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Preparation of the initial solid–liquid interface and melt in directional solidification
Journal of Crystal Growth 253 (2003) 539–548
Preparation of the initial solid–liquid interface and melt in directional solidification H. Nguyen Thia,*, B. Drevetb, J.M. Debierrea, D. Camelb, Y. Daboa, B. Billiaa a
# L2MP, UMR 6137–CNRS, Facult!e des Sciences & Tech. de Saint-J!erome, Universit!e d’Aix-Marseille III, Case 151, F-13397 Marseille Cedex 20, France b CEA-CEREM, 17 Rue des Martyrs, F-38054 Grenoble Cedex 9, France Received 23 December 2002; accepted 18 February 2003 Communicated by D.T.J. Hurle
Abstract The preparation of the initial conditions (solid–liquid interface morphology and solute segregation in the liquid phase) on which growth is started is a very critical step in directional-solidification experiments. Dedicated experiments on Al–1.5 wt% Ni consisting in directional melting followed by thermal stabilisation with different lengths, show that precise control is in practice not straightforward. Indeed, in the mushy zone created by melting the original solid sample, temperature gradient zone melting (TGZM) causes migration of solute-rich liquid droplets and channels. A model is proposed to describe this process and validate the physical interpretation of the experiments through numerical simulation. Knowing the status of the preparation, the intriguing observations in the partially melted region of the Al– 1.5 wt% Ni alloys solidified in the Advanced Gradient Heating Facility of European Space Agency during the LMS and STS-95 space missions can now be explained. Finally, the influence of initial interface morphology and melt segregation on directional-solidification transient is discussed, based on a comparison of Al–Ni alloys with hypoeutectic Al–Li alloys previously grown on Earth and in space. It follows that for experiments achieved on original rods with equiaxed microstructure, the efficiency of the preparatory melting and stabilisation phases can be evaluated from the solute macrosegregation profile in the region in between the non-melted solid and directional solidification. The major conclusion is that when the melt is mixed by fluid flow, the initial conditions are near to their asymptotic state at the end of TGZM whereas, when solute diffusion is the mode of transport into the bulk liquid, the condition of homogeneous melt becomes limiting and too much time-consuming to be fulfilled, which in particular holds for the 3D-experiments carried out in the reduced-gravity environment of space. r 2003 Elsevier Science B.V. All rights reserved. PACS: 61.72.Qq; 61.72.Ss; 81.05.Bx; 81.10.Fq; 81.30.Fb Keywords: A1. Directional solidification; A1. Initial state; A1. Segregation; A1. Solid–liquid interface; A1. TGZM; B1. Alloys
1. Introduction *Corresponding author. Tel.: +33-491-288673; fax: +33491-288775. E-mail address: [email protected] (H. Nguyen Thi).
During directional solidification of a binary alloy the solid–liquid interface can exhibit spatial organisation (cellular/dendritic array) due to the
0022-0248/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-0248(03)01041-8
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
Mullins–Sekerka instability [1] that is governed by the growth parameters (alloy composition C0 ; thermal gradient GL and pulling rate V ). Recent theoretical models [2–4] have highlighted the critical role played by the initial transient on the asymptotic solidification microstructure. In these analyses, the main goal was to describe the front recoil due to solute build-up at the interface in the moments following an instantaneous jump in pulling rate from zero to a given value. In theory, the system is initially at rest with a flat solid–liquid interface and uniform concentration in the liquid phase. However, in real experimental situations, solidification starts on a prepared state, which results from a thermal stabilisation stage preceded by a melting phase. This initial state is in most cases not characterised and may strongly depart from that assumed in the models. Hence, the precise knowledge of the initial state from which growth is initiated and its influence on the subsequent growth transient is critical in order to check the soundness and predictions of theory, and thus improve the understanding of the formation of the solidification microstructure. The work described in this paper was actually motivated by observations made during LMS and STS-95 space missions. Al–1.5 wt% Ni samples were directionally solidified in the advanced gradient heating facility (AGHF) of the European Space Agency (ESA), which is a Bridgman-type furnace [5]. In all specimens, the composition profile was qualitatively obtained by X-ray radiography and then calibrated by chemical and EDS analyses (Fig. 1a). For all experiments, no longitudinal macrosegregation occurred when the stationary growth conditions were reached and a plateau at the nominal concentration C0 was obtained as expected for solidification either in diffusive conditions in microgravity (mg samples) or with convection driven by radial gradients (1 g samples solidified vertically upwards on ground). Indeed, it is well known that this type of convection induces strong radial macrosegregation of solute but with only weak axial macrosegregation [5,6]. Furthermore, in the intermediate region between the non-melted part of the sample and the plateau at constant concentration, the solute variation was rather complex and could not be
3
partially melted fully melted
non-melted
Concentration (wt% Ni)
540
2 stationary solidification
1 directional solidification
0 -10 (a)
0
10 X (mm)
(b)
(c)
(d)
(e)
20
30
Fig. 1. (a) Longitudinal segregation in Al–1.5 wt% Ni sample solidified in microgravity (GL ¼ 33 K/cm, V ¼ 3:83 mm/s). Labels above the curve indicate the three different zones of the specimen at the end of melting, labels below locate the beginning and the stationary regime of directional solidification. (b)–(e) Quarters of transverse sections (8 mm in diameter) at X ¼ 1; 3.8, 5.8 and 10.2 mm, respectively, along the intermediate part of the sample.
explained by the theoretical models mentioned above. Profiles first showed a sharp drop from the nominal concentration C0 to nearly pure aluminium (as shown in Fig. 1a, the origin of the X -axis is chosen near this minimum). This was the boundary between the non-melted zone, below the eutectic temperature TE ; and the partially melted region. A second minimum was observed at X E6 mm, which, as explained below, indicated both the limit between the partially melted region
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
and the melt and the beginning of the initial solidification transient. This transient could not be described by theoretical models mentioned above due to the very low value of the partition coefficient k (k ¼ 3:7 103 ), which leads to a very fast destabilisation of the planar front. The samples solidified at 1 g exhibited longitudinal solute macrosegregation almost identical to that in mg (see Fig. 8a), which confirmed that mixing of the bulk liquid by fluid flow did not occurred. Microstructure changes along the intermediate region between the non-melted solid and stationary solidification were analysed by metallography performed on cross-sections. Close to X ¼ 0; the transverse section showed aluminium grains bounded by a thin eutectic layer (Fig. 1b). In the subsequent sections (Figs. 1c and d), Ni-rich intragranular droplets are visible in addition to these eutectic layers. The surface fraction covered by Nirich droplets and inter-granular channels, and thus the nickel concentration, first increased progressively with the distance X from the non-melted zone and then reached a maximum (Fig. 1c) before decreasing again (Fig. 1d). After the second minimum, i.e. after the beginning of directional solidification, the intra-granular droplets disappeared and the solute composition increased again, as expected during the initial solidification transient. The solidification front became morphologically unstable and an array of cells covered the whole transverse section (Fig. 1e). In this paper, our aim of general interest is to show that, contrary to what is largely believed, the preparation of the initial solid–liquid interface is a very critical moment of directional-solidification experiments, which should be precisely characterised. Being aware of the effects of the experimental protocol used before the inception of growth, it will in particular be possible to fully explain the intriguing observations in the partially melted region of the AGHF samples. To this end, dedicated experiments consisting in directional melting followed by thermal stabilisation with different lengths are carried out. First, we will discuss the mushy zone induced by the melting of the original solid sample. Then, we will analyse the temperature gradient zone melting (TGZM) process [7–9], which occurs during both the melting
541
and the stabilisation stages and causes the migration of Ni-rich liquid droplets and channels. In parallel, a simple model will be introduced to validate the physical interpretation of the experiments through numerical simulations. Finally, we will discuss the effect of initial interface morphology and melt segregation on solidification transient in experiments, by means of a comparison of those Al–Ni alloys with Al–Li alloys previously grown on Earth and in space [10].
