boundary
(MGB) and a driving force (F):
v ≈ dΦ/dt with: v = MGBF
The driving force is due to the pressure difference caused by the curvature of the
boundary:
ΔP = γGB (1/r´ + 1/r´´)
γGB 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/ KΦ where K is a constant.
Pure monophased material
A simple reasoning based on a two-dimensional microstructure (section of a
polycrystal), where the equilibrium configuration of a “triple point” corresponds to
angles of 120°, is that grains with less than six sides are limited by convex
boundaries and therefore tend to decrease, whereas those with more than six sides
are limited by concave boundaries and therefore tend to grow (see Figure 3.6). If the
curvature radius of a grain is proportional to its diameter, the driving force and the
growth rate are inversely proportional to its size:
dΦ/dt = Cte/Φ hence Φ ≈ t1/2 [3.11]
The grain size must increase by the square root of the time.
Among the simplistic assumptions that have been made, we note that only the
curvature of the boundary has been considered and not the crystalline anisotropy.
Obstacles to grain growth
When we express experimental results of grain growth in the form of a graph
lnΦ = f(lnt), we obtain a straight line whose slope is, in general, less than the
exponent 1/2 predicted by the parabolic law. This means that the growth is slowed
down by various obstacles. Based on the interaction between a mobile grain
boundary and an obstacle, we can distinguish three main cases: i) impurities in solid
solution or liquid phase wetting the boundaries, ii) immobile obstacles, which block
76 Ceramic Materials
any movement of the boundary, and iii) mobile obstacles capable of migrating with
the boundary.
The impurities in solid solution can slow down the movement of the boundaries
because they prefer to lodge themselves close to the grain boundary and therefore
the boundary can migrate either by carrying these impurities along – which slows
down the movement – or by leaving them in the intragranular position – which puts
them in an energetically less favorable position than before the migration of the
boundary. The growth law is thus modified because of the presence of these
impurities and we get:
dΦ/dt ≈ 1/Φ2 Φ ≈ K t1/3 [3.12]
The growth law Φ ≈ t1/3 (impure phase) is more frequently observed than the law
Φ ≈ t1/2 (pure phase).
The presence of a liquid phase that wets the boundaries tends to reduce the grain
growth, by reducing the driving energy and increasing the diffusion path, since there
now is a double interface. It is true that diffusion in a liquid is fast; however, the
dissolution-diffusion-reprecipitation process is generally slower than the simple
jump through a grain boundary. Thus, the presence of a small quantity of a molten
silicate phase limits the grain growth of the sintered alumina with liquid phase. On
the other hand, the presence of a liquid phase can favor chemical reactions of type
A + B → C and therefore allow the growth of the grains C to the detriment of the
grains A and B. This type of growth often leads to secondary recrystallization
(exaggerated growth). The growth law is Φ ≈ t1/3, as for an impure phase.
The immobile obstacles, such as precipitates and inclusions, “pin” the
boundaries, reducing their energy by a quantity equal to the product of the specific
pinning energy and the surface area of the inclusion. To be “undragged”, the
boundary must be subjected to a tearing force. As long as the migration driving
force of the boundary, due to the effects of curvature, does not exceed this tearing
force, the boundary remains pinned and the grain size is stable. For grains anchored
by inclusions, the growth can occur only if:
– the inclusions coalesce by diffusion, to give less numerous but more
voluminous inclusions (Ostwald ripening). If the coalescence takes place by volume
diffusion, the radius of the inclusion (r) increases as r3 ≈ t, which again yields a
grain growth obeying a law Φ ≈ t1/3;
– the inclusions disappear by dissolution in the matrix: Φ ≈ t;
– secondary recrystallization occurs: this is the end of normal growth.
Sintering and Microstructure of Ceramics 77
The mobile obstacles are essentially pores. If vP and vGB are the speeds of the
pore and the boundary, MP and MGB are the mobilities, and FP and FGB are the
corresponding “forces”, we have vP = MPFP and vGB = MGBFGB. The pore separates
itself from the boundary if vGB > vP.
