**2. Fundamentals of microwave heating**

Microwaves are electromagnetic waves in the frequency band of 300 MHz (3 × 108 cycles/second) to 300 GHz (3 × 1011 cycles/second), which correspond to a wavelength range of 1 m to 1 mm. Within this portion of the electromagnetic spectrum there are frequencies that are used for cellular phones, radar, and television satellite communications (Thostenson & Chou, 1999). Typical frequencies for materials processing are 915 MHz, 2.45 GHz, 5.8 GHz, 22.00 GHz, 24.12 GHz, 28GHz and 60GHz, but only 915 MHz and 2.45 GHz are widely applied ((Katz, 1992; Committee on Microwave Processing of Materials: An Emerging Industrial Technology et al., 1994). The advantages of higher frequencies are more uniform electric field distribution in the cavity and higher power dissipated in dielectric materials. However, microwave apparatus is available on a very limited basis and at extremely high cost.

The interaction of an electric field with a material may elicit several responses, and microwaves can be reflected, absorbed and/or transmitted by the material. In a conductor, electrons move freely in the material in response to the electric field, resulting in electric current. Unless the material is a superconductor, the flow of electrons will heat the material through resistive heating. However, microwaves will be largely reflected from metallic conductors, and therefore such conductors are not effectively heated by microwaves. In insulators, electrons do not flow freely, but electronic reorientation or distortions of induced or permanent dipoles can give rise to heating (Committee on Microwave Processing of Materials: An Emerging Industrial Technology et al., 1994).

Because microwaves generate rapidly changing electric fields, these dipoles change their orientations rapidly in response to the changing fields. If the electric field change takes place close to the natural frequency at which reorientation can occur, the maximum amount of energy is consumed, resulting in optimum heating. In microwave processing terminology, this event is described by the term "well-coupled" material.

It is known that in dielectric materials the external electric field causes a redistribution of internal bound charges, which results in the polarization of the material. A measure of the response of a material to an external electric field is its dielectric permittivity, *ε*. If the

Microwave Fast Sintering of Ceramic Materials 7

" " tan ' ' ε ε

ε ε

The charging current for a simple dielectric plate with a sinusoidal applied voltage is given by *I*c = *i*ωε'*E* and the loss current by *I*l = ωε"*E = I*l = σ*E*, where σ is the dielectric conductivity. Engineers concerned with dielectric heating will generally use the dielectric constant, ε', and the dielectric conductivity, σ, to characterize the processed material and express its response

The power absorbed per unit volume, considering that the electric field is uniform

( ) ( ) <sup>1</sup> 22 2 2

 ω ε

 μ"" " " (5)

*P rms rms* = Ε+ Η = Ε + Η

where *Erms* and *Hrms* are the root mean squares of the internal electric and magnetic fields.

Equation (5) shows that the power dissipated in a ceramic body during microwave processing is directly related to the applied frequency (ω = 2πf) and the material's conductivity, σ (σ = ωε"). For instance, 25 times more power can be dissipated in alumina at

Depending on their electrical and magnetic properties, materials can be divided into three categories according to their microwave absorption properties. Materials with a very low dielectric loss factor (or conductivity) allow microwaves to pass through with very little absorption and are said to be transparent to microwaves. Materials with an extremely high dielectric loss factor, i.e. metals, reflect microwaves and are said to be opaque. Materials

Ceramics with loss factors between the limits of 10-2 < ε < 5 are good candidates for microwave heating. Ceramics with ε < 10-2 would be difficult to heat, while those with ε >

Absorption energy is quantified by the absorbed power per unit volume and by the attenuation distance, *D* (or depth of penetration), which expresses the magnitude of the

A plane wave varying periodically in time with the frequency f = ω/2π and advancing in the + x direction through space presents a complex propagation factor, γ (Metaxas & Binner, 1990):

= =+ *j j*

Equating the real and imaginary parts of Equation (6), the attenuation and phase factors can

<sup>4</sup> ( ' " " ')

2

π

 ε μ ε μ

λω

α β

= + (7)

(6)

δ

at a given frequency.

28 GHz, than at 2.45 GHz.

energy attenuation inside the material.

throughout the volume, can be expressed by:

2

ωε

 ωμ

with intermediate loss tangents will absorb microwaves (Katz, 1992).

5 would absorb most of the heating on the surface and not in the bulk.

γ

where α is the attenuation factor and β is the phase factor of the wave.

be expressed in terms of permittivity and permeability (Von Hippel, 1954a):

α

ω ε \* \* μ

*r r*

= = (4)

external electric field is alternating (ac), the dielectric response of the material follows it, generally with some lag behind the field changes. To describe this phenomenon quantitatively, a complex dielectric permittivity that depends on the field frequency, *ω* (ω is equal to 2π*f,* where *f* is the frequency in cycles per second), is formally introduced:

$$\mathbf{e}(\alpha)\_\* = \mathbf{e}(\alpha)' - i\mathbf{e}(\alpha)'' = \mathbf{e}^\circ \left(\mathbf{e}^\circ(\alpha)' - i\mathbf{e}^\circ(\alpha)''\right) \tag{1}$$

where *i* = (–1)1/2, ε' is the permittivity (or dielectric constant), ε'' is the dielectric loss factor, εo is the permittivity of a vacuum, and εr is the relative permittivity (or relative dielectric constant) (εr' equals ε'/εo and εr" equals ε''/εo).

The real component of complex permittivity, ε', is commonly referred to as the dielectric constant. However, because ε' is not constant but may vary significantly with frequency and temperature, it is generally referred to simply as permittivity.

However, microwave propagation in air or in materials depends on the dielectric and magnetic properties of the medium. Thus, the electromagnetic properties of a medium are characterized by complex permittivity and also complex permeability, μ\* (Equation 2). In magnetic materials, the dipoles may be able to couple with the magnetic component of the electromagnetic field and provide an additional heating mechanism. Similarly to the dielectric properties of materials, their magnetic permeability, μ', and magnetic loss, μ"*,*  must be considered in microwave processing,

$$
\mu(\alpha)\_\* = \mu \text{ (co)}\_\text{,} - \text{ i } \text{tr (co)}\_\text{,} \tag{2}
$$

where μ' and μ'' are the permeability and magnetic loss factor, respectively.

In an ideal dielectric, the electric charge adjusts instantaneously to any change in voltage or field. In practice, however, there is an inertia-to-charge movement that shows up as a relaxation time for charge transport. Relaxation time, τ, can be defined as the time interval in which a disturbed system is restored to its equilibrium configuration after the application of a microwave field. The behavior of τ determines the frequency and temperature dependencies of ε' and ε" and varies widely in liquids and solids (Committee on Microwave Processing of Materials: An Emerging Industrial Technology et al., 1994). Thus, when an alternate electric field interacts with a dielectric, the time required for polarization appears as a phase retardation of the charging current. Instead of advancing by 90o, it advances by some angle, δ, other than 90o. This phase shift, which corresponds to a time lag between an applied voltage and induced current, causes loss of current and dissipation of energy in the material (Kingery et al, 1976). The imaginary term in equation (1), ε'', which quantifies the power dissipated in the material, is known as the dielectric loss factor.

