3.1: Pyroelectricity
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\(\newcommand{\avec}{\mathbf a}\) \(\newcommand{\bvec}{\mathbf b}\) \(\newcommand{\cvec}{\mathbf c}\) \(\newcommand{\dvec}{\mathbf d}\) \(\newcommand{\dtil}{\widetilde{\mathbf d}}\) \(\newcommand{\evec}{\mathbf e}\) \(\newcommand{\fvec}{\mathbf f}\) \(\newcommand{\nvec}{\mathbf n}\) \(\newcommand{\pvec}{\mathbf p}\) \(\newcommand{\qvec}{\mathbf q}\) \(\newcommand{\svec}{\mathbf s}\) \(\newcommand{\tvec}{\mathbf t}\) \(\newcommand{\uvec}{\mathbf u}\) \(\newcommand{\vvec}{\mathbf v}\) \(\newcommand{\wvec}{\mathbf w}\) \(\newcommand{\xvec}{\mathbf x}\) \(\newcommand{\yvec}{\mathbf y}\) \(\newcommand{\zvec}{\mathbf z}\) \(\newcommand{\rvec}{\mathbf r}\) \(\newcommand{\mvec}{\mathbf m}\) \(\newcommand{\zerovec}{\mathbf 0}\) \(\newcommand{\onevec}{\mathbf 1}\) \(\newcommand{\real}{\mathbb R}\) \(\newcommand{\twovec}[2]{\left[\begin{array}{r}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\ctwovec}[2]{\left[\begin{array}{c}#1 \\ #2 \end{array}\right]}\) \(\newcommand{\threevec}[3]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\cthreevec}[3]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \end{array}\right]}\) \(\newcommand{\fourvec}[4]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\cfourvec}[4]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \end{array}\right]}\) \(\newcommand{\fivevec}[5]{\left[\begin{array}{r}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\cfivevec}[5]{\left[\begin{array}{c}#1 \\ #2 \\ #3 \\ #4 \\ #5 \\ \end{array}\right]}\) \(\newcommand{\mattwo}[4]{\left[\begin{array}{rr}#1 \amp #2 \\ #3 \amp #4 \\ \end{array}\right]}\) \(\newcommand{\laspan}[1]{\text{Span}\{#1\}}\) \(\newcommand{\bcal}{\cal B}\) \(\newcommand{\ccal}{\cal C}\) \(\newcommand{\scal}{\cal S}\) \(\newcommand{\wcal}{\cal W}\) \(\newcommand{\ecal}{\cal E}\) \(\newcommand{\coords}[2]{\left\{#1\right\}_{#2}}\) \(\newcommand{\gray}[1]{\color{gray}{#1}}\) \(\newcommand{\lgray}[1]{\color{lightgray}{#1}}\) \(\newcommand{\rank}{\operatorname{rank}}\) \(\newcommand{\row}{\text{Row}}\) \(\newcommand{\col}{\text{Col}}\) \(\renewcommand{\row}{\text{Row}}\) \(\newcommand{\nul}{\text{Nul}}\) \(\newcommand{\var}{\text{Var}}\) \(\newcommand{\corr}{\text{corr}}\) \(\newcommand{\len}[1]{\left|#1\right|}\) \(\newcommand{\bbar}{\overline{\bvec}}\) \(\newcommand{\bhat}{\widehat{\bvec}}\) \(\newcommand{\bperp}{\bvec^\perp}\) \(\newcommand{\xhat}{\widehat{\xvec}}\) \(\newcommand{\vhat}{\widehat{\vvec}}\) \(\newcommand{\uhat}{\widehat{\uvec}}\) \(\newcommand{\what}{\widehat{\wvec}}\) \(\newcommand{\Sighat}{\widehat{\Sigma}}\) \(\newcommand{\lt}{<}\) \(\newcommand{\gt}{>}\) \(\newcommand{\amp}{&}\) \(\definecolor{fillinmathshade}{gray}{0.9}\)Pyroelectricity in Crystalline Materials
Pyroelectric devices are energy conversion devices which convert a temperature difference to or from electricity through changes in material polarization. The pyroelectric effect was first studied by Hayashi in 1912 and by Rontgen in 1914 [3] [40]. This effect occurs in insulators, so it is different from the thermoelectric effect. The thermoelectric effect, to be discussed in Chapter 8, is a process that converts between energy of a temperature difference and electricity and occurs because heat and charges flow at different rates through junctions.
| Material | Chemical Composition |
Piezoelectric strain const. \(d\) in \(\frac{m}{V}\) from [38] [39] |
Pyroelectric coeff. \(|\overrightarrow{b}|\) in \(\frac{C} {m^2K}\) from [38] [39] | Pockels electro-optic coeff. \(\gamma\) in \(\frac{m}{V}\) from [27] |
|---|---|---|---|---|
| Sphalerite | \(\text{ZnS}\) | \(1.60 \cdot 10^{-12}\) | \(4.34 \cdot 10^{-7}\) | \(1.6 \cdot 10^{-12}\) |
| Quartz | \(\text{SiO}_2\) | \(2.3 \cdot 10^{-12}\) | \(1.67 \cdot 10^{-6}\) | \(0.23 \cdot 10^{-12}\) |
| Barium Titanate | \(\text{BaTiO}_3\) | \(2.6 \cdot 10^{-10}\) | \(12 \cdot 10^{-6}\) | \(19 \cdot 10^{-12}\) |
Table \(\PageIndex{1}\): Example piezoelectric strain constants, pyroelectric coefficients, and Pockels electro-optic coefficients. Values for sphalerite assume the \(\bar{4}3m\) crystal structure. Pockels coefficients assume a wavelength of \(\lambda = 633 nm\). Average values specied in the references are given. See the cited references for additional assumptions. The Pockels electro-optic coefficient \(\gamma\) is defined in Sec. 3.2.1.
