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Stresses and defects in the formation of a cellular pattern in directional solidification. Real-time observation by synchrotron X-ray topography on a
Al-0.73 wt% Cu alloy
G. Grange, C. Jourdan, J. Gastaldi, B. Billia
To cite this version:
G. Grange, C. Jourdan, J. Gastaldi, B. Billia. Stresses and defects in the formation of a cellular pattern in directional solidification. Real-time observation by synchrotron X-ray topography on a Al-0.73 wt%
Cu alloy. Journal de Physique III, EDP Sciences, 1994, 4 (2), pp.293-304. �10.1051/jp3:1994130�. �jpa- 00249103�
Stresses and defects in the formation of a cellular pattern in
directional solidification. Real-time observation by synchrotron X-ray topography on a Al.0.73 wt'Jb Cu alloy
G. Grange ('), C. Jourdan ('), J. Gastaldi (') and B. Billia (2)
(') CRMC2-CNRS, Campus de Luminy, case 913, 13288 Marseille Cedex 09, France
(2) Laboratoire
« Matdriaux Organisation et Propridtds » (*), Facultd des Sciences de St-Jdr6me, Case lsl, 13397 Marseille Cedex ?0, France
(Receii,ed 24 May J993. accepted J5 November J993)
Rdsumd.-On dtudie in situ la solidification unidirectionnelle d'dchantillons minces (0,2 h 0,3 mm) d'un alliage Al-0,73 pdsfb Cu h l'aide de la mdthode de topographie aux rayons X en
faisceau blanc synchrotron. On analyse les contraintes assocides h la formation de l'instabilitd
morphologique et de la structure cellulaire. Des contrastes de contraintes apparaissent prks de l'interface dks le debut de l'amplification des perturbations ; ces contraintes sent provoqudes par
les compressions et dilatations dues h la courbure locale du front de solidification (loi de Laplace).
On montre que, dans le cas d'une interface cellulaire, dislocations et sous-joints dmergent dans le
liquide au fond des gorges entre cellules. Une Emission quasi-pdriodique de gouttelettes depuis les fends de cellules et de forts gradients de solutd crdent localement des rdgions h d£saccord
paramdtrique important produisant deux types de contraintes dans le solide. On dtudie dgalement
en fonction du temps l'dvolution de l'amplitude des cellules et de leur espacement moyen. On ddduit de la variation de l'espacement cellulaire en fonction de la vitesse de croissance que cette sdrie d'expdriences se situe entre le rdgime de cellules d'amplitude finie et le rdgime de cellules
profondes.
Abstract. In situ observations by the synchrotron white beam X-ray topographic method are
carried out during the directional solidification of thin samples (0.2-0.3 mm) of a Al-0.73 wtfl Cu alloy. Stresses associated to morphological instability and pattem formation are analysed. Due to compressions and dilatations induced by the local curvature of the solidification front (Laplace law), strain contrasts in crystal parts close to the interface appear in the early stages of amplification of perturbations. Advection of dislocations into the grooves and subboundaries
outcropping are evidenced for a cellular solid-liquid interface. Two types of strains are left in the grown solid by a cellular microstructure, related to nearly periodic emission of droplets and high gradients of solute, which locally create regions with important parametric mismatch. The time evolution of average cell spacing and amplitude is studied. It follows from the variation of cell spacing with growth speed that the present series of experiments are straddling the finite amplitude
cellular and deep cellular regimes.
(*) Associd au CNRS.
1. Introduction.
In recent years, the formation of a cellular interface morphology during directional
solidification of alloys has attracted considerable theoretical and experimental attention [1-4].
Experimental results are obtained by solidifying either metallic alloys [5-7], for which sample quenching during solidification enables aposteriori observation of interface pattem, or
transparent organic mixtures, for which the growth front is directly observable in plan-view
under an optical microscope [8-10]. Although they provide detailed information on the
morphological instability of the planar solid-liquid interface, the subsequent evolution of the cellular, or dendritic, microstructure towards a steady-state and the changes in cellular pattern with experimental conditions, the latter studies give no indication on the alteration of the
quality of the grown solid induced by a nonplanar interface morphology through the generation
of stresses and crystalline defects.
In the present work, we use the real time X-ray topographic method to observe in situ the evolution of the solid-liquid interface in an Al-0.73 wt§b Cu alloy. Experiments are carried out with the white beam synchrotron radiation at LURE (Orsay, France). Thanks to the capability
of the topographic method to reveal structural defects, namely dislocations and strain fields,
we are able to characterize the effect of the formation and selection of a cellular pattem on the perfection of the resulting crystal.
