Sintering

sintering process
the firing of the wet clay rough shape solidifies the object in its final
form while simultaneously allowing physicochemical reactions
transforming the raw materials into ceramic phases. this process converts
the weak green sample into a strong article of low (or zero) porosity, by
the formulation of a glassy phase which flows into the pores between
particles and solidifies on cooling.
– for solid phase sintering, the quantity of liquid is zero or is at least
too low to be detected. consolidation and elimination of the porosity
require a disruption of the granular architecture: after the sintering, the
grains of the polycrystal are generally much larger than the particles of
the starting powder and their morphologies are also different. solid phase
sintering requires very fine particles (micrometric) and high treatment
temperatures it is reserved for demanding uses, for example, transparent
alumina for public lamps.
– for liquid phase sintering, the quantity of liquid formed is too low
(a few vol.%) to fill the inter-particle porosities. however, the liquid
contributes to the movements of matter, particularly thanks to phenomena
of dissolution followed by reprecipitation. the partial dissolution of the
particles modifies their morphology and can lead to the development of
new phases. a number of technical ceramics (refractory materials,
alumina for insulators, batio3-based dielectrics) are sintered in liquid
phase.
– lastly, for vitrification, there is an abundant liquid phase (for
example, 20 vol.%), resulting from the melting of some of the starting
components or from products of the reaction between these components.
this liquid fills the spaces between the non-molten particles and
consolidation occurs primarily by the penetration of the liquid into the
interstices due to capillary forces, then solidification during cooling, to
give crystallized phases or amorphous glass. this type of sintering is the
rule for silicate ceramics, for example, porcelains. however, the quantity
of liquid must not be excessive, and its viscosity must not be too low,
otherwise the object would collapse under its own weight and would lose
the shape given to it.
sintering -lecture(2)
2
the three stages of sintering
– initial stage: the particle system is similar to a set of spheres in
contact,between which the sintering necks develop. if x is the radius of
the neck and r the radius of the particles, the growth of the ratio x/r in
time t, for an isothermal sintering, takes the form:
(x/r)n = bt/dm
where b is a characteristic parameter of the material and the exponents n
and m vary according to the process brought into play.
– intermediate stage: the system is schematized by a stacking of
polyhedric grains intertwined at their common faces, with pores that form
a canal system along the edges common to three grains, connected at the
quadruple points . the porosity is open. this diagram is valid as long as
the densification does not exceed ? 90-92%, a threshold beyond which
the interconnection of the porosity disappears.
– final stage: the porosity is closed only isolated pores remain, often
located at the quadruple points between the grains (“triple points” on a
two-dimensional section) but which can be trapped in intergranular
position.
thermodynamics of sintering
sintering is the consolidation, under the effect of temperature, of a
powdery agglomerate, a non-cohesive granular material (often called
compact, even though its porosity is typically 40% and therefore its
compactness is only 60%), with the particles of the starting powder
“welding” with one another to create a mechanically cohesive solid,
generally a polycrystal.
the surface of a solid has a surplus energy (energy per unit area: ?sv,
where s is for “solid” and v is for “vapor”) due to the fact that the atoms
here do not have the normal environment of the solid which would
minimize the free enthalpy. in a polycrystal, the grains are separated by
grain boundaries whose surplus energy (denoted ?ss, or ?gb, where ss
is for “solid-solid” and gb for “grain boundary”) is due to the structural
disorder of the boundary. in general, ?ss < ?sv, so a powder lowers its
energy when it is sintered to yield a polycrystal: the thermodynamic
engine of sintering is the reduction of system’s interfacial energies.
mechanical energy is the reduction of the system’s free enthalpy:
sintering -lecture(2)
3
mechanical energy is the reduction of the system’s free enthalpy:
?gt = ?gvol + ?ggb + ?gs
where ?gt is the total variation of g and where vol, gb and s
correspond to the variation of the terms associated respectively with the
volume, the grain boundaries and the surface.
the interfacial energy has the form g = ?a, where ? is the specific
interface energy and a its surface area. the lowering of energy can
therefore be achieved in three ways:
1) by reducing the value of ?,
2) by reducing the interface area a,
3) by combining these effects.
the term sintering includes four phenomena, which take place
simultaneously and often compete with each other:
1- consolidation: development of necks that “weld” the particles to
one another.
2- densification: reduction of the porosity, therefore overall
contraction of the part(sintering shrinkage).