2. Experimental procedure In order to study the effect of both melting and stabilisation preparatory phases on the initial solidification transient, a series of experiments are carried out in a Bridgman-type furnace under 1 g conditions. The original Al–1.5 wt% Ni rods, with an outer diameter of 8 mm, are placed in a boron nitride crucible. The rods used in these experiments are taken from the same ingot than those solidified in the AGHF experiments during the LMS and STS-95 missions. A transverse section taken in the non-melted part of the sample (Fig. 2a) illustrates the equiaxed grain structure of the original solid which, since the solid solubility limit of nickel in aluminium is close to zero, in particular leaves Al3Ni inclusions a few micrometers in size within aluminium grains (Fig. 2b). The experimental protocol is as follows. For each experiment, the first step consists in a partial melting of the original rod achieved by moving the furnace downwards along the vertical sample, which imposes a melting rate Vf ¼ 7:8 mm/s and a thermal gradient in the liquid phase GL (deduced from the temperature profile measured by two thermocouples) about 30 K/cm. The furnace displacement is stopped when the length of the nonmelted part of the sample is about 35 mm. In the second step, the sample is submitted to thermal stabilisation of variable length (Table 1). Finally, the microstructure is frozen by a rapid quench. For all experiments, a post-mortem analysis is carried out. To reveal the solid morphology after the melting and stabilisation phases, both a longitudinal section parallel to the sample axis and transverse sections spaced along the whole
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
542
(a)
(b)
20 µm
Fig. 2. Original Al–1.5 wt% Ni rod: (a) transverse section showing equiaxed grain structure (8 mm in diameter), (b) SEM picture showing Al3Ni inclusions within the Al matrix of a grain.
Table 1 Parameters of the experiments for Al–1.5 wt% Ni alloys Experiment Alloy composition Melting velocity Vf Thermal gradient GL Stabilisation length
Exp. 1
Exp. 2
Exp. 3
0h
Al–1.5 wt% Ni 7.8 mm/s 30 K/cm 1 h20 2 h35
Exp. 4
7h
intermediate region of each sample are mechanically polished. There is no need of chemical etching as primary-aluminium and Al3Ni give strong enough contrast under the optical microscope.
3. The mushy zone induced by melting and its evolution during thermal stabilisation 3.1. Experimental results The experimental microstructures are displayed in Fig. 3. In a melting experiment without thermal stabilisation stage (Fig. 3a), a solid–liquid zone is observed on the longitudinal section: the light areas are primary-aluminium solid and the dark ones quenched Ni-rich liquid droplets and channels. In our experiments, a mushy zone forms due to the multiphase nature of the original alloy (Al+Al3Ni). Indeed, when the solid temperature reaches the eutectic temperature TE ¼ 913 K, the liquid phase nucleates at the interface between the
Al3Ni inclusions and the Al matrix, with eutectic composition CE ¼ 5:7 wt% Ni. From the phase diagram (Fig. 4a) and the distance between the two minima on the axial segregation profile, we can deduce that this mushy zone extends from a temperature close to TE up to some temperature TL at its hot top (E924 K for Fig. 3a) somewhat below the liquidus temperature for concentration C0 ; namely TL0 ¼ 927:7 K. It also results from local thermodynamic equilibrium that the Ni-rich molten inclusions contains more nickel at their cold bottom end than at their hot top end. It is worth noting that, even when the initial solid is homogeneous, there can also be a mushy zone but, in this case, it is caused by constitutional superheating of the solid ahead of the planar melting front [11,12], which can exist without any morphological instability occurring at the front. Indeed, this constitutional superheating leads to the nucleation and growth of liquid inclusions in the solid as reported by Verhoeven and Gibson [13] for Sn–Sb and Sn–Bi alloys, and recently observed in situ on transparent succinonitrile— acetone alloys [14]. Figs. 3b–d show the effect of thermal stabilisation on the mushy zone. As the stabilisation length is increased, the liquid fraction in the mushy zone decreases. In particular, for the last experiment (Fig. 3d), almost all horizontal channels and small inclusions have disappeared. These strong changes in the macrostructure can be explained by taking into account the TGZM mechanism introduced by
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
1mm
Liquid
Liquid
Liquid
543
Liquid
TE (a)
Solid
(b)
Solid
(c)
Solid
(d)
Solid
Fig. 3. Longitudinal sections of Al–1.5 wt% Ni illustrating the microstructure of the mushy zone after melting and for four thermal stabilisation lengths: (a) 0 h, (b) 1 h20, (c) 2 h35, (d) 7 h.
different compositions as local thermodynamic equilibrium holds at solid–liquid interface of the droplet. Hence, there is a concentration gradient across the liquid droplet and solute diffuses from cold side to hot side. This causes solidification at the cold side and melting at the hot one, so that a droplet migrates up the thermal gradient. The mean velocity of migration can be deduced from the solute balance at the cold side of the droplet [8]: Vmig ¼
Fig. 4. Schematic representation of both mushy zone and average concentration evolutions during thermal stabilisation subsequent to directional melting process: (a) just at the end of melting, (b) at intermediate time during the stabilisation phase, (c) final asymptotic state, and (d) Ni axial segregation profile after a stabilisation length of 7 h measured by X-ray radiography.
Pfann years ago [7]. If one considers a liquid droplet inside a solid matrix subjected to a thermal gradient, the hot and cold sides of the droplet have
Gd DL ; mL CL ðk 1Þ
ð1Þ
where DL is the liquid solute diffusion coefficient, mL the liquidus slope, CL the mean droplet composition, k the distribution coefficient and Gd the thermal gradient in the droplet. As droplets are small, the temperature field inside them is in first approximation imposed by the surrounding solid aluminium so that Gd EGS EKL GL =KS ; with GS the temperature gradient in the solid and KL and KS the thermal conductivity of liquid and solid, respectively. Insertion of typical values shows that this velocity is generally of the order of 1 mm/s. In our experiments, DL ¼ 3 105 cm2/s [15], Gd ¼ 15 K/cm, mL ¼ 3:51 K/wt% Ni, C0 (1:5 wt%Þ pCL pCE (5.7 wt%), and k ¼ 3:7 103 ; so that 0:27 mm=spVmig p0:85 mm/s.
