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X-ray radiography observations of columnar dendritic growth and constitutional undercooling in an Al–30wt%Cu alloy
Acta Materialia 53 (2005) 947–956 www.actamat-journals.com
X-ray radiography observations of columnar dendritic growth and constitutional undercooling in an Al–30wt%Cu alloy Ragnvald H. Mathiesen
a,*
, Lars Arnberg
b
a b
SINTEF Materials and Chemistry, Department of Applied Physics, Hogskoleringen 5, N-7465 Trondheim, Norway Department of Materials Technology, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Received 27 July 2004; received in revised form 22 October 2004; accepted 27 October 2004 Available online 16 December 2004
Abstract In situ synchrotron X-ray radiography of columnar dendritic and eutectic growth under directional solidification of Al–30wt%Cu has been carried out with nominal spatial and temporal resolutions of 1.4 lm and 150 ms, respectively. The images can be processed to reveal spatiotemporal co-ordinates of the solid–liquid phase fronts for both a-dendrites and the proceeding eutectic. Also estimates for local solute boundary layers ahead of and in the mushy zone can be extracted from image processing. Steady-state growth could not be realized in the experiments. Presumably this relates to a combination of: (a) insufficient time available for initial instabilities to evolve into a steady state; (b) primary a-branches may interact through solute diffusion in the confined sample volume; (c) the inevitable presence of thermo-solutal flow; and (d) a long-term sample position dependent drift in the furnace to sample heat transfers. Nevertheless, the data collected contain information that may be valuable for microstructure modelling of dendritic growth. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Synchrotron radiation; Aluminium alloys; Dendritic growth; Directional solidification; Constitutional undercooling
1. Introduction Metallurgical industries are continuously seeking to improve the efficiency and performance of their components while simultaneously reducing cost. Cast components can often be produced at considerably lower cost than wrought or machined parts; however, obtaining adequate control over the microstructure evolution during the solidification process is often a bottleneck for manufacturing components that perform as required. The final microstructure depends, in addition to alloy composition and heat-treatment, to a large extent on the thermodynamics and the kinetics of the solidification process. Accordingly, there is strong industrial and aca*
Corresponding author. Tel.: +47 73 597 052; fax: +47 73 597 040. E-mail address: [email protected] (R.H. Mathiesen).
demic motivation for a better understanding of and control over the fundamental aspects of solidification. Over the last couple of decades advanced modelling has evolved to cover many aspects of solidification science, from fundamental issues (interfacial energies, kinetics and dendritic growth in 2 or 3D) and important phenomena (porosity, fragmentation, segregation) to the numerical modelling of real casting processes – spanning length scales from the atomic to the macroscopic. While computer simulations have been firmly established on all levels, provision of new experimental data to guide theory and modelling and assist in their refinement has fallen behind. In particular there is a gap to bridge in devising experimental methods for in situ observations of metal and alloy solidification microstructures and phenomena allowing for proper assessment of kinetics.
1359-6454/$30.00 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.10.050
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Experimental studies of solidification microstructures in metals have mostly been conducted ex situ with samples produced by quenching the system during growth. Investigations in optical or electron microscopy must account for the effects caused to the front morphology and the solid microstructure by destabilization of the growing front and subsequent coarsening of the solid. Consequently, it can be difficult to conclude from such observations the microstructural features truly relevant only to the solidification process itself. Furthermore, such experiments reveal no direct information on dynamical aspects, which must be provided by other means, e.g., in situ calorimetry, or assigned indirectly from microstructure features such as dendrite arm spacing. In contrast, direct observations of various growth dynamics, which in many aspects are of relevance to metal solidification, has been carried out in situ on various organic model systems, the so-called transparent analogs (TAs) [1–4]. TAs can be studied under the light microscope owing to contrast arising from a shift in the optical density crossing the solid–liquid boundary. Studies in these systems have been decisive in the refinement of various theoretical/empirical models for dendritic growth leading up to the first self-consistent models for growth by diffusion from the anisotropic interface of a free dendrite [5–8]. Today, several of the most frequently applied techniques for solidification microstructure modeling are evaluated against or compared with observations obtained in studies of TAs [9]. The transparent systems have also been used to study specific topics, such as growth under extraterrestrial micro gravity conditions [10,11], growth by chemical diffusion [12] or fragmentation phenomena [13]. Despite their well-demonstrated impact on solidification science over four decades, the transparent systems are limited as full analogues to metallic systems due to differences apparent in several physicochemical quantities, such as freezing temperatures, heat capacities, chemical potentials, viscosities, solute mass gradients, and diffusion lengths, all of importance to solidification. Important effects influenced by or related to such physicochemical quantities, cannot always be transferred easily from observations in a model system to the alloy of interest. Confocal scanning laser microscopy has been used to carry out in situ studies of solidification microstructures in metals [14,15]. This technique has a limited penetration depth, enough to go through shielding oxides; furthermore, combined with monochromatic light, confocal optics effectively reduce problems associated with signal detection over a strong thermally radiated background. The use of this method in solidification science is quite recent, and more time is needed for it to demonstrate its full potential. However, being a scanning technique it will be limited in temporal resolution compared to standard video microscopy, which conse-
quently will impose limits also on its achievable spatial resolution by the blurring of rapidly evolving objects. X-ray transparency of metals has to some extent been exploited to obtain in situ information on alloy solidification fronts, microstructures, segregates and convection [16–18]. In common with this work, the spatial and in particular the temporal resolutions reported are poor compared to those obtained in microscopy on TA, due to limitations in signal-to-noise. These limitations can be related to either insufficient brightness of the X-ray source, insufficient output signal from the sample, inadequate detection efficiency, or to a combination of the three. Some setups have improved on this situation increasing the brightness by employing focusing X-ray optics [19]. Focusing decreases the degree of transversal coherence in the incident wave field, hence only the attenuating part of the X-ray optical density function can contribute to the image contrast. Such setups are therefore only applicable to systems in which the segregates that form have boundaries that can be associated with a relatively sharp transition in the X-ray attenuation. Recently, new in situ X-ray studies of solidification microstructures and phenomena in alloys have been made possible by the photon source and detector improvements provided at third generation synchrotron facilities [19–22]. These advances allow X-ray radiography to be carried out with spatiotemporal resolutions approaching true video microscopy, which was first demonstrated with the real-time imaging of various solidification modes (cells, columnar and equiaxed dendrites) for a series of Sn–Pb alloys [19]. Later, the setup was refined and used for in situ studies of several growth modes and process phenomena (dendrite fragmentation, gas porosity) in various Al–Cu alloys [20]. Here, we report on results obtained through data analysis of one particular image sequence on columnar dendritic growth in Al–30wt%Cu.
