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Rapid solidification of Al-Cu eutectic alloy by laser remelting
Acta metall. Vol. 37, No. 12, pp. 3305-3313. 1989
0001-6160/89 $3.00 + 0.00 Copyright © 1989 Pergamon Press plc
Printed in Great Britain. All rights reserved
RAPID SOLIDIFICATION OF A1-Cu EUTECTIC ALLOY BY LASER R E M E L T I N G M. Z I M M E R M A N N l, M. C A R R A R D z and W. K U R Z t ~Department of Materials, Swiss Federal Institute of Technology, 1007 Lausanne and 2Department of Physics, Swiss Federal Institute of Technology, 1015 Lausanne, Switzerland (Received 12 April 1989)
Abstract--Rapid surface resolidification using a high powered CO2-1aser has been performed on eutectic A1-32.7 wt% Cu at speeds between 0.2 and 8 m/s. By means of longitudinal cuts through the centre of the laser trace, the local growth rate has been measured by observation of the orientation of the microstructure using transmission electron microscopy. The various microstructures as a function of growth rate, are: (a) regular lamellar eutectic ~t-Al/0 AlzCu structure for growth rates below 20 cm/s with interlamellar spacing as fine as 17 nm; (b) a new wavy eutectic ~-AI/0'--A12Cu morphology for growth rates of between 20 and 50 cm/s; (c) a banded structure formed by alternating supersaturated ct-Al solid solution and the wavy eutectic for growth rates greater than 50 cm/s. A recent analytical model for eutectic growth under rapid solidification condition is compared to the experimental results. Contrary to the classical 22V~ = const, relationship, which predicts a continuous decrease in spacing as the growth rate increases, this new theoretical model clearly predicts a limit for the coupled eutectic growth which finds its analogy in single phase solidification in the limit of absolute stability. R6sum6--De la resolidification rapide superficielle avec un laser CO2 de haute puissance a 6t6 effectu6e sur un eutectique AI-32.7% pds Cu fi des vitesses comprises entre 0.2 et 8 m/s. A l'aide de coupes longitudinales au centre de la trace laser, la vitesse locale de croissance a pu 6tre mesur6e en observant par microscopie 61ectronique ~i transmission l'orientation de la microstructure. En fonction de la vitesse de croissance les diverses microstructures obtenues sont: (a) une structure eutectique lamellaire r6guli6re ~t-A1/0-AI2Cu pour des vitesses de croissance inf6rieures fi 20 cm/s avec un espacement interlamellaire aussi fin que 17 nm; (b) une nouvelle morphologie eutectique ondul6e ~t-AI/0'-A12Cu pour des vitesses de croissance comprises entre 20 cm/s et 50 cm/s; (c) une structure en bandes, pour des vitesses de croissance sup+rieures b. 50 cm/s, form6e alternativement par une solution solide ct-Al sursatur6e et par l'eutectique ondul6. Un mod61e analytique r6cent de la croissance eutectique fi haute vitesse est compar6 aux r6sultats exp6rimentaux. Contrairement a la relation classique 22 Vs = cte, qui pr6dit une diminution continue de l'espacement lorsque la vitesse de croissance augmente, ce nouveau mod61e th6orique pr6dit clairement une limite pour la croissance eutectique coupl6e qui peut 6tre compar6e fi la limite de stabilit6 absolue lors d'une croissance monophas6e. Zusammenfassung--Mittels eines Hochleistungs-CO2-Lasers wurde eine eutektische A1-32.7 Gew% Cu-Legierung bei Geschwindigkeiten von 0.2 bis 8 m/s umgeschmolzen. Anhand von longitudinalen Schnitten durch die Spurmitte wurde im Transmissionselektronenmikroskop die lokale Geschwindigkeit der Erstarrungsfront ermittelt. In Abhfingigkeit von dieser Wachstumsgeschwindigkeit wurden verschiedene Gef6ge beobachtet; (a) regulfires lamellares Wachstum des ct-Al/0-A12Cu-Eutektikums bei Wachstumsgeschwindigkeit unter 20 cm/s mit einem minimalen Phasenabstand von 17 nm; (b) eine neue wellige eutektische ~-A1/0'-A12Cu-Struktur zwischen 20 and 50 cm/s; (c) ein Gefiige, das aus alternierenden Bfindern yon total fibers/ittigter ~-AI Phase und welligem Eutektikum besteht bei Geschwindigkeiten gr6sser als 50 cm/s. Die experimentellen Ergebnisse werden mit einem vor kurzem entwickelten Modell raschen eutektischen Wachstums verglichen. Im Gegensatz zur bekannten 22 V, = konst.-Beziehung, die eine unbegrenzte Abnahme des Lamellenabstandes mitder Wachstumsgeschwindigkeit voraussagt, fiihrt dieses neue Modell zu einer Grenzgeschwindigkeit des eutektischen Wachstums, die der Grenze der absoluten Stabilit~it im Fall einphasiger Erstarrung entspricht.
INTRODUCTION It is n o w well k n o w n that the rapid solidification of alloys permits the extension o f solubility limits a n d refinement of the scale of a microstructure, a n d often leads to the a p p e a r a n c e of n o n - e q u i l i b r i u m phases. These effects are potentially useful for practical applications. R a p i d solidification o f alloys of eutectic c o m p o s i t i o n is especially interesting as such alloys can exhibit very fine two-phase structures a n d in some cases, also a m o r p h o u s phases.
Several authors have studied the effect of high cooling rates on the microstructure of the A1-Cu eutectic alloy. This binary eutectic is widely used as a model system because of its well-defined physical c o n s t a n t s a n d its regular eutectic growth morphology. By using rapid cooling techniques, various m o r p h o l o gies of the A1-Cu eutectic alloy were f o u n d with increasing cooling rate: lamellar structures with spacings decreasing to some tens o f n a n o m e t r e s [1-3], a degenerate eutectic m o r p h o l o g y [1, 2], a dendritic/cellular structure with microsegregation [3, 4], a
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banded structure [1, 4], a supersaturated solid solution [1-3, 5J and finally an amorphous A1-Cu phase [6]. The mechanism for the appearance of the various microstructures as a function of cooling rate are currently not well defined. The reason is that the cooling rate is a lumped parameter which cannot be simply related to the observed microstructure. Moreover, with rapid cooling techniques such as splatquenching or melt-spinning, the heat transfer coefficients and the nucleation temperature remain difficult to determine quantitatively and are the subject of some disagreement concerning the interpretation of the observed microstructures [7, 8]. Surface treatments, using high-energy laser or electron-beams, overcome this difficulty because the liquid pool is in contact with its own solid, and solidification therefore does generally not involve nucleation. Furthermore, the morphology and scale of eutectic microstructures depend mainly upon the growth rate (rate of interface advance) and the influence of the thermal gradient can be neglected. In surface resolidification, the local growth rate can be determined quantitatively and this allows the comparison of experimental results with theoretical models of rapid solidification. The local growth rate is obtained by taking a longitudinal section through the center-line of the remelted trace, see Fig. 1, and by measuring the orientation of the microstructure, which tends to be perpendicular to the local solid-liquid interface, with respect to the direction of beam displacement. The relationship between the beam rate, Vb, and the local growth rate, G , is simply V~= Vb cos 0
(1)
where 0 is the angle between the vectors representing Vs (parallel to the microstructure) and Vb (parallel to the surface), as shown in Fig. l(b). Between the bottom and the top of a trace, the solidification rate varies from zero to a maximum beam
axis
,
(a)
V b (beam rate)
(b)
Fig. 1. (a) Typical form of the molten pool during laser treatment at high speeds. (b) At the centre-plane of the remelted trace, the solidification rate, Vs, and the beam rate, Vb, are related via the angle, 0.
