistent set of axes for each of the relevant crystal classes. Unfortunately, in the particular case of quartz, subsequent standards have not used the same sets of axes, and the adoption of the most recent standard has not been widespread. Therefore, it is important to understand exactly which standard a given set of material properties is defined in.

The two relevant standards are:

• The IEEE standard:
  • This is usually employed for materials other than quartz in most of the literature. Sometimes, it is used to specify the quartz material properties, for example, B. A. Auld’s book Acoustic Fields and Waves in Solids employs this standard.
• The IRE standard:
  • This is usually used for the material properties of quartz in literature.

The orientation of the axes set with the crystal can be determined by specifying the orientation with respect to the atoms in the unit cell of the crystal (which is not that helpful in practice) or by specifying the orientation with respect to the crystal forms. A crystal form is a set of crystal faces or planes that are related by symmetry. Particular forms commonly appear in crystal specimens found in rocks and are used to identify different minerals.

The Quartz Page has a series of helpful figures for identifying the common crystal forms, termed m, r, s, x, and z, as well as a further page specifying the Miller indices of the corresponding planes. Since the standards typically use crystal forms to orientate the axes, this approach is adopted in the figure below, which shows the two axes sets that relate to the and standards. Note that both left- and right-handed quartz are shown in the figure.

Crystallographic axes defined for quartz within the IEEE standard (solid lines) and the standard (dashed lines). Click on the image to view a larger version.

As a result of the different crystal axes, the signs of the material properties for both right- and left-handed quartz can change depending on the particular standard employed. The table below summarizes the different signs that occur for the quartz material properties:

IRE Standard

IEEE Standard

Material Property

Right-Handed Quartz

Left-Handed Quartz

Right-Handed Quartz

Left-Handed Quartz

sE14

+

+

—

—

cE14

—

—

+

+

d11

—

+

+

—

d14

—

+

—

+

e11

—

+

+

—

e14

+

—

+

—

Two Definitions for the Crystal Cut

Usually, piezoelectrics, such as quartz, are supplied in thin wafers that have been cut at a particular angle, with respect to the crystallographic axes. The orientation of a piezoelectric crystal cut is frequently defined by the system used in both the and standards. The orientation of the cut, with respect to the crystal axes, is specified by a series of rotations, using notation that takes the form illustrated below:

Diagram showing how a GT cut plate of quartz is defined in the IEEE standard. The crystal shown is right-handed quartz.

The first two letters of the notation given in the brackets describe the orientation of the thickness and length of the plate that is being cut from the crystal. From the figure on the left, it is clear that the thickness direction (t) is aligned with the Y-axis and the length direction (l) is aligned with the X-axis. The plate also has a third dimension, its width (w). After the first two letters, a series of rotations are defined about the edges of the plate.

In the example above, the first rotation is about the l-axis, with an angle of -51°. The negative angle means that the rotation takes place in the opposite direction to a right-handed rotation about the axis. Finally, an additional rotation about the resulting t-axis is defined, with an angle (in a right-handed sense) of -45°.

Most practical cuts use one or two rotations, but it is possible to have up to three rotations within the standard, allowing for completely arbitrary plate orientations.

Note that since the crystallographic axes are defined differently in the and the standards, the crystal cut definitions differ between the two. A common cut for quartz plates is the AT cut, which is defined in the two standards in the following manner:

Standard

AT Cut Definition

IRE

(YXl) 35.25°

IEEE

(YXl) -35.25°

The figure below shows how the two alternative definitions of the AT cut correspond to the two alternative definitions of the axes employed in the standards.

The AT cut of quartz is defined as (YXl) 35.25° in the IRE standard and (YXl) -35.25° in the IEEE standard. The figure shows the cut defined in a right-handed crystal of quartz. The reason for the difference between the standards is related to the different conventions for the orientation of the crystallographic axes. In the IRE standard, the rotation occurs in a positive or right-handed sense about the l-axis (which in this case is aligned with the X-axis). As a result of the different axes set employed in the IEEE standard, the rotation corresponds to a negative angle in this standard.

