Solidification of Pb particles embedded in Al

Acta metall, mater. Vol. 38, No. 7, pp. 1327-1342, 1990 Printed in Great Britain. All rights reserved

0956-7151/90 $3.00 + 0.00 Copyright © 1990 Pergamon Press plc

SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN AI K. I. MOORE, D. L. ZHANG and B. CANTOR Department of Materials, University of Oxford, Parks Road, Oxford OXI 3PH, England (Received 27 September 1989)

A~traet--Hypermonotectic alloys of A1-5 wt% Pb and AI-5 wt% Pb4).5 wt% X where X = Mn, Cu, Zn, Fe and Si have been manufactured by chill-casting and melt-spinning. The resulting microstructures have been examined by a combination of optical microscopy, scanning and transmission electron microscopy, and electron probe microanalysis. The as-solidified hypermonoteetic alloys exhibit a homogeneous bimodal distribution of faceted Pb particles embedded in a matrix of Al, with chill-cast Pb particle sizes of 1-2 p m and 5-50 pm, and melt-spun Pb particle sizes of 5-10 nm and 50-100 nm. The larger Pb particles are formed during cooling through the region of liquid immiscibility while the smaller Pb particles are formed during monotectic solidification of the A1 matrix. The Pb particles exhibit a cube-cube orientation relationship with the Al matrix, and a truncated octahedral shape with { l I l } and { 100} facets. The as-solidified Pb particle distributions are resistant to coarsening during post-solidification heat treatment. The equilibrium Pb particle shape and therefore the anisotropy of solid Al-solid Pb and solid Al-liquid Pb surface energies have been monitored by in situ heating in the transmission electron microscope over the temperature range between room temperature and 550°C. The anisotropy of solid Al-solid Pb surface energy is constant between room temperature and the Pb melting point, with the { 100} surface energy 14% greater than the {lll} surface energy, in good agreement with geometric nearneighbour bond energy calculations. The {100} facets disappear when the Pb particles melt, and the anisotropy of solid Al-liquid Pb surface energy decreases gradually with increasing temperature above the Pb melting point, until the Pb particles become spherical at about 550°C. The kinetics of Pb particle solidification have been examined by heating and cooling experiments in a differential scanning calorimeter. Pb particle solidification is nucleated catalytically by the A1 matrix on the {111 } facet surfaces, with an undercooling o f 22K and a contact angle of 21°C. Ternary additions of Mn, Cu, Zn and Fe do not influence the Pb particle solidification behaviour, but Si is a potent catalyst and stimulates the Pb particles to solidify close to the equilibrium Pb melting point. Rrsum&--Des alliages hypermonotectiques de AI-Pb fi 5% en poids et AI-Pb fi 5% en poids -X ~. 0.5% en poids (avec X = Mn, Cu, Zn, F e e t Si) sont 61aborrs par coulre en moule froid et par fusion sur roue tournante. Les microstructures rrsultantes sont examinres par microscopic optique microscopic 61ectronique ~. balayage et en transmission et par microanalyse 61ectronique. Les alliages hypermonotectiques fi l'rtat brut de solidification rrvrlent une distribution bimodale homogrne de particules de Pb fi facettes enchassres dans une matrice d'Al, avec des tailles 1-2 p m e t 5-50 # m pour les particules coulres en moule froid, et des tailles 5-10 nm et 50-100 nm pour les particules obtenues par fusion sur roue. Les plus grandes particules de Pb se forment pendant le refroidissement en traversant la rrgion de non-miscibilit6 du liquide tandis que les particules les plus petites se forment pendant la solidification monotectique de la matrice d'Al. Les particules de Pb ont des relations d'orientation cube-cube avec la matrice et une forme de cubooctardres avec des facettes {111} et {100}. Les distributions de particules de Pb fi l'rtat brut de solidification rrsistent au grossissement pendant le traitement thermique suivant la solidification. La forme d'equilibre des particules de Pb et par consrquent l'anisotropie des 6nergies superficielles A1 solide-Pb solide et A1 solide-Pb liquide sont contrrlres par chauffage in-situ dans le microscope 61ectronique en transmission, entre la temprrature ambiante et 550°C. L'anisotropie de l'rnergie superficielle A1 solide-Pb solide est constante entre la temp&ature ambiante et le point de fusion du Pb, avec une 6nergie superficielle de { I00} de 14% suprrieure fi celle { 111 }, en bon accord avec les calculs grom&riques d'rnergie de liaison entre proches voisins. Les facettes { 100} disparaissent lorsque les particules de Pb fondent et l'anisotropie de l'rnergie superficielle AI solide Pb liquide drcroit graduellement lorsque la temprrature drpasse le point de fusion du Pb, jusqu'fi ce que les particules de Pb deviennent sph&iques fi environ 550°C. Les cinrtiques de solidification des particules de Pb sont examinres par des exprriences de chauffage et de refroidissement dans un calorimrtre diffrrentiel fi balayage. La germination des particules de Pb solide est produite catalytiquement par la matrice d'Al sur des facettes { I 11 } avec un retard ~. la solidification de 22K et une angle de contact de 21 °. Des additions ternaires de Mn, Cu, Zn et Fe n'ont pas d'influence sur la solidification des particules, mais Si est un catalyseur puissant et incite les particules fi se solidifier au voisinage du point de fusion du plomb.

Zasammenfassung--Die hypermonotektischen Legierungen AI-5 Gew.-%Pb und AI-5 Gew.-Pb~,5 Gew.-X, mit X = Mn, Cu, Zn, Fe und Si, wurden durch GieBen und Schmelzspinnen hergestellt. Die sich ergebende Mikrostruktur wurde mit einer Kombination von optischer Mikroskopie, Raster- und Durchstrahlungselektronenmnikroskopie und der Mikrosonde analysiert. Die erstarrten hypermonotektischen Legierungen weisen eine homogene bimodale Verteilung von facettierten Pb-Teilchen auf, die in der A1-Matrix eingebettet sind; die Gr6Be der Teilchen war im gegossenen Material 1-2 und 5-50/~m, im gegossenen Material I-2 und 5-50#m, im schmelz-gesponnenen 5-10 und 50-100 nm. Die grrBeren Pb-Teilchen werden wfihrend des Abkiihlens durch den Schmelzbereich der Nichtmischbarkeit gebildet, 1327