which depends upon the size and shape of the melt pool, which themselves depend upon the processing conditions [9]. Therefore, with just one experiment performed at high scanning rate one can obtain a whole series of data as a function of growth rate. Various theoretical predictions of the resultant eutectic microstructures have been made but, until recently, only models developed under low P6clet number assumption, for example by Jackson and Hunt [10], were available. (The P6clet number, P, is defined as the ratio of a microstructural length, 2, to a diffusive length, 2 D / V s , where 2 is the interlamellar spacing and D is the diffusion coefficient of solute in the liquid.) These models, which are valid for low to medium growth rates, predict that the interlamellar spacing is related to the solidification rate via a 22V~ = const, relationship. Recently, Trivedi et al. [11] have developed a model (TMK model) for eutectic growth at high velocities. This model predicts that 22 Vs is no longer constant at high solidification rates, and that an upper limiting velocity exists for the formation of a regular, coupled eutectic structure. Several investigations have been carried out using directional solidification experiments [12-15]. However, the highest growth rates in such experiments are limited, for technical reasons, to some millimetres per second. To the present author's knowledge, no quantitative experiments on the rapid solidification of AI-Cu eutectic alloy have been carried out using a laser or electron beam. The aim of the present paper is to report experimental results on the morphological evolution and the scale of the microstructure of an A1-32.7 wt% Cu eutectic alloy, rapidly solidified by laser treatment, as a function of the growth rate. The high solidification rates (several meters per second) which are attainable using laser surface treatment, permit the verification of the existence of such a limit to coupled eutectic growth. EXPERIMENTAL
The AI-32.7 wt% Cu eutectic alloy was produced by melting the 99.99wt% pure components in a graphite crucible. The alloy was then cast into a cylindrical copper mould with an inside diameter of 40 mm and a height of 100 mm. In order to eliminate inhomogeneities at the surface and possible contamination from the mould, the samples were machined down to 34 mm in diameter. Before laser treatment, the samples were polished using 1000 grit SiC paper in order to enhance absorption of the laser beam as well as to ensure the same surface quality for each sample. The experiments were carried out using a continuous wave CO2-1aser with a nominal power of 1000W or 1500W. The laser beam was focused, using a parabolic copper mirror, to give a spot diameter of 240 #m. This corresponded to a power intensity of 2.2.106 W/cm 2 or 3.3- 106 W/cm 2, respectively. Controlled-velocity surface melting of single traces was carried out by rotating the cylindrical
ZIMMERMANN et al.:
RAPID SOLIDIFICATION BY LASER REMELTING
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b
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Fig. 2. Preparation of the longitudinal sections for TEM observations (shown is a transverse section of the laser trace). (a) Deposition of a nickel layer. (b) Mechanical polishing up to the centre of the trace. (c) One-side etching of the disc, from left to right (S = protecting shellac). specimen on its axis at peripheral speeds, lib, between 0.2 and 8 m/s. The laser beam was oriented at normal incidence to the specimen surface. As the as-cast microstructure was already fine (interlamellar spacing of about 1 #m), no laser pre-treatment was necessary in order to homogenize the material. Even at the highest peripheral velocity, optical metallographic examinations of the surface showed that the molten pool shape has reached a stationary state. During the laser treatment, a continuous flow of He (3 l/min) was blown onto the surface through a pipe of 5 mm diameter in order to reduce oxidation of the molten pool. As mentioned above, transmission electron microscopic (TEM) observations of a longitudinal section through the centre of the trace permit direct measurements of both the interlamellar spacing and the local growth rate. In order to prepare these thin longitudinal sections, a nickel layer (approx. 2 m m thick) was electrolytically deposited onto the treated surface, using the technique described by D u p o n t e t al. [16] [see Fig. 2(a)]. The sample was then mechanically polished until the centre of the trace was reached [Fig. 2(b)]. Disks which were 3 m m in diameter and 0.3 m m thick were then extracted by spark machining. The electrolytic thinning of these sections was performed in two successive stages. Firstly, the side which contained the laser trace was protected with shellac (lacomit) and then thinned from the opposite side [Fig. 2(c)] in order to obtain a regular hole at the interface between aluminium and nickel (polishing 1). Secondly, after removing the shellac, slight thinning from this side was necessary in order to achieve a perfect electron-transparent area over the laser trace (polishing 2). The thinning conditions for these two steps are given in Table 1. For the purpose of qualitative observations of the microstructure, sections in the X Y plane and close to the surface [see Fig. l(a)] were also studied.
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Table 2. Experimentalvalues of melt pool depth, d, and width, w, as a function of power and beam rate No. Power(W) Vb (m/s) Depth(•m) Width(pm) 1 2 3 4 5 6 7 8 9 10 11 12 13
1500 1500 1500 1500 1500 1500 1500 1500 1500 1000 1000 1000 1000
0.2 0.3 0.4 0.6 0.8 1 2 5 8 0.8 I 2 4
130 120 100 90 70 70 50 20 5 15 55 50 35 15-25
350 320 300 290 260 240 200 170 140 150 220 210 180 110-150
The T E M observations were performed using an Hitachi H700H microscope operating at 200 kV. RESULTS The depth, d, and width, w, of various single laser traces are shown in Table 2. Laser traces with depths of less than 20/~m are not continuous along the length of the sample; thus limiting the upper peripheral speed, Vu, to about 5 m/s. The maximum growth rate can differ significantly from the beam rate; especially at high peripheral speeds [9, 17]. The maximum growth rate which was obtained under the above mentioned limiting conditions was estimated, using heat flow models, to be of the order of 2 m/s. The sequence of the occurrence of the various observed microstructures is given schematically in Fig. 3. At the interface between the laser trace and the non-treated base material, the resolidifying eutectic branches out from the A12Cu phase, as shown in Fig. 4(a). The new eutectic structure begins to grow like a bundle but, after a few microns, only those lamellae lying parallel to the heat flow direction survive. This figure also reveals a rapid decrease in spacing, from
Table I. Thinning conditions Electrolyte TemperatureCC) Potential (V) Polishing 2 Polishing I
300 ml HNO~ 600 ml CH3OH 600 ml CH3OH 300 ml C4H 10O 60 ml HCIO4
- 20
1I
- 30
35
Fig. 3. Schematic representation of the various microsctructures observed on a longitudinal section of A1 32.7 wt% Cu surface material, laser treated at high beam rates (VD > 1 m/s).
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(a)
Fig. 4. Various microstructures observed by TEM. (a) Transition between treated and non-treated zones. White lamellae are the ~-AI phase and black lamellae are the 0-A12Cu phase. (b) Finest eutectic spacing observed at Vs = 20 cm/s. (c) Wavy eutectic structure. This structure appears in A1-32.7 wt% Cu, under the present conditions, at solidification rates of between 20 cm/s and 50 cm/s. 1 # m in the non-treated zone to about 50 nm at a distance of about 3 p m into the resolidified zone. This corresponds to an extremely rapid increase in growth rate, from zero to some centimetres per second, over a few microns. At solidification rates of below 20 cm/s, the microstructure consists of parallel lamellae. As the surface is approached, i.e. as the growth rate increases, these eutectic lamellae tend to reorient themselves into the laser beam scanning direction and the interlamellar spacing decreases. In this zone, for various peripheral velocities and laser powers, the experimental values of 2 a n d Vs follow a 2 2 V s = c o n s t . relationship. The minimum eutectic spacing, observed at Vs = 20 cm/s, is 17 nm; as shown in Fig. 4(b).
Above a solidification rate of about 20 cm/s, the eutectic lamellar structure becomes more and more wavy. The typical microstructure of this undulating eutectic morphology is shown in Fig. 4(c). The form of this structure is difficult to quantify but the waves seem to oscillate out of phase. As the growth rate increases, the amplitude of these waves increases, but the wavelength (in growth direction) remains more or less constant at about 50 nm. The mean interlamellar spacing varies from about 17-20 nm at Vs = 20 cm/s to a maximum spacing near to 40 nm when the growth rate reaches a value of 50 cm/s. Inspite of these undulations, the overall orientation of the microstructure with respect to the scanning direction is still measurable. This therefore permits the determination of the corresponding solidification rate.
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Electron diffraction patterns from this zone indicate the presence of the ~-A1 phase and the 0-AlzCu phase, as in the first zone, but also the appearance of the 0' phase which has the same morphology as the eutectic 0-A12Cu phase. Weak spots, due to precipitation of the metastable 0" phase, also appear. As the growth rate increases, the metastable 0' phase (as the second eutectic phase) predominates over the stable 0 phase. Note that the crystallography of this observed 0' phase is the same as that observed for conventional precipitation. For the alloys examined here, there is a second critical growth rate (of about 50 cm/s) at which the continuous wavy eutectic structure disappears and bands, lying approximately parallel to the solid-liquid interface, appear. This transition occurs very abruptly, as shown in Fig. 5, in contrast to the more gradual transition between the regular and wavy eutectic structures. As can be seen in this figure, the wavy microstructure which precedes the onset of the bands is made up of fine oriented grains (dark and light regions), while the banded structure is monocrystalline over large areas, including several bands. The spacing between these bands is approximately constant around a value of 0.8 #m but, as the growth rate increases, the relative volume fraction of the light bands tends to increase. In the direction of growth, the transition from white to dark bands is
Fig. 6. (a) Diffraction pattern from the banded structure. The principal spots (marked by a cross) correspond to the ~-A1 phase (zone axis, [001]). The secondary spots correspond to O' and 0" phases. (b) Enlarged view of the banded structure. Dark bands are formed essentially of z~-AIphase, with aligned O" ribbons/globules and white bands of :~-AI phase with very fine 0" solid state precipitates.
