The growth and structure of eutectics with silicon and germanium

THE GROWTH A N D STRUCTURE OF EUTECTICS WITH SILICON AND GERMANIUM A. Hellawell Department of Metallurgy, Oxford University

I.

INTRODUCTION

Although much pure and applied research has been directed towards understanding and controlling the structure of eutectic alloys, there are still only two alloy systems in which the eutectic alloys are of established economic importance--namely, cast irons and aluminium-silicon alloys containing 5-25 wt. ~o silicon. It is evident also, that while the growth of uniform lamellar or fibrous structures is fairly well understood and susceptible to quantitative analyses,< 1-8) the industrially important materials are typical of metal/non-metal combinations about which our understanding is not even qualitatively complete. Both cast irons and aluminium-silicon alloys are important foundry materials, but the importance of the latter arises because small ( ~ 0.01 wt. ~o) concentrations of sodium produce a spectacular refinement of the scale and distribution of the phases which is accompanied by a great improvement in the mechanical properties. The refined structure is said to be "modified", and although the material is attractive because it has low specific gravity and good casting characteristics, it is the process of modification which makes the alloys economically significant. As will become evident, the problems arising during the solidification of aluminium-silicon alloys are largely connected with the mechanisms of crystal growth of silicon in metal solutions, and are therefore common to other eutectic materials containing silicon or structurally similar germanium. The present article, therefore, is an attempt to discuss the general problem of silicon or germanium growth in metallic solutions of aluminium, silver and gold, but is necessarily focused upon the aluminium-silicon system for which so much data is available. The susceptibility of this material to structural modification by minor impurity additions, with consequent useful properties, has resulted in nearly fifty years of largely uncontrolled experiment and speculation. 3

4

PROGRESS IN MATERIALS SCIENCE

A.

Binary Eutectic Systems containing Silicon and Germanium

Binary systems including silicon and germanium are illustrated in Fig. 1 and various details about the phase equilibria are listed in Table 1.

100C

J /

13.2 0

577 50(

12.5 18.6

A I Si

A g Si

I00(

A u Si

\'~ 26

50c 3o

[ A I Ge

AgGe

,~ A u Ge

FIG. l. Equilibrium phase diagrams for silicon and germanium with aluminium, silver and gold.(4,5) Compositions in at. ~, temperatures in °C.

The phase diagrams are based upon those published in Hansen(4) and supplemented by Elliott.(5) The six systems are of simple eutectic form and have in common a combination of a metal having a face-centred cubic structure and a non-metal or metalloid having the diamond cubic structure. No stable intermetallic phases are formed, but extended ranges of solid solubility and some metastable compounds have been reported in "splat cooled" specimens of A g - G e alloys,(6) while in similar specimens of A u - G e eutectic alloy it has been reported(7) that the liquid phase can be retained at low temperatures for short periods.

GROWTH AND STRUCTURE OF EUTECTIC SILICON

5

Details of liquidus curves are not well established in the silver and gold alloys except in the vicinity o f the eutectic points. The liquidus slopes in Table 1 are mean values and should probably be somewhat greater at eutectic compositions. The eutectic composition has been determined with some certainty in the A1-Si system (see below) although the significance o f a precise eutectic composition is rather lost in the context of microstructures which can be formed over a range of conditions. There are ranges o f solid solubility of both silicon and germanium in the TABLE 1

Silicon and GermaniumEutectic Systems System

.A. . . B

AI Ag Au A1 Ag Au

Si Si Si Ge Ge Get

Eutectic composition

a/? ~/o

12.3 13.2 18.6 30.3 25.9 / 27.0 /

12.7 Si 3-8 Si 3.15 Si 53 Ge 19 Ge 12 Ge

Eutectic temperatureoc

577 855 370 424 561 356

Volume fraction

Solid-liquid distribution coefficients, k, and liquidus slopes, m °C/wt. ks atTE

ms °C/~ linear

k/3 atTE

m~ linear

14"6 ~o Si 0'13 15-4 ~o Si 10-1 21 ~ Ge 10 1 36.5 ~ Ge 0"1 41 ~ Ge 0"35 31 ~ Ge 0"1

6.5 25 230 5 15 60

10-5 10-7 10-6 10-z 10-8 10-5

9.5 5 lO 10 4 7

metals although these have not been established with any certainty for silicon in silver or gold. Except in the case of A1-Ge, where the solid solubility in germanium exceeds 1 wt. ~ AI, solubility limits in silicon and germanium are small unless considered as semiconductor impurity levels. In all systems the silicon and germanium solidus lines appear to be retrograde, i.e. solid solubilities increase above the eutectic temperatures and reach maxima closer to the melting points of the pure components. The solubility ranges based on resistivity and diffusion data are small, e.g. 10 -z at. ~ , and those based on microhardness measurements a p p r o a c h 1 at. ~ but are probably less reliable. It follows that uncertainty about the solid solubilities is reflected in the values given for the solid-liquid distribution coefficients, but those for the metallic constituents are o f the order 10 -t while those for the non-metals are p r o b a b l y several orders of magnitude smaller, the solid solubilities decreasing with temperature to the eutectic temperatures.

B. Properties and Applications AI-Si The specific gravity o f silicon is 2.3 g/cm 3 and that of aluminium 2-7g/cm 3 so that silicon is one of the few elements which may be added to aluminium

6

PROGRESS IN MATERIALS SCIENCE

without loss of the weight advantage. Commercial alloys are produced which contain up to 25 wt. ~ silicon with a variety of minor additions of copper, magnesium, iron, nickel and others, and these are used particularly in the pistons, connecting rods and casings of motor engines. The problems peculiar to this system are those connected with the above-mentioned modification by sodium additions and similar effects which can be produced by chill casting--Table 2 illustrates these features.IS) TABLE2 Mechanical Properties of Aluminium, 13 ~ Silicon(s) Condition Normal Modified Normal Modified

Tensile strength Elongation Brinell % hardness lb/in2

Sand cast Sand cast Chill cast Chill cast

2 13 3"6 8

18,000

28,000 28,000 32,000

5o 58 63 71

Extracts from the original patent by Pacz(9) in 1920 explain the situation well: referring to unmodified alloys containing some 12-15 % silicon, Pacz wrote." " T h e resulting alloy if cast directly has a very coarse, dark, crystalline fracture and its physical properties are quite low, the tensile strength running from about 15,000 to 18,000 pounds per square inch with an elongation of from one half to one fourth per cent." Pacz modified the alloy by stirring in a fluoride flux and reported: " I f now the alloy be cast it will be found that the fracture instead of being coarse, dark and glassy, is fine grained, light and dense. The physical properties have undergone a most remarkable change, the tensile strength rising to a point between 23,000 and 27,800 pounds per square inch and the elongation to a point between 3½ and 6½ %." Present-day materials, whether chill cast or sand cast, are generally modified with sodium which is usually added in metallic form. High silicon contents, i.e. > 13 %, contain primary silicon crystals and have better resistance to wear than eutectic or hypo-eutectic alloys. The modification of silicon in hypo-eutectic and hyper-eutectic alloys can be effected by sodium additions in proportion to the silicon concentration (see later). Additions of other metals such as copper or magnesium are made to improve the mechanical properties of the aluminium-rich matrix phase by age hardening. Table 3 TABLE3 Mechanical properties tons/in 2 and

Alloy composition, wt.

Chill cast

Sand cast Si Cu 0"3 0'03 10-13 0.1 5-7 3-5

Mg 0-03 0.1 0.14).3

Fo 0.4 0"6 1.0

Mn 0'03 0.5 0.3-0.6

A 2.0 3-5 5

B 5.0 10.5 10

Specific gravity

C A 30 2.0 5 4'5 1

5

A = Proof stress. B = U.T.S. C = ,%oelongation to fracture.

B 5.0 12 I1

C 40 2'7 7 2"65 1 2'81

GROWTH

A N D S T R U C T U R E OF E U T E C T I C S I L I C O N

7

includes some details of commercially available alloys which may be compared with properties of commercially pure aluminium. In general the eutectic and hypo-eutectic alloys are moderately well suited to welding, but those which are age hardening are unsuitable for welding. The principal method of fabrication is always that of casting and the essential sodium additions both produce the desirable refinement and may also confer an extra advantage in reducing the surface tension.( TM In common with many other eutectic alloys, A1-Si becomes superplastic at elevated temperatures > 500°C,(m when silicon becomes plastic.m3)

Silver and Gold Alloys Eutectic alloys are formed when silver or gold wires are fused to silicon or germanium crystals, and since the eutectic temperatures are well below those of the components, good local electrical contacts can be made with semiconductor devices. Such contacts can be made by spot welding methods or by pressure welding. Aluminium is not suitable for this purpose because of oxide layers which prevent rapid alloy formation. With the minute thermal capacity of liquid alloy concerned in such welds, the microstructures are characteristic of very rapid freezing rates indeed. Gold-silicon eutectic alloy is notable as being the medium by which the growth of silicon whiskers was first demonstrated,(12) droplets of molten alloy acting as a transfer path for silicon from vapour to crystalline material. The growth of silicon as whiskers occurs because the molten alloy does not wet the silicon crystal surface and continues almost indefinitely because eutectic alloy is not used up during the transfer. Presumably the V.L.S. growth of silicon would also be possible from the corresponding silver alloy and of germanium from either gold or silver alloys. The more attractive prospect of growing a continuous epitaxial layer of semiconductor crystal in this way would seem to be possible only if the liquid phase can be made to wet the crystal surface, and there have been no reports of such success as yet. II.

GENERAL PRINCIPLES

It is difficult to describe the solidification of these materials without some general comments about eutectic solidification and the growth mechanisms of non-metallic crystals. The following notes therefore summarize some of the more important points concerned with metal/non-metal systems and may be regarded as supplementing the previous review of eutectic solidification in this journal by Chadwick.(13)

A.

Nucleation

Several authors(14-1s) have discussed eutectic microstructures with particular reference to the effects of primary phases and the nucleating efficiency of impurity particles, and this latter aspect has some obvious relevance to the above-mentioned modification process.

8

PROGRESS IN MATERIALS SCIENCE

In eutectic systems the order of precipitation of the solid phases may be important because primary particles of one phase may act as heterogeneous substrate for the nucleation of the other phase(s). As Holloman and Turnbull(I°) and Sundquist and Mondolfo(14) note, the nucleating behaviour of the primary phases will not necessarily be reciprocal and this difference has been illustrated by undercooling measurements in a number of systems. The nucleation of one phase by another is important because (a) it may be the source of an epitaxial preferred orientation(la, 15, 20, 21) and (b) the undercooling at which eutectic material nucleates will influence the number of nuclei and the rate, composition and temperature gradients at which initial growth occurs. In the silicon and germanium systems described here the evidence would seem to be that preferred epitaxial orientations are absent, but the ease of nucleation of the various phases are undoubtedly different. Crossley and Mondolfo (is) have emphasized the nucleation behaviour in aluminium-silicon alloys because it is possible that impurity additions, such as sodium or phosphorus, moy provide alternative nuclei or poison others already present, thereby changing the nucleation sequences and the resulting microstructures. These arguments are discussed in more detail in section IV.

B.

Growth in Eutectic Systems

In a eutectic system, liquid may freeze by the independent growth of relatively large crystals, typically as primary growth at non-eutectic compositions, or the two phases may be organized in the solid in such a way as to allow diffusion in the liquid to take place more efficiently at a duplex solidliquid front. The latter process has been termed "coupled" growth(18, 22-25) and produces the fine polyphase distribution which is usually regarded as typical of eutectic alloys. It has long been realized, however, that coupled growth is not restricted to eutectic compositions and temperatures but covers a range of conditions which may be depicted on a phase diagram as in Fig. 2(a). The line which includes the so-called "coupled" zone represents the

\/ .

,,-.

a

b

FIG.2. Regionsof coupledgrowthin (a) symmetricalsystemsand (b) asymmetrical systems.

