**2. Defects in α-alumina**

The α-alumina, exhibits the hexagonal corundum structure. In this structure, Al3+ cations occupy only two-thirds of the available sites and an interstitial unoccupied site arises between alternate pairs of Al3+. Charge trapping in alumina may take place around defects that can be intrinsic in nature or stemming from the dissolution of impurities (i.e., the foreign cations and their charge compensating defects). In sintered materials, one has also to take into account the effect of grain boundaries, segregation of impurities and defects at interfaces. These defects are characterized by energy levels within the wide band gap (of about 9 eV in alumina).

#### **2.1 Point defects**

#### **2.1.1 Intrinsic point defects (Schottky and Frenkel defects)**

The Schottky defects consist of pairs of negatively charged cationic vacancies ''' *VAl* and positively charged anionic vacancies *VO* •• . The vacancies must be formed in the stoichiometric ratio (two aluminium for three oxygen) in order to preserve the electrical neutrality of the crystal. Using the Kröger-Vink notation, the formation of Schottky defects obey to the reaction:

$$2\,\text{Al}\_{\text{Al}}^{\text{x}} + 3\,\text{O}\_{\text{O}}^{\text{x}} \Leftrightarrow 2\,\text{V}\_{\text{Al}}^{\text{''}} + 3\,\text{V}\_{\text{O}}^{\bullet\text{•}} + \text{Al}\_{2}\text{O}\_{3} \tag{1}$$

The Frenkel defects are formed when the Al3+ cation (Eq. 2) or the O2– anion (Eq. 3) is displaced from its normal site onto an interstitial site giving a vacancy and an interstitial pair:

$$\text{Al}\_{\text{Al}}^{\text{x}} \Leftrightarrow \text{V}\_{\text{Al}}^{\text{''}} + \text{Al}\_{\text{i}}^{\text{\*\*\*}} \tag{2}$$

$$\mathbf{O}\_{\rm O}^{\times} \Leftrightarrow \begin{aligned} \mathbf{V}\_{\rm O}^{\bullet \bullet} + \mathbf{O}\_{\rm i}^{\circ} \end{aligned} \tag{3}$$

Simulation results show that the formation energies of intrinsic point defects in α-alumina are relatively high (Atkinson et al., 2003). They are estimated respectively for Schottky defects, cation Frenkel and anion Frenkel at 5.15, 5.54 and 7.22 eV.

#### **2.1.2 Extrinsic point defects**

554 Sintering of Ceramics – New Emerging Techniques

to a release of stored energy. If the amount of this energy is sufficient, breakdown could set in causing irreversible damages of the material (Blaise & Le Gressus, 1991; Moya & Blaise,

It appears that an improvement of the breakdown strength would require that conduction, which tends to decrease density of trapped charges, be favored to some extent without, however, substantially altering the insulating properties. Conduction will also be referred as the ability of the material to spread charges. Therefore, the control of the competition between charge accumulation (trapping) and spreading (conduction), via the fabrication processes, is a key technological concern. The foregoing arguments motivate the need to develop methods for the characterization of charge conduction (conversely charge trapping) and underscore furthermore the importance of controlling the microstructural development during sintering of ceramic insulators. The purpose of this chapter is to provide the physical background for a more comprehensive understanding of the effects of the microstructure (and the various defects) induced by the sintering conditions on charge conduction in alumina. This understanding, which could be generalized to other ceramics, appears as prerequisite for the fabrication of

The α-alumina, exhibits the hexagonal corundum structure. In this structure, Al3+ cations occupy only two-thirds of the available sites and an interstitial unoccupied site arises between alternate pairs of Al3+. Charge trapping in alumina may take place around defects that can be intrinsic in nature or stemming from the dissolution of impurities (i.e., the foreign cations and their charge compensating defects). In sintered materials, one has also to take into account the effect of grain boundaries, segregation of impurities and defects at interfaces. These defects are characterized by energy levels within the wide band gap (of

The Schottky defects consist of pairs of negatively charged cationic vacancies ''' *VAl* and

stoichiometric ratio (two aluminium for three oxygen) in order to preserve the electrical neutrality of the crystal. Using the Kröger-Vink notation, the formation of Schottky defects

The Frenkel defects are formed when the Al3+ cation (Eq. 2) or the O2– anion (Eq. 3) is displaced from its normal site onto an interstitial site giving a vacancy and an interstitial

x x '''

•• . The vacancies must be formed in the

Al O Al O 2 3 2 Al 3 O 2 V 3 V Al O •• +⇔ ++ (1)

x ''' Al V Al Al Al i ⇔ + ••• (2)

1998; Stoneham, 1997).

**2. Defects in α-alumina** 

about 9 eV in alumina).

**2.1 Point defects** 

obey to the reaction:

pair:

insulators of improved dielectric breakdown strength.

**2.1.1 Intrinsic point defects (Schottky and Frenkel defects)** 

positively charged anionic vacancies *VO*

Extrinsic point defects are entailed by the dissolution of foreign elements. The solubility of an impurity depends mainly on its cation size (generally, small size elements exhibit high solubility). The charge compensating defects accompanying the dissolution of aliovalent impurities (i.e, defects that are required for ensuring the electrical neutrality) are determined not only by their valence (charge) but also by their position (interstitial or substitutional) in the host lattice.

