Skip to main content
main-content

Über dieses Buch

The expansion of the application of ferroelectric crystals in engineering as well as of a number of fundamental problems of solid-state physics, which have not yet been solved and which bear a direct relation to ferro electricity, has lately stimulated much interest in the problem of ferroelectricity. In courses of solid-state physics ferroelectricity is studied today along with traditional disciplines, such as magnetism, superconductivity, and 'semiconducting phe­ nomena. Moreover, new specialities have been born concerned directly with the development and utilization of ferroelectric material~ in optics, acous­ tics, computer technology, and capacitor engineering. Special courses in the physics of ferroelectrics are read in a number of colleges and universities. The study of the nature of ferro electricity has currently reached such a level of development that we may speak of having gained a rather deep insight into the physical essence of a number of phenomena, which contribute to the generation of a spontaneous electric polarization in crystals. It is exactly at this level that it has become possible to single out that part of the problem, the physical picture of which can be depicted in a rather unsophisticated manner and which is the foundation for the construction of a building of "complete understanding".

Inhaltsverzeichnis

Frontmatter

1. General Characteristics of Structural Phase Transitions in Crystals

Abstract
The great majority of crystals can exist in several crystalline phases. As a rule, such phases appear to be stable in a certain range of temperatures and pressures and the transition from one phase to another is accompanied by significant discontinuous changes in the volume and entropy of the crystal. This involves the displacement of various structural elements to distances of the order of the unit cell dimensions and no limitations are imposed on a change in the crystal symmetry. The temperature hysteresis of a phase transition, i.e., the difference between the transition temperatures upon cooling and heating of the crystal, may reach hundreds of degrees and is an indication of the possible formation of relatively stable metastable states: one of the crystalline phases can exist in the region of temperatures and pressures in which another phase is more stable.
Boris A. Strukov, Arkadi P. Levanyuk

2. Phenomenological Theory of Second-Order Structural Transitions in Crystal

Abstract
Having established how the distortion of the crystal lattice, which occurs at the Curie point of a second-order phase transition (or a first-order transition close to it), can be described by the order parameter, we come to the following important conclusion: in phase transitions of this type the nonsymmetric phase may be represented as a distorted symmetrical phase. This statement is the basis of the phenomenological theory of second-order phase transitions. Below we will try to explain how the character of variation of the physical properties of a crystal in the temperature range, including the Curie point, can be predicted if we know the change of its symmetry at the Curie point. Especially important is the result of the phenomenological theory, which shows that the information about a “symmetry jump”, i.e., about the symmetry elements lost by the crystal at the Curie point, is sufficient for a description of the anomalies of practically all thermodynamic properties of the crystal.
Boris A. Strukov, Arkadi P. Levanyuk

3. Proper Ferroelectrics: Anomalies of Physical Properties in Phase Transitions

Abstract
Before we turn to the analysis of the main consequences of the theory of second-order phase transitions for ferroelectric crystals, we are going to discuss the conditions, the fulfilment of which leads us to believe that the inferences of the theory will be quantitative. The most important question is evidently the following: Is the representation of the nonequilibrium thermodynamic potential in the form of a power series of the order parameter at the point T = Tc permissible? The answer to this question is known and it can be shown that this point is a singular point of the thermodynamic potential and the expansion coefficients vanish at this point or go to infinity. A special temperature dependence is also exhibited by the quantity Φ0(p,T), which is the part of the thermodynamic potential containing the contributions of all degrees of freedom of a crystal, except η.
Boris A. Strukov, Arkadi P. Levanyuk

4. Dielectric Anomalies in Structural Nonferroelectric and Improper Ferroelectric Phase Transitions

Abstract
As was shown in the preceding chapter, the Landau theory allows one to successfully account for anomalies of the basic thermodynamic quantities for ferroelectric crystals in second-order transitions and also in first-order transitions close to second-order ones. While applying this theory to ferroelectrics, we presumed that the order parameter has the same transformation properties as the component of the electric field vector. As a result, it turns out that the equilibrium value of order parameter is proportional to the electric polarization of the crystal. However, there may exist ferroelectric phase transitions in which such a proportionality is not observed.
Boris A. Strukov, Arkadi P. Levanyuk

5. Anomalies of Elastic and Electromechanical Characteristics of Crystals in Second-Order Phase Transitions

Abstract
In the preceding chapters we have seen that, according to a simple treatment based on the Landau theory, the temperature dependence of the dielectric constant (dielectric permittivity) experiences anomalies of three types in second-order phase transitions. If the transition is a proper ferroelectric transition, i.e., if the order parameter exhibits the transformation properties of a component (or components) of the polarization vector, then one or more components of the permittivity tensor goes to infinity at T = Tc, obeying the Curie-Weiss law in a certain vicinity of this point. If the transition is an improper ferroelectric transition, i.e., if the transformation properties of the order parameter differ from those for polarization but have a certain specific form (see Chap. 4), then the dielectric constant remains slightly temperature dependent in both phases, but one or more components of it increase discontinuously upon transition into the polar phase. Finally, in the most general case, when the order parameter has no specific transformation at all with respect to an electric field, the temperature dependence of the dielectric constant undergoes only a kink at T = Tc.1 In order to establish these differences, we did not need to know either the physical meaning of the order parameter or the character of interactions leading to a phase transition; it was sufficient to take into account the symmetry properties of a crystal and the order parameter.
Boris A. Strukov, Arkadi P. Levanyuk