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SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN AI

die kleineren w~ihrend der monotektischen Erstarrung der AI-Matrix. Die Pb-Teilchen haben eine Wfirfel-Wfirfel-Orientierungsbeziehungmit der Al-Matrix und eine wiirfeloktaedrischeForm mit {111}und {100}-Facetten. Die Verteilung der Pb-Teilchen in dem frisch erstarrten Material widersteht einer Vergrrberung wfihrend nachfolgender Wiirmebehandlung. Die Gleichgewichtsformder Pb-Teilchen und damit die Anisotropie der Energie der Grenzfl/ichen zwischen festem A1 und festem Pb und zwischen festem AI und fl/issigem Blei wurden in-situ im Durchstrahlungselektronenmikroskop durch Aufheizen fiber einen Temperaturbereich zwischen Raumtemperatur und 550°C verfolgt. Die Anisotropie der Grenzfl~ichenenergiefestes Al/festes Pb ist zwischen Raurntemperatur und dem Schmelzpunkt des Bleis konstant. Die Energie der {100}-Fl~icheist 14% hrher als die der {111}-Fl/iche;dieser Befund stimmt gut mit geometrischen Rechnungen der Energie N~ichster-Nachbar-Bindungeniiberein. Die {100}-Facetten verschwinden,wenn die Pb-Teilchen schmelzen. Die Anisotropie der Grenzflfichezwischen festem AI und fliissigem Pb nimmt kontinuierlich mit steigender Temperatur oberhalb der Schmelztemperatur des Bleis ab, bis die Pb--Teilchenbei etwa 550° rund werden. Die Kinetik der Erstarrung der Pb-Teilchen wurde in Heiz- und Kfihlexperimenten in einem differentiellen Abtastkalorimeter studiert. Die Erstarrung der Pb-Teilchen beginnt katalytisch in der A1-Matrixauf der {I 11}-Facettenfl/ichebei einer Unterkfihlung yon 22 K und einem Kontaktwinkel yon 21°. Tern~ire Anteile yon Mn, Cu, Zn und Fe beeinflussen das Erstarrungsverhalten der Pb--Teilchennicht. Si jedoch ist ein wichtiger Katalysator, der dazu ffihrt, dab die Pb--Teilchenschon nahe an dem Gleichgewichtsschmelzpunktdes Pb erstarren. 1. INTRODUCTION There are serious fundamental and experimental difficulties in providing an adequate description of nucleation behaviour during solidification and melting [1, 2]. From a fundamental point of view, the formation of a nucleus involves rather too many atoms for simple atomistic modelling, and rather t o o few atoms for straightforward application of macroscopic thermodynamics. From an experimental point of view, controlled and reproducible nucleation studies are difficult to achieve, because the nuclei are too small for direct microscopic observation, and are sensitive to the presence of trace impurities. This is unfortunate, because the pattern of nucleation during the solidification of an ingot or casting determines many important microstructural features, such as phase composition, grain size and structure, and distribution of second phase particles, all of which influence the final material properties. A variety of different experimental techniques have been devised to undercool liquid metals and alloys below their equilibrium melting point, in order to investigate the subsequent nucleation behaviour at the onset of solidification. The main objective of these experimental techniques is to eliminate stray impurities, so as to prevent uncontrolled catalytic nucleation of solidification. The probability of an unknown impurity particle being present in a mass of liquid is directly proportional to the size of the liquid mass, and the most common method of trying to reduce impurity effects has therefore been to study small, typically 1-100/~m sized liquid droplets. Organic emulsifying agents have been used to prepare a liquid foam, i.e. to divide a liquid mass into a large number of small droplets [3-14], and individual droplets have also been studied, either on carefully prepared substrates [15-21], without substrates in flight tubes [22-26], by levitation [27], or after fluxing to scavenge unwanted impurities [28-34]. In most of these experimental studies, a technique such as calorimetry, dilatometry or microscopy has been used to monitor the onset of soldification, so as

to determine the thermal driving force needed in the liquid to overcome any kinetic barrier to nucleation. Unfortunately, the reported measurements of liquid undercooling are far from reproducible, as shown in Table 1, and only emphasise the experimental difficulty of removing unknown catalytic impurities. An elegant experimental technique which gives more reproducible measurements of liquid undercooling was first devised by Wang and Smith [35], and subsequently used by Chadwick and co-workers [36-38]. A binary alloy is thermomechanically manipulated to produce a microstructure of low melting point particles embedded in a high melting point matrix, and is then heat treated to melt the particles and monitor subsequent particle solidification. Embedded particle experiments of this type are particularly suitable for controlled studies of heterogeneous nucleation, i.e. particle solidification which is catalytically nucleated by the surrounding high melting point matrix. This is important, since ingot and casting microstructures are usually dominated by heterogeneous nucleation effects. Table 1. Reported valuesof maximumliquidundercoolingbefore the onset of solidificationin a varietyof pure metals Melting Undercooling Undercooling/ Metal point(K) (K) meltingpoint Reference Bi 544 90 0.17 15 100 0.18 17 173 0.32 5 227 0.42 6 Sn 505 105 0.21 3 122 0.24 17 175 0.35 5 187 0.37 6 Pb 600 67 0.11 15 80 0.13 16 153 0.25 6 240 0.40 18 Ga 303 76 0.25 4 99 0.33 17 102 0.34 7 150 0.50 6 Hg 234 52 0.22 17 58 0.25 16 88 0.38 6

MOORE et al.: SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN A1 The present paper describes the results of an investigation into the solidification behaviour of Pb particles embedded in an A1 matrix. An AI-5 wt% Pb alloy composition was selected for the investigation for a variety of reasons: (1) Binary Al-Pb alloys form a monotectic system, with Al and Pb virtually immiscible in the solid and liquid except at high temperatures [39]. The thermodynamics of solidification of Pb particles embedded in an Al matrix are therefore not significantly influenced by solubility effects. (2) A homogeneous alloy of hypermonotectic composition Al-5 wt% Pb can however be manufactured by chill-casting or melt-spinning from a relatively accessible temperature of about 1000°C, leading directly to a suitable microstructure of Pb particles embedded in an A1 matrix [40,41]. Chill-cast Pb particles are typically 1-50pm in size, similar to previous embedded particle nucleation studies, whereas melt-spun Pb particles are much smaller, typically 5-100 nm in size [40, 41]. (3) The small size of the Pb particles in chillcast and melt-spun hypermonotectic A1-5 wt% Pb is convenient for ensuring that their solidification behaviour is dominated by nucleation, and for eliminating unwanted impurity effects by segregating impurities into relatively few particles. Differential scanning calorimetry during subsequent heat treatment then gives extremely reproducible measurements of the Pb particle solidification exotherms [42,43]. The small size of melt-spun Pb particles is also convenient for detailed microstructural and crystallographic examination at high magnification in a transmission electron microscope. (4) Hypermonotectic Al-5 wt% Pb can readily be doped with ternary element additions without significantly modifying the Pb particle microstructure [40, 41], in order to study microchemical influences on the nucleation of Pb particle solidification. 2. EXPERIMENTAL TECHNIQUE Chill-cast ingots of hypermonotectic composition A1-5 wt% Pb and A1-5 wt% Pb-0.5 wt% X where X = Mn, Cu, Zn, Fe and Si were manufactured by induction-melting 99.999% pure components in recrystallised alumina crucibles under a dynamic Ar atmosphere, using an immersed thermocouple to monitor alloy temperatures during melting. Liquid Al and Pb are immiscible below 900°C for an alloy composition of AI-5 wt% Pb [39], so the molten alloys were held at 1000cC for 600s to ensure homogeneous mixing, and then chill-cast by plunging the crucible and melt into water to prevent gravity segregation while cooling through the region of liquid immiscibility. The resulting chill-cast ingots were cylindrical in shape, typically 20 mm in diameter and 20 mm in length.