In the case of a cation (M) greater in valence than the host cation (Al3+), the dissolution mode in substitutional position is most likely the cationic vacancy compensation mechanism (Atkinson et al., 2003). Accordingly, for tetravalent cations, in MO2 (such as SiO2 or TiO2), the dissolution reaction is:

$$2\,\text{3 MO}\_2 + 4\,\text{Al}\_{\text{Al}}^{\text{x}} \Leftrightarrow \,\text{3 M}\_{\text{Al}}^{\bullet} + \text{V}\_{\text{Al}}^{\text{v}} + 2\,\text{Al}\_2\text{O}\_3 \tag{4}$$

This compensation by a cationic vacancy is somewhat corroborated by experiments involving solution of Ti4+ in α-Al2O3 (Mohapatra & Kröger, 1977; Rasmussen & Kingery, 1970).

For divalent cations, in MO (such as MgO or CaO), the anionic vacancy compensation of substitutional ' M , is suggested (Atkinson et al., 2003): Al

$$2\,\mathrm{MO} + 2\,\mathrm{Al}\_{\mathrm{Al}}^{\infty} + \mathrm{O}\_{\mathrm{O}}^{\infty} \Leftrightarrow \,\mathrm{2}\,\mathrm{M}\_{\mathrm{Al}}^{\dagger} + \mathrm{V}\_{\mathrm{O}}^{\bullet\bullet} + \mathrm{Al}\_{2}\mathrm{O}\_{3} \tag{5}$$

The interstitial dissolution of monovalent elements, in M2O (such as Na2O or Ag2O), can be governed by a host cationic vacancy compensation mechanism. However, a selfcompensating dissolution mode, involving both interstitial and substitutional positions of M, is also expected (Gontier-Moya et al., 2001).

In the case of isovalent elements, in M2O3 (such as Cr2O3 or Y2O3), the dissolution will not create charged defects in the lattice but can induce a stress field due to the misfit arising from the difference in cation radii.

As previously pointed out, the formation energies of intrinsic defects are very high in α-alumina. Consequently, a few ppm of impurities will make the concentrations of extrinsic defects higher than those of the intrinsic ones, even at temperatures near the melting point (Kröger, 1984; Lagerlöf & Grimes, 1998).

#### **2.1.3 Point defects association**

Isolated point defects can be associated, at appropriate temperature, to form neutral or charged defect clusters. This association leads to a substantial reduction in the solution

Effects of the Microstructure Induced by Sintering on the Dielectric Properties of Alumina 557


**Alumina powders** "**pure**" **(Criceram)** 90 5 < 5 40 12 --- --- ---

"**impure**" **(Reynolds)** 1497 686 723 404 415 --- --- ---

**Single crystal (RSA)** 290 16 < 10 19 48 --- --- ---

**Single crystal (Pi-Kem)** --- 0.6 0.2 1.5 9 2.5 0.4 0.3

**SiO2 CaO MgO Na2O Fe2O3 K2O Cr2O3 TiO2**



Table 1. Composition of alumina materials (impurities in ppm).

**1K/min** 

**120min** 

Fig. 1. Schematic description of the firing schedule of the sintering process.

**1K/min** 

**60min** 

diameter of the impure polycrystalline alumina sample.

The grain diameters, d, and densities of the sintered samples, which were achieved via the control of the sintering temperature, Ts, and the dwelling time, ts, are given in Table 2.

**Time (min)**

**500 1000 1500 2000** 

**2K/min 10K/min** 

**ts**

The grain sizes were determined by the intercept method. The sample surfaces were first polished and then thermally etched to reveal the grain boundaries. Etching was performed by holding the sample at 50 K below the sintering temperature Ts (during 15 to 30 min) after a rapid heating. The average grain sizes were calculated from the values of 100 to 200 grain size measurements from Scanning Electron Microscope "SEM" images of the surface using different magnifications. Figure 2 shows, as example, the microstructure of the 1.2 µm grain

three steps during 5 hours,

**Alumina powders** 

**773 623 453** 

**300** 

**Temperature (K)** 

**1K/min** 

**120min** 

**Ts**


energy due to strong coulombic interaction and lattice relaxation. A typical example of defect clustering is the association of defects induced by the dissolution of tetravalent cations (Eq. 4):

$$\text{\textbullet M}\_{\text{Al}}^{\bullet} + \text{V}\_{\text{Al}}^{\bullet} \Leftrightarrow \text{\textbullet (\text{\textbullet M}}\_{\text{Al}}^{\bullet} : \text{V}\_{\text{Al}}^{\bullet})^{\text{\textbullet}} \tag{6}$$

Mass action calculations (Lagerlöf & Grimes, 1998) have shown that the relative concentrations of extrinsic defects (point defects and defect associations) depend on the equilibrium temperature under which they are created. In sintered alumina, they can be determined by the sintering temperature and time, i.e. isothermal part of the firing schedule.
