11 Dielectric Properties Lecture 10

K Asokan

Learning Outcomes:

From this module students may get to know about the following:

1.     Detailed study pyroelectricity, crystal symmetry and pyroelectric materials..

2.     The modeling of pyroelectric effect.

3.     You will learn about application of pyroelectric.

10.1 Pyroelectricity:

Pyroelectricity is the property presented by certain materials that exhibit an electricpolarization ΔP when a temperature variation ΔT is applied uniformly:

ΔP = γ.ΔT                                                                  ……….(1)

where γ is the pyroelectric coefficient at constant stress. Pyroelectric crystals actually have a spontaneous polarization, but the pyroelectric effect can only be observed during a temperature change.

yroelectric coefficient can be expressed as:

where: PS – spontaneous polarization.

The unit of pyroelectric coefficient is

If a pyroelectric crystal with an intrinsic dipole moment (top) is fashioned into a circuit with electrodes attached on each surface (FIG. 1), an increase in temperature T prompts the spontaneous polarization PS to decrease as the dipole moments, on average, diminish in magnitude. The horizontal tilting of the dipoles, (pictured at bottom of FIG. 1), signifies the effect. A current flows to compensate for the change in bound charge that accumulates on the crystal edges

FIG. 1 Schematic drawing showing the origin of the pyroelectric current

Another definition of pyroelectricity is ability to generation of induced charges on the crystal surface when they are heated or cooled. It is explained as a migration of positive and negative charges (and therefore establishment of electric polarization) to opposite ends of a crystal’s polar axis as a result of change in temperature. This can be expressed as follows:

Where:

Q – charges generated on the crystal surface,

S – surface of the crystal.

The relation between generated charges and polarization is:

Pyroelectricity can be visualized as one side of a triangle, where each corner represents energy states in the crystal: kinetic, electrical, and thermal energy (FIG. 2). The lines joining pairs of circles signify that a small change in one of the variables produces a corresponding change in the other. The three short bold lines that connect pairs of thermal, elastic, and electric variables define the physical properties of heat capacity, elasticity, and electrical permittivity, respectively. As an example, a small increase in temperature T produces an increase in entropy S proportional to the heat capacity divided by temperature. The diagram also illustrates coupled effects, denoted by lines joining pairs of circles at different corners of the diagram. The diagram’s colored lines indicate that the two contributions make up pyroelectric effect. In the first, the crystal is rigidly clamped under constant strain S, to prevent expansion or contraction. A change in temperature causes a change in electric displacement as shown by the green line, which signifies the primary pyroelectric effect. The second contribution—the secondary pyroelectric effect—is a result of crystal deformation: Thermal expansion causes a strain that alters the electric displacement via a piezoelectric process, as shown by the dashed red lines. Measuring the primary effect directly is extremely difficult. But the secondary effect can  be  readily  calculated  from  the  values  of  the  thermal  expansion  coefficient,  the  elastic stiffness, and the piezoelectric strain constant. So experimentally, the pyroelectric effect under the constraint of constant stress-the so-called total effect, the sum of red and green lines is usually measured [3].

FIG. 2  The  triangular  diagram illustrating the  thermodynamically reversible interactions  that  may  occur  among  the  thermal,  mechanical,  and  electrical properties of a crystal.

10.2 Simple model of the pyroelectric effect

In the microscopic scale, the pyroelectric effect occurs because of the asymmetric interaction potential caused by electrically charged atoms within the crystal structure of the material. This can be viewed schematically as presented in FIG. 3, which shows a two-dimensional lattice of cations and anions. The cations are displaced relative to the unit cells “centre” to give rise to an electrical dipole moment (or spontaneous polarization PS along the line (x1 – x2)

FIG. 3 Schematic two-dimensional presentation of pyroelectricity.

    The potential energy of any cation along this line will be an asymmetric form as illustrated in FIG.

Any excitation caused by an increase in lattice temperature will make it change its quantised energy level (E1 to En) within the well, and lead to a change in its mean equilibrium position in the lattice along the line A-B in FIG. 4. This gives a change in the overall electrical dipole moment, which appears as the macroscopic pyroelectric effect [13].