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Specimens of each alloy ingot were rapidly solidified by melt-spinning [44, 45]. Alloy charges of approximately l0 g were re-melted in quartz crucibles under a dynamic Ar atmosphere, using a calibrated pyrometer to monitor alloy temperatures during re-melting. After holding at 1000°C for 200s to ensure homogeneous mixing, the molten alloys were then ejected with an Ar overpressure of 14-21 kPa through a 1 mm orifice onto the outer surface of a polished Cu drum rotating with a surface speed of 15 ms -l. The resulting melt-spun materials were in the form of thin ribbons, typically 100 #m thick, 3 mm wide and several metres long. Some additional chill-cast ingots and melt-spun ribbons were manufactured in a similar way: (1) hypermonotectic AI-5 wt% Pb chill-cast ingots made from lower, 9 9 . 9 9 % purity components; (2) hypermonotectic A1-5wt% Pb melt-spun ribbons containing greater, 1-2 wt% additions of Si; and (3) chill-cast ingots and melt-spun ribbons with lower alloy compositions, monotectic AI-1.5 wt% Pb and near-monotectic AI-2 wt% Pb. To check for possible non-equilibrium solidification effects during chillcasting and melt-spinning, some specimens of each of the chill-cast and melt-spun alloys were equilibrated by heat-treatment at 350°C for 7.105 and 2.103s respectively under a dynamic Ar atmosphere. Only the hypermonotectic A l - 5 w t % P b and A1-5 wt% Pb-0.5 wt% Si, monotectic Al-l.5 wt% Pb, and near-monotectic Al-2 wt% Pb chill-cast and melt-spun alloys were subject to detailed metallographic examination. Sections of the chill-cast ingots were polished to 1/4#m diamond paste and/or alumina powder and etched in dilute citric acid for metallographic examination in an Olympus BH optical microscope, a JEOL JSM35X scanning electron microscope and a Cameca Camebax electron microprobe analyser. The rapidly solidified melt-spun ribbons were jet-electropolished in a mixture of 20% perchloric acid and 80% methanol at - 4 0 ° C for examination in JEOL 100C, Philips EM300 and CM12, and AEI EM7 transmission electron microscopes. The different electron microscopes were used for a combination of general metallographic examination, electron microprobe anlaysis, and in-situ heating experiments. The Pb solidification behaviour in each of the chill-cast and melt-spun alloys was investigated in a Dupont 1090 thermal analyser fitted with 910 differential scanning calorimeter module. Individual 10-50 mg samples were sealed in Al cans, heated from 250°C to a temperature in the range 327-380°C at a heating rate in the range 0.5-10 K min -~, held for up to 600 s, and then re-cooled to 250°C at a cooling rate in the range 0.5-10 K min -~, all under a dynamic Ar atmosphere. During each heating and cooling cycle, differences in heat flow to and from the sample and a similarly heat-treated reference were continuously recorded at maximum sensitivity on a microcomputer for subsequent detailed examination.

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SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN A1 Table 2. Pb particle number densities in chill-cast and melt-spun hypermonotectic AI-5 wt% Pb and AI5 wt% Pb-0.5 wt% Si, and monotectic Al-I.5 wt% Pb Alloy

b-..-,.,,.I

5~m

Fig. 1. Scanning electron micrograph of chill-cast AI5 wt% Pb, showing bimodal distribution of Pb particles. 3. RESULTS 3.1. Alloy microstructures Metallographic examination confirmed that in chill-cast and melt-spun hypermonotectic A1-5 wt% Pb and A 1 - 5 w t % P b 4 ) . 5 w t % Si the Pb and Si were distributed homogeneously throughout the AI matrix. Typical microstructures of the chill-cast and melt-spun alloys are shown in Figs 1 and 2 respectively. Chill-cast AI-5 wt% Pb and AI-5 wt% Pb-0.5 wt% Si contained a bimodal distribution of discrete Pb particles, with typical sizes of 1-2 #m and 5-50 #m. Melt-spun AI-5 wt% Pb and A1-5 wt% Pb-~).5 wt% Si also contained a bimodal distribution of discrete Pb particles, but with much smaller typical sizes of 5-10nm and 50-100nm, because of the higher speed of solidification. Microstructures similar to those in Figs 1 and 2 were found in chill-cast and melt-spun monotectic Al-l.5wt% Pb and nearmonotectic AI-2 wt% Pb, except that the larger Pb particles were absent or reduced in quantity. Thus, in chill-cast and melt-spun hypermonotectic AI-5 wt% Pb and AI-5 wt% Pb-0.5 wt% Si, the larger Pb par-

Small particle density (m -3)

Large particle density (m -3)

Chill-cast AI-Pb AI-5 Pb-0.5 Si AI-I.5 Pb

5.5.1015 2.5.1015 2.5.1014

7.10 I° 7 . 1 0 I° --

Melt -spun AI-5 Pb AI-5 Pb-0.5 Si AI-1.5 Pb

2.1024 2.1024 2.5- 1023

1.5" 1019 1.5- 1019 --

ticles were formed during cooling through the region of liquid immiscibility, while the smaller Pb particles were formed by the monotectic reaction during solidification of the A1 matrix. Typical Pb particle number densities and spacings are given in Tables 2 and 3 for the chill-cast and melt-spun hypermonotectic and monotectic alloys. Compared with chill-casting, rapid solidification by melt-spinning increased the Pb particle number density by a factor of approximately 10~°, and decreased the Pb particle spacing by a factor of approximately 103. Electron probe microanalysis showed that Si was segregated into a cellular network after chill-casting, but was dissolved in the AI matrix after melt-spinning. As shown in Figs 1 and 2, the Pb particles were faceted in melt-spun A1-5 wt% Pb and AI-5 wt% Pb-0.5 wt% Si, and partially faceted in the chill-cast alloys. Establishing the facet crystallography was not straightforward and the following procedure was adopted. First, superimposed A1 and Pb electron diffraction patterns were generated in order to determine the AI-Pb orientation relationship. The f.c.c. Pb particles were found to have a cube-cube orientation relationship with the f.c.c. A1 matrix. Figure 3 shows a typical electron diffraction pattern with superimposed A1 and Pb (011) zones. Secondly, the Pb particle cross-sectional shape was examined as a function of A1 matrix crystallographic orientation. This was achieved by tilting until a low index AI zone axis was parallel to the electron beam, as shown by a symmetrical distribution of Kikuchi lines or diffraction spots, followed by recording the bright field image and diffraction pattern. The Pb particles were found to be truncated octahedral in shape, bounded by {111} and {100} facets. Figure 4 shows typical distorted hexagonal and octagonal Pb particle crossTable 3. Pb interparticle spacings in chill-cast and meltspun hypermonotectic AI-5 wt% Pb and AI-5 wt% P b 0.5 wt% Si, and monotectic AI-1.5 wt% Pb Alloy Chill-cast AI-Pb AI-15 Pb-0.5 Si Al-1.5 Pb

Fig. 2. Transmission electron micrograph of melt-spun AI5 wt% Pb, showing bimodal distribution of Pb particles.