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
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The time required for a liquid droplet to go through the whole mushy zone can be estimated by t¼
TL TE 1 : GS Vmig
In our experimental conditions, t is of the order of 8 h. Actually, the situation is somewhat more complex as, in addition to droplets, there are thin liquid channels separating the solid grains. The behaviour of those channels can be discussed by considering how TGZM acts on their vertical and horizontal segments. For the latter, which are perpendicular to the temperature gradient and thus transmit the heat flux from the solid above to the solid below, Gd is close to GL as the alloy is metallic. Thus, TGZM migration at given temperature is about two times faster than that of the droplets. This effect is already visible in Fig. 3a: going from the bottom to the top of the mush, one can see that a layer void of droplets progressively develops in the aluminium grains, whose shape roughly follows that of the upper part of the grain envelope (see close-up in Fig. 3a). This means that, due to their slower climbing, the droplets inside each grain are progressively overtaken and captured by the horizontal channel underneath so that the TGZM migration is with time reduced to a channel problem, which is already realised on top of the mush in Fig. 3a and complete except at the bottom of the mush in Figs. 3b and c. For the vertical segments, which are parallel to the temperature gradient and thus transmit the same heat flux that the solid aside, Gd EGS as in the droplets. However, the persistence of vertical channels even in Fig. 3d suggests that TGZM is delayed, possibly due to some capillary anchoring of their extremities at the triple point where the melt and the two solid grains join. In the AGHF solidification experiments, the thermal stabilisation time, typically about 1 h, was definitely always much shorter than the time necessary for complete liquid evacuation by TGZM. Consequently, the microstructure of the mushy zone was similar to that in Fig. 3b and the solute profile were similar to the one shown in Fig. 4b. These experimental results unambiguously establish that both the first minimum (at X E0 mm) and the subsequent maximum (at
X E3 mm) in the solute profile of Fig. 1a were induced by the two preparatory stages preceding directional solidification, namely melting and thermal stabilisation. Concomitantly to liquid migration leading to solid aluminium ahead of the bottom limit at eutectic temperature, solute is rejected in the liquid phase due to the TGZM mechanism, causing back-melting of the upper interface and build-up of a Ni-rich boundary layer adjacent to this interface. The net result of the conjugation of those two effects, which are already active during melting of the sample, is the progressive reduction from both sides of the size of the solid–liquid mushy zone, as qualitatively sketched in Figs. 4a and b. Yet, the time scale of TGZM, of the order of 10 h, is much shorter than that of complete mixing of the melt by solute diffusion, of the order of L2 =DL E900 h for a melt of length L ¼ 10 cm, so that the melt at start of solidification is never homogeneous in the experiments (Fig. 4d). It results that, when using an original solid made of equiaxed grains, the asymptotic state at very long times, which for dilute Al–Ni alloys would be a solid layer of pure aluminium in equilibrium with a homogeneous liquid at a concentration slightly higher than C0 (Fig. 4c), is in practice never reached and, without the assistance of fluid-flow mixing, even likely to be poorly approximated only in many of the experimental studies available in the literature, in which this point is very rarely documented. 3.2. Model and numerical calculations With the assumption that all the liquid inclusions undergoing TGZM are either droplets or horizontal channels, a simple numerical model can be derived to describe the melting and subsequent thermal stabilisation regimes observed in the experiments. As shown in Fig. 5a, the relevant section of the sample extends from X ¼ 0 (bottom) to X ¼ H (top). Using the same physical parameters as in the experiments, we have H ¼ ðTL0 2TE Þ=GS ¼ 9:8 mm. Although back-melting at the top reduces the height of the mush, it has no influence on the TGZM process so that taking the maximum value of H by using TL0 in its
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548 T
T
TE+GSH
H
Vf
ρ/ρ0
TE XB t TE-GSH
0
(a)
TE-GSXB
(b)
TE
(c)
(d)
Fig. 5. Schematic representation of the sample longitudinal section relevant for TGZM analysis showing the notations used in modelling: (a) initial time t ¼ 0 is taken at starting of melting, eutectic isotherm is indicated by a bold line; (b) partial melting of sample at velocity Vf ; (c) at t ¼ t0 ; directional melting of the sample is stopped; and (d) t > t0 ; thermal stabilisation phase with TGZM only.
evaluation is a convenient way to circumvent the problem of the variation of mush height with time. We denote rðX ; tÞ the number-density of Ni-rich droplets at time t and altitude X : This density is governed by the linear temperature field TðX ; tÞ imposed by the furnace. Initially, TðH; 0Þ ¼ TE and Tð0; 0Þ ¼ TE GS H; and we assume a homogeneous density, rðX ; 0Þ ¼ r0 ; of Ni-rich inclusions. During the melting phase, the furnace is moved down at velocity Vf (Fig. 5b). It is stopped at time t0 ¼ H=Vf ; when Tð0; t0 Þ ¼ TE (Fig. 5c) and the temperature profile remains constant afterwards, during the thermal stabilisation phase (Fig. 5d). The desired relation between rðX ; tÞ and TðX ; tÞ; qr=qt ¼ qðrVmig Þ=qx;
ð2Þ
is obtained by writing a conservation law which neglects droplet coalescence. The migration velocity of a droplet, V ðz; tÞ; is calculated by inserting Gd ¼ GS ¼ 15 K/cm, k ¼ 0 and cL ¼ ðT T0 Þ=mL in Eq. (1), where T0 ¼ 933 K is the melting temperature of pure aluminium. Note that this equation equally applies to the number-density of horizontal channels, but with Gd ¼ GL ¼ 30 K/cm as discussed previously. Eq. (2) is then solved by a finite-difference scheme on a one-dimensional (1D) grid with mesh size h ¼ 0:1 mm. During the melting phase (tpt0 ) we use a moving boundary condition rðXB ; tÞ ¼ r0 at the altitude XB where TðXB ; tÞ ¼ TE (see Fig. 5b). During the thermal stabilisation phase the furnace does not move
1
1.5
0.8
1.2
0.6
0.9
0.4
0.6
0.2
0.3
0
C wt %
T
T TE
545
0 0
0.2
0.4 0.6 X (cm)
0.8
1
Fig. 6. Profiles giving both the number-density and solute concentration calculated from our model for Al–1.5 wt% Ni alloys. Continuous lines are calculated with Gd ¼ GS ; from top to bottom: t ¼ t0 ¼ 1250 s (complete melting), t1 ¼ t0 þ 1 h, t2 ¼ t0 þ 3 h, t3 ¼ t0 þ 5 h, t4 ¼ t0 þ 7 h. Dashed line is calculated with Gd ¼ GL and for t1 ¼ t0 þ 1 h.
anymore and the boundary condition rð0; tÞE0 is constantly imposed. The numerical droplet density profiles obtained at different times are displayed in Fig. 6. At the end of the melting phase (t ¼ t0 ¼ 1250 s), the profile is monotonously decreasing because the droplets near the top of the mushy zone have already migrated into the liquid phase while those at the bottom are only starting to migrate. During the thermal stabilisation phase the droplets move higher and a depletion zone forms at the bottom of the sample, so that a maximum appears in the density profile. The number-density profile of horizontal channels for t0 þ 1 h is also displayed in Fig. 6a for comparison; here the temperature gradient Gd is twice higher, so that the liquid inclusions migrate twice faster. Since the solid matrix is practically pure aluminium, which means that almost all Ni stays in the droplets, there is a direct link between the numerical number-density profiles and the meanconcentration profiles. If Cav ðX ; tÞ is the average concentration in the slice and CðX ; tÞ the concentration in the droplets, we have at time t Cav ðX ; tÞ ¼ Cav ð0; t0 ÞrðX ; tÞ=r0 ;
tXt0
ð3Þ
with Cav ð0; tO Þ ¼ 1:5 wt% Ni. At about the same time (t0 þ 1 h), the numerical profile is similar to the one observed in the AGHF experiment (Fig. 1a), with a better agreement (maximum around X ¼ 2:5 mm) when using Gd ¼ GL : It
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
546
follows that the contribution of horizontal channels to the TGZM process is likely to be dominant since early times, which is supported by the almost complete disappearance of droplets in between Figs. 3a and b. The comparison with a stabilisation experiment carried over 7 h on Earth (Fig. 4d) is less satisfactory as the experimental profile shows a bump that is absent in numerical simulation. We believe that this remaining solute segregation has to be related to the vertical Ni-rich channels which are still there as visible in Fig. 3d.
