**3.1 Sintering of α-alumina and induced microstructure**

The polycrystalline alumina samples (of 0.2 cm thickness and 1.6 cm diameter) were processed, at Ecole Nationale Supérieure des Mines "ENSM" of Saint Etienne (France), by sintering from two types of powders of different purities (Table 1). The first referred below as "pure", elaborated by the Exal process and provided by CRICERAM Co., contains about 150 ppm of different impurities (with 90 ppm of silicon). The second referred as "impure", elaborated by the Bayer process and provided by REYNOLDS Co., has an impurity content near 4000 ppm (with 1497 ppm of silicon). In Table 1, the compositions of single crystals, which will be considered as reference material, are also given (cf. next section).

Before sintering, the powders were prepared according to conventional procedures involving successively aqueous dispersion, adding of organic binders, spray drying, uniaxial die forming and cold isostatic pressing. Sintering near theoretical density was performed in air with a firing schedule (Fig. 1), which comprises:


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

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

to form F centers (or V centers). In fact, upon trapping one electron (or two electrons), VO

becomes a F+ center (or a F center). Anionic vacancies can also be associated with a substitutional divalent cation ' M to form F Al cation center (such as FMg or FCa). The F, F+ and Fcation act as a donor centers. The energy levels of F and F+ are respectively estimated around

Grain boundaries are the interfaces between like crystals, at which atomic planes are always disrupted to some extent. The atomic order of the lattice is preserved up to within approximately a unit cell of the dividing plane. Thus, the disordered region of a grain boundary is typically only 0.5—1 nm wide, although it does vary somewhat with the type of boundary and the crystal lattice periodicity. Grain boundaries provide segregation sites for

The polycrystalline alumina samples (of 0.2 cm thickness and 1.6 cm diameter) were processed, at Ecole Nationale Supérieure des Mines "ENSM" of Saint Etienne (France), by sintering from two types of powders of different purities (Table 1). The first referred below as "pure", elaborated by the Exal process and provided by CRICERAM Co., contains about 150 ppm of different impurities (with 90 ppm of silicon). The second referred as "impure", elaborated by the Bayer process and provided by REYNOLDS Co., has an impurity content near 4000 ppm (with 1497 ppm of silicon). In Table 1, the compositions of single crystals,

Before sintering, the powders were prepared according to conventional procedures involving successively aqueous dispersion, adding of organic binders, spray drying, uniaxial die forming and cold isostatic pressing. Sintering near theoretical density was

which will be considered as reference material, are also given (cf. next section).

performed in air with a firing schedule (Fig. 1), which comprises:

''' x

Al Al Al Al 3 M V (3 M : V ) • • + ⇔ (6)

•• (or cationic vacancies ''' V ) can be associated with electrons (or holes) Al

••

'''

**2.1.4 Association of point defects with charges** 

**2.2 Extended defects: Grain boundaries** 

3 and 3.8 eV below the edge of the conduction band (Kröger, 1984).

**3.1 Sintering of α-alumina and induced microstructure** 

cations (Eq. 4):

schedule.

Anionic vacancies VO

impurities and defects.

**3. Sintering of α-alumina** 


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

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

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.

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 diameter of the impure polycrystalline alumina sample.

Effects of the Microstructure Induced by Sintering on the Dielectric Properties of Alumina 559

**3.3 Characterization of defects in sintered alumina using positron annihilation lifetime** 

In this section, complementary investigations concerning the use of Positron Annihilation Lifetime Spectroscopy "PALS" for the characterization of defects in alumina will be summarized (Moya et al., 2003; Si Ahmed et al., 2005). After a short description of the

The positron lifetime spectra of the samples, identical to those described in Table 1, were recorded at room temperature using a conventional fast-fast coincidence system with γ detectors consisting of plastic scintillators characterized by a time resolution of 270 ps. The 22Na positron source, 10 μCi sealed by 0.75 μm thick nickel foils, was sandwiched between two identical samples (of 20 mm diameter and 2 mm thickness). The spectra were measured in 2000 channels, with a calibration of 27 ps/channel, collecting 6.9×106 to 20×106 counts.

The experimental spectra were fitted via a LTV.9 program (Kansy, 1996), in which a three-state trapping model was introduced into the source code (Krause-Rehberg & Leipner, 1999).

In the case of single crystal Pi-Kem, the spectra analysis reduces to only one lifetime component (τb = 117 ± 1 ps) associated with reasonable confidence to annihilation in bulk free defects. The quite high intensity of this component, (98.4 ± 1.6) %, appears as an unequivocal justification of the absence of discernable defects that are able to trap positrons (e.g., dislocations, negatively charged vacancies, neutral complexes). This result is also interpreted as a confirmation of the very low impurity content, which therefore justifies its choice as reference material for assessing the effects of both the microstructure achieved by the sintering process and the impurity content. For the sintered samples, three lifetime components were deduced. The shortest lifetime (τb = 122 ± 4 ps) was attributed to annihilation in the bulk free defects as it is very close to the one of the reference material, the intermediate (τg = 137 ± 2 ps) to trapping in defects within the grains and the longest

Since Silicon is the main impurity in sintered samples, the possible defects felt by positrons

sintering temperatures and dwelling times (Lagerlöf & Grimes, 1998). In any case, the positron lifetime in all these defects is expected to have about the same value (τg = 137 ± 2 ps) because it is primarily determined by ''' V (Moya et al., 2003). The nature of clusters at Al grain boundaries is more difficult to ascertain because of the competition between all impurities for the segregation sites. However, one can speculate that the lifetime of about 400 ps (τgb = 397 ± 22 ps) reflects positron trapping in neutral or negatively charged clusters

that have the strongest tendency for segregation, for instance SiO2, MgO and CaO. In

•• could stem from the dissolution of CaO (Eq. 5), which, incidentally displays

''' '' Al Al (Si :V ) • , ''' '

Al Al (3Si :V ) • is more likely than the others due to the

•• , which are induced by the impurities

Al Al (2Si :V ) • , ''' x

Al Al (3Si :V ) •

procedure, we will spotlight the results relevant to the charging properties.

(τgb = 397 ± 22 ps) to trapping in clusters located at grain boundaries.

by far the highest enrichment ratio, about 1300 (Dörre & Hübner, 1984).

within the grains are isolated vacancies ''' V and Al

of charge compensating native vacancies ''' V and Al VO

particular, VO

clusters. However, the neutral cluster ''' x

**spectroscopy** 

**3.3.1 Experimental procedure** 

**3.3.2 Spectra analysis** 


Table 2. Sintering temperature, dwelling time at the sintering temperature and corresponding grain diameters and densities (Liebault, 1999).

Fig. 2. Microstructure of the 1.2 µm grain diameter of the impure polycrystalline alumina sample (SEM image).