Next Steps

We have now seen how the two different standards result in different definitions of the material properties and different definitions of the crystal cuts.

In a follow-up blog post, we will explore how to set up a COMSOL Multiphysics model using the two standards. COMSOL Multiphysics provides material properties for quartz using both of the available standards, so it is possible to set up a model using whichever standard you are most familiar with. Stay tuned for that.

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Exploring Piezoelectric Materials: Types, Properties, and Technological Impact

Over the years, advances in material science have created different piezoelectric materials such as single crystals, ceramics, and thin films. This article takes a close look at piezoelectric materials including their properties, types, how they work, and their uses. It highlights their importance in linking mechanical and electrical engineering, driving innovation in many areas.

Catalog

Figure 1: Piezoelectric Material

What Is Piezo?

The word "piezo" comes from the Greek word "piezein," means "to press" or "pressure." This fits well with its use in science for piezoelectricity. In , French physicists Jacques and Pierre Curie discovered piezoelectricity. They found that when certain crystals like tourmaline, quartz, topaz, and Rochelle salt, were pressed, they produced an electrical charge. They also saw that these crystals could change shape when an electrical current was applied showing that the process could work both ways.

This discovery led to the creation of various piezoelectric devices. During World War I, piezoelectricity was mainly used in ultrasonic submarine detectors. Today, piezoelectric materials are used in many things. They are found in everyday items like electric cigarette lighters and inkjet printers, as well as in advanced technologies like medical ultrasound imaging and precision motion control in robotics.

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Types of Piezoelectric Materials

Figure 2: Examples of Piezoelectric Materials

Single Crystal Piezoelectric Materials

Single crystal piezoelectric materials are characterized by their continuous and uniform crystal lattice, free from grain boundaries. This uniform structure often leads to better electromechanical coupling efficiencies compared to other piezoelectric materials. Examples of such materials include quartz and langasite. These single crystals are produced using precise growth methods like the Czochralski process or hydrothermal synthesis. Their exceptional performance makes them perfect for precise applications like advanced medical imaging systems, telecommunications resonators and filters, and vibration monitoring in aerospace.

Figure 3: Piezo Crystal Quartz Material

Ceramic Piezoelectric Materials

Piezoelectric ceramics are made from perovskite-structured materials like lead zirconate titanate (PZT). These materials are polycrystalline and are created by sintering powdered substances. Their piezoelectric properties are developed through a poling process and aligns the electric dipoles by applying an external electric field. These ceramics can be easily shaped into various forms and sizes. Their durability and cost-effectiveness make them popular for use in actuators, sensors, ultrasonic transducers, and consumer electronics buzzers.

Figure 4: Structure of PZT Type Piezoelectric Ceramic

Thin Film Piezoelectric Materials

Thin film piezoelectrics are made by depositing layers that range from a few nanometers to several micrometers in thickness using advanced fabrication techniques like sputtering, chemical vapor deposition or pulsed laser deposition. Common materials used in thin films include PZT, zinc oxide (ZnO), and aluminum nitride (AlN). The thinness of these films allows them to be integrated into microelectromechanical systems (MEMS) and nanoelectromechanical systems (NEMS), enhancing their functionality in compact devices such as microphones, microswitches and advanced sensor arrays. Their compatibility with standard semiconductor processes and scalability makes them suitable for integrated circuits and flexible electronics.

Figure 5: AlN Piezoelectric Thin Films

Figure 6: Bulk Piezo Elements

Choosing between thin-film and bulk piezoelectric materials depends on the application's specific needs for precision, power and durability. Thin-film piezo materials are suited in small-scale technologies. In contrast, bulk piezo materials are preferred in more demanding, larger-scale applications. The table below compares thin-film piezo materials and bulk piezo materials based on their thickness, manufacturing techniques, key features and applications.

