Unique polar axis

Pyroelectrics. Pyroelectric ceramics are materials that possess a uoique polar axis and are spontaneously polarized ia the abseace of an electric field. Pyroelectrics are also a subset of piezoelectric materials. Ten of the 20 crystal classes of materials that display the piezoelectric effect also possess a unique polar axis, and thus exhibit pyroelectricity. In addition to the iaduced charge resultiag from the direct pyroelectric effect, a change ia temperature also iaduces a surface charge (polarizatioa) from the piezoelectric aature of the material, and the strain resultiag from thermal expansioa. 

Ferroelectrics. Among the 32 crystal classes, 11 possess a centre of symmetry and are centrosymmetric and therefore do not possess polar properties. Of the 21 noncentrosymmetric classes, 20 of them exhibit electric polarity when subjected to a stress and are called piezoelectric one of the noncentrosymmetric classes (cubic 432) has other symmetry elements which combine to exclude piezoelectric character. Piezoelectric crystals obey a linear relationship P,- = gijFj between polarization P and force F, where is the piezoelectric coefficient. An inverse piezoelectric effect leads to mechanical deformation or strain under the influence of an electric field. Ten of the 20 piezoelectric classes possess a unique polar axis. In nonconducting crystals, a change in polarization can be observed by a change in temperature, and they are referred to as pyroelectric crystals. If the polarity of a pyroelectric crystal can be reversed by the application on an electric field, we call such a crystal a ferroelectric. A knowledge of the crystal class is therefore sufficient to establish the piezoelectric or the pyroelectric nature of a solid, but reversible polarization is a necessary condition for ferroelectricity. While all ferroelectric materials are also piezoelectric, the converse is not true for example, quartz is piezoelectric, but not ferroelectric. 

Among the 20 crystal classes lacking a center of symmetry ten of them contain a unique polar axis and exhibit pyroelectricity in addition to piezoelectricity, i.e. in the unstrained dipolar network of these crystals the dipole moment components remain and add to a resultant polar-axis moment. The term pyroelectricity is assigned because thermal expansion will expand or contract the dipole. The pyroelectric constant is defined by ... 

Fig. 10. The leh-hand diagram shows an organic superlattice with a unique polar axis. The two types of molecule involved could be a fatty acid and a fatty amine. The insert is designed to show that these two materials have dipole moments in opposite senses with respect lo the hydrophobic chain. Thus, the V-lype film has a resultant dipole moment...

For the present purpose it is only necessary to distinguish polar crystals, i.e. those that are spontaneously polarized and so possess a unique polar axis, from the non-polar variety. Of the 32 crystal classes, 11 are centrosymmetric and consequently, non-piezoelectric. Of the remaining 21 non-centrosymmetric classes, 20 are piezoelectric and of these 10 are polar. An idea of the distinction between polar and non-polar structures can be gained from Fig. 2.3 and Eqs (2.70) and (2.71). 

Pyroelectricity The observation of a pyroelectric effect implies a noncentrosymmetric space group. It can only exist if there is a unique polar axis in the point group of the crystal. If no effect is observed, it is presumed (but not certain ) that the crystal possesses a center of symmetry. 

As in the case of piezoelectrics, the elementary dipoles will cancel out if the crystallographic unit cell has a centre of symmetry. However, another condition is also needed to produce a spontaneous polarisation, the presence of a unique polar axis, which is a direction in the crystal unrelated by symmetry to any other direction, not even the antiparallel direction. The dipoles lie parallel to the polar axis of the crystal (see Section 5.1.3). Of the 20 piezoelectric crystal classes, only 10 fulfil this criterion and give rise to the pyroelectric effect. The relationship between the appearance of piezoelectricity and pyroelectricity and the symmetry of the crystal is set out in Figure 11.12. 

The semiprecious gemstone tourmaline, with an approximate formula CaLi2Al7(OH)4-(B03)3Si60i8, has a pyroelectric coefficient, 7r of 4 X 10 C m K-. The unique polar axis is the crystallographic c axis. What is the change in polarisation caused by a change of temperature of 100 °C ... 

The pyroelectric effect is used in pyroelectric energy harvesting, and the electrocaloric effect is currently being explored for refrigeration. Perovskite aystals that show the pyroelectric effect contain a unique polar axis and a spontaneous electric polarisation, P, directed along this axis. As all ferroelectrics are also pyroelectrics (Chapter 6),... 