2. Experimental.
Molten plates of the binary Alcu alloy are directionally solidified at constant pulling rate in
graphite crucibles. The temperature gradient is fixed at 20 K.cm~ and pulling rates range from 0.5 to 10 ~Lm s.' The samples, with main surfaces (40 x 6 mm2) perpendicular to the incident
X-ray beam and thicknesses about 0.2-0.3 mm, are crystallized from a tip and get a random crystallographic orientation. During horizontal displacement of the sample, the interface is held in position within the large X-ray synchrotron beam. Samples thinner than those used in the first series of experiments [I Ii are employed here in order to minimize the convective
effects in the melt and have a better survey on the interfacial pattem by, as far as possible, allowing space for only one row of cells through the sample thickness.
3. Results.
3. I GROWTH CHARACTERISTICS.
3. I. I Interface shape. Topographs show that many dislocation lines, which were originated
in the bulk crystal, emerge into the melt far away from the leading part of the solidification
front (Fig. I). It was previously observed that outcropping dislocations generally have a
prevalent screw character, remain parallel to the solidification axis and lengthen their line
during growth [12]. In the present case the observations show that this type of dislocations behave likewise but, on account of the curved shape of the interface, they bend their line when
emerging into the liquid. Such a configuration indicates that there is a protrusion of the
growing solid into the liquid phase, so that the foremost lateral surfaces of the solid are never in
contact with the crucible walls.
This particular shape of the solidification front is the direct consequence of lateral
confinement in the third dimension which, by lowering the threshold of morphological
instability of the planar solid-liquid interface [8], favors the growth of a solid finger in the thickness of the experimental cell [13]. Steeping of the phase boundary has one advantage and
one drawback. The advantage is that most of the Solidification front is maintained almost dislocation free as it is not in direct contact with the crucible, which is a major source of strains
L
_ ~s Fig. I. - In
situ ynchrotron white beam X-ray of a
Alcu crystal from the right to
he left : v = 3.4 ~m.s~'-31i
axis
: [431], L = liquid, S =
I mm. This opographshows the estabilization of a flat
solidificationfront. The
interface shape is
and dislocations, and is purified from dislocations existing prior to morphological instability,
which are opportunely advected down the sides of the solid finger. Consequently, stresses and
defects generated in the solid by the development of a cellular interface can be properly
analyzed. The drawback is that it is the formation of a cellular pattem by morphological instability of the crest of a solid finger that is actually investigated.
After destabilization, in most cases the cells grow parallel to the horizontal pulling axis. For thicker samples II ], bending of the cellular stems was observed, which was attributed to the
effect of the downward motion of the convective flow in the melt, along the solid-liquid
'i ~~g~~ '~"~~
Fig. 2. Two topographs of the same growth stage of a Alcu crystal. v
= 4.2 ~m.s~ ' Growth axis :
[142]. a) II I reflection. b) 3 II reflection. Marker represents 500 ~m.
interface. Now, the growth direction of the cells is that of heat flow and, for the different
crystallographic orientations of the samples solidified up to now, there is no clear manifestation of any crystalline anisotropy.
For transparent organic compounds, growth is observed normaly to the main surfaces of the
samples so that one gets a direct picture of the shape and dimensions of cells, without
geometric distortion. For synchrotron white beam topographic observation, the interpretation
of the diffraction images is not so easy. As the images are projections of the cellular
microstucture located in the sample volume, one has to be careful in interpreting them. Indeed, the perspective shape of the cells may vary drastically with the azimuth of observation, in
particular the shape of the cell cap whose exactitude is critical for sound determination of the
tip radius (Fig. 2). This figure shows two topographs of the same stage of growth of an Alcu crystal projected in different directions. In figure 2a, which corresponds to a Laue spot close to the axis of the incident X-ray beam and whose diffraction vector g is nearly horizontal (close to the growth direction of cells), the distorsion of the cellular pattern is limited so that the intercellular liquid grooves are clearly visible and a reliable estimate of the tip radius can be obtained (50 ~Lm). Figure 2b is taken from a Laue spot farther away with a diffraction vector nearly in a vertical plane, which gives a quite different picture, with flatter cell tips and a
compact arrangement of cells, due to the hiding of liquid grooves by overlapping of the images
of individual cells.
3.1.2 Dislocations and subboundaries at the solid-liquid interface. -When dislocations
reach the foremost part of a destabilized interface, more precisely when they emerge into the
liquid on the convex part of shape perturbations, it is observed that their lines bend and, in the vertical amplification and lateral spreading of undulations, their emerging points progressively
recede from the tip regions, along the solid-liquid interface, to finally assemble in the concave
cusps behind the cells (Fig. 3). These phenomena, which are striking in figure 3 taken during
the break-up of a crystal-melt interface into a cellular array, are very similar to those observed in figure I, as the solid finger in the thickness of the sample is nothing but a deep cell.