Another term sometimes used to quantify the "lossiness" of a material is the loss tangent (Equation 3). The inverse of the loss tangent is the quality factor, *Q*, which is widely used in waveguide technology (Von Hippel, 1954a).

$$\tan \delta = \frac{\varepsilon^\circ \mu^\circ - \varepsilon^\circ \mu^\circ}{\varepsilon^\circ \mu^\circ + \varepsilon^\circ \mu^\circ} \tag{3}$$

For negligible magnetic loss (μ'' = 0) the loss tangent is expressed as:

external electric field is alternating (ac), the dielectric response of the material follows it, generally with some lag behind the field changes. To describe this phenomenon quantitatively, a complex dielectric permittivity that depends on the field frequency, *ω* (ω is

where *i* = (–1)1/2, ε' is the permittivity (or dielectric constant), ε'' is the dielectric loss factor, εo is the permittivity of a vacuum, and εr is the relative permittivity (or relative dielectric

The real component of complex permittivity, ε', is commonly referred to as the dielectric constant. However, because ε' is not constant but may vary significantly with frequency and

However, microwave propagation in air or in materials depends on the dielectric and magnetic properties of the medium. Thus, the electromagnetic properties of a medium are characterized by complex permittivity and also complex permeability, μ\* (Equation 2). In magnetic materials, the dipoles may be able to couple with the magnetic component of the electromagnetic field and provide an additional heating mechanism. Similarly to the dielectric properties of materials, their magnetic permeability, μ', and magnetic loss, μ"*,* 

In an ideal dielectric, the electric charge adjusts instantaneously to any change in voltage or field. In practice, however, there is an inertia-to-charge movement that shows up as a relaxation time for charge transport. Relaxation time, τ, can be defined as the time interval in which a disturbed system is restored to its equilibrium configuration after the application of a microwave field. The behavior of τ determines the frequency and temperature dependencies of ε' and ε" and varies widely in liquids and solids (Committee on Microwave Processing of Materials: An Emerging Industrial Technology et al., 1994). Thus, when an alternate electric field interacts with a dielectric, the time required for polarization appears as a phase retardation of the charging current. Instead of advancing by 90o, it advances by some angle, δ, other than 90o. This phase shift, which corresponds to a time lag between an applied voltage and induced current, causes loss of current and dissipation of energy in the material (Kingery et al, 1976). The imaginary term in equation (1), ε'', which quantifies the

Another term sometimes used to quantify the "lossiness" of a material is the loss tangent (Equation 3). The inverse of the loss tangent is the quality factor, *Q*, which is widely used in

> "' '" tan '' "" ε μ

ε μ

δ

ε μ

ε μ

ε(ω)\* = ε(ω)' – *i*ε(ω)" = εo (εr(ω)' – *i*ε*r*(ω)") (1)

μ(ω)\* = μ (ω)' – *i* μ (ω)" (2)

<sup>−</sup> <sup>=</sup> + (3)

equal to 2π*f,* where *f* is the frequency in cycles per second), is formally introduced:

constant) (εr' equals ε'/εo and εr" equals ε''/εo).

must be considered in microwave processing,

waveguide technology (Von Hippel, 1954a).

temperature, it is generally referred to simply as permittivity.

where μ' and μ'' are the permeability and magnetic loss factor, respectively.

power dissipated in the material, is known as the dielectric loss factor.

For negligible magnetic loss (μ'' = 0) the loss tangent is expressed as:

$$\tan \delta = \frac{\varepsilon''}{\varepsilon'} = \frac{\varepsilon\_r''}{\varepsilon\_r'} \tag{4}$$

The charging current for a simple dielectric plate with a sinusoidal applied voltage is given by *I*c = *i*ωε'*E* and the loss current by *I*l = ωε"*E = I*l = σ*E*, where σ is the dielectric conductivity. Engineers concerned with dielectric heating will generally use the dielectric constant, ε', and the dielectric conductivity, σ, to characterize the processed material and express its response at a given frequency.

The power absorbed per unit volume, considering that the electric field is uniform throughout the volume, can be expressed by:

$$P = \frac{1}{2} \left( \alpha \rho \varepsilon \, ^\circ \text{E}^2 + \alpha \mu \, ^\circ \text{H}^2 \right) = \alpha \left( \varepsilon \, ^\circ \text{E}^2 \, \_{rms} + \mu \, ^\circ \text{H}^2 \, \_{rms} \right) \tag{5}$$

where *Erms* and *Hrms* are the root mean squares of the internal electric and magnetic fields.

Equation (5) shows that the power dissipated in a ceramic body during microwave processing is directly related to the applied frequency (ω = 2πf) and the material's conductivity, σ (σ = ωε"). For instance, 25 times more power can be dissipated in alumina at 28 GHz, than at 2.45 GHz.

Depending on their electrical and magnetic properties, materials can be divided into three categories according to their microwave absorption properties. Materials with a very low dielectric loss factor (or conductivity) allow microwaves to pass through with very little absorption and are said to be transparent to microwaves. Materials with an extremely high dielectric loss factor, i.e. metals, reflect microwaves and are said to be opaque. Materials with intermediate loss tangents will absorb microwaves (Katz, 1992).

Ceramics with loss factors between the limits of 10-2 < ε < 5 are good candidates for microwave heating. Ceramics with ε < 10-2 would be difficult to heat, while those with ε > 5 would absorb most of the heating on the surface and not in the bulk.

Absorption energy is quantified by the absorbed power per unit volume and by the attenuation distance, *D* (or depth of penetration), which expresses the magnitude of the energy attenuation inside the material.

A plane wave varying periodically in time with the frequency f = ω/2π and advancing in the + x direction through space presents a complex propagation factor, γ (Metaxas & Binner, 1990):

$$
\gamma = j\alpha \sqrt{\varepsilon^\* \mu^\*} = \alpha + j\beta \tag{6}
$$

where α is the attenuation factor and β is the phase factor of the wave.

Equating the real and imaginary parts of Equation (6), the attenuation and phase factors can be expressed in terms of permittivity and permeability (Von Hippel, 1954a):

$$
\alpha = \frac{\lambda \,\alpha^2}{4\,\pi} (\varepsilon^\prime \mu^\prime + \varepsilon^\prime \mu^\prime) \tag{7}
$$

Microwave Fast Sintering of Ceramic Materials 9

tens of meters to fractions of a millimeter. For example, at 2.45 GHz and room temperature, graphite and alumina have skin depths of 38 μm and 25 m (according to data in Von Hippel,

In general, at room temperature, many ceramics do not absorb microwaves appreciably at 2.45 GHz, and thus present high attenuation distances. However, their absorption can be increased by raising the temperature, adding absorbents (e.g., SiC, carbon, binders), altering their microstructure and defect structure (Agrawal, 1998) by changing their form (e.g., bulk vs. powder), or by changing the frequency of incident radiation (Clark &

The dielectric properties of ceramic materials are highly dependent on temperature, and their loss factor generally increases with temperature, improving the ability of "transparent" materials to couple with microwaves. The rate of temperature increase depends upon the type of ceramic and the operating frequency, but a sharp increase in microwave losses begins at temperatures of about 0.4–0*.*5 *Tm* (where *Tm* is the melting temperature of the material). In this temperature range, the bonds between ions in ionic crystals begin to break, and the electrons in covalent materials begin to populate the conduction bands. Due to this sharp increase in dielectric losses, "transparent" materials couple efficiently with microwaves. This is characteristic of solids with both ionic (Al2O3, ZrO2) and covalent (Si3N4, AlN) bonds. For instance, the attenuation distances of alumina and zirconia (Y-stabilized) change from meters at 20oC to 23 and 1 cm at 1200oC,

When the skin depth is greater than the dimension of the sample, this effect may be neglected. Conversely, when dimensions of samples are greater than its penetration depth penetration of microwave energy will be limited, making uniform heating impossible

Historically, there is a paucity of data on the dielectric properties of most materials as a function of temperature in the microwave range. The data reported in the literature indicate that there is a complex interdependence of dielectric properties on temperature and frequency (Clark & Sutton, 1996). Figures 1 and 2 illustrate the behavior of loss tangent, attenuation distance and reflection coefficient according to complex permittivity data

Von Hippel (1954b) compiled the first tabulation of measurements for numerous materials over a wide range of frequencies (10 Hz - 10 GHz). The materials he characterized were both organic and inorganic in nature and both liquid and solid. Subsequently, dielectric data on high temperature solid materials, including oxides, nitrides, silicates, rocks and minerals were obtained by Inglesias and Westphal (Inglesias & Westphal, 1967, as cited in Metaxas & Binner, 1990). Since then, four reports have been produced at the same MIT Laboratory for Insulation Research where Von Hippel obtained his results as described by Metaxas & Binner (Metaxas & Binner, 1990). These reports contain much valuable information on the frequency and temperature dependence of the dielectric properties of a large number of ceramic materials (both oxide and some non-oxide), as well as various minerals, many organic compounds and some foodstuffs. The frequency and temperature varied up to 25

published in the literature (Andrade et al., 1992; Arai et al., 1993; Batt et al., 1995).