The force on the boundary FGB has two components, one due to the curvature
(F’GB) and the other due to the pinning effect by the pores, which equals NFP, if
there are N pores. The condition for non-separation is therefore:
vP = MPFP = vGB = MGB (F’GB – N FP) vGB = FGB (MP MGB)/(N MGB + MP)
– if NMGB >> MP, then vGB = FGB (MP/N): the rate of migration of the
boundaries is controlled by the characteristics of the pores;
– if NMGB << MP, then vGB = FGB (MGB): the rate of migration of the
boundaries is controlled by the characteristics of the boundaries themselves.
Different mechanisms lead to different laws of type Φ ≈ t1/n. The values of the
exponent n depend on the mechanism and the diffusion path that control the process.
For example, for control by the pores: n = 4 for surface diffusion, n = 2 for volume
diffusion, and n = 3 for vapor phase diffusion; for control by the boundaries: n = 2
for a pure phase and n = 3 for the coalescence of a second phase by volume
diffusion. The experimental studies of the grain growth consist of: i) quantifying the
grain size Φ, ii) determining the exponent n of the growth law Φ ≈ t1/n, and iii)
determining the apparent activation energy E of the process. The results are semi-
quantitative, because of two difficulties: i) inaccuracy of the measures of the grain
size and ii) simultaneous occurrence of several processes – with different values of n
and E. The law of normal grain growth that is most frequently observed is the law
Φ ≈ t1/3.
3.5.5. 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 (see Figure 3.6). When the grain reaches this critical size ΦC, much higher
than the average size of the other grains in the matrix Φaverage, the concave
curvature is determined by the size of the small grains and is therefore proportional
to 1/Φaverage. Hence, this apparent paradox that the use of a very fine starting
powder can sometimes increase the risk of secondary recrystallization, because the
presence of a few particles of size much higher than Φaverage, is more probable there
than in coarser powders where Φaverage is higher.
78 Ceramic Materials
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 (see Figure 3.7). 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 Φ ≈ t, whereas normal growth
leads to laws Φ ≈ t1/3 or Φ ≈ t1/2: the abnormal growth must be fought from the
beginning, because, once started, its kinetics is rapid.
Figure 3.7. Abnormal grain growth in In2O3 sintered at high temperature (1,500°C for 50 h).
Some grains have grown exaggeratedly in a fine-grain matrix [NAD 97]
3.6. Sintering with liquid phase: vitrification
3.6.1. 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 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
Sintering and Microstructure of Ceramics 79
wettability with respect to the solid, and 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 drop
placed on a solid, because the equilibrium shape of the drop minimizes the
interfacial energies. If γLV is the liquid-vapor energy, γSV the solid-vapor energy and
γSL the solid-liquid energy, the angle of contact (θ) is such that (see Figure 3.8):
γLVcosθ = γSV – γSL [3.13]
When γSL is high, the drop minimizes its interface with the solid, hence a high
value of θ: θ > 90° corresponds to non-wetting (depression of the liquid in a
capillary). On the contrary, when γSL << γSV, the liquid spreads on the surface of the
solid: θ < 90° corresponds to wetting (rise of the liquid in a capillary); and for θ = 0,
the wetting is perfect.
In a granular solid that contains a liquid, the respective values of γSL and γGB
(grain boundary energy) determine the value of the dihedral angle Θ:
2γSLcosΘ/2 = γGB [3.14]
Figure 3.9 shows the penetration of the liquid between the particles of a granular
solid according to the value of Θ. For low Θ (0 to 30°), the liquid wets the
boundaries; when Θ continues to grow, the occurrence of the liquid phase becomes
less marked and for a high value of Θ (Θ > 120°), the liquid tends to form pockets
located at the “triple points” – on a two-dimensional view, but at the “quadruple
points” in three-dimensional space. Based on mutual solubilities we can distinguish
four cases (see Table 3.2).
