SOLIDIFICATION MICROSTRUCTURE:

EUTECTIC AND PERITECTIC

5.1 Regular and Irregular Eutectics
Due to the fact that they are composed of more than one phase, eutectics can exhibit a wide
variety of geometrical arrangements. With regard to the number of phases present, as many as
four phases have been observed to grow simultaneously. However, the vast majority of
technologically useful eutectic alloys are composed of two phases. For this reason, only the latter
type of eutectic will be considered here (figure 5.1).
At high volume fractions of both phases (f≈0.5), a situation which is encouraged by a
symmetrical phase diagram, there is a marked preference for the formation of lamellar structures
(e.g. Pb-Sn). On the other hand, if one phase is present in a small volume fraction, there is a
tendency to the formation of fibres of that phase (e.g. Cr in NiAl-Cr). As a rule of thumb, one
can suppose that when the volume fraction of one phase is between zero and 0.25, the eutectic
will probably be fibrous, especially if both phases are of non-faceted type. If it is between 0.25
and 0.50, the eutectic will tend to be lamellar. If both phases possess a low entropy of fusion, the
eutectic will exhibit a regular morphology. Fibres will become faceted if one phase has a high
entropy of fusion or when interfaces having a minimum energy exist between the two phases.
When faceting occurs, the eutectic morphology often becomes irregular and this is particularly
true of the two eutectic alloys of greatest practical importance: Fe-C (cast iron) and Al-Si (*).
The regularity of an eutectic has a marked effect upon its mechanical properties, and this
becomes especially important when it is required to control the orientation of the phases in order
to obtain what are known as in situ composites. These are alloys where, using a controlled heat
flux (figure 1.4), the eutectic phases can be caused to grow in a well-aligned manner. When the
fibres are strong, as in the case of TaC in Ni-TaC eutectic, a marked increase in the creep strength
of the alloy is found. Because eutectic alloys exhibit small interphase spacings which are
typically one tenth of the size of those of dendrite trunks under similar conditions of growth, a
large interfacial area exists between the two solid phases. For a lem cube, this area
*Nodular graphite in cast iron is an exception in non-faceted/faceted growth. In this case, the
graphite grows as a primary faceted phase, together with austenite dendrites, and there is no
eutectic-like growth of both phases. Such a behaviour has been called divorced growth. If both
phases are faceted, the types of coupled growth described in the present chapter are not
observed.

is of the order of 1m2. Moreover, the specific energy of the interface is usually high and increases
with increasing dissimilarity of the phases. As a result, there is a tendency for certain, lowest-
energy, crystallographic orientations to develop between
Figure 5.1: TYPES OF BINARY EUTECTIC MORPHOLOGY. Seen in transverse cross-section,
eutectic microstructures can be fibrous or lamellar, regular or irregular. The condition is that
one phase (here the white alpha-phase) must always have a low entropy of fusion, so that α-2. If
both phases possess a low entropy of fusion, their growth is easy on all crystallographic planes
(chapter 2.3) and the resultant structures are regular (non-faceted/non-faceted eutectic - upper
part of the above figure). When the low volume fraction phase possesses a high entropy of
melting, as do semiconductors and intermetallic compounds for instance, the eutectics are of
non-faceted/faceted type and the microstructures are usually irregular. The important eutectic
casting alloys, Fe-C and Al-Si, belong to the latter class (lower right of the figure). In general,
fibres are the preferred growth form when a small volume fraction of one phase is present,
especially in the case of non-faceted/non-faceted eutectics. This is so because, for λ = constant,
the interface area, A, and therefore the total interface energy attributed to the surfaces between
the phases decreases with decreasing volume fraction of the fibres (A ∞ √fg), while the interface
area is constant for lamellae. The interface area of fibres is lower than that for lamellae at
volume fractions which are smaller than about 0.25. However, if the specific interface energy
between the two phases is very anisotropic, lamellae may also be formed at a much lower volume
fraction (as in Fe-C where fc = 0.07).
the phases and there by minimize the interfacial energy. This is also the reason why graphite
exposes a maximum extent of its (0001) planes to the iron in cast iron. This can be done by the
preferential formation of lamellae, even at a volume fraction as low as 0.05. Extensive
experimental studies have been made of the crystallography of eutectic alloys and the results
have been reviewed by Hogan, Kraft and Lemkey (1971). Table 5.1 indicates the results for a
number of systems. A list of most of the eutectics studied by means of directional solidification
as well as their properties can be found in Kurz and Sahm (1975).
Table 5.1: CRYSTALLOGRAPHY OF EUTECTIC ALLOYS