GROWTH

AND

STRUCTURE

OF E U T E C T I C

SILICON

9

locus of temperatures at which primary crystals grow at the same rate as a fine scale duplex front of the same mean composition. It follows that the coupled zone concept can be interpreted in terms of the relative contributions to interfacial undercooling at the alternative fronts.(~6) In a metal/non-metal system where one phase has directed covalent bonding (Si, Ge, etc.) the latter tends to grow anisotropically to give faceted crystals which have a significant kinetic barrier to growth in certain directions. Consequently, for a given undercooling, the growth of primary crystals proceeds less rapidly than that for the isotropic growth of a metal and less rapidly also than the various duplex solid-liquid fronts which may be possible. The region within which coupled growth occurs in such a system is therefore asymmetric, Fig. 2(b), and independent growth of the faceted phase is suppressed at large undercoolings. This feature of such systems is illustrated by the micrograph of Fig. 3(a), which is of aluminium-germanium alloy and corresponds to a rapid increase in the growth rate and associated undercooling. As may be seen, the duplex front which was advancing in a loosely coupled arrangement at a slow freezing rate breaks down at rapid freezing rates into a mixture of primary aluminium and a finer duplex structure. According to the coupled growth concept, this result is not regarded as one caused by the retarded nucleation upon aluminium by germanium because in this case both phases were present before the acceleration and no nucleation event was necessary. Indeed, the extent of the original orientation appears as an irregular boundary ,-~ 1 mm ahead of the front. More recently, Mollard and Flemingst27) have demonstrated with directionally frozen alloys that not only both composition and freezing rate are important variables controlling the growth of primary crystals, but that the stability of these crystals is also sensitive to the prevailing temperature gradients. Moreover, in the systems concerned here it is also known that the morphologies of the duplex solid-liquid fronts are likewise controlled by freezing rate composition and temperature gradients.t2s-30) Therefore, any analysis of the coupled zone limits which can reasonably be attempted for regular lamellar morphologytal-a2) becomes extremely complicated in systems involving phases with essentially different growth mechanisms. A change in the composition of the liquid which freezes at a two-phase solid-liquid front can be accommodated in the solid either by a change in the volume proportions of the phases and/or by a change in composition of the phases themselves. Of these alternatives, the latter is less probable because it implies considerable increases in undercooling corresponding to compositions along the extrapolated solidus lines on the phase diagram, and in typically lamellar eutectic structurest27, aa) the composition difference seems to be accommodated primarily by changes in the volume proportions. In a system where the phases grow with different kinetic mechanisms, change in liquid composition will again involve a probable adjustment in volume proportions of the phases, but it is also characteristic of systems containing silicon and germanium (and other systems where one phase grows

l0

PROGRESS IN MATERIALS SCIENCE

Fro. 3(a)

in a faceted manner, such as bismuth)( 34, ,~5) that faceted two-phase cells develop at the growth front.( 13, ao, 36-z9) These cells incorporate the duplex arrangement in a regular lamellar form which means that the reaction must have taken place at a stable solid-liquid profile rather than a fluctuating front which is more usual in these alloys. Where silicon and germanium are concerned, these regular arrangements have a common geometry, but their incidence varies from system to system and with composition in any one system--in this article they are considered separately as a general phenomenon, section IIID. C.

Undercooling and Stability

Following Zener,(1) Tiller(2) used a lamellar model to show that the lamellar spacing ,~, which gives maximum growth rate at a given undercooling, is related to the growth rate, V, by A = A V -n, where A is a constant (10 -4 to 10 -6) and n ----½. While in practice (lz, 41) the expectation of such an optimization principle is approximately confirmed in bulk specimens, it is clear that

GROWTH

AND S T R U C T U R E

OF E U T E C T I C

SILICON

1l

FIG. 3(b) FIG. 3. Quenched growth front in AI-Ge eutectic alloy, (a) × 25, showing the appearance of primary aluminium with accelerated growth rate. The extent of the original orientation is perceptible as a n irregular b o u n d a r y ~ l mm ahead of the original front, and (b) × 450, showing an envelope of aluminium which encloses the faceted germanium crystals.

this is so only because some mechanism(s) is available for changing tl~e spacing,(a, 42) and in thin films of organic materials(36) it has been illustrated how lamellar spacings much larger than the optimum can be maintained indefinitely. In the context o f a lamellar model for coupled growth, adjustmer, t of the interlamellar spacing is not possible in a perfect arrangement if or.e phase is unable to overgrow the other at the growth front. Considerations of interfacial stability are particularly pertinent to silicon or germanium-metal systems, because if a difference in growth kinetics frequently allows one phase to occlude the other during growth, either totally or partially, an optimum profile and liquid diffusion distance cannot be achieved or maintained. In the alloys under consideration, it is to be expected that the metallic phase will more easily overgrow the silicon or germanium than the reverse, and the repeated fluctuations in the short-range diffusion process are responsible for the haphazard phase distributions which are typical of these alloys. Quite apart from the kinetic mobility of the phases, it is also characteristic of silicon or germanium alloys that the phases have significant differences in thermal conductivities, by factors in the range 3-10, which must also contribute to the instability of the growth front as Thall and Chalmers (8) have suggested. The stability of various interfacial configurations is discussed in sections III-IV, but the combined effects of kinetic and conductivity differences can be illustrated by reference to the detail of a quenched growth front as in Fig. 3(b). In this micrograph, of the germanium-aluminium eutectic

12

P R O G R E S S IN M A T E R I A L S S C I E N C E

alloy, it is apparent that the faceted outlines of germanium crystals have been enveloped at the growth front by a skin of aluminium. This envelope of metal could not have been present at the original growth front (unless it were supposed that faceted germanium crystals grew by diffusion through a solid metal layer) and must have formed during the quenching operation when the slowly growing {111 } faces of germanium (see later) fail to respond to the fall in temperature as quickly as aluminium. In general, therefore, duplex growth of phases which differ in growth rates is unlikely to take place at a stable front, and the mean interphase separation cannot be regarded as an optimum. As noted above, it is most probable that the metallic phases will be the more mobile, but as will become apparent (section III) there are also examples where exposure of the less close-packed faces of silicon or germanium crystals to the liquid can result in rapid lateral growth of these phases. Therefore, since the fluctuations at the growth front are rarely of given amplitude or frequency, nor occur in a given direction, the most that could be hoped for in a mathematical analysis of the diffusion process would be an estimate of when a stable growth front might be expected--i.e, within what limits of composition, growth rates and temperature gradients this should be possible. In the case of a reaction front where one phase may be periodically enveloped by the other, there is then one further question, that of how the occluded phase continues to crystallize from the liquid. Superficially it might seem reasonable to suppose that local enrichment at the growth front of one or other component would lead to renucleation of the phase rich in that component, and indeed, the haphazard nature of the phase distributions in many metal/non-metal alloys is easily interpreted in this way--i.e, one phase (that having the major volume fraction such as aluminium in the Al-Si case) constitutes a matrix in which are distributed isolated particles of the other. However, from what is known about the very large undercoolings which are required to produce rapid homogeneous or heterogeneous nucleation,( 19, 43) it is clear that for there to occur a large number of repetitive nucleation events the liquid at the solid-liquid front must either fall to a temperature far below the eutectic temperature (with undercoolings of the order of 0.2Tin where Tm is the melting point in °A(aa)), or the density of efficient heterogeneous sites must be at least as great as the apparent number of particles. As will become clear, there is no evidence that nucleation of crystals from liquid in these or any eutectic systems is such as to allow a continual succession of nucleation events rather than the growth of a front at which both phases are continuous, and in the cases described here it has been observed that however irregular the phase outlines in two or three dimensions, crystals are in fact continuous over relatively large distances. D. Faceted Growth in Eutectic Crystals It follows from the above that some discussion of the modes of growth of silicon and germanium from the melt is very relevant to understanding the eutectic microstructures.

GROWTH

AND STRUCTURE

OF

EUTECTIC

SILICON

13

To a first approximation, the distinction between faceted and non-faceted materials may be made as Jackson( TM has suggested, in terms of a factor a. This factor is expressed as nl/n2AS, where nl and n2 are respectively the surface and internal coordination numbers for the crystal and AS is the entropy of fusion. For values of a -< 2 a crystal surface should be of lower free energy if it is atomically rough, but with ~ > 2 there will be only a small concentration of holes or terraces on the more closely packed surfaces. This treatment is approximate inasmuch as it considers only a monomolecular layer,(45) but on this criterion most metals have a < 1 while silicon, ct ~ 5, and germanium, a ~ 3, are typically faceted on the close-packed {1 1 1 ) faces of the diamond cubic structure. Such calculations, as to whether or not crystals are likely to have singular or non-singular surfaces and therefore assume faceted or non-faceted morphologies, relate only to the equilibrium shape of the crystal in contact with its own liquid. Therefore, although it is possible to classify eutectic alloys in a general way into combinations of faceted and non-faceted constituents, as Hunt and Jackson suggest,( z6, 47) such a scheme should not be expected to hold rigorously. In eutectic systems, where phases are essentially growing from dilute solutions, the tendency to a faceted morphology may be much greater than it is in the pure material, since the entropy difference between it and the solution is likely to be greater than it is between crystal and the pure liquid. As an extreme example, sodium chloride forms non-faceted crystals in molten salt, but is characteristically faceted in aqueous solution. Likewise, as Chadwick(46) observes, aluminium crystals grow from tin-rich liquid with a faceted appearance. There is little doubt, however, that as far as the systems considered here are concerned, it is justifiable to regard them as combinations of faceting (Si and Ge) and non-faceting (Al, Ag, Au) crystals. Whether or not a faceted morphology actually is adopted by a material also depends upon the shape of the temperature isotherms, as Hulme and Mullin(4s) have pointed out for Czochralski grown crystals, Thus, if the solid-liquid front is convex to the liquid, facets will develop as the less closely packed faces grow out, Fig. 4(a). On the other hand, if the isotherm is concave, facets do not develop because a continuous series of steps is presented to the liquid, Fig. (4b), and there is no problem in the nucleation of fresh crystal layers. Hunt and Hurle(49) have extended this argument to eutectic alloys in which one phase tends to be faceted. Thus, Fig. 4(c), faceted outlines will only develop at the two-phase solid-liquid junctions if the faceting phase presents convex faces in two dimensions towards the liquid, and when the faceting phase constitutes the matrix, Fig. 4(d), and surrounds fibres of the second phase, the solid-liquid front of the former cannot develop facets because it is concave towards the liquid in one dimension. Finally, in all materials where the concentration of step sources on certain crystallographic faces is low, lattice defects must contribute significantly to the growth rate, as Frank originally suggested.(5o) Of particular importance

14

PROGRESS

IN MATERIALS

SCIENCE

\

• ,.7

."

Y.

•

•

.

-.

,

f

b

a

c

d

FIG. 4. Illustrating facet formation oft solid-liquid interfaces, (a) single crystal convex towards the liquid, (b) single crystal concave towards the liquid, (c) faceted/ non-faceted eutectic in which the faceted phase (shaded) presents a convex interface in two planes and (d) when the faceted phase is the major constituent and presents an interface which is concave in one plane.O8,49)

in the diamond cubic structure of silicon and germanium, are the external features of crystals which are produced by twinning on {111} planes. As Wagnert51) and Hamilton and Seidenstickert~Z) have illustrated, the presence of two or more twinning events in such materials then provide re-entrant grooves on at least two crystal faces which are able to propagate growth of the crystal in three dimensions, Fig. 5. These grooves have an included angle at the external surface of the crystal of 141 °04' and can act as preferential sites for molecular attachment, and, since they are self-perpetuating, allow the crystal to grow indefinitely. The incidence of growth twins is an important feature of eutectic silicon or germanium.

GROWTH

AND

STRUCTURE

OF

EUTECTIC

SILICON

15

plan

I,+,1

I? [nS_]

L

section

IL r

Fl(;. 5. Multiple twinning in diamond cubic crystal showing alternate re-entrant edges and grooves, o1,'~')

111. PURE BINARY ALLOYS A. (a)

Aluminium-Silicon

The Eutectic Po&t and Thermal Analyses

In the ten years following the discovery of the modification effect by Pacz in 1920t9) there appeared a number of papers which were understandably concerned with this effect rather than with the structure of the pure alloys. Moreover, while papers describing sodium-free alloys were relatively few, the silicon then available would be considered to be impure by present-day standards. The widely accepted(4) values for the eutectic point of 11.7 wt. ~ silicon and 577°C, were based on thermal analyses by Gwyer and Phillips,('53) the composition being located by extension of the aluminium and silicon liquidus lines. Subsequent determinationsO4-57) with purer materials confirm the eutectic temperature, but indicate a eutectic composition at 12.5 to i 2.7 wt. % silicon. This slightly higher value was confirmed by Willey (59) who used a method of hot filtration at 578°C, and from alloys in the composition range 9-19 wt. % silicon obtained filtrates of composition 12.5 _~: 0.1 wt. ~. Uncertainty about the eutectic point arises because the incidence of primary aluminium or silicon, and the temperature of the eutectic arrest on cooling

16

PROGRESS

IN MATERIALS SCIENCE

are all dependent on the cooling rate. Thus, Gayler(57) showed how primary silicon would undercool further below the liquidus temperature than would aluminium and the fine two-phase structure--generally termed the eutectic structure--might form at as much as 10-12°C below the accepted eutectic temperature, with the "eutectic point" apparently shifted to higher silicon contents by 1-2 wt. ~ . These results illustrate the so-called coupled region which was originally based on experiments with transparent organic materials by Tamman and Botschwar(2z) and K6fler.(23) The microstructures for slowly cooled and chill cast material, Figs. 6(a) and (b), show the change in scale of the two-phase distribution and the incidence of primary aluminium in the more rapidly frozen specimen. This is the same effect as that illustrated in Figs. 2(b) or 3(a) for the AI-Ge system. It appears from Gayler's work and subsequent reports( s, 18, 39, 61-64) that the depression of the eutectic arrest on cooling at rapid rates does not much exceed ~-~I0°C, i.e. this might be the order of undercooling at freezing rates of the order of 10 -1 cm/sec, which might be expected in small chill castings. The arrests did not show recalescence such as would be expected if the depression were the result of delayed nucleation only, nor is the eutectic arrest on heating curves ever depressed below the apparent equilibrium temperature of 577°C. Thermal arrests with rapid cooling fall below the equilibrium liquidus as shown, Fig. 7, and as may be seen, the silicon undercools at high rates more than the aluminium so that the eutectic point is displaced more than 1 wt. ~ to higher silicon concentrations, as would be expected for coupled growth in such a system.(22-25) At the same time, there are undoubtedly variations in the ease of nucleation of one phase by the other and Crosley and Mondolfo (is) report differences in the undercooling of small droplets. These observations were made in the same way as those reported by Sundquist and Mondolfo(14) where freezing was detected in a hot stage microscope, but surface contamination made it difficult to obtain precise values of the undercooling in these alloys. Crosley and Mondolfo report, however, that for a given cooling rate in the presence of primary aluminium the undercooling for nucleation of the eutectic was 5-7°C, the aluminium itself nucleating on some unknown substrate, while primary silicon in hyper-eutectic alloys had no such nucleating effect. These workers then compared the pure alloys with those to which various impurities had been added and their results are discussed more fully in section IV. It should follow from their reported undercooling values that the initial growth rates and temperature gradients will differ in hyper- and hypo-eutectic alloys, and nucleation of the eutectic fine structure should always be preceded by the formation of some primary aluminium if their interpretation is correct.