Fig. 5. Transition between the wavy eutectic structure (columnar grains) and the banded structure at about 50 cm/s (specimen No. 6).
diffuse while the reverse transition is always sharp. Electron diffraction patterns from this banded structure, shown in Fig. 6(a), reveal the presence of the ct-Al phase and of the 0' and 0" phases; but no longer any 0 phase. The disappearance of the 0-AI2Cu phase proves the cessation of coupled eutectic growth between the ~-A1 and 0 phases. An enlarged view of the darkest bands, shown in Fig. 6(b), are made up of 0' ribbons and globules (typically 10-30 nm in spacing) in an ~-A1 matrix. The 0' phase is, more or less aligned in the growth
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ZIMMERMANN et al.: RAPID SOLIDIFICATION BY LASER REMELTING
direction and the structure resembles to the wavy eutectic observed just before the transition to bands [Fig. 4(c)]. No dislocations are observed around these globules. The lighter bands consist of ~-A1 and of very fine 0" precipitates (platelets < 2 nm in thickness) which have no particular arrangement with respect to the growth direction. These 0" platelets are parallel to the {001} planes of the ct-A1 phase and do not diffract in Fig. 6(b). Preliminary analyses of the chemical compositions show that the average composition of the banded region is about 33 wt% Cu, and that there is no significant difference in mean composition between the dark and light bands. No signs of an amorphous structure were observed.
700 660.45
oO
600-
~
soo-
°C
~t'
=
-800
E
-z99 409 -
- 699 300 9 AI
r 10
r 29 Weight
r 39 Percent
40
50
60
Cu
Fig. 8. Assumed phase diagram for the AI~Cu system (Al-rich side only). The full lines are as given by Murray [20], and the dotted lines represent a proposed metastable phase diagram which is consistent with the present observations.
DISCUSSION In a recent study of laser remelting, involving a three-dimensional macroscopic heat flow model without convection [18], it was shown that the solidification front velocity typically increases as the square root of the distance z :i.e. V~= A .z~/2 (where z = 0 at the bottom of the trace). Combining this macroscopic result with the 22Vs = const, relationship results in a 2 = A ' . z - ° 2 ~ depth-dependence of the lamellar spacing. This predicted behaviour corresponds well with the present observations, as shown in Fig. 7. It is interesting to note that, in this laser trace, most of the depth of material formed has a fine structure (less than 30 nm). The interlamellar spacing tends to large values only at the depth of trace where the growth rate approaches zero. The rapid acceleration of the moving solid-liquid interface, from a zero solidification rate at the bottom of the trace to a maximum value at the surface, could make steady state growth theory inappropriate for the interpretation of the experimental results. As demonstrated in the appendix [19], the equation which gives the criterion for the establishment of a quasi-steady state in term of the solidification rate and acceleration is OOVs
v, Ox - -
E
<< 1.
v,
(2)
80
70 ¸
,~,
~sufface
f
30' E_
20'
/
/
10"
_c 0
•
.
,
30
.
.
,
60
.
.
,
90
.
.
,
120
.
,
~
150
depth, z ~um]
Fig. 7. Measured interlamellar eutectic spacings, 2 vs depth z, within the longitudinal section. The fitted curve corresponds to: 2 = A-z-°28 (Specimen No. 1).
The quasi-steady state condition is satisfied if the change in Vs, when the interface moves through a distance D/Vs, is much less than Vs. This condition is fulfilled, over the entire depth of a laser trace, regardless of the laser treatment conditions. Typical maximum values of the interface acceleration (AVs/Ax) are of the order of 103-104[s-~], which corresponds to values of 10-5-10 -4 for the LHS of equation (2). Therefore, the application of steady state growth theory to laser resolidification is reasonable. In their paper, Trivedi et al. [11] gave solutions for two different cases of steady state eutectic growth; depending upon the phase diagram. In one case, the partition coefficient, k, varies from its value at the eutectic temperature to unity as the undercooling is increased ("cigar shape"). In the other case, k is a constant but k= = ka. For the AI-Cu system, the metastable phase diagram given in Fig. 8 is assumed. This corresponds to a simple extrapolation of the stable solidus and liquidus lines to temperatures below the eutectic temperature. The theoretical model where k= = kp = constant is more appropriate in this case, see Fig. l of Ref. [l 1]. The value of k was chosen to be that of the or-phase at the eutectic temperature. The metastable phase diagram proposed by Murray [20] was not used. The observed appearance of eutectic growth between ct-Al and 0' phases suggested the existence of a metastable eutectic such as that proposed in Fig. 8. Figure 9 shows the corresponding results of the T M K growth model (dashed line) and the experimentally determined relationship, 22Vs = 88 #m3/s (full line) [21]. Also shown are the experimentally measured interlamellar spacings, 2, as a function of the growth rate, Vs, and the transition velocities between the three observed morphologies. The physical constants used in the calculations are given in Table 3. It is to be noted that the experimentally determined 2 -- Vs relationship is independent of laser conditions such as power density or beam rate. The fineness of the eutectic lamellar structure seems to be limited to about 17 nm. Other work on rapid eutectic solidifi-
ZIMMERMANN et al.:
RAPID SOLIDIFICATION BY LASER REMELTING
Table 3. Physical constants for the AI4Su system [20, 22, 23] 32.7 wt% 821 K 0.54 0.17
1000 ~"
mellar eutectlc
bands
"~. =
~
11111.
> ~
,<
: .
10
e 1
.01
.1
1
10
Growth rate
100
3311
1000
Eutectic composition, C¢ Eutectic temperature, Tc Volume fraction of the a-phase, f Equilibrium partition coetficientof the ~t-phase, ke Length of eutectic tie-line, Co Liquidus slope of the ~t-phase, ms Liquidus slope of the /%phase, rn~ Preexponential constant, DO Activation energy for diffusion Gibbs-Thompson cte for the ~t-phase, F~ Gibbs-Thompson cte for the /J-phase, Fa Capillarity constant, a L Length scale for solute trapping, a0 For the definition of these constants see II 1].
46.9 wt% -4.6 K/wt% 3.5 K/wt% 1.1-t0 7m2/s 23.8 kJ/mol 2.4-10 7K'm 5.5.10 8K.m 2.7"10 7m-wt% 50 A
[cm/s]
Fig. 9. Interlamellar spacing, 2, as a function of growth rate, V~. The experimental points at Vs < 1 cm/s are from (©) Livingston et al. [151 and (V3) Burden and Jones [12]. The experimental points at V~> 1 cm/s (A) were determined by the authors. Full line: experimentally determined 22V~=const. relationship [21], dashed and dotted line: TMK model with k~=k~=0.17 respectively k~=kp= k(V3.
olated solidus line as shown in Fig. 8 gives an estimation for metastable eutectic temperature of about 770 K. A change from stable to metastable eutectic growth condition could also lead to an oscillatory morphology. According to this new metastable phase diagram, the initial composition (32.7 wt% Cu) is now strongly off-eutectic. U n d e r such conditions, the appearance cation [17, 24] has shown about the same value for the of oscillatory and tilting morphologies has been minimum eutectic spacing. theoretically predicted to occur when the interlamelF o r growth rates below 0.1 m/s, which correspond lar spacing, 2, approaches the same value as the to small P6clet numbers, i.e. P < 1, and for which the Mullins-Sekerka [25] instability wavelength, Jackson and Hunt theory is valid, the 22Vs = const. 2MS = 2 ~ x / ( D F / V A T e ) , of one phase [26-28] where curve and the predictions of the new model are in A T e is the difference between stable and metastable good agreement with the experimental points. eutectic temperature. Use of this theory, together The appearance of undulations in the microstrucwith the physical parameters given in Table 3, leads ture, at solidification rates greater than 20cm/s, is not to a critical instability wavelength of about 50 nm, predicted by the growth models. However, it may be which is in good agreement with the observed spacing significant that the P6clet number is of the order of (20-40nm). Therefore, the proposed metastable unity in this zone. This means that the microstrucphase diagram and the theoretical predictions of the tural length becomes equal to the diffusive length, i.e. appearance of oscillations are sell-consistent. diffusion will become localized. As the P6clet number becomes larger than unity, A continuous transition between stable coupled the coupled eutectic growth is replaced by a banded growth, i.e. A1-0, and a new metastable coupled structure. This limit of coupled growth which is growth, A1-0', is observed in this zone. An extrapopredicted by the theoretical model is higher than the lation of the metastable (AI) solvus curve for 0' experimentally observed one (dashed curve). The precipitation [20] to the intersection with the extrappredictions do not exhibit the observed increase in spacings of the preceding wavy microstructure; but 1.0" rather a decrease. As the equilibrium partition coefficient is small (ke = 0.17) and independent of undercooling, the reason for this limiting velocity on 0.8 cooperative lamellar growth is the large undercooling at solidification front which affects the solute diffu0.6 sion. This is the reason for the bending back of the theoretical curve. 0.4 At high growth rates, the interface kinetics may significantly alter the partition coefficient, k. There0.2 fore, a velocity dependence of the partition coefficient should be taken into account. Thus, by including O.G Aziz's model [29] in the calculations via the relation.1 1 10 100 1000 .01 ship, k ( Vs) = (k c + ao Vs/ D )/ (1 + ao Vs/ D ), a new theGrowth rate [cm/s] oretical curve is predicted as shown by the dotted line Fig. 10. Growth rate dependent partition coefficient, k(V~), in Fig. 9. (It is assumed that this solute trapping as a function of solidification rate, Vs for eutectic model gives the appropriate behaviour also for very A1-32.7 wt% Cu according to the TMK model (k~ = k s) high solute concentrations.) This curve is in good with Aziz's distribution coefficient.