Melt -spun AI-5 Pb AI-5 Pb-0.5 Si AI-1.5 Pb

Small particle spacing (#m) 15 20 20 0.01 0.01 0.02

Large particle spacing (#m) 300 300 -0.5 0.5 --

MOORE et al.: SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN AI

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Fig. 3. High voltage transmission electron diffraction pattern from melt-spun AI-5 wt% Pb, showing superimposed AI and Pb (011) zones in a cube~:ube orientation relationship. sections with the electron beam parallel to AI (011) and (001) zones respectively. The microstructures of chill-cast and melt-spun hypermonotectic A1-5 wt% Pb and AI-5 wt% Pb-0.5wt% Si were very resistant to heat-treatment. After 7.105s at 35(I C, the chill-cast Pb particles became more faceted, and the cellular Si formed into discrete 1-2 #m sized particles as shown in Fig. 5. Otherwise. chill-cast A l - 5 w t % Pb and A l - 5 w t % P b - 0.5 wt% Si microstructures remained unaffected by heat-treatment. No microstructural changes were detected in melt-spun AI-5 wt% Pb and AI-5 wt% Pbq).5wt% Si after heat-treatment for 2.103s at 350°C. 3.2. Surface energy anisotropy

For melt-spun AI-5 ~ t % Pb and AI-5 wt% P b 0.5 wt% Si alloys, the shapes of individual Pb particles were monitored as a function of temperature during in situ step-heating in the transmission electron microscope. Before heating, specimens were tilted until the electron beam was parallel to an A1 (011) zone. As shown in Fig. 4, the Pb particle shape was then distorted hexagonal, bounded by one pair of {100} facets and two pairs of {111} facets, all parallel to the electron beam. With this specimen orientation, the observed separation of each pair of opposite facets was equal to the true separation, and from the Gibbs-Wulff theorem was directly proportional to the facet surface energy [46,47]. After careful orientation in this way, specimens were heated in steps of 50 K up to a maximum temperature of 550°C, with the Pb particle shape recorded at each temperature after an equilibrating anneal of 180s. Approximate diffusion calculations indicate ample time for equilibration of the 5-100 nm Pb particles during a 180 s anneal at temperatures above about 200~C. This was confirmed by in situ step-cooling experiments in which the Pb particles changed shape in an exactly reverse sequence to that seen during heating, with no time lag from insufficient equilibration during annealing. Figure 6 shows a typical series of bright field images of the Pb particle shape as a function of

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temperature during in situ heating in the transmission electron microscope for melt-spun AI-5 wt% P b 0.5 wt% Si. Almost identical results were obtained for a number of individual Pb particles in both alloys, and Fig. 7 shows the resulting variation of surface energy anisotropy as a function of temperature. The Pb particle shape was constant between room temperature and the Pb melting point of 327°C, with a {100}/{111} surface energy anisotropy of 1.14. The {100} facets disappeared sharply when the Pb particles melted at 327°C. However, the {111} facets disappeared only slowly with increasing temperature above the Pb melting point, and the surface energy anisotropy decreased gradually from 1.14 to 1, until the Pb particles finally became spherical at about 550°C. 3.3. Pb particle solidification

Figure 8 shows typical differential scanning calorimeter traces of Pb particle solidification exotherms from the chill-cast AI-Pb binary alloys. In general, solidification exotherms from the chill-cast alloys were found to be slightly variable from specimen to specimen, although not enough to obscure the main features of the results. Onset and peak temperatures of solidification exotherms in the chillcast alloys were typically reproducible to within + 1 - 2 K. In as-chill-cast 99.999% pure hypermonotectic A1-5 wt% Pb, the Pb particles solidified with a characteristic shape to the calorimeter traces. A broad solidification exotherm extended over approximately 25-30 K below the equilibrium Pb melting point of 327°C, and superimposed on this broad exotherm was a sharper solidification exotherm at an onset temperature of approximately 305°C, i.e. at an undercooling of 22 K below the Pb melting point. No significant difference in Pb particle solidification behaviour was found after heat-treating chill-cast hypermonotectic A1-5 wt% Pb for 7. 105s at 350°C. In as-chill-cast monotectic A l - l . 5 wt% Pb and nearmonotectic A I - 2 w t % Pb, however, there was no evidence of solidification between 305 and 327°C, and all the Pb particles solidified with a single sharp exotherm at about 305cC. Thus, the broad high temperature exotherm corresponded to solidification of the larger 5-50/~m Pb particles formed by liquid phase separation during chill-casting, while the sharp 305°C exotherm correspond to solidification of the smaller 1-2 #m Pb particles formed by the monotectic reaction during chill-casting. The differential scanning calorimeter traces in Fig. 9 show the typical effects on the Pb particle solidification exotherms caused by doping chillcast hypermonotectic A1-5 wt% Pb with 0.5 wt% of ternary additions. Apart from minor variations in the relative magnitude of the two types of exotherm, no significant differences in Pb particle solidification behaviour were detected after additions of 0.5 wt% Mn, Cu, Zn or Fe. However, Si proved to be a potent catalyst of Pb particle solidification. After adding

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SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN A1

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Fig. 4. Transmission electron micrographs and corresponding electron diffraction patterns from melt spun AI-5 wt% Pb, showing: (a) distorted hexagonal cross-section of Pb particles perpendicular to (011 >; and (b) octagonal cross-section of Pb particles perpendicular to <001>.

MOORE et al.: SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN AI

1333

number of 5-100nm rather than 1-50pm sized droplets was clearly effective in inhibiting trace impurity catalysis, and removing the broad Pb particle solidification exotherm between 305 and 327°C. As shown in Fig. 10, the shape of the Pb particle solidification exotherm in melt-spun A1-5 wt% Pb depended upon the imposed cooling rate in the differential scanning calorimeter. Figure 12 shows the variation of the solidification onset, peak and end temperatures and the exothermic peak height as functions of the cooling rate in the calorimeter. The solidification onset temperature was independent of cooling rate, but the peak and end temperatures decreased and the peak height increased with increasing cooling rate. Once again Si proved to be a potent catalytic ternary addition. As shown in Fig. 11, increasing the level of Si addition to 1 or 2 wt% in melt-spun AI-5 wt% Pb reduced the size of the 305°C solidification exotherm, and stimulated a significant number of the small 5-100 nm Pb particles to solidify at higher temperature. 4. DISCUSSION 4.1. Alloy microstructures

Fig. 5. X-ray intensity maps from chill-cast Al-5wt% Pb4).5 wt% Si, showing: (a) as-solidified cellular Si distribution; and (b) 12 pm Si particles after heat treatment for 7.105 s at 350°C. 0.5 wt% Si to chill-cast hypermonotectic AI-5 wt% Pb, the 305cC exotherm disappeared completely, and all the Pb particles solidified close to their melting point. As shown in Fig. 8, a similar but weaker effect was produced when the chill-cast AI-5 wt% Pb alloy purity was reduced to 99.99%, presumably caused by the trace Si content usually present in commercial purity AI. Figures 10 and 11 sho~ typical differential scanning calorimeter traces of Pb particle solidification exotherms from the melt-spun binary and ternary A1-Pb alloys respectively. Compared with the chillcast alloys, solidification exotherms from the meltspun alloys were reproducible from specimen to specimen, as expected from the small 5-100 nm Pb particle size shown in Fig. 2, and the 101° times greater Pb particle number density shown in Table 2. Onset and peak temperatures of solidification exotherms in the melt-spun alloys were typically reproducible to within _+0.2~).3 K. In almost all the melt-spun alloys, the Pb particles solidified with a single sharp exotherm at 305°C, independent of alloy purity, heat-treatment, Pb content, and doping with 0.5 wt% of ternary additions. Compared with the chill-cast alloy solidification exotherms shown in Figs 8 and 9, dividing the liquid Pb into a larger