Category Thin-Film Piezo Materials Bulk Piezo Materials Thickness A few nanometers to several micrometers Several millimeters to centimeters Manufacturing Techniques Sputtering, pulsed laser deposition, chemical vapor deposition Pressing, extrusion, machining Features High-Frequency Response: Quick response times High Power Generation: Produces power under mechanical stress Flexibility: Applicable to flexible surfaces Durability: Strong and durable, suitable for heavy loads and harsh conditions Precision: Precise control on a microscopic level Versatility: Easily shaped and sized for specific needs Applications Microelectronics and MEMS: Accelerometers, gyroscopes, inkjet printer heads Energy Harvesting: Converts mechanical stress from vibrations into electrical energy Medical Devices: Ultrasonic transducers for imaging and therapy Actuators and Sensors: Large actuators in automotive and aerospace industries, high-load sensors Telecommunications: Filters and resonators in mobile phones and communication devices Sonar and Ultrasonic Devices: Sonar systems for naval use, industrial ultrasonic cleaners

Thin-Film PZT and Deposition Methods

Thin-film lead zirconate titanate (PZT) materials are used in sensors, actuators, and microelectromechanical systems (MEMS) because of their great piezoelectric properties. The composition and effectiveness of PZT thin films depend a lot on their deposition methods that may affect their structure, orientation, and piezoelectric performance. The three main deposition techniques: sol-gel, sputtering, and Metal Organic Chemical Vapor Deposition (MOCVD).

Figure 7: Flexible Thin-Film PZT

Sol-Gel Process

The sol-gel process is a cost-effective way to deposit PZT thin films and allowing control over film composition at the molecular level. This technique starts with preparing a colloidal solution (sol) that turns into a gel. Important steps include hydrolyzing and polymerizing metal alkoxides. The resulting gel is applied to a substrate using spin coating or dip-coating, followed by heat treatment to remove organic components and crystallize the PZT phase.

Figure 8: Sol-Gel Process for PZT Thin Films

Advantages

• Allows fine control over stoichiometry, improving piezoelectric properties

• Uses lower temperatures compared to other methods

Challenges

• It's hard to get consistent thickness and composition across large areas

• High shrinkage during drying and firing often causes cracks

Sputtering

Sputtering is a physical vapor deposition (PVD) technique where high-energy particles knock material off a target then deposits onto a substrate. For PZT films, RF magnetron sputtering is used involving a plasma of argon ions hitting the PZT target.

Figure 9: Sputter Deposition Method of Thin-Film Deposition

Advantages

• Produces films with good adhesion and density

• Suitable for coating large substrates uniformly

Challenges

• Stress can build up in the films affecting their properties

• The target's composition may change during sputtering due to differential sputtering yields

Metal Organic Chemical Vapor Deposition (MOCVD)

MOCVD involves decomposing metal-organic precursors in a vapor phase and react or decompose on a heated substrate to form a thin film. This method is preferred for producing high-purity, well-crystallized films suitable for electronic applications.

Advantages

• Provides excellent film uniformity and conformity even on complex-shaped substrates

• Good for high-volume production

Challenges

• Requires higher temperatures than other methods

• Handling and storage of metal-organic precursors can be hazardous

Figure 10: Metal Organic Chemical Vapor Deposition

How Materials Act Under Stress

Behavior Under Compression

When materials like quartz or barium titanate are squeezed, they change in ways that impact their use in various devices. These materials have special structures that create electrical charges when they are pressed. As they are compressed, they shrink and their internal structure changes.

This squeezing causes the electrical charges inside the crystal to become unevenly distributed. The pressure moves ions in the crystal's structure, creating an electric field. This happens because the positive and negative charge centers in the material shift. The amount of electrical response depends on the type of crystal, the force applied and the crystal's direction relative to the force.

For example, in sensors, the voltage produced by the crystals can measure the force applied making them perfect for detecting pressure and monitoring loads. In actuators, applying an electrical field can make the crystal change shape, allowing precise control of movements in things like ultrasonic devices and car fuel injectors.