B. Primary Phases As indicated in Table 1, the aluminium solid solution extends to 1.65 wt. 7o silicon at the eutectic temperature, a figure which is based on microscopical studies and tensile tests at elevated temperatures by Singer and Cottrell.(66)

t~

T1

m~

m~

m~

q~

18

P R O G R E S S IN MATERIALS SCIENCE

FIG. 6('o) Fio. 6. A1-Si, 12.5 wt. ~o Si, (a) after slow cooling with a growth rate of ~ 5 ~ sec unetched, × 200; and (b) the same alloy after chill casting, unetched, × 500.

GROWTH

AND S T R U C T U R E

OF E U T E C T I C

SILICON

19

°C

650

//-.

600 •

~.-"~'~, "*/

576 567

550

I

Ib

'

20

FIG. 7. Thermal arrests, 0 , with rapid cooling rates of 1-2°C/sec. Full lines show the equilibrium diagram.(57)

The primary aluminium phase characteristically appears as in Figs. 3(a) or 16, as dendrites which have the usual (100~ growth axis of face-centred cubic metals. The observation of a (100) growth texture in aluminiumsilicon alloys (67) may relate either to the orientation of primary aluminium dendrites or to that of eutectic silicon (see below). The silicon-rich phase probably has a very low solid solubility, i.e. below 10 -2 ~ aluminium, but as noted earlier there is some discrepancy between resistivity and microhardness measurements. Segregation measurements at low aluminium concentrations(5) give a value for the solid-liquid distribution coefficient of 2 × 10 -3, but, also as noted, the retrograde solidus line would imply a lower value at the eutectic temperature. The morphology of primary silicon in pure alloys is based on that of a regular octahedron faceted on {111} planes and frequently twinned. In hyper-eutectic alloys, sections through primary silicon crystals appear as a variety of complex shapes, Fig. 8, but sometimes as almost regular hexagons which would correspond to a (111 } section through an octahedron. As already described, the primary phase grows at undercoolings and compositions outside a coupled region of the form shown in Fig. 2(b). The situation is, however, more complicated, because in addition to massive solid crystals of primary silicon, several investigators(30, 38, 39) have described "feathery" or "web" crystals, Fig. 9, which are also a feature of hyper-eutectic alloys. The structural outline of these crystals is based on sections through faceted octahedra, but within the shape of the octahedron there occurs lamellar growth at a short-range diffusion front. The morphology and crystallography of these crystals are common to the other systems, as are those of the primary crystals, and their incidence and structure are therefore considered separately, pages 49-55.

20

PROGRESS

IN MATERIALS SCIENCE

FIc. 8. Silicon polyhedra in hyper-eutectic alloy--slow cooled, 20 wt. ~ Si, × 300.(81)

C. Eutectic Microstructure after Unconstrained Growth The coarse flake morphology of silicon in Fig. 6(a) is typical of the microstructure of approximately eutectic alloy after "slow cooling". In foundry practice, "slow cooling" might correspond to cooling rates of the order of 1-10°C/min. With a specific heat of 0.1 cal/°C/g, a 1 kg ingot would be then losing heat at 102-103 cal/min, and with a latent heat of ~ 2 0 cal/g, would solidify in 20-200 min. Assuming that nucleation centres were of the order of 1 cm apart, solidification rates of the order 1 /~m/sec, would be involved. A similar estimate for chill cast material would suggest that freezing rates approaching 1 mm/sec might apply to advancing growth fronts in such cases, and would correspond to the barely resolved dispersion of Fig. 6(b). In both the coarse flake and fine dispersion of chilled alloy, silicon particles are not demonstrably connected when viewed in microsections and this has sometimes lead to the impression that each particle might be an isolated crystal. Chadwick,tla) for example, has termed this structure "discontinuous" to distinguish it from more regular lamellar or fibrous arrangements. However, GiJrtler(89) has drawn attention to the radial growth of flakes from apparent nucleation centres, and colonies of roughly aligned silicon crystals can be traced across primary dendrites of aluminium, Fig. 10. Crosley and Mondolfo

GROWTH

AND

STRUCTURE

OF

EUTECTIC

SILICON

21

FIG. 9. Silicon "feather" or "web" crystal in AI-15 wt. ~ Si, slow cooled, freezing rate 5 um/sec. Longitudinal section, unetched, x 100. infer that what appears as a needle in a two-dimensional section must be a sheet or flake, and what appears as an isolated "globule" in the fine chilled structure probably corresponds to a section through a fibre. Both suppositions are confirmed by scanning electron microscopy of heavily etched specimens, Figs. 1 l(a) and (b). The growth of these forms is considered later, but the point here is that in the three-dimensional growth of, for example, cast specimens, whatever the true density of silicon nuclei, it is very far below the apparent density of individual particles--i.e, there is appreciable radial growth following nucleation. While it is difficult to make realistic estimates of the grain or "cell" size in pure alloys, additions of soluble impurity can be made

22

PROGRESS IN MATERIALS SCIENCE

FIG. 10. A1-12.5 wt. ~ Si, quenched during freezing---eutecticflakes appearing to continue around a primary aluminiumdendrite, × 500.as)

to delineate the intercellular or intergranular boundaries as in grey cast iron and studies of this type have recently been made by Day~6s) using sodium-free and modified alloys--these results are discussed in section IV. In the slowly cooled material it is possible to obtain some information about the pattern of solidification--i.e, the density of nucleation sites and the outlines of the growth fronts--by quenching specimens before they are entirely solid, and recently Kim and Heine~64) and Crosley and Mondolfo~is) have illustrated the cellular or grain structure in this way, Figs. 10 and 12. The nucleating behaviour of the primary phases is not obvious from the microstructures. Figure 10 shows the coarse silicon flake apparentlygrowingaround a primary aluminium dendrite, while Fig. 8 shows the eutectic structure around primary silicon crystals. Contrary to the undercooling measurements of Crosley and Mondolfo it is difficult from the microscopical evidence not to form the impression that eutectic silicon flakes do in fact radiate from primary silicon and not aluminium. The impression from the microstructures of quenched specimens is, Fig. 12, that silicon flakes precede the metal at the growth front and it would follow from previous discussion, p. 12, that the enveloping layer of aluminium forms during quenching. To what extent silicon is wetted by aluminium close to the

GROWTH

AND S T R U C T U R E

OF E U T E C T I C

SILICON

FI~. l l ( a )

FIG. l l ( b ) FIG. 11. Microstructures of Figs. 6(a) and (b) after slow deep etching of the aluminiurn-scarming electron micrographs, incident beam at 45 ° to surface, (a) flake structure, × 2500 and (b) chill cast material showing filamentary silicon, × 15,000.(3035)

23

24

PROGRESS IN MATERIALS SCIENCE

F~o. 12. A1-12.5 wt. ~o Si, slow cooled and quenched when partially solid, showing radial growth of duplex "cell" or "grain", × 50.t64~

growth front cannot be judged from such microscopical evidence, but comparison with transparent organic analogues by Hunt and Jackson, t36) Fig. 13, suggests that the non-faceted phase covers the faceted phase except at the growing tips or edges, although between these tips the non-faceted phase does indeed fall far behind. The organic example is the eutectic between succinonitrile and borneol which represents a combination of two phases which not only have low and high entropies of fusion, respectively, as do aluminium and silicon, but also have similar volume proportions. The analogy is therefore a close one. To a point, therefore, the growth ofeutectic silicon can be traced at relatively slow growth rates, although the density and nature of nuclei remain somewhat obscure. In all these microscopical studies the aluminium appears as an enveloping matrix, the grain structure of which bears little superficial relation to the silicon flakes, except that metal grains appear to grow from the same nuclei as operate for the silicon. Aluminium grain boundaries can be revealed by etching/a0, 6s, 69) see later, Fig. 14, and can be traced between silicon crystals or along silicon-metal interfaces with which they are often common. As shown, the silicon dispersion at rapid cooling rates has changed from a lamellar or flake habit to one of irregular and branched filaments, Fig. 11(b), which has been likened to seaweed.tT0) Somewhere between the extremes there must therefore be a transition in morphology, although this is probably gradual rather than abrupt. However, there is probably no difference in the orientations of the crystals and both forms are heavily twinned--see later. As with any crystal growth process, morphological or crystallographic control is limited in castings or ingots in which growth takes place in three

GROWTH AND STRUCTURE OF EUTECTIC SILICON

25

FIG. | 3. Growth front of faceted/non-faceted eutectic mixture of borneol (faceted minor constituent) and succinonitrile. Phase contrast, × 2000.(~6) dimensions at a radiating front. In such cases the problem is not merely three-dimensional, but also involves continuously changing growth rates and temperature gradients. For this reason it is illuminating to observe how the microstructure of this and other alloys vary when the more obvious variables are controlled independently, and also when these are extended outside the ranges which are characteristic of foundry practice. D.

Constrained or Directional Growth Experiments

Structures of directionally frozen alloys have been described by several workers(2S-80, 70) and apart from the flake and fibrous shapes referred to above, Bell and Winegard(28) have reported a structure containing aligned

26

P R O G R E S S 1N M A T E R I A L S SCIENCE

FIG. 14. Showing the grain structure of aluminium in a regular assembly of silicon crystals, etched in aqueous HCI, × 100.

silicon crystals which grow at very slow rates, < 10-4 cm/sec. Further, Cooksey, Day and Hellawell(~9) described the same structure and showed that the dimensions and shapes of silicon crystals are also sensitive to temperature gradients. A detailed study of all the growth forms of silicon and a rationalization of their occurrence in terms of growth rate, temperature gradient and alloy composition has been made by Day and Hellawell,(8°) and although this work was primarily concerned with very pure materials and directionally

GROWTH AND STRUCTURE OF EUTECTIC SILICON

27

frozen specimens, the results go a long way towards clarifying the microstructures which grow in any circumstances. The following account is largely taken from this work. Using pure components ( < 5 ppm total impurity) alloys in the range 12-20 wt. 9/0 silicon were directionally frozen over a range of rates from 0.3 to 30/~m/sec, with temperature gradients which ranged from 0.35 to 40 °C/mm. The microstructures which occurred were tabulated into three regimes, A, B and C, and the limits within which they occurred depicted as in Fig. 15. O f these three regions, C includes the growth conditions which are thought I000

G °C/cm

I00

A

[]

B

®

®

®

®

® ®®®

®

®

®

C

B+C ®

I

I0

®

®

I I00

V ¢m/sec.lO FIG. 15. Microstructures of directionally frozen A1-Si eutectic alloys classified in terms of the prevailing growth mechanisms which operate within restricted ranges of growth rate, V, and temperature gradient, G. A. Long-range diffusion between large silicon particles at a planar aluminium front, El. B. Short-range diffusion between silicon fibres, (3, and various plate-like morphologies, 0 , having a (100) fibre texture. C. Short-range diffusion between silicon particles containing multiple {11 I) twins, ®.

28

PROGRESS IN MATERIALS SCIENCE

to be typical of foundry or laboratory alloy preparation, region B includes the textured silicon crystals first reported by Bell and Winegard,(2s) while region A defines the conditions within which coupled growth does not occur. Details of these structures are as follows.