J
Fig. 3. -Gathering of dislocations in the cusps behind the cellular interface. Crystal directionally solidified at v
=
3 ~m.s- ' II I reflection. Growth axis : [11 3]. Marker represents 500 ~m.
©y'
#
-/ ).~P
~ - '
ig. 4.
ages lcu
a) partly
destabilized. b)-c) Cellular structure. Time
topographs
: a-b : 220 s
b-c : 170 s. Marker represents 500 ~m.
Therefore, for a cellular microstructure one should conclude that, by bending their lines towards the bottom of the cells, dislocations eventually adopt the shortest path to emerge into the melt which, while reducing their length and minimizing energy, allows the cellular bodies
to remain free from dislocations during the course of directional growth. This process of
dislocation purification in the dynamical formation of the convex cellular caps furthermore contributes to the creation of the array of subboundaries which is long known to underline the cellular array itself [14, 15]. A last interesting point is that, in the multiple-scale analysis of cellular growth [16], in which a cell is divided into several parts (tip, tail and bubble-like closure), only the closure is actually affected by the accumulation of dislocations, which should be included in the theory as it might among others limit the mobility and flexibility of the intercellular grooves.
The bunching of dislocations in the time-evolution of an interface undergoing morphological instability results in similar patterns (Fig. 4). In figure 4a many dislocations reach the planar part of an interface partly covered with cells and remain perpendicular to that interface. In
figures 4b and 4c the interface has evolved into a cellular structure and the dislocations have
gathered to form two subgrain boundaries which outcrop the interface at cell grooves. As in the
case of pure Al [17], the emergence of low-angle boundaries into the melt gives rise to a strain field visualized by the black contrasts, which also can be seen in figure 3 at the outcropping of
subboundaries on the interface in the upper and lower parts of the topograph. This strain field may be due to the slight misorientation (not discemible here by using white radiation) between the subgrains on either side of the subboundary when they encounter on the solidification
front [12].
3.2 INTERFACIAL DYNAMICS.
3.2.I Strain contrasts and cells. Due to its high sensitivity to elastic strains, the
topographic method is appropriate to bring out information on the mechanical characteristics of
jg -
§
a
- b ~
~
Fig. 5. Real-time X-ray topographs of growing Alcu crystals. a) v
=
3.9 ~m.s- ' l13 reflection.
Growth axis [431]. Marker represents 500 ~m. b) v
=
4.2 ~m.s- ' 022 reflection. Growth axis
[12i]. Marker represents 250 ~m. In both diffraction images the interface areas display strain contrasts
just before visible destabilization.
the dynamics of morphological instability, even in the earlier moments. Figure 5 shows the interface break-up in two different Alcu crystals growing from the melt.
In figure 5a one can see regions of enhanced diffracted intensity spanning over a large planar portion of the solidification front. These regions, which are rather regularly spaced, are likely
to correspond to the very beginning of formation of a cellular pattem. The presence of incipient
cells in the lower part of the interface gives funher support to this assumption, more especially
as the diffracted images of these cells also present a higher intensity comparatively to the
neighbouring bulk crystal. As the pt product (p linear absorption coefficient, t : sample thickness) is low for this i13 reflection, the observed contrasts are those given by a thin crystal
and the stress fields produce modulated contrasts along the interface. The regions of enhanced
intensity correspond to regions under compression, which appear to be the first detectable precursors of the incoming cells. Black needle-like contrasts, indicating compressive stresses,
were previously observed at the tip regions by Ge, Xu and Feng [18], who used birefringence topography to investigate the stress field in Czochralski-grown YAG crystals doped with
neodymium.
Figure 5b shows an alternation of black contrasts and white contrasts in the central region in which, from the sole observation of the outline of the solidification front, there is still no clear
evidence of the destabilization of the interface. This 022 reflection now corresponds to
pt = 6.5. For a crystal with such high pt product one can determine the sense of the curvature of the lattice planes in the interfacial region from the observed contrasts and taking into account
the sense of the diffraction vector g. It follows that a black contrast corresponds to a lattice
under compression, I-e- to a cell cap, and a white contrast to a lattice under dilatation, I.e. to an
intercellular groove.