4. Influence of initial interface morphology and melt segregation on solidification transient in experiments In the theoretical models of solidification transient, the initial solid–liquid interface is assumed planar with uniform concentration in the liquid phase. As shown above, in all the Al–Ni experiments, growth started on an initial interface resulting from a melting phase followed by a thermal stabilisation period that was not long enough. Thus, the initial state was strongly different from that used in the models. Then, the solid–liquid interface was of the type shown in Fig. 7, corrugated because the solid side consisted
(a) z LIQUID [CL]
SOLID (b) Fig. 7. (a) Photograph of the solid–liquid interface of Exp. 2 (thermal stabilisation length of 1 h20) and (b) schematic drawing of the interface before onset of directional solidification in microgravity experiments.
of several grains separated by enriched liquid channels of varying width and presenting here and there droplets emerging into the bulk liquid (Figs. 7a and b). Also, due to solute release at the mouths of vertical channels and by emerging droplets and horizontal channels there was solute pile-up on the liquid side, ahead of the mushy zone (e.g. Figs. 1a and 4d). For Al–1.5 wt% Ni, the distribution coefficient k is close to zero so that the composition of the first grown solid was approaching zero in the AGHF experiments, even though the solute pile-up made the composition ½CL f of the bulk liquid in contact with the top of the mushy zone, somewhat larger than the nominal value 1.5 wt% Ni (about 2.6 wt% Ni as measured in quenched fronts Figs. 3a–d). After the inception of directional solidification by application of the pulling velocity Vf ; the solute content in the solid first increased from k½CL f up to a maximum followed by a smooth decrease down to the asymptotic value C0 : This behaviour is in strong contrast with the monotonous increase to C0 predicted by the models and observed when the initial material is a solid solution and the melt homogeneous in composition, in which case the solute boundary at the solid–liquid interface fully builds up from zero after solidification has been started from rest [16]. Therefore, the peculiar maximum in the profile has to be attributed to the presence of eutectic inclusions in the original Al–1.5 wt% Ni samples which, by the TGZM process, caused the enriched liquid layer at the interface. By prefiguring the solute boundary at the solid–liquid interface, this layer in practice shortens the solidification transient and leads to a more rapid breakdown of the planar interface. During the solidification transient, the solute excess was partially incorporated into the solidification front so that an overshoot in composition profile is visible, at X E8 mm in Fig. 1a. This overshoot phenomenon is recovered at 1 g (Figs. 8a and 4d) because the Al–1.5 wt% Ni samples were solidified in a solute stabilising configuration (i.e. rejected solute denser than solvent) so that there was no fluid flow to induce mixing with the bulk liquid. For the sake of completeness, it is worth to make a comparison with the results on the
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
0.8 Partially melted
2
0.6
1.5 ρ
Nickel concentration (wt%)
2.5
0.2 0.5
µg 1g -5
0
5
(a)
0
10
15
0 20
X (mm)
Partially melted
4
µg
3.5 3
1g
2.5 2 -5
0
0.2
0.4 X (cm)
0.6
0.8
Fig. 9. Number-density profiles calculated from our model for Al–Li alloys with Gd ¼ GS ; from top to bottom: t1 ¼ 15 min, t2 ¼ 30 min, t3 ¼ 45 min and t4 ¼ 60 min.
4.5 Lithium concentration (wt %)
0.4
1
0
(b)
547
5
10
X (mm)
Fig. 8. Comparison of typical axial solute concentration profiles in the intermediate zone for samples solidified in microgravity environment (mg), when diffusion is the mode of solute transport in the melt, and on Earth (1 g), with natural convection: (a) Al–1.5 wt% Ni, GL ¼ 34 K/cm and (b) Al– 3.5 wt% Li, GL ¼ 70 K/cm.
observed in that region on Al–1.5 wt% Ni. It follows from numerical simulation during thermal stabilisation that, because lithium diffusion is fast (DL ¼ 1:9 104 cm2/s [10]), the TGZM process was finished when directional solidification was started (Fig. 9). The nearly linear Li decrease in the intermediate region can be explained by the fact that, for original solid rods made of equiaxed grains, the solute profile built by TGZM directly reflects the solidus. This is merely because in their migration by melting-solidification the horizontal parts of inter-granular channels overlap over the entire cross-section at constant temperature which, due to local equilibrium, imposes uniform solute concentration at the solidus.
5. Conclusion Al–3.5 wt% Li alloys we previously studied [10], for which TL0 ¼ 908 K, TE ¼ 873 K, CE ¼ 8:3 wt% Li, k ¼ 0:55 and mL ¼ 8:3 K/wt%. Indeed (Fig. 8b), the overshoot peak in segregation profile, also present in microgravity experiments, was in the case of solute-destabilising upward solidification on Earth destroyed by strong mixing of the melt caused by thermosolutal convection, giving way to a plateau as in theory but inappropriately below nominal composition. Besides, it should be noticed that the linear decrease of the Li concentration in the intermediate section differed drastically from the solute variation
The precise control of the initial conditions (solid–liquid interface morphology and solute segregation in the liquid phase) on which directional solidification is started is critical for experiments to provide the benchmark results needed for the reliable validation of the predictions of theory and numerical simulation. This is particularly true for the 3D-experiments carried out in the limit of diffusion transport in the reduced-gravity environment of space, which remain rare and costly. It stems from the present investigations on Al– 1.5 wt% Ni, and on hypoeutectic Al–Li, alloys
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that this control is in practice far from being an easy task, which should deserve high consideration, and exhaustive characterisation. For directional-solidification experiments achieved on original rods with equiaxed microstructure, the efficiency of the preparatory melting and stabilisation phases can be evaluated from the solute macrosegregation profile in the region in between the non-melted solid and directional solidification. When this profile follows the solidus line of the phase diagram, the solid–liquid interface has globally reached good smoothness as then no liquid inclusion will emerge from behind by the TGZM process. Experimental results and numerical simulation establish that this step needs several hours. If some fluid flow ensures mixing of the melt while solute is rejected by TGZM, the prepared initial conditions have also neared their asymptotic state when TGZM is completed, as it is the case on Earth by thermosolutal convection for Al–Li (Fig. 8). When solute diffusion is the mode of transport into the bulk liquid, the situation differs drastically as the condition of homogeneous melt becomes the most limiting and the most timeconsuming to fulfil, as made clear from the analysis of the Al–1.5 wt% Ni alloys. Very strikingly, the enriched liquid layer due to the back-melting of the mushy zone from its top surface is present in all experiments, and would persist for tens of hours more. This suggests to conclude that future experiments without mixing by natural (buoyancy- or/and capillary-driven) convection, and more especially those in microgravity conditions, should either make use of already homogeneous original solid samples, possibly obtained by stationary growth with a planar interface, or implement electromagnetic [17,18] or vibrational [19] stirring.
Acknowledgements The financial and technical support of CNES (Centre National d’Etudes Spatiales) is very
gratefully acknowledged. The authors also benefited from ESA (European Space Agency) support for the space experiments in AGHF, and subsequent ground work through the CETSOL MAP.