Region A Witha G/Vratio > 10 7 °C sec/cm z the two phases grow from the liquid almost independently by a process involving diffusion distances of the order of lmrn. The reaction front, Figs. 16(a), (b), appears as a planar metal-liquid interface

FIG. 16(a) FIG. 16. Longitudinal section thlough a quenched growth front in A1-12.5 wt. Si, corresponding to region A of Fig. 15, G/V = 105 °C sec. (a) × 50, (b) × 400.

GROWTH AND STRUCTURE OF EUTECTIC SILICON

29

at which there project occasional sections of faceted silicon crystal. Dissolution of the aluminium with dilute HC1 reveals that the silicon crystal is all

FIG.

16(b)

interconnected and etched sections show that the crystal is heavily twinned. From the G/V ratio above which this type of growth front is stable and the magnitude of the diffusion distance at the growth front, Day and Hellawell estimate a liquid diffusion coefficient for silicon of ~ 5 × 10 -6 cm2/sec. If the aluminium solid-liquid front is regarded as a planar interface, the estimated diffusion coefficient would involve a corresponding undercooling of ,-~ 40°C, and a higher value of the diffusion coefficient and lower value of the interracial undercooling are more likely.

Region B Below the critical G/V ratio, Fig. 15, the planar aluminium front breaks down and silicon occurs as rods which are only some 5 ~m apart and are almost close packed, Figs. 17, 18(a). If the precipitation of silicon is regarded as taking place at depressions in the metal-liquid front the close-packed distribution would correspond to the formation of " p o c k s " rather than the development of a cellular front,( 72, 7~) the intercellular nodes of which are not situated in a close-packed array. In any case, the front changes abruptly from one at which there is relatively long-range liquid diffusion to an arrangement suited to steady state diffusion over short ranges. However, the silicon

30

P R O G R E S S IN M A T E R I A L S SCIENCE

FIG. 17. Longitudinal section through rod-like silicon, Fig. 18 (a). G / V = 6 × 104 °C see. Unetched, × 50.

I~G. 18(a) FIG. 18. (a-d) Transverse sections through directionally frozen AI-12.5 wt. % Si, illustrating ~he effect of reducing the imposed temperature gradient. Freezing rate, V = 0.3 m/sec. (a) G = 20°C/mm, (b) G = 12°C/ram, (c) G = 3°C/mm, (d) G = 0-3°C/mm. Unetched, x 50 (30).

•T1

•

t~

T~

,.q

m~

x~

32

PROGRESS IN MATERIALS SCIENCE

FIG. 18(d)

rods obtained in this work were uneven in section, Fig. 17, and there were frequent instability bands at which silicon and aluminium spread alternately across the interface. In this structure the silicon has a very highly preferred (100) fibre texture, but the metal showed no preferred orientation. Decrease in the G/Vratio from that close to the transition region produced a variety of faceted shapes which radiated as from the rod axes to give arrangements less well suited to steady state diffusion. These are the continuous crystals reported by Bell and Winegardt28) and Cooksey, Day and Hellawell(29) Figs. 18(a-d). The principal faceted forms in these crystals are plates having (100} faces and corrugated crystals having alternating {111 ) faces. A longitudinal section of a quenched growth front in this region, Fig. 19, shows traces of the crystals and how they grow at a non-isothermal front. Extracted fragments, Figs. 20(a) and (b), are joined so that they share a common (100) texture, Fig. 21, the growing edges having (110) directions and the composite crystal growing like a small dendrite in which the growing faces are {111}. Side planes are mutually inclined at a variety of angles which can be accounted for by the presence of a twin configuration having (210} mirror planes. Day and Hellawell measured the mean distance between rods and the nodes of faceted crystals which develop from them, ~, as functions of the freezing rate and temperature gradient. They also measured the average length, d, of the side plates, as seen in (100} transverse sections, and suggested that the lateral extent of the side plates is related to the lengths of the growing

GROWTH

AND S T R U C T U R E

OF E U T E C T I C

SILICON

33

FIG. 19. A1-12-5 wt.% Si, quenched growth front corresponding to the section Fig. 18 (c).

(110) edges of the silicon, Fig. 22, while it is further supposed that the rapidly growing {100} faces of the facets are stable only because they are wetted by the metal, Figs. 13 and 37. For a given temperature gradient the influence of freezing rate, Fig. 23, is important only at higher rates and both d and A are similarly influenced. The rate dependence does not therefore alter the general form of the growth profile but alters the scale of the dispersion up to a critical rate above which the (100) textured forms are entirely replaced by the irregular flake structure of region C, Fig. 15. Day and Hellawell suggest that the relatively sharp c

34

PROGRESS 1N MATERIALS SCIENCE

FIG. 20(a) FIG. 20. Extracted silicon crystals corresponding to Figs. 18(c) and 19. Growth textures <100>, (a) smooth {100} side plate, (b) corrugated plate having <{110}> corrugation axis, × 50.

Fro. 20(b)

GROWTH

AND S T R U C T U R E

OF E U T E C T I C

SILICON

[~lo]

FIG. 21. Diagrammatic construction of eutectic crystal consisting of smooth and corrugated plates which share the common < 100> axis and have the growing ends enclosed by {111} facets.(3°)

AI

FIG. 22. To show how the width of a side plate, d, is related to the solid-liquid growth profile.

35

36

P R O G R E S S IN MATERIALS SCIENCE

20

I

I

I

I

X .--. 1C v

::k v

,-<

I

I

0"2

I

I

0.5 1 V (/zm/s)

2

FIG. 23. Variation of d and A with freezing rate at constant temperature gradient, region B, Fig. 15.

transition at V ~ 3 t~m/sec corresponds to the freezing rate above which growth on the {111 } facet faces of silicon cannot keep up with the metal. Above this rate it would follow that there was a prohibitively large kinetic undercooling and the onset of multiple twinning in region C would suggest that this represented a change in the kinetics of growth for silicon. Over a range of temperature gradients, Fig. 24, both the dimensions A and d v a r y linearly until at a G/Vratio of ~ 5 × 103 °C, sec/cm2, d exceeds A and both dimensions become less sensitive to temperature gradient. It would appear, I

I

g

I

I

o!s

l

2

I

50

20 v

'~ 10

2

1

I

o.z

I

s

I

I

lo

G (°C/rr~) FIG. 24. Variation of d and 2 with temperature gradient, see Figs. 18 (a-d). Region B, Fig. 15.

GROWTH

AND

STRUCTURE

OF E U T E C T I C

SILICON

37

therefore, that an approximately steady state arrangement is possible until the profile ratio, d/)t, is about unity, and thereafter the internodal areas at the growth front contain an increasing fraction of non-steady state growth forms, Figs. 18 and 25. Day and Hellawell suggested that the formation of irregular-shaped silicon crystal corresponds to failure of the metal to wet the entire {100 } face of silicon side plates, an effect which might be expected when the metal-liquid front is depressed by a high silicon concentration in the liquid. In the region designated B, therefore, the metal and silicon contrive to freeze in a loosely coupled manner which derives from the arrangement of close-packed fibres, as described above. With a decreasing G/V ratio this arrangement looses its regularity and is replaced by a regime in which coupled growth is not even approximately steady. Throughout the region B, the aluminium matrix may assume any orientation, and thus, epitaxial orientations between the phases must be of secondary importance in controlling the growth profile and microstructure. Etched microstructures, Fig. 14, reveal the more or less haphazard traces of aluminium grain boundaries, although, as mentioned earlier, it is apparent that grain boundaries are often common to the metal-silicon interfaces, and this implies that reduction of interfacial area also reduces interfacial energy correspondingly.

Region C As already noted, the freezing conditions in this region of Fig. 15 include those generally applying to laboratory or foundry practice, and the irregular structure(s) which occur are virtually indistinguishable from those growing unidirectionally or otherwise. The presence of multiple twins in this form of silicon (a) provides a growth mechanism by which silicon can grow more rapidly(51,~2) and thus keep up with (or grow ahead of) the aluminium matrix, and (b) explains how apparently random orientation is compatible with a continuous aggregate of silicon. (a) Extracted silicon flakes, Fig. l l(a), have an approximately {111 } habit and contain multiple twin traces, Fig. 26, in the plane of the sheets, which therefore cut the surfaces of crystals at their growing edges, as would be necessary if they are a relevant feature of the growth process. It is not surprising that X-ray diffraction photographs from even directionally frozen silicon aggregate in the region C, produce Debye rings(30) characteristic of a wide range of orientations, and loss of the preferred (100) texture can be traced gradually in the region (B -+- C) of Fig. 15.(80) The multitude of silicon configurations are distributed in a relatively coarse polycrystalline aluminium matrix, and there can therefore be no preferred epitaxial orientation in this region. Presumably, also, the aluminium-silicon interfacial energy again varies continuously, as it must in region B, and this can but contribute to the instability of the growth front. It is understandable that in this region the twin density and variable orientation allow rapid growth in many directions,

38

PROGRESS

IN MATERIALS SCIENCE

P P

4

¢

FIG. 25(a) FIG. 25. (a) Optical micrograph, × 400, of longitudinal section through structure of Figs. 18(c) or 19, etched with modified C.P.4 solution~3°,75) to reveal multiple twinning in irregular silicon crystals and (b) scanning electron micrograph of deeply etched transverse section showing the continuity of platelike and irregular silicon electron beam inclined at 70 ° to the specimen surface, × 2000. so that the diffusion process, although o f relatively short range, is very loosely coupled and fluctuates continually. The inter-particle spacing varies over at least a factor o f three on any section, but such measurements as have been made o f the mean spacings, Fig. 27,~3°) correspond to a relationship, A = 0.14V-0.56 It should be noted that the estimated average spacing in this type o f structure is greater than that o f the pseudo-steady-state arrangement o f region B extrapolated to the same rate---compare Figs. 23 and 27.

GROWTH

A N D S T R U C T U R E OF E U T E C T I C S I L I C O N

39

(b) Twin configurations. There is a general observation in crystals containing multiple twins that a wide range of orientations is possible, and this has been demonstrated by Ellis( TM in ingots of germanium. For agiven crystal,

FIG. 25(b)

twinning may occur on four possible {111 } faces, Fig. 28, and so produce a total of five possible orientations. Of the four first-order twin orientations, each one might itself produce four further twin configurations, only one of which has the orientation of the original crystal--i.e, there are then twelve distinguishable second-order twins which do not coincide on a stereographic projection. In general, the possible number of different orientations is 3n -}- 2, where n is the number of initial orientations, and thus,~ 30) sixth-order twinning could produce up to 1457 non-repetitive configurations, effectively covering all areas of a stereographic projection with such a range of orientations as to appear random. This result has often led to the impression that silicon crystals must be unconnected and the particles regarded aS "discontinuous". The transition from a pseudo-steady-state arrangement, region B, to one where coupled growth fluctuates continually is a direct consequence of the onset of twinning, and, as implied, the most obvious explanation for the rapid increase in the incidence of twinning is in terms of the kinetic limitations of silicon. Day and Hellawell suggest that in the course of such a change, the kinetic undercooling will change its velocity dependence from a form: V <100> ~ ki AT n t o V { l l l } = kii exp (kiii • AT) where ki to km are constants and the exponential function represents an activation energy for the formation of twins. In either case, the rate dependence of a kinetic barrier would eventually force silicon into a position

40

PROGRESS IN MATERIALS SCIENCE

r

FIG. 26. Multiple twin traces in silicon plate, region C of Fig. 15. Etched in modified C.P.4 solution, ~0,75~ × 450.

(temperature) at the growth front where it was easily overgrown by the kinetically mobile metal. As Hunt and Jackson(a6~ observe, if a steady-state growth profile is to be maintained in a faceted/non-faceted combination, the faceted phase must project forward at the growth front so that solute rejection is efficient, while the kinetically mobile phase is retarded by a solute accumulation which is almost normal to the front. In the region B, Fig. 15, such a co-operative coupled front is apparently maintained without twin formation, while in region C, at relatively slow freezing rates the same sort of profile is maintained irregularly with twinned crystals. It follows, however, that with further rate increase even'growth at twinned silicon-liquid surfaces

GROWTH

AND

STRUCTURE

OF E U T E C T I C

SILICON

41

will be too slow to allow such a solid-liquid profile, and the silicon will fall to lower temperatures (larger undercoolings) in order to continue growing in a coupled manner. As this occurs the overgrowth of silicon will become more frequent, the crystal shapes more complex, e.g. Fig. 29, until the silicon is effectively growing at dimples or holes in the metal-liquid front and consequently adopts a filamentary habit. This is the flake-filament transition

l

i

~lk, l~.g"e

I0

I

i

... ,a 1~1r-0"56

#nl v

%=0"114V-°~

1

~

2

I

5

I

10

I

20

V (~m/s) FI~. 27. Variations o f m e a n interparticle spacings, ~, with freezing rate, IS, m e a s u r e d o n sections transverse to the freezing direction in region C o f Fig. 15.

referred to between slow-cooled and chill cast material. The transition was not discussed by Day and Hellawell because directional freezing methods do not lend themselves to freezing rates of the order of 10 1 _ 1 mm/sec, which are the order of magnitude typical of small chill castings in which the filamentary morphology occurs. It is not known for certain if the fine filaments of silicon grow by a twin mechanism, because the crystals are of the order of only 10 -1 tLm in width, but by analogy with the flake crystal and the continuity of apparently randomly oriented crystal, the twin density must be very high indeed. The conclusion that the filamentary form is produced when the silicon falls behind the aluminium-liquid front would also imply that no other kinetic mechanism is available to the silicon by which it could maintain a co-operative profile of the types referred to. To date, there have been no mathematical analyses of diffusion models which might resemble those described above, but an analysis of the type made by Hunt and Jackson~ 3) for non-faceted binary eutectic reactions with lamellar or rod-like geometry, might be extended by introducing a kinetic term for one phase. Solutions to such a treatment might then be expected to show the extent of facet formation at different freezing rates and with a realistic

42

PROGRESS

IN

MATERIALS

SCIENCE

model might indicate limits within which steady-state growth occurs. The observation that some of the short-range diffusion profiles are sensitive to temperature gradient, must, however, add to the complication of any quantitative treatment.