80 Ceramic Materials
Figure 3.8. Drop placed on a liquid; the value of θ characterizes the wettability:
wetting on the left; non-wetting on the right
Figure 3.9. Penetration of the liquid between the grains
depending on the value of Θ [GER 96]
Low solubility of the solid
in the liquid
High solubility of the solid
in the liquid
Low solubility of the liquid
in the solid
Low assistance
to densification
High assistance
to densification
High solubility of the
liquid in the solid
Swelling, transitory liquid Swelling, and/or
densification
Table 3.2. Effects of mutual solubilities on sintering [GER 96]
3.6.2. The stages in liquid phase sintering
The shrinkage curve recorded during an isothermal treatment of liquid phase
sintering 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.
Sintering and Microstructure of Ceramics 81
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 by
the 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;
– reaction between liquid and solid, solid with congruent melting: there is no
appearance of new solid phases but modification of the existing ones. This is the
case for silicate ceramics made of quartz sand (SiO2) and clay (whose primary
mineral is kaolinite, written as (Al2O3.2SiO2.2H2O), fired at rather low
temperatures. The high viscosity of the silicate liquid prevents the system from
reaching the equilibrium; in particular, glass of the eutectic composition does not
decompose into mullite plus cristobalite, as suggested by the equilibrium diagram.
Only the finest particles react; the coarsest do not dissolve. The coarse quartz grains,
for example, hardly react with clay – but firing transforms them, almost completely,
into cristobalite (a high temperature variety of crystallized silica);
– reaction between liquid and solid, solid with incongruent melting: an example
is that of the system containing quartz (SiO2) + kaolinite (Al2O3-2SiO2-2H2O) +
potassic feldspar (6SiO2-K2O-Al2O3), which is the basic system of porcelains.
82 Ceramic Materials
At about T = 1,150°C, the feldspar melts to give leucite (4SiO2.Al2O3.K2O) and a
vitreous phase (with a composition close to 9SiO2. Al2O3.K2O). Leucite dissolves
gradually into glass to produce a flow that is very viscous until it melts at about
1,530°C: at 1,300°C, the viscosity is equal to 106 poises and it decreases only slowly
with temperature: at 1,400°C it is still 5.105 poises. Potassic feldspar is a flux (a
component that, by reaction with the other components, gives rise to a phase with low
melting point) which produces a liquid whose viscosity does not vary too quickly with
the temperature, and which therefore does not require a very strict control of this
temperature: the firing range is broad. On the contrary, certain fluxes (for example,
calcic phases) have a sudden effect because they create phases with too low viscosity.
3.7. Sintering additives: sintering maps
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
a liquid phase at about 1,550°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 1,700°C).
The explanation of the role of this second category of additives is primarily
phenomenological. It considers the respective values of the diffusion coefficients
and the mobility of the boundaries:
– DL characterizes volume diffusion (L = lattice), Db grain boundary diffusion
and DS surface diffusion;
– Mb characterizes the mobility of the grain boundaries.
The sintering maps [HAR 84] place the diameter of the grain (G) on the ordinate
and densification (ρ = d/d0) on the abscissa (see Figure 3.10). The two extreme cases
Sintering and Microstructure of Ceramics 83
would be i) a grain coarsening without densification (vertical trajectory) and ii) a
densification with unchanged grain size (horizontal trajectory).
Experimentally, we always observe an intermediate trajectory between these two
extremes because the densification is inevitably accompanied by grain growth.
In order to densify the material to 100%, the key point is to prevent the pores and
the boundaries from separating because then, as we already said, the residual pores
are trapped in the intragranular position, where it is practically impossible to
eliminate them. The trajectory G = f(ρ) must therefore be as flat as possible and
must, in particular, go below the lowest point of the pore-boundary separation area
(in the figure: the point ordinate G* abscissa ρ*). Densification cannot reach 100%
if the trajectory cuts this separation area. Various ratios characterize the relationship
between “contribution of the diffusion to densification” and “contribution of the
diffusion to grain coarsening”, with the first term in the numerator and the second
term in the denominator. For example, DL/DL means: “densification controlled by
volume diffusion” and “grain coarsening controlled by volume diffusion”, whereas
Db/DS means “densification by boundary diffusion” and “grain coarsening
controlled by surface diffusion” (see Figure 3.11). The possible effect of an additive
can be seen from the following observations:
– an increase in DL flattens the trajectory without affecting the separation area:
this increase of DL is favorable to the densification;
– a decrease in Mb increases G* and therefore shifts the separation area towards
the top and slightly flattens the trajectory: this decrease in Mb also has a favorable
effect on the densification;
– a decrease in DS flattens the trajectory (which is favorable), but decreases G*
and therefore shifts the separation area to the bottom (which is unfavorable). All in
all this decrease in surface diffusion – which as we said earlier leads to a non-
densifying sintering – would not have a significantly useful (or harmful) effect.
