26
A. Hu et al.
surface plasmonic excitation. As aforementioned, the locally excited plasmonic resonance can only heat the adjacent particles with the narrowest gap. Besides, plasmonic
sintering is more energy efficient by selected wavelength for excitation than the
thermal sintering. The most unique feature of photonic sintering is “smart” and selfterminated: once the adjacent particles are fused together the new plasmonic excitation will automatically move to the new adjacent positions which usually locate at
the edge of a pore [94, 101, 102]. Thus, the particle fusion induced by plasmonic
sintering will lead to the eventual disappearance of pores.
The nature of photonic sintering that photothermally induced diffusion. For the
diffusion, the liquid phase diffusion is much faster than a solid-state diffusion since
the diffusivity in a liquid is much higher than in a solid [103]. As discussed in
Sect. 1.1.2, the surface atoms are much activated than the inner atoms due to less
bonding and the surface defects [40]. As a result, the sintering temperature can be
much lower than the melting point of a particle. The onset sintering temperature as
a function of the melting temperature can be written as
T s (d) = αT m (d)
(1.3.1)
where the d is the particle diameter. For microparticles, α ranges from 0.5 to 0.8
[40], but for nanoparticles, this value decreases to 0.1–0.3 [45]. This indicates that
the sintering of nanoparticles can occur at a very low temperature, only 10% of the
melting point. This explains nanomaterials can be joined even at a room temperature
without external heating [47]. Considering a possible surface melting of nanoparticle
and thereby associated a liquid phase sintering, sintering of nanoparticles for 2D to
3D printed electronics and functional mechanical components are extremely attracted
in micro-to-nanomanufacturing.
Diffusion Mechanisms Based on a conventional sintering theory, the driving force
for sintering is dependent on the curvature of two touched particles, i.e., (Fig. 1.21)
σ = γ
1
R 1
+
1
R 2
(1.3.2)
where γ is the specific surface energy, R 1 and R 2 are principle radii of two spherical
particles. For two identical particles with a radium of r, the neck size can be expressed
a function of r [104],
x
r
=
Bt
r m
1/n
(1.3.3)
where t is the sintering holding time, B is a temperature-dependent sintering function,
and the values of m and n are defined by individual diffusion mechanisms. Three
dominant mechanisms have been discussed as the surface diffusion, grain boundary
diffusion and the lattice diffusion. If sintering is driven by surface diffusion, (1.3.3)
becomes
A. Hu et al.
surface plasmonic excitation. As aforementioned, the locally excited plasmonic resonance can only heat the adjacent particles with the narrowest gap. Besides, plasmonic
sintering is more energy efficient by selected wavelength for excitation than the
thermal sintering. The most unique feature of photonic sintering is “smart” and selfterminated: once the adjacent particles are fused together the new plasmonic excitation will automatically move to the new adjacent positions which usually locate at
the edge of a pore [94, 101, 102]. Thus, the particle fusion induced by plasmonic
sintering will lead to the eventual disappearance of pores.
The nature of photonic sintering that photothermally induced diffusion. For the
diffusion, the liquid phase diffusion is much faster than a solid-state diffusion since
the diffusivity in a liquid is much higher than in a solid [103]. As discussed in
Sect. 1.1.2, the surface atoms are much activated than the inner atoms due to less
bonding and the surface defects [40]. As a result, the sintering temperature can be
much lower than the melting point of a particle. The onset sintering temperature as
a function of the melting temperature can be written as
T s (d) = αT m (d)
(1.3.1)
where the d is the particle diameter. For microparticles, α ranges from 0.5 to 0.8
[40], but for nanoparticles, this value decreases to 0.1–0.3 [45]. This indicates that
the sintering of nanoparticles can occur at a very low temperature, only 10% of the
melting point. This explains nanomaterials can be joined even at a room temperature
without external heating [47]. Considering a possible surface melting of nanoparticle
and thereby associated a liquid phase sintering, sintering of nanoparticles for 2D to
3D printed electronics and functional mechanical components are extremely attracted
in micro-to-nanomanufacturing.
Diffusion Mechanisms Based on a conventional sintering theory, the driving force
for sintering is dependent on the curvature of two touched particles, i.e., (Fig. 1.21)
σ = γ
1
R 1
+
1
R 2
(1.3.2)
where γ is the specific surface energy, R 1 and R 2 are principle radii of two spherical
particles. For two identical particles with a radium of r, the neck size can be expressed
a function of r [104],
x
r
=
Bt
r m
1/n
(1.3.3)
where t is the sintering holding time, B is a temperature-dependent sintering function,
and the values of m and n are defined by individual diffusion mechanisms. Three
dominant mechanisms have been discussed as the surface diffusion, grain boundary
diffusion and the lattice diffusion. If sintering is driven by surface diffusion, (1.3.3)
becomes