2. Experiment A description of the experimental setup and sample preparation and the more fundamental issues concerning high-energy synchrotron X-ray imaging are given in detail in [20], and references therein. Here, only a brief presentation will be given to utilize the issues most central to the analysis and discussion of the results presented. The fundamental aspects of X-ray transmission imaging is governed by the interactions of X-rays with matter [20]. Through an object transmission function, summing up the alterations of the incident wave field as it propagates through the specimen, image contrast can be related exclusively to quantities constituting the complex optical density or refractive index of the sample. The
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imaginary component relates to the attenuation of the X-ray beam by the sample, and is predominantly sensitive to constitutional variations. The real component relates to refraction of the beam which for X-rays is weak with all materials, but nevertheless sensitive to variations in density. In the sample transmitted wave field, attenuation directly affects the amplitudes, whereas refraction affects its phase components. Hence constitutional variations are visible mainly by amplitude contrast, whereas variations only in density can be studied with phase contrast. The latter, however, require an X-ray wave field with a high degree of transversal coherence; in particular since the detector resolution is five to six orders of magnitude coarser than the X-ray wavelength. Therefore, for time-resolved imaging, where high collimation at the cost of low beam intensity is unacceptable, conditions for phase contrast imaging can only be provided by bright, naturally collimated insertiondevices at third generation synchrotron sources. The experiment was carried out at the micro focusing and imaging (l-FID) beam line ID22 at the European Synchrotron Radiation Facility (ESRF) under experimental code HS-1332. In a parallel beam geometry the incident 15 keV monochromatic beam provided a wave-field at the sample with a flux of 5 · 1012 photons/(s mm2) and horizontal and vertical transverse coherence lengths of about 5 and 50 lm, respectively. A quadratic beam was defined by horizontal slits to match the full vertical width, measuring 1.35 · 1.35 mm2 at the sample position. A vertical temperature gradient stage, used to control the conditions for directional solidification, was built following the principles outlined by Hunt and et al. [23], but modified to deal with solidification temperatures up to 1200 K [20]. The samples were prepared by melting 99.999 wt% purity Al and Cu alloys in alumina crucibles and cast in an insulated, bottom-chilled mould to promote directional solidification. A region free of porosity located about 1 cm from the chill was cut into a rectangular slice measuring 1.5 · 3.0 cm2 (H · V). The slice was polished down to a thickness of 190(5) lm and pre-oxidized at 720 K for 2 h, followed with a Boron– Nitride spray coating, before being concealed into a container made by welding together two rectangular 100 lm thick quartz glass plates around the metal sheet. Upon the first melting process, the metal settled to the bottom of the container and filled it uniformly, with a thickness closely equivalent to the maximum of the original sheet, measured to be about 200 lm. Accordingly, after initial melting the vertical sample length was reduced with respect to its original size by about 2 mm. The data presented here are the second series from a total of five independent solidification experiments carried out with this particular sample. After five consecutive solidification sequences, the sample showed no signs of deterioration or decay.
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Data acquisition was carried out using a dedicated Fast Readout Low Noise (FReLoN II) high-resolution X-ray microscope [20,24]. The microscope consists of a thin X-ray to visible light converting transparent absorptive–emissive screen (Te or Eu doped Lu3Al4.4Sc0.6O12), placed in the X-ray beam in the front focal plane of a lens system. The microscopeÕs rear focal plane falls onto a custom made 4.2 M pixel CCD with a physical pixel size of 14 lm and a dynamical range of 14 bits, i.e., 16 384 grey levels. The CCD can be readout as four separate channels and transferred by optical fibres directly to computer memory. The highest nominal spatial resolution of the system, Drnom, is about 0.6 lm with a readout dead time, tro 300 ms. For time-resolved imaging, a 2 · 2 hardware rebinning of the CCD allows both for shorter exposure times and shorter readout dead time at the cost of a poorer spatial resolution; nominal features for the rebinned mode are Drnom 1.2 lm with tro 150 ms. These are available only in the highest spatial resolution mode employing a 3.5 lm thin luminescent screen at the highest magnification available, resulting in a field of view of about 0.7 · 0.7 mm2 and a detection quantum efficiency of about 4%. In this study, a 12 lm thick screen with about 7% efficiency was employed together with a lower magnification to have better photon statistics at short exposure times. The thicker screen introduce a slight aberration, Drnom 1.4 lm, but since steady-state growth was not realised in the experiment, the spatial resolution was limited by the smearing of details, or temporal blurring, Drtemp = texpvs, where texp is the exposure time, and vs is the local propagation velocity of the solid relative to the imaging system. The field of view obtained was about 1.4 · 1.4 mm2, closely similar to a full quadratic beam cross section. For the solidification sequence presented here a thermal gradient, G = 27 K/mm, was imposed over the sample, in parallel to gravity, g. In general, the top down directional approach is thermally less stable than the conventional opposite, antiparallel with g. The primary source for bouyancy flow is by the solutal gradient for which a Rayleigh number can be derived as, Ras ¼
ðDq=q0 ÞgL3 ; vDl
ð1Þ
where (Dq/q0) 4.2 · 102 is the solutal density gradient relative to the 30wt%Cu density, L = 200 lm is a critical length corresponding to the sample thickness, v = 6 · 107 m2/s is the kinematic viscosity and Dl = 3 · 109 is the solute diffusion coefficient in the liquid. Numeric evaluation yields Ras 1800, corresponding to a solutal flow at the verge of what is normally considered necessary to establish sustainable convection rolls, yet definitely large enough to create significant solutal imbalance. Alternatively, the driving force for solutal flow can be quantified in terms of
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characteristic microstructure lengths following the model proposed by Beckermann et al. [25], modifying it to the particular experimental geometry where L3 in Eq. (1) is replaced by F(fs)k1ltL, with L as the sample thickness, F(fs) as a function of the fraction solid accounting for change in the mush permeability (modified to handle permeability drop only in one dimension), k1 as the primary dendritic arm spacing, and lt as the characteristic length of the solidification interval, gives Ras 1650. The corresponding thermal flow is negligible for the vertical thermal gradient, but the slightly curved shape of the isotherms may result in thermally driven flow. However quantifying this effect is difficult and will not be attempted here. Curved isotherms were also observed in the upwards directed solidification geometry. In fact, out of a total of 200 directional solidification sequences with this system, we did not find it significantly easier to obtain steady state by solidifying in either of the two opposite directions. The applied exposure, texp = 0.3 s/frame. The sample was solidified from the melt, initially positioned with its upper edge just below the cold furnace at T = 748 K in contact only with the hot furnace at T = 882 K. Pushing the sample at constant velocity, vsp = 22.4 lm/s, directed opposite to G, multiple nuclei would form and hopefully evolve into a columnar front propagating parallel to G, originating from one nucleus selected by competing kinetics. The sample was monitored online at the pre-calibrated position, with acquisition of images starting as soon as the solidification front appeared in the field of view. The computer memory configuration allowed for the acquisition of 120 consecutive frames.
3. Results Fig. 1 shows three frames of the columnar dendritic solidification series collected with the Al–30wt%Cu alloy. Contrast from the internal dendrite structures and liquid segregates are caused mainly by absorption. The bright horizontally oriented lines seen in all frames are eutectic fronts, which are provided by phase contrast as constructive interference fringes from beams refracted differently across the eutectic solid–liquid boundary due to the density difference between the aggregates. At the dendrite–liquid interface both attenuation and refraction contribute to the contrast. In Fig. 1 it can be seen that the eutectic interface normal varies slightly along the horizontal direction indicating isotherms not to be fully perpendicular to the imposed thermal gradient. This effect can probably be ascribed to a combination of thermo-solutal flow and a slightly larger heat transfer at the outer sample edges. The centre of the sample is roughly 0.5 mm to the right of the image sequence field of view. Assuming local equilibrium at the solid–liquid
Fig. 1. Columnar dendritic and eutectic growth in Al–30wt%Cu. Primary arms are labelled 1–5 from left to right in the images: (a) at t0; (b) at t0 + 3.15, or 7 frames later; (c) at t0 + 6.3 s, or 14 frames later. G and gravitation, g, are parallel upward, while vsp is downward.