The chill-cast and melt-spun hypermonotectic AI-5 wt% Pb and AI-5 wt Pb-0.5 wt% Si alloy microstructures shown in Figs 1 and 2 correspond to a solidification sequence which can be described as follows: (1) Liquid phase separation: Pb-rich liquid droplets nucleate and grow in the region of liquid immiscibility between about 900°C and the monotectic temperature of 659°C [39]. Nucleation is continuous in the miscibility gap, and growth is relatively fast with high liquid diffusivity at high temperature. At 659°C, the alloys therefore contain relatively large Pb-rich droplets in an Al-rich monotectic liquid matrix, with droplet sizes of 5-50/~m during chill-casting and 50-100 nm during melt-spinning. (2) Monotectic solidification: On cooling below 659°C, the Al-rich liquid solidifies at high speed by a duplex monotectic reaction, producing additional small Pb-rich droplets, with droplet sizes of 1-2/~m during chill-casting and 5-10nm during meltspinning. At this stage, all the droplets are virtually pure Pb trapped in a pure A1 solid matrix. The irregular Pb particle monotectic microstructures in Figs 1 and 2 are consistent [48-50] with relatively low values of approximately 100Ks/mm 2 for the ratio of thermal gradient to solidification velocity G/V during both chill-casting and melt-spinning, estimated from G / V = Tt/y 2

(1)

where T is the melt temperature, y is the section size and t is the solidification time [41]. (3) Droplet coarsening: During cooling from 659°C to room temperature, average diffusion distances x in

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MOORE et al.:

SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN A1

Fig. 6. Sequence of transmission electron micrographs showing the variation in shape of a Pb particle in melt-spun AI-5 wt% Pb as a function of temperature during/n situ heating: (a) room temperature; (b) 100°C; (c) 300°C; (d) 350°C; (e) 400°C; (f) 450°C; (g) 500°C; and (h) 550°C.

MOORE et al.: SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN AI

1335

1.2

0"100 0~

• 1.1

1.o l No heot

I

I

100

200

I

i

500

4.00

5 0 0

TEMPERATURE (°C)

Fig. 7. AI-Pb surface energy anisotropy as a function or temperature, from measurements of {100} and {111} facet separations in melt spun AI-5wt% Pb and AI-Swt% Pb-0.5 wt% Si, during in situ heating in the transmission electron microscope. solid AI are approximately 3 # m and 0.01/tm during chill-casting and melt-spinning respectively, estimated from (2)

x 2 = 4Dt

where D is the average diffusivity and t is the cooling time. These diffusion distances are relatively small compared with the Pb interparticle spacings in Table 3, i.e. 15 and 300#m for small and large Pb particles respectively in chill-cast AI-5 wt% Pb, and 0.01 and 0.5pro for small and large Pb particles respectively in melt-spun AI-5 wt% Pb. Thus, there is insufficient time during chill-casting and meltspinning for significant Pb particle coarsening to take place. (4) Droplet solidification: On cooling below the eutectic temperature of 327°C, the Pb droplets solidify by heterogeneous nucleation on the { l l l } facets of the surrounding AI matrix as shown in Fig. 6, with an epitaxial cube-cube orientation relationship as shown in Fig. 3. Transmission electron

i

,500

;

:

320

:

w

-

-

540

TEMPERATURE (*C)

Fig. 9. Differential scanning calorimeter traces of Pb particle solidification exotherms from chill-cast hyperrnonotectic A1-5 wt% Pb alloys doped with 0.5 wt% ternary additions: (a) Mn; (b) Cu; (c) Zn; (d) Fe; and (e) Si. micrographs and electron diffraction patterns such as Figs 4 and 6 show that the resulting solid Pb particles embedded in the AI matrix have a truncated octahedral equilibrium shape, bounded by {100} and { 111 } facets. Details of the Pb particle solidification behaviour are clarified by the differential scanning calorimeter results obtained during subsequent heattreatment, and are discused further in Sections 4.3-4.5. The solidification sequences in chill-cast and meltspun monotectic Al-I.5 wt% Pb and near-monotectic A l - 2 w t % Pb are similar to the hypermonotectic alloys, except for the absence or near-absence of the larger Pb particles formed by liquid phase separation. As-solidified and heat-treated microstructures in chill-cast and melt-spun hypermonotectic AI-5 wt% Pb and A1-5 wt% Pb-0.5 wt% Si and monotectic A l - l . 5 wt% Pb are discussed in more detail elsewhere [4l]. 4.2. Surface energy anisotropy

t5

c c ~.L..

:

;

! 30O

*

J

J

; : :520

:

:

; 340

:

:

TEMPERATURE I°C)

Fig. 8. Differential scanning calorimeter traces of Pb particle solidification exotherms from chill-cast AI-Pb alloys: (a) 99.999% pure hypermonotectic AI-5 wt% Pb; (b) 99.99wt% pure hypermonotectic AI-5wt% Pb; and (c) 99.999% pure near-monotectic AI-2 wt% Pb.

Transmission electron micrographs and electron diffraction patterns such as Figs 4 and 6 show that solid Pb particles embedded in an AI matrix have a truncated octahedral equilibrium shape, bounded by {100} and {111} facets. Measurements of {100} and { 111 } facet separations during in situ heating in the electron microscope are shown in Figs 6 and 7, and indicate that the small Pb particles in melt-spun A1-Pb alloys can equilibrate quickly to form facets, during either heating and melting, or cooling and solidification, even when the temperature changes rapidly. Sundquist [51] has used a simple near-neighbour bond energy calculation to estimate the anisotropy of solid-vapour surface internal energies in f.c.c, and

MOORE et al.: SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN A1

1336

E

"7.

.. °

o ~

o~

0

~

"

(c)

~

~______-

"

~-""-~"

-

(72.I

"1"

280

300

320

TEMPERATURE

:

~C)

'

300

320

340

TEMPERATURE (*C)

Fig. 11. Differential scanning calorimeter traces of Pb particle solidification exotherms from melt-spun hypermonotectic A1-5 wt% Pb alloys doped with: (a) 0.5 wt% Cu; (b) 0.Swt% Zn; (c) 0.5wt% Fe; (d) 0.5wt% Si and (e) l wt% Si.