5.2 Diffusion-Coupled Growth

In order to determine the growth behaviour of the two eutectic phases, the simplest morphology
for the solid/liquid interface will be assumed, i.e. that which exists during the growth of a
regular, lamellar eutectic. For this simple case, the problem can be treated in two dimensions
and, for reasons of symmetry (appendix 2), only half of a lamellae of each phase need be
considered (figure 5.2). In this figure, the alloy is imagined to be growing in a crucible which is
being moved vertically downwards at the rate, V. In a steady-state thermal environment, this is
equivalent to moving the solid/liquid interface upwards at a rate, V = V'. The alloy of eutectic
composition is growing with its essentially isothermal interface at a small temperature difference
(AT = constant) below the equilibrium eutectic temperature, Te. The alpha- and beta-phase
interfaces are perpendicular to the solid/liquid interface and parallel to the growth direction. In
order to proceed further, it is necessary to know more about the mass transport involved. It can
be seen from the phase diagram that the two solid phases are of very different composition, while
the melt composition, Co, is situated in between. Obviously, the mean composition of the solid is
equal to the composition of the melt. This makes it clear that eutectic growth is largely a question
of diffusive mass transport. Firstly, imagine that the two eutectic phases are growing separately
from the eutectic melt with a plane solid/liquid interface (left-hand side of figure 5.3). During
growth, the solid phases reject solute into the liquid. Thus, the alpha-phase will reject B-atoms
into the melt, while the beta-phase will reject A-atoms. Note here that, expressed as atomic
fractions, CB= (1-CA). When the phases are supposed to be growing separately with a plane
front, solute transport must occur in the direction of growth. This involves long-range diffusion
and, in the steady-state, the solute distribution is described by the exponential decay discussed in
chapter 3, with a boundary layer, & = 2D/V. Such a long-range diffusion field will involve a very
large solute build-up and a correspondingly low (much lower than T) growth temperature at the
interface. During steady-state growth, each phase would have the interface temperature indicated
by the corresponding metastable solidus line when extended as far as the eutectic composition
(see figure 3.4).