interfaces this horizontal gradient can be estimated to be about 1.2 K/mm from the sample centre and outwards horizontally to both sides. This shape was pre-
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served throughout the 120 frames collected in this particular sequence, and similar observations were done in other sequences with this and other samples. The images shown in Fig. 1 have been flattened by a beam structure reference image, and then stretched in a non-linear manner that reserve most of its dynamical range to liquid contrast. The darker bands surrounding the primary crystal phase front is due to local Cu-enrichment. In order to analyze supercooling quantitatively, however, other image processing routes are required. The primary challenge in a quantitative analysis of chemical gradients lies in phase separation. In the full solid–liquid frame up to 70% of the contrast range available in a flattened and linearly stretched image can be assigned to the difference in transmission between primary a crystals solidifying with 5.3wt%Cu, and the other regions which either contain liquid of constitutions between 30wt%Cu and a eutectic at 33.1wt%Cu, or a eutectic solid. Indeed, if the primary crystals are considered to fully span the container along the beam path, x, so that all domain boundaries are fully resolved in the 2D image plane, the 15 keV X-ray transmissions through 200 lm are 0.966, 0.292 and 0.24 for 5.7wt%Cu (max a solid solubility at Te), 30wt%Cu and 33.1wt%Cu domains respectively, relative to a domain of primary crystals at 5.3wt%Cu (Tl 832 K). Hence, only about 6.5% contrast is left for liquid constitution analysis. In order to retrieve this information, an image processing procedure has been devised where the first part concerns tracking of the a and eutectic solid–liquid boundaries, and then to employ this information to create a binary mask that can be used to separate the aggregates. Setting pixels associated with solid domains to zero by use of the binary mask, the liquid pixels may be smoothed and filtered without having to be smeared by solid pixels, also with a full dynamical range available to liquid contrast with all subsequent operations on contrast being linear and reversible. In Fig. 2 liquid constitution contour plots of mushy zones around primary arms 2, 3 and 4 plus regions that extend deeper into the liquid are presented for the three frames of Fig. 1. An increment at every 0.5wt%Cu corresponds closely to a 2.3r contouring level. The analysis has been restricted to a region which falls within the full width half maximum plateau for the incident beam profile. Extending outside this region to pixels positioned further away from the image centre, analysis becomes less accurate, due to weaker beam illuminations and correspondingly poorer statistics. The images of Figs. 1 and 2 have been selected to demonstrate a part of the sequence where the solute boundary ahead of arm 2 has just been altered rapidly by a plume flowing out of the inter dendritic region, leading to a substantial increase in super cooling at the local front, as shown in Fig. 2(a). Fig. 2(b) and (c) shows the subsequent evolution of the solute layers and solid– liquid interface.
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Fig. 2. Mushy zone liquid constitution contour plots. Solid regions are white, liquid contours start at 33wt%Cu (black) with increments of 0.5wt%Cu (corresponding roughly to a 2.3r contouring) up to the deep-in liquid constitution at 30wt%Cu. The frame region presents primary arms 2–4 (left to right) in Fig. 1 with: (a) at t0; (b) at t0 + 3.15, or 7 frames later; (c) at t0 + 6.3 s, or 14 frames later.
Images phase filtered by binary masks can be combined into 3D volumes, spanned by the two spatial image dimensions, with time along the third axis, as presented in Fig. 3. Such liquid volumes can be analysed to yield structures such as isoconstitutional surfaces,
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Fig. 3. Mushy zone + liquid volume (t,y,z), and zt-contour plots at: (a) y = 11.8 lm, interdendritic liquid to the left of primary arm 2; (b) y = 145.4 lm, close to the primary arm 2 tip centerline; (c) at y = 390.4 lm, close to the tip 3 centerline. Contouring levels are identical to those of Fig. 2.
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Fig. 4. (yz) plan-view of absolute solid liquid interface coordinates corrected for sample pulling. The black, yellow and ochre coloured curves correspond to interface coordinates at t0, t0 + 3.15, and t0 + 6.3 s, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
alternatively they can be sliced along any direction and contoured to reveal temporal variations in constitution, for example in between dendrites and at dendrite tips, as illustrated in Fig. 3, or at different depth levels in the mush. Notice in Figs. 3(a) and (b) the temporal evolutions of the local liquid constitution, where solute enrichment introduced by flow can be seen both at the dendrite tip and in the inter dendritic region. Routines have been made to allow for tracking of the solid–liquid phase front, which again opens for direct extraction of morphological details such as primary and secondary arm spacing. The relative coordinates can be put on an absolute scale by correcting for the sample pulling velocity, from which estimates of the local front propagation velocities can be assessed. In Fig. 4, the absolute coordinates corresponding to the three image frames of Fig. 1 are plotted. In plan-view one can follow directly the time evolution of secondary and ternary arms via the superposition of interface segments in the absolute coordinate system.
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Hence, eventual data extracted can not be compared directly with any detailed model for microstructure evolution. Nevertheless, by presenting here various characteristic growth quantities extracted, the potential application of SR X-ray video microscopic radiography to solidification science can be demonstrated. Velocity estimates for the dendrite tips are found straight forward as vtip,n(t) = (rtip,n(t + Dt) rtip,n(t Dt))/ 2Dt, where n = 2–4 for each of the three primary arms, respectively, and rtip,n(t) are the tip positions related to a fixed origin. In Fig. 5 the total tip velocities for primary dendrites 2, 3 and 4 are plotted against time, together with their corresponding y and z components, vtipiy,n(t) and vtipiz,n(t). The tip velocities are found to be closely parallel to z. Extremal values for vtipiy,n(t) are 10.8, 8.5 and 7.7 lm/s, for n = 2–4, respectively, that occur for each tip simultaneously with its maximum in both vtip(t) and vtipiz(t), and is partly due to tip sharpening involving slight shifts of the primary crystal centrelines. Still these velocities are rather small, corresponding to a maximal horizontal shift of the tips between consecutive frames of about 3–4.2 lm, equivalent to about 2.2–3Drnom. Tip motions along y are not completely random. Time averaged values are 0.67, 0.81, and 0.02 lm/s for vtipiy,2(t), vtipiy,3(t) and vtipiy,4(t), respectively. Hence, the long term drift along y of tips 2, 3 and 4 throughout the analysed part of the sequence are about 20 lm for tips 2 and 3, whereas tip 4 remains more or less in the same position. This drift can also be observed in Fig. 6, where temporal evolution of the primary dendrite arm spacings, k12–3(t) and k13–4(t) are plotted. Although stability analysis has shown that primary arm spacing is not uniquely fixed by growth conditions [26], k12–3 which is quite stable as a function of time, agrees reasonably well with the primary arm spacing relation proposed by Trivedi and Kurz [27],
4. Discussion In the previous section the potential for using time resolved X-ray radiography as a method for studying solidification microstructures and liquid constituents has been outlined. Both quantitative and qualitative results could be of value for demonstrations of fundamental solidification phenomena, but would also be relevant in evaluation and refinement of models on solidification microstructure evolution. In the study reported here, steady-state growth conditions were not met, and real thermal and solutal liquid velocity fields could not be handled properly without a quantitative description.
Fig. 5. Solid–liquid interface velocities. Total velocities, |vtip,n(t)|, for n = 2–4 are drawn with connected lines, whereas their orthogonal components, vtipiz(t) and vtipiy(t), are plotted as diamonds (}) and stars (*), respectively, with separate colours for each n. The eutectic front velocity, ve(t), is plotted as a connected line with triangle (n) symbols at each point.
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3–4 Fig. 6. Primary dendrite arm spacing, k2–3 1 ðtÞ (stars (*)) and k1 ðtÞ (diamonds (})).
k1 ¼ 5:98ðCDDT s Þ
0:25 a b vsl G ;
9
Fig. 7. Image at t0 + 35.55 s. Primary arms from left to right have labels n = 0–5, in accordance with those introduced in Fig. 1. At this point, arm 4 has been overrun by arm 3 and 5, and their ternary branches with its tip fully embedded in the eutectic solid.
