34 3 Surfaces in Nanomaterials
Figure 3.13 Vapor pressure ratio of the vapor pressure p of a curved plane over that of a flat
plane p ∞ for zinc. A positive curvature is related to convex surfaces, negative curvature to
concave surfaces.
–50
–25
0
25
50
inverse curvature [nm]
10
–4
10
–3
10
–2
10
–1
10
0
10
1
10
2
10
3
10
4
vapor
pressure
ratio
p curved
/p flat
Convex
Concave
Figure 3.14 Material transport by evaporation and condensation during sintering. The
material is transported from ranges with positive curvature to ranges with negative curvature.
NegaƟve curvature
PosiƟve
curvature
Material
transport
Sintering
grains
To understand the material transport by evaporation and condensation during
sintering, one has to realize that the curvature is positive at the particle surface.
At the point of contact of two particles, the curvature is negative. For negative
curvature, the vapor pressure is very small. Therefore, bodies consisting of pressed
nanoparticles start sintering very rapidly, as small particles have a high vapor
pressure. The evaporated material is deposited at the points of contact of two
particles and other areas, where the curvature is negative. In total, this type of
material transport by evaporation and condensation leads, in the case of nanoparticles, to an early start of the sintering process at comparatively low temperatures.
Figure 3.13 Vapor pressure ratio of the vapor pressure p of a curved plane over that of a flat
plane p ∞ for zinc. A positive curvature is related to convex surfaces, negative curvature to
concave surfaces.
–50
–25
0
25
50
inverse curvature [nm]
10
–4
10
–3
10
–2
10
–1
10
0
10
1
10
2
10
3
10
4
vapor
pressure
ratio
p curved
/p flat
Convex
Concave
Figure 3.14 Material transport by evaporation and condensation during sintering. The
material is transported from ranges with positive curvature to ranges with negative curvature.
NegaƟve curvature
PosiƟve
curvature
Material
transport
Sintering
grains
To understand the material transport by evaporation and condensation during
sintering, one has to realize that the curvature is positive at the particle surface.
At the point of contact of two particles, the curvature is negative. For negative
curvature, the vapor pressure is very small. Therefore, bodies consisting of pressed
nanoparticles start sintering very rapidly, as small particles have a high vapor
pressure. The evaporated material is deposited at the points of contact of two
particles and other areas, where the curvature is negative. In total, this type of
material transport by evaporation and condensation leads, in the case of nanoparticles, to an early start of the sintering process at comparatively low temperatures.