f
A.M. 3 7 , 1 2 - - M
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ZIMMERMANN et al.: RAPID SOLIDIFICATION BY LASER REMELTING
agreement with the experimental results for solidification rates below 20 cm/s. The increase in the interlameilar spacing for solidification rates above 20 cm/s is also qualitatively predicted. Here the reason for the limit on coupled eutectic growth is not the temperature-dependent diffusion coefficient but the partition coefficient, which tends to unity as the growth rate increases as shown in Fig. 10. At high velocities, the liquidus and solidus curves converge to a single line which is near, but below, the To curve; reflecting the increasing partition coefficient [30]. Furthermore, the interface temperature is constrained by the phase diagram since it cannot be lower than the solidus temperature under local equilibrium conditions. When the interface temperature reaches the solidus temperature for a given phase, the diffusion field becomes identical to that for an independently growing planar interface of that phase, so that no cooperation is needed in order to redistribute the solute effectively. Consequently, the theoretical model predicts that ,l will increase and approach infinity when the interface temperature reaches the solidus temperature; thus signifying the appearance of a planar front [11]. Once this planar front is obtained, complete supersaturation occurs. What happens beyond this limit on coupled eutectic growth is not predicted by the theoretical model for eutectic growth. A banded structure has also been found in various aluminium-based alloys [31-33] and in a Ag-Cu alloy [17]; but no definite explanation for the origin of these bands was given. A more detailed study of this interesting microstructure is currently under way and will be presented in a later paper.
CONCLUSIONS From a microstructural point of view, three different zones have been observed, as a function of growth rate, in laser resolidified A1-Cu eutectic alloy: - - A t solidification rates below 20 cm/s, the eutectic microstructure is regular and lamellar. The interlamellar spacing decreases as the velocity increases, in accordance with the experimentally and theoretically determined 22Vs=const. relationship. The finest spacing observed is 17 nm. The phases present in the eutectic are the ~-A1 phase and the 0-AI2Cu phase. --Between 20 and 50 cm/s, the observed eutectic microstructure is wavy, with an average lamellar spacing which increases with growth rate up to a value of about 40 nm. The phases present are the ~-A1 phase, the 0-AI2Cu phase, and 0' and 0" phases. The 0' phase appears as lamellae which gradually predominate over the 0 phase and seem to grow in a coupled manner with the ~t-Ai phase. --Above 50 cm/s, where P > 1, the eutectic structure is replaced by a banded one which is made up of alternating aligned 0' ribbons and globules, and 0" precipitates in supersaturated ~-AI phase. No 0 phase is formed.
Contrary to the 22V~ = const, relationship, which predicts a continuous decrease in spacing as the growth rate increases, the new theoretical model clearly predicts a limit in growth rate for the coupled eutectic. The reason for this is that the partition coefficient increases with growth rate and a planar front morphology of the ~-A1 phase appear, leading to a completely supersaturated solid solution.
Acknowledgements--The authors are grateful to A. Karma for helpful discussions concerning the appendix and to J.-D. Wagnirre for his technical assistance during the laser treatments. The authors would also like to acknowledge the "Swiss National Fund for ScientificResearch", Bern, for its financial support.
REFERENCES
1. D. B. Williams and J. W. Edington, J. Mater. Sci. 12, 126 (1977). 2. P. Ramachandrarao, M. Laridjani and R. W. Cahn, Z. Metallk. 63, 43 (1972). 3. R. K. Singh, K. Chattopadhyay, S. Lele and T. R. Anantharaman, J. Mater. Sci. 17, 1617 (1982). 4. T. Sato, T. T. Long, H. Tezuka, A. Kamio and T. Takahashi, J. Japan Inst. Metals 48, 748 (1984). 5. M. G. Scott and J. A. Leake, Acta metall. 23, 503 (1975). 6. H. A. Davies and J. B. Hull, J. Mater. Sci. 9, 707 (1974). 7. M. G. Scott, M. Kijek and H. Matyja, J. Mater. Sci. 13, 1354 (1978). 8. D. B. Williams and J. W. Edington, J. Mater. Sei. 13, 1356 (1978). 9. M. Rappaz, M. Gremaud, R. Dekumbis and W. Kurz, Proe. Europ. Conf. Laser Treat. of Materials, ECLAT,
Bad Nauheim DGM, p. 43 (1987). 10. K. A. Jackson and J. D. Hunt, Trans. Am. Inst. Min. Engrs 236, 1129 (1966). 11. R. Trivedi, P. Magnin and W. Kurz, Acta metall. 35, 971 (1987). 12. M. H. Burden and H. Jones, J. Inst. Metals 98, 249 (1970). 13. J. N. Clark and R. Elliott, Metall. Trans. 7A, 1197 (1976). 14. D. J. S. Cooksey, D. Munson, M. P. Wilkinson and A. Hellawell, Phil. Mag. 10, 745 (1964). 15. J. D. Livingston, H. E. Cline, E. F. Koch and R. R. Russell, Acta metall. 18, 399 (1970). 16. F. Dupont, C. A. Brown and E. El-Batawi, Prakt. Metall. 23, 493 (1986). 17. W. J. Boettinger, D. Schechtman, R. J. Schaefer and F. S. Biancaniello, Metall. Trans. 15A, 55 (1984). 18. M. Rappaz, B. Carrupt, M. Zimmermann and W. Kurz, Helv. Phys. Acta 60, 924 (1987). 19. A. Karma, private communication (1988). 20. J. L. Murray, Int. Metall. Rev. 30, 211 (1985). 21. H. Jones, in Rapid Solidification of Metals and Alloys, Inst. of Metallurgists, London (1982). 22. T. Ejima, T. Yamamura, N. Uchida, Y. Matsuzaki and M. Nikaido, J. Japan Inst. Metals 44, 316 (1980). 23. M. Giindfiz and J. D. Hunt, Acta metall. 33, 1651 (1985). 24. D. Schechtman, W. J. Boettinger, T. Z. Kattamis and F. S. Biancaniello, Acta metall. 32, 749 (1984). 25. W. W. Mullins and R. F. Sekerka, J. appl. Phys. 35, 444 (1964). 26. D. T. J. Hurle and E. Jakeman, J. Cryst. Growth 3,4, 574 (1968). 27. V. Datye and J. S. Langer, Phys. Rev. B 24, 4155 (1981).
Z I M M E R M A N N et al.:
RAPID SOLIDIFICATION BY LASER R E M E L T I N G
28. 29. 30. 31.
A. Karma, Phys. Rev. Lett. 59, 71 (1987). M. J. Aziz, J. appl. Phys. 53, 1158 (1982). M. J. Aziz and T. Kaplan, Aeta metall. 36, 2335 (1988). S. K. Pandey, D. K. Gangopadhyay and C. Suryanarayana, Z. Metallk 77, 13 (1986). 32. G. V. S. Sastry and C. Suryanarayana, Mater. Sci. Engng. 47, 193 (1981). 33. M. Gremaud, M. Carrard and W. Kurz. To be published.
3313
The right-hand-side of equation (1) has a maximum when z = D/V. One can also write.
1 ~C ~< C~k~?V ~t
~ VD ~ - x exp-I.
(3)
The condition for a quasi-steady state is then 1 ~C D ?4
<<
V~C ~
and
[ 1 ~C << ~2C D~t ?~z2
.
(4)
This can be expressed more simply as:
APPENDIX Test f o r Steady State in Laser Treatment [19] Consider the general diffusion equation for an interface moving in one direction ~2C V ~ C 1 ~?C Oz 2 ~ D c3z D c~t (1)
VD gt Finally one obtains
<<
(7
D?V ~V ~ t <~l.
D
"
(5)
(6)
where V is the solidification rate, D is the diffusion coetfieient of solute and C is the solute concentration in the liquid. Following Karma [19], one can assume that the solution for the steady state: -V C(z) = C Oexp ~ - z
This inequality expresses the criterion for a quasi-steady state in terms of a solidification rate and acceleration. This can also be expressed as D~V D OVOx D c~V VOx ~ 1 (7) V 3 ~x ~t V 20x V
is still valid for the quasi-steady case
where x is the position of the interface with respect to a fixed frame of reference. Therefore, the quasi-steady state condition is ensured if the change in V, when the interface moves through a distance D/V, is much less than V.
C(z,t) = C0ex p
-
v(t)
D
z.