ð2Þ
2
where Dl = 3.0 10 m /s is the solute diffusivity in the liquid, C = 2.4 · 107 Km the isotropic interface Gibbs– Thomson coefficient, and DT 0s ¼ mðC s C l Þ, with m = 3.4 K/wt% as the liquidus slope, and finally Cs and Cl as the solidus and liquidus concentrations at the denrite tip, respectively. vsl = 36.8 · 106 m/s, is the growth velocity, which has been assigned its value form the average tip velocities of arms 2 and 3. Fixing b = 0.5 in accordance with the model, yields a = 0.251, which agrees well with the model where a = 0.25 [27]. The spacing between arms 3 and 4 keeps on decreasing with time after the part of the data analysed here, and toward the end of the full image sequence, at t0 + 35.55 s, primary tip 4 has been overrun by side branching from arms 3 and 5, and gets caught up by the eutectic front, as shown in Fig. 7. Exact tracing of the interface at the primary dendrite tip is challenging. If the tip propagates with a velocity, vtip(t) = vtipiz(t)ez + vtipiy(t)ey, 1 with ey and ez as unit vectors along y and z, the geometrical smearing is Dztemp(t) = |(vtipiz(t) + vsp)|texp, and Dytemp(t) = |vtipiy(t)|texp. In this sequence vtipiz,n(t), n = 2–4, varies from 2 to 90 lm/s. Time average values for the three arms are closely similar and about 37 lm/s, giving an average temporal smearing of the tips of about 4.5 lm, but at the most extreme velocity encountered, Dztemp is as large as 20 lm. Dytemp(t) varies from 0 to 4.5 lm. Accordingly, the real resolutions obtained vary geometrically and temporally, but are predominantly determined by smearing of the dendrite tips during frame exposure. Secondly, the tips also have a 3D curvature, where con-
1 Eventual components along ex cannot be determined from the experimental data.
trast at the exact tip is vanishing since the solid fraction of the local pixel volumes approaches zero. Nevertheless, from a least-squares fitting of parabolas to the traced interface coordinates in the tip area, estimates for the tip radius of curvature, Rn(t), have been extracted. Over the transient sequence analysed Rn(t) varies between 1.5 and 22.5 lm, with its smallest values tending toward being overestimated as they approach the nominal resolution limit. The total undercooling at tip n is given by DTn(t)=DTt,n(t) + DTc,n(t) DTr,n(t), where the two first terms refer to thermal and solutal supercooling, whereas the third is a Gibbs–Thomson term accounting for the interface curvature. For Al, Cu diffusion in the solid is about four orders of magnitude slower than in the liquid, so that assuming Scheil conditions for solutal diffusion is reasonable. In several experiments with TAs [2–4] it has been demonstrated that dendrite tip kinetics in steady state is closely described by the marginal stability selection criterion [28], although strictly this criterion should be replaced by the solvability condition [5–8] which accounts properly for surface tension anisotropy. Marginal stability predicts the steady state dendrite tip to adapt to a radius of curvature dominated by diffusion rather than surface tension. Hence, in growth of an alloy constrained by this criterion, the curvature undercooling can be neglected. Furthermore, as the thermal diffusivity in both liquid and solid is typically four orders of magnitude larger than the solutal diffusion in the liquid, DTt(t) can also be neglected, leaving steady state tip kinetics in the growth of an Al–Cu alloy predominantly determined by the transport at the growing interface of Cu into the liquid. In the presence of thermo-solutal flow, however, such assumptions do not hold as both heat and solute may be transported to and from the
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tip at any given time, and not accounted for without knowledge of the spatiotemporal liquid velocities. In a purely diffusive model the solutal tip undercooling is given as DTc,n(t) = Tl mDCn(t), where Tl is the equilibrium liquidus temperature at C0 = 30wt%Cu, and DCn(t) = Cn(t) C0, where Cn(t) are the time dependent tip liquid constitutions for dendrites 2–4 extracted from the solutal contouring data (see Figs. 2–4). Strictly, Tl may be varying with time due to macro segregation, but such effects cannot be separated from experimental uncertainties such as variations in sample thickness, etc. In Fig. 8, DTc,n(t) is plotted over the range over which the constitutional analysis was restricted. Finally, DTr,n(t) = 2C/Rn(t), where C in general also should account for the surface energy anisotropy. However, assuming surface isotropy, C = 2.4 · 107 Km, which yields average and maximum curvature contributions to the undercooling of about 0.07 and 0.3 K, respectively, based on the Rn estimates. In comparison to DTc,n(t) shown in Fig. 8, DTr,n(t) is small, its average and maximum correspond to constitutional differences of about 0.02 and 0.1wt%Cu, respectively, which is equivalent to contour analysis of the liquid at levels 0.1–0.4r. Accordingly, clear evidence or disclosure of eventual curvature effects to the super cooling at the dendrite tips would require improvements in spatial but also in constitutional resolution. A comparison of estimated tip curvatures with simple stability analysis shows that Rn(t) falls closer to values given by extremum velocity, Re(V), than to values based on marginal stability, Rs(V) [28]. Indeed, averages ÆRn(t)/Re(V)æ, taken from t0, where the solutal undercooling of tip 2 is at maximum, throughout the transient period to the end of the analysis at t0 + 12.6 s, are 0.96, 1.37 and 1.07, for n = 1–3, respectively, with corresponding standard deviations of 0.6, 0.53 and 0.42.
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As illustrated in this section, state of the art SR radiography can be a valuable method for studies of solidification microstructure evolution. However it is necessary for some improvements to be made before the technique can be used to validate more detailed models for columnar dendritic growth. Enhanced spatiotemporal resolutions may not be the only route to success, although one clearly would benefit from higher sampling rates. By revisions to the Bridgman furnace it may be possible to have solidification fronts reproducible within the camera field of view, employing more favourable growth conditions at G = 1–3 K/ mm and low vsp. This should lead to coarser dendrites propagating at velocities where the temporal resolution could be sufficient to approach the nominal resolution of the detector system. The modifications to the furnace will also focus on minimizing the variations in heat transfer encountered at different sample positions.
5. Conclusion Recent advances in X-ray sources and detector systems make possible high resolution fast acquisition radiographic imaging of evolving solidification microstructures and local liquid constitutions in metal alloys. Subsequent image analysis can be used to extract the morphology and velocity of the solid–liquid interface, as well as the constitutional super cooling at the tip of the growing crystals. Improvements to the experimental setup are necessary if studies with less variant solidification conditions and at lower gradients are to be performed.
Acknowledgements The European Synchrotron Radiation Facility is acknowledged for granting beam time to experiments MI-467, HS-1332 and ME-595. This work has been funded by the Project NorLight Shaped Castings, with the following partners: Alcoa Automotive Castings, Scandinavian Casting Center ANS; Elkem Aluminium ANS; Fundo Wheels AS; Hydro Aluminium Metal Products; Hydro SA, Hydro Magnesium; the Netherlands Institute for Metals Research; NTNU; and SINTEF. The authors thank the industrial partners and the Norwegian Research Council for financial support.
Appendix A. Supplementary data
Fig. 8. Solutal supercooling DTc, n(t) at primary dendrite tips n = 2–4.
Supplementary data associated with this article can be found, in the online version at doi:10.1016/ j.actamat.2004.10.050.
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Jackson KA, Hunt JD. Acta Metall 1963;13:1212. Huang SC, Glicksman MJ. Acta Metall 1981;29:701. Esaka H, Kurz W. J Cryst Growth 1985;72:578. Somboonsuk K, Trivedi R. Acta Metall 1985;33:1051. Kessler DA, Koplik J, Levine H. Phys Rev A 1985;31:1712. Langer JS. Phys Rev A 1986;33:435. Meiron DI. Phys Rev A 1986;33:2704. Saito Y, Goldbeck-Wood G, Mu¨ller-Krumbhaar H. Phys Rev A 1988;38:2148. Murray BT, Wheeler AA, Glicksman ME. J Cryst Growth 1995;154:386. Glicksman ME, Koss MB, Winsa EA. Phys Rev Lett 1994;73:573. Lacombe JC, Koss MB, Glicksman ME. Phys Rev Lett 1999;83:573. Losert W, Shi BQ, Cummins HZ. Proc Natl Acad Sci USA 1998;95:431. Liu S, Shu-Zu L, Hellawell A. J Cryst Growith 2002;234:740. Chikama H, Shibata H, Emi T, Suzuki M. Mater Trans JIM 1996;37:620. Orrling C, Fang Y, Phinichka N, Sridhar S. J Metals E 1999;51.