Figure 5.2: PHASE DIAGRAM AND REGULAR EUTECTIC STRUCTURE. The figure shows an
eutectic phase diagram and a regular lamellar two-phase eutectic morphology growing
unidirectionally in a positive temperature gradient. The alpha and beta lamellae grow side by
side and are perpendicular to the solid/liquid interface. The form of the junctions where the three
phases (alpha, beta, liquid) meet is determined by the condition of mechanical equilibrium. In
order to drive the growth front at a given rate, V, an undercooling, AT, is necessary. Due to the
perfection and symmetry of the regular structures, only a small volume element of width, X/2,
need be considered in order to characterise the behaviour of the whole interface under steady-
state conditions.
Imagining now that both phases are placed side-by-side and that the solid/liquid interfaces are at
the same level (figure 5.3b). This situation is much more favorable since the solute which is
rejected by one phase is needed for the growth of the other. Therefore, lateral diffusion along the
solid/liquid interface, at right-angles to the lamellae, will become dominant and lead to a huge
decrease in the maximum solute build-up at both phases. A periodic diffusion field will be
established. The varying melt composition at the interface will cause the liquidus temperature to
vary along
Figure 5.3: EUTECTIC DIFFUSION FIELD. If it is imagined that the two eutectic phases are
growing from a melt of eutectic composition in separate, adjacent containers (a), very large
boundary layers, like that in figure 3.4, will be created. If both phases are constitutionally
undercooled, their solid/liquid interfaces will break down to give dendrites, making solute
rejection easier. If the two containers are now brought together and the intervening wall is
removed (b), extensive lateral mixing will take place because of the concentration jump at the
alß interface. The large boundary layers of the planar interfaces of 'a' (approximately equal to
2D/V) are replaced by a very limited layer whose thickness is approximately equal to the phase
separation, X. This marked change in the extent of the boundary layer is due to the diffusion flux
which is established at, and parallel to, the eutectic solid/liquid interface and permits the
rejection of solute by one phase to be balanced by incorporation of the solute into the other
phase (diffusion coupling). The interface composition in the boundary layer oscillates, by a very
small amount, about the eutectic composition, and the amplitude of the oscillation will decrease
as A decreases, when V is constant. The lateral concentration gradients create free energy
gradients which exert a 'compressive' force perpendicular to the alpha/beta interface and tend to
decrease . The corresponding phase diagram has been placed next to the solid/liquid interface in
such a way that the local phase equilibria can be determined. it can be seen that the amplitude of
the concentration variation at the solid/liquid interface is proportional to a solute undercooling,
ATS.
the solid/liquid interface of the corresponding phase. Because the maximum concentration
differences at the interface (compared to the eutectic composition) are much smaller than in the
case of single-phase growth, the temperature of the growing interface will be close to the
equilibrium eutectic temperature. The proximity of the lamellae, while making diffusion easier,
also causes a departure, from the equilibrium described by the phase diagram, due to capillarity
effects (figure 5.4).
Both effects, diffusion and capillarity, are considered together in figure 5.5. In figure 5.5a, the
diffusion paths at the interface are shown schematically. These are most densely packed (higher
flux) at points near to the interface. They rapidly become less significant as the distance from the
interface increases. The characteristic decay distance for the lateral diffusion is of the order of
one interphase spacing, A. Note that the diffusion paths for the other species, in the

Figure 5.4 :CURVATURE EFFECTS AT THE EUTECTIC INTERFACE. diffusion field causes
the A-value of the structure to be minimised, and this leads to more rapid growth. There is an
opposing effect which arises from the increased energy associated with the increased curvature
of the solid/liquid interface as decreases. The latter can be expressed in terms of a curvature
undercooling, AT, which depresses the liquidus lines of the equilibrium phase diagram as shown.
The positive curvature of the solid phases in contact with the liquid arises from the condition of
mechanical equilibrium of the interface forces at the three-phase junction (lower figure, see also
appendix 3).
Figure 5.5: EUTECTIC INTERFACE CONCENTRATION AND TEMPERATURE. If one
considers the concentration field shown on the right-hand-side of figure 5.3 more closely, it can
be seen that the diffusion paths of component B will be as shown in diagram (a). The
concentration in the liquid at the interface will vary as in diagram (b). (Note that the eutectic
composition is not necessarily found at the junction of the two phases, and that CB=1-CA). This
sinusoidal concentration variation decays rapidly over one interphase spacing, in the direction
perpendicular to the solid/liquid interface, as shown in figure 5.3. The equilibrium between an
attractive force arising from the diffusion field, and a repulsive force between the eutectic
lamellae arising from capillarity effects at small determines the eutectic spacing. The growing
interface can be regarded as being in a state of local thermodynamic equilibrium. This means
that the measurable temperature, 1/2) of the interface which is constant along the solid/liquid
interface (over X/2) corresponds to equilibrium at all points of the interface. The latter is a
function of the local concentration and curvature (c). The sum of the solute (ATC) and curvature
(AT) undercoolings must therefore equal the interface undercooling, AT. A negative curvature, as
shown here at the centre of the beta lamella, is required when the solute undercooling, ATe, is
higher than AT. The discontinuity in the solute undercooling, as the alpha/beta interface is
crossed, is only a discontinuity in equilibrium temperature and not a real temperature
discontinuity.
opposite direction, are analogous. According to the phase diagram, the sinusoidal concentration
variation at the solid/liquid interface (figure 5.5b) leads to a change in the liquidus temperature
of the melt in contact with the phases (figure 5.5c). The points where the liquid composition, C*
is equal to Ce are exactly at the eutectic temperature, while those points of the alpha-phase close
to the alpha/beta interface are at a higher liquidus temperature because the liquid in these regions
has a lower content of B, as determined by the lateral diffusion field. On the other hand, the melt
ahead of the beta-phase is always richer in A than is the equilibrium eutectic composition.
Therefore, its liquidus temperature is lower, compared to the equilibrium eutectic temperature,
and decreases with increasing values of C (These relationships can be understood with the aid of
the phase diagram exercises 5.7 and 5.8).
In order to determine the solute distribution, the flux condition (appendix 2) must first be
applied. In the present calculation, it is assumed that the interface is planar and that the
sinusoidal concentration variation of figure 5.5b can be approximated by using a saw-tooth
waveform with amplitude, , and diffusion distance, λ/2. In this way, the
concentration gradient in the liquid at the solid/liquid interface is found to be:
and the flux transporting atoms from one solid phase to the other via
the liquid is:

[5.1]
The rejected flux per unit solid/liquid interface area is equal to V(C* - C_*), giving:

[5.2]
This relationship holds for deviations of the melt concentration, AC, which are small compared
to Ce, and C-Ce. This is the case for many eutectics, where AC is typically of the order of 1%,
and C is of the order of 50%.
Under steady-state conditions, the flux balance, J1 = Jp, can then be written:

[5.3]
which is, in fact, entirely analogous to the previously presented equation for the diffusional
growth of a hemispherical needle. The left-hand-side of equation 5.3 corresponds to a
supersaturation, while the right-hand-side is the Péclet number for eutectic growth. Therefore,
one can also write equation 5.3 in the form:

[5.4]
The concentration difference, AC, required to drive solute diffusion in eutectic growth can be
used to determine a temperature difference (undercooling) from the phase diagram, via the
constant liquidus slopes
leading, via equation 5.3, to a relationship of the form:

[5.5]
From equation 5.4 or 5.5, it can be seen that this problem is not completely solved because, as in
the case of dendritic growth, the above equations apply equally well to a fine eutectic growing at
high rates or a coarse eutectic growing at low rates.
5.4 Operating Range of Eutectics
Upon considering equation 5.8, it becomes clear that it is not uniquely determined since Δ T is a
function of the product, λV. Therefore, another equation is required in order to determine the
growth behaviour of an eutectic. This situation is analogous to that existing in dendrite growth.
In the case of dendrite growth, the assumption of growth at the limit of morphological stability as
the operating point has been found to correspond well with the experimental results. In the case
of eutectic growth, both a point analogous to this one, and the extremum point, have been found
to explain various experimental results. Eutectic alloys which grow in a regular manner (e.g. Pb-
Sn) can be described well by the use of the extremum criterion. Using this assumption, the first
derivative of equation 5.8 is determined and set equal to zero:

[5.9]

Figure 5.6: CONTRIBUTIONS TO THE TOTAL UNDERCOOLING IN EUTECTIC GROWTH.

The condition that ΔT be a minimum implies, since ΔT = ΔG/ΔS, that d(ΔG}/dλ = 0 and means
that the driving force for spacing changes is zero. Insertion of the corresponding value of the
spacing leads to the final result for growth at the extremum:

The situation is more complex when irregular eutectics are considered. In this case, the local
spacing corresponding to the extremum values can be found, but the mean spacing is much larger
(figure 5.8). Such large spacings can be explained by the difficulty which this class of eutectic
experiences in branching. The latter is an essential mechanism which permits the eutectic to
adapt its scale to the local growth conditions and to approach the extremum point. If one of the
phases does not easily change direction during growth, and instead grows in a highly anisotropic
manner (e.g.the faceted phases, C and Si, in Fe- and Al-alloys respectively), due to its atomic
structure or planar defect growth mechanism, the lamellae of the phase must diverge until one of
them can branch. This behaviour can be understood with the aid

Figure 5.7: OPTIMISATION OF THE EUTECTIC SPACING.

of figure 5.9. When two adjacent lamellae are growing with the extremum spacing and begin to
diverge, the interface of the matrix will first become depressed because of the consequent
increase in solute concentration at its centre (lower middle of figure 5.9). As the solute builds up
more and more at the interface of the diverging phases, the growth temperature must decrease
because ΔT increases. Finally, the diverging phases will reach a spacing which is so large that
even the low volume fraction phase will exhibit depressions at its solid/liquid interface. Under
these conditions, the single lamella may branch into two. When a new lamella has been created,
it will usually diverge from the other one of the pair and tend to converge towards other lamellae
at the interface (figure 5.10). In this case, since the phase separation is decreasing, the interface
temperature will increase, due to the