B. Other Silicon-Metal Systems Ag-Si As shown in Fig. 1 and Table 1, the Ag-Si system resembles that of A1-Si very closely. The microstructures of the Ag-Si alloys have been examined in slowlycooled ingots and in directionally frozen specimens by Day,< 75) and although the

FIG. 28. Diagrammatic representation of the number of different orientations resulting from multiple twinrting.Cao, 75). Original crystal 0, 1st order A, 2rid order ©, 3rd order ~. investigation was much less detailed than that with A1-Si alloys, the microstructures were found to be identical to those of the latter system at approximately the same conditions. In Fig. 30 the transverse section of material frozen within the region B of Fig. 15 should be compared with Fig. 18(c) which is a similar micrograph of the AI-Si alloy. Metallography and X-ray diffraction of the extracted silicon confirms the identical morphology and the preferred (I00) growth texture. Likewise, at higher freezing rates the same twinned morphology occurs and in hyper-eutectic alloys there are the same lamellar colonies (section IIID) and also a similar sensitivity to sodium additions (section IVA). The precise values for the transitions in growth mechanism have not been reported for this system, but a superficial inspection indicates that they cannot be widely different to those observed in the aluminium system. Au-Si It has been observed< la) that this material does not exhibit a similar flake morphology to that of the other systems. Thus, at freezing rates and temperature gradients which produce the textured crystals of AI-Si, Fig. 18(c), or Ag-Si, Fig. 30, the corresponding structure of Au-Si eutectic alloy, Figs. 31(a) and (b), appears as one of fine-rounded silicon particles which are not

GROWTH

AND S T R U C T U R E

OF E U T E C T I C

SILICON

43

FIG. 29. Optical rnicrograph of extracted silicon fragment, region C, Fig. 15, × 125.

closely aligned in the freezing direction. Apart from a few isolated shapes reminiscent of the (100) crystals and side plates, the silicon dispersion is generally non-faceted. Scanning electron micrographs show that the apparently globular dispersion is probably a section through a continuous sculptured network of silicon, and removal of the gold matrix by electrolytic etching in cyanide solutions~TM leaves a coherent aggregate of crystal. By comparison with the other systems the mean spacing of the dispersion in this system is much smaller and increase in freezing rate refines this structure without apparently changing the morphology. There would therefore appear to be no transitions in growth mechanism of the type found in A1-Si and Ag-Si, and if the (100~ growth texture ever develops, it does so

44

P R O G R E S S IN M A T E R I A L S SCIENCE

FIG. 30. Transverse section through directionally frozen specimen of Ag-Si eutectic alloy----compare with that of Al-Si, Fig. 18 (c), × 100.

only with steep temperature gradients and at very slow rates of freezing indeed. By analogy with the AI-Si alloys it would seem probable that the silicon is heavily twinned, but this has not been ascertained. There are two factors which will contribute to the difference between the gold base alloys and those of aluminium or silver: (a) the very steep liquidus slope on the gold-rich side of the eutectic point, and (b) the slightly greater volume fraction of silicon ( 2 1 ~ as compared with ~-~ 15~). The second difference might be expected to involve more interaction between the diffusion fields of adjacent particles which would hinder the development of welldefined faceted shapes, but since the increase is small this effect can only be

GROWTH

AND

STRUCTURE

OF E U T E C T I C

SILICON

45

marginal. The very large liquidus slope, however, will magnify the solute undercooling at the metal-liquid front by almost an order of magnitude, so that for any solid-liquid profile of the form illustrated in Figs. 19 and 22, the position of the metal-liquid front would lie so far behind that of the silicon as to preclude the maintenance of a stable coupled growth arrangement--the growth front for the organic analogue, Fig. 13, probably corresponds to such a situation. From the measurements and microscopy of aluminium-silicon alloys, Day and Hellawell(~0) concluded that a profile ratio > 1 could not be

Fia. 31(a) FIG. 31. Au-Si eutectic alloy directionally frozen under similar conditions to A1-Si, Fig. 18 (c), or Ag-Si, Fig. 30. (a) Transverse section, × 450, (b) longitudinal section, x 225. Unetched,

46

PROGRESS

IN MATERIALS SCIENCE

Fio. 3109) maintained without breaking down to irregularly shaped forms, and with allowance for the liquidus scope in the gold base system this would require very high gradients indeed. It follows that since a fluctuating diffusion process is general in this alloy there is negligible difference between unidirectional growth and that in cast specimens. It is also a consequence of the steep liquidus slope that the coupled region is narrow and in quenched specimens of eutectic composition there is little evidence of a shift in the eutectic point to higher silicon concentrations. C. Germanium Eutectic Systems The germanium-containing systems, Table 1, differ from those containing silicon in that the volume fraction of germanium is larger than that of silicon

GROWTH

AND

STRUCTURE

OF

EUTECTIC

SILICON

47

in the corresponding systems. The principal difference between the growth mechanisms of silicon and germanium is that the latter forms growth twins more easily and there may be no growth regime in which germanium can grow with a preferred (100) texture. It should be noted, however, that twinning occurs in both materials at freezing rates which produce twin free crystal in pure silicon or germanium, i.e. the twinning is connected with the geometry of the duplex solid-liquid front rather than the absolute growth conditions. Probably in consequence of the more symmetrical forms of the phase diagrams, especially that for A1-Ge, Fig. 1, the coupled zones are wider (in composition) and complex regular growth forms more common. Details of these forms are discussed below, but the microstructure of Fig. 32(a) illustrates the transverse section of a directionally frozen A1-Ge alloy and shows the mixed lamellar and irregular arrangements. In ingot form or at rapid freezing rates in directionally frozen specimens the germanium crystals are heavily twinned on all planes and grow in a similar manner to twinned eutectic silicon, i.e. with a random distribution of shapes and orientations. The morphology is, however, slightly altered by the higher volume fraction of the germanium which prevents the development of well-defined flakes except in the lamellar regular colonies. Longitudinal sections through eutectic alloys grown at slow rates, Fig. 32(b), show that the germanium is still heavily twinned, but that the twin traces extend only in the freezing direction. Twin traces can be followed through germanium crystals of irregular outline showing that it is in fact part of an extensive three-dimensional aggregate. In transverse section twin traces are mutually inclined at 109o20' and most particles include multiple traces. This inclination of traces would be expected if the germanium grew with a ~110) preferred orientation, and X-ray rotation photographs of A1-Ge show a highly preferred (110) texture, which is probably present in the other germanium alloys. The presence of re-entrant twin grooves at the growing surfaces of germanium crystals must allow this phase to advance at relatively rapid rates with a small kinetic undercooling, but whether this is essential to the growth or is a consequence of instability and overgrowth by the metal is not clear. The presence of two axial twin planes, however, running in two directions at the growth front, must contribute to the instability of the diffusion process by increasing the interaction between adjacent sections of the germanium crystal. Limited X-ray and metallographic studies~~7) suggest, as in alloys with silicon, that the metallic phases do not have preferred orientations with respect either to the germanium or to the freezing direction. As noted for these other cases, the range of epitaxial configurations and consequentially variable interfacial energy must contribute to the lack of stability at the growth front. Nucleation studies involving eutectic germanium have been carried out by Sundquist and Mondolfot14) in the system Ag-Ge, using a dispersion of droplets in a hot stage microscope. The undercoolings below the liquidus curves at which primary crystals nucleate are reported to be 60°C and 30°C for silver and germanium respectively, while the undercoolings below the eutectic

48

PROGRESS IN MATERIALS SCIENCE

FIG. 32(a) FIG. 32. AI-Ge eutectic alloy, (a) transverse section through specimen directionally frozen at 0.3 tzm/sec,etched dilute aqueous HCI, × 50, and (b) longitudinal section through irregular region of Fig. 32 (a) etched in oxalic acid to reveal twin traces in the germanium aggregate, × 500.(87) temperature in the presence of either primary phase differed only slightly. Thus, in the presence of primary silver, germanium was reported to nucleate at 17 °C below the eutectic temperature while primary germanium acted as a marginally better substrate for silver at 16°C below the same temperature. It is perhaps debatable whether this difference is significant, but following the argument of Sundquist and Mondolfo that phase with the higher entropy of fusion (germanium or silicon in all these systems) should have the higher solid-liquid surface energy and therefore act as a better catalyst. In all the

GROWTH

AND

STRUCTURE

OF E U T E C T I C

SILICON

49

Fro. 32(b)

systems considered here it would therefore follow that the non-metals are the better nucleants As in the silicon systems, also, the coupled zone is displaced with undercooling towards higher germanium concentrations so that quenched alloys of eutectic composition inevitably contain primary dendrites of metal--as illustrated in Fig. 3.

D.

Regular Eutectic Crystals

In all eutectic systems, under some conditions, silicon and germanium occur as regular crystals within which the phase distribution is lamellar--Figs. 9, 32 and 33. Such crystals are a common feature of eutectic alloys where one phase grows anisotropically. In silicon and germanium these structures have been studied in some detail by Meussner,( TM Hellawell(37) and Day and Hellawell(30) and the aspects of interest are (i) the morphology and crystallography, and (ii) the incidence and dimensions of these structures.

50

PROGRESS IN MATERIALS SCIENCE

FIG. 33(a) I~G. 33. Extracted aggregate of eutectic germanium (a) with reflected light and (b) with transmitted light, × 150, showing lamellae variously inclined to the axis and larnellar colonies inter-connected. With reference to Figs. 32 and 33, it is characteristic of the crystals that they appear as lamellar colonies in which the lamellae are linked by common sheets of crystal which appear as "spines" in a microsection. The resulting arrangement is then one in which lamellae extend in directions parallel to, or inclined to, the growth direction. Lamellar crystals are, moreover, often continuous with irregularly shaped material. The microscopy of quenched growth fronts, Fig. 3, shows how lamellar growth takes place at a non-isothermal front, the outline of a colony projecting forward into the liquid within a profile which

GROWTH

A N D S T R U C T U R E OF E U T E C T I C S I L I C O N

51

FIG. 33(b)

is geometrically the same as that of faceted impurity cells in silicon or germanium. (77) X-ray diffraction from small extracted colonies and individual lamellae of silicon or germaniumt 8°, a7) shows that lamellae coincide with (111 } faceting planes, while photographs taken with rotation about the original growth axis indicate a highly preferred (110) growth axis. On a {110} section through a crystal (which is that of a section transverse to the growth axis) the included angles between the traces of parallel lamellae and the connecting "spines" are then found to be 55 °, 62-63 ° and 70 °, a histogram for either silicon or germanium showing that the most common inclination is at 62-63 °. As has been