3- grain coarsening: coarsening of the particles and the grains.
4- physicochemical reactions: in the powder, then in the material
under consolidation.
ceramic microstructures
crystalline solids exist as either single crystals or polycrystalline solids.
a single crystal is a solid in which the periodic and repeated arrangement
of atoms is perfect and extends throughout the entirety of the specimen
without interruption.
a polycrystalline solid, typically, in ceramics the grains are in the range
of 1 to 50 |im and are visible only under a microscope. the shape and size
of the grains, together with the presence of porosity, second phases, etc.,
and their distribution describe what is termed the microstructure. as
discussed in later chapters, many of the properties of ceramics are
microstructure-dependent.
sintering -lecture(2)
4
interface effects
the driving force behind the sintering of a powder to form a
polycrystalline material is the reduction of energy resulting from the
reduction of solid-vapor surfaces in favor of the grain boundaries. the
necessary condition for sintering is therefore that the grain boundary
energy (?gb) is low compared to the energy (?sv) of the solid-vapor
surfaces. but this condition is not always achieved, as shown by silicon
carbide (sic) or silicon nitride (si3n4):
the solution for sintering materials can be:
i) the use of sintering additives chosen to increase ?sv or to decrease
?gb .
ii) the use of pressure sintering, which provides external work.
grain size distribution: scale effects
an essential objective in controlling the microstructure of a sintered
material is to be able to control densification and grain growth separately.
in a ceramic filter, for example, we want to preserve a notable porosity,
with pores of sizes calibrated with respect to the medium to be filtered.
the objective is to play on the sintering parameters in order to favor a
particular mechanism. the size of the powder particles is one of the
parameters although the powders in general consist of particles of
irregular size and shape, the simplistic approach that considers spherical
particles makes a useful results possible.
grain growth
as the energy of the interfaces has the form ?a, where ? is the specific
energy of the interface and a is the surface area of the interface, the
system’s energy can be reduced using two cases:
– pure densification: the particles preserve their original size, but the
solid-gas interfaces (?sg) are replaced by grain boundaries (?ss), with a
change in the shape of the particles.
– coalescence and pure grain growth: the particles preserve their original
form,but they change in size by coalescence, thus reducing the surface
areas.
pure densification has never been observed: there is always a grain
growth. owing to the difference in pressure (?p ? ?/r), the atoms diffuse
from the high pressure area towards the low pressure area. in addition, a
sintering -lecture(2)
5
curved boundary blocked at its ends tends to reduce its length while
evolving to a line segment.
in normal grain growth, the average grain size increases regularly,
without marked modification of the relative distribution of the size the
microstructure expands homothetically. this type of grain growth is the
one observed in as uccessful sintering. secondary recrystallization (or
abnormal growth, or discontinuous grain growth) makes a few grains
grow rapidly, to the detriment of the more moderately sized grains. the
final microstructure is very heterogenous, with coexistence of very coarse
grains and very small grains. this type of microstructure rarely leads to
favorable properties and therefore is generally avoided.
the majority of ceramics are multiphased materials that comprise both
crystallized and vitreous phases. porcelain thus consists of silicate glass
“reinforced” by acicular crystals of crystallized mullite, but we can also
observe millimetric crystal agglomerates with a very porous
microstructure (iron and steel refractory materials), or fine grained
polycrystals (< 10 ?m) without vitreous phases and with very low
porosity (hip prosthesis in alumina or zirconia).
competition between consolidation and grain growth
densification and therefore the elimination of the pores occurs effectively
only if the pores remain located on the grain boundaries (intergranular
position), because then the matter movements can take of the grain
boundary diffusion. however, a too rapid grain growth – and therefore a
migration of the boundaries leads to a separation of the pores and the
boundaries: the pores are then trapped in the intergranular position, where
they are difficult to eliminate.
if the objective is to sinter a material to it density material, and therefore
eliminate all the pores, the growth of the grains must be limited.
in addition to its role in the coupling between densification and grain
growth, the size of the grains (?) of the sintered ceramics is, together
with the porosity, the essential microstructural parameter. we can give
some examples:
– the brittle fracture of the ceramics is controlled by the size of the
microscopic cracks, because the mechanical strength ?f is proportional to
kcac-1/2 , where kc is the toughness and ac the length of the critical
microscopic crack. however, ac is of the same order as the size of the
grain. this means that ?f varies typically by ?-1/2:
sintering -lecture(2)
6
ceramics with high mechanical strength (machine parts, cutting tools, hip
prostheses, etc.) must be very fine-grained.