(b)

b.c.c, metals, and a similar method can be used for solid A1--solid Pb surfaces. The surface internal energy Uhkt of a general {hkl} solid Al-solid Pb facet can be estimated from [40, 46, 51]

d 1

2Uhk/= nhkt bhkt (2eAI-Pb-- eal AI-- epb-pb)

J

:

=

:

:

:

280

,

:

:

:

300

:

:

•

:

320

TEMPERATURE

:

:

340

where nhk~ is the number of surface atoms per unit area, bhkl is the number of near-neighbour bonds per surface atom, and e~a-pb, eA] ^l and epb-pb are the A1-Pb, AI-A1 and Pb-Pb near-neighbour bond energies respectively. The ratio of { 100}/{ 111 } surface internal energies is therefore given by

(*C)

Uloo/Ulll = nloo bloo/nltl bnl .

(4)

For the f.c.c, structure of Al and Pb, bt00 --- 4, b,~ = 3, n]oo = 1/d 2 and n m = 2/3 o.5d 2, where d is the nearneighbour separation. Equation (4) then gives the {100}/{111} anisotropy of surface internal energy as u]~o/um=2/3°'5=l.15, in excellent agreement with the measured average value of aloo/trt] l --- 1.14 in Fig. 7 for the anisotropy of {100}/{111} solid A I solid Pb surface energy in the melt spun Pb particles. The surface energy anisotropy of solid and liquid Pb particles embedded in an AI matrix is discussed in more detail elsewhere [40].

(e)

i r ~

.J LL

(3)

.__

-r

4.3. Pb particle solidification

i

I

280

'

'

i

I

,

i

,

300 TEMPERATURE

I

,

320

-

-

,'

-"

340

(oc)

Fig. 10. Differential scanning calorimeter traces of Pb particle solidification exotherms from melt-spun hypermonotectic AI-5 wt% Pb alloys as a function of cooling rate in the calorimeter: (a) 10 K min-I; (b) 5 K rain-t; and (c) 2 K rain- t.

Differential scanning calorimeter traces such as Figs 8-11 give detailed information about the Pb particle solidification kinetics in chill-cast and meltspun A1-Pb and A I - P b - X alloys. The large number of Pb particles ensures reproducibility in the differential scanning calorimeter traces, particularly for the melt-spun alloys as can be seen in Fig. 10. The small size of the Pb particles ensures that their solidification kinetics are dominated by nucleation, since each

MOORE et al.: SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN AI 31o

(a)

305

o.-o

0.05

n

1337

(b)

~n

0.04

?

300

-

; 0.03

._~

2 9 5 ~-

.~

E ~

290

--

285

i I ~-

g

0.02

[] Onset temperature

280

' C

,'~ Peak temperature

0.01

tx

o End temperature

I 2

I 6

I

I

8

10

CooLing rate

(K/rain)

I 4

0

2

6

8

CooLing rate

(K/rain)

4

10

Fig. 12. Exotherrnic peak shape from Pb particle solidification in melt-spun hypermonotectic A1-5 wt% Pb alloys as a function of cooling rate in the differential scanning calorimeter: (a) solidification onset, peak and end temperatures; and (b) exothermic peak height. particle must be nucleated independently during cooling below the melting point in the differential scanning calorimeter. The Pb particle solidification behaviour in chillcast and melt-spun AI-Pb and Al-Pb-X alloys can be described as follows. On cooling below the melting point, Pb particles containing catalytic trace impurities nucleate and solidify, with variable undercoolings because of the variable catalytic potency of the different impurities. Trace impurities are distributed homogeneously throughout the alloys, so that the larger Pb particles are more likely to be nucleated than the smaller ones. At about 305°C, Pb particles which have not been nucleated by catalytic trace impurities are nucleated by the surrounding Al matrix. In other words, the broad 305-327°C exotherm on the differential scanning calorimeter traces of Figs 8-11 corresponds to the solidification of Pb particles catalytically nucleated by trace impurities; and the sharp 305°C exotherm on the differential scanning calorimeter traces of Figs 8-11 corresponds to the solidification of Pb particles catalytically nucleated by the surrounding A1 matrix. This type of Pb particle solidification behaviour explains the following experimental observations: (1) As shown in Fig. 8, the broad solidification exotherm is more pronounced in 99.99% pure chillcast hypermonotectic AI-5 wt% Pb than in the corresponding 99.999% pure alloy, because of the greater concentration of catalytic trace impurities. (2) As shown in Fig. 8, the broad solidification exotherm is absent in chill-cast monotectic A1 1.5 wt% Pb and near-monotectic AI-2wt% Pb, unlike the corresponding hypermonotectic A1-5 wt% Pb alloy. Chill-cast Al-l.5 and 2wt% Pb contain mostly the smaller 1-2/~m Pb particles, so that the Pb AM 38,7--J

content nucleated by catalytic trace impurities is reduced below the detection level in the differential scanning calorimeter. (3) As shown in Fig. 10, the broad solidification exotherm is absent in melt-spun hypermonotectic AI-5wt% Pb, unlike the corresponding chill-cast alloy. Melt-spun hypermonotectic AI-5 wt% Pb contains only small 50-100 and 5-10 nm Pb particles, so that the Pb content nucleated by catalytic trace impurities is again reduced below the detection level of the differential scanning calorimeter. (4) As shown in Fig. 3, the small Pb particles in melt-spun hypermonotectic A1-5 wt% Pb exhibit a cube-cube orientation relation with the surrounding AI matrix, because of the catalytic effect of the AI matrix in nucleating Pb particle solidification. As shown in Figs 6 and 7, Pb particle nucleation can take place on the {111 } AI facets which survive above the Pb melting point. (5) As shown in Fig. 9, the broad solidification exotherm in chill-cast hypermonotectic AI-5 wt% Pb is enhanced by 0.5 wt% ternary addition of catalytic Si. As shown in Fig. 11, the broad solidification exotherm in melt-spun hypermonotectic AI-5 wt% Pb is only enhanced by a higher 1-2 wt% ternary addition of catalytic Si, because of the smaller size of the melt-spun Pb particles. 4.4. Nucleation kinetics

The equilibrium melting point of the Pb particles in chill-cast and melt-spun AI-Pb and A1-Pb-X alloys may not be the same as the bulk equilibrium Pb melting point of 327°C, because of pressure effects caused by a combination of differential thermal contraction, solidification shrinkage and capillarity. However, previous work on chill-cast and melt-spun A1-Pb alloys [42] shows that differential thermal contraction and solidification shrinkage stresses are

1338

MOORE et al.: SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN AI

relieved by a combination of cavitation and vacancy creep, and that capillarity forces have an insignificant effect on the Pb particle melting point. In melt-spun A1-Pb and A1-Pb-X alloys, the 5-100 nm Pb particles begin to nucleate and solidify at a temperature 22 K below the Pb melting point, as shown in Figs 8-11. Complete particle solidification is expected to follow almost instantaneously after nucleation for such small Pb particles at relatively high undercooling. At any temperature T below the Pb particle melting point, the fraction of solid particles Z is therefore given by the differential equation [43] d Z / d t = I(1 - Z )

(5)

where I is the nucleation frequency within each Pb particle. Equation (5) is less suitable for the chill-cast AI-Pb and A1-Pb--X alloys, with larger Pb particles and correspondingly longer post-nucleation solidification times. With decreasing temperature below the Pb particle melting point, the Pb particle solidification rate d Z / d t increases with increasing nucleation frequency L reaches a maximum, and then decreases as the solid fraction Z approaches 1. At a constant cooling rate T, the Pb particle solidification rate has its maximum value when d / d T ( d Z / d t ) = - 7"-~ d2Z/dt 2 = 0, which by differentiating equation (5) is equivalent to dl/dt = - T d I / d T = 12.