The use of these sintering maps to explain the effectiveness of MgO as a
sintering additive for Al2O3 suggests that MgO increases DL (first favorable effect)
and especially decreases Mb (second favorable effect). This phenomenological
explanation does not, however, provide information on the mechanisms brought into
play and in particular it does not give the reason for which MgO reduces the
mobility of the boundaries. An explanation [BAE 94] would be that the traces of
impurities (SiO2 and CaO), which continue to exist even in so-called high purity
alumina powders, are located along the grain boundaries, to form at the sintering
temperature a thin liquid film which promotes the grain growth – “solid phase
sintering” then becoming a sintering controlled by a very insignificant liquid phase.
The influence of MgO would then be “to purify” the grain boundaries while reacting
with SiO2 or CaO.
84 Ceramic Materials
Grain size
Density
Pore-boundary
Density
Grain size
separation
trajectory
Thickness
Figure 3.10. Sintering map showing the grain size depending on the densification [HAR 84].
On the left: principle of the map; on the right: for complete densification to be possible,
the sintering trajectory must not cut the hatched pore-boundary separation area
Figure 3.11. Role of a sintering additive [HAR 84]. On the left, the effect of the doping agent
is to multiply DL by 10: the influence is favorable by the flattening of the trajectory.
On the right, the effect of the doping agent is to divide Mb by 10: the influence is doubly
favorable by the raising of the separation area and flatness of the trajectory
Sintering and Microstructure of Ceramics 85
The doping of Al2O3 by MgO has been transposed to various ceramic systems,
for which we have determined which sintering additives limit the grain growth and
make a densification close to 100% possible [NAD 97]. These studies provide
answers on a case-by-case basis and there is still no general theory for the selection
of the optimal additive.
The choice of the sintering temperature also plays on the relative values of the
diffusion coefficients and therefore favors a densifying or a non-densifying
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.
3.8. Pressure sintering and hot isostatic pressing
3.8.1. Applying a pressure during sintering
In most cases, ceramics are sintered by pressureless sintering and it is only for
very special applications that we use “pressure sintering” or “hot pressing”, which
consists of applying a pressure during the heat treatment itself. The characteristic of
pressure sintering is that the pressures brought into play – which are usually about
10 to 70 MPa, but can exceed 100 MPa – have considerable effects compared to
capillary actions, thus offering four advantages:
i) thickening of materials whose interfacial energy balances are unfavorable;
ii) rapid densification at appreciably lower temperatures (several hundred
degrees sometimes) than those demanded by pressureless sintering;
iii) possibility of reaching the theoretical density (zero porosity);
iv) possibility of limiting the grain growth.
Furthermore, it can be possible to obtain the sintered part with its exact
dimensions (net shape), without the need for a machine finishing in applications that
require high dimensional accuracy. The other side of the coin is the technical
complexity of the process and the high costs incurred, as well as the limitations on
the geometry of the parts, which can only have simple forms and a rather reduced
size. We must have pressurization devices manufactured in materials that resist the
temperatures required by sintering – and even if these temperatures are lower
86 Ceramic Materials
compared to those required by pressureless sintering, they are still high – and the
chemical reactions between these materials and the environment (for example,
oxidation of refractory metals), like the reactions between the mould and the
ceramic powder, must be limited. One last difficulty: if the manufacture of parts
with simple geometry (pellets) can be done in a piston + cylinder mould (“uniaxial
pressure pressing”), obtaining more complex shapes, in particular undercut parts,
cannot be done by pressure sintering. We must then apply the technique of hot
isostatic pressing or “HIP”, where the pressure is not transmitted by a piston but by a
gas, hence the hydrostaticity (isostaticity) of the efforts, in analogy with “cold
isostatic pressing” described in Chapter 5, but where the pressure transmitting fluid
is a liquid and not a gas.
