Additional symmetries, ferroelectrics

It should be noted that, whereas ferroelectrics are necessarily piezoelectrics, the converse need not apply. The necessary condition for a crystal to be piezoelectric is that it must lack a centre of inversion symmetry. Of the 32 point groups, 20 qualify for piezoelectricity on this criterion, but for ferroelectric behaviour a further criterion is required (the possession of a single non-equivalent direction) and only 10 space groups meet this additional requirement. An example of a crystal that is piezoelectric but not ferroelectric is quartz, and ind this is a particularly important example since the use of quartz for oscillator stabilization has permitted the development of extremely accurate clocks (I in 10 ) and has also made possible the whole of modern radio and television broadcasting including mobile radio communications with aircraft and ground vehicles. 

From this discussion the clear similarity between the SmAPA and SmCsPA structures is easily seen. In addition, the suggestion of Brand et al.29 that a bilayer smectic with all anticlinic layer interfaces (the SmAPF) would produce an achiral ferroelectric smectic follows directly. The unanticipated tilt of the director in the tilt plane, leading to a chiral layer structure, seems to be a general response of the bent-core mesogens to the spontaneous nonpolar symmetry breaking occurring in these rigid dimer structures. 

Measurements of NMR for Ti, Ti [33], and Sr [34,35] were carried out for STO 16 and STO 18-96. Ti and Sr nuclear magnetic resonance spectra provide direct evidence for Ti disorder even in the cubic phase and show that the ferroelectric transition at Tc = 25 K occurs in two steps. Below 70 K, rhomb ohedral polar clusters are formed in the tetragonal matrix. These clusters subsequently grow in concentration, freeze out, and percolate, leading to an inhomogeneous ferroelectric state below Tc. This shows that the elusive ferroelectric transition in STO 18 is indeed connected with local symmetry lowering and impHes the existence of an order-disorder component in addition to the displacive soft mode [33-35]. Rhombohedral clusters, Ti disorder, and a two-component state are found in the so-called quantum paraelectric... 

Since the issue of order/disorder versus (or with) displacive aspects has remained an active field of research, most of the chapters presented in this book are devoted to it. In addition, new fields of applications are reviewed, since material optimization has considerably enlarged this area. A new aspect of ferroelectricity has been discovered recently by the finding of isotope-induced ferroelectricity in the quantum paraelectric SrTiOa. Here conclusive ideas about its microscopic origin are still missing and also the experimental situation remains controversial, since the symmetry of the low-temperature phase is unclear. But, there seems to be stringent evidence that polar clusters are... 

The main changes from the first edition are two new chapters Chapter 2 on X-ray diffraction and Chapter 3 on preparative methods. A short discussion of symmetry elements has been included in Chapter 1. Other additions include an introduction to ALPOs and to clay minerals in Chapter 7 and to ferroelectrics in Chapter 9. We decided that there simply was not enough room to cover the Phase Rule properly and for that we refer you to the excellent standard physical chemistry texts, such as Atkins. We hope that the book now covers most of the basic undergraduate teaching material on solid state chemistry. 

In addition, the SmC, SmI, and SmF phases may exist as chiral modifications (SmC", SmI," and SmF ) either by doping with a chiral additive or by resolving a racemic material that shows one or more of the phases. Because of the low (C2) symmetry in these phases, the molecular dipoles align within the layers that are then ferroelectric. However, the chirality also requires that the direction of the ferroelectricity precesses through space from one layer to the next and so in the bulk sample, the ferroelectricity is lost unless the helix is unwound by the use of surface anchoring and thin cells. 

The existence or nonexistence of mirror symmetry plays an important role in nature. The lack of mirror symmetry, called chirality, can be found in systems of all length scales, from elementary particles to macroscopic systems. Due to the collective behavior of the molecules in liquid crystals, molecular chirality has a particularly remarkable influence on the macroscopic physical properties of these systems. Probably, even the flrst observations of thermotropic liquid crystals by Planer (1861) and Reinitzer (1888) were due to the conspicuous selective reflection of the helical structure that occurs in chiral liquid crystals. Many physical properties of liquid crystals depend on chirality, e.g., certain linear and nonlinear optical properties, the occurrence of ferro-, ferri-, antiferro- and piezo-electric behavior, the electroclinic effect, and even the appearance of new phases. In addition, the majority of optical applications of liquid crystals is due to chiral structures, namely the ther-mochromic effect of cholesteric liquid crystals, the rotation of the plane of polarization in twisted nematic liquid crystal displays, and the ferroelectric and antiferroelectric switching of smectic liquid crystals. 

The reduced symmetry of chiral phases results in additional contributions to the low frequency permittivity. Tilted chiral phases such as smectic C, F and I lack a centre of symmetry, and it is possible for these materials to be ferroelectric. The resulting spontaneous polarization is directed along the C2 symmetry axis, and is perpendicular to the tilt plane it also depends di-... 

Figure 6. The hierarchy of dielectric materials. All are of course dielectrics in a broad sense. To distinguish between them we limit the sense, and then a dielectric without special properties is simply called a dielectric if it has piezoelectric properties it is called a piezoelectric, if it further has pyroelectric but not ferroelectric properties it is called a pyroelectric, etc. A ferroelectric is always pyroelectric and piezoelectric, a pyroelectric always piezoelectric, but the reverse is not true. Knowing the crystal symmetry we can decide whether a material is piezoelectric or pyroelectric, but not whether it is ferroelectric. A pyroelectric must possess a so-called polar axis (which admits no inversion). If in addition this axis can be reversed by the application of an electric field, i.e., if the polarization can be reversed by the reversal of an applied field, the material is called ferroelectric. Hence a ferroelectric must have two stable states in which it can be permanently polarized.

The paraelectric phase has higher symmetry than the ferroelectric phase. However, it might have sufficiently low symmetry to allow piezoelectricity. In the case where the paraelectric phase is piezoelectric, it will become strained when electrically polarized. In addition to the term -PE there will appear a term -5(Tin the free energy, where s designates the strain and a the applied... 

Symmetry influences a range of physical properties. Selecting structures with specific symmetry yields candidates with certain properties. Calculation of additional parameters from the atomic coordinates allows one to predict for example ferroelectricity, piezoelectricity or optical rotatory power. ... 

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