GHz and 1000°C, respectively (Metaxas & Binner, 1990).

1954b; Metaxas & Binner, 1990), respectively.

Sutton, 1996).

respectively.

$$\beta = \alpha \sqrt{\frac{\varepsilon' \mu' - \varepsilon'' \mu''}{2} \left( 1 + \sqrt{1 + \left( \frac{\langle \varepsilon' \mu'' + \varepsilon'' \mu' \rangle}{\langle \varepsilon' \mu' + \varepsilon'' \mu'' \rangle} \right)^2} \right)} \tag{8}$$

where λ is the wavelength of the plane wave inside the material.

The attenuation produced by a dielectric is frequently expressed as the attenuation distance (or penetration depth or skin depth), *D*, defined as 1/α, through which the field strength decays to 1/e (0.368) of its original value. For materials with negligible magnetic loss (μ" = 0), and considering the permeability of the vacuum (μ' = μo):

$$D = \frac{1}{\alpha} = \frac{c}{o\nu} \sqrt{\frac{2}{\varepsilon\_r \left(\sqrt{1 + \tan^2 \delta} - 1\right)}}\tag{9}$$

where *c* is the speed of light.

Another parameter that can be defined is power penetration depth, *DP*, which is the distance at which the power drops to 1/e (0.368) from its value at the surface (Metaxas & Binner, 1990):

$$D\_P = \frac{1}{2\alpha} = \frac{D}{2} \tag{10}$$

It is important to differentiate between power penetration depth and electric field attenuation distance or skin depth (*D*), because at frequencies allocated for industrial use in the microwave regime, the power penetration depths could be very small indeed and the size of the ceramic to be treated, particularly when it is fairly lossy, could be many times larger than *Dp*, resulting in unacceptable temperature non-uniformities (Metaxas & Binner, 1990).

The index of absorption, *k*, can be expressed in terms of the attenuation, α, and the phase factor β, according to Equation (11). The reflection coefficient, *R* (the fraction of reflected power), for a normal incidence of the electromagnetic wave on a plane boundary between material and vacuum can also be expressed in terms of loss tangent (Equation 12) (Von Hippel, 1954b; Bykov et al., 2001):

$$k = \frac{\alpha}{\beta} = \sqrt{\frac{\sqrt{1 + \tan 2\delta} - 1}{\sqrt{1 + \tan 2\delta} + 1}}\tag{11}$$

$$R = \frac{1 - \sqrt{2\varepsilon\_r \text{"} \left[1 + \sqrt{1 + \text{tg}^2 \delta \text{"}} \right]} + \varepsilon\_r \text{"} \sqrt{1 + \text{tg}^2 \delta}}{1 + \sqrt{2\varepsilon\_r \text{"} \left[1 + \sqrt{1 + \text{tg}^2 \delta \text{"}} \right]} + \varepsilon\_r \text{"} \sqrt{1 + \text{tg}^2 \delta} \tag{12}$$

The absorption properties of non-metallic materials vary greatly in the microwave frequency range. The loss tangent, tan *δ*, varies at room temperature from 10−4–10−3 (for example in pure alumina and silicon nitride) up to 1 and higher (in carbides, borides, some oxides, and intermetallic compounds). Correspondingly, the penetration depth varies from

1 1

The attenuation produced by a dielectric is frequently expressed as the attenuation distance (or penetration depth or skin depth), *D*, defined as 1/α, through which the field strength decays to 1/e (0.368) of its original value. For materials with negligible magnetic loss (μ" =

1 2

− + <sup>=</sup> + +

'' "" ( ' " " ')

2

*<sup>c</sup> <sup>D</sup>*

= =

α ω ε

in unacceptable temperature non-uniformities (Metaxas & Binner, 1990).

*k*

ε

ε

α

β

εμ ε μ

where λ is the wavelength of the plane wave inside the material.

0), and considering the permeability of the vacuum (μ' = μo):

β ω

where *c* is the speed of light.

Hippel, 1954b; Bykov et al., 2001):

1990):

2

= = (10)

(8)

(9)

(11)

(12)

( ' ' " ")

εμ ε μ

εμ ε μ

<sup>+</sup>

( ) <sup>2</sup>

+ −

 δ

1 1 *<sup>r</sup>*

' tan

Another parameter that can be defined is power penetration depth, *DP*, which is the distance at which the power drops to 1/e (0.368) from its value at the surface (Metaxas & Binner,

> 1 2 2 *<sup>P</sup> <sup>D</sup> <sup>D</sup>* α

It is important to differentiate between power penetration depth and electric field attenuation distance or skin depth (*D*), because at frequencies allocated for industrial use in the microwave regime, the power penetration depths could be very small indeed and the size of the ceramic to be treated, particularly when it is fairly lossy, could be many times larger than *Dp*, resulting

The index of absorption, *k*, can be expressed in terms of the attenuation, α, and the phase factor β, according to Equation (11). The reflection coefficient, *R* (the fraction of reflected power), for a normal incidence of the electromagnetic wave on a plane boundary between material and vacuum can also be expressed in terms of loss tangent (Equation 12) (Von

> 1 21 1 21

δ

δ

2 2

 δ

 δ

2 2

*tg tg*

tan tan

+ − = = + +

1211 1

*tg tg <sup>R</sup>*

− ++ + + <sup>=</sup> + ++ + +

1 211 1 *r r*

*r r*

The absorption properties of non-metallic materials vary greatly in the microwave frequency range. The loss tangent, tan *δ*, varies at room temperature from 10−4–10−3 (for example in pure alumina and silicon nitride) up to 1 and higher (in carbides, borides, some oxides, and intermetallic compounds). Correspondingly, the penetration depth varies from

' [ ] '

 δε

 δε

' [ ] '

tens of meters to fractions of a millimeter. For example, at 2.45 GHz and room temperature, graphite and alumina have skin depths of 38 μm and 25 m (according to data in Von Hippel, 1954b; Metaxas & Binner, 1990), respectively.

In general, at room temperature, many ceramics do not absorb microwaves appreciably at 2.45 GHz, and thus present high attenuation distances. However, their absorption can be increased by raising the temperature, adding absorbents (e.g., SiC, carbon, binders), altering their microstructure and defect structure (Agrawal, 1998) by changing their form (e.g., bulk vs. powder), or by changing the frequency of incident radiation (Clark & Sutton, 1996).

The dielectric properties of ceramic materials are highly dependent on temperature, and their loss factor generally increases with temperature, improving the ability of "transparent" materials to couple with microwaves. The rate of temperature increase depends upon the type of ceramic and the operating frequency, but a sharp increase in microwave losses begins at temperatures of about 0.4–0*.*5 *Tm* (where *Tm* is the melting temperature of the material). In this temperature range, the bonds between ions in ionic crystals begin to break, and the electrons in covalent materials begin to populate the conduction bands. Due to this sharp increase in dielectric losses, "transparent" materials couple efficiently with microwaves. This is characteristic of solids with both ionic (Al2O3, ZrO2) and covalent (Si3N4, AlN) bonds. For instance, the attenuation distances of alumina and zirconia (Y-stabilized) change from meters at 20oC to 23 and 1 cm at 1200oC, respectively.