3.8.2. Pressure sintering
Graphite is the most used material for the manufacture of the mould and the
piston of uniaxial pressure sintering equipments, because of its exceptional
refractarity, with this originality that the mechanical strength grows when the
temperature rises (until beyond 2,000°C), also taking into account its easy
machinability and the generally limited speed of the reactions with the ceramic
powders – often protected by a fine boron nitride deposit. But the oxidation ability
of the graphite requires a reducing or neutral processing atmosphere, which is
appropriate for non-oxides (primarily carbides, like HPSC, and nitrides, like HPSN;
see Chapter 7), but can lead to oxygen under-stoichiometry for those oxides that are
reduced easily. Refractory metals (Mo or W) and ceramics (Al2O3 or SiC) have also
been used for the piston-cylinder couple of the mould.
The powders to be sintered are generally very fine (< 1 μm) and it is not always
necessary for them to contain additives required by pressureless sintering (for
example, MgO for the sintering of Al2O3). The justifiable applications of pressure
sintering are, for example, cutting tools (ceramics or cermets) or optical parts, with
the essential objectives of achieving a 100% densification and/or very fine grains –
but the microstructure and the crystallographic texture can present anisotropy effects
because of the uniaxiality of the pressing. Alumina for cutting tools, carbides (B4C,
for instance) or cermets are examples of materials that can benefit from pressure
sintering and HIP (see further down); the same is true for metallic “superalloys”
used in the hot parts of turbojets. High temperature composite materials are another
example where the application of a pressure during heat treatments can be necessary
to allow the impregnation of the fibrous wicks and favor the densification.
Functional ceramics (BaTiO3 or, especially, magnetic ferrites) can gain from very
fine grains and the absence of residual porosity made possible by pressure sintering.
As optical transparency is no doubt the property that is most quickly degraded by the
presence of pores, even in extremely small numbers, perfectly transparent
Sintering and Microstructure of Ceramics 87
polycrystalline ceramics (MgAl2O4, Al2O3, Y2O3, etc.) are examples of materials
that benefit from the use of pressure sintering.
As regards the mechanisms, pressure sintering implies: i) rearrangement of the
particles, ii) lattice diffusion, iii) grain boundary diffusion, and finally iv) plastic
deformation and a viscous flow. Pressureless sintering involves much less the effects
i) and iv) and, as for the effects ii) and iii), the high level of the mechanical stresses
(often close to and even exceeding the stresses caused by the normal operation of a
part, for example a refractory part in a high temperature facility) brings them close
to creep effects. This can be diffusion creep (Nabarro-Herring creep due to
intragranular diffusion, Coble creep due to the grain boundary diffusion) or creep
due to the movement of dislocations.
The creep equation, modified for pressure sintering, can be written as:
(1/ρ)(dρ/dt) = (CD)/(kTΦm) [σn + 2γ/r] [3.15]
where ρ is the density, C a constant, D the coefficient that controls the diffusion
process, k the Boltzmann constant and T the temperature, Φ the average grain size, σ
the pressure applied on the particles, γ the surface energy and r the radius of the
pores. The exponents m and n characterize respectively the role of the grain size and
that of the pressure applied. Table 3.3 recapitulates the relevant parameters (see
Chapter 8).