Figure 5.8: EUTECTIC AND EUTECTOID SPACINGS AS A FUNCTION OF GROWTH RATE.

decreasing solute build-up, and eventually reach the maximum in temperature (or minimum in
undercooling). As the faceted phase cannot easily change its growth direction, its growth will
decrease the local spacing to a value below the extremum value. However, smaller values will
soon decrease the temperature appreciably due to the steep slope of the curve in this region. As a
result, any spacing smaller than the extremum value will tend to be increased by the cessation of
growth of one of the neighbouring lamellae (a termination appears).

Figure 5.9: SPACING-CONTROLLING MECHANISMS IN IRREGULAR EUTECTICS.

 Figure 5.10: GROWTH OF IRREGULAR EUTECTICS.
Thus, the range of stable eutectic growth is located between the extremum value, λe, and the
branching spacing, Only those eutectics with branching difficulties will exploit the whole range
and this explains their coarse spacing (figure 5.8), large undercoolings, large spacing variations
(irregularity), and sensitivity to temperature gradient variations.
The branching point can be calculated by using a stability analysis which is analogous to the
criterion used in the case of dendritic growth. The main difficulty involved in using this approach
is the estimation of the concentration gradient at the non-isothermal interface. This has been done
by the use of numerical methods (Fisher & Kurz, 1980).
 5.5 Competitive Growth of Dendritic and Eutectic Phases

As shown in figure 5.11, binary eutectics can undergo two types of morphological
instability; single-phase or two-phase. The latter is analogous to the morphological
instability of a planar single-phase interface (chapter 3) but, due to the very complex
behaviour involved, quantitative analysis is difficult. In general, it can be said that a third
alloying element which is similarly partitioned between both solid phases will lead to
two-phase instability and the appearance of cells or even eutectic dendrites (figure
5.11b).
When the third element is incorporated preferentially into one phase, or during off
eutectic growth of a pure binary eutectic, single-phase instability can occur and result in
the appearance of mixed structures, that is, dendrites of one phase and

Figure 5.11 TYPES OF OF EUTECTIC INTERFACE INSTABILITY. The planar eutectic solid/liquid interface can become
unstable just as in the case of a single-phase interface. Here, there are two different ways in which an instability can develop;
instability of one phase (a), or instability of both phases (b). The former leads to the appearance of dendrites of one phase
(plus interdendritic eutectic) and is mainly seen in off-eutectic alloys in binary systems. Alternatively, a third (impurity)
element may destabilise the morphology as a whole because a long-range diffusion boundary layer is established ahead of
the composite solid/liquid interface. (Recall that the eutectic tie-line of a binary system degenerates to an eutectic three-
phase (++) region in a ternary system). This can lead to the appearance of two-phase eutectic cells or dendrites (b).

interdendritic two-phase eutectic (figure 5.11a). The reason for the latter effect is that,
due to the long-range boundary layer built up ahead of the solid/liquid interface in this
case, one phase becomes heavily constitutionally undercooled. This can be appreciated
from the fact that, in an off-eutectic composition, the alloy liquidus is always higher than
the eutectic temperature (figure 5.12). That is, the corresponding
Figure 5.12: COUPLED ZONE OF EUTECTICS. From consideration of the equilibrium eutectic-type phase diagram alone,
it might be thought that microstructures consisting entirely of the eutectic can only be obtained at the exact eutectic
composition. In fact, due to the growth characteristics of dendrites and eutecties, the latter can often grow more rapidly than
the dendrites and therefore outgrow them over a range of growth conditions. This occurs during directional growth, in a
Bridgman furnace for instance (figure 1.4a), when the dendrite tip temperature is low. This can happen at both low and high
growth rates (figure 4.13). The coupled zone (grey region) represents the growth temperature/composition region where the
eutectic grows more rapidly (or at a lower undercooling) than dendrites of the alpha or beta phases. This zone, corresponding
to an entirely eutectic microstructure, may take the form of an anvil, where the upper widening is detected in experiments
carried out at low growth rates and high temperature gradients, and the lower widening is found for growth at high growth
rates, corresponding to high undercoolings. Within the coupled zone, an increased growth rate (decreased temperature) will
destabilise the solid/liquid interface due to the presence of impurities. This leads firstly to the formation of two-phase cells and
later to the formation of two-phase dendrites (figure 5.1 lb). Outside of the coupled zone, primary dendrites and interdendritic
eutectic will grow simultaneously (figure 5.11a).