(2)
0001-6160/89 $3.00 + 0.00 Copyright © 1989 Pergamon Press plc
Printed in Great Britain. All rights reserved
RAPID SOLIDIFICATION OF A1-Cu EUTECTIC ALLOY BY LASER R E M E L T I N G M. Z I M M E R M A N N l, M. C A R R A R D z and W. K U R Z t ~Department of Materials, Swiss Federal Institute of Technology, 1007 Lausanne and 2Department of Physics, Swiss Federal Institute of Technology, 1015 Lausanne, Switzerland (Received 12 April 1989)
Abstract--Rapid surface resolidification using a high powered CO2-1aser has been performed on eutectic A1-32.7 wt% Cu at speeds between 0.2 and 8 m/s. By means of longitudinal cuts through the centre of the laser trace, the local growth rate has been measured by observation of the orientation of the microstructure using transmission electron microscopy. The various microstructures as a function of growth rate, are: (a) regular lamellar eutectic ~t-Al/0 AlzCu structure for growth rates below 20 cm/s with interlamellar spacing as fine as 17 nm; (b) a new wavy eutectic ~-AI/0'--A12Cu morphology for growth rates of between 20 and 50 cm/s; (c) a banded structure formed by alternating supersaturated ct-Al solid solution and the wavy eutectic for growth rates greater than 50 cm/s. A recent analytical model for eutectic growth under rapid solidification condition is compared to the experimental results. Contrary to the classical 22V~ = const, relationship, which predicts a continuous decrease in spacing as the growth rate increases, this new theoretical model clearly predicts a limit for the coupled eutectic growth which finds its analogy in single phase solidification in the limit of absolute stability. R6sum6--De la resolidification rapide superficielle avec un laser CO2 de haute puissance a 6t6 effectu6e sur un eutectique AI-32.7% pds Cu fi des vitesses comprises entre 0.2 et 8 m/s. A l'aide de coupes longitudinales au centre de la trace laser, la vitesse locale de croissance a pu 6tre mesur6e en observant par microscopie 61ectronique ~i transmission l'orientation de la microstructure. En fonction de la vitesse de croissance les diverses microstructures obtenues sont: (a) une structure eutectique lamellaire r6guli6re ~t-A1/0-AI2Cu pour des vitesses de croissance inf6rieures fi 20 cm/s avec un espacement interlamellaire aussi fin que 17 nm; (b) une nouvelle morphologie eutectique ondul6e ~t-AI/0'-A12Cu pour des vitesses de croissance comprises entre 20 cm/s et 50 cm/s; (c) une structure en bandes, pour des vitesses de croissance sup+rieures b. 50 cm/s, form6e alternativement par une solution solide ct-Al sursatur6e et par l'eutectique ondul6. Un mod61e analytique r6cent de la croissance eutectique fi haute vitesse est compar6 aux r6sultats exp6rimentaux. Contrairement a la relation classique 22 Vs = cte, qui pr6dit une diminution continue de l'espacement lorsque la vitesse de croissance augmente, ce nouveau mod61e th6orique pr6dit clairement une limite pour la croissance eutectique coupl6e qui peut 6tre compar6e fi la limite de stabilit6 absolue lors d'une croissance monophas6e. Zusammenfassung--Mittels eines Hochleistungs-CO2-Lasers wurde eine eutektische A1-32.7 Gew% Cu-Legierung bei Geschwindigkeiten von 0.2 bis 8 m/s umgeschmolzen. Anhand von longitudinalen Schnitten durch die Spurmitte wurde im Transmissionselektronenmikroskop die lokale Geschwindigkeit der Erstarrungsfront ermittelt. In Abhfingigkeit von dieser Wachstumsgeschwindigkeit wurden verschiedene Gef6ge beobachtet; (a) regulfires lamellares Wachstum des ct-Al/0-A12Cu-Eutektikums bei Wachstumsgeschwindigkeit unter 20 cm/s mit einem minimalen Phasenabstand von 17 nm; (b) eine neue wellige eutektische ~-A1/0'-A12Cu-Struktur zwischen 20 and 50 cm/s; (c) ein Gefiige, das aus alternierenden Bfindern yon total fibers/ittigter ~-AI Phase und welligem Eutektikum besteht bei Geschwindigkeiten gr6sser als 50 cm/s. Die experimentellen Ergebnisse werden mit einem vor kurzem entwickelten Modell raschen eutektischen Wachstums verglichen. Im Gegensatz zur bekannten 22 V, = konst.-Beziehung, die eine unbegrenzte Abnahme des Lamellenabstandes mitder Wachstumsgeschwindigkeit voraussagt, fiihrt dieses neue Modell zu einer Grenzgeschwindigkeit des eutektischen Wachstums, die der Grenze der absoluten Stabilit~it im Fall einphasiger Erstarrung entspricht.
INTRODUCTION It is n o w well k n o w n that the rapid solidification of alloys permits the extension o f solubility limits a n d refinement of the scale of a microstructure, a n d often leads to the a p p e a r a n c e of n o n - e q u i l i b r i u m phases. These effects are potentially useful for practical applications. R a p i d solidification o f alloys of eutectic c o m p o s i t i o n is especially interesting as such alloys can exhibit very fine two-phase structures a n d in some cases, also a m o r p h o u s phases.
Several authors have studied the effect of high cooling rates on the microstructure of the A1-Cu eutectic alloy. This binary eutectic is widely used as a model system because of its well-defined physical c o n s t a n t s a n d its regular eutectic growth morphology. By using rapid cooling techniques, various m o r p h o l o gies of the A1-Cu eutectic alloy were f o u n d with increasing cooling rate: lamellar structures with spacings decreasing to some tens o f n a n o m e t r e s [1-3], a degenerate eutectic m o r p h o l o g y [1, 2], a dendritic/cellular structure with microsegregation [3, 4], a
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RAPID SOLIDIFICATION BY LASER REMELTING
banded structure [1, 4], a supersaturated solid solution [1-3, 5J and finally an amorphous A1-Cu phase [6]. The mechanism for the appearance of the various microstructures as a function of cooling rate are currently not well defined. The reason is that the cooling rate is a lumped parameter which cannot be simply related to the observed microstructure. Moreover, with rapid cooling techniques such as splatquenching or melt-spinning, the heat transfer coefficients and the nucleation temperature remain difficult to determine quantitatively and are the subject of some disagreement concerning the interpretation of the observed microstructures [7, 8]. Surface treatments, using high-energy laser or electron-beams, overcome this difficulty because the liquid pool is in contact with its own solid, and solidification therefore does generally not involve nucleation. Furthermore, the morphology and scale of eutectic microstructures depend mainly upon the growth rate (rate of interface advance) and the influence of the thermal gradient can be neglected. In surface resolidification, the local growth rate can be determined quantitatively and this allows the comparison of experimental results with theoretical models of rapid solidification. The local growth rate is obtained by taking a longitudinal section through the center-line of the remelted trace, see Fig. 1, and by measuring the orientation of the microstructure, which tends to be perpendicular to the local solid-liquid interface, with respect to the direction of beam displacement. The relationship between the beam rate, Vb, and the local growth rate, G , is simply V~= Vb cos 0
(1)
where 0 is the angle between the vectors representing Vs (parallel to the microstructure) and Vb (parallel to the surface), as shown in Fig. l(b). Between the bottom and the top of a trace, the solidification rate varies from zero to a maximum beam
axis
,
(a)
V b (beam rate)
(b)
Fig. 1. (a) Typical form of the molten pool during laser treatment at high speeds. (b) At the centre-plane of the remelted trace, the solidification rate, Vs, and the beam rate, Vb, are related via the angle, 0.
which depends upon the size and shape of the melt pool, which themselves depend upon the processing conditions [9]. Therefore, with just one experiment performed at high scanning rate one can obtain a whole series of data as a function of growth rate. Various theoretical predictions of the resultant eutectic microstructures have been made but, until recently, only models developed under low P6clet number assumption, for example by Jackson and Hunt [10], were available. (The P6clet number, P, is defined as the ratio of a microstructural length, 2, to a diffusive length, 2 D / V s , where 2 is the interlamellar spacing and D is the diffusion coefficient of solute in the liquid.) These models, which are valid for low to medium growth rates, predict that the interlamellar spacing is related to the solidification rate via a 22V~ = const, relationship. Recently, Trivedi et al. [11] have developed a model (TMK model) for eutectic growth at high velocities. This model predicts that 22 Vs is no longer constant at high solidification rates, and that an upper limiting velocity exists for the formation of a regular, coupled eutectic structure. Several investigations have been carried out using directional solidification experiments [12-15]. However, the highest growth rates in such experiments are limited, for technical reasons, to some millimetres per second. To the present author's knowledge, no quantitative experiments on the rapid solidification of AI-Cu eutectic alloy have been carried out using a laser or electron beam. The aim of the present paper is to report experimental results on the morphological evolution and the scale of the microstructure of an A1-32.7 wt% Cu eutectic alloy, rapidly solidified by laser treatment, as a function of the growth rate. The high solidification rates (several meters per second) which are attainable using laser surface treatment, permit the verification of the existence of such a limit to coupled eutectic growth. EXPERIMENTAL
The AI-32.7 wt% Cu eutectic alloy was produced by melting the 99.99wt% pure components in a graphite crucible. The alloy was then cast into a cylindrical copper mould with an inside diameter of 40 mm and a height of 100 mm. In order to eliminate inhomogeneities at the surface and possible contamination from the mould, the samples were machined down to 34 mm in diameter. Before laser treatment, the samples were polished using 1000 grit SiC paper in order to enhance absorption of the laser beam as well as to ensure the same surface quality for each sample. The experiments were carried out using a continuous wave CO2-1aser with a nominal power of 1000W or 1500W. The laser beam was focused, using a parabolic copper mirror, to give a spot diameter of 240 #m. This corresponded to a power intensity of 2.2.106 W/cm 2 or 3.3- 106 W/cm 2, respectively. Controlled-velocity surface melting of single traces was carried out by rotating the cylindrical
ZIMMERMANN et al.:
RAPID SOLIDIFICATION BY LASER REMELTING
!!iiiiiiii!iiiiiiiiii!ii!iiiiii!iiiiii! ! zi¸¸iiiiiiiiiiiiii
s
.......