(6)

Figure 13 shows schematically the heterogeneous nucleation of a spherical cap of solid Pb on a catalytic {hkl} facet of the AI matrix surrounding a liquid Pb particle in chill-cast or melt-spun A1-Pb. The nucleation frequency I within each Pb particle is given by [52, 53] I = A e x p [ - B / ( T m - T) 2 T]

(7)

where Tm is the Pb particle melting point, A = N c ( k T / h ) e x p ( - Q / k T ) , Nc is the number of catalytic nucleation sites per Pb particle, k and h are Boltzmann's and Plank's constants respectively, Q is the activation free energy for transporting a Pb atom across the Pb solid-liquid interface, B = Ktr3T2mf(O)/kL 2, K is a shape factor equal to 16rr/3 for a hemispherical cap shaped nucleus, tr is the Pb solid-liquid surface energy, f ( 0 ) = (2 - 3cos 0 + cos30)/4, 0 is the contact angle at the solid Al-solid Pb-liquid Pb triple point as shown in Fig. 13, and L is the Pb latent heat of solidification per unit volume. 4.5. Contact angle

On differential scanning calorimeter traces such as shown in Figs 8-11, the Pb particle solidification rate d Z / d t at each temperature is directly proportional to the measured excess heat flow, i.e. to the height of the

¢r Liquid Pb

(hkL) o"L

o"S

SoLid AL

Fig. 13. Schematic diagram of the heterogeneous nucleation of Pb particle solidification on a catalytic {hkl} facet of the surrounding A1 matrix during heating and cooling of chillcast and melt-spun hypermonotectic AI-5 wt% Pb alloys in the differential scanning calorimeter.

exothermic solidification peak. The fraction of solid Pb particles Z can also be obtained at each temperature by partial integration of the exothermic solidification peak. Equations (5)-(7) and the differential scanning calorimeter traces in Figs 8-11 can then be used in several different ways [43] to calculate the contact angle 0 at the solid Al-solid Pb-liquid Pb triple point, and the number of catalytic nucleation sites per Pb particle Arc: (1) From equations (5) and (7), the Pb particle solidification onset temperature is independent of cooling rate in the differential scanning calorimeter, in agreement with the experimental measurements shown in Fig. 12 for melt-spun hypermonotectic A I - 5 w t % P b . From equations (5) and (7), the Pb particle solidification onset temperature is given by (dZ/dt) onset = I = (dZ/dt)*, where (dZ/dt)* is the detection limit of the calorimeter. The calorimeter traces in Figs 8-11 were obtained with a typical specimen size of 10 mg and a calorimeter sensitivity of 0.01 mW, corresponding to a detection limit of 8.6 x 10-3/s for the melt-spun AI-Pb and A1-Pb-X alloys. Assuming that all AI atoms at the Pb particle surface can act as catalytic nucleation sites, Nc = 1.9 x 1 0 4 for an average Pb particle diameter of 20 nm. Taking e x p ( - Q / k T ) = 10 -2 [52, 53], tr = 55mJ/m 2 and L = 2 5 0 m J / m 3 [55], a solidification onset temperature of 305°C gives f ( 0 ) = 0.010 and 0 = 28 °. (2) Equations (5) and (7) can also be used to describe the shape of individual Pb particle solidification exotherms in the differential scanning calorimeter. Combining equations (5) and (7), In [(dZ/dt)/ ( 1 - Z ) ] varies linearly with 1 / ( T ~ - T ) 2T, with a slope and intercept of - B and In A respectively. Figure 14(a)-(c) shows Pb particle solidification exotherms from melt-spun hypermonotectic AI-5 wt% Pb, obtained at cooling rates of 10, 5 and 2 K/min respectively in the differential scanning calorimeter, and re-plotted in the form In [(dZ/dt)/(l - Z)] versus 1~(Tin - T)2T. The linear variation predicted by equations (5) and (7) is obeyed well over the temperature range between the solidification onset and peak temperatures. Best fit slopes and intercepts give values of A and B which correspond to contact angles 0 in the range 23-27 °, and numbers of catalytic nucleation sites per Pb particle N c in the range 2.6 x 10-6-0.5.

MOORE et al.: SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN A1 (a)

I/(Tm-T)2/T -2

N

1.0

1,5

2.0

(b)

x 10 6

2,5

3.0

3,5

1 / ( T m - T ) Z / T x 10 s

4.0

-2

I

(o)

1339

-3

-3

-4

-4

-5

N!

-6

g -6

1.0

(b)

1.5

2.0

I

I

2.5

I\

3.0

3.5

l

I

4.0 I

\

-5

I

~"

N

z .J

Z -J -8

--8

-9

--9

-10

--10

(c)

I/(Tm-T)2/T

_z~.o :(c)

1.5 I

2.0 I

2.5

X 10 6 3.0

3.5

4.0 I

-3

-4 N !

-5

"o

-6

N

-o z ,,_1 -8

-9

-10

Fig. 14. Differential scanning calorimeter traces of Pb particle solidification exotherms from melt-spun hypermonotectic A1-5wt% Pb alloys, re-plotted according to equations (5) and (7) in the form ln[(dZ/dt)/(l- Z)] vs 1/(Tin- T)2T: (a) I0 K/rain; (b) 5 K/min; and (c) 2 K/min. (3) From equations (5) and (7), the maximum Pb particle solidification rate (dZ/dt)m~x is given by [43] (dZ/dt)r~x = A(I -- Zm~)

x exp[-B/(T,.

-

Tmax) 2

Tmax] (8)

and corresponds to a temperature Tm~x, which can be obtained from equation (6) after differentiating equation (7) with A approximately independent of temperature [43, 52, 53]

B'['(3T~,~- Tm)/r,4(Tm- Tm~x)3 Tin,x2 =exp[--B/(T m - Tmax)2 Tm,~]. (9) Equations (8) and (9) describe the variation in shape of the Pb particle solidification exotherms as a function of cooling rate in the differential scanning calorimeter, as shown in Figs 10 and 12.

From equations (8) and (9), the Pb particle solidification peak temperature /"max decreases and the exothermic peak height (dZ/dt)max increases with increasing cooling rate, in agreement with the experimental results shown in Fig. 12 for meltspun hypermonotectic AI-5wt% Pb. From equation (8), ln[dZ/dt)maff(l -Zm~x) ] varies linearly with l](Tm-Ttnax)2.Tmax, with a slope and intercept of - B and In A respectively; from equation (9), In {/~(3Tm=~- T~)/(Tm- T~x)3T~,x} also varies linearly with l/(T~-Tmx)2"Tm~, with a slope and intercept of - B and In (A/B) respectively. Figures 15(a) and (b) show the cooling rate variation of the Pb particle solidification peak temperature and exothermic peak height respectively, for meltspun hypermonotectic AI-5wt%Pb, re-plotted from Fig. 12 according to equations (8) and (9). The

1340

MOORE et al.:

SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN AI

I / ( Tm-Tmo~12/T~o~x 106 2.0

1 7. o-

2.2

24

I

~

2.6

2.8

3.0

~.a

3.4

i

I

a o-

i (o)

) (b

-17.5

1.5 ,

J

0 0

-18.0

~

!