[16] Koster JN. J Mater 1997;49:31. [17] Grange G, Jourdan C, Gastaldi J. J Phys D: Appl Phys 1993;26:A98. [18] Kaukler WF, Rosenberger F, Curreri PA. Metall Mater Trans A 1997;A28:1705. [19] Mathiesen RH, Arnberg L, Mo F, Weitkamp T, Snigirev A. Phys Rev Lett 1999;83:5062. [20] Mathiesen RH, Arnberg L, Ramsøskar K, Weitkamp T, Rau C, Snigirev A. Metall Mater Trans B 2002;B33:613. [21] Thi HN, Jamgotchian H, Gastaldi J, Ha¨rtwig J, Schenk T, Klein H. J Phys D: Appl Phys 2003;33:A83. [22] Yasuda H, Ohnaka I, Kawasaki K, Sugiyama A, Iwane J, Umetani K. J Cryst Growth 2004;262:645. [23] Hunt JD, Jackson KA, Brown H. Rev Sci Inst 1966;37:805. [24] Weitkamp T. Ph.D. thesis, Imaging and tomography with high resolution using coherent hard synchrotron radiation, University of Hamburg, Germany, 2002. [25] Beckermann C, Gu JP, Boettinger W. Metall Mater Trans A 2000;31:2545. [26] Warren JA, Langer JS. Phys Rev 1989;A42:3518. [27] Trivedi R, Kurz W. Met Trans 1990;A21:1311. [28] Langer JS, Mu¨ller-Krumbhaar H. Acta Metall 1978;26:1681.
X-ray radiography observations of columnar dendritic growth and constitutional undercooling in an Al–30wt%Cu alloy Ragnvald H. Mathiesen
a,*
, Lars Arnberg
b
a b
SINTEF Materials and Chemistry, Department of Applied Physics, Hogskoleringen 5, N-7465 Trondheim, Norway Department of Materials Technology, Norwegian University of Science and Technology, N-7491 Trondheim, Norway Received 27 July 2004; received in revised form 22 October 2004; accepted 27 October 2004 Available online 16 December 2004
Abstract In situ synchrotron X-ray radiography of columnar dendritic and eutectic growth under directional solidification of Al–30wt%Cu has been carried out with nominal spatial and temporal resolutions of 1.4 lm and 150 ms, respectively. The images can be processed to reveal spatiotemporal co-ordinates of the solid–liquid phase fronts for both a-dendrites and the proceeding eutectic. Also estimates for local solute boundary layers ahead of and in the mushy zone can be extracted from image processing. Steady-state growth could not be realized in the experiments. Presumably this relates to a combination of: (a) insufficient time available for initial instabilities to evolve into a steady state; (b) primary a-branches may interact through solute diffusion in the confined sample volume; (c) the inevitable presence of thermo-solutal flow; and (d) a long-term sample position dependent drift in the furnace to sample heat transfers. Nevertheless, the data collected contain information that may be valuable for microstructure modelling of dendritic growth. 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. Keywords: Synchrotron radiation; Aluminium alloys; Dendritic growth; Directional solidification; Constitutional undercooling
1. Introduction Metallurgical industries are continuously seeking to improve the efficiency and performance of their components while simultaneously reducing cost. Cast components can often be produced at considerably lower cost than wrought or machined parts; however, obtaining adequate control over the microstructure evolution during the solidification process is often a bottleneck for manufacturing components that perform as required. The final microstructure depends, in addition to alloy composition and heat-treatment, to a large extent on the thermodynamics and the kinetics of the solidification process. Accordingly, there is strong industrial and aca*
Corresponding author. Tel.: +47 73 597 052; fax: +47 73 597 040. E-mail address: [email protected] (R.H. Mathiesen).
demic motivation for a better understanding of and control over the fundamental aspects of solidification. Over the last couple of decades advanced modelling has evolved to cover many aspects of solidification science, from fundamental issues (interfacial energies, kinetics and dendritic growth in 2 or 3D) and important phenomena (porosity, fragmentation, segregation) to the numerical modelling of real casting processes – spanning length scales from the atomic to the macroscopic. While computer simulations have been firmly established on all levels, provision of new experimental data to guide theory and modelling and assist in their refinement has fallen behind. In particular there is a gap to bridge in devising experimental methods for in situ observations of metal and alloy solidification microstructures and phenomena allowing for proper assessment of kinetics.
1359-6454/$30.00 2004 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.actamat.2004.10.050
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Experimental studies of solidification microstructures in metals have mostly been conducted ex situ with samples produced by quenching the system during growth. Investigations in optical or electron microscopy must account for the effects caused to the front morphology and the solid microstructure by destabilization of the growing front and subsequent coarsening of the solid. Consequently, it can be difficult to conclude from such observations the microstructural features truly relevant only to the solidification process itself. Furthermore, such experiments reveal no direct information on dynamical aspects, which must be provided by other means, e.g., in situ calorimetry, or assigned indirectly from microstructure features such as dendrite arm spacing. In contrast, direct observations of various growth dynamics, which in many aspects are of relevance to metal solidification, has been carried out in situ on various organic model systems, the so-called transparent analogs (TAs) [1–4]. TAs can be studied under the light microscope owing to contrast arising from a shift in the optical density crossing the solid–liquid boundary. Studies in these systems have been decisive in the refinement of various theoretical/empirical models for dendritic growth leading up to the first self-consistent models for growth by diffusion from the anisotropic interface of a free dendrite [5–8]. Today, several of the most frequently applied techniques for solidification microstructure modeling are evaluated against or compared with observations obtained in studies of TAs [9]. The transparent systems have also been used to study specific topics, such as growth under extraterrestrial micro gravity conditions [10,11], growth by chemical diffusion [12] or fragmentation phenomena [13]. Despite their well-demonstrated impact on solidification science over four decades, the transparent systems are limited as full analogues to metallic systems due to differences apparent in several physicochemical quantities, such as freezing temperatures, heat capacities, chemical potentials, viscosities, solute mass gradients, and diffusion lengths, all of importance to solidification. Important effects influenced by or related to such physicochemical quantities, cannot always be transferred easily from observations in a model system to the alloy of interest. Confocal scanning laser microscopy has been used to carry out in situ studies of solidification microstructures in metals [14,15]. This technique has a limited penetration depth, enough to go through shielding oxides; furthermore, combined with monochromatic light, confocal optics effectively reduce problems associated with signal detection over a strong thermally radiated background. The use of this method in solidification science is quite recent, and more time is needed for it to demonstrate its full potential. However, being a scanning technique it will be limited in temporal resolution compared to standard video microscopy, which conse-
quently will impose limits also on its achievable spatial resolution by the blurring of rapidly evolving objects. X-ray transparency of metals has to some extent been exploited to obtain in situ information on alloy solidification fronts, microstructures, segregates and convection [16–18]. In common with this work, the spatial and in particular the temporal resolutions reported are poor compared to those obtained in microscopy on TA, due to limitations in signal-to-noise. These limitations can be related to either insufficient brightness of the X-ray source, insufficient output signal from the sample, inadequate detection efficiency, or to a combination of the three. Some setups have improved on this situation increasing the brightness by employing focusing X-ray optics [19]. Focusing decreases the degree of transversal coherence in the incident wave field, hence only the attenuating part of the X-ray optical density function can contribute to the image contrast. Such setups are therefore only applicable to systems in which the segregates that form have boundaries that can be associated with a relatively sharp transition in the X-ray attenuation. Recently, new in situ X-ray studies of solidification microstructures and phenomena in alloys have been made possible by the photon source and detector improvements provided at third generation synchrotron facilities [19–22]. These advances allow X-ray radiography to be carried out with spatiotemporal resolutions approaching true video microscopy, which was first demonstrated with the real-time imaging of various solidification modes (cells, columnar and equiaxed dendrites) for a series of Sn–Pb alloys [19]. Later, the setup was refined and used for in situ studies of several growth modes and process phenomena (dendrite fragmentation, gas porosity) in various Al–Cu alloys [20]. Here, we report on results obtained through data analysis of one particular image sequence on columnar dendritic growth in Al–30wt%Cu.
