**3. New processing step for varistor ceramics**

#### **3.1. Microwave sintering**

scale and also allows the preparation of ceramic powders with high surface area and films or gels fibers, which have high technological importance. The method has advantages over other conventional methods such as high purity, resin calcination at low temperatures, and synthesis

Also, the controlled precipitation method (CPM) can be used to prepare precursor powders. In this case, the solution containing the cation of interest is added to another solution contain‐ ing a precipitating agent that can be a base or anion (ammonia, urea, and oxalic acid). In this way, the final product precipitate is separated by filtration, washed, dried, and calcined to obtain the oxide. The precipitation process has a complex mechanism, which is dependent on the degree of saturation of the ion to be used. The process starts by formation of cluster from chemical species in the solution, known as nucleation process. Reaching the ion solubility limits

To check the influence of the chemical synthesis route the electrical properties of the SnO2 based varistors, Mosquera et al. [36] carried out the synthesis of tin oxide by controlled precipitation and polymeric precursor (Pechini) methods that's offering the strict control of the chemical purity and the particle size of the raw material. The system SnO2.Co3O4.Nb2O5.TiO.Al2O3, with 1 mol% Co3O4, 0.05 mol% Nb2O5, and 1 mol% TiO2 and variations of 0.05 (named SCNT05A), 0.1 (named SCNT1A), and 0.2 mol% (named SCNT2A) of Al2O3 were prepared. Following synthesis, the materials were submitted to heat treatment at 600°C/1 h (controlled precipitation method, CPM) and 600°C/2 h (Pechini method, PCH) to eliminate organic matter and obtain the full formation of the oxide. The use of dopants in both methods resulted in no change in the SnO2-crystal structure or formation of secondary phases due to have been added small amounts of dopants (Figure 4). The SEM micrographs indicated the influence of the addition of the aluminum grain growth control. The Pechini method

**Figure 4.** SEM for sintered samples at 1350°C, obtained by CPM and PCH (a) 0.05% Al2O3 and (b) 0.1% Al2O3. XRD for

the growth stage of formed centers and finally the formation of precipitates [35].

of oxides with defined and controlled properties [32–34].

32 Advanced Ceramic Processing

showed smaller grains and more porous samples.

varistor system whit 0.2% Al2O3 synthesized by CPM and PCH [36].

#### *3.1.1. Thermodynamics of sintering*

Sintering is the processing step that aims to confer mechanical strength to ceramic or metal powders, shaped by pressing or deposited as films. The process occurs by coalescence of the particles in solid or liquid phase to form a more dense mass. The sintering is an irreversible process and results in decrease of the total free energy of the system. Mathematically, the equation related to total energy of the system is

$$
\Delta G = \Delta G\_s + \Delta G\_l < 0 \tag{10}
$$

where Δ*G* is the total free energy, Δ*G*<sup>s</sup> is the surface free energy, and Δ*G*<sup>i</sup> is the energy of each particular system [37].

#### *3.1.2. Driving force*

For the decrease of free energy of the system, there is a force that induces microstructural changes, replacing the contact points between the particles by grain boundaries, closing the pores, densifying, and making the material a hard solid. In addition to the system power source, the sintering mechanisms are also a contributing factor induced by driving forces. Figure 6 shows the possible forces involved in the sintering process: surface free energy, applied external pressure, and chemical reaction [38].

**Figure 6.** The three main drivers for solid densification: surface free energy, applied pressure, and chemical reaction [38].

**Figure 7.** Diagram flow of vacancies on the surface. The atoms flow is opposite to the vacancy [38].

The surface energy is related to the surfaces curve and characterized by vacancies and gaps. The surfaces energy is the main force that sinters the material by mass flow through the region of higher concentration to a lower concentration region where vacancies and gaps, as shown in Figure 7.

The variation of free energy during sintering is represented by Eq. 11:

$$
\delta \mathcal{G} = \left. \delta \right| \mathcal{Y}\_{\text{SS}} dA\_{\text{SS}} + \left. \delta \right| \mathcal{Y}\_{\text{SV}} dA\_{\text{SV}} \tag{11}
$$

where the free energy variation depends on the variation on interfacial energy as a function of the surface area. The surface tension solid–solid (*γ*S/S) is smaller than the surface tension between vapor-solid (*γ*S/V), and the interfacial energy is higher when there are many vacancies in the material, so there is a mass transfer gradient that favors the formation of necks between the particles and the resulting in joint, reducing the solid–vapor area (pore) [37].