When the skin depth is greater than the dimension of the sample, this effect may be neglected. Conversely, when dimensions of samples are greater than its penetration depth penetration of microwave energy will be limited, making uniform heating impossible

Historically, there is a paucity of data on the dielectric properties of most materials as a function of temperature in the microwave range. The data reported in the literature indicate that there is a complex interdependence of dielectric properties on temperature and frequency (Clark & Sutton, 1996). Figures 1 and 2 illustrate the behavior of loss tangent, attenuation distance and reflection coefficient according to complex permittivity data published in the literature (Andrade et al., 1992; Arai et al., 1993; Batt et al., 1995).

Von Hippel (1954b) compiled the first tabulation of measurements for numerous materials over a wide range of frequencies (10 Hz - 10 GHz). The materials he characterized were both organic and inorganic in nature and both liquid and solid. Subsequently, dielectric data on high temperature solid materials, including oxides, nitrides, silicates, rocks and minerals were obtained by Inglesias and Westphal (Inglesias & Westphal, 1967, as cited in Metaxas & Binner, 1990). Since then, four reports have been produced at the same MIT Laboratory for Insulation Research where Von Hippel obtained his results as described by Metaxas & Binner (Metaxas & Binner, 1990). These reports contain much valuable information on the frequency and temperature dependence of the dielectric properties of a large number of ceramic materials (both oxide and some non-oxide), as well as various minerals, many organic compounds and some foodstuffs. The frequency and temperature varied up to 25 GHz and 1000°C, respectively (Metaxas & Binner, 1990).

Microwave Fast Sintering of Ceramic Materials 11

branch of the response curve. If the power is increased to exceed the upper critical power, the temperature will jump to the upper branch of the temperature-power curve, giving rise

> 0,0 0,2 0,4 0,6 0,8 1,0 1,2 1,4 1,6 1,8 b)

0 200 400 600 800 1000 1200

**C)**

**Temperature (o**

Another important characteristic of the interaction of microwaves with ceramic materials is the non-thermal influence of microwave fields on mass transport. Many investigators have reported unexpected effects resulting from the use of microwave radiation as an alternative energy source during the processing of materials. This has included apparent evidence for accelerated kinetics for a range of processes in ceramic, polymeric, and organic systems, including the microwave sintering of ceramic materials. This unexpected effect was named "microwave effect". As a general rule, the kinetics of synthesis and sintering reactions of ceramic materials is reportedly augmented by two or three orders of magnitude or even

In principle, the term "microwave effect", or, more strictly, "microwave field non-thermal effect", should be reserved for the deviations of microwave processes from conventional processes that occur given the identical temperature dynamics of these processes. Over the last decade, considerable effort has been focused on the development of theoretical models

Fig. 2. a) Attenuation distance b), loss tangent, and c) reflection coefficient of ZrO2.

more when conventional heating is substituted for microwave radiation.

**LossTangent, tan** δ

0 200 400 600 800 1000 1200

**C)**

**Temperature (o**

to thermal runaway.

**Attenuation Distance (cm)**

0 200 400 600 800 1000 1200

0,40 0,45 0,50 0,55 0,60 0,65 0,70 0,75 c)

**C)**

**Temperature (o**

**Reflection Coefficient** 

Fig. 1. a) Attenuation distance b), loss tangent, and c) reflection coefficient of SiC.

Studies (Sutton, 1989; Meredith, 1998) showed that when low-loss dielectric materials exhibit an abrupt increase in ε" with increasing temperature, the potential exists for very rapid changes in temperature. The temperature at which this abrupt change in ε" occurs is known as critical temperature, *Tc.* Above this temperature, the dielectric loss factor begins to increase, and the material begins to couple with microwaves. Figure 2 illustrates this behavior is when the loss tangent of zirconia increases significantly increases after 600oC.

However, many researchers have shown that thermal runaway in microwave-heated materials often occurs when critical temperature is reached. The sharp increase in microwave absorption with temperature may cause thermal instability, which is commonly known as temperature runaway.

The rapid rise in the dielectric loss factor with temperature is the main issue in thermal runaway (unstable accelerated heating). An increase in local temperature is accompanied by an enhanced microwave energy absorption, which results in local acceleration of heating, a further rise in temperature and the development of thermal runaway. This instability develops when microwave power exceeds some threshold value, which corresponds to an Stype dynamic curve of temperature versus power (Bikov et al., 2001). Below a "critical power level", the material will heat in a stable manner to a steady state value on the lower

0,4 0,5 0,6 0,7 0,8 0,9

0 200 400 600 800 1000 1200 1400

**C)**

**Temperature (o**

Studies (Sutton, 1989; Meredith, 1998) showed that when low-loss dielectric materials exhibit an abrupt increase in ε" with increasing temperature, the potential exists for very rapid changes in temperature. The temperature at which this abrupt change in ε" occurs is known as critical temperature, *Tc.* Above this temperature, the dielectric loss factor begins to increase, and the material begins to couple with microwaves. Figure 2 illustrates this behavior is when the loss tangent of zirconia increases significantly increases after 600oC.

However, many researchers have shown that thermal runaway in microwave-heated materials often occurs when critical temperature is reached. The sharp increase in microwave absorption with temperature may cause thermal instability, which is commonly

The rapid rise in the dielectric loss factor with temperature is the main issue in thermal runaway (unstable accelerated heating). An increase in local temperature is accompanied by an enhanced microwave energy absorption, which results in local acceleration of heating, a further rise in temperature and the development of thermal runaway. This instability develops when microwave power exceeds some threshold value, which corresponds to an Stype dynamic curve of temperature versus power (Bikov et al., 2001). Below a "critical power level", the material will heat in a stable manner to a steady state value on the lower

Fig. 1. a) Attenuation distance b), loss tangent, and c) reflection coefficient of SiC.

**LossTangent, tan** δ

1,0 b)

0 200 400 600 800 1000 1200 1400

**C)**

**Temperature (o**

0 200 400 600 800 1000 1200 1400

0,70 0,72 0,74 0,76 0,78 0,80 0,82 0,84 0,86 0,88 c)

known as temperature runaway.

**C)**

**Temperature (o**

**Reflection Coefficient**

0,16 0,20 0,24 0,28 0,32 0,36 0,40 0,44 0,48 a)

**Attenuation Distance (cm)**

branch of the response curve. If the power is increased to exceed the upper critical power, the temperature will jump to the upper branch of the temperature-power curve, giving rise to thermal runaway.

Fig. 2. a) Attenuation distance b), loss tangent, and c) reflection coefficient of ZrO2.

Another important characteristic of the interaction of microwaves with ceramic materials is the non-thermal influence of microwave fields on mass transport. Many investigators have reported unexpected effects resulting from the use of microwave radiation as an alternative energy source during the processing of materials. This has included apparent evidence for accelerated kinetics for a range of processes in ceramic, polymeric, and organic systems, including the microwave sintering of ceramic materials. This unexpected effect was named "microwave effect". As a general rule, the kinetics of synthesis and sintering reactions of ceramic materials is reportedly augmented by two or three orders of magnitude or even more when conventional heating is substituted for microwave radiation.