References [1] W.W. Mullins, R.F. Sekerka, J. Appl. Phys. 35 (1964) 444. [2] W. Huang, Q. Wei, Y. Zhou, J. Crystal Growth 100 (1990) 26. [3] J.A. Warren, J.S. Langer, Phys. Rev. E 47 (1993) 2702. [4] B. Caroli, C. Caroli, L. Ramirez-Piscina, J. Crystal Growth 132 (1993) 377. [5] H. Nguyen Thi, B. Billia, Y. Dabo, D. Camel, B. Drevet, M.D. Dupouy, J.J. Favier, in: V.S. Avduyevsky, V.I. Polezhaev (Eds.), Proceedings of the Joint 10th European and Sixth Russian Symposium on Physical Sciences in Microgravity, Vol. 2, Association for the Promotion of Conversion, Moscow, Russia, 1997, p. 193. [6] M.D. Dupouy, D. Camel, J. Crystal Growth 18 (1998) 469. [7] W.R. Pfann, Trans. AIME 203 (1955) 961. [8] W.A. Tiller, J. Appl. Phys. 34 (1963) 2757. [9] D.J. Allen, J.D. Hunt, Solidification and Casting of Metals, Metals Society, London, 1979, p. 39. [10] B. Drevet, H. Nguyen Thi, D. Camel, B. Billia, M.D. Dupouy, J. Crystal Growth 218 (2000) 419. [11] D.P. Woodruff, Philos. Mag. 17 (1968) 283. [12] D.P. Woodruff, A.J. Forty, Philos. Mag. 15 (1971) 985. [13] J.D. Verhoeven, E.D. Gibson, J. Crystal Growth 11 (1971) 29; J.D. Verhoeven, E.D. Gibson, J. Crystal Growth 11 (1971) 39. [14] D. Benielli, N. Bergeon, H. Jamgotchian, B. Billia, P. Voge, Phys. Rev. E 65 (2002) 051604. [15] J.P. Praizey, J.P. Garandet, G. Frohberg, A. Griesche, K.H. Kraatz, in: Proceedings of the First International Symposium ‘‘Microgravity Research and Applications in Physical Sciences and Biotechnology’’, Vol. 1, ESA-SP454, European Space Agency, Noordwijk, The Netherlands, 2001, p. 481. [16] W. Losert, B.Q. Shi, H.Z. Cummins, Proc. Natl. Acad. Sci. USA 95 (1998) 431. [17] R. Moreau, Magnetohydrodynamics, Kluwer, Dordrecht, 1990. [18] T. Alboussi"ere, A.C. Neubrand, J.P. Garandet, R. Moreau, J. Crystal Growth 181 (1997) 133. [19] G.Z. Gershuni, D.V. Lyubimov, Thermal Vibrational Convection, Wiley, Chichester, UK, 1998.
Preparation of the initial solid–liquid interface and melt in directional solidification H. Nguyen Thia,*, B. Drevetb, J.M. Debierrea, D. Camelb, Y. Daboa, B. Billiaa a
# L2MP, UMR 6137–CNRS, Facult!e des Sciences & Tech. de Saint-J!erome, Universit!e d’Aix-Marseille III, Case 151, F-13397 Marseille Cedex 20, France b CEA-CEREM, 17 Rue des Martyrs, F-38054 Grenoble Cedex 9, France Received 23 December 2002; accepted 18 February 2003 Communicated by D.T.J. Hurle
Abstract The preparation of the initial conditions (solid–liquid interface morphology and solute segregation in the liquid phase) on which growth is started is a very critical step in directional-solidification experiments. Dedicated experiments on Al–1.5 wt% Ni consisting in directional melting followed by thermal stabilisation with different lengths, show that precise control is in practice not straightforward. Indeed, in the mushy zone created by melting the original solid sample, temperature gradient zone melting (TGZM) causes migration of solute-rich liquid droplets and channels. A model is proposed to describe this process and validate the physical interpretation of the experiments through numerical simulation. Knowing the status of the preparation, the intriguing observations in the partially melted region of the Al– 1.5 wt% Ni alloys solidified in the Advanced Gradient Heating Facility of European Space Agency during the LMS and STS-95 space missions can now be explained. Finally, the influence of initial interface morphology and melt segregation on directional-solidification transient is discussed, based on a comparison of Al–Ni alloys with hypoeutectic Al–Li alloys previously grown on Earth and in space. It follows that for experiments achieved on original rods with equiaxed microstructure, the efficiency of the preparatory melting and stabilisation phases can be evaluated from the solute macrosegregation profile in the region in between the non-melted solid and directional solidification. The major conclusion is that when the melt is mixed by fluid flow, the initial conditions are near to their asymptotic state at the end of TGZM whereas, when solute diffusion is the mode of transport into the bulk liquid, the condition of homogeneous melt becomes limiting and too much time-consuming to be fulfilled, which in particular holds for the 3D-experiments carried out in the reduced-gravity environment of space. r 2003 Elsevier Science B.V. All rights reserved. PACS: 61.72.Qq; 61.72.Ss; 81.05.Bx; 81.10.Fq; 81.30.Fb Keywords: A1. Directional solidification; A1. Initial state; A1. Segregation; A1. Solid–liquid interface; A1. TGZM; B1. Alloys
1. Introduction *Corresponding author. Tel.: +33-491-288673; fax: +33491-288775. E-mail address: [email protected] (H. Nguyen Thi).
During directional solidification of a binary alloy the solid–liquid interface can exhibit spatial organisation (cellular/dendritic array) due to the
0022-0248/03/$ - see front matter r 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0022-0248(03)01041-8
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
Mullins–Sekerka instability [1] that is governed by the growth parameters (alloy composition C0 ; thermal gradient GL and pulling rate V ). Recent theoretical models [2–4] have highlighted the critical role played by the initial transient on the asymptotic solidification microstructure. In these analyses, the main goal was to describe the front recoil due to solute build-up at the interface in the moments following an instantaneous jump in pulling rate from zero to a given value. In theory, the system is initially at rest with a flat solid–liquid interface and uniform concentration in the liquid phase. However, in real experimental situations, solidification starts on a prepared state, which results from a thermal stabilisation stage preceded by a melting phase. This initial state is in most cases not characterised and may strongly depart from that assumed in the models. Hence, the precise knowledge of the initial state from which growth is initiated and its influence on the subsequent growth transient is critical in order to check the soundness and predictions of theory, and thus improve the understanding of the formation of the solidification microstructure. The work described in this paper was actually motivated by observations made during LMS and STS-95 space missions. Al–1.5 wt% Ni samples were directionally solidified in the advanced gradient heating facility (AGHF) of the European Space Agency (ESA), which is a Bridgman-type furnace [5]. In all specimens, the composition profile was qualitatively obtained by X-ray radiography and then calibrated by chemical and EDS analyses (Fig. 1a). For all experiments, no longitudinal macrosegregation occurred when the stationary growth conditions were reached and a plateau at the nominal concentration C0 was obtained as expected for solidification either in diffusive conditions in microgravity (mg samples) or with convection driven by radial gradients (1 g samples solidified vertically upwards on ground). Indeed, it is well known that this type of convection induces strong radial macrosegregation of solute but with only weak axial macrosegregation [5,6]. Furthermore, in the intermediate region between the non-melted part of the sample and the plateau at constant concentration, the solute variation was rather complex and could not be
3
partially melted fully melted
non-melted
Concentration (wt% Ni)
540
2 stationary solidification
1 directional solidification
0 -10 (a)
0
10 X (mm)
(b)
(c)
(d)
(e)
20
30
Fig. 1. (a) Longitudinal segregation in Al–1.5 wt% Ni sample solidified in microgravity (GL ¼ 33 K/cm, V ¼ 3:83 mm/s). Labels above the curve indicate the three different zones of the specimen at the end of melting, labels below locate the beginning and the stationary regime of directional solidification. (b)–(e) Quarters of transverse sections (8 mm in diameter) at X ¼ 1; 3.8, 5.8 and 10.2 mm, respectively, along the intermediate part of the sample.