FIG. 4 Potential energy of cation in lattice of FIG. 3 along the line x1-x2, E1 to En represent the quantised energy levels for the cation and the locus A-B is the change in its equilibrium position with change in energy [13].

In dielectrics exhibiting pyroelectricity the dipole moment can arise as a consequence of the packing in an ionic crystal, because of the alignment of polarized covalent bonds in molecular crystals or crystalline polymers or because of atomic displacements controlled by the position of hydrogen ions in a hydrogen bonded crystal [13].

10.3. Theory of pyroelectricity

The first quantum theory of primary pyroelectric effect for the case of ionic crystals was formulated by Max Born in the year 1945 [14]. In this paper, Born had indicated that primary pyroelectric coefficient would be proportional to temperature T, though in his later treatise on lattice dynamics he predicted the T3 law for the pyroelectric coefficient [15]. Successively the physicists in their papers have proved clearly many interesting features of the theory, especially the role of mechanical and electrical anharmonicity in primary pyroelectricity which in fact was not noticed by Born. In principle, in order to understand pyroelectricity in any material, one has to consider the various mechanisms of the spontaneous polarization (such as ionic, electronic, orientational or surface charge) and study their variation with temperature. Generally in dielectrics, both the electronic polarization and the ionic polarization are due mainly to the elastic displacement of electron clouds and lattice vibrations within the atoms or molecules. Their interaction is an intramolecular phenomenon, and restoring force against the displacement is relatively insensitive to temperature, so electronic and ionic polarization processes are only slightly dependent on temperature. However, orientational polarization is a rotational process, which includes not only the thermal stimulation, but also mechanical friction processes. The rotation of a dipole in a material is like a small ball rotating in a viscous fluid. Under an external force, it tends to change from its original equilibrium state to a new, dynamic equilibrium state, and when the force is removed, it then relaxes back to its original equilibrium state. This polarization involves the inelastic movement of particles, and its interaction is an intermolecular phenomenon; hence, orientational polarization is strongly temperature-dependent. In the case of ionic crystals, there are two important mechanisms of polarization. One being responsible for absorption in the infrared i.e. the lattice or ionic polarization and the other in the ultraviolet i.e. the electronic polarization. In the very simplest and crude model known as the rigid ion model, the electron cloud around the ion is assumed to be rigid and consequently there is no contribution from electronic polarization.

10.4. Pyroelectricity and a crystal symmetry

By Neumann’s Principle polarization P must conform to the point-group symmetry of the crystal. It follows immediately that a pyroelectric effect cannot exist in a crystal possessing a centre of symmetry, a fact which provides a practical method of testing for the absence of a centre. A little thought shows that a pyroelectric effect can only proceed along a direction in a crystal which is unique, in the sense that it is not repeated by any symmetry element. If there should exist in the point group a unique direction which is an axis of symmetry (2-, 3-, 4- or 6-fold), this will necessarily be the direction of P. But the presence of such a unique symmetry axis is not essential for the existence of a pyroelectric effect. It may be noted, in passing, that a unique direction as defined above is not synonymous with a polar direction.

A polar direction is any direction of which the two ends are not related by any symmetry element of the point group. Thus, a diad axis in class 32 is a polar direction, but it is not a unique direction. All unique direction are polar, but only some polar directions are unique. The direction of the polarization vector P and the form of it components in the 21 non–centro symmetrical classes are depicted in Table 1.

Table 1. Crystal symmetry and a direction of polarization P.

Thus, the following 10 classes may theoretically show pyroelectricity under uniform heating or cooling:

1             2             3             4             6

m mm2 3m        4mm    6mm They are called the polar classes.

10.5. Pyroelectric materials

The highest pyroelectric figures of merit have been observed in ferroelectric materials. The transition from the paraelectric to ferroelectric states in most of these (the ‘proper’ ferroelectrics) can be modeled in terms of an expansion of the free energy in a power series of the spontaneous polarization.