In principle, the term "microwave effect", or, more strictly, "microwave field non-thermal effect", should be reserved for the deviations of microwave processes from conventional processes that occur given the identical temperature dynamics of these processes. Over the last decade, considerable effort has been focused on the development of theoretical models

Microwave Fast Sintering of Ceramic Materials 13

sufficiently uniform heating of the body can be difficult. High heating rates can lead to localized heating, which can cause non-uniform properties and even cracking of the sample; as well thermal runaway when the temperature of the sample increases rapidly (Rahaman,

In microwave sintering, heat is generated internally through the interaction of the microwaves with the atoms, ions, and molecules of the material, which produces an inverse heating profile. Figure 3 presents a schematic diagram of heating by conventional and microwave processes. The microwave heating process is more volumetric, thus allowing higher heating rates. However, most research to date is based on conventional lowfrequency (2.45 GHz) microwave applicators, and at this frequency, many ceramics present poor microwave absorption characteristics. Thus, materials, that are transparent to microwaves, such as SiO2 and Al2O3 (ceramics with low-loss, as pure oxides and nitrides),

Many ceramic materials that are difficult to heat at room temperature possess electrical conductivity or dielectric loss factors that rapidly increase in magnitude as the temperature rises. Thus, these materials will absorb microwave energy if they can be preheated to a suitable temperature using another heat source. This has led to the development of hybrid heating methods (Krage, 1981; Kimrey et al., 1991). Hybrid heating can be achieved by using either an independent heat source, such as a gas or electric furnace in combination with microwaves, or an external susceptor material (high-loss material) that couples with the microwaves. In the latter case, the material is exposed simultaneously to radiant heat produced by the susceptor material and to microwaves (usually, the susceptor material is

Fig. 3. Heating patterns in: a) conventional, and b) microwave furnaces.

b)

Increasing the temperature (with radiant heat) is a common method many researchers employ to couple microwaves with poorly absorbing (low-loss) materials. Once a material is heated to its critical temperature, *Tc,* microwave absorption becomes sufficient to cause selfheating. This hybrid method can result in more uniform temperature gradients because the

1995).

are difficult to heat at room temperature.

simply named as "susceptor").

a)

for microwave non-thermal enhancement of transport phenomena in solids and experimental justification of these models (Bikov et al., 2001). Studies (Rybakov & Semenov, 1994a, 1994b; Freeman et al., 1994; Booske et al., 1997) observed that, through an amplification and rectification process, the electric fields inside a microwave oven are sufficient to significantly affect the sintering behavior of ceramics, inducing an additional driving force for diffusion in solid materials (Clark & Sutton, 1996). They demonstrated that, under certain conditions, microwave-induced oscillating vacancy fluxes are rectified, leading to directional macroscopic mass transport; and that when the electromagnetic field interacts with the free surfaces of interfaces, an additional driving force for diffusion is created. This driving force has been named "ponderomotive" driving force. This force can compete with different thermochemical driving forces and significantly affect mass transport in solids during sintering.

### **3. Microwave fast sintering of ceramics**

The initial surge in the development of microwave technology was driven by the military needs of World War II. The tremendous effort that went into the development of radar during World War II generated am enormous body of knowledge on the properties of microwaves and related technologies (Committee on Microwave Processing of Materials: An Emerging Industrial Technology et al., 1994). In the post-war years, further development resulted in microwaves used for heating, especially for domestic purposes (Meredith, 1998). The first commercial microwave oven was a large floor-standing model was developed by the Raytheon Company of North America in 1951. Microwave ovens for domestic use were launched on the market in the early 1960s, initiating the mass market for this product. Soon thereafter, industrial microwave applications began to emerge, beginning with rubber extrusion, plastic manufacturing, and the treatment of foundry core ceramics.

Microwave processing of materials is a technology that has proven useful in a number of applications, presenting some important advantages over conventional heating methods. The main benefits of exploiting microwave energy in thermally activated processes stem from the specificity of microwave energy absorption. In contrast to all the other methods commonly used, microwaves allow for volumetric heating of materials. Microwave energy transforms into heat inside the material, which generally result in significant energy savings and shorter processing times. This factor plays a decisive role in most applications that have gained industrial acceptance to date.

Studies on microwave processing of ceramics started in the mid 1960s by Tinga (Tinga & Voss, 1968; Tinga & Edwards, 1968) and, since then, interest in the use of microwaves for heating and sintering ceramics has grown steadily. However, the particular requirements for ceramic powder sintering make this process one of the most challenging applications for microwave processing. These requirements often include high temperatures, high heating rates, uniform temperature distribution, etc. (Menezes et al., 2007). Moreover, during microwave heating, the absorption of electromagnetic energy raises the temperature of the entire sample, but heat loss from the surface causes the near-surface temperatures to become lower than the internal temperatures. Thus, in ceramics with poor thermal conductivity, large temperature gradients can develop in the body. The shape of the ceramic body and the microwave frequency strongly influence the temperature gradients, and achieving

for microwave non-thermal enhancement of transport phenomena in solids and experimental justification of these models (Bikov et al., 2001). Studies (Rybakov & Semenov, 1994a, 1994b; Freeman et al., 1994; Booske et al., 1997) observed that, through an amplification and rectification process, the electric fields inside a microwave oven are sufficient to significantly affect the sintering behavior of ceramics, inducing an additional driving force for diffusion in solid materials (Clark & Sutton, 1996). They demonstrated that, under certain conditions, microwave-induced oscillating vacancy fluxes are rectified, leading to directional macroscopic mass transport; and that when the electromagnetic field interacts with the free surfaces of interfaces, an additional driving force for diffusion is created. This driving force has been named "ponderomotive" driving force. This force can compete with different thermochemical driving forces and significantly affect mass

The initial surge in the development of microwave technology was driven by the military needs of World War II. The tremendous effort that went into the development of radar during World War II generated am enormous body of knowledge on the properties of microwaves and related technologies (Committee on Microwave Processing of Materials: An Emerging Industrial Technology et al., 1994). In the post-war years, further development resulted in microwaves used for heating, especially for domestic purposes (Meredith, 1998). The first commercial microwave oven was a large floor-standing model was developed by the Raytheon Company of North America in 1951. Microwave ovens for domestic use were launched on the market in the early 1960s, initiating the mass market for this product. Soon thereafter, industrial microwave applications began to emerge, beginning with rubber

Microwave processing of materials is a technology that has proven useful in a number of applications, presenting some important advantages over conventional heating methods. The main benefits of exploiting microwave energy in thermally activated processes stem from the specificity of microwave energy absorption. In contrast to all the other methods commonly used, microwaves allow for volumetric heating of materials. Microwave energy transforms into heat inside the material, which generally result in significant energy savings and shorter processing times. This factor plays a decisive role in most applications that have

Studies on microwave processing of ceramics started in the mid 1960s by Tinga (Tinga & Voss, 1968; Tinga & Edwards, 1968) and, since then, interest in the use of microwaves for heating and sintering ceramics has grown steadily. However, the particular requirements for ceramic powder sintering make this process one of the most challenging applications for microwave processing. These requirements often include high temperatures, high heating rates, uniform temperature distribution, etc. (Menezes et al., 2007). Moreover, during microwave heating, the absorption of electromagnetic energy raises the temperature of the entire sample, but heat loss from the surface causes the near-surface temperatures to become lower than the internal temperatures. Thus, in ceramics with poor thermal conductivity, large temperature gradients can develop in the body. The shape of the ceramic body and the microwave frequency strongly influence the temperature gradients, and achieving

extrusion, plastic manufacturing, and the treatment of foundry core ceramics.

transport in solids during sintering.

gained industrial acceptance to date.

**3. Microwave fast sintering of ceramics** 

sufficiently uniform heating of the body can be difficult. High heating rates can lead to localized heating, which can cause non-uniform properties and even cracking of the sample; as well thermal runaway when the temperature of the sample increases rapidly (Rahaman, 1995).

In microwave sintering, heat is generated internally through the interaction of the microwaves with the atoms, ions, and molecules of the material, which produces an inverse heating profile. Figure 3 presents a schematic diagram of heating by conventional and microwave processes. The microwave heating process is more volumetric, thus allowing higher heating rates. However, most research to date is based on conventional lowfrequency (2.45 GHz) microwave applicators, and at this frequency, many ceramics present poor microwave absorption characteristics. Thus, materials, that are transparent to microwaves, such as SiO2 and Al2O3 (ceramics with low-loss, as pure oxides and nitrides), are difficult to heat at room temperature.