2. Experiment A description of the experimental setup and sample preparation and the more fundamental issues concerning high-energy synchrotron X-ray imaging are given in detail in [20], and references therein. Here, only a brief presentation will be given to utilize the issues most central to the analysis and discussion of the results presented. The fundamental aspects of X-ray transmission imaging is governed by the interactions of X-rays with matter [20]. Through an object transmission function, summing up the alterations of the incident wave field as it propagates through the specimen, image contrast can be related exclusively to quantities constituting the complex optical density or refractive index of the sample. The
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imaginary component relates to the attenuation of the X-ray beam by the sample, and is predominantly sensitive to constitutional variations. The real component relates to refraction of the beam which for X-rays is weak with all materials, but nevertheless sensitive to variations in density. In the sample transmitted wave field, attenuation directly affects the amplitudes, whereas refraction affects its phase components. Hence constitutional variations are visible mainly by amplitude contrast, whereas variations only in density can be studied with phase contrast. The latter, however, require an X-ray wave field with a high degree of transversal coherence; in particular since the detector resolution is five to six orders of magnitude coarser than the X-ray wavelength. Therefore, for time-resolved imaging, where high collimation at the cost of low beam intensity is unacceptable, conditions for phase contrast imaging can only be provided by bright, naturally collimated insertiondevices at third generation synchrotron sources. The experiment was carried out at the micro focusing and imaging (l-FID) beam line ID22 at the European Synchrotron Radiation Facility (ESRF) under experimental code HS-1332. In a parallel beam geometry the incident 15 keV monochromatic beam provided a wave-field at the sample with a flux of 5 · 1012 photons/(s mm2) and horizontal and vertical transverse coherence lengths of about 5 and 50 lm, respectively. A quadratic beam was defined by horizontal slits to match the full vertical width, measuring 1.35 · 1.35 mm2 at the sample position. A vertical temperature gradient stage, used to control the conditions for directional solidification, was built following the principles outlined by Hunt and et al. [23], but modified to deal with solidification temperatures up to 1200 K [20]. The samples were prepared by melting 99.999 wt% purity Al and Cu alloys in alumina crucibles and cast in an insulated, bottom-chilled mould to promote directional solidification. A region free of porosity located about 1 cm from the chill was cut into a rectangular slice measuring 1.5 · 3.0 cm2 (H · V). The slice was polished down to a thickness of 190(5) lm and pre-oxidized at 720 K for 2 h, followed with a Boron– Nitride spray coating, before being concealed into a container made by welding together two rectangular 100 lm thick quartz glass plates around the metal sheet. Upon the first melting process, the metal settled to the bottom of the container and filled it uniformly, with a thickness closely equivalent to the maximum of the original sheet, measured to be about 200 lm. Accordingly, after initial melting the vertical sample length was reduced with respect to its original size by about 2 mm. The data presented here are the second series from a total of five independent solidification experiments carried out with this particular sample. After five consecutive solidification sequences, the sample showed no signs of deterioration or decay.
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Data acquisition was carried out using a dedicated Fast Readout Low Noise (FReLoN II) high-resolution X-ray microscope [20,24]. The microscope consists of a thin X-ray to visible light converting transparent absorptive–emissive screen (Te or Eu doped Lu3Al4.4Sc0.6O12), placed in the X-ray beam in the front focal plane of a lens system. The microscopeÕs rear focal plane falls onto a custom made 4.2 M pixel CCD with a physical pixel size of 14 lm and a dynamical range of 14 bits, i.e., 16 384 grey levels. The CCD can be readout as four separate channels and transferred by optical fibres directly to computer memory. The highest nominal spatial resolution of the system, Drnom, is about 0.6 lm with a readout dead time, tro 300 ms. For time-resolved imaging, a 2 · 2 hardware rebinning of the CCD allows both for shorter exposure times and shorter readout dead time at the cost of a poorer spatial resolution; nominal features for the rebinned mode are Drnom 1.2 lm with tro 150 ms. These are available only in the highest spatial resolution mode employing a 3.5 lm thin luminescent screen at the highest magnification available, resulting in a field of view of about 0.7 · 0.7 mm2 and a detection quantum efficiency of about 4%. In this study, a 12 lm thick screen with about 7% efficiency was employed together with a lower magnification to have better photon statistics at short exposure times. The thicker screen introduce a slight aberration, Drnom 1.4 lm, but since steady-state growth was not realised in the experiment, the spatial resolution was limited by the smearing of details, or temporal blurring, Drtemp = texpvs, where texp is the exposure time, and vs is the local propagation velocity of the solid relative to the imaging system. The field of view obtained was about 1.4 · 1.4 mm2, closely similar to a full quadratic beam cross section. For the solidification sequence presented here a thermal gradient, G = 27 K/mm, was imposed over the sample, in parallel to gravity, g. In general, the top down directional approach is thermally less stable than the conventional opposite, antiparallel with g. The primary source for bouyancy flow is by the solutal gradient for which a Rayleigh number can be derived as, Ras ¼
ðDq=q0 ÞgL3 ; vDl
ð1Þ
where (Dq/q0) 4.2 · 102 is the solutal density gradient relative to the 30wt%Cu density, L = 200 lm is a critical length corresponding to the sample thickness, v = 6 · 107 m2/s is the kinematic viscosity and Dl = 3 · 109 is the solute diffusion coefficient in the liquid. Numeric evaluation yields Ras 1800, corresponding to a solutal flow at the verge of what is normally considered necessary to establish sustainable convection rolls, yet definitely large enough to create significant solutal imbalance. Alternatively, the driving force for solutal flow can be quantified in terms of
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characteristic microstructure lengths following the model proposed by Beckermann et al. [25], modifying it to the particular experimental geometry where L3 in Eq. (1) is replaced by F(fs)k1ltL, with L as the sample thickness, F(fs) as a function of the fraction solid accounting for change in the mush permeability (modified to handle permeability drop only in one dimension), k1 as the primary dendritic arm spacing, and lt as the characteristic length of the solidification interval, gives Ras 1650. The corresponding thermal flow is negligible for the vertical thermal gradient, but the slightly curved shape of the isotherms may result in thermally driven flow. However quantifying this effect is difficult and will not be attempted here. Curved isotherms were also observed in the upwards directed solidification geometry. In fact, out of a total of 200 directional solidification sequences with this system, we did not find it significantly easier to obtain steady state by solidifying in either of the two opposite directions. The applied exposure, texp = 0.3 s/frame. The sample was solidified from the melt, initially positioned with its upper edge just below the cold furnace at T = 748 K in contact only with the hot furnace at T = 882 K. Pushing the sample at constant velocity, vsp = 22.4 lm/s, directed opposite to G, multiple nuclei would form and hopefully evolve into a columnar front propagating parallel to G, originating from one nucleus selected by competing kinetics. The sample was monitored online at the pre-calibrated position, with acquisition of images starting as soon as the solidification front appeared in the field of view. The computer memory configuration allowed for the acquisition of 120 consecutive frames.