explained by the theoretical models mentioned above. Profiles first showed a sharp drop from the nominal concentration C0 to nearly pure aluminium (as shown in Fig. 1a, the origin of the X -axis is chosen near this minimum). This was the boundary between the non-melted zone, below the eutectic temperature TE ; and the partially melted region. A second minimum was observed at X E6 mm, which, as explained below, indicated both the limit between the partially melted region
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
and the melt and the beginning of the initial solidification transient. This transient could not be described by theoretical models mentioned above due to the very low value of the partition coefficient k (k ¼ 3:7 103 ), which leads to a very fast destabilisation of the planar front. The samples solidified at 1 g exhibited longitudinal solute macrosegregation almost identical to that in mg (see Fig. 8a), which confirmed that mixing of the bulk liquid by fluid flow did not occurred. Microstructure changes along the intermediate region between the non-melted solid and stationary solidification were analysed by metallography performed on cross-sections. Close to X ¼ 0; the transverse section showed aluminium grains bounded by a thin eutectic layer (Fig. 1b). In the subsequent sections (Figs. 1c and d), Ni-rich intragranular droplets are visible in addition to these eutectic layers. The surface fraction covered by Nirich droplets and inter-granular channels, and thus the nickel concentration, first increased progressively with the distance X from the non-melted zone and then reached a maximum (Fig. 1c) before decreasing again (Fig. 1d). After the second minimum, i.e. after the beginning of directional solidification, the intra-granular droplets disappeared and the solute composition increased again, as expected during the initial solidification transient. The solidification front became morphologically unstable and an array of cells covered the whole transverse section (Fig. 1e). In this paper, our aim of general interest is to show that, contrary to what is largely believed, the preparation of the initial solid–liquid interface is a very critical moment of directional-solidification experiments, which should be precisely characterised. Being aware of the effects of the experimental protocol used before the inception of growth, it will in particular be possible to fully explain the intriguing observations in the partially melted region of the AGHF samples. To this end, dedicated experiments consisting in directional melting followed by thermal stabilisation with different lengths are carried out. First, we will discuss the mushy zone induced by the melting of the original solid sample. Then, we will analyse the temperature gradient zone melting (TGZM) process [7–9], which occurs during both the melting
541
and the stabilisation stages and causes the migration of Ni-rich liquid droplets and channels. In parallel, a simple model will be introduced to validate the physical interpretation of the experiments through numerical simulations. Finally, we will discuss the effect of initial interface morphology and melt segregation on solidification transient in experiments, by means of a comparison of those Al–Ni alloys with Al–Li alloys previously grown on Earth and in space [10].
2. Experimental procedure In order to study the effect of both melting and stabilisation preparatory phases on the initial solidification transient, a series of experiments are carried out in a Bridgman-type furnace under 1 g conditions. The original Al–1.5 wt% Ni rods, with an outer diameter of 8 mm, are placed in a boron nitride crucible. The rods used in these experiments are taken from the same ingot than those solidified in the AGHF experiments during the LMS and STS-95 missions. A transverse section taken in the non-melted part of the sample (Fig. 2a) illustrates the equiaxed grain structure of the original solid which, since the solid solubility limit of nickel in aluminium is close to zero, in particular leaves Al3Ni inclusions a few micrometers in size within aluminium grains (Fig. 2b). The experimental protocol is as follows. For each experiment, the first step consists in a partial melting of the original rod achieved by moving the furnace downwards along the vertical sample, which imposes a melting rate Vf ¼ 7:8 mm/s and a thermal gradient in the liquid phase GL (deduced from the temperature profile measured by two thermocouples) about 30 K/cm. The furnace displacement is stopped when the length of the nonmelted part of the sample is about 35 mm. In the second step, the sample is submitted to thermal stabilisation of variable length (Table 1). Finally, the microstructure is frozen by a rapid quench. For all experiments, a post-mortem analysis is carried out. To reveal the solid morphology after the melting and stabilisation phases, both a longitudinal section parallel to the sample axis and transverse sections spaced along the whole
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
542
(a)
(b)
20 µm
Fig. 2. Original Al–1.5 wt% Ni rod: (a) transverse section showing equiaxed grain structure (8 mm in diameter), (b) SEM picture showing Al3Ni inclusions within the Al matrix of a grain.
Table 1 Parameters of the experiments for Al–1.5 wt% Ni alloys Experiment Alloy composition Melting velocity Vf Thermal gradient GL Stabilisation length
Exp. 1
Exp. 2
Exp. 3
0h
Al–1.5 wt% Ni 7.8 mm/s 30 K/cm 1 h20 2 h35
Exp. 4
7h
intermediate region of each sample are mechanically polished. There is no need of chemical etching as primary-aluminium and Al3Ni give strong enough contrast under the optical microscope.
3. The mushy zone induced by melting and its evolution during thermal stabilisation 3.1. Experimental results The experimental microstructures are displayed in Fig. 3. In a melting experiment without thermal stabilisation stage (Fig. 3a), a solid–liquid zone is observed on the longitudinal section: the light areas are primary-aluminium solid and the dark ones quenched Ni-rich liquid droplets and channels. In our experiments, a mushy zone forms due to the multiphase nature of the original alloy (Al+Al3Ni). Indeed, when the solid temperature reaches the eutectic temperature TE ¼ 913 K, the liquid phase nucleates at the interface between the
Al3Ni inclusions and the Al matrix, with eutectic composition CE ¼ 5:7 wt% Ni. From the phase diagram (Fig. 4a) and the distance between the two minima on the axial segregation profile, we can deduce that this mushy zone extends from a temperature close to TE up to some temperature TL at its hot top (E924 K for Fig. 3a) somewhat below the liquidus temperature for concentration C0 ; namely TL0 ¼ 927:7 K. It also results from local thermodynamic equilibrium that the Ni-rich molten inclusions contains more nickel at their cold bottom end than at their hot top end. It is worth noting that, even when the initial solid is homogeneous, there can also be a mushy zone but, in this case, it is caused by constitutional superheating of the solid ahead of the planar melting front [11,12], which can exist without any morphological instability occurring at the front. Indeed, this constitutional superheating leads to the nucleation and growth of liquid inclusions in the solid as reported by Verhoeven and Gibson [13] for Sn–Sb and Sn–Bi alloys, and recently observed in situ on transparent succinonitrile— acetone alloys [14]. Figs. 3b–d show the effect of thermal stabilisation on the mushy zone. As the stabilisation length is increased, the liquid fraction in the mushy zone decreases. In particular, for the last experiment (Fig. 3d), almost all horizontal channels and small inclusions have disappeared. These strong changes in the macrostructure can be explained by taking into account the TGZM mechanism introduced by
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
1mm
Liquid
Liquid
Liquid
543
Liquid
TE (a)
Solid
(b)
Solid
(c)
Solid
(d)
Solid
Fig. 3. Longitudinal sections of Al–1.5 wt% Ni illustrating the microstructure of the mushy zone after melting and for four thermal stabilisation lengths: (a) 0 h, (b) 1 h20, (c) 2 h35, (d) 7 h.
different compositions as local thermodynamic equilibrium holds at solid–liquid interface of the droplet. Hence, there is a concentration gradient across the liquid droplet and solute diffuses from cold side to hot side. This causes solidification at the cold side and melting at the hot one, so that a droplet migrates up the thermal gradient. The mean velocity of migration can be deduced from the solute balance at the cold side of the droplet [8]: Vmig ¼
Fig. 4. Schematic representation of both mushy zone and average concentration evolutions during thermal stabilisation subsequent to directional melting process: (a) just at the end of melting, (b) at intermediate time during the stabilisation phase, (c) final asymptotic state, and (d) Ni axial segregation profile after a stabilisation length of 7 h measured by X-ray radiography.
Pfann years ago [7]. If one considers a liquid droplet inside a solid matrix subjected to a thermal gradient, the hot and cold sides of the droplet have
Gd DL ; mL CL ðk 1Þ
ð1Þ
where DL is the liquid solute diffusion coefficient, mL the liquidus slope, CL the mean droplet composition, k the distribution coefficient and Gd the thermal gradient in the droplet. As droplets are small, the temperature field inside them is in first approximation imposed by the surrounding solid aluminium so that Gd EGS EKL GL =KS ; with GS the temperature gradient in the solid and KL and KS the thermal conductivity of liquid and solid, respectively. Insertion of typical values shows that this velocity is generally of the order of 1 mm/s. In our experiments, DL ¼ 3 105 cm2/s [15], Gd ¼ 15 K/cm, mL ¼ 3:51 K/wt% Ni, C0 (1:5 wt%Þ pCL pCE (5.7 wt%), and k ¼ 3:7 103 ; so that 0:27 mm=spVmig p0:85 mm/s.