Many ceramic materials that are difficult to heat at room temperature possess electrical conductivity or dielectric loss factors that rapidly increase in magnitude as the temperature rises. Thus, these materials will absorb microwave energy if they can be preheated to a suitable temperature using another heat source. This has led to the development of hybrid heating methods (Krage, 1981; Kimrey et al., 1991). Hybrid heating can be achieved by using either an independent heat source, such as a gas or electric furnace in combination with microwaves, or an external susceptor material (high-loss material) that couples with the microwaves. In the latter case, the material is exposed simultaneously to radiant heat produced by the susceptor material and to microwaves (usually, the susceptor material is simply named as "susceptor").

Fig. 3. Heating patterns in: a) conventional, and b) microwave furnaces.

Increasing the temperature (with radiant heat) is a common method many researchers employ to couple microwaves with poorly absorbing (low-loss) materials. Once a material is heated to its critical temperature, *Tc,* microwave absorption becomes sufficient to cause selfheating. This hybrid method can result in more uniform temperature gradients because the

Microwave Fast Sintering of Ceramic Materials 15

Fig. 5. SEM micrographs of MHFS alumina (Alcoa - A1000SG): at 1550oC (100oC/min up to 1100oC and 50oC/min up to 1550oC, soak time of 30 min – density of 95.3%) a) interior, b) surface; using 1.5kW for 25min (density of 96.6%), c) interior, d) surface; using 1.8kW for 20

min (density of 97.1%), e) interior, and f) surface.

microwaves heat volumetrically and the external heat source minimizes surface heat losses. Therefore, one of the most important characteristics associated with the use of microwave hybrid heating (MHH) is the potential to achieve uniform heating throughout the crosssection of a material, as illustrated in Figure 4. In the early 1990s, Dé (Dé et al., 1991a, 1991b) showed that microwave hybrid heating (MHH) could result in samples with no significant density gradient throughout the cross-section and that this phenomenon was enhanced with increased sample size. The consequences of more uniform temperature gradients are homogenous microstructures and improved properties of the final body.

Fig. 4. Temperature distribution in ceramic material heated by conventional fast firing, microwave fast firing and microwave hybrid heating (TS – Surface temperature, TI – Internal temperature).

Figure 5 displays homogeneous microstructures of microwave hybrid fast sintered (MHFS) alumina samples (low-loss material). The samples sintered for 20min reached 97% densification and presented internal and surface microstructures with a similar grain size distribution, which reinforces the efficiency of hybrid fast firing in the densification and uniform heating of low-loss ceramic materials. Using hybrid heating, our research group has also microwave fast sintered other ceramic materials, such as mullite, zirconia, ZnO, porcelains, ferrites, and zirconia (Menezes et al., 2005, 2007, 2008, 2010; Souto et al., 2007; 2011), which has yielded similar homogenous microstructures in fast sintering cycles.

On the other hand, our researchers have also observed that, in two conditions, microwave hybrid fast heating can produce non-uniform microstructures. This was verified when susceptor material responded very rapidly to microwaves and the sample presented a very low loss, leading to a heating behavior similar to that of the conventional fast firing. The other condition was detected when processing high-loss materials. These materials coupled very efficiently with microwaves and their temperature rose very rapidly without similar heating of the susceptor. However, both conditions can be controlled by using different susceptors or by optimizing the sintering cycle. Figure 6 depicts the homogeneous microstructure of microwave hybrid fast sintered Ni-Zn ferrite (high-loss material). Using heating rates of up to 100oC/min up to 1000oC allied with lower heating rates at higher temperatures it was possible to reach high densification, 99% and uniform microstructures. Grain size distribution in the region near the surface and in the core of the samples was practically equal, highlighting the uniform temperature distribution inside the material, notwithstanding their high loss and rapid sintering.

microwaves heat volumetrically and the external heat source minimizes surface heat losses. Therefore, one of the most important characteristics associated with the use of microwave hybrid heating (MHH) is the potential to achieve uniform heating throughout the crosssection of a material, as illustrated in Figure 4. In the early 1990s, Dé (Dé et al., 1991a, 1991b) showed that microwave hybrid heating (MHH) could result in samples with no significant density gradient throughout the cross-section and that this phenomenon was enhanced with increased sample size. The consequences of more uniform temperature gradients are

Fig. 4. Temperature distribution in ceramic material heated by conventional fast firing, microwave fast firing and microwave hybrid heating (TS – Surface temperature, TI – Internal

Figure 5 displays homogeneous microstructures of microwave hybrid fast sintered (MHFS) alumina samples (low-loss material). The samples sintered for 20min reached 97% densification and presented internal and surface microstructures with a similar grain size distribution, which reinforces the efficiency of hybrid fast firing in the densification and uniform heating of low-loss ceramic materials. Using hybrid heating, our research group has also microwave fast sintered other ceramic materials, such as mullite, zirconia, ZnO, porcelains, ferrites, and zirconia (Menezes et al., 2005, 2007, 2008, 2010; Souto et al., 2007; 2011), which has yielded similar homogenous microstructures in fast sintering cycles.

On the other hand, our researchers have also observed that, in two conditions, microwave hybrid fast heating can produce non-uniform microstructures. This was verified when susceptor material responded very rapidly to microwaves and the sample presented a very low loss, leading to a heating behavior similar to that of the conventional fast firing. The other condition was detected when processing high-loss materials. These materials coupled very efficiently with microwaves and their temperature rose very rapidly without similar heating of the susceptor. However, both conditions can be controlled by using different susceptors or by optimizing the sintering cycle. Figure 6 depicts the homogeneous microstructure of microwave hybrid fast sintered Ni-Zn ferrite (high-loss material). Using heating rates of up to 100oC/min up to 1000oC allied with lower heating rates at higher temperatures it was possible to reach high densification, 99% and uniform microstructures. Grain size distribution in the region near the surface and in the core of the samples was practically equal, highlighting the uniform temperature distribution inside the material,

notwithstanding their high loss and rapid sintering.

temperature).

homogenous microstructures and improved properties of the final body.

Fig. 5. SEM micrographs of MHFS alumina (Alcoa - A1000SG): at 1550oC (100oC/min up to 1100oC and 50oC/min up to 1550oC, soak time of 30 min – density of 95.3%) a) interior, b) surface; using 1.5kW for 25min (density of 96.6%), c) interior, d) surface; using 1.8kW for 20 min (density of 97.1%), e) interior, and f) surface.

Microwave Fast Sintering of Ceramic Materials 17

ceramics (such as Al2O3, SiO2, Fe2O3, ZrO2, etc.), and was a serious problem in the processing of materials whose dielectric properties are abruptly altered with rising temperature. Studies (Spotz et al., 1995) demonstrated that the insulation normally used to contain heat inside the cavity can exacerbate the problem of thermal runaway. However, the data also suggested that thermal runaway may be minimized or controlled by hybrid

However, care must be taken in designing the shape and size of the susceptor arrangement, because some susceptor materials, e.g., SiC, have high loss factors and therefore low penetration depths. Raising temperature leads to higher dielectric losses and significantly decreased penetration depths (see Figure 1). In this condition, it may not be possible to determine what the fraction of the sintering resulted from the interaction with microwaves and what fraction was sintered conventionally (by radiation of the susceptor material), as

Nanostructured materials have received much attention in recent years, due to their potential unusual physical and mechanical properties, such as superplasticity in ceramics at elevated temperatures, high hardness and mechanical strength, transparency for usually opaque materials, etc. However, one of the most challenging goals of modern ceramic technologies is still the manufacture of dense ceramic parts with submicrometric or nanostructured grains. Thus, controlled grain growth during the final steps of densification

heating, thus allowing low-loss ceramic materials to be processed using rapid firing.

illustrated in Figure 8.

Fig. 7. Illustration of the "picket fence" arrangement.