52

PROGRESS

IN

MATERIALS

SCIENCE

shown,t a°,37) these angles can be accounted for in terms of those between {111 } and {100} in twinned and twin-free crystals, the most common configuration being one involving two twinning events across axial and non-axial {111 } planes. Metallographic evidence for the location of twins comes from cusps where lamellae join the interconnecting "spine", Fig. 34, and from etched specimens such as that of Fig. 32(b). Two geometric possibilities are illustrated in Fig. 35. It has been suggested~37) that re-entrant twin grooves at the apices of faceted crystals, Fig. 35, contribute significantly to the growth process, and indeed, the high incidence of two twin events (necessary to act as step sources for two sides of a crystal'S1-52)) might support this. The incidence of twins may, however, be incidental, because as Bardesley e t al.t 7v) point out, impurity cells in a faceted material include solid-liquid interfaces between them which are concave towards the liquid and can therefore act as constant sources of growth steps for a faceted material, Fig. 36. The orientation of the metallic phase has also been examined in the A1-Si and A1-Ge systems. In A1-Si Meussnerl 3s) showed by anodic etching that aluminium on different sides of complex regular crystals differed in orientation across the {100} "spines", and concluded from this observation that the metal-silicon orientations were related in some preferred manner, from which it might be concluded that the lamellar arrangement was stabilised by an epitaxial preferred orientation. On the other hand, X-ray rotation photographsl 3°,37) of fine rods of alloy do not show any preferred orientation in the metal, and it may be that the change in orientation of the metal on different sides of a lamellar colony is simply a result of the metal grain boundary coinciding with the two-phase interface as illustrated in Fig. 14. The shape and stability of these regular crystals therefore appears to be related only to the crystallographic structure of the faceted phase. In eutectic alloys in which the faceted phase has the major volume fraction,t 78, 79) similar faceted cells develop at the growth front and the non-faceted phase of the eutectic is incorporated as a fibrous dispersion within the cell. As implied, the incidence of regular forms differs from system to system and with composition in any one system. It seems that in the more symmetrical (with respect to volume fraction, liquidus slopes and solid-liquid distribution coefficients) systems, A1-Ge (~7) and Ag-Ge (75), the complex faceted forms occur frequently over a composition range on either side of the nominal eutectic point, but in cases where the faceted phase is a minor constituent they are found only in hyper-eutectic alloys (i.e. alloys rich in the faceted component with respect to the eutectic composition). Moreover, since the lamellar crystals are a product of short-range diffusion or coupled growth, their occurrence is also related to the width of the coupled zone--which is least for steep liquidus slopes as in the systems Au-Si or Au-Ge. Inasmuch as these growth forms are more common in hyper-eutectic alloys they are sometimes(3s) regarded as particular examples of primary growth, and as may be seen at a growth front, Fig. 3, they do grow at a slightly higher

GROWTH

AND

STRUCTURE

OF

EUTECTIC

SILICON

53

FIG. 34. Polished transverse section of lamellar germanium crystal, x 500, showing cusps at the lamellar-"spine" junctions. temperature than the rest of the front. However, since they also incorporate a short-range diffusion front the solute undercooling is less than that for solid or massive primary crystals and in this respect they may be regarded as intermediate between eutectic and primary growth. Since lamellar growth takes place as at impurity cells the dimensions of the colonies are an inverse function of the imposed temperature gradient, while both the colony size and lamellar spacing are dependent on freezing rate. Figure 27 shows how the variation of lamellar spacing follows an approximately inverse power relation of the freezing rate and it is notable that the spacing is significantly smaller than the corresponding mean value for the irregular distribution at the same rate. The interphase diffusion distance in these lamellar arrangements is

54

PROGRESS

IN M A T E R I A L S S C I E N C E

[ol J.l

FIG. 35. Diagrammatic construction of lamellar crystals composed of axial and non-axial lamellae---asin Figs. 32-34.(37)

I

•

•

s

I

I'

I

•

I

"

•

°

•

"

-

o

*

•

•

"

.

s,

•

"

t

•

*

•

*

.

'

,"

,

.

J

.

•

,

"

,

• "

.

o~

•

"

°

"

FiG. 36. Illustrating how intercellular grooves in faceted materials can provide unlimited step sources from surfaces concave towards the liquid.(4s,77)

comparable with that found in other lamellar eutectic materials frozen at the same rates, (18, 41) but the spacing associated with the fluctuating front is more than twice as great--with a solute undercooling which is presumably larger also. In hyper-eutectic alloys, i,e. in systems such as A1-Si, the volume proportion of the faceted phase in the regular form is slightly greater than it is in the irregular material.(S0) The crystallography of regular colonies indicates that the lamellar habit in these crystals is dictated by the growth anisotropy of the faceted phase, and a section through the solid-liquid profile must be of the form shown in Fig. 37.

G R O W T H AND S T R U C T U R E OF E U T E C T I C S I L I C O N

55

liquid 3

metal

ElOl-l-

non-

metal

metal

Fla. 37. Diagrammatic solid-liquid profile for a faceted/non-faceted eutectic front with different positions of the non-faceted interface, positions 1-3.

For the solid-liquid profile to be stable the faceted faces of the silicon or germanium must not be overgrown by metal, and it can be appreciated qualitatively that overgrowth will occur less easily when the faceted phase has a larger volume fraction--as in A1-Ge.(sT) The effect of increasing the liquid concentration by adding an excess of the faceted phase, will, of course, increase the corresponding volume fraction, but the quantity necessary to produce stable lamellae in A1-Si, for example, is small, about 2-3 ~ silicon, so that any increase in volume proportion cannot be significant. On the other hand, an excess of one or other component immediately increases the solute accumulation ahead of one phase, and if this addition is such as to increase the solute undercooling for the metallic constituent a corresponding distortion of the growth profile, Fig. 37, may be sufficient to stabilize the solidliquid triple junction and allow lamellar growth to occur. Lamellar colonies of some size will be able to develop where the twin density is relatively low and will be an automatic result of stabilizing the growth front when one phase has a characteristic faceted growth habit. IV.

A. (a)

IMPURITY EFFECTS

Modification by Sodium Structure and Undercooling

As explained in the introduction, this is the principal focus of interest in these alloys and it has been the subject of many papers and a number of reviews.(a, la, 18, 6a, 64, s0) The original patent by Pacz in 1920(9) described the

5.6

PROGRESS IN MATERIALS SCIENCE

refining of aluminium-silicon alloys after they had been melted under a sodium fluoride flux, an effect which could be expressed quantitively in terms of the improved mechanical properties, cf. Tables 2 and 3. Following Pacz, Edwards, TABLE4 Additions for Eutectic Modification<64)

Element added Li Na

K Rb Cs Mg Ca

Wt. % added 0.075 0.075

0.075 4"20 4"2 0'0733 0"0824)'16

Temp. of addition, °C

Max. % modification

710-1213 610 638 677 696 899 610 899 857 869 591-1195 820-1188

0 0

20 80 100 100 0

60 70 20 0

25

Frary and Churchillt s2) showed that additions of metallic sodium and other alkali metals were also effective, as has been confirmed since, while Gwyer and Phillips~ 58) produced a similar effect with alkaline-earth metals and their hydroxides. Additions of metallic solium are now the usual method of modification. It is difficult or impossible to say categorically that all these metals or their compounds produce an identical effect, but generally they change the mechanical properties by increasing the ductility and raising the U.T.S., and qualitatively they act by refining the scale of the silicon distribution and make the particles less angular. Primary silicon, faceted lamellar crystals and the flaky eutectic material are all affected. There are other minor additions, such as phosphorus, which produce smaller angular silicon crystals and their action seems to be distinctly different from that of the G r o u p I and G r o u p II elements, see section IVB. Of the "modifying" additions, sodium appears to be the most effective, but whether this is because of some chemical property of the metal and its ability to react with silicon, or whether it is a result of its physical properties-melting point, vapour pressure, etc., is not known. The quantity of sodium necessary to produce the maximum improvement in elongation and mechanical strength in alloy of eutectic composition is ~ 0.01 wt. ~,ts, 63) but higher concentrations are needed to " m o d i f y " the primary crystal--see later. It is also clear that the sodium content falls rapidly while the alloy is molten, so that to achieve a final concentration in the casting of 0.01 ~o, as much as 0.1 ~o of metallic sodium may be added to the melt3 s, is, 63, 64) The loss of sodium is most rapid at higher temperatures, but at the same time, the addition is most effective if it is made at a higher temperature. Table 4 is taken from

GROWTH

AND

STRUCTURE

OF E U T E C T I C

SILICON

57

the work of Kim and Heinet 64) and indicates the relative efficiencies of various metals as compared with sodium additions made at various temperatures. It seems appropriate at this point to note that sodium additions to other eutectic alloys containing silicon and germanium also produce a refining effect on the microstructures,~ 75) although the effect is generally less obvious than it is in aluminium-silicon alloys because the eutectic structures are often finer, e.g. Au-Si, and the shapes of the silicon crystals less angular.

The Structure of Modified Alloys Eutectic Alloy. The structure of modified material cooled at relatively slow rates changes from the flake-like morphology of Fig. 6(a) or 1 l(a) to an apparently globular dispersion of dimensions close to the resolving power of an optical microscope. Scanning electron microscopy of the deeply etched surface, Fig. 38, shows that as in pure alloy after quenching, Fig. 1 l(b), the silicon is in a fibrous form380, 70, 8a) The structure is very similar to that of quenched alloy but the silicon "wool" appears to be rather more regular and less frequently branched, it is also somewhat coarser in the examples shown, but this is a function of the freezing rate as well as the sodium content. Again, by analogy with the flake structure in sodium-free alloy, it is probable that the threads of crystal are heavily twinned. Such a microstructure necessarily requires loosely coupled growth at an advancing duplex solid-liquid front, and partially solidified specimens show the radial growth of duplex grains when solidification is accelerated by quenching, Fig. 39364) It is also apparent from such micrographs that the silicon no longer projects forward into the liquid, but rather appears to grow behind the aluminium metal front--which would be compatible with the rounded section of crystals as discussed in connection with filamentary dispersion found in quenched material. The modification of slowly cooled alloy increases with sodium content up to 0.01 wt. ~ , but while autoradiographic studies by Plumb and Lewis163) confirm that the sodium is probably associated with the silicon there are no particularly high local concentrations in this range. At higher concentrations the extra sodium is localized within small acicular particles,~ 68, s4, as, 96) Fig. 42, and simultaneously the eutectic "grains" assume a banded structure, Fig. 40, which is characteristic of an "overmodified" alloy3 is, 63, sl) There is some doubt as to the exact composition of the sodium-rich phase, but it is a ternary compound of the form NaA1Sin, in which n is uncertain. Both Nowotny and Scheilt85) and Ransley and Neufeldt 9a) confirm a tetragonal structure, but while the former consider that the compound is isomorphous with NaSi2 and extends in the ternary system up to NaA1Si4, the latter report that extracted crystals had an analysed composition of NaA1Sil.3. Crosley and Mondolfot is) note that with the appearance of the ternary compound the undercooling for the nucleation of silicon is much reduced (see later) and

FIG. 38(b)

FIG, 38. Scanning electron micrograph of deeply etchodA1-Si eutoctic a l | o y a f t e r m o d i f i c a t i o n by sodium. Electron b e a m a t 45 ° to soction, (a) × 2500 ~" and (b) × 12,000. Compare Fig. 1 l(b).( a°, as)

FIG. 38(a)

.¢1 )o

GROWTH AND STRUCTURE OF EUTECTIC SILICON

59

FIG. 39. Radial growth of eutoctic cell or grain in sodium-modified AI-Si, revealed by quenching when partially solidified, 5< 50.~64~ Davies and Westt 81~ suggest that the excess sodium (above 0-01 wt ~ ) accumulates at the duplex solid-liquid front until the ternary compound and associated bands of silicon are nucleated--these being the overmodification bands of Figs. 40 and 42. As in the quenched material of nominal eutectic composition, sodium addition not only influences the silicon dispersion, but also involves a shift in the composition of the fine structure to higher silicon contents as the incidence of aluminium dendrites increases. Hyper-eutectic alloys. Larger additions than that needed to modify the nominal eutectic alloy produce a parallel change in structure in the faceted lamellar colonies, Fig. 41, and also modify angular massive crystals of primary silicon to an approximately spherical morphology, the change in morphology taking place progressively with addition of sodium--Figs. 42(a), (b). The structural changes which take place in primary crystals appear to be (a) an increase in the density of twins, and (b) a failure of the crystals to develop faceted {111 } faces3 sl, 87) The levels of sodium content necessary to produce significant changes in the morphology of massive primary crystals have not been measured in the solidified material, but in an A1-20 wt. ~ silicon alloy, additions of up to 1 wt. ~ of sodium may be made immediately prior to casting. In the work of Davies and West,(81) modification studies of lamellar or primary silicon were carried out under sodium vapour and in this way the concentration could be maintained at a constant level during experiments.

60

PROGRESS

IN MATERIALS

SCIENCE

FIG. 40. Banded structure in "over-modified" eutectic alloy, quenched when partly solidified,~18) × 500. Thermal analyses. The second feature of modified alloys is the increased undercooling at which the reaction proceeds, as numerous investigatorslS, 39, 58, 57, 63, 64, is, 86) have demonstrated by thermal analyses. In general, as Gayler(57) showed, Fig. 44, the temperatures of arrests with sodium present are similar to those obtained with rapid cooling rates, and the arrests in Fig. 43 show maximum undercooling for the eutectic arrest of about 10-12°C. Primary silicon is undercooled further than aluminium which leads to the observed shift in composition, and undercoolings up to 18°C have been reported.~ is) It is important to note that the undercoolings with sodium added are those of the horizontal part of the cooling curve, i.e. are not those which might correspond to delayed nucleation because there is characteristically no recalescence, Fig. 43. The suppression of the freezing arrests is not matched by any corresponding depression of the heating arrests, as Gwyer and Phillips~ 58) and subsequent workers have shown, i.e. the eutectic material appears to melt at the equilibrium temperature of ~ 576°C. As in rapidly cooled material, therefore, addition of sodium appears to affect the actual growth process, quite apart from any changes in the nucleating efficiency of primary phases or foreign substrates. It is important to note also that sodium additions do not suppress the cooling arrests for primary aluminium and if anything, actually reduce the initial undercooling, only affecting primary silicon or the coupled eutectic front. On the other hand,~ is, 39, 94) large excesses of sodium (1 wt. ~ ) which produce particles of the compound NaA1Si4 can

GROWTH

AND

STRUCTURE

OF

EUTECTIC

SILICON

61

reduce the undercooling for silicon, it being suggested that particles of the compound act as nuclei for silicon.