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
544
The time required for a liquid droplet to go through the whole mushy zone can be estimated by t¼
TL TE 1 : GS Vmig
In our experimental conditions, t is of the order of 8 h. Actually, the situation is somewhat more complex as, in addition to droplets, there are thin liquid channels separating the solid grains. The behaviour of those channels can be discussed by considering how TGZM acts on their vertical and horizontal segments. For the latter, which are perpendicular to the temperature gradient and thus transmit the heat flux from the solid above to the solid below, Gd is close to GL as the alloy is metallic. Thus, TGZM migration at given temperature is about two times faster than that of the droplets. This effect is already visible in Fig. 3a: going from the bottom to the top of the mush, one can see that a layer void of droplets progressively develops in the aluminium grains, whose shape roughly follows that of the upper part of the grain envelope (see close-up in Fig. 3a). This means that, due to their slower climbing, the droplets inside each grain are progressively overtaken and captured by the horizontal channel underneath so that the TGZM migration is with time reduced to a channel problem, which is already realised on top of the mush in Fig. 3a and complete except at the bottom of the mush in Figs. 3b and c. For the vertical segments, which are parallel to the temperature gradient and thus transmit the same heat flux that the solid aside, Gd EGS as in the droplets. However, the persistence of vertical channels even in Fig. 3d suggests that TGZM is delayed, possibly due to some capillary anchoring of their extremities at the triple point where the melt and the two solid grains join. In the AGHF solidification experiments, the thermal stabilisation time, typically about 1 h, was definitely always much shorter than the time necessary for complete liquid evacuation by TGZM. Consequently, the microstructure of the mushy zone was similar to that in Fig. 3b and the solute profile were similar to the one shown in Fig. 4b. These experimental results unambiguously establish that both the first minimum (at X E0 mm) and the subsequent maximum (at
X E3 mm) in the solute profile of Fig. 1a were induced by the two preparatory stages preceding directional solidification, namely melting and thermal stabilisation. Concomitantly to liquid migration leading to solid aluminium ahead of the bottom limit at eutectic temperature, solute is rejected in the liquid phase due to the TGZM mechanism, causing back-melting of the upper interface and build-up of a Ni-rich boundary layer adjacent to this interface. The net result of the conjugation of those two effects, which are already active during melting of the sample, is the progressive reduction from both sides of the size of the solid–liquid mushy zone, as qualitatively sketched in Figs. 4a and b. Yet, the time scale of TGZM, of the order of 10 h, is much shorter than that of complete mixing of the melt by solute diffusion, of the order of L2 =DL E900 h for a melt of length L ¼ 10 cm, so that the melt at start of solidification is never homogeneous in the experiments (Fig. 4d). It results that, when using an original solid made of equiaxed grains, the asymptotic state at very long times, which for dilute Al–Ni alloys would be a solid layer of pure aluminium in equilibrium with a homogeneous liquid at a concentration slightly higher than C0 (Fig. 4c), is in practice never reached and, without the assistance of fluid-flow mixing, even likely to be poorly approximated only in many of the experimental studies available in the literature, in which this point is very rarely documented. 3.2. Model and numerical calculations With the assumption that all the liquid inclusions undergoing TGZM are either droplets or horizontal channels, a simple numerical model can be derived to describe the melting and subsequent thermal stabilisation regimes observed in the experiments. As shown in Fig. 5a, the relevant section of the sample extends from X ¼ 0 (bottom) to X ¼ H (top). Using the same physical parameters as in the experiments, we have H ¼ ðTL0 2TE Þ=GS ¼ 9:8 mm. Although back-melting at the top reduces the height of the mush, it has no influence on the TGZM process so that taking the maximum value of H by using TL0 in its
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548 T
T
TE+GSH
H
Vf
ρ/ρ0
TE XB t TE-GSH
0
(a)
TE-GSXB
(b)
TE
(c)
(d)
Fig. 5. Schematic representation of the sample longitudinal section relevant for TGZM analysis showing the notations used in modelling: (a) initial time t ¼ 0 is taken at starting of melting, eutectic isotherm is indicated by a bold line; (b) partial melting of sample at velocity Vf ; (c) at t ¼ t0 ; directional melting of the sample is stopped; and (d) t > t0 ; thermal stabilisation phase with TGZM only.
evaluation is a convenient way to circumvent the problem of the variation of mush height with time. We denote rðX ; tÞ the number-density of Ni-rich droplets at time t and altitude X : This density is governed by the linear temperature field TðX ; tÞ imposed by the furnace. Initially, TðH; 0Þ ¼ TE and Tð0; 0Þ ¼ TE GS H; and we assume a homogeneous density, rðX ; 0Þ ¼ r0 ; of Ni-rich inclusions. During the melting phase, the furnace is moved down at velocity Vf (Fig. 5b). It is stopped at time t0 ¼ H=Vf ; when Tð0; t0 Þ ¼ TE (Fig. 5c) and the temperature profile remains constant afterwards, during the thermal stabilisation phase (Fig. 5d). The desired relation between rðX ; tÞ and TðX ; tÞ; qr=qt ¼ qðrVmig Þ=qx;
ð2Þ
is obtained by writing a conservation law which neglects droplet coalescence. The migration velocity of a droplet, V ðz; tÞ; is calculated by inserting Gd ¼ GS ¼ 15 K/cm, k ¼ 0 and cL ¼ ðT T0 Þ=mL in Eq. (1), where T0 ¼ 933 K is the melting temperature of pure aluminium. Note that this equation equally applies to the number-density of horizontal channels, but with Gd ¼ GL ¼ 30 K/cm as discussed previously. Eq. (2) is then solved by a finite-difference scheme on a one-dimensional (1D) grid with mesh size h ¼ 0:1 mm. During the melting phase (tpt0 ) we use a moving boundary condition rðXB ; tÞ ¼ r0 at the altitude XB where TðXB ; tÞ ¼ TE (see Fig. 5b). During the thermal stabilisation phase the furnace does not move
1
1.5
0.8
1.2
0.6
0.9
0.4
0.6
0.2
0.3
0
C wt %
T
T TE
545
0 0
0.2
0.4 0.6 X (cm)
0.8
1
Fig. 6. Profiles giving both the number-density and solute concentration calculated from our model for Al–1.5 wt% Ni alloys. Continuous lines are calculated with Gd ¼ GS ; from top to bottom: t ¼ t0 ¼ 1250 s (complete melting), t1 ¼ t0 þ 1 h, t2 ¼ t0 þ 3 h, t3 ¼ t0 þ 5 h, t4 ¼ t0 þ 7 h. Dashed line is calculated with Gd ¼ GL and for t1 ¼ t0 þ 1 h.
anymore and the boundary condition rð0; tÞE0 is constantly imposed. The numerical droplet density profiles obtained at different times are displayed in Fig. 6. At the end of the melting phase (t ¼ t0 ¼ 1250 s), the profile is monotonously decreasing because the droplets near the top of the mushy zone have already migrated into the liquid phase while those at the bottom are only starting to migrate. During the thermal stabilisation phase the droplets move higher and a depletion zone forms at the bottom of the sample, so that a maximum appears in the density profile. The number-density profile of horizontal channels for t0 þ 1 h is also displayed in Fig. 6a for comparison; here the temperature gradient Gd is twice higher, so that the liquid inclusions migrate twice faster. Since the solid matrix is practically pure aluminium, which means that almost all Ni stays in the droplets, there is a direct link between the numerical number-density profiles and the meanconcentration profiles. If Cav ðX ; tÞ is the average concentration in the slice and CðX ; tÞ the concentration in the droplets, we have at time t Cav ðX ; tÞ ¼ Cav ð0; t0 ÞrðX ; tÞ=r0 ;
tXt0
ð3Þ
with Cav ð0; tO Þ ¼ 1:5 wt% Ni. At about the same time (t0 þ 1 h), the numerical profile is similar to the one observed in the AGHF experiment (Fig. 1a), with a better agreement (maximum around X ¼ 2:5 mm) when using Gd ¼ GL : It
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
546
follows that the contribution of horizontal channels to the TGZM process is likely to be dominant since early times, which is supported by the almost complete disappearance of droplets in between Figs. 3a and b. The comparison with a stabilisation experiment carried over 7 h on Earth (Fig. 4d) is less satisfactory as the experimental profile shows a bump that is absent in numerical simulation. We believe that this remaining solute segregation has to be related to the vertical Ni-rich channels which are still there as visible in Fig. 3d.