Mechanism Grain size
exponent, m
Stress exponent, n Coefficient
of diffusion, D
Nabarro-Herring 2 1 Volume diff. DV
Coble 3 1 Boundary diff. DJ
Intergranular sliding 1 1 or 2 DJ, DV
Interface reactions 1 2 DJ, DV
Plastic flow 0 ≥ 3 DV
Table 3.3. Mechanisms of pressure sintering [HAR 91]
In most cases, the use of fine grained ceramics on the one hand, and the high
level of plastic flow required by iono-covalent crystals on the other, are such that the
diffusion terms (Nabarro-Herring or Coble) override the plastic flow. Grain
boundary diffusion dominates over volume diffusion all the more when the grains
are finer and the temperature lower, because the volume exponent of the former is 3
whereas that of the latter is only 2, and the activation enthalpy of DJ is in general
lower than that of DV.
88 Ceramic Materials
Boundary sliding is necessary in order to accommodate the variations in shape
caused by the diffusion creep, which implies that the mechanisms must act
sequentially and therefore that the overall kinetics is controlled by the slowest
mechanism. Nonetheless, when the mechanisms can act concurrently (as is the case
with diffusion creep and plastic flow), it is the fastest process that controls the
overall kinetics.
An illustration [TAI 98] of pressure sintering (1 hour at 1,360°C, p = 20 MPa,
graphite matrix, antiadhesive layer of BN, in vacuum) is obtaining particle
composites 10%Al2O2-80%WC-10%Co with a mechanical strength of 1,250 MPa:
pressureless sintering would not allow the densification of this type of material,
whose microstructure exhibits an inter-connected matrix of WC, with precipitates of
Al2O3 and Co3W3C (see Figure 3.12).
Figure 3.12. 10% Al2O3-80% WC-10% Co composite, sintered under pressure [TAI 98]
3.8.3. Hot isostatic pressing (HIP)
Whereas for cold isostatic pressing (CIC – see Chapter 5), the pressurization
fluid is a liquid, it is a gas (in general argon, but reactive atmospheres are also used,
for example oxygen) that provides the pressurization in HIP. This technique was
invented by the Battelle institute (USA) in the 1950s. We can imagine the risks of
destructive explosions (use of a compressible fluid instead of an incompressible
fluid) and the difficulties in ensuring air-tightness as well as the problems of
pollution and control of thermal transfers: under a pressure of 1,000 atmospheres, a
gas like argon has a density higher than that of liquid water at 20°C!
The two main methods involving HIP are direct consolidation by HIP, and HIP
perfecting a pressureless sintering having preceded it (see Figure 3.13).
Sintering and Microstructure of Ceramics 89
Sintering
HIP post-sintering
Powder preparation Forming
Powder preparation Forming
Wrapped in a
glass envelope
HIP treatment
Envelope elimination
Figure 3.13. Direct HIP (on the left) and post-sintering HIP (on the right) [DAV 91]
Consolidation by HIP
When HIP is used directly to consolidate a powder, the “compact” must be
encapsulated in an envelope in a form homothetic to that of the part to be obtained,
with vacuum evacuation of gases, followed by sealing of the envelope. Soft or
stainless steels can be used as envelope materials for relatively low temperature
treatments (1,100–1,200°C), whereas it is necessary to use refractory metals (Ta,
Mo) for higher temperatures treatments. As the risks of distortion become higher
when the overall pressing increases, we gain from a powder pressed at a high rate
and homogenously (by CIC primarily). An alternative is to carry out a “pre-
sintering” providing sufficient cohesion to the part to make its handling possible,
and then to coat it powdered glass which, at sufficient temperature, will become
viscous enough to coat the piece with an impermeable layer. This will make it
possible for HIP to take place without the pressurized gas being able to penetrate the
open porosity.
HIP as post-sintering operation
This involves sintering the part until the inter-connected open porosity is
eliminated (which requires a densification of about 95%) and then subjecting this
part to a secondary HIP treatment. The greatest advantage is avoiding the need for
an envelope (cost, complexity, restrictions on the possible forms, necessity to clean
the end product to eliminate the envelope). It is furthermore possible, for
manufacturers who do not have an HIP equipment, to sub-contract this stage to a
specialized partner. There are HIP chambers whose size is more than one meter,
which makes it possible to treat large parts or a great number of small parts.
90 Ceramic Materials
The densification of metallic powders (“powder metallurgy”) involves HIP much
more frequently than the densification of ceramic powders: a search on the Web
shows that most sites dealing with HIP relate to metallic products (the term taken in
its largest sense and including cermets).