............. ,
E
0.3ram a
b
c
Fig. 2. Preparation of the longitudinal sections for TEM observations (shown is a transverse section of the laser trace). (a) Deposition of a nickel layer. (b) Mechanical polishing up to the centre of the trace. (c) One-side etching of the disc, from left to right (S = protecting shellac). specimen on its axis at peripheral speeds, lib, between 0.2 and 8 m/s. The laser beam was oriented at normal incidence to the specimen surface. As the as-cast microstructure was already fine (interlamellar spacing of about 1 #m), no laser pre-treatment was necessary in order to homogenize the material. Even at the highest peripheral velocity, optical metallographic examinations of the surface showed that the molten pool shape has reached a stationary state. During the laser treatment, a continuous flow of He (3 l/min) was blown onto the surface through a pipe of 5 mm diameter in order to reduce oxidation of the molten pool. As mentioned above, transmission electron microscopic (TEM) observations of a longitudinal section through the centre of the trace permit direct measurements of both the interlamellar spacing and the local growth rate. In order to prepare these thin longitudinal sections, a nickel layer (approx. 2 m m thick) was electrolytically deposited onto the treated surface, using the technique described by D u p o n t e t al. [16] [see Fig. 2(a)]. The sample was then mechanically polished until the centre of the trace was reached [Fig. 2(b)]. Disks which were 3 m m in diameter and 0.3 m m thick were then extracted by spark machining. The electrolytic thinning of these sections was performed in two successive stages. Firstly, the side which contained the laser trace was protected with shellac (lacomit) and then thinned from the opposite side [Fig. 2(c)] in order to obtain a regular hole at the interface between aluminium and nickel (polishing 1). Secondly, after removing the shellac, slight thinning from this side was necessary in order to achieve a perfect electron-transparent area over the laser trace (polishing 2). The thinning conditions for these two steps are given in Table 1. For the purpose of qualitative observations of the microstructure, sections in the X Y plane and close to the surface [see Fig. l(a)] were also studied.
3307
Table 2. Experimentalvalues of melt pool depth, d, and width, w, as a function of power and beam rate No. Power(W) Vb (m/s) Depth(•m) Width(pm) 1 2 3 4 5 6 7 8 9 10 11 12 13
1500 1500 1500 1500 1500 1500 1500 1500 1500 1000 1000 1000 1000
0.2 0.3 0.4 0.6 0.8 1 2 5 8 0.8 I 2 4
130 120 100 90 70 70 50 20 5 15 55 50 35 15-25
350 320 300 290 260 240 200 170 140 150 220 210 180 110-150
The T E M observations were performed using an Hitachi H700H microscope operating at 200 kV. RESULTS The depth, d, and width, w, of various single laser traces are shown in Table 2. Laser traces with depths of less than 20/~m are not continuous along the length of the sample; thus limiting the upper peripheral speed, Vu, to about 5 m/s. The maximum growth rate can differ significantly from the beam rate; especially at high peripheral speeds [9, 17]. The maximum growth rate which was obtained under the above mentioned limiting conditions was estimated, using heat flow models, to be of the order of 2 m/s. The sequence of the occurrence of the various observed microstructures is given schematically in Fig. 3. At the interface between the laser trace and the non-treated base material, the resolidifying eutectic branches out from the A12Cu phase, as shown in Fig. 4(a). The new eutectic structure begins to grow like a bundle but, after a few microns, only those lamellae lying parallel to the heat flow direction survive. This figure also reveals a rapid decrease in spacing, from
Table I. Thinning conditions Electrolyte TemperatureCC) Potential (V) Polishing 2 Polishing I
300 ml HNO~ 600 ml CH3OH 600 ml CH3OH 300 ml C4H 10O 60 ml HCIO4
- 20
1I
- 30
35
Fig. 3. Schematic representation of the various microsctructures observed on a longitudinal section of A1 32.7 wt% Cu surface material, laser treated at high beam rates (VD > 1 m/s).
3308
ZIMMERMANN et al.:
RAPID SOLIDIFICATION BY LASER REMELTING
(a)
Fig. 4. Various microstructures observed by TEM. (a) Transition between treated and non-treated zones. White lamellae are the ~-AI phase and black lamellae are the 0-A12Cu phase. (b) Finest eutectic spacing observed at Vs = 20 cm/s. (c) Wavy eutectic structure. This structure appears in A1-32.7 wt% Cu, under the present conditions, at solidification rates of between 20 cm/s and 50 cm/s. 1 # m in the non-treated zone to about 50 nm at a distance of about 3 p m into the resolidified zone. This corresponds to an extremely rapid increase in growth rate, from zero to some centimetres per second, over a few microns. At solidification rates of below 20 cm/s, the microstructure consists of parallel lamellae. As the surface is approached, i.e. as the growth rate increases, these eutectic lamellae tend to reorient themselves into the laser beam scanning direction and the interlamellar spacing decreases. In this zone, for various peripheral velocities and laser powers, the experimental values of 2 a n d Vs follow a 2 2 V s = c o n s t . relationship. The minimum eutectic spacing, observed at Vs = 20 cm/s, is 17 nm; as shown in Fig. 4(b).
Above a solidification rate of about 20 cm/s, the eutectic lamellar structure becomes more and more wavy. The typical microstructure of this undulating eutectic morphology is shown in Fig. 4(c). The form of this structure is difficult to quantify but the waves seem to oscillate out of phase. As the growth rate increases, the amplitude of these waves increases, but the wavelength (in growth direction) remains more or less constant at about 50 nm. The mean interlamellar spacing varies from about 17-20 nm at Vs = 20 cm/s to a maximum spacing near to 40 nm when the growth rate reaches a value of 50 cm/s. Inspite of these undulations, the overall orientation of the microstructure with respect to the scanning direction is still measurable. This therefore permits the determination of the corresponding solidification rate.
ZIMMERMANN et al.:
RAPID SOLIDIFICATION BY LASER REMELTING
3309
Electron diffraction patterns from this zone indicate the presence of the ~-A1 phase and the 0-AlzCu phase, as in the first zone, but also the appearance of the 0' phase which has the same morphology as the eutectic 0-A12Cu phase. Weak spots, due to precipitation of the metastable 0" phase, also appear. As the growth rate increases, the metastable 0' phase (as the second eutectic phase) predominates over the stable 0 phase. Note that the crystallography of this observed 0' phase is the same as that observed for conventional precipitation. For the alloys examined here, there is a second critical growth rate (of about 50 cm/s) at which the continuous wavy eutectic structure disappears and bands, lying approximately parallel to the solid-liquid interface, appear. This transition occurs very abruptly, as shown in Fig. 5, in contrast to the more gradual transition between the regular and wavy eutectic structures. As can be seen in this figure, the wavy microstructure which precedes the onset of the bands is made up of fine oriented grains (dark and light regions), while the banded structure is monocrystalline over large areas, including several bands. The spacing between these bands is approximately constant around a value of 0.8 #m but, as the growth rate increases, the relative volume fraction of the light bands tends to increase. In the direction of growth, the transition from white to dark bands is
Fig. 6. (a) Diffraction pattern from the banded structure. The principal spots (marked by a cross) correspond to the ~-A1 phase (zone axis, [001]). The secondary spots correspond to O' and 0" phases. (b) Enlarged view of the banded structure. Dark bands are formed essentially of z~-AIphase, with aligned O" ribbons/globules and white bands of :~-AI phase with very fine 0" solid state precipitates.