An outstanding example of the use of microwave hybrid heating was the sintering of, ZrO2/8% Y2O3 and zirconia/12% CeO2 at 2.45 GHz by Janney (Janney et al., 1992). Although these materials could be sintered readily at 28 GHz, attempts to use 2.45 GHz, which involves lower equipment costs, were unsuccessful until SiC rods were inserted into the insulation surrounding the specimens, in what is referred to as the "picket fence" arrangement (Figure 7). The microwave energy initially heated the SiC rods, which resulted in uniform heating of the zirconia, and hence, in a homogenous coupling with microwaves after the critical temperature was reached.

Fig. 6. SEM micrographs of homogeneous microstructures of Ni-Zn ferrite (Ni0,5Zn0,5Fe2O4): microwave hybrid fast sintered at 1220oC (100oC/min up to 1000oC and 50oC/min up to 1200oC, soak time of 20 min – density of 99%): a) sample interior (core), b) sample surface, c) sintered conventionally at 1200oC (5oC/min, soak time of 120min – density of 95.4%), and d) internal and near-surface grain size distribution of microwavesintered sample.

Inside the insulation system, the thermal uniformity provided by susceptors plays an important role in reducing thermal runaways during fast sintering. Catastrophic overheating (thermal runaway) of processed material was observed in a large variety of

An outstanding example of the use of microwave hybrid heating was the sintering of, ZrO2/8% Y2O3 and zirconia/12% CeO2 at 2.45 GHz by Janney (Janney et al., 1992). Although these materials could be sintered readily at 28 GHz, attempts to use 2.45 GHz, which involves lower equipment costs, were unsuccessful until SiC rods were inserted into the insulation surrounding the specimens, in what is referred to as the "picket fence" arrangement (Figure 7). The microwave energy initially heated the SiC rods, which resulted in uniform heating of the zirconia, and hence, in a homogenous coupling with microwaves

0 2 4 6 8 10 12

 Internal Region (Core) Near-Surface Region

**Grain Size (**μ**m)**

0

(Ni0,5Zn0,5Fe2O4): microwave hybrid fast sintered at 1220oC (100oC/min up to 1000oC and 50oC/min up to 1200oC, soak time of 20 min – density of 99%): a) sample interior (core), b) sample surface, c) sintered conventionally at 1200oC (5oC/min, soak time of 120min – density of 95.4%), and d) internal and near-surface grain size distribution of microwave-

Inside the insulation system, the thermal uniformity provided by susceptors plays an important role in reducing thermal runaways during fast sintering. Catastrophic overheating (thermal runaway) of processed material was observed in a large variety of

Fig. 6. SEM micrographs of homogeneous microstructures of Ni-Zn ferrite

sintered sample.

3

6

9

Percentage (%)

12

15 **d**)

after the critical temperature was reached.

ceramics (such as Al2O3, SiO2, Fe2O3, ZrO2, etc.), and was a serious problem in the processing of materials whose dielectric properties are abruptly altered with rising temperature. Studies (Spotz et al., 1995) demonstrated that the insulation normally used to contain heat inside the cavity can exacerbate the problem of thermal runaway. However, the data also suggested that thermal runaway may be minimized or controlled by hybrid heating, thus allowing low-loss ceramic materials to be processed using rapid firing.

However, care must be taken in designing the shape and size of the susceptor arrangement, because some susceptor materials, e.g., SiC, have high loss factors and therefore low penetration depths. Raising temperature leads to higher dielectric losses and significantly decreased penetration depths (see Figure 1). In this condition, it may not be possible to determine what the fraction of the sintering resulted from the interaction with microwaves and what fraction was sintered conventionally (by radiation of the susceptor material), as illustrated in Figure 8.

Fig. 7. Illustration of the "picket fence" arrangement.

Nanostructured materials have received much attention in recent years, due to their potential unusual physical and mechanical properties, such as superplasticity in ceramics at elevated temperatures, high hardness and mechanical strength, transparency for usually opaque materials, etc. However, one of the most challenging goals of modern ceramic technologies is still the manufacture of dense ceramic parts with submicrometric or nanostructured grains. Thus, controlled grain growth during the final steps of densification

Microwave Fast Sintering of Ceramic Materials 19

As mentioned early, the objective of fast firing is to enhance the densification rate in detriment to the coarsening rate by a rapidly approaching to the sintering temperature. Because coarsening mechanisms (e.g., surface diffusion and vapor transport) commonly prevail over densification mechanisms (e.g., lattice and grain-boundary diffusion) at lower temperatures, it has been suggested that rapid heating to higher temperatures can be beneficial to achieve high density allied to fine grain size. In this case, the shorter time spent at lower temperatures serves to reduce the extent of coarsening while the driving force for

The authors' research group employed microwave hybrid fast heating to sinter submicrometric alumina (Sumitomo, AKP 53 – average particle size of 0.2 μm and surface area of 10.4m2/g). Rapid densification, 98.9%, suppression of grain growth, and submicrometric grain size microstructures were achieved (SEM micrographs in Figure 9)

 Fig. 9. SEM micrographs of the fracture surface of MHFS alumina (Sumitomo AKP - 53) processed at 2.45GHz with power level of 1.8kW for 26min (98.9% density): a) and c) grains

in a internal region, b) and d) grains in a near-surface region.

densification is not decreased significantly.

is an extremely important processing concern that requires the development of processing routes to effectively suppress grain growth during densification.

When ceramic materials are processed by traditional sintering techniques, the high temperatures required to fully densify ceramic powders result in large grain sizes due to Ostwald ripening. This makes it extremely difficult to obtain dense materials with nanometric and submicrometric grain sizes. Thus, although suitably uniform nanophase powder materials are becoming increasingly available, the fabrication of fully dense nanostructured products still offers challenges. In this context, the microwave fast sintering appears as an alternative for the sintering and densification of ceramics with suppressed grain growth.

Fig. 8. Microwave hybrid heating arrangement/effect of susceptor material volume on the final heating pattern.

is an extremely important processing concern that requires the development of processing

When ceramic materials are processed by traditional sintering techniques, the high temperatures required to fully densify ceramic powders result in large grain sizes due to Ostwald ripening. This makes it extremely difficult to obtain dense materials with nanometric and submicrometric grain sizes. Thus, although suitably uniform nanophase powder materials are becoming increasingly available, the fabrication of fully dense nanostructured products still offers challenges. In this context, the microwave fast sintering appears as an alternative for the sintering and densification of ceramics with suppressed

**Microwaves Reduced Amplitude Microwaves**

Fig. 8. Microwave hybrid heating arrangement/effect of susceptor material volume on the

**Susceptor**

**Infrared/Conventional Heating**

**Ceramic Material**

**Ceramic Material**

**Heat/Direction of Heat**

routes to effectively suppress grain growth during densification.

**Susceptor**

grain growth.

final heating pattern.

As mentioned early, the objective of fast firing is to enhance the densification rate in detriment to the coarsening rate by a rapidly approaching to the sintering temperature. Because coarsening mechanisms (e.g., surface diffusion and vapor transport) commonly prevail over densification mechanisms (e.g., lattice and grain-boundary diffusion) at lower temperatures, it has been suggested that rapid heating to higher temperatures can be beneficial to achieve high density allied to fine grain size. In this case, the shorter time spent at lower temperatures serves to reduce the extent of coarsening while the driving force for densification is not decreased significantly.

The authors' research group employed microwave hybrid fast heating to sinter submicrometric alumina (Sumitomo, AKP 53 – average particle size of 0.2 μm and surface area of 10.4m2/g). Rapid densification, 98.9%, suppression of grain growth, and submicrometric grain size microstructures were achieved (SEM micrographs in Figure 9)

Fig. 9. SEM micrographs of the fracture surface of MHFS alumina (Sumitomo AKP - 53) processed at 2.45GHz with power level of 1.8kW for 26min (98.9% density): a) and c) grains in a internal region, b) and d) grains in a near-surface region.