A second important point about the proper ferroelectrics is that both their dielectric properties and the pyroelectric coefficient tend to diverge as TC is approached. This means that the ratio γ/ ε and hence the pyroelectric responsivity, stay reasonably constant over a wide temperature range below TC. This is important from a technological point of view as it means that the devices require no thermal stabilization. The following discussion reviews the present state of the art in pyroelectric materials and assesses their relative merits for different applications.

Table 2 summarizes the selected pyroelectric materials studied so far along with their figures of merit for voltage responsivity and detectivity.

Table 2. Figure of merit for various pyroelectric materials.

TC (oC) – Curie temperature; T (oC) – temperature in °C at which measurements were made; ε – dielectric permittivity; γ – pyroelectric coefficient in C/cm2K.

The choice of the pyroelectric material is mainly determined by (a) its figure of merit, (b) the detector size, (c) availability and durability of the pyroelectric material, (d) environment in which the material has to operate, (e) the radiation levels to be detected, (f) the purpose for which the detector is employed, (g) the maximum ambient temperature of operation and the range over which stable operation is desired. The importance of factors (b) and (c) in the choice of pyroelectric material does not need much of an explanation. It should be possible to grow large crystals of pyroelectric material and fabricate them into thin slices. The durability is also an important factor [20].

10.6 Applications

Pyroelectric detectors possess a number of characteristics which are of significance when considering their use in a given application. Their ‘AC coupled’ nature makes them insensitive to unvarying fluxes of radiation so that they are ideally suited to detecting small changes in a relatively large background level of incident energy. They can be used over a large spectral bandwidth, the only requirement being that the energy be absorbed. They can be used over a wide range of temperatures without recourse to cooling systems. They have low power requirements and can operate for long periods on battery power, and last, but not least, they are generally low-cost devices [32].

10.7 Movement detector

This is an ideal application for pyroelectric detectors. In the absence of an intruder, the interior of an unoccupied building present a fairly constant thermal scene. An intruder moving into the area surveyed by the detector provides a varying flux of IR radiation, which can be detected and used to trigger an alarm. Most commercial detectors use a series of faceted mirrors designed to concentrate the radiation and improve the detection efficiency. Signals are generated as the intruder moves into and out of the areas covered by the mirrors. These signals are usually in the range 0.1-10 Hz, where the detectors work very well. The alarms usually operate in the 8 to 14 pm wavelength range, around the emission peak at 10 pm for bodies at 300 K. Using a filter which blocks all radiation at wavelengths shorter than 6 or 7 pm makes the detector insensitive to visible radiation and prevents false signals from, for example, sun glint. It is usual to use compensated detectors in this application to prevent false alarm signals due to environmental temperature changes.

10.8 Pollution monitoring and gas analysis

The concentrations of gases in the atmosphere can be measured from the strength of particular lines in their absorption spectra. For example, CO2 has a strong absorption at 4.3pm. The analysis systems generally employ a modulated broad-band source of IR illuminating two pyroelectric detectors equipped with filters at the chosen wavelength. The radiation falling on one detector is allowed to pass through the gas being analyzed, while that falling on the other passes through a reference cell. By taking the ratio of the outputs from the detectors, the concentration of the pollutant can be measured.

Summary:

In this Chapter we have done a detailed study of pyroelectricity, crystal symmetry and pyroelectric materials. Also we studied the modeling of pyroelectric effect. We learnt application of pyroelectricity.

    References:

1. Webster, John G (1999). The measurement, instrumentation, and sensors handbook. pp. 32–113. ISBN 978-0-8493-8347-2.
2. In this article, the term “voltage” is used in the everyday sense, i.e. what a voltmeter measures. This is actually the electrochemical potential, not the electrostatic potential (Galvani potential).
3. Buchanan, Relva C. (2004). Ceramic Materials for Electronics: Third Edition, Revised and Expanded (Third ed.). Cincinnati, Ohio: Marcel Dekker, Inc. p. 217. ISBN 0-8247-4028-9. Retrieved 10 November 2015.
4. Johann Georg Schmidt, Curiöse Speculationes bey Schalflosen Nächten [Curious Speculations During Sleepless Nights] (Chemnitz and Leipzig (Germany): Conrad Stössen, 1707), pages 269-270. An English translation of the relevant passage appears in: Sidney B. Lang, Sourcebook of Pyroelectricity, vol. 2 (New York, New York: Gordon and Breach, 1974), page 96.
5. “Diverse observations de la physique generale,” Histoire de l’Académie des Sciences (1717); see pages 7-