It results from the Laplace law extended to solid-liquid interfaces [19], that the compressive and dilative stresses, which respectively cause the black contrasts in figures 5a, b and the
white contrasts in figure 5b, are a direct consequence of the local curvature of the phase
3.2.2 Cellular pattern evolution process. -A sequence of diffracted images is given in
figure 6, which show the changes in the interface shape with time during directional solidification at constant rate. The Bragg angle is equal to 14° and the g vector is nearly
horizontal so that the topographs do not display large distortions and the interface images can
be considered as those of the true interface profiles. Initially, a growth velocity of
2.5 ~Lm.s~ (above the critical velocity of about 2.2 ~Lm.s~ for a truly planar interface) was
s
~
a 'i .l~ c d_
g
o
e "fl- f g
~_~~
Fig. 6. Sequence of in situ synchrotron X-ray topographs showing the time-evolution of the cellular
structure of an Alcu crystal. v 3.9 ~m.s-' iii reflection. Growth axis : [43 Ii- Marker represents
500 ~m. Time intervals between topographs : a-b 145 s b-c 155 s c-d : 95 s d-e
: 180 s ; e-f :
115 s f-g 380 s.
applied for 4 500 s. As the solidification front remained planar, which is attributed to the fact that morphological instability in reality develops on the crest of a solid finger (see Fig. I), the
velocity was increased to 3.9 ~Lm.s~ at which a cellular structure formed, whose evolution is shown in figure 6.
The average cell spacing first increases with time and then approaches an asymptotic value, about 150 ~Lm, in an oscillatory way (Fig. 7a). The interface never reaches a cellular steady
state but an adjustment of the average wavelength takes place with time by tip-splitting and
cell-elimination mechanisms, as previously observed in transparent substances for a compar- able distance from the threshold of instability [9]. Some cells initially have a spacing larger than the others (cells marked A in Fig. 6b, B in Fig. 6c and C in Fig. 6d) and break up first into two (B in Fig. 6d and C in Fig. 6f~ or even three cells (A in Fig. 6d) by the tip-splitting
mechanism. Yet, the spacing is too much reduced by the creation of new cells so that certain created cells should be eliminated (one of the three cells of A in Fig. 6e and one cell of B in
Fig. 6f~. Then, cells which enlarge the most in figure 6e again suffer a splitting of their tip in figure 6f. Although the oscillatory comportment of the cell spacing seems to be somewhat
damped, the last state shown in figure 6g is not a steady state ; some cells continue to lower the local spacing by tip-splitting (cells marked D) while others, such as one of the C cells, get
eliminated.
170
(al
I~160
W
fj 150
#
7
° 140
~~§00
1000 1500 2000
t#ne(s)
iooo
~
Boo @~I
I
# Boo
fl
400
%
° 200
§00 loco lsoo 2000
true(s)
Fig. 7. Variations of the cell spacing (a) and the cell amplitude (b) with time. Growth conditions as in
figure 6.
o
it
~ 120 o
loo
5.0 7.5 lo-o
velocity (wn/s)
Fig. 8.- Variation of the cell spacing with growth rate in the region above the threshold of
morphological instability.
By carefully considering the variation of the cellular amplitude along the interface in
figures 6c, d, it can be seen that the larger cells (marked A, B and C), which then tip-split, correspond to junctions of wavepackets of cells. This finding is to compare with the
experimental results of Trivedi and Somboonsuk in the succinonitrile-acetone system [211, where a short wavelength and a long wavelength were found to be operative in the birth of the shape perturbations, the long wavelength being ultimately eliminated in the cellular range. In the present experiments, the long wavelength would correspond to the wavepacket spacing, as recently observed in the formation of cellular doublets [221.
As shown in figure 7b, the average cell amplitude increases with time. This increase, which is rapid during the cell spacing adjustment, slows down at the end of the experiment and the amplitude then seems to reach a stationary value. A larger cellular amplitude has been
theoretically attributed to low temperature gradients [231, which agrees well with the present experimental situation (G
=
20 °C cm~ ).
For the same temperature gradient but different growth directions of the Al-0.73 wt% Cu alloy, the variation of the average cell spacing with velocity is shown in figure 8. The
measurements were carried out on cellular interfaces located in the final oscillatory part of the
cell spacing evolution. Two regimes can be identified. The finite cellular one, in which the
spacing decreases, starts at the threshold of morphological instability. The minimum in
spacing and the small increase that follows correspond to the transition to deep cells.
3.3 MECHANICAL EFFECTS ASSOCIATED TO DROPLET EMISSION IN CELLULAR
GROWTH. During the directional solidification at constant rate, the liquid grooves limiting
the cells deepen and become narrower as the cells increase in amplitude (Figs. 4, 6). The
rounded parts that terminate the grooves decrease their diameter and may form droplet-like closures attached at the bottom of narrow liquid tails. By pinching of facing solid sidewalls, liquid droplets can be trapped, which enter the bulk crystal, as reported in the literature [24- 27l. When they have just separated from the grooves, droplets are directly seen in topographs by both a local lack of contrast (white spots in Figs. 4b, c and Figs. 6e, f, g) and a bordering
black contrast due to elastic stresses. The lack of contrast of the droplets is due to the fact that the liquid inside the droplets does not diffract X-rays. When the droplets are farther from the
interface they are visible only by their dark contrasts (Figs. 4, 6).