If an insulating crystal is placed in an external electric field, the material will polarize. The electrons will displace slightly forming electric dipoles, and energy can be stored in this material polarization. In some pyroelectric materials, heating or cooling will also cause the material to polarize. We can model the material polarization by adding a term to Equation 2.2.1 to account for the temperature dependence [3, p. 327].
\[\overrightarrow{P} =\overrightarrow{D} -\epsilon_0 \overrightarrow{E} + \overrightarrow{b}\Delta T. \label{3.1.1} \]
As in Equation 2.3.1, \(\overrightarrow{P}\) represents material polarization in \(\frac{C}{m^2}\), \(\overrightarrow{D}\) represents displacement flux density in C m2 , \(\overrightarrow{E}\) represents electric field intensity in \(\frac{V}{m}\), and \(\epsilon_0\) is the permittivity of free space in \(\frac{F}{m}\). The pyroelectric coefficient \(\overrightarrow{b}\) has units \(\frac{C}{m^2K}\), and \(\Delta T\) represents the change in temperature. The coefficient \(\overrightarrow{P}\) is a vector because the material polarization may be different along different crystal directions. Table \(\PageIndex{1}\) lists example values for the pyroelectric coefficient as well as for other coefficients. (Note that this definition of \(\overrightarrow{b}\) is similar but not identical to the definition in [3].) In some materials, the material polarization depends linearly on the temperature as described by Equation \ref{3.1.1}. In other materials, more terms are needed to describe the dependence of the material polarization on temperature.
\[\overrightarrow{P} =\overrightarrow{D} - \epsilon_0 \overrightarrow{E} + \overrightarrow{b}\Delta T + \overrightarrow{b_{quad}} (\Delta T)^2 ... \nonumber \]
Many materials exhibit pyroelectricity only below a temperature known as the pyroelectric Curie temperature.
In the last chapter, we saw that we could determine whether or not a crystalline material was piezoelectric from its crystal structure. To do so, we identified the symmetries of the crystal structure. Crystal structures are grouped into 32 classes called crystal point groups based on the symmetries they contain. Crystal structures in the 21 of the crystal point groups that do not have a center of symmetry can be piezoelectric. We can use a similar technique to determine if a crystalline material is or is not pyroelectric. All pyroelectric crystals are piezoelectric, but not all piezoelectric crystals are pyroelectric. To determine if a crystalline material can be pyroelectric, identify its crystal structure and determine the corresponding crystal point group. Crystals in the 10 crystal point groups listed in Table 2.3.1 are pyroelectric [3, p. 366] [26, p. 557].
Pyroelectricity in Amorphous and Polycrystalline Materials and Ferroelectricity
In the Sec. 2.2.3 we saw that some materials, called ferroelectric piezoelectric materials, had a material polarization that depended nonlinearly on the mechanical stress applied. These materials could be crystalline, amorphous, or polycrystalline. When a charge separation occurred in one atom, the charges from that electric dipole induce dipoles to form in nearby atoms, and electrical domains with aligned material polarization form in the material. This effect depends on the mechanical stress applied to the material previously, and the dependence on past history is called hysteresis. Materials can also be ferroelectric pyroelectric, and these materials can be crystalline, amorphous, or polycrystalline. In these materials, the material polarization depends nonlinearly on the temperature, as opposed to the mechanical stress. As with the piezoelectric version of this effect, polarization of one atom induces a material polarization in nearby atoms. Such materials can have a material polarization even when no temperature gradient is applied, and they can exhibit hysteresis.
Materials and Applications of Pyroelectric Devices
Pyroelectricity has been studied in a number of materials including barium titanate BaTiO\(_3\), lead titanate PbTiO\(_3\), and potassium hydrogen phosphate KH\(_2\)PO\(_4\) [25] [26]. It has also been studied in chalcogenide glasses which are sulfides, selenides, and tellurides such as GeTe [25] [26]. When selecting a pyroelectric material for an application, the pyroelectric coefficient should be considered. Thermal properties are important too. The material should be able to withstand repeated heating and cooling, and it should have a relatively high melting temperature to be useful.
The pyroelectric effect does not have many applications. Some optical detectors designed to detect infrared light are made from pyroelectric materials [41] [42]. However, most optical detectors are photovoltaic devices made from semiconductor junctions, and this technology will be discussed in Chapter 6. While sensors using the pyroelectric effect could be used to measure temperature, other types of temperature sensors, such as thermocouples, are typically used. Thermocouples, which operate based on the thermoelectric effect which is discussed in Chapter 8, are more convenient to build and operate. Additionally, in many pyroelectric materials, the effect is nonlinear while linear sensors are easier to work with and calibrate.