    References and Suggestive Readings

1. Damjanovic, Dragan, 1998, Ferroelectric, dielectric and piezoelectric properties of ferroelectric thin films and ceramics, Rep. Prog. Phys. 61, 1267–1324.
2. Sebald, Gael; Pruvost, Sebastien; Guyomar, Daniel (2008). “Energy harvesting based on Ericsson pyroelectric cycles in a relaxor ferroelectric ceramic” (PDF). Smart Materials and Structures 17: 015012. Bibcode:2008SMaS…17a5012S. doi:10.1088/0964-1726/17/01/015012.
3. Sebald, Gael; Guyomar, Daniel; Agbossou, Amen (2009). “On thermoelectric and pyroelectric energy harvesting”. Smart Materials and Structures 18: 125006. Bibcode:2009SMaS…18l5006S. doi:10.1088/0964-1726/18/12/125006.

     Web Links

1.     Substantial explanations of pyroelectric detector operation

2.     Pyroelectric Infrared Detectors DIAS Infrared

3.     DoITPoMS Teaching and Learning Package- “Pyroelectric Materials”

Additional Topics to be studied

1) History of pyroelectricity

One of the least-known properties of solid materials, pyroelectricity is rigorously defined as the temperature dependence of the spontaneous polarization in certain anisotropic solids.1⊗6 To appreciate the meaning of that definition and the nature of the pyroelectric effect, consider a simple example: a thin, parallel-sided sample of material, such as a tourmaline crystal or a ceramic disk of barium titanate, cut so that its crystallographic symmetry axis is perpendicular to the flat surfaces. The unit cells of pyroelectric materials have a dipole moment. The dipoles are packed so that the components of the dipole moment in each unit cell add up in the direction normal to the flat surfaces. The dipole moment per unit volume of the material is called the spontaneous polarization PS. Always nonzero in a pyroelectric material, PS exists in the absence of an applied electric field and is equivalent to a layer of bound charge on each flat surface of the sample. Nearby free charges such as electrons or ions will be attracted to the sample (see figure 1). Imagine that conductive electrodes are then attached to the surfaces and connected through an ammeter having a low internal resistance. If the temperature of the sample is constant, then so is PS and no current flows through the circuit. But in most single crystals and ceramics, an increase in temperature causes the net dipole moment and, consequently, the spontaneous polarization to decrease. The quantity of bound charge then decreases, and the redistribution of free charges to compensate for the change in bound charge results in a current flow—the pyroelectric current—in the circuit. If the sample had been cooled instead of heated, the current’s sign would be reversed. Note that the pyroelectric effect is only observable during the period in which the temperature changes. In an open circuit, the free charges would simply remain on the electrodes and a voltage could be measured. A large number of pyroelectric materials exist, including minerals such as tourmaline, single crystals such as triglycine sulfate, ceramics such as lead zirconate titanate, polymers such as polyvinylidene fluoride, and even biological materials, such as collagen. For a detailed treatment of the relations between various properties of a material and how those properties contribute to the pyroelectric effect, see box 1.

Historical threads

This treatment of pyroelectricity in terms of a change in net dipole moment emerged in modern times. But as a phenomenon, the pyroelectric effect has been known for 24 centuries—the Greek philosopher Theophrastus probably wrote the earliest known account.7 He described a stone, called lyngourion in Greek or lyncurium in Latin, that had the property of attracting straws and bits of wood. Those attractions were no doubt the effects of electrostatic charges produced by temperature changes most probably in the mineral tourmaline. Sidney Lang is an emeritus professor of chemical engineering at Ben-Gurion University of the Negev in Israel.