– the high temperature creep of refractory materials is often due to
diffusion mechanisms: volume diffusion leads to the creep and grain
boundary diffusion to the creep, refractory materials must therefore be
coarse-grained in order to slow down the creep.
normal grain growth
in a fine-grained polycrystalline heated to a sufficient temperature, the
size of the grains grows and correlatively the number of grains decreases.
the driving energy is the one that corresponds to the disappearance of the
grain boundaries (it is of the order of a fraction of j.m-2).
the grain growth rate is proportional to the rate of migration of the
boundary this rate (v) can be written as the product of the mobility of the
grain boundary (mgb) and a driving force (f):
v ? d?/dt with: v = mgbf
the driving force is due to the pressure difference caused by the
curvature of the boundary:
?p = ?gb (1/r´ + 1/r´´)
?gb is the energy of the grain boundary and r´ and r´´ are the curvature
radii at the point in question.
when the grain growth is normal, the distribution of the grain sizes
remains significantly unchanged, with a homothetic growth consequently:
(1/r´ + 1/r´´) ? 1/ k? where k is a constant.
abnormal grain growth
some grains develop in an exaggerated manner, the process occurring
when a grain reaches a significant size with a shape limited by many
concave sides: there is then a rapid growth of the coarse grain, to the
detriment of fine convex grains that border it. when the grain reaches this
critical size ?c, much higher than the average size of the other grains in
the matrix ? average, the concave curvature is determined by the size of
the small grains and is therefore proportional to 1/? average. hence, this
apparent paradox that the use of a very fine starting powder can
sometimes increase the risk of secondary recrystallization, because the
sintering -lecture(2)
7
presence of a few particles of size much higher than ? average, is more
probable there than in coarser powders where ? average is higher .in
some sintered materials, we observe very coarse grains with straight
sides, whose growth cannot be explained by the surface tension on the
curved boundaries. these are often materials whose grain boundary
energy is very anisotropic where the growth favors the low energy facets.
this effect is observed in many rocks. they can also be materials where
the impurities lead to the appearance of a small quantity of intergranular
phase between the coarse grain and the matrix, which favor the growth
but a larger quantity of liquid phase would make the penetration in all the
boundaries possible, limiting both normal and exaggerated growth.
abnormal grain growth generally obeys a law
? ? t, whereas normal growth leads to laws
? ? t1/3 or ? ? t1/2
the abnormal growth must be fought from the beginning, because, once
started, its kinetics is rapid.
sintering -lecture(2)
8
sintering additives
the spectacular effect of the addition of a few hundred ppm of magnesia
on the sintering of alumina is the best example of the role of sintering
additives. these additives help to control the microstructure of the
sintered materials they can be classified under two categories:
– additives that react with the basic compound to give a liquid phase, for
example by the appearance of an eutectic at a melting point less than the
sintering temperature. we then go from the case of solid phase sintering
to liquid phase sintering – even if the liquid is very insignificant. silicon
nitride si3n4 ceramics are an example of where some sintering additives
are selected to react with the silica layer (sio2) that covers the nitride
grains, in order to produce a eutectic. thus, magnesia mgo reacts with
sio2 to form the enstatite mgsio3, from which we have liquid phase at
about 1550°c. the liquid film wets the grain boundaries and shapes of the
pockets at the triple points
– additives that do not lead to the formation of a liquid phase and which
consequently enable the sintering to take place in solid phase. this is the
case of the doping of al2o3 with a few hundred ppm of mgo , because
the lowest temperature at which a liquid can appear in the al2o3-mgo
system exceeds the sintering temperature (which, for alumina, does not
go beyond 1700°c).
the choice of the sintering temperature also plays on the relative values
of the diffusion coefficients and therefore favors a densifying or a nondensifying
mechanism. for example, surface diffusion has an apparent
activation energy generally less than the volume diffusion. the
chronothermic effect (“a long duration heat treatment at lower
temperature is equivalent to a short duration heat treatment at higher
temperature”) therefore offers broader possibilities than those offered by
the arrhenius law with a single activation energy: low temperature
sintering primarily bringing into play surface diffusion (non-densifying
mechanism), and high temperature sintering volume diffusion or the grain
boundary diffusion (densifying mechanisms). a high temperature
treatment favors, all things being equal, high densification.
