2.1 Crystal structure

Fig. 1 shows a schematic representation of the TTB structure projection along the [001] direction. For a general A₂BC₂M₅X₁₅ (X = O, F) formulation, large cations occupy the pentagonal 15 C.N. (A) and square 12 C.N. (B) sites, small cations are in the triangular 9 C.N. (C) sites, and small and highly charged cations are in the octahedral M sites.

2.2 Ion localization

Table 1 gives the localization of various ions (or chemical entities) in the different crystallographic sites. The chemical stability is the highest when:

• ● big cations (e.g., Ba²⁺ or Pb²⁺) occupy an A site;
• ● small and low-charged cations (e.g. a Li⁺) are in C site;
• ● small and highly charged cations (e.g., Nb⁵⁺, Ta⁵⁺) are in a M site;
• ● for high-oxygen-rate compositions (e.g., O₁₅);
• ● for high-fluorine-rate compositions (e.g., F₁₅).

The various types of stoichiometry depend on the existence of vacancies (□) in either one or another site:

• ● all sites full: A₂BC₂M₅X₁₅ (e.g., K₃Li₂Nb₅O₁₅);
• ● half C sites empty: A₂BC□M₅X₁₅ (e.g., K₃NiNb₅O₁₅);
• ● C sites empty: A₂B□₂M₅X₁₅ (e.g., Ba₂NaNb₅O₁₅);
• ● B and C sites empty: A₂□□₂M₅X₁₅ (e.g., BaBiNb₅O₁₅).

Several solid solutions can be obtained between each kind of non-stoichiometric compositions (e.g. (Ba_{1. 5}Sr_0.5)(Sr_0.5□_0.5)□ ₂Nb₅O₁₅).

2.3 Phase transitions

In TTB crystals, there is a permanent anisotropy, even in centrosymmetric phases; it is not thus possible to reach the cubic symmetry. The prototype high temperature variety is tetragonal (4/mmm). The following Table 2 gives the various phase transition sequences with the corresponding properties as described in sections 3 and 5 [4]:

• ● no transition: it is the case of oxyfluorides with a relatively high fluorine substitution rate; very low degree of covalence in octahedral bonds prevent the formation of non-centro-symmetric phase;
• ● one transition: when the temperature decreases, a ferroelectric phase appears in either the tetragonal system (4mm) or the orthorhombic one (mm2) giving rise here to ferroelastic properties. Polar axis is along [001] for spherical cations (e.g., alkaline and alkaline earth cations); it is oriented along [010] when cations with 6s² lone pair, easily polarizable, are introduced (Tl⁺, Pb²⁺, Bi³⁺);
• ● two transitions: compounds with tantalum belong to this family (Table 2);
• ● three transitions were announced for Ba₂NaNb₅O₁₅: a ferroelastic phase is included between two other more symmetric phases with the same point space group [5]. Such a transition sequence is in fact more complicated with appearance of incommensurate phases. From room temperature to 523 K, the first incommensurate phase is nearly commensurate. On the contrary, from 523 to 561 K, the corresponding phase is clearly incommensurate. These anomalous effects were attributed to the influence of defects having their origin in either an off-stoichiometry or off-equilibrium distribution of the cations in the structure [6].

3.1 Generalities

Dielectric and pyroelectric studies have shown several TTB non-centrosymmetric phases to be ferroelectric. The values of T_c of the various samples are between 7 K (K₃Li₂Ta₅O₁₅) and 899 K (Ba_2.02Li_0.96Nb₅O₁₅). Fig. 2 gives, as an example, the temperature dependence of the permittivity ε′_r for a ceramic with Pb₂KNb₅O₁₅ composition.

3.2 Origin of the ferroelectricity

Ferroelectrics may be divided into two basic types (‘displacive’ and ‘order–disorder’):

• ● Displacive ferroelectrics: in the paraelectric phase, the small charged cation (e.g., Nb⁵⁺ in Ba₂KNb₅O₁₅) is situated at the barycentre of the oxygen octahedron. The polar variety is characterized by correlated shifts of the Nb⁵⁺ ions away from the centre of gravity of the octahedra.
• ● Order–disorder ferroelectrics: while the ions in the paraelectric phase are located randomly in equivalent sites within the polar phase, they are preferentially positioned in some of these sites, thus giving rise to local polarization and thus ferroelectricity. The fluoride K₃Fe₅F₁₅ of mixed valency is an interesting example: in this case, it is the Fe²⁺ and Fe³⁺ ions that are arranged in non-equivalent octahedral sites [K₃Fe²⁺(Fe²⁺₂Fe³⁺₂)F₁₅] by shifts along the polar axis.

