The ferroelectric materials possess the following typical properties:
i. They lack centre of symmetry, i.e., non centrosymmetric.
ii. Their static dielectric constant changes with temperature according to the relation
ԑ= C/T – Tc (Provided T > Tc)
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Where C is a constant independent of temperature. This relation is known as the Curie-Weiss law. C and T are the parameters of a dielectric; C is usually called the Curie constant and Tc the Curie temperature. This relation is plotted in Fig. 6.19 (a)
iii. They possess spontaneous electric polarization i.e. polarization without the help of an external field. However, this polarization occurs only in the temperature range T < Tc. The variation of spontaneous polarization without temperature is shown in Fig. 6.19 (b).
iv. They exhibit hysteresis under the action of an alternating voltage It is possible to obtain a ferroelectric hysteresis loop-a polarization versus electric field curve-for a ferroelectric. Such a curve is shown in Fig. 6.19 (c); it is seen that the curve is very similar to the B-H curve of a ferromagnetic material. The behaviour of ferroelectrics with respect to an electric field is thus analogous with that of ferromagnetic with respect to a magnetic field.
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Some of the ferroelectric properties are explained theoretically:
Property # 1. Crystal Symmetry:
The lattice structure described by the Bravais unit cell of the crystal governs the crystal symmetry. Though there are thousands of crystals in nature, they all can be grouped together into 230 microscopic symmetry types or space groups based on the symmetry elements. Most of the crystals possess symmetry elements in addition to the repetitions expressed by the crystal lattice. The operation of any single symmetry element of the group leaves the pattern of symmetry unchanged.
In studying the physical properties of crystals, only the orientations of the symmetry elements are taken into account, then the macroscopic symmetry elements in crystals reduce to a center of symmetry, mirror plane, 1-, 2-, 3-, 4- or 6- fold rotation axes and 1-, 2-, 3- 4- or 6-fold inversion axes. A combination of these symmetry elements gives us the macroscopic symmetry also called as point groups. It can be shown by the inspection of the 230 space groups that there are just 32 points groups.
The thirty-two point groups can be further classified into (a) crystals having a center of symmetry and (b) crystals which do not possess a center of symmetry. Crystals with a center of symmetry include the 11 point groups labelled centrosymmetric. These point groups do not show polarity. The remaining 21 point groups do not have a center of symmetry (i.e. non-centrosymmetric).
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A crystal having no center of symmetry possesses one or more crystallographically unique directional axes. All non-centrosymmetric point groups, show piezoelectric effect along unique directional axes. Out of the twenty point groups which show the piezoelectric effect, ten point groups have only one unique direction axis. Such crystals are called polar crystals as they show spontaneous polarization.
Property # 2. Dielectric Behaviour above Tc:
The most obvious theory of ferroelectricity seems to be the dipole theory. This theory is based on the assumption that a ferroelectric substance consists of a system of freely rotating dipoles; it uses the Lorentz local field and proceeds analogously to the Langevin-Weiss theory of ferromagnetism. For the high temperature region the theory indeed leads to the Curie-Weiss law (8). However, the theory is inadequate to account for observations.
For example, it predicts that below 1200°K water would be ferroelectric; whereas actually it never becomes ferroelectric, not even below its freezing point. Another serious objection against the dipole theory is its prediction that any dipolar material should become ferroelectric at a sufficiently low temperature; we know, on the other hand, that all known ferroelectrics are non-dipolar in nature. We must therefore seek any other explanation for ferroelectricity.
In fact, ferroelectricity is associated with ionic polarizability. It is believed that the local fields produced by the polarization itself increase at a faster rate than the elastic restoring forces on the ions in the crystal and the ions thereby suffer ultimately an asymmetrical shift in their positions. The dielectric constant e of a ferroelectric substance may therefore be obtained from the Clausius-Mossotti relation-
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ԑ – 1/ ԑ+ 2 = 4π/3. N α= βN (say) … (9)
Here N represents the number of ions per unit volume and is the polarizability of an ion; it will be assumed that is independent of temperature. The temperature dependence of is hidden in the quantity N, which changes as a result of thermal expansion; it is seen from (9) that small changes in N may cause large changes in E. Let us relate those changes. Differentiating (9) with respect to T yields.
where is the volume expansion coefficient of the substance. Making use of the fact that for ferroelectric substance >> 1, so that ( ԑ- 1) ( + 2) ≅ ԑ2, we now obtain;
This expression has indeed the form of the Curie-Weiss law (8). The Curie constant (3/γ) agrees fairly satisfactorily with experimental values for most of the ferroelectric substances. For BaTiO3, for example, the linear expansion coefficients is ≈ 10-5 per °K and γ is therefore ≈ 3 × 10-5 °K giving Curie constant ≈ 105 °K. Thus the temperature dependence of the dielectric substances is definitely associated with lattice expansion.