3.8.4. Densification/conformity of shapes in HIP
Densification
The densification of the parts by HIP implies primarily three phenomena: i)
fragmentation of the particles and rearrangement, ii) deformation of the inter-
particle areas of contact and iii) elimination of the pores. The first process is
transitory and hardly contributes to the overall densification, at least if the initial
forming (for example, by CIC) has been correctly carried out. The second process
brings into play effects of plastic deformation by movement of dislocations and
diffusion phenomena that are similar to those indicated in the case of uniaxial
pressure sintering. Lastly, by considering the final reduction of porosity, we can
write phenomenologically:
(1/ρ)(dρ/dt) i = Bifi (ρ) [3.16]
where ρ is the relative density, Bi constant kinetics (implying the terms relating to
the material and those relating to the characteristics of the HIP process) and fi(ρ) a
geometrical function that depends only on the relative density. Each process i is
described by specific expressions for Bi and fi [LI 87]. For example:
Ki = 270δDjgΩP/kTR3 and fi (ρ) = (1-ρ)1/2 if ρ > 90% [3.17]
for grain boundary diffusion (Coble), if δ is “the thickness” of the boundary, Djg the
corresponding diffusion coefficient, Ω the volume of the atom that diffuses and R
the radius of the grain assumed to be spherical, k, T and P having their usual
meaning.
Ashby et al. [LI 87] have developed the approach of “HIP maps”, where, for a
material under given conditions, the areas in two-dimensional space (relative density
depending on the pressure), in which the predominant phenomenon that controls the
densification has been identified, are traced (in particular the grain size and
temperature). These maps make the pendant of the “creep maps” and “deformation
maps” also credited to Ashby et al. (see Figure 7.2 in Chapter 7). The principle of
these maps is certainly attractive, but their applicability requires three conditions: i)
having a sufficient number of experimental data, ii) establishing, for each of these
data, the nature of the predominant mechanism, and lastly iii) verifying the
Sintering and Microstructure of Ceramics 91
similarity of the treated cases (for example, the fact that the powders used contain
the same impurities as the powders used for tracing the maps). The application of
the maps is therefore qualitative more than quantitative. Let us use an example to
illustrate this comment: when we compare the case of a metal with that of a ceramic,
we observe that the mobility of dislocations in the former material is much higher
than it is in the latter. This means that the relationship between the effect of an
increase in temperature and that of an increase in pressure is higher for ceramics
than it is for metal, which suggests different managements of the parameters T and p
for the two categories of material.
Conformity of the shapes
The key point for HIP, which is an expensive treatment and therefore dedicated
to high added value products, is to obtain parts whose final dimensions are as close
as possible to the desired dimensions. However, this conformity of dimensions
requires a perfect control of the shrinkage: it must occur particularly in a
homothetical way, starting from the shape of the raw part until the consolidated and
stripped part. However, this “homothetic shrinkage” is affected by various causes,
including the envelope effect (in the case where there is not post-densification HIP)
and the manner in which the consolidation front develops.
As regards the envelope effect: even if the “compact” is overheated perfectly
homogenously throughout the HIP cycle, the various areas of the part do not offer
the same resistance to the effects of isostatic pressure. Geometrical compatibilities
require that the volume deformations should be accompanied by shearing strains, a
requirement which introduces distortions. For the simple example of a cylindrical
part (see Figure 3.14), the presence of the envelope causes a distortion of the
“corners”. The numerical calculation methods like finite elements are used widely
for the study of such distortions in order to eliminate them by redrawing the
envelope [NCE 00].
As regards densification: this progresses from outside the part towards the core,
causing the formation of a consolidated crust whose thermal conduction is higher
than that of the core that is not yet consolidated. The heat fluxes thus provoked lead
to heterogenities in temperature, which lead to the accentuation of the shell effect of
the crust with respect to the core. The effect is all the more marked the bulkier part
is.