Figure 11: Piezoelectric Materials Works

Piezoelectric Response to Pressure

When piezoelectric materials face mechanical pressure, their molecules realign, affecting their electrical properties. The force changes the molecular structure, aligning regions with uniform electrical direction, increases electrical polarization.

This alignment boosts the charge separation in the material, enhancing its electrical polarization. In simple terms, the pressure makes the dipoles (molecules with two opposite charges) more uniform, creating a stronger electric field for a given force.

The ability to control this response accurately under different pressures makes piezoelectric materials very useful in many technologies. Their capability to convert mechanical pressure into electrical signals and vice versa allows them to be used effectively in tasks like generating precise electronic frequencies and monitoring vibrations in industrial settings.

The Piezoelectric Effect

Figure 12: The Piezoelectric Effect

Turning Mechanical Energy into Electrical Energy with the Piezoelectric Effect

The piezoelectric effect changes mechanical energy into electrical energy by deforming certain crystal materials. These materials, known as piezoelectrics include natural substances like quartz and synthetic ones like advanced ceramics.

When a piezoelectric material faces mechanical stress such as being squeezed, twisted, or bent, its crystal structure, doesn't have a central symmetry and gets disturbed. This disturbance shifts the charge centers in the crystal causing polarization and creating an electrical potential at certain points in the material.

Key points of this process:

The electrical charge produced matches the amount of mechanical stress applied. This means the electrical output can be precisely controlled based on the known force applied;

When the force is removed, the material returns to its original state and the electrical charge goes away. This ensures the material's durability and reliability good for devices that need to work well repeatedly.

Turning Electrical Energy into Mechanical Energy with the Reverse Piezoelectric Effect

The reverse piezoelectric effect changes electrical energy back into mechanical energy. Applying an electrical voltage to a piezoelectric material creates an electric field that changes the crystal lattice structure, altering the material's dimensions.

This effect is used in precision actuators in optical instruments and micro-positioning systems. The reverse piezoelectric effect ensures that small electrical inputs result in precise, controlled mechanical adjustments, helping advancements in robotics, automotive technology, medical instruments, and telecommunications.

The dual ability of the piezoelectric effect to act as both a mechanical-to-electrical and electrical-to-mechanical transducer supports technological advancements. It connects the mechanical and electrical domains, expanding modern engineering and innovation.

Figure 13: Direct and Reverse Piezoelectric Effect

Comparing Non-Piezoelectric and Piezoelectric Materials

Non-piezoelectric and piezoelectric materials are different in how they handle mechanical and electrical energy. Non-piezoelectric materials like steel and aluminum can conduct electricity but don't create an electric charge when stressed. Piezoelectric materials, such as quartz and certain ceramics, can change mechanical energy into electrical energy because of their special crystal structure.

Non-piezoelectric materials have symmetrical crystal lattices, so they don't produce an electric dipole when stressed. Piezoelectric materials have asymmetrical crystal lattices, that allows them to generate an electric charge when under stress. This deformation causes internal polarization and creating electrical potential.

Non-piezoelectric materials behave like regular conductors or insulators based on their electron mobility and band structure and they don't create an electric charge when deformed. Piezoelectric materials exhibit two effects: the direct piezoelectric effect, where mechanical stress generates an electric charge, and the inverse piezoelectric effect, where an electric field causes mechanical deformation. These characteristics make piezoelectric materials suitable for use in sensors and actuators.

Due to their different properties, non-piezoelectric and piezoelectric materials are used in different applications. Non-piezoelectric materials are used in structural components, electrical wiring, and standard electronic parts where strength and conductivity are important. Piezoelectric materials are utilized in fields that require precise control and mechanical-electrical energy conversion, such as ultrasound equipment, precision positioning devices, and various sensors and actuators good for advanced technologies.

Applications of Piezoelectricity

Consumer Electronics: In smartphones and other devices, piezoelectric parts are used in speakers and microphones. They turn electrical signals into sound vibrations or sound vibrations into electrical signals for audio input.