6. Fluctuations of the Order Parameter in Phenomenological Theory

Abstract
We will now be concerned with the assumptions that were made in the construction of the Landau phenomenological theory of phase transitions. The basic assumption of the theory is the assumption of the normal, “nonsingular” temperature dependence of the coefficients in the expansion of the incomplete themodynamic potential. It was assumed, for example, that the dependence Φ0(p,T) in the vicinity of the phase transition point is the same as it is far away from it. By definition, the incomplete thermodynamic potential Φ0(p,T) takes account of the contribution of all degrees of freedom, except η, to the complete thermodynamic potential. It was assumed implicitly that these degrees of freedom “do not feel” a phase transition. The concept that the phase transition does not “touch upon” other degrees of freedom, except η, lies also implicitly at the basis of the assumption of the “nonsingular” temperature dependence of the coefficients in the expansion of the thermodynamic potential.
Boris A. Strukov, Arkadi P. Levanyuk

7. Structural Phase Transitions in the Single-Ion Model

Abstract
We have so far used an approach which is usually referred to as the phenomenological theory of phase transitions. Recall that within the framework of this theory we proceeded from the presence of a phase transition and used at the outset only the assumption of a regular, nonsingular temperature dependence of the coefficients contained in the theory (Landau coefficients of the thermodynamic potential). We also found that this assumption is invalid, unsubstantiated, but this was also done within the scope of the phenomenological theory. In this theory we were not interested, as a matter of fact, in the concrete structure, the chemical composition of a crystal, and the character of forces that are operating between particles (examples given in Chap. 1 were aimed at rendering the treatment more spectacular, but they were not required for constructing the theory). The only essential point that we took into account was the character of variation of the crystal symmetry at the Curie point. Therefore, we could say nothing of the values of the coefficients included in the theory and interpret the nature of the interactions leading to a phase transition.
Boris A. Strukov, Arkadi P. Levanyuk

8. Statistical Theory of Ferroelectric Phase Transitions of the Order-Disorder Type

Abstract
As has been noted earlier, from the standpoint of the microscopic mechanism of a phase transition it is reasonable to consider separately a group of ferroelectric crystals with an order-disorder phase transition. In accordance with Chap. 1, we will use the term order-disorder ferroelectrics for crystals in which at least one of the sublattices consists of particles having two or more equilibrium positions. It may be said that the remaining (ordered) sublattices create, as it were, a “skeleton” of the crystal and the atoms that belong to these sublattices perform slight oscillations relative to fixed equilibrium positions. It is their configuration that creates potentials of two or more minima for sublattice atoms (see Fig. 7.2).
Boris A. Strukov, Arkadi P. Levanyuk

9. Dynamics of Displacive and Order-Disorder Phase Transitions

Abstract
In the preceding chapters we have dealt with the thermodynamic characteristics of crystals, i.e., we have considered the various equations of state relating the equilibrium values of the generalized thermodynamic forces and coordinates. An example of such an equation is (3.3) or the relation derived from it: ??? (A = 1/2α (TTc)), which characterizes the variation of the order parameter for a proper ferroelectric under the action of a low electric field with TTc. The quantity aE may here be regarded as a “force” coupled to the order parameter and the coefficient A has the meaning of “rigidity” (corresponding to η) or of inverse susceptibility. It can be seen that with TTc the quantity A also tends to zero, i.e., upon approach to Tc the rigidity of the system falls off.
Boris A. Strukov, Arkadi P. Levanyuk

10. Domain Structure and Defects

Abstract
In Chaps. 2–9 it was assumed that the nonsymmetric phase is spatially homogeneous, i.e., that a phase transition occurs into a monodomain state. Domains were mentioned only in connection with the fact that the system of equations for an equilibrium order parameter has several solutions; it was pointed out that these solutions correspond to different domains.
Boris A. Strukov, Arkadi P. Levanyuk

11. Ferroelectrics with an Incommensurate Phase

Abstract
In a series of ferroelectrics (NaN02, (NH4)2BeF4 etc.) the transition into the polar phase is preceded by a transition into a rather peculiar intermediate phase called the incommensurate phase, i.e., when the the temperature falls off, there is observed the following sequence of phases: symmetric/incommensurate/polar (commensurate) (Fig. 11.1).
Boris A. Strukov, Arkadi P. Levanyuk

12. Ferroelectric Liquid Crystals

Abstract
In the preceding chapters we have dealt with the phenomena associated with the origination of a spontaneous polarization in crystalline media. The basic mechanisms leading to ferroelectricity involved spontaneous displacements of charged particles in unit cells or redistributions of the probabilities of their localization at certain positions. A characteristic feature of such transitions is the change of the crystal symmetry into a group with a special polar direction, with the original and polar phases belonging to one of the 32 discrete crystallographic groups.
Boris A. Strukov, Arkadi P. Levanyuk

13. Crystallochemical Aspects of the Theory of Ferroelectric Phenomena

Abstract
In Chaps. 8 and 9, while considering the microscopic theory of phase transitions, we used simple model Hamiltonians: the Hamiltonian (7.1) for displacive-type phase transitions and the Hamiltonian (8.8) for order-disorder phase transitions. The form of these Hamiltonians was specified so as to render the theory as simple as possible. The only requirement was the occurrence of a phase transition in a model system. Naturally, the coefficients in the Hamiltonians remained indeterminate; only certain plausible assumptions have been made as to the order of magnitude of their values. Of course, such an approach is insufficient for explaining the predictions of the properties of particular crystals. The problem therefore is to find Hamiltonians, though not as simple as (7.1) and (8.8), such that they would reflect more accurately the properties of concrete crystals.
Boris A. Strukov, Arkadi P. Levanyuk

14. Recommended Literature

Without Abstract
Boris A. Strukov, Arkadi P. Levanyuk

Backmatter

Weitere Informationen