As an extension of pressureless sintering HIP confirms that a major concern for
the production of ceramic parts – “traditional” ceramics as well as “technical”
ceramic – is the maintenance of the shape and dimensions of the parts. As we said
previously: the ceramist works on the product at the same time as he works on the
material and therefore his efforts must be devoted to both sides of the problem.
92 Ceramic Materials
Figure 3.14. HIP: at the top, distortion due to envelope effects; at the bottom,
example of an iterative approach to determine the shape of the envelope, which
allows the correction of the distortions [NCE 00]
3.9. Bibliography
[ASH 75] ASHBY M.F., “A first report on sintering diagrams”, Acta Metall., 22, p. 275,
1975.
[BAE 94] BAE S.I. and BAIK S., “Critical concentration of MgO for the prevention of
abnormal grain growth in alumina”, J. Am. Ceram. Soc., 77 (101), p. 2499, 1994.
[BER 93] BERNACHE-ASSOLLANT D. (ed.), Chimie-physique du frittage, Hermès, 1993.
[BOC 87] BOCH P. and GIRY J.P., “Preparation of zirconia-mullite ceramics by reaction
sintering”, High Technology Ceramics, Materials Science Monographs 38, Elsevier, 1987.
[BOC 90] BOCH P., CHARTIER T. and RODRIGO, “High purity mullite by reaction
sintering”, Mullite and Mullite Matrix Composites, Ceramic Transactions, Vol. 6, The
Am. Ceramic Society, p. 353, 1990.
Sintering and Microstructure of Ceramics 93
[DAV 91] DAVIS R.F., “Hot isostatic pressing”, in Brook R.J. (ed.), Concise Encyclopedia of
Advanced Ceramic Materials, Pergamon Press, p. 210, 1991.
[GER 96] GERMAN R.M., Sintering Theory and Practice, J. Wiley, 1996.
[HAR 84] HARMER M.P., “Use of solid-solution additives in ceramic processing”, Advances
in Ceramics, Am. Ceram. Soc., Vol. 10, p. 679, 1984.
[HAR 91] HARMER P.P., “Hot pressing: technology and theory”, in Brook R.J. (ed.),
Concise Encyclopedia of Advanced Ceramic Materials, Pergamon Press, p. 222, 1991.
[HER 50] HERRING C., “Diffusional viscosity of a polycrystalline solid”, J. Appl. Phys.,
21(5), p. 437-445, 1950.
[KIN 76] KINGERY W.D., BOWEN H.K. and UHLMANN D.R., Introduction to Ceramics,
2nd edition, John Wiley and Sons, 1976.
[KUC 49] KUCZYNSKI G.C., “Self-distribution in sintering of metallic particles”, Trans.
AIME, 185, p. 169, 1949.
[LEE 94] LEE W.E. and RAINFORTH W.M., Ceramic Microstructures, Chapman & Hall,
1994.
[LI 87] LI W.B., ASHBY M.F., EASTERLING K.E., “On densifiaction and shape-change
during hot isostatic pressing”, Acta Metallurgica, 35, p. 2831-2842, 1987.
[NAD 97a] NADAUD N., KIM D.Y. and BOCH P., “Titania as Sintering Additive in Indium
Oxide Ceramics”, J. Am. Ceram. Soc., 80(5), p. 1208-1212, 1997.
[NAD 97b] NADAUD N., “Relations entre frittage et propriétés de matériaux à base d’oxyde
d’indium dopé à l’étain (ITO)”, Thesis, Paris-6 University, 1997.
[NCE 00] National Center for Excellence in Metalworking Technology, CTC, 100 CTC
Drive, Johnstown, Pa, USA.
[PHI 85] PHILIBERT J., Diffusion et transport de matière dans les oxydes, Editions de
Physique, 1985.
[RIN 96] RING T.A., Fundamentals of Ceramic Powder Processing and Synthesis, Academic
Press, 1996.
[TAI 88] TAI W.T. and WATANABE T., “Fabrication and mechanical properties of Al2O3 –
WC–Co composites by vacuum hot pressing”, J. Am. Ceram. Soc., 81(6), p. 1673-1676,
1998.
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