**3. Thermodynamics and kinetics of sintering**

The basic of sintering is the formation of necks between powder particles. While neck formation depends on system thermodynamics, the rate of sintering is mostly due to the temperature of the process. At room temperature, the atoms in a material are not noticeably mobile, so the particles do not sinter. When a material is heated at a temperature close to its melting point, the atoms increase their mobility and produce bonding formation, which lowers the overall system energy. The energy changes in sintering are small so that the rate of change during sintering is slow [22].

At the beginning of sintering, the interparticle neck grows to the point where its size is less than one-third of the particle size, often associated with a little dimensional change. Sintering proceeds with necks growing to a dimension which is larger than one-third of the particle size but still lower than half of the particle dimension, corresponding to a density between 70 and 92% for spheres. The pores are tubular

**85**

*Prologue: The New Era of Sintering*

*DOI: http://dx.doi.org/10.5772/intechopen.85338*

pores are filled with process atmosphere.

element, as shown by thermodynamics.

energy, and *μ<sup>v</sup>*

sive, and *cv*(*H*) < *cv*

mechanism [22].

**4. Conclusions**

efforts concerning sintering.

opposite, and *cv*(*H*) > *cv*

0

0

0

and connected to the external surface, and the green sintering body is compact but not fully dense so that gas can still pass through it. In the end, the final stage of sintering corresponds to the elimination of surface pores, while internal isolated

Sintering is mainly driven by the reduction of surface energy associated with the decrease in the pore-solid surface area. Locally, there is a chemical potential shift on each component of surface on the interface, from the value for a flat interface in the same system, which is proportional to the local mean curvature *H* at the surface

Assuming that local equilibrium exists at each interfacial element, the chemical potential of vacancies in a volume close to a curved surface element is given by Eq. (1):

where *V* is the molar volume of the solid phase, *γ* is the specific interfacial free

given temperature and external pressure of the system. The chemical potential shift reflects in a change in the molar concentration of vacancies (*cv*(*H*)), which form a dilute solution. Given that a system with a flat surface has a local mean curvature equal to zero, the shift in vacancy molar concentration can be written as Eq. (2):

<sup>0</sup> −

where *T* is the absolute temperature and *k* is Boltzmann's constant. This theoretical treatment shows that the local mean curvature on the surface determines the distribution of vacancy concentrations in volume elements close to the pore-solid interface. Therefore, for convex surface elements, the local stress state is compres-

their flow distribution, and grain boundaries act like sinks, while surface elements defined by *H* = 0 are source of vacancies. The densification in conventional sinter-

In terms of kinetics, there is a variety of mechanisms which control the sintering process at different levels, such as volume, grain boundary and surface diffusions, plastic deformation, and vapor transport. Densification is mainly influenced only by the first two mechanisms, being defined as a decrease in volume of the pore-solid structure. Plastic deformation generates only a limited amount of surface tensions and gives, namely, a negligible contribution to sintering densification control. Vapor transport is the dominant mechanism when the solid phase has a high vapor pressure, although it is not able to produce densification since both vacancy sources and sinks are on the surface. This limitation is verified also for the surface diffusion

Conventional and new sintering systems, based on various mechanisms of heat

generation, are changing the world of powder metallurgy. The combination of different parameters, which can be related to the materials used or to the particular process, allows the production of objects having properties which can make them suitable for different applications. This book inspires materials scientists to carry on

is the chemical potential of vacancies adjacent to a flat surface at a

2*V cv* \_ 0

, while for concave surface elements, the local stress state is the

. The vacancy molar concentration distribution modifies

<sup>0</sup> + 2*VH* (1)

*kT <sup>H</sup>* (2)

*μv*(*H*) = *μv*

*cv*(*H*) = *cv*

ing is, therefore, due to the vacancy annihilation at the grain boundaries.

*Prologue: The New Era of Sintering DOI: http://dx.doi.org/10.5772/intechopen.85338*

and connected to the external surface, and the green sintering body is compact but not fully dense so that gas can still pass through it. In the end, the final stage of sintering corresponds to the elimination of surface pores, while internal isolated pores are filled with process atmosphere.

Sintering is mainly driven by the reduction of surface energy associated with the decrease in the pore-solid surface area. Locally, there is a chemical potential shift on each component of surface on the interface, from the value for a flat interface in the same system, which is proportional to the local mean curvature *H* at the surface element, as shown by thermodynamics.

Assuming that local equilibrium exists at each interfacial element, the chemical potential of vacancies in a volume close to a curved surface element is given by Eq. (1):

$$
\mu\_v(H) = \mu\_v^0 + 2\gamma V H \tag{1}
$$

where *V* is the molar volume of the solid phase, *γ* is the specific interfacial free energy, and *μ<sup>v</sup>* 0 is the chemical potential of vacancies adjacent to a flat surface at a given temperature and external pressure of the system. The chemical potential shift reflects in a change in the molar concentration of vacancies (*cv*(*H*)), which form a dilute solution. Given that a system with a flat surface has a local mean curvature equal to zero, the shift in vacancy molar concentration can be written as Eq. (2):

ешичи ини а паи чилае наз а поса пеан си чиле су моolar сосетнота са ве чтtitten as Eq. (2):

 $\mathcal{c}\_v(H) = \mathcal{c}\_v^0 - \frac{2\gamma V \mathcal{c}\_v^0}{kT} H$ 

where *T* is the absolute temperature and *k* is Boltzmann's constant. This theoretical treatment shows that the local mean curvature on the surface determines the distribution of vacancy concentrations in volume elements close to the pore-solid interface. Therefore, for convex surface elements, the local stress state is compressive, and *cv*(*H*) < *cv* 0 , while for concave surface elements, the local stress state is the opposite, and *cv*(*H*) > *cv* 0 . The vacancy molar concentration distribution modifies their flow distribution, and grain boundaries act like sinks, while surface elements defined by *H* = 0 are source of vacancies. The densification in conventional sintering is, therefore, due to the vacancy annihilation at the grain boundaries.

In terms of kinetics, there is a variety of mechanisms which control the sintering process at different levels, such as volume, grain boundary and surface diffusions, plastic deformation, and vapor transport. Densification is mainly influenced only by the first two mechanisms, being defined as a decrease in volume of the pore-solid structure. Plastic deformation generates only a limited amount of surface tensions and gives, namely, a negligible contribution to sintering densification control. Vapor transport is the dominant mechanism when the solid phase has a high vapor pressure, although it is not able to produce densification since both vacancy sources and sinks are on the surface. This limitation is verified also for the surface diffusion mechanism [22].

#### **4. Conclusions**

Conventional and new sintering systems, based on various mechanisms of heat generation, are changing the world of powder metallurgy. The combination of different parameters, which can be related to the materials used or to the particular process, allows the production of objects having properties which can make them suitable for different applications. This book inspires materials scientists to carry on efforts concerning sintering.