Fig. 5. Transition between the wavy eutectic structure (columnar grains) and the banded structure at about 50 cm/s (specimen No. 6).
diffuse while the reverse transition is always sharp. Electron diffraction patterns from this banded structure, shown in Fig. 6(a), reveal the presence of the ct-Al phase and of the 0' and 0" phases; but no longer any 0 phase. The disappearance of the 0-AI2Cu phase proves the cessation of coupled eutectic growth between the ~-A1 and 0 phases. An enlarged view of the darkest bands, shown in Fig. 6(b), are made up of 0' ribbons and globules (typically 10-30 nm in spacing) in an ~-A1 matrix. The 0' phase is, more or less aligned in the growth
3310
ZIMMERMANN et al.: RAPID SOLIDIFICATION BY LASER REMELTING
direction and the structure resembles to the wavy eutectic observed just before the transition to bands [Fig. 4(c)]. No dislocations are observed around these globules. The lighter bands consist of ~-A1 and of very fine 0" precipitates (platelets < 2 nm in thickness) which have no particular arrangement with respect to the growth direction. These 0" platelets are parallel to the {001} planes of the ct-A1 phase and do not diffract in Fig. 6(b). Preliminary analyses of the chemical compositions show that the average composition of the banded region is about 33 wt% Cu, and that there is no significant difference in mean composition between the dark and light bands. No signs of an amorphous structure were observed.
700 660.45
oO
600-
~
soo-
°C
~t'
=
-800
E
-z99 409 -
- 699 300 9 AI
r 10
r 29 Weight
r 39 Percent
40
50
60
Cu
Fig. 8. Assumed phase diagram for the AI~Cu system (Al-rich side only). The full lines are as given by Murray [20], and the dotted lines represent a proposed metastable phase diagram which is consistent with the present observations.
DISCUSSION In a recent study of laser remelting, involving a three-dimensional macroscopic heat flow model without convection [18], it was shown that the solidification front velocity typically increases as the square root of the distance z :i.e. V~= A .z~/2 (where z = 0 at the bottom of the trace). Combining this macroscopic result with the 22Vs = const, relationship results in a 2 = A ' . z - ° 2 ~ depth-dependence of the lamellar spacing. This predicted behaviour corresponds well with the present observations, as shown in Fig. 7. It is interesting to note that, in this laser trace, most of the depth of material formed has a fine structure (less than 30 nm). The interlamellar spacing tends to large values only at the depth of trace where the growth rate approaches zero. The rapid acceleration of the moving solid-liquid interface, from a zero solidification rate at the bottom of the trace to a maximum value at the surface, could make steady state growth theory inappropriate for the interpretation of the experimental results. As demonstrated in the appendix [19], the equation which gives the criterion for the establishment of a quasi-steady state in term of the solidification rate and acceleration is OOVs
v, Ox - -
E
<< 1.
v,
(2)
80
70 ¸
,~,
~sufface
f
30' E_
20'
/
/
10"
_c 0
•
.
,
30
.
.
,
60
.
.
,
90
.
.
,
120
.
,
~
150
depth, z ~um]
Fig. 7. Measured interlamellar eutectic spacings, 2 vs depth z, within the longitudinal section. The fitted curve corresponds to: 2 = A-z-°28 (Specimen No. 1).
The quasi-steady state condition is satisfied if the change in Vs, when the interface moves through a distance D/Vs, is much less than Vs. This condition is fulfilled, over the entire depth of a laser trace, regardless of the laser treatment conditions. Typical maximum values of the interface acceleration (AVs/Ax) are of the order of 103-104[s-~], which corresponds to values of 10-5-10 -4 for the LHS of equation (2). Therefore, the application of steady state growth theory to laser resolidification is reasonable. In their paper, Trivedi et al. [11] gave solutions for two different cases of steady state eutectic growth; depending upon the phase diagram. In one case, the partition coefficient, k, varies from its value at the eutectic temperature to unity as the undercooling is increased ("cigar shape"). In the other case, k is a constant but k= = ka. For the AI-Cu system, the metastable phase diagram given in Fig. 8 is assumed. This corresponds to a simple extrapolation of the stable solidus and liquidus lines to temperatures below the eutectic temperature. The theoretical model where k= = kp = constant is more appropriate in this case, see Fig. l of Ref. [l 1]. The value of k was chosen to be that of the or-phase at the eutectic temperature. The metastable phase diagram proposed by Murray [20] was not used. The observed appearance of eutectic growth between ct-Al and 0' phases suggested the existence of a metastable eutectic such as that proposed in Fig. 8. Figure 9 shows the corresponding results of the T M K growth model (dashed line) and the experimentally determined relationship, 22Vs = 88 #m3/s (full line) [21]. Also shown are the experimentally measured interlamellar spacings, 2, as a function of the growth rate, Vs, and the transition velocities between the three observed morphologies. The physical constants used in the calculations are given in Table 3. It is to be noted that the experimentally determined 2 -- Vs relationship is independent of laser conditions such as power density or beam rate. The fineness of the eutectic lamellar structure seems to be limited to about 17 nm. Other work on rapid eutectic solidifi-
ZIMMERMANN et al.:
RAPID SOLIDIFICATION BY LASER REMELTING
Table 3. Physical constants for the AI4Su system [20, 22, 23] 32.7 wt% 821 K 0.54 0.17
1000 ~"
mellar eutectlc
bands
"~. =
~
11111.
> ~
,<
: .
10
e 1
.01
.1
1
10
Growth rate
100
3311
1000
Eutectic composition, C¢ Eutectic temperature, Tc Volume fraction of the a-phase, f Equilibrium partition coetficientof the ~t-phase, ke Length of eutectic tie-line, Co Liquidus slope of the ~t-phase, ms Liquidus slope of the /%phase, rn~ Preexponential constant, DO Activation energy for diffusion Gibbs-Thompson cte for the ~t-phase, F~ Gibbs-Thompson cte for the /J-phase, Fa Capillarity constant, a L Length scale for solute trapping, a0 For the definition of these constants see II 1].
46.9 wt% -4.6 K/wt% 3.5 K/wt% 1.1-t0 7m2/s 23.8 kJ/mol 2.4-10 7K'm 5.5.10 8K.m 2.7"10 7m-wt% 50 A
[cm/s]
Fig. 9. Interlamellar spacing, 2, as a function of growth rate, V~. The experimental points at Vs < 1 cm/s are from (©) Livingston et al. [151 and (V3) Burden and Jones [12]. The experimental points at V~> 1 cm/s (A) were determined by the authors. Full line: experimentally determined 22V~=const. relationship [21], dashed and dotted line: TMK model with k~=k~=0.17 respectively k~=kp= k(V3.
olated solidus line as shown in Fig. 8 gives an estimation for metastable eutectic temperature of about 770 K. A change from stable to metastable eutectic growth condition could also lead to an oscillatory morphology. According to this new metastable phase diagram, the initial composition (32.7 wt% Cu) is now strongly off-eutectic. U n d e r such conditions, the appearance cation [17, 24] has shown about the same value for the of oscillatory and tilting morphologies has been minimum eutectic spacing. theoretically predicted to occur when the interlamelF o r growth rates below 0.1 m/s, which correspond lar spacing, 2, approaches the same value as the to small P6clet numbers, i.e. P < 1, and for which the Mullins-Sekerka [25] instability wavelength, Jackson and Hunt theory is valid, the 22Vs = const. 2MS = 2 ~ x / ( D F / V A T e ) , of one phase [26-28] where curve and the predictions of the new model are in A T e is the difference between stable and metastable good agreement with the experimental points. eutectic temperature. Use of this theory, together The appearance of undulations in the microstrucwith the physical parameters given in Table 3, leads ture, at solidification rates greater than 20cm/s, is not to a critical instability wavelength of about 50 nm, predicted by the growth models. However, it may be which is in good agreement with the observed spacing significant that the P6clet number is of the order of (20-40nm). Therefore, the proposed metastable unity in this zone. This means that the microstrucphase diagram and the theoretical predictions of the tural length becomes equal to the diffusive length, i.e. appearance of oscillations are sell-consistent. diffusion will become localized. As the P6clet number becomes larger than unity, A continuous transition between stable coupled the coupled eutectic growth is replaced by a banded growth, i.e. A1-0, and a new metastable coupled structure. This limit of coupled growth which is growth, A1-0', is observed in this zone. An extrapopredicted by the theoretical model is higher than the lation of the metastable (AI) solvus curve for 0' experimentally observed one (dashed curve). The precipitation [20] to the intersection with the extrappredictions do not exhibit the observed increase in spacings of the preceding wavy microstructure; but 1.0" rather a decrease. As the equilibrium partition coefficient is small (ke = 0.17) and independent of undercooling, the reason for this limiting velocity on 0.8 cooperative lamellar growth is the large undercooling at solidification front which affects the solute diffu0.6 sion. This is the reason for the bending back of the theoretical curve. 0.4 At high growth rates, the interface kinetics may significantly alter the partition coefficient, k. There0.2 fore, a velocity dependence of the partition coefficient should be taken into account. Thus, by including O.G Aziz's model [29] in the calculations via the relation.1 1 10 100 1000 .01 ship, k ( Vs) = (k c + ao Vs/ D )/ (1 + ao Vs/ D ), a new theGrowth rate [cm/s] oretical curve is predicted as shown by the dotted line Fig. 10. Growth rate dependent partition coefficient, k(V~), in Fig. 9. (It is assumed that this solute trapping as a function of solidification rate, Vs for eutectic model gives the appropriate behaviour also for very A1-32.7 wt% Cu according to the TMK model (k~ = k s) high solute concentrations.) This curve is in good with Aziz's distribution coefficient.
