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...minimum supplemented by graphical representations to make the article more accessible.
1 Introduction
It is easy to describe what a ferroelectric is in essence: a material that, in the absence of an applied electric field, has a spontaneous polarisation (explained later) below a critical temperature [T.sub.c] which can be reversed by an external electric field; above Tc the spontaneous polarisation disappears and then only an applied electric field will create a polarisation. Despite the simplicity of this description, however, the scientific study of ferroelectric phenomena involves a broad range of ideas from condensed matter physic (1-3), which themselves are built from many basic subjects in physic (4-13). Nonetheless, a general picture is readily painted without the need to uncover all the details and approaches. Quite a few books are available specifically covering ferroelectric phenomena; a selection is given in refs 14-23, where many references to original articles can be found.
Here mostly ferroelectrics made up of single crystal solids will be considered. Table 1 shows some typical ferroelectric materials. Note that they do not contain iron despite the ferro- prefix. The connection is as follows. Ferromagnetic materials (2,3) have a spontaneous magnetisation below a critical temperature due to the alignment of magnetic dipoles and the prefix was given because the first discovered contained iron. Only because of the analogy between the magnetic and electric dipole behaviour are ferroelectrics so named. See ref. 17 for a historical perspective on the discovery of ferroelectrics.
2 General Properties
2.1 Dipole moments and polarisation
First we need some explanation of the basic element responsible for ferroelectricity: a dipole. Whenever a separation between charges of equal magnitude, q, but opposite sign exists there is a dipole with a moment whose magnitude is denned by p = qd; d is the distance separating the charges.
This idea is useful when considering solids which are electrical insulators, since the charges in them do not move much in an electric field, but some separation between the charges does occur. The field exerts a force on each charge; opposite charges are pushed in opposite directions. In this context the general name for such solids is dielectric (2,3). Usually there are no dipoles in a dielectric unless an electric field is applied to it (this could be done for example by putting a slab of dielectric between two electrodes and connecting a battery to the electrodes). In the absence of an applied field any collection of positive charges has a centre that coincides with the centre of a collection of negative charges. The atoms that make up a dielectric material can be thought of as clouds of negative charge with a positively charged nucleus at the centre of the cloud--there is no overall charge separation. However the total negative charge may not have the same magnitude as that of the positive charge, in which case the atom as a whole is charged because the total charge is the sum of the positive and negative charges. The atom is then called an ion (ref. 2, Chap. 3).
Ionic crystalline solids are made up of more than one type of ion arranged in a regularly repeating structure (a crystal lattice). Each ion can be considered to have a charge at its centre and the total charge of all the ions added together is zero. Also, the charge centres are normally arranged in a way that cancels overall. This is illustrated in Figure 1(a); if the black ions have a charge of +q and the white ones, -q then every black ion has as its four nearest neighbours white ions and every white ion has as its four nearest neighbour black ions, causing the sum of the charges at each ion position to cancel to zero. In such a case there are no dipoles. This is the natural arrangement of the dielectric--the net effect of all the forces acting between the ions. (Unlike charges attract; like charges repel. See also Section 4.2.1.) It turns out that in nature there exist certain kinds of dielectrics in which the natural balance does not cause charge cancellation at each ion site. Such a balance would occur if the ions were arranged as shown in Figure 1(b). Now the negative charge at the centre of a rectangular group of ions is not cancelled by a negative charge coming from a corresponding group of black ions because the centre of this group is higher: there is a separation of positive and negative charges, equal in magnitude as can be seen from the symmetry of each rectangular group, and hence there are dipole moments, all pointing up. The dipole moments add up to give a net polarisation, which is defined as dipole moment per unit volume; a more detailed definition is given in Section 2.10.2.
For simplicity Figure 1 only depicts a two dimensional lattice. Real crystals of course are three-dimensional and can involve more than two types of ion. However, the basic argument should be clear from the two-dimensional depiction and the extension to the extra dimension (rectangles go to boxes--see Figure 5, for example) should not be too difficult to imagine.
