Matter transport
Sintering is possible only if the atoms can diffuse to form the necks that
weld the particles with one another. The transport of matter can occur in
vapor phase, in a liquid, by diffusion in a crystal, or through the viscous
flow of a glass.
J = (D/kT)(dP/dx) (vapor phase)
J is the flow of atoms passing through a unit surface, per time
unit, D the diffusion coefficient of the species that diffuses and k
is the Boltzmann constant ,T temperature, dP/dx the difference in
pressure between the two sides of an interface causes a matter flow.
J = (– DLiquid/ kT)(?P/L) (liquid phase)
where DLiquid is transport coefficient in the liquid , L viscous
liquid flow rate , ?P grows homothetically, particles p at times
coarser imply neck.
Most mechanisms are activated thermally because the action of
temperature is necessary to overcome the potential barrier between the
initial state of higher energy (compacted powder) and the final state of
lower energy (consolidated material). Atomic diffusion in ceramics is
sufficiently rapid only at temperatures higher than 0.6-0.8 TF, where TF
is the melting point (in K). For alumina, for example, which melts at
around 2,320 K the sintering temperature chosen is generally around
1,900 K.
The matter movement takes place from the high energy areas towards the
low energy areas , primarily, the sintering neck between the particles. We
must distinguish two cases depending on the location of the source of
matter:
– when the source of matter is the surface, the mechanism is nondensifying,
which means that the spheres take an ellipsoidal form,
without their centers approaching one another. There is no macroscopic
shrinkage and the porosity of the granular compact is not reduced
significantly. The decrease in interfacial energy primarily comes from the
grain coarsening.
– when the source of matter is inside the grains (near the boundaries, or
near defects such as dislocations), the mechanism is densifying: there is
shrinkage and reduction in porosity.
Sintering -------------------Lecture (4)
13
For solid phase sintering, there are four ways of diffusion:
i) surface diffusion.
ii) volume diffusion (often called lattice diffusion).
iii) vapor phase transport (evaporation-condensation.
iv) grain boundary diffusion: the boundaries are very disturbed areas,
which allow “diffusion short-circuits”.
For liquid phase sintering, we must add dissolution-reprecipitation
effects or a vitreous flow. Finally, for pressure sintering the pressure
exerted allows the plastic deformation of the crystallized phases and the
viscous flow of the amorphous phases.
SINTERING AND DIFFUSION
There is a significant difference between the paths for matter transport.
Transfer of material into the “pore” must occur if the porosity of the
compact is to shrink. You can imagine that in three dimensions (3D), this
requires that matter transfer from the bulk of the grain, from the GB
between particles, or from the outer surface by diffusion through the grain
or through the GB.
(Alternatively, you can think of vacancies moving out from the pores.)
For the case of matter transport from the grain boundary to the neck by
lattice diffusion, we can derive an equation for the rate of growth of the
neck area between particles.
x
r
= (
40?a3D?
kT
)1/5 r-3/5 t1/5
Here, the volume of the diffusing vacancy is a3 and D* is the selfdiffusion
coefficient , x is the neck radius , r the radius of the particles, t
time , ? is the specific interface energy.
REACTION SINTERING
reactive sintering, is a particular type of sintering process in which the
chemical reaction of the starting materials and the densification of the
powder compact are both achieved in a single heat treatment step.
These systems can be divided into two main classes depending on
whether single-phase solids or composites are produced. For a powder
compact consisting of a mixture of two reactant powders, the simplest
example of reaction.
Sintering -------------------Lecture (4)
14
During sintering, reaction between two starting powders A (e.g., ZnO)
and B (e.g., Fe2O3) and densification occur to produce a polycrystalline,
single-phase solid C (e.g., ZnFe2O4):
ZnO + Fe O ? ZnFe2O4
A more complex example of reaction sintering .Reaction between two
starting powders D (e.g., Al2O3) and E (e.g., zircon, ZrSiO4) and
densification occur to produce a composite solid consisting of two phases
F (mullite, 3Al2O3_2SiO2) and G (ZrO2):
3 Al2O3 +2 (ZrO2 . SiO2)? 3Al2O3+2SiO2 +2 ZrO2
The energy changes for chemical reaction are much larger than those for
surface area changes and it would be very desirable if the free energy of
the reaction could be used to drive the densification process.
ZnFe2O4 as an example, the conventional route for producing a dense
polycrystalline solid involves calcinations of a loose mixture of ZnO
and Fe2O3 powders to form a single-phase ZnFe2O4 powder, milling the
calcined powder to break down agglomerates, followed by powder
compaction and sintering.
In reaction sintering, the reaction and densification occurs in the same
heating cycle, so the calcination and subsequent milling steps in the
conventional route are eliminated.
المادة المعروضة اعلاه هي مدخل الى المحاضرة المرفوعة بواسطة استاذ(ة) المادة . وقد تبدو لك غير متكاملة . حيث يضع استاذ المادة في بعض الاحيان فقط الجزء الاول من المحاضرة من اجل الاطلاع على ما ستقوم بتحميله لاحقا . في نظام التعليم الالكتروني نوفر هذه الخدمة لكي نبقيك على اطلاع حول محتوى الملف الذي ستقوم بتحميله .
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