3. Results Fig. 1 shows three frames of the columnar dendritic solidification series collected with the Al–30wt%Cu alloy. Contrast from the internal dendrite structures and liquid segregates are caused mainly by absorption. The bright horizontally oriented lines seen in all frames are eutectic fronts, which are provided by phase contrast as constructive interference fringes from beams refracted differently across the eutectic solid–liquid boundary due to the density difference between the aggregates. At the dendrite–liquid interface both attenuation and refraction contribute to the contrast. In Fig. 1 it can be seen that the eutectic interface normal varies slightly along the horizontal direction indicating isotherms not to be fully perpendicular to the imposed thermal gradient. This effect can probably be ascribed to a combination of thermo-solutal flow and a slightly larger heat transfer at the outer sample edges. The centre of the sample is roughly 0.5 mm to the right of the image sequence field of view. Assuming local equilibrium at the solid–liquid
Fig. 1. Columnar dendritic and eutectic growth in Al–30wt%Cu. Primary arms are labelled 1–5 from left to right in the images: (a) at t0; (b) at t0 + 3.15, or 7 frames later; (c) at t0 + 6.3 s, or 14 frames later. G and gravitation, g, are parallel upward, while vsp is downward.
interfaces this horizontal gradient can be estimated to be about 1.2 K/mm from the sample centre and outwards horizontally to both sides. This shape was pre-
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served throughout the 120 frames collected in this particular sequence, and similar observations were done in other sequences with this and other samples. The images shown in Fig. 1 have been flattened by a beam structure reference image, and then stretched in a non-linear manner that reserve most of its dynamical range to liquid contrast. The darker bands surrounding the primary crystal phase front is due to local Cu-enrichment. In order to analyze supercooling quantitatively, however, other image processing routes are required. The primary challenge in a quantitative analysis of chemical gradients lies in phase separation. In the full solid–liquid frame up to 70% of the contrast range available in a flattened and linearly stretched image can be assigned to the difference in transmission between primary a crystals solidifying with 5.3wt%Cu, and the other regions which either contain liquid of constitutions between 30wt%Cu and a eutectic at 33.1wt%Cu, or a eutectic solid. Indeed, if the primary crystals are considered to fully span the container along the beam path, x, so that all domain boundaries are fully resolved in the 2D image plane, the 15 keV X-ray transmissions through 200 lm are 0.966, 0.292 and 0.24 for 5.7wt%Cu (max a solid solubility at Te), 30wt%Cu and 33.1wt%Cu domains respectively, relative to a domain of primary crystals at 5.3wt%Cu (Tl 832 K). Hence, only about 6.5% contrast is left for liquid constitution analysis. In order to retrieve this information, an image processing procedure has been devised where the first part concerns tracking of the a and eutectic solid–liquid boundaries, and then to employ this information to create a binary mask that can be used to separate the aggregates. Setting pixels associated with solid domains to zero by use of the binary mask, the liquid pixels may be smoothed and filtered without having to be smeared by solid pixels, also with a full dynamical range available to liquid contrast with all subsequent operations on contrast being linear and reversible. In Fig. 2 liquid constitution contour plots of mushy zones around primary arms 2, 3 and 4 plus regions that extend deeper into the liquid are presented for the three frames of Fig. 1. An increment at every 0.5wt%Cu corresponds closely to a 2.3r contouring level. The analysis has been restricted to a region which falls within the full width half maximum plateau for the incident beam profile. Extending outside this region to pixels positioned further away from the image centre, analysis becomes less accurate, due to weaker beam illuminations and correspondingly poorer statistics. The images of Figs. 1 and 2 have been selected to demonstrate a part of the sequence where the solute boundary ahead of arm 2 has just been altered rapidly by a plume flowing out of the inter dendritic region, leading to a substantial increase in super cooling at the local front, as shown in Fig. 2(a). Fig. 2(b) and (c) shows the subsequent evolution of the solute layers and solid– liquid interface.
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Fig. 2. Mushy zone liquid constitution contour plots. Solid regions are white, liquid contours start at 33wt%Cu (black) with increments of 0.5wt%Cu (corresponding roughly to a 2.3r contouring) up to the deep-in liquid constitution at 30wt%Cu. The frame region presents primary arms 2–4 (left to right) in Fig. 1 with: (a) at t0; (b) at t0 + 3.15, or 7 frames later; (c) at t0 + 6.3 s, or 14 frames later.
Images phase filtered by binary masks can be combined into 3D volumes, spanned by the two spatial image dimensions, with time along the third axis, as presented in Fig. 3. Such liquid volumes can be analysed to yield structures such as isoconstitutional surfaces,
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Fig. 3. Mushy zone + liquid volume (t,y,z), and zt-contour plots at: (a) y = 11.8 lm, interdendritic liquid to the left of primary arm 2; (b) y = 145.4 lm, close to the primary arm 2 tip centerline; (c) at y = 390.4 lm, close to the tip 3 centerline. Contouring levels are identical to those of Fig. 2.
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Fig. 4. (yz) plan-view of absolute solid liquid interface coordinates corrected for sample pulling. The black, yellow and ochre coloured curves correspond to interface coordinates at t0, t0 + 3.15, and t0 + 6.3 s, respectively. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
alternatively they can be sliced along any direction and contoured to reveal temporal variations in constitution, for example in between dendrites and at dendrite tips, as illustrated in Fig. 3, or at different depth levels in the mush. Notice in Figs. 3(a) and (b) the temporal evolutions of the local liquid constitution, where solute enrichment introduced by flow can be seen both at the dendrite tip and in the inter dendritic region. Routines have been made to allow for tracking of the solid–liquid phase front, which again opens for direct extraction of morphological details such as primary and secondary arm spacing. The relative coordinates can be put on an absolute scale by correcting for the sample pulling velocity, from which estimates of the local front propagation velocities can be assessed. In Fig. 4, the absolute coordinates corresponding to the three image frames of Fig. 1 are plotted. In plan-view one can follow directly the time evolution of secondary and ternary arms via the superposition of interface segments in the absolute coordinate system.
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Hence, eventual data extracted can not be compared directly with any detailed model for microstructure evolution. Nevertheless, by presenting here various characteristic growth quantities extracted, the potential application of SR X-ray video microscopic radiography to solidification science can be demonstrated. Velocity estimates for the dendrite tips are found straight forward as vtip,n(t) = (rtip,n(t + Dt) rtip,n(t Dt))/ 2Dt, where n = 2–4 for each of the three primary arms, respectively, and rtip,n(t) are the tip positions related to a fixed origin. In Fig. 5 the total tip velocities for primary dendrites 2, 3 and 4 are plotted against time, together with their corresponding y and z components, vtipiy,n(t) and vtipiz,n(t). The tip velocities are found to be closely parallel to z. Extremal values for vtipiy,n(t) are 10.8, 8.5 and 7.7 lm/s, for n = 2–4, respectively, that occur for each tip simultaneously with its maximum in both vtip(t) and vtipiz(t), and is partly due to tip sharpening involving slight shifts of the primary crystal centrelines. Still these velocities are rather small, corresponding to a maximal horizontal shift of the tips between consecutive frames of about 3–4.2 lm, equivalent to about 2.2–3Drnom. Tip motions along y are not completely random. Time averaged values are 0.67, 0.81, and 0.02 lm/s for vtipiy,2(t), vtipiy,3(t) and vtipiy,4(t), respectively. Hence, the long term drift along y of tips 2, 3 and 4 throughout the analysed part of the sequence are about 20 lm for tips 2 and 3, whereas tip 4 remains more or less in the same position. This drift can also be observed in Fig. 6, where temporal evolution of the primary dendrite arm spacings, k12–3(t) and k13–4(t) are plotted. Although stability analysis has shown that primary arm spacing is not uniquely fixed by growth conditions [26], k12–3 which is quite stable as a function of time, agrees reasonably well with the primary arm spacing relation proposed by Trivedi and Kurz [27],
4. Discussion In the previous section the potential for using time resolved X-ray radiography as a method for studying solidification microstructures and liquid constituents has been outlined. Both quantitative and qualitative results could be of value for demonstrations of fundamental solidification phenomena, but would also be relevant in evaluation and refinement of models on solidification microstructure evolution. In the study reported here, steady-state growth conditions were not met, and real thermal and solutal liquid velocity fields could not be handled properly without a quantitative description.
Fig. 5. Solid–liquid interface velocities. Total velocities, |vtip,n(t)|, for n = 2–4 are drawn with connected lines, whereas their orthogonal components, vtipiz(t) and vtipiy(t), are plotted as diamonds (}) and stars (*), respectively, with separate colours for each n. The eutectic front velocity, ve(t), is plotted as a connected line with triangle (n) symbols at each point.