sintering with liquid phase
parameters of the liquid phase
in general, the presence of a liquid phase facilitates sintering.
vitrification is the rule for silicate ceramics where the reactions between
the starting components form compounds melting at a rather low
temperature, with the development of an abundant quantity of viscous
sintering -lecture(2)
9
liquid. various technical ceramics, most metals and cermets are all
sintered in the presence of a liquid phase. it is rare that sintering with
liquid phase does not imply any chemical reactions, but in the simple case
where these reactions do not have a marked influence, surface effects are
predominant. the main parameters are therefore:
i) quantity of liquid phase.
ii) its viscosity.
iii) its wettability with respect to the solid.
iv) the respective solubilities of the solid in
the liquid and the liquid in the solid:
– quantity of liquid: as the compact stacking of isodiametric spheres
leaves a porosity of approximately 26% this value is the order of
magnitude of the volume of liquid phase necessary to fill all the
interstices and allow the rearrangement of the grains observed at the
beginning of the vitrification. however, the presence of a small quantity
of liquid (a few volumes percent) does not make it possible to fill the
interstices
– viscosity of the liquid: this decreases rapidly when the temperature
increases (typically according to the arrhenius law). pure silica melts
only at a very high temperature to produce a very viscous liquid. the
presence of alkalines and alkaline earths quickly decreases the softening
temperature and the viscosity of the liquid.
the viscosity of the liquid should be neither too low – because then the
sintered part becomes deformed in an unacceptable way – nor too high –
because then the viscous flow is too limited, making grain rearrangement
difficult
– wettability: wettability is quantifiable by the experiment of the liquid
droping placed on a solid, because the equilibrium shape of the droping
minimizes the interfacial energies. if ?lv is the liquid-vapor energy, ?sv
the solid-vapor energy and ?sl the solid-liquid energy, the angle of
contact (?) is such that
?lvcos? = ?sv – ?sl
when ?sl is high, the droping minimizes its interface with the solid, hence a
high value of ?: ? > 90° corresponds to non-wetting (depression of the
liquid in a capillary). on the contrary, when ?sl << ?sv, the liquid
spreads on the surface of the solid: ? < 90° corresponds to wetting (rise of
the liquid in a capillary) and for ? = 0, the wetting is perfect.
in a granular solid that contains a liquid, the respective values of ?sl and
?gb (grain boundary energy) determine the value of the dihedral angle ?:
2?slcos?/2 = ?gb
the stages in liquid phase sintering
sintering -lecture(2)
10
the shrinkage curve recorded during an isothermal treatment of liquid
phases intering shows three stages:
– viscous flow and grain rearrangement: when the liquid is formed, the
limiting process consists of a viscous flow, which allows the
rearrangement of the grains. the liquid dissolves the surface asperities
and also dissolves the small particles. the granular rearrangement is
limited to the liquid phase sintering itself, but it can be enough to allow
complete densification if the liquid phase is in sufficient quantity,
as is the case in the vitrification of silicate ceramics.
– solution-reprecipitation: the solubility of the solid in the liquid increases
at the inter-particle points of contact. the transfer of matter followed by
reprecipitation in the low energy areas results in densification.
– development of the solid skeleton: the liquid phase is eliminated
gradually bythe formation of new crystals or solid solutions we tend to
approach the case of solid phase sintering and the last stage of the
elimination of porosity is similar to the
one observed in this case.
the disintegration of the particles attacked by the liquid results in the
ostwald ripening (coalescence of small particles to give a larger particle)
and changes in the shape of the particles, with flattening of the areas of
contact. as the anisotropy of crystalline growth is less hampered when a
crystal grows in a liquid than when it remains in contact with solid
obstacles, we sometimes observe grains whose morphology reflects these
anisotropy effects: for instance, they are elongated and faceted.
the role of chemical reactions is still significant, because they bring into
play energies much higher than the interfacial ones and frequently the
reactions between liquid and solid result in the formation of new phases.
we can thus distinguish three cases:
– weak reaction between liquid and solid: the liquid has the primary role,
after cooling, of forming the matrix in which the grains that have not
reacted have been glued. this is the case of abrasive materials where the
grains (silicon carbide sic or alumina al2o3) are bound by a solidified
vitreous phase.