Directional freezing experiments. Constrained growth of sodium-free and sodium-modified alloys has been reported by Chadwick (71) and by Day and Hellawell.(30) In Chadwick's experiment the alloy was contained in graphite which is pervious to sodium vapour and the failure to produce a change in structure with sodium additions can probably be traced to the use of this refractory. In the experiments by Day, alumina refractories were used and alloys were analysed for sodium content after solidification. It was found that with analysed sodium levels of ~ 0.01 wt. ~ the slowly grown material did not change structure and the aligned silicon crystals of Figs.18(a-d), region B of Fig. 15, were reproduced. At more rapid freezing rates, however, the coarse flake arrangement was modified in the usual way, but insufficient experiments were carried out to determine whether the onset of the modifying action coincided exactlywith the structural changewhich occurs in pure alloys.

FIo. 41. "Feather" or "web" silicon crystals growing in sodium-modified alloy,t81) × 700. Compare Fig. 9.

62

PROGRESS IN MATERIALS SCIENCE

FiG. 42(a) Fro. 42. Primary silicon spherulites in AI-20 wt. % Si with large additions of sodium (250-1000 ppm) also showing needles of the ternary compound NaAISi4 and ever-modification bands. Etched in modified C.P.4 solution.t87) (a) Through centre of spherulite and fb) off centre section, × 100. Compare Fig. 8.

Fro. 42(b)

G R O W T H A N D S T R U C T U R E OF EUTECTIC SILICON

63

1 v

SSS

(a)~

~ 58S I-

'_G5

COOKING

~STS

HEA IN

STO S•S

3

£

•

IZ

IS

L•

ZI

E4

Z7

0

3

°

•

IZ

IS

IO

2~

Z4

TIME, MINUTES ECO

$9S

.E..,.0}

S90

~ SIS

COOLING

SlO

~ 57S $70

J

S•S

I

I

I

I

I

•

S

II

IS

IS

I

21

~4 IT O TIME, MINUTE•

$

$

S

I tZ

I

t

IS

18

21

Thermal analysis curves for aluminium-silicon alloy of eutectic composition (12.5~ silicon): (a) containing >0"1 sodium; (b) unmodified (>0.001 ~ sodium). lOG S~S u .

$90 COOKING

SE5

N[ [ATI ~ , G /

S•O ~ 575

-

5TO

(a)

~6S

'o°

TIME, MINUTE•

,

~;sgs

.,''NG/

~'$90

SIS

kIN

i S•O w 57S S?O 5•5

0

I

3

I •

I • "

I 12

I

I ¢1

0 TIME,

$

•

I •

ill

I15

ill

t

ZI4

MINUT ES

Thermal analysis curves for: (a) hypo-eutectic (A1-10'5 Si + Na) alloy; (b) hyper-eutectic (A1-14"5~ Si %- Na) alloy. Fro. 43. The form of eutectic arrests in eutectic, hypo and hyper-eutectic alloys, with and without sodium additions.(n3)

64

PROGRESS IN MATERIALS SCIENCE

°C

650

/ 600

\ ~'~

/"

Io

'

°

a

576

55C

~o

-/oSl

FIG. 44. The position of thermal arrests in sodium-modified alloys<5a) which should be compared with those in rapidly cooled alloys, Fig. 7. Full lines show the equilibrium diagram, broken lines corresponding to arrests in the modified alloys.

(b)

Theories of Modification

A variety of explanations have been forwarded since the original discovery, and in terms of what is now known about the growth of pure and modified material these ideas and the relevant evidence for them can be summarized as follows. (i) The impurity (sodium) is partly soluble in the liquid and the form of the ternary phase diagram, involving immiscible liquids, is in some way responsible for the modification. (ii) Sodium suppresses nucleation (notably of silicon) so that eutectic or silicon growth begin at a lower temperature--the structure being related to the undercooling in terms of the nature of the nuclei and their density. (iii) Sodium modifies the actual growth process (as distinct from what it may do to the nucleation) either, (i) by surface adsorption which may poison the growth mechanisms of silicon, (ii) by altering the solid-solid or solidliquid interracial energies and consequently changing the solid-liquid profile, or (iii) by altering the liquid diffusion rates in such a way as to retard the reaction rate. These possible mechanisms and the hypotheses based on them are as follows. (i) Theories based on the Al-Si-Na phase diagram The form of the ternary equilibrium diagram is not known and information about the forms of the binary systems, A1-Na and Si-Na, is limited. There is general agreement(4) that sodium is almost totally insoluble in solid aluminium and dissolves in the liquid only to a limited extent. On a basis of thermal analyses and solubility measurements, Scheuer(9o) and Ransley and Neufeld(s°) consider that there is a monotectic reaction at 0.14 wt. ~o sodium and 659°C--i.e., about one degree below the freezing point of pure aluminium. From the monotectic point the liquid miscibility gap rises very steeply and is presumably closed at the sodium-rich side of the diagram by a similar or eutectic reaction,
GROWTH

AND

STRUCTURE

OF E U T E C T I C

65

SILICON

"/,Si 13-0 Si 2

NaSi

•d

Na

0"$

%

Na

I-a

FIG. 45. Outline phase diagram for the ternary system A1-Na-Si: (a) indicating the known phases, and (b) a possible construction in the immediate vicinity of the Al-Si eutectic point.

The Si-Na phase diagram has not been determined at all, but compounds NaSi and NaSi2 have been reported and their crystal structures determined. (91, 9~) The NaSi compound can be made from the elements at 600-650°C, but there are no reports of the melting point of this or the second compound. Within the ternary diagram, the only established point is that corresponding to the ternary compound which appears in over-modified alloys when the sodium content exceeds 0.01 to 0.03 w t . ~ , Fig. 42. The most probable formula for this compound would seem to be NaA1Si4(sS) but as noted, other lower silicon contents have been reported.(s6) Whatever the precise composition, the appearance of this compound at low sodium concentrations suggests that the liquidus curve must rise very steeply'from close to the binary A1-Si eutectic p o i n t - - a t least as steeply as does the silicon liquidus in the binary system. The form of the diagram can then only be inferred from the above information and the following possibility is compatible with what little is known. There is probably a ternary monotectic reaction which is almost coincident with the binary A1-Si eutectic point, while there is presumably a phase reaction, eutectic or peritectic, between silicon and the ternary compound, and another between this compound and the liquid miscibility g a p - as suggested in Fig. 45. The combination of phases would imply at least two isothermal reactions in the immediate vicinity of the binary AI-Si eutectic point, e.g. with reference to Fig. 45, these could be A1 -k Si + L2-~ L1, or Si q- NaA1Si4 q- L2 ~ L1, or variations of these.(93)Figure 45 differs somewhat from a construction suggested by Thall and Chalmers(8) who supposed that the Si-Na system involved a miscibility gap similar to that in A1-Na. To relate the modification process to the equilibrium diagram Schultz(s4) suggested simply that the modified structure was that of the ternary eutectic, although there is no evidence for this--see above. Such a reaction would necessarily be at a very low sodium concentration and at silicon content about 1 ~ higher than the binary eutectic point. However, as Scheil and

66

PROGRESS

IN MATERIALS SCIENCE

Zimmermann(94) observed, a ternary reaction at 10°C below the binary eutectic and at such concentrations would imply an improbably large liquidus slope of 300°C/~ sodium, and in any case, the fact that the melting point of the modified alloy is not depressed in the same way as the cooling arrests (e.g. Fig. 43) must mean that discussions in terms of the equilibrium diagram are unprofitable. A more rational explanation by Curran(96) which was developed by Otani(6°) and Ransley and Neufeld(st) supposed that the course of the ternary monotectic reaction, Fig. 45, was complicated by the production of a layer of sodium-rich liquid which suppressed the freezing point until further nucleation occurred. Again, however, there is little evidence for such suggestions and they are not compatible with what is now known about the continuous nature of the eutectic microstructure. Moreover, there are no miscibility gaps in the systems Ag-Na or Au~Na and another explanation would be needed to explain modification in these systems.

(ii) Nucleation theories One interpretation of the observed effects is in terms of retarded nucleation followed by more rapid growth or further nucleation. In the first place this was the basis of a so-called "true flux" hypothesis by Guillet(97) in 1922, it being supposed that the action of sodium lay in its poisoning alumina and silica impurity particles which were regarded as the operative heterogeneous nuclei in unmodified alloys. There have been variations on this theme, e.g. by Gwyer and Phillips(53) or Plumb and Lewis,(63) but these have assumed that the silicon dispersion was globular, which is now known not to be the case, and arguments in terms of repeated nucleation of each and every silicon particle cannot be relevant. More recently Crosley and Mondolfo,(is) recognizing that the silicon dispersion was probably of a fibrous form, have discussed the influence of sodium in terms of its influence on various nucleating surfaces. Figure 46 is based on thermal analysis of hypo- and hyper-eutectic alloys with and without sodium additions, and in one case with minor phosphorus additions (but see below), the curves representing the so-called nucleation temperatures although there is no recalescence with sodium additions. If the change in structure were produced by changes in the efficiency of nuclei it is difficult to understand why there is no rise in temperature after the nucleation event, because as illustrated, the modified structure must be produced at an advancing duplex solid-liquid front and any initial effect during nucleation would have to continue during subsequent growth. Some recent experiments have been made by Day(6s) in which a soluble impurity, copper, was added to sodium-free and modified alloys in order to delineate the grain boundaries by segregation, much as can be done in graphitic cast irons. Although these experiments may have the disadvantage of introducing yet another component to the material, they indicate that there is essentially no change in the density of nuclei with or without sodium. Since it is known (see later) that the

G R O W T H AND S T R U C T U R E OF EUTECTIC SILICON

°C ~

Sl byAIP S ~/ //~_ Sl by

590 ~--

~

--..

/ //

\

AlbyXJ"\ \ 58o-

-,\

/#

/,'~

-... \

//;' ~

,,

/;/

\

",

SibyY...It//

/ / ,

V

,,

/,/

",./~ ~¢~c Si by AI,

57o

67

......

~. . . . .

SibyAI+No -

__

///.,

~//"

_,,L_~ ,

/

,,

\

_ _ _ \ . . . .

A,,\

i/j/

\

\

~,O

-"c--x

-'v"

i I

~\

/

\

#

,I

"

12

I

\

\

,,

L

._ ,~

\

//

/I

/

/\

"xi,"/ \

/ 1~\

560

11

i

I', '

13

\114

%Si

FIG. 46. Indicating the temperatures of thermal arrests for different possibilities-interpreted as nucleation dependent on various substrates. (18)

morphology of silicon is not affected by copper, these results must throw considerable doubt on any theories which attempt to explain the modification process even partially in terms of nucleation behaviour. (iii) Modifiedgrowth It is a matter of fact that the morphology of eutectic silicon changes as its freezing temperature falls, i.e. as the undercooling increases, and Scheil and Zimmerman(94) emphasize this feature. There is no change in the crystal structure,(98) but a distinct change in the shape of crystals. Kim and Heine(64) have drawn anologies between the silicon which grows at various temperatures and the different forms of ice which crystallize under different ranges of temperature and pressure,(99) but this is little more than a restatement of the observed structures and does nothing to explain how and why the growth profile, and therefore the morphology, change as they do. The problem of eutectic silicon relates moreover to the metal/non-metal combination and not to a single solid phase. Early theories, mentioned above, have supposed that some poisoning action by sodium could prevent silicon crystals from growing at the same rate as aluminium, or vice versa,(6s) so that the interface advanced by some repetitive

68

P R O G R E S S IN MATERIALS SCIENCE

nucleation process, and this was assumed by Thall and Chalmers (s) and Plumb and Lewis.(~3) Since, however, the quenched and modified forms of silicon are known to be continuous these and other theories must be reexamined with reference to the shape of the growth front. Discussing the duplex solid-liquid front, Thall and Chalmers(8) suggested that aluminium might be expected to project ahead of silicon because (a) it is a better thermal conductor (0.53:0.20 cal/cm/°C) and (b) the latent heat of the metal is smaller (94.6: 337 cal/g). This "lag-lead" separation at the growth front would further be expected to increase with freezing rate until the silicon became totally occluded by the metal, the sequence being as in Fig. 47. The similar influence of sodium could be explained on this model by supposing that adsorption at the aluminium-silicon interfaces reduced the surface energy and hence increased the solid-liquid contact angle at the duplex solid-liquid triple junctions, again leading to overgrowth of the silicon by the metal. In both cases it was supposed that increased undercooling followed the overgrowth until further nucleation occurred. The same argument might still be applicable if it were supposed that overgrowth is only partial and results in bursts of rapid growth with further twinning--as envisaged by Day and Hellawell, but the model differs qualitatively from the general impression that with either increased growth rate or sodium additions, the interfacial profile undergoes a transition from one in which silicon "leads" the aluminium to the reverse. Thus, it could still be argued that changes in the solid-solid interfacial energy (with modifying agents) might produce some such reversion of the growth profile.