Microwave Fast Sintering of Ceramic Materials 21

Grain growth suppression was also achieved in the processing of submicrometric zirconia (Zirconia Tosoh TZ-3Y, Tosoh Corporation, D50 ≈ 0,4μm), which yielded a high densification of 99% a fine-grained microstructure with an average grain size of 0.6μm. The micrographs (Figure 12) of the internal and near-surface regions are practically identical, showing intergranular fracture, uniform grain size distribution, and no visible cracks, pores or

Fig. 11. SEM micrographs of the fracture surface of MHFS nanocomposite alumina (Sumitomo AKP - 53)/zirconia (Nanostructured & Amorphous Materials, 3YSZ) (3 vol.% zirconia) processed at 2.45GHz with power level of 1.8kW for 35min (99% density).

abnormal grain growth.

Figure 10 shows samples of these alumina bodies sintered in a multimode furnace operating at 2.45 GHz. Microwave fast sintered alumina bodies were devoid of cracks, which is a reliable indicator of homogeneous temperature distribution in the bodies. In contrast, conventionally fast fired samples (50oC/min) presented cracks and non-uniform microstructures.

A alumina-zirconia nanocomposites were also rapid-sintered using the heating system developed for fast heating of alumina samples. Alumina (Sumitomo AKP 53)/ zirconia (yttria-stabilized zirconia powder, 3YSZ, Nanostructured & Amorphous Materials Inc., 58– 76nm particle size) nanocomposites containing up to 5 vol.% zirconia, reached densities of approximately 99% in 35 min. Uniform microstructures and suppression of grain growth were obtained using rapid hybrid sintering. Figure 11 presents SEM micrographs of sintered nanocomposite containing 5%vol.% zirconia.

Fig. 10. Alumina samples processed by microwave hybrid fast sintering.

Figure 10 shows samples of these alumina bodies sintered in a multimode furnace operating at 2.45 GHz. Microwave fast sintered alumina bodies were devoid of cracks, which is a reliable indicator of homogeneous temperature distribution in the bodies. In contrast, conventionally fast fired samples (50oC/min) presented cracks and non-uniform

A alumina-zirconia nanocomposites were also rapid-sintered using the heating system developed for fast heating of alumina samples. Alumina (Sumitomo AKP 53)/ zirconia (yttria-stabilized zirconia powder, 3YSZ, Nanostructured & Amorphous Materials Inc., 58– 76nm particle size) nanocomposites containing up to 5 vol.% zirconia, reached densities of approximately 99% in 35 min. Uniform microstructures and suppression of grain growth were obtained using rapid hybrid sintering. Figure 11 presents SEM micrographs of sintered

microstructures.

nanocomposite containing 5%vol.% zirconia.

Fig. 10. Alumina samples processed by microwave hybrid fast sintering.

Grain growth suppression was also achieved in the processing of submicrometric zirconia (Zirconia Tosoh TZ-3Y, Tosoh Corporation, D50 ≈ 0,4μm), which yielded a high densification of 99% a fine-grained microstructure with an average grain size of 0.6μm. The micrographs (Figure 12) of the internal and near-surface regions are practically identical, showing intergranular fracture, uniform grain size distribution, and no visible cracks, pores or abnormal grain growth.

Fig. 11. SEM micrographs of the fracture surface of MHFS nanocomposite alumina (Sumitomo AKP - 53)/zirconia (Nanostructured & Amorphous Materials, 3YSZ) (3 vol.% zirconia) processed at 2.45GHz with power level of 1.8kW for 35min (99% density).

Microwave Fast Sintering of Ceramic Materials 23

uniform heating, thus avoiding thermal runaway and cracks. The rapid sintering of zirconia specimens without cracked, allied to the high densities achieved ( > 97%), indicate a highly uniform distribution of temperature in the processed bodies. The non-uniform distribution of temperature in zirconia hinders its densification and may lead to thermal runaway may. The results obtained by our research group indicate the successful use of microwave hybrid fast sintering in the densification of ceramic bodies and its effectiveness in suppressing grain growth in the final stages of sintering. The rapid densification achieved, accompanied by only minor grain growth, seems to be an indication of the microwave effect. However, regardless of the presence or absence of the microwave effect, the results of our research group indicate that microwave hybrid heating is a great potential method for rapid sintering of low and high-loss ceramic materials, yielding uniform microstructures and allowing for

Studies by our research group confirm that microwave hybrid fast sintering can be employed successfully to sinter low and high dielectric loss ceramics, producing highly dense ceramics and suppressing grain growth in the final stages of sintering. Controlled heating schedules and the use of suitably designed susceptor materials yield uniform microstructures without stress-related cracking or the development of incipient fusion, hot spots or thermal runaway. Thus, successful microwave fast sintering depends on the strict control of sintering conditions, striking an adequate balance between power and time or

The authors gratefully acknowledge the Brazilian agencies FAPESP (proc. 07/59564-0) and

Agrawal, D. K. (1998). Microwave processing of ceramics. *Current Opinion in Solid State &* 

Andrade, O. M., Iskander, M. F. & Bringhurst, S. (1992). High temperature broadband

Arai, M., Binner J. G. P, Carr, G. E. & Cross, T. E. (1993). High temperature dielectric

Batt, J. Binner, J. G. P., Cross, T. E., Greenacre, N. R., Hamlyn, M. G., Hutcheon, R. M.,

dielectric properties measurement techniques. In: *Microwave Processing of Materials III,* (*Materials Research Society Symposium Proceedings)* Vol. 269, Beatty, R. L., Sutton, W. H. & Iskander, M. F., pp. (527-539), Materials Research Society, 1-55899-164-6,

property measurements of engineering ceramics. In: *Microwaves: Theory and Application In Materials Processing II*, *Ceramics Transactions*, Vol. 36, Clark, D. E., Tinga, W. R. & Laia Jr, J. R., pp (483-492), The American Ceramic Society, 0-944904-

Sutton, W. H. & Weil, C. M. (1995). A parallel measurement programme in high temperature dielectric property measurements: An update. In: *Microwaves: Theory* 

temperature and time to obtain highly dense and homogeneous microstructures.

CNPq (Proc. 577201/2008-5/ and 303388/2009-9) for their financial aid.

*Materials Science*, Vol. 3, pp. (480-485), 1359-0286.

suppressed grain growth (when necessary).

**4. Conclusions**

**5. Acknowledgements** 

Pittisburg.

66-1, Westerville.

**6. References**

Fig. 12. SEM micrographs of the fracture surface of MHFS zirconia (Tosoh TZ-3Y) processed at 2.45GHz with power level of 1.8kW for 20min (99% density), a) internal region, b) near-surface region.

It is difficult to process zirconia in a 2.45GHz microwave furnace because the dielectric properties of this material change rapidly with temperature (see Figure 2) and its thermal conductivity is very low. Therefore, the use of hybrid heating is very important to produce uniform heating, thus avoiding thermal runaway and cracks. The rapid sintering of zirconia specimens without cracked, allied to the high densities achieved ( > 97%), indicate a highly uniform distribution of temperature in the processed bodies. The non-uniform distribution of temperature in zirconia hinders its densification and may lead to thermal runaway may.

The results obtained by our research group indicate the successful use of microwave hybrid fast sintering in the densification of ceramic bodies and its effectiveness in suppressing grain growth in the final stages of sintering. The rapid densification achieved, accompanied by only minor grain growth, seems to be an indication of the microwave effect. However, regardless of the presence or absence of the microwave effect, the results of our research group indicate that microwave hybrid heating is a great potential method for rapid sintering of low and high-loss ceramic materials, yielding uniform microstructures and allowing for suppressed grain growth (when necessary).