primary phase will be more highly undercooled and tend to grow faster than the
eutectic. This case is of considerable importance because the properties of a casting
can be appreciably impaired or enhanced when single-phase dendrites appear. Under
some circumstances, dendrites can be observed in alloys having an exactly eutectic
composition if the growth rate is sufficiently high. The reason for this behaviour is
qualitatively explained by figure 5.13. The undercooling of the eutectic interface as a
function of V is described by equation 5.11, while the undercooling of the dendrite tips
obeys an analogous relationship when the temperature gradient is equal to zero. When
growth occurs in a positive temperature gradient, the temperature-velocity curve
exhibits a maximum (figure 4.13) and the eutectic curve (which is usually unaffected by
G) may be cut at both high and low growth rates. When the dendrite curve is below the
eutectic curve, only eutectic will be observed. When the dendrite curve is higher, both
dendrites and eutectic are observed. If the undercoolings which lead to entirely eutectic
growth are determined for a range of compositions, they make up what is known as the
coupled zone. When the coupled zone is symmetrical (figure 5.12), the eutectic
morphology will obviously be obtained for eutectic.
Figure 5.13: ORIGIN OF SKEWED COUPLED ZONES. Symmetrical coupled zones (figure 5.12) are associated with regular
eutectics and reflect the similar undercoolings of the two primary dendrite types. When the eutectic is irregular, the associated
high undercoolings at high growth rates of the eutectic and the faceted (f) primary B-phase, compared to that of the non-faceted
(nf) α-phase, lead to the establishment of a skewed zone. The most important practical effect of this is that a fully eutectic
microstructure may not be obtained when an alloy of eutectic composition is rapidly solidified. Because the zone is skewed
towards the phase which has growth problems (such as Si in the Al-Si system), it is necessary to use a starting composition
which is richer than Ce in the faceted element in order to obtain dendrite-free eutectic microstructures.

compositions at all growth rates (undercoolings). However, in the case of skewed

coupled zones, high growth rates may lead to the formation of alpha-dendrites even on
the beta-rich side of the eutectic composition. Such skewed zones are usually
associated with eutectics which contain one phase having anisotropic growth
characteristics. Thus, a skewed zone is normally associated with irregularity of the
eutectic morphology (e.g. Al Si or Fe C). These assumptions hold only for normal growth
conditions. In the case of rapid solidification processing (for example: fibre-spinning,
strip-casting, laser surface remelting), new phenomena may occur due to the extremely
high undercooling reached. These have been summarised in an interesting paper by
Boettinger (1982).
Figure 5.14: DIRECTIONAL PERITECTIC GROWTH. This is an important reaction which occurs in steels, bronzes, and
other alloys. It has been suggested that conditions similar to those used in off-eutectic solidification might suppress primary
dendrite growth and lead to the formation of an eutectic-like microstructure, at least over short distances. This has not been
clearly demonstrated, and the usual sequence of events is that primary dendrite trunks form close to T and begin to react with
the liquid to form B-phase close to Tp. Because this involves diffusion through the solid B-phase, the reaction is very slow
and is rarely completed before the remaining, un-reacted liquid disappears or undergoes an eutectic reaction at Te (if there is
an eutectic in the phase diagram). Normal solidification conditions will tend to produce a microstructure which consists of
primary a-dendrites, with a surface layer of B-phase, separated by interdendritic aß eutectic. Dissolution of the interdendritic
peritectic phase by preferential chemical etching reveals the form of the dendrites (as on the cover of this book).