~= ~.o

I

E N I

-18.5

--

-19.0

--

4~ I

0.5

°°

o

0

0

"o

N

J

I,O .F-

o

~

"O Z

-19.5 -

0

"J

I 2.2

2.4

2.6

2.8

\3.0

I 3.2

I

3.4

1/ITrn-Trnox IZ/Tmax X10 6 °to ~

Z .J

-2o.o -

-20.5

,,,,~

--

o%

-o.5

-1.0

Fig. 15. Pb particle solidification peak temperature and exothermic peak height for melt-spun hypermonotectic AI-5 wt% Pb alloys as a function of cooling rate in the differential scanning calorimeter, re-plotted from Fig. 12 according to equations (8) and (9) in the form: (a) ln[]P(3Tmax - Tm)/(T m - Tmax)3 T~x ] vs 1/(Tm--Tma,)2Tmax; and (b) l n { ( d Z / d t ) m a x / ( 1 - Zmx)} vs 1/(Tm--T,~)2Tm~x.

experimental measurements are in good agreement with the linear variations predicted by equations (8) and (9). Best fit slopes and intercepts give values of A and B which correspond to contact angles 0 of 22 ° and 20 °, and numbers of catalytic nucleation sites per Pb particle Nc of 1.1 × 10 -7 and 1.8 x 10 -7, for the peak temperature and peak height variations respectively. The best method of analysing the Pb particle solidification exotherms from DSC traces such as shown in Figs 8-11 is probably the cooling rate variation of peak shape shown in Fig. 15, which averages over a large number of independent DSC experiments. The best measured value of contact angle 0 at the solid Al-solid Pb-liquid Pb triple point is therefore 21 ° . All measured values of the number of catalytic nucleation sites per Pb particle Nc are unreasonably low by several orders of magnitude, a common observation for pre-exponential factors measured by analysing nucleation kinetics during solidification [52, 53]. Investigations of the solidification of Cd, In and Sn particles embedded in an A1 matrix [42, 43], taken together with the present results, indicate that measured Nc values become more unreasonable as nucleation catalysis becomes more efficient. As discussed elsewhere [43], this effect may be associated with a progressive breakdown of the classical hemispherical cap model of heterogeneous nucleation at the low values of contact angle corresponding to efficient catalysis. As shown in Fig. 13, the contact angle 0 at the solid Al-solid Pb--liquid Pb triple point during Pb particle

solidification is determined by the relative magnitudes of the solid Al-liquid Pb, solid Al-solid Pb and solid Pb-liquid Pb surface energies, a L, tTs and tT respectively c o s 0 = (OL -- o s ) / ~ .

(10)

The surface energies of t7L and t~s in equation (10) depend upon the crystallography of the { h k l } Al facet which catalyses the nucleation of solidification. Liquid Pb particles can nucleate on the atomically ordered {l 11} Al facets which survive above the Pb melting point as shown in Figs 6 and 7, giving relatively small values of t7s and 0, and a strong cube-cube orientation relationship as shown in Fig. 3. Taking the best value of 0 = 21 °, equation (10) gives the difference in solid Al-liquid Pb and solid Al-solid Pb surface energies as (7L - - O " s ~ - - - 5 1 mJ/m 2 on the { 111 } AI facets. 5. CONCLUSIONS 1. The as-solidified microstructures of chill-cast and melt-spun hypermonotectic AI-5 wt% Pb and AI-5 wt% Pb4).5 wt% Si alloys consist of a homogeneous bimodal distribution of faceted Pb particles embedded in a matrix of Ai, with chill-cast Pb particle sizes of 1-2 and 5-50 #m, and melt-spun Pb particle sizes of 5-10 and 50-100 nm. The larger Pb particles are formed during cooling through the region of liquid immiscibility, while the smaller Pb particles are formed during monotectic solidification of the A1 matrix. The as-solidified microstructures of chill-

MOORE et al.: SOLIDIFICATION OF Pb PARTICLES EMBEDDED IN A1 cast and melt-spun monotectic AI-1.5 wt% Pb and near-monotectic A I - 2 w t P b alloys are similar to the hypermonotectic alloys, except that the larger Pb particles are absent or reduced in quantity. Irregular Pb particle monotectic microstructures are consistent with relatively low values of approximately 100 K s / m m 2 for the ratio of thermal gradient to solidification velocity during chill-casting and melt-spinning. The Pb particle distributions in monotectic A l - l . 5 w t % Pb, near-monotectic A I - 2 w t % Pb, and hypermonotectic Al-5 wt% Pb and A I 5 w t % Pb-0.5 wt% Si alloys are very resistant to coarsening during manufacture by chill-casting and melt-spinning, and during post-solidification heattreatment. 2. Second-phase particles in melt-spun monotectic and hypermonotectic alloys are suitable for in situ heating experiments in a transmission electron microscope to measure the anisotropy of solid-solid and solid-liquid surface energy as a function of temperature. The Pb particles in melt-spun hypermonotectic AI-5 wt% Pb and A1-5 wt% Pb4).5 wt% Si alloys exhibit a cube-cube orientation relationship with the Al matrix, and are truncated octahedral in shape, bounded by { l l l } and {100} facets. In melt-spun hypermonotectic Al-5 wt% Pb and A1-5 wt% P b 0.5 wt% Si alloys, the anisotropy of solid Al-solid Pb surface energy is constant between room temperature and the Pb melting point, with the {100} surface energy 14% greater than the {11 l} surface energy, in good agreement with geometric near-neighbour bond energy calculation. The {100} facets disappear when the Pb particles melt, and the anisotropy of solid Al-liquid Pb surface energy decreases gradually with increasing temperature above the Pb melting point, until the Pb particles become spherical at about 550°C. 3. Second-phase particles in chill-cast and meltspun monotectic and hypermonotectic alloys are suitable for heating and cooling experiments in a differential scanning calorimeter to determine the kinetics of heterogeneous nucleation during particle solidification. Temperature measurements during particle solidification experiments are reproducible to within + 1-2 K after chili-casting, and +0.2-0.3 K after melt-spinning. Pb particle solidification is nucleated catalytically by the surrounding AI matrix on the { 111 } facet surfaces, with an undercooling of 22 K and a contact angle of 21 ° at the solid Al-solid Pb-liquid Pb triple point. Ternary additions of Mn, Cu, Zn and Fe have little influence on the Pb particle solidification behaviour, but Si is a potent catalyst for solidification of Pb and stimulates the Pb particles to solidify close to the equilibrium melting point. Acknowledgements--The authors would like to thank Pro-

fessor Sir Peter Hirsch for provision of laboratory facilities, UKAE Harwell for financial support of this research programme and Drs E. A. Feest, K. Chattopadhyay and W. T. Kim for helpful discussions.

1341

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