3.3 Relation between composition, Curie temperature and chemical bonding

For a given structural type, the value of T_c depends on the composition. The variations of T_c may be correlated with factors of chemical bonding such as size, coordination or electronic configuration of cations, bond covalency, order–disorder, etc. [7,8].

3.4 Prediction of ferroelectricity

The transition from paraelectric to ferroelectric phase can occur through atomic shifts associated with distortion and/or rotation of octahedra. In both cases, when there is a transition from the non-polar to the polar form, low-amplitude atomic shifts Δz occur (< 1 Å) in the direction of the polar axis, thus giving a resultant polarization along the same axis. An empirical relationship between T_c and Δz has been demonstrated: T_c = 2 × 10⁴(Δz)² (Ų) [14].

Examination of the atomic positions of a polar crystalline network (having no centre of symmetry but a polar axis) makes it possible not only to predict the ferroelectric properties but also the value corresponding of T_c. Such relation was applied for various TTB crystals derived from (Ba,Sr)_2.5Nb₅O₁₅, K₃Li₂Nb₅O₁₅…

4.1 Introduction

According to their particular dielectric behaviour, materials may be divided into two different classes, depending on whether they are classical ferroelectric or relaxor:

• ● a maximum of ε′_r and a value of the Curie temperature T_c, no frequency-dependent for ferroelectrics;
• ● a maximum of ε′_r at a temperature called T_m, the two corresponding values varying with frequency for relaxors [15].

Concerning the relaxors, at least two different cations have to be localised in the same crystallographic site. Although relaxors have no macroscopic polarization (thus no P–E hysteresis loop), they are of great interest for dielectrics in capacitors and actuators [16]. The relaxor materials usually used are perovskite lead-based ceramics, for example PbMg_1/3Nb_2/3O₃ (PMN) and derived compounds. To date, various physical models have been described to explain the properties of relaxors [17]: compositional fluctuations and diffuse phase transition [18,19], the superparaelectric model [20], the nanostructure-octahedral model [21–24], the dipole-glass or the more recent derived model [25], the random-field model [26], the domain-wall model [27] and the random-layer model [28].

4.2 Lead-based TTB relaxors

Contrary to the perovskite class, the TTB Pb-based relaxors are not very numerous and have not been widely studied. However, some recent studies have been dedicated to this material class [17,29]. As an example, Fig. 3 shows the temperature dependence of ε′_r at various frequencies. At least one cation ferroelectrically active in the octahedral site must be present. The relaxor effect is simultaneously due to a disorder of the lead position and to a disorder of the cationic distribution in the A and B sites. The substitutions in the M site induce a relaxor state if the long-range order is not induced by a local dipolar order (e.g., tantalates).

4.3 Lead-free TTB relaxors

Such materials are of great interest as environment-friendly applications. The first compositions announced as relaxors concerned the Ba_2.5(1–x)Sr_2.5xNb₅O₁₅ solid solution [30–32]. Very recently, relaxor behaviour was demonstrated in other compositions: e.g. BaLaNb₅O₁₅, BaBiNb₅O₁₅, SrK₂Nb₅O₁₄F, BaNa₂Nb₅O₁₄F… [33]. Some solid solutions situated between classical ferroelectric and relaxor have also been studied. Such is the case with A₂B(Nb_1–xTa_x)₅O₁₅: the replacement of very ferroelectrically active Nb⁵⁺ by the less active Ta⁵⁺ transforms the macroscopic polarization into a local one for the highest values of x. This is also the case with the Ba₂NaNb₅O₁₅–BaNa₂Nb₅O₁₄F system; for compositions close to the oxide, the behaviour is ferroelectric, while it becomes relaxor when the fluorine rate and thus the sodium rate is sufficiently high (Fig. 4) [34]. The frequency dependence of the permittivities of a ceramic with a composition BaNa₂Nb₅O₁₄F clearly displays a frequency relaxation at 77 K, while it disappears at 300 K, i.e. for T > T_m (T_m = 140 K at 10³Hz) (Fig. 5). The crystal structure determination of this compound is in good agreement with the dielectric properties: the A-site is statistically occupied by equal quantities of Ba²⁺ and Na⁺, thereby giving a cationic disorder in this A-site, while the B-site is filled by Na⁺ cations [35].

Of all the lead-free compounds studied, it is with Bi³⁺, another 6 (sp)² lone pair cation, that the highest value of T_m was obtained: T_m (BaBiNb₅O₁₅ = 319 K at 10³ Hz). Such a result is in good agreement with that obtained for lead-free compositions derived from BaTiO₃ [36].