4. Influence of initial interface morphology and melt segregation on solidification transient in experiments In the theoretical models of solidification transient, the initial solid–liquid interface is assumed planar with uniform concentration in the liquid phase. As shown above, in all the Al–Ni experiments, growth started on an initial interface resulting from a melting phase followed by a thermal stabilisation period that was not long enough. Thus, the initial state was strongly different from that used in the models. Then, the solid–liquid interface was of the type shown in Fig. 7, corrugated because the solid side consisted
(a) z LIQUID [CL]
SOLID (b) Fig. 7. (a) Photograph of the solid–liquid interface of Exp. 2 (thermal stabilisation length of 1 h20) and (b) schematic drawing of the interface before onset of directional solidification in microgravity experiments.
of several grains separated by enriched liquid channels of varying width and presenting here and there droplets emerging into the bulk liquid (Figs. 7a and b). Also, due to solute release at the mouths of vertical channels and by emerging droplets and horizontal channels there was solute pile-up on the liquid side, ahead of the mushy zone (e.g. Figs. 1a and 4d). For Al–1.5 wt% Ni, the distribution coefficient k is close to zero so that the composition of the first grown solid was approaching zero in the AGHF experiments, even though the solute pile-up made the composition ½CL f of the bulk liquid in contact with the top of the mushy zone, somewhat larger than the nominal value 1.5 wt% Ni (about 2.6 wt% Ni as measured in quenched fronts Figs. 3a–d). After the inception of directional solidification by application of the pulling velocity Vf ; the solute content in the solid first increased from k½CL f up to a maximum followed by a smooth decrease down to the asymptotic value C0 : This behaviour is in strong contrast with the monotonous increase to C0 predicted by the models and observed when the initial material is a solid solution and the melt homogeneous in composition, in which case the solute boundary at the solid–liquid interface fully builds up from zero after solidification has been started from rest [16]. Therefore, the peculiar maximum in the profile has to be attributed to the presence of eutectic inclusions in the original Al–1.5 wt% Ni samples which, by the TGZM process, caused the enriched liquid layer at the interface. By prefiguring the solute boundary at the solid–liquid interface, this layer in practice shortens the solidification transient and leads to a more rapid breakdown of the planar interface. During the solidification transient, the solute excess was partially incorporated into the solidification front so that an overshoot in composition profile is visible, at X E8 mm in Fig. 1a. This overshoot phenomenon is recovered at 1 g (Figs. 8a and 4d) because the Al–1.5 wt% Ni samples were solidified in a solute stabilising configuration (i.e. rejected solute denser than solvent) so that there was no fluid flow to induce mixing with the bulk liquid. For the sake of completeness, it is worth to make a comparison with the results on the
H. Nguyen Thi et al. / Journal of Crystal Growth 253 (2003) 539–548
0.8 Partially melted
2
0.6
1.5 ρ
Nickel concentration (wt%)
2.5
0.2 0.5
µg 1g -5
0
5
(a)
0
10
15
0 20
X (mm)
Partially melted
4
µg
3.5 3
1g
2.5 2 -5
0
0.2
0.4 X (cm)
0.6
0.8
Fig. 9. Number-density profiles calculated from our model for Al–Li alloys with Gd ¼ GS ; from top to bottom: t1 ¼ 15 min, t2 ¼ 30 min, t3 ¼ 45 min and t4 ¼ 60 min.
4.5 Lithium concentration (wt %)
0.4
1
0
(b)
547
5
10
X (mm)
Fig. 8. Comparison of typical axial solute concentration profiles in the intermediate zone for samples solidified in microgravity environment (mg), when diffusion is the mode of solute transport in the melt, and on Earth (1 g), with natural convection: (a) Al–1.5 wt% Ni, GL ¼ 34 K/cm and (b) Al– 3.5 wt% Li, GL ¼ 70 K/cm.
observed in that region on Al–1.5 wt% Ni. It follows from numerical simulation during thermal stabilisation that, because lithium diffusion is fast (DL ¼ 1:9 104 cm2/s [10]), the TGZM process was finished when directional solidification was started (Fig. 9). The nearly linear Li decrease in the intermediate region can be explained by the fact that, for original solid rods made of equiaxed grains, the solute profile built by TGZM directly reflects the solidus. This is merely because in their migration by melting-solidification the horizontal parts of inter-granular channels overlap over the entire cross-section at constant temperature which, due to local equilibrium, imposes uniform solute concentration at the solidus.
5. Conclusion Al–3.5 wt% Li alloys we previously studied [10], for which TL0 ¼ 908 K, TE ¼ 873 K, CE ¼ 8:3 wt% Li, k ¼ 0:55 and mL ¼ 8:3 K/wt%. Indeed (Fig. 8b), the overshoot peak in segregation profile, also present in microgravity experiments, was in the case of solute-destabilising upward solidification on Earth destroyed by strong mixing of the melt caused by thermosolutal convection, giving way to a plateau as in theory but inappropriately below nominal composition. Besides, it should be noticed that the linear decrease of the Li concentration in the intermediate section differed drastically from the solute variation
The precise control of the initial conditions (solid–liquid interface morphology and solute segregation in the liquid phase) on which directional solidification is started is critical for experiments to provide the benchmark results needed for the reliable validation of the predictions of theory and numerical simulation. This is particularly true for the 3D-experiments carried out in the limit of diffusion transport in the reduced-gravity environment of space, which remain rare and costly. It stems from the present investigations on Al– 1.5 wt% Ni, and on hypoeutectic Al–Li, alloys
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that this control is in practice far from being an easy task, which should deserve high consideration, and exhaustive characterisation. For directional-solidification experiments achieved on original rods with equiaxed microstructure, the efficiency of the preparatory melting and stabilisation phases can be evaluated from the solute macrosegregation profile in the region in between the non-melted solid and directional solidification. When this profile follows the solidus line of the phase diagram, the solid–liquid interface has globally reached good smoothness as then no liquid inclusion will emerge from behind by the TGZM process. Experimental results and numerical simulation establish that this step needs several hours. If some fluid flow ensures mixing of the melt while solute is rejected by TGZM, the prepared initial conditions have also neared their asymptotic state when TGZM is completed, as it is the case on Earth by thermosolutal convection for Al–Li (Fig. 8). When solute diffusion is the mode of transport into the bulk liquid, the situation differs drastically as the condition of homogeneous melt becomes the most limiting and the most timeconsuming to fulfil, as made clear from the analysis of the Al–1.5 wt% Ni alloys. Very strikingly, the enriched liquid layer due to the back-melting of the mushy zone from its top surface is present in all experiments, and would persist for tens of hours more. This suggests to conclude that future experiments without mixing by natural (buoyancy- or/and capillary-driven) convection, and more especially those in microgravity conditions, should either make use of already homogeneous original solid samples, possibly obtained by stationary growth with a planar interface, or implement electromagnetic [17,18] or vibrational [19] stirring.
Acknowledgements The financial and technical support of CNES (Centre National d’Etudes Spatiales) is very
gratefully acknowledged. The authors also benefited from ESA (European Space Agency) support for the space experiments in AGHF, and subsequent ground work through the CETSOL MAP.
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