[FIGURE 1 OMITTED]
2.2 Spontaneous polarisation
It is the existence of a polarisation as part of the natural balance of the crystal, that characterises a ferroelectric material together with the property that the polarisation direction--indicated by the arrows in Figure 1 (b)--is reversed if an electric field is applied in the opposite direction. Furthermore, this polarisation is temperature dependent: it decreases as temperature increases until a critical temperature, T = [T.sub.c] is reached; this is also called the Curie temperature. Above [T.sub.c] the ferroelectric phase does not exist. The language often used is this: below [T.sub.c] the ferroelectric is in a ferroelectric phase, above [T.sub.c] it is in a paraelectric phase. The natural polarisation observed in ferroelectrics is often referred to as spontaneous polarisation, [P.sub.s].
[FIGURE 1 OMITTED]
2.3 Charge compensation
An external electric field occurs because of the surfaces charges present when [P.sub.s] exists. To clarify this, imagine dipoles, all pointing in the same direction to form a spontaneous polarisation in a slab of ferroelectric material. Inside the slab the head-to-tail alignment of the dipoles (Figure 2) means that the positively charged heads and negative tails result in charge cancellation--there is zero charge inside; however, on the face at which the dipoles point there is a positive charge distribution due to each uncompensated head; and on the opposite face there is a negative charge distribution from the uncompensated tails, shown in Figure 2. These oppositely charged faces create an electric field of magnitude E acting on the slab.
[FIGURE 2 OMITTED]
It is often not necessary to consider this field because the charged faces are usually compensated for by free charges in the ferroelectric (it is a poor electrical conductor but does contain some free charges that move to compensate the charges at the faces (14); furthermore the surrounding medium, often air, can contain charges, such as positive and negative ions, free to move to contribute to charge cancellation at the faces. In any case, cancellation can be assured, by electrically connecting the faces.
2.4 Relation of ferroelectrics to other types of dielectric
Some materials have a spontaneous polarisation that cannot be reversed by an electric field. Strictly speaking they are not ferroelectric, but are said to be pyroelectric meaning that the spontaneous polarisation is temperature dependent (so all ferroelectrics are pyroelectrics but not all pyroelectrics are ferroelectric). Spontaneous polarisation also changes if an external stress is applied (for example, by clamping the crystal--compressive stress--or by stretching it in some way--tensile stress) since stress alters the relative distance between the positive and negative charge centres hence the dipole moments change. This property is piezoelectricity. Some non-pyroelectric (hence non-ferroelectric) materials can become polarised by an applied stress. So from this a hierarchy emerges: all ferroelectrics are pyroelectric; all pyroelectrics are piezoelectric; all piezoelectrics are dielectrics. The reverse, all dielectrics are piezoelectrics etc., is not true.
2.5 Electronic and ionic polarisation
In an applied electric field relative movement between the electron clouds and their nuclei occurs leading to electronic polarisation. However in many cases it is not important in ferroelectrics because the dipoles caused by the relative shift of the positive and negative ion lattices (ionic polarisation) are of much larger magnitude; so ignoring electronic polarisation does not usually make much difference, at least when the applied electric field is static or slowly varying. If the field varies rapidly electronic polarisation becomes important but then ionic polarisation does not respond because, unlike the electron clouds, the ions are too heavy to respond to fast variations.
2.6 Anomalies
The dielectric constant, [element of], of a ferroelectric increases to very large values, said to be anomalous, when the temperature is at or near [T.sub.c]. This is shown in Figure 3. Even away from [T.sub.c] the dielectric constant tends to be larger than for non-ferroelectric dielectrics. The dielectric constant is a quantity related to how easily the polarisation responds to an electric field E. The equation of relevance here is P = [X.sup.E], where X is the susceptibility. [dagger] It implies that, for a given value of E, a large value of X would result in a large value of polarisation P; but if X is small, the same E value would produce a smaller polarisation. It is possible to show (11) that [element of] and X are related like this: [element of] = 1 + X. In a ferroelectric we are really dealing with X since it is polarisation that is important. However, since X is large for ferroelectrics adding one to it to get e does not make much difference, that is [element of] [approximately equals] X, especially near [T.sub.c]. In the literature it is often e rather than [element of] that is referred to, more or less by convention.
[FIGURE 3 OMITTED]
2.7 Hysteresis
Imagine a ferroelectric crystal slab of thickness s sandwiched between two electrodes (Figure 4 (a)); it is in the ferroelectric phase with T < [T.sub.c]. Next assume that P, is uniform throughout the slab in a direction perpendicular to the faces, as shown in Figure 2. A voltage V applied to the electrodes will create a uniform electric field...
NOTE: All illustrations and photos
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