Thomson 1878). Pyroelectric crystals have a unique polar axis, which does not necessarily coincide with any direction derived from symmetries of the crystal. Lord Kelvin postulated that such crystals are in a state of permanent polarization. This theory links changes in spontaneous polarization APs with changes of temperature A by means of linear equation. The constant connecting these two quantities is the pyroelectric coefficient n... 

Pyroelectrics are materials that possess a unique polar axis and are spontaneously polarized in the absence of an electric field. Of the 20 crystal classes that display piezoelectricity, 10 exhibit pyroelectricity. Since pyroelectric ceramics are a subset of piezoelectric materials, they are also piezoelectric in nature. The polarization exhibited by pyroelectric materials is also a function of temperature, and the change in polarization with temperature may be expressed by... 

Usually, the value of the spontaneous polarization P, depends on the temperature. Figure 22-4 shows the temperature dependence of the spontaneous polarization in barium titanate (BaTiOs) crystal. As temperature changes, a variation of the charge density can be observed on those surfaces of the sample which are perpendicular to the unique polar axis in a crystal without twins, or in a poled polycrystalline solid (ceramic) with oriented grains. The phenomenon, where the spontaneous polarization changes with temperature, is called pyroelectric effect . All ferroelectric materials exhibit pyroelectric effect. 

There are materials, for example in the form of certain specially prepared polymer films, which, for light incident normal to the film, absorb to an extent dependent on the inclination of the plane of polarization to a unique axis in the plane of the film. Devices made from such films are termed polarizers approximately 60% of the incident unpolarized light is absorbed, and that part transmitted is plane polarized. The E vectors for the transmitted light are perpendicular to the high-absorbance direction. If the incident light is plane polarized, the intensity transmitted depends on the orientation of the polarizer axis with respect to the plane of polarization of the light. A device used in this mode is usually referred to as an analyser . 

An example of tests for chirality is provided by studies of mandelic acid crystals (Figure 14.23). These crystals are polar and noncentrosymmetric, space group T 2i, but no hemihedral faees develop and therefore there are no external indications that allow one to distinguish the two ends of its polar axis b. Other techniques have to be used. In order to differentiate between the two ends of the hexagonally-shaped crystals (which were shown, by X-ray diffraction studies to have the c axis along the unique axis of the crystal). The directions of the a and b axes with respect to crystal habit were also established by X-ray diffraction studies. 

It is interesting to note that another polarized spectrum c(a,a)b is quite different from a(c,c)b. It resembles the depolarized c(b,a)b spectrum. The resemblance can be attributed to the appearance of structural domains in XI phase, since the three equivalent b-axes in the hexagonal Ih phase would produce three different orthorhombic structures in XI phase with the unique b-axis rotated by 120degrees. Then, even if the incident light is a- or b-polarized, in some domains it would be the mixture of a- and b- polarization (e.g., a -> (Sa b)l2). Thus, in the c(b,a)b not only the non-diagonal aba but also the diagonal ttaa and abb contribute to the spectrum. 

Classically, there is only one way to obtain a noncentrosymmetric crystal packing. The use of enantio-merically pure dipolar compounds ensures crystallization in one of the 11 enantiomorphic groups, whereof 10 show a piezoelectric effect. Only five (namely, those featuring an unique rotational axis 1, 2, 3, 4. 6) of the enan-tioinorphic groups that are piezoelectric also allow for pyroelectricity (see Table 1). At present, there is no design eoneept with whieh to obtain a polar point group by spontaneous nueleation. 

Ferroelectricity was discovered in Rochelle salt in 1921. A ferroelectric crystal exhibits a spontaneous polarization P, in a certain temperature range and the direction of P, can be reversed by an external electric field. From a physical point of view, ferroelectric crystals are those crystalline compounds, which possess one or more ferroelectric phases. The ferroelectric phase is a particular state exhibiting spontaneous polarization, which can be reversed by an external field. A reversal ofpolarization is considered as a special case of the polarization reorientation. From a crystallographic point of view, ferroelectricity can be foimd in polar crystals. A polar crystal is a piezoelectric crystal (without center of symmetry) crystal whose point-group symmetry has a unique rotational axis, but does not have any mirror plane perpendicular to this axis. Along a unique rotational axis, the atomic arrangement at one end is different from that at the other (opposite end). Therefore, they display spontaneous polarization. Polar crystal, which can be found in ten point groups, are 1, 2, m, mm2,4, 4 mm, 3, 3 m, 6, 6 mm. 

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