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3–4 Fig. 6. Primary dendrite arm spacing, k2–3 1 ðtÞ (stars (*)) and k1 ðtÞ (diamonds (})).
k1 ¼ 5:98ðCDDT s Þ
0:25 a b vsl G ;
9
Fig. 7. Image at t0 + 35.55 s. Primary arms from left to right have labels n = 0–5, in accordance with those introduced in Fig. 1. At this point, arm 4 has been overrun by arm 3 and 5, and their ternary branches with its tip fully embedded in the eutectic solid.
ð2Þ
2
where Dl = 3.0 10 m /s is the solute diffusivity in the liquid, C = 2.4 · 107 Km the isotropic interface Gibbs– Thomson coefficient, and DT 0s ¼ mðC s C l Þ, with m = 3.4 K/wt% as the liquidus slope, and finally Cs and Cl as the solidus and liquidus concentrations at the denrite tip, respectively. vsl = 36.8 · 106 m/s, is the growth velocity, which has been assigned its value form the average tip velocities of arms 2 and 3. Fixing b = 0.5 in accordance with the model, yields a = 0.251, which agrees well with the model where a = 0.25 [27]. The spacing between arms 3 and 4 keeps on decreasing with time after the part of the data analysed here, and toward the end of the full image sequence, at t0 + 35.55 s, primary tip 4 has been overrun by side branching from arms 3 and 5, and gets caught up by the eutectic front, as shown in Fig. 7. Exact tracing of the interface at the primary dendrite tip is challenging. If the tip propagates with a velocity, vtip(t) = vtipiz(t)ez + vtipiy(t)ey, 1 with ey and ez as unit vectors along y and z, the geometrical smearing is Dztemp(t) = |(vtipiz(t) + vsp)|texp, and Dytemp(t) = |vtipiy(t)|texp. In this sequence vtipiz,n(t), n = 2–4, varies from 2 to 90 lm/s. Time average values for the three arms are closely similar and about 37 lm/s, giving an average temporal smearing of the tips of about 4.5 lm, but at the most extreme velocity encountered, Dztemp is as large as 20 lm. Dytemp(t) varies from 0 to 4.5 lm. Accordingly, the real resolutions obtained vary geometrically and temporally, but are predominantly determined by smearing of the dendrite tips during frame exposure. Secondly, the tips also have a 3D curvature, where con-
1 Eventual components along ex cannot be determined from the experimental data.
trast at the exact tip is vanishing since the solid fraction of the local pixel volumes approaches zero. Nevertheless, from a least-squares fitting of parabolas to the traced interface coordinates in the tip area, estimates for the tip radius of curvature, Rn(t), have been extracted. Over the transient sequence analysed Rn(t) varies between 1.5 and 22.5 lm, with its smallest values tending toward being overestimated as they approach the nominal resolution limit. The total undercooling at tip n is given by DTn(t)=DTt,n(t) + DTc,n(t) DTr,n(t), where the two first terms refer to thermal and solutal supercooling, whereas the third is a Gibbs–Thomson term accounting for the interface curvature. For Al, Cu diffusion in the solid is about four orders of magnitude slower than in the liquid, so that assuming Scheil conditions for solutal diffusion is reasonable. In several experiments with TAs [2–4] it has been demonstrated that dendrite tip kinetics in steady state is closely described by the marginal stability selection criterion [28], although strictly this criterion should be replaced by the solvability condition [5–8] which accounts properly for surface tension anisotropy. Marginal stability predicts the steady state dendrite tip to adapt to a radius of curvature dominated by diffusion rather than surface tension. Hence, in growth of an alloy constrained by this criterion, the curvature undercooling can be neglected. Furthermore, as the thermal diffusivity in both liquid and solid is typically four orders of magnitude larger than the solutal diffusion in the liquid, DTt(t) can also be neglected, leaving steady state tip kinetics in the growth of an Al–Cu alloy predominantly determined by the transport at the growing interface of Cu into the liquid. In the presence of thermo-solutal flow, however, such assumptions do not hold as both heat and solute may be transported to and from the
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tip at any given time, and not accounted for without knowledge of the spatiotemporal liquid velocities. In a purely diffusive model the solutal tip undercooling is given as DTc,n(t) = Tl mDCn(t), where Tl is the equilibrium liquidus temperature at C0 = 30wt%Cu, and DCn(t) = Cn(t) C0, where Cn(t) are the time dependent tip liquid constitutions for dendrites 2–4 extracted from the solutal contouring data (see Figs. 2–4). Strictly, Tl may be varying with time due to macro segregation, but such effects cannot be separated from experimental uncertainties such as variations in sample thickness, etc. In Fig. 8, DTc,n(t) is plotted over the range over which the constitutional analysis was restricted. Finally, DTr,n(t) = 2C/Rn(t), where C in general also should account for the surface energy anisotropy. However, assuming surface isotropy, C = 2.4 · 107 Km, which yields average and maximum curvature contributions to the undercooling of about 0.07 and 0.3 K, respectively, based on the Rn estimates. In comparison to DTc,n(t) shown in Fig. 8, DTr,n(t) is small, its average and maximum correspond to constitutional differences of about 0.02 and 0.1wt%Cu, respectively, which is equivalent to contour analysis of the liquid at levels 0.1–0.4r. Accordingly, clear evidence or disclosure of eventual curvature effects to the super cooling at the dendrite tips would require improvements in spatial but also in constitutional resolution. A comparison of estimated tip curvatures with simple stability analysis shows that Rn(t) falls closer to values given by extremum velocity, Re(V), than to values based on marginal stability, Rs(V) [28]. Indeed, averages ÆRn(t)/Re(V)æ, taken from t0, where the solutal undercooling of tip 2 is at maximum, throughout the transient period to the end of the analysis at t0 + 12.6 s, are 0.96, 1.37 and 1.07, for n = 1–3, respectively, with corresponding standard deviations of 0.6, 0.53 and 0.42.
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As illustrated in this section, state of the art SR radiography can be a valuable method for studies of solidification microstructure evolution. However it is necessary for some improvements to be made before the technique can be used to validate more detailed models for columnar dendritic growth. Enhanced spatiotemporal resolutions may not be the only route to success, although one clearly would benefit from higher sampling rates. By revisions to the Bridgman furnace it may be possible to have solidification fronts reproducible within the camera field of view, employing more favourable growth conditions at G = 1–3 K/ mm and low vsp. This should lead to coarser dendrites propagating at velocities where the temporal resolution could be sufficient to approach the nominal resolution of the detector system. The modifications to the furnace will also focus on minimizing the variations in heat transfer encountered at different sample positions.
5. Conclusion Recent advances in X-ray sources and detector systems make possible high resolution fast acquisition radiographic imaging of evolving solidification microstructures and local liquid constitutions in metal alloys. Subsequent image analysis can be used to extract the morphology and velocity of the solid–liquid interface, as well as the constitutional super cooling at the tip of the growing crystals. Improvements to the experimental setup are necessary if studies with less variant solidification conditions and at lower gradients are to be performed.
Acknowledgements The European Synchrotron Radiation Facility is acknowledged for granting beam time to experiments MI-467, HS-1332 and ME-595. This work has been funded by the Project NorLight Shaped Castings, with the following partners: Alcoa Automotive Castings, Scandinavian Casting Center ANS; Elkem Aluminium ANS; Fundo Wheels AS; Hydro Aluminium Metal Products; Hydro SA, Hydro Magnesium; the Netherlands Institute for Metals Research; NTNU; and SINTEF. The authors thank the industrial partners and the Norwegian Research Council for financial support.
Appendix A. Supplementary data
Fig. 8. Solutal supercooling DTc, n(t) at primary dendrite tips n = 2–4.
Supplementary data associated with this article can be found, in the online version at doi:10.1016/ j.actamat.2004.10.050.
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