Property # 3. Spontaneous Polarization and Pyroelectric Effect:
The spontaneous polarization is given by the value of the dipole moment per unit volume or by the value of the charge per unit area on the surface perpendicular to the axis of spontaneous polarization. The axis of spontaneous polarization is usually along a given crystal axis.
Although a crystal with polar axes (20 non-centrosymmetric point groups) shows the piezoelectric effect, it is not necessary for it to have a spontaneous polarization vector. It could be due to the cancelling of the electric moments along the different polar axes to give a zero net polarization vector Ps along this axis.
The value of the spontaneous polarization depends on the temperature, i.e., a change in the temperature of the crystal produces a change in its polarization, which can be detected. This is called the pyroelectric effect which was first discovered in tourmaline by Teophrast in 314 B.C. and so named by Brewster in 1824. The pyroelectric effect can be described in terms of the pyroelectric coefficient λ. A small change in the temperature ΔT, in a crystal in a gradual manner, leads to a change in the spontaneous polarization vector ΔPs given by,
ΔPs = λΔT
Fig. 6.19(b), shows the variation of the spontaneous polarization Ps with temperature for a BaTiO3 ferroelectric crystal. An increase in the temperature leads to a decrease in the spontaneous polarization. BaTiO3 has a negative pyroelectric coefficient. This polarization suddenly falls to zero on heating the crystal above the Curie point.
It is possible to reverse the polarization direction of a pyroelectric crystal by applying a sufficiently intense external field then the crystal is said to be a ferroelectric. It should be noted that both piezoelectricity and pyroelectricity are inherent properties of a crystal due, entirely, to its atomic arrangement or crystal structure. Ferroelectricity, on the other hand, is an effect produced in a pyroelectric crystal by the application of an external electric field.
It has been observed that all ferroelectrics are pyroelectric and piezoelectric. All pyroelectric arc piezoelectrics but the converse is not true. Further, all pyroelectrics are not necessarily ferroelectrics. Tourmaline and polyvinylidene fluoride are pyroelectric materials and are used for building insulation and as detectors for faulty steam traps in industry. These materials can also be used an infrared detectors.
Property # 4. Ferroelectric Domains and Hysteresis Loop:
As described above, pyroelectric crystals show a spontaneous polarization Ps in a certain temperature range. If the magnitude and direction of Ps can be reversed by an external electric field, then such crystals are said to show ferroelectric behaviour. Hence, all single crystals and successfully poled ceramics which show ferroelectric behaviour are pyroelectric, but not vice versa. For example tourmaline shows pyroelectricity but is not ferroelectric.
Ferroelectric crystals possess regions with uniform polarization called ferroelectric domains. Within a domain, all the electric dipoles are aligned in the same direction. There may be many domains in a crystal separated by interfaces called domain walls.
A ferroelectric single crystal, when grown, has multiple ferroelectric domains. A single domain can be obtained by domain wall motion made possible by the application of an appropriate electric field. A very strong field could lead to the reversal of the polarization in the domain, known as domain switching.
The main difference between pyroelectric and ferroelectric materials is that the direction of the spontaneous polarization in ferroelectric can be switched by an applied electric field. The polarization reversal can be observed by measuring the ferroelectric hysteresis as shown in Fig. 6.19 (c).
As the electric field strength is increased, the domains start to align in the positive direction giving rise to a rapid increase in the polarization. At very high field levels, the polarization reaches a saturation value (Psalt). The polarization does not fall to zero when the external field is removed. At zero external fields, some of the domains remain aligned in the positive direction; hence the crystal will show a remanent polarization Pr.
The crystal cannot be completely depolarized until a field of magnitude OEc is applied in the negative direction. The external field needed to reduce the polarization to zero is called the coercive field strength Ec. If the field is increased to a more negative value, the direction of polarization flips and hence a hysteresis loop is obtained. The value of the spontaneous polarization Ps is obtained by extrapolating the curve into the polarization axes.