f
A.M. 3 7 , 1 2 - - M
3312
ZIMMERMANN et al.: RAPID SOLIDIFICATION BY LASER REMELTING
agreement with the experimental results for solidification rates below 20 cm/s. The increase in the interlameilar spacing for solidification rates above 20 cm/s is also qualitatively predicted. Here the reason for the limit on coupled eutectic growth is not the temperature-dependent diffusion coefficient but the partition coefficient, which tends to unity as the growth rate increases as shown in Fig. 10. At high velocities, the liquidus and solidus curves converge to a single line which is near, but below, the To curve; reflecting the increasing partition coefficient [30]. Furthermore, the interface temperature is constrained by the phase diagram since it cannot be lower than the solidus temperature under local equilibrium conditions. When the interface temperature reaches the solidus temperature for a given phase, the diffusion field becomes identical to that for an independently growing planar interface of that phase, so that no cooperation is needed in order to redistribute the solute effectively. Consequently, the theoretical model predicts that ,l will increase and approach infinity when the interface temperature reaches the solidus temperature; thus signifying the appearance of a planar front [11]. Once this planar front is obtained, complete supersaturation occurs. What happens beyond this limit on coupled eutectic growth is not predicted by the theoretical model for eutectic growth. A banded structure has also been found in various aluminium-based alloys [31-33] and in a Ag-Cu alloy [17]; but no definite explanation for the origin of these bands was given. A more detailed study of this interesting microstructure is currently under way and will be presented in a later paper.
CONCLUSIONS From a microstructural point of view, three different zones have been observed, as a function of growth rate, in laser resolidified A1-Cu eutectic alloy: - - A t solidification rates below 20 cm/s, the eutectic microstructure is regular and lamellar. The interlamellar spacing decreases as the velocity increases, in accordance with the experimentally and theoretically determined 22Vs=const. relationship. The finest spacing observed is 17 nm. The phases present in the eutectic are the ~-A1 phase and the 0-AI2Cu phase. --Between 20 and 50 cm/s, the observed eutectic microstructure is wavy, with an average lamellar spacing which increases with growth rate up to a value of about 40 nm. The phases present are the ~-A1 phase, the 0-AI2Cu phase, and 0' and 0" phases. The 0' phase appears as lamellae which gradually predominate over the 0 phase and seem to grow in a coupled manner with the ~t-Ai phase. --Above 50 cm/s, where P > 1, the eutectic structure is replaced by a banded one which is made up of alternating aligned 0' ribbons and globules, and 0" precipitates in supersaturated ~-AI phase. No 0 phase is formed.
Contrary to the 22V~ = const, relationship, which predicts a continuous decrease in spacing as the growth rate increases, the new theoretical model clearly predicts a limit in growth rate for the coupled eutectic. The reason for this is that the partition coefficient increases with growth rate and a planar front morphology of the ~-A1 phase appear, leading to a completely supersaturated solid solution.
Acknowledgements--The authors are grateful to A. Karma for helpful discussions concerning the appendix and to J.-D. Wagnirre for his technical assistance during the laser treatments. The authors would also like to acknowledge the "Swiss National Fund for ScientificResearch", Bern, for its financial support.
REFERENCES
1. D. B. Williams and J. W. Edington, J. Mater. Sci. 12, 126 (1977). 2. P. Ramachandrarao, M. Laridjani and R. W. Cahn, Z. Metallk. 63, 43 (1972). 3. R. K. Singh, K. Chattopadhyay, S. Lele and T. R. Anantharaman, J. Mater. Sci. 17, 1617 (1982). 4. T. Sato, T. T. Long, H. Tezuka, A. Kamio and T. Takahashi, J. Japan Inst. Metals 48, 748 (1984). 5. M. G. Scott and J. A. Leake, Acta metall. 23, 503 (1975). 6. H. A. Davies and J. B. Hull, J. Mater. Sci. 9, 707 (1974). 7. M. G. Scott, M. Kijek and H. Matyja, J. Mater. Sci. 13, 1354 (1978). 8. D. B. Williams and J. W. Edington, J. Mater. Sei. 13, 1356 (1978). 9. M. Rappaz, M. Gremaud, R. Dekumbis and W. Kurz, Proe. Europ. Conf. Laser Treat. of Materials, ECLAT,
Bad Nauheim DGM, p. 43 (1987). 10. K. A. Jackson and J. D. Hunt, Trans. Am. Inst. Min. Engrs 236, 1129 (1966). 11. R. Trivedi, P. Magnin and W. Kurz, Acta metall. 35, 971 (1987). 12. M. H. Burden and H. Jones, J. Inst. Metals 98, 249 (1970). 13. J. N. Clark and R. Elliott, Metall. Trans. 7A, 1197 (1976). 14. D. J. S. Cooksey, D. Munson, M. P. Wilkinson and A. Hellawell, Phil. Mag. 10, 745 (1964). 15. J. D. Livingston, H. E. Cline, E. F. Koch and R. R. Russell, Acta metall. 18, 399 (1970). 16. F. Dupont, C. A. Brown and E. El-Batawi, Prakt. Metall. 23, 493 (1986). 17. W. J. Boettinger, D. Schechtman, R. J. Schaefer and F. S. Biancaniello, Metall. Trans. 15A, 55 (1984). 18. M. Rappaz, B. Carrupt, M. Zimmermann and W. Kurz, Helv. Phys. Acta 60, 924 (1987). 19. A. Karma, private communication (1988). 20. J. L. Murray, Int. Metall. Rev. 30, 211 (1985). 21. H. Jones, in Rapid Solidification of Metals and Alloys, Inst. of Metallurgists, London (1982). 22. T. Ejima, T. Yamamura, N. Uchida, Y. Matsuzaki and M. Nikaido, J. Japan Inst. Metals 44, 316 (1980). 23. M. Giindfiz and J. D. Hunt, Acta metall. 33, 1651 (1985). 24. D. Schechtman, W. J. Boettinger, T. Z. Kattamis and F. S. Biancaniello, Acta metall. 32, 749 (1984). 25. W. W. Mullins and R. F. Sekerka, J. appl. Phys. 35, 444 (1964). 26. D. T. J. Hurle and E. Jakeman, J. Cryst. Growth 3,4, 574 (1968). 27. V. Datye and J. S. Langer, Phys. Rev. B 24, 4155 (1981).
Z I M M E R M A N N et al.:
RAPID SOLIDIFICATION BY LASER R E M E L T I N G
28. 29. 30. 31.
A. Karma, Phys. Rev. Lett. 59, 71 (1987). M. J. Aziz, J. appl. Phys. 53, 1158 (1982). M. J. Aziz and T. Kaplan, Aeta metall. 36, 2335 (1988). S. K. Pandey, D. K. Gangopadhyay and C. Suryanarayana, Z. Metallk 77, 13 (1986). 32. G. V. S. Sastry and C. Suryanarayana, Mater. Sci. Engng. 47, 193 (1981). 33. M. Gremaud, M. Carrard and W. Kurz. To be published.
3313
The right-hand-side of equation (1) has a maximum when z = D/V. One can also write.
1 ~C ~< C~k~?V ~t
~ VD ~ - x exp-I.
(3)
The condition for a quasi-steady state is then 1 ~C D ?4
<<
V~C ~
and
[ 1 ~C << ~2C D~t ?~z2
.
(4)
This can be expressed more simply as:
APPENDIX Test f o r Steady State in Laser Treatment [19] Consider the general diffusion equation for an interface moving in one direction ~2C V ~ C 1 ~?C Oz 2 ~ D c3z D c~t (1)
VD gt Finally one obtains
<<
(7
D?V ~V ~ t <~l.
D
"
(5)
(6)
where V is the solidification rate, D is the diffusion coetfieient of solute and C is the solute concentration in the liquid. Following Karma [19], one can assume that the solution for the steady state: -V C(z) = C Oexp ~ - z
This inequality expresses the criterion for a quasi-steady state in terms of a solidification rate and acceleration. This can also be expressed as D~V D OVOx D c~V VOx ~ 1 (7) V 3 ~x ~t V 20x V
is still valid for the quasi-steady case
where x is the position of the interface with respect to a fixed frame of reference. Therefore, the quasi-steady state condition is ensured if the change in V, when the interface moves through a distance D/V, is much less than V.
C(z,t) = C0ex p
-
v(t)
D
z.
(2)