Automotive Industry: Modern cars use piezoelectric sensors for many purposes like controlling the fuel injection in engines and monitoring tire pressure.

Environmental Monitoring: Piezoelectric sensors detect pressure changes, vibrations, and sounds. They are used for checking environmental conditions and ensuring the safety of buildings and bridges.

Energy Harvesting: Piezoelectric materials can capture energy from mechanical stress. For example, floors that convert footsteps into electrical energy can power lights and electronics in busy areas, helping create sustainable environments.

High-Voltage Piezoelectric Lighters: These lighters used for lighting gas stoves and barbecues and create a high voltage from a small mechanical click, producing a spark to light the burner. This shows the practical use of piezoelectric materials.

Medical Imaging: Piezoelectric crystals are useful in ultrasound machines. They produce sound waves that bounce off tissues and organs, creating images for diagnosis.

Precision Actuators in Scientific Instruments: Piezoelectric materials in precision actuators create tiny movements for optics and nanotechnology. These actuators adjust mirrors, lenses, and other parts with microscopic accuracy for scientific research and semiconductor manufacturing.

Conclusion

Studying piezoelectric materials shows a strong connection between physics and engineering, demonstrating how their natural properties can be used for many technological purposes. The versatility of piezoelectric materials available as both strong bulk materials and flexible thin films, makes them suitable for various applications, such as energy harvesting, environmental monitoring, and developing sustainable technologies. As innovation continues, research and development in piezoelectric materials are more important, promising improvements in efficiency, precision, and functionality for future technologies.

Frequently Asked Questions [FAQ]

1. What causes electricity to be produced from piezoelectric effect?

The piezoelectric effect occurs when certain materials produce an electric charge in response to mechanical stress. These materials, a crystals like quartz, ceramics like barium titanate and some polymers, possess a crystal lattice structure that is non-centrosymmetric, meaning it lacks a center of symmetry. When mechanical force such as pressure or vibration is applied, this structure becomes distorted. This distortion displaces the ions within the lattice, creating areas with positive and negative charges. The spatial separation of these charges results in an electric potential generating electricity. This effect is reversible and applying an electric field to these materials will also induce mechanical stress.

2. What device uses the piezoelectric effect?

Devices that utilize the piezoelectric effect are varied and include both everyday and specialized equipment. Common applications are:

Quartz watches: Using the regular vibrations of quartz under an electric field to keep time accurately.

Medical ultrasound devices: Generating sound waves that echo inside the body to create diagnostic images.

Fuel injectors in cars: Using piezoelectric actuators to control the timing and amount of fuel injected into the engine cylinders.

Piezoelectric sensors and accelerometers: Measuring changes in pressure, acceleration, strain, or force by converting them into an electrical signal.

3. How many volts is a piezo?

The voltage output of a piezoelectric element can vary widely depending on its size, material, and the amount of mechanical stress applied. A small piezo element like those found in lighters or electronic devices can produce a voltage spike ranging from a few volts to several hundred volts. However, these outputs are generally at very low currents and last only microseconds.

4. Does a piezo need a resistor?

In many applications, a resistor is used with a piezoelectric element to limit the current and protect other components in the circuit from the high voltage spike produced when the piezo is activated. The value of the resistor depends on the specific requirements of the circuit including the desired response time and sensitivity. Without a resistor, the piezo can potentially damage connected electronic components due to the high initial voltage spike.

5. How is piezoelectric related to human power?

The piezoelectric effect is directly applicable to harnessing human power in innovative ways. It can convert mechanical energy from human activities, such as walking or pressing buttons, into electrical energy. This technology is explored in various applications:

Energy-harvesting floor tiles: These tiles generate electricity from the pressure of footfalls in busy areas like subway stations or malls.

Wearable technology: Embedding piezoelectric materials in shoes or clothing to generate power for small devices through normal body movements.

Medical implants: Using body movements to power devices like pacemakers, reducing or eliminating the need for external batteries.