AI s~

AI

)

) b

¢

FIG. 47. Suggested(s) sequence showing how aluminium might occlude silicon at a n advancing duplex solid-liquid front.

While Thall and Chalmers discussed the solid-liquid profile with reference to the solid-solid interfaces, there is also the possibility that preferential adsorption at the solid-liquid interfaces might be responsible for the change in growth profile, either because the relative surface energies change or because the growth kinetics of the silicon are affected. Experiments by Davies and West(81) have shown that the latter reason is probably the correct one. Davies and West examined grain boundary and twin boundary contact angles between liquid eutectic alloy and clean silicon specimens after they had been annealed for 4-6 hr at 580°C, Fig. 48, this treatment then being

GROWTH

AND STRUCTURE

OF EUTECTIC

~i! ~

SILICON

~

69

ii~i~i~i ii~iiiili!¸

FIG. 48(a) FIG. 48. (a) Grain boundary and (b) twin traces at silicon-eutectic liquid interfaces without sodium present) (81) × 700.

|

FIG. 48(b)

repeated under an atmosphere of sodium, Fig. 49. Cumulative distributions(10°) suggested equilibrium angles of ~--~120° between silicon grain boundaries and the liquid in the pure alloy. Experiments under sodium failed to indicate any typical dihedral angles but suggested rather that growth of silicon was restricted at the interface, it being observed that cooling produced

70

PROGRESS IN MATERIALS SCIENCE

a negligible growth layer in this case, compare Figs. 48 and 49. Solid aluminium in contact with the liquid gave a dihedral angle of zero whether or not there was sodium present--showing merely that the grain boundary energy is more than double that of the metal-liquid surface in both cases. These authors (Davies and West) conclude, therefore, that modification is primarily caused by sodium adsorption at growth sites on the silicon-eutectic liquid interface and are unable to comment on the shape of the solid-liquid profile. They also discuss the nature of the adsorption, noting that failure of silicon to develop faceted faces, which is very evident in the modification of primary crystals, Fig. 42, must mean that rapidly growing faces or active growth sites are affected. The observation that modification does not take place when silicon is relatively free of twinst 3°) would be compatible with poisoning of re-entrant twin grooves by sodium adsorption, and whatever the precise sites, the need only for surface activity would explain why the sodium or other elements are effective at such low concentrations. Why elements of the alkali and alkaline earth groups, and sodium in particular, should be so effectiye is not known. Silicon is known to form stable compounds with the alkali metalst s~) and these metals have in common

F~o. 490) FIo. 49. Silicon-eutectic liquid interfaces in the presence of sodium, (a) single

crystal, × 400 and (b) twinned crystal, × 700. the most polarizable atoms and lowest ionisation potentials--which might account for their retention on the less closely packed faces of electronegative elements such as silicon or germanium. The apparent efficiency of sodium may then be a function only of its vapour pressure and oxidation rate which together will determine how rapidly the modifying agent is dispersed throughout the bulk of the liquid and how long it remains there after dispersion.

GROWTH

:

AND

STRUCTURE

OF E U T E C T I C

SILICON

71

ii

Fx~. 49(b) It would follow from the above, that the chilled eutectic structure and that produced by modification can both be accounted for in terms of the kinetic limitations of silicon (or germanium), being important either because of the imposed growth rate and inability of the faceted material to grow as quickly as the metal, or because the growth process is susceptible to poisoning. Such reasoning is also compatible with the general occurrence of the modifying action in systems other than A1-Si.(75) In addition to kinetic or surface tension considerations of the type mentioned, Tsamura(1°1) and Haworth and Whelan(102) have discussed the modification process by supposing that sodium additions might reduce the liquid diffusion rate and thereby produce an effect similar to increase in growth rate. Tsamura and Davies and West(81) have made estimates of diffusion rates in eutectic alloy, with and without sodium additions, and both found some evidence of decreased diffusion rates. However, the results were partially invalidated because there was convective mixing in the liquid and values for the diffusion coefficient were an order of magnitude greater than is usual in aluminium alloys.(~03) On a basis of activity measurements Haworth and Whelan(102) suggested that the diffusion rate in this system should be relatively low, and an estimate of 5 × 10 -6 cm2/sec by Day and Hellawell(30) would be compatible with this. However, as noted, addition of sodium does not modify the pseudo-steady-state growth of eutectic silicon at slow growth rates and it would seem to follow therefore, that it does not affect the liquid diffusion rate significantly. (c) Modification and Mechanical Properties The most reasonable interpretation of the modification process from the above direct and indirect evidence, is that undercooling of silicon during

72

PROGRESS

IN M A T E R I A L S

SCIENCE

growth is much more sensitive to rate or to certain absorbed species than is the metal-liquid front. It is also clear that the microstructures of both the chill cast and modified materials are very similar, except that the modified silicon may occur as more regular filaments which branch less frequently. It is not clear, however, why the ductility is greatly increased not only by comparison between the flake morphology and the modified alloy, but also, see Table 2, if the chill cast alloy is compared with that which has been modified. When it was assumed that the silicon dispersion in modified material was globular, rather than fibrous, it seemed reasonable that fine, rounded particles would not transmit cracks through the material as easily as would coarse flakes of silicon and the modified material could be regarded as a dispersion-hardened aluminium solid solution. However, since the observed structure is what it is, and the number of nuclei or grains does not appear to change with modification, the change in properties must primarily be caused by differences in the shape of the silicon crystals. Qualitatively, it would be expected that the filamentary form transmit cracks for shorter distances because individual strands of crystal do not extend over large areas in any plane, and the twin density which is probably higher will involve more frequent changes in orientation than occur in the coarse structure. The higher ductility and strength of the modified alloy rather than the chill cast, unmodified material, can be related only to the perfection of the rods or fibres and it might be suggested that the less regular and branched filaments of the chilled material offer many sites for higher stress concentrations and subsequent crack propagation than are found in the modified alloys, compare Figs. 1 l(b) and 38. The marginal increase in ductility on adding sodium to chill cast alloy, Table 2, can be related only to further refinement in the scale of the dispersion. There is a remarkable lack of systematic study in this connection.

B.

Other Minor Impurity Additions--Phosphorus

As noted, sodium is not the only impurity which changes the microstructure when it is added in small quantities, and in addition to the alkali and alkaline earth metals, Scheuer,(90) Schultz,(84) Gurtler(39) and Grand(105) have illustrated that very small quantities of phosphorus produce a refining effect which is distinctly different from that caused by the "modifying" agents. As with modification, primary and eutectic silicon are affected, and Figs. 50(a-c) show

(a) (b) (c) FIG. 50. A1-Si, 20 wt. % Si, with increasing concentrations of phosphorus, (a) to (C).(39)

GROWTH

AND

STRUCTURE

OF E U T E C T I C

SILICON

73

how the morphology of a hyper-eutectic alloy changes from flakes to a more granular form with increasing phosphorus concentrations.(39) The levels of phosphorus content which are effective are very low indeed, it being reported, e.g. by Kroll,(107) that 0.00015~o produces satisfactory refining of hypereutectic alloys. Gurtler(39) and Crosley and Mondolfo(is) show that with phosphorus present there is negligible undercooling (3-5°C) even at very rapid rates of cooling, and cooling arrests characteristically show recalescence which suggests that the growth process is not hindered in the same way as it is in modified alloys. It has been suggested( 18, 39) that the active ingredient in this refining action is the compound AlP, and Crosley and Mondolfo particularly draw attention to the presence of small inclusions within silicon crystals which they suggest are particles of this compound. In contrast to the modification process by sodium and others, the action of phosphorus does seem to be that of a heterogeneous nucleating agent and it may be that silicon particles are relatively isolated in the structure which has been refined by phosphorus-each one nucleating separately as the microstructure might suggest. This action has been supported by reports(39) that filtration of liquid alloys containing phosphorus caused a reversion to the unrefined flake morphology. The compound AlP is isomorphous with silicon and its nucleating potential has been discussed in terms of lattice matching.( 18, 39, 108) Lohberg(106) has also shown that phosphorus additions to A1-Ge alloys refine primary germanium which by analogy with the silicon alloys might involve a compound GeP. It is not known if phosphorus has any refining action in other siliconcontaining alloys, nor has any refining action by other elements of the same group (As, Sb, Bi) been reported. Phosphorus additions are without effect on the morphology of primary aluminium and are made primarily to refine hyper-eutectic alloys.(104) Since sodium and phosphorus react together, additions of either are not effective unless one is in excess(18, 39) when the refining actions and results are essentially different. The effect on mechanical properties is not, however, dissimilar to that produced by sodium modification-there being an increase in the ductility and U.T.S. If the action of phosphorus is to produce isolated granular silicon crystals instead of extensive flake crystals, then the improved properties are qualitatively understandable although here again there have been no reports of systematic studies.

C.

Ternary Alloys

There are a number of ternary equilibrium diagrams which have been determined in some detail(114) and which contain the pseudo-binary A1-Si eutectic and ternary eutectics such as A1-Si-CuA12, AI-Si-A13Ni and others with magnesium and zinc. The microstructures of cast alloys in these systems are illustrated in some detail b y Hannemann and Schr~ider(114) and in general it is clear that the morphology of silicon is little affected by the presence of a second metallic component or phase. Slowly frozen ternary alloys of A-1CuFig. 51, illustrate how the morphology of silicon develops in a binary

74

PROGRESS IN MATERIALS SCIENCE

FIG. 51. A1-Si-CuAI2 ternary eutectic alloy. Transverse section of slowly grown material showing textured silicon crystals similar to those found in binary alloys, Fig. 18, with some association between aluminium and silicon phases, x 100.

matrix of A1 -[- CuAl2, much as it does in the binary alloys with aluminium. There is some tendency for silicon crystals to be surrounded by aluminium in such alloys--probably on account of the relative surface energies between phases. There are no detailed reports but sodium (or similar) additions are able to effect similar modification of silicon in ternary alloys as in binary, indicating again that the process is not peculiar to any one system. Ternary alloys based on the other silicon or germanium systems have not been studied, but in systems of the type Si-Ge-metal, where the metal is aluminium, silver or gold, there exist continuous binary eutectic valleys from one binary system to the other, silicon and germanium forming a continuous solid solution. V.

COMPARISON WITH CAST IRONS

A number of authors( s, 109, 65) have drawn attention to similarities between aluminium-silicon alloys and eutectic alloys containing graphite with the metals Fe, Co, Ni and the platinum metals. These systems have in common a combination of faceted and non-faceted phases and all alloys exhibit similar sensitivities to minor additions--of the alkali and alkaline earth metals to silicon, magnesium and the rare earth metals to graphite. There are a number of parallel features. (i) In cast ingots the grain structure is discernible as radiating colonies or cells of the non-metallic phases, the word "cell" being usual in the terminology of cast irons.

GROWTH

AND STRUCTURE

OF E U T E C T I C

SILICON

75

(ii) With directional growth at slow rates eutectic silicon can adopt an approximately steady-state arrangement based on faceted fibres while the layer structure of graphite allows it to grow as continuous laths or flakes which are approximately parallel over small areas of the front.( n0, 111) (iii) At moderate or rapid freezing rates--10 -3 cm/sec--both materials exhibit less regular arrangements and growth proceeds by fluctuating shortrange diffusion processes. (iv) It is characteristic of both silicon and graphite that they contain crystallographic defects; multiple twins in the former and more complex stacking and twin configurations in the latter.(nl) These defects may contribute to the growth processes in either material, and in any case account for the crystallographic continuity of complex shapes and a wide range of orientations. (v) At rapid rates of growth both silicon and graphite appear to adopt complex filamentary forms--typically that found in chill cast A1-Si alloys and the so-called "undercooled" graphite. These forms appear to grow as if behind the metal-liquid front whereas the more angular and crystallographic forms seem to be formed when the leading growth edges are those of the non-metal. (vi) Addition of the modifying agents prior to casting produces a refined filamentary form of silicon but a spheroidal form of graphite. Primary silicon or graphite are also affected and then occur with a spherical morphology. The modified structures differ in that eutectic silicon is still produced at a short range growth front and extends more or less continuously in the growth direction, while graphite spherulites are isolated from one another and must therefore grow from individual nuclei. (vii) In primary silicon spherulites the structure differs only from that of unmodified crystals in that the external morphology is not faceted and that the twin density is higher. In graphite spherulites the crystal is segmented into many radial crystals which appear to grow in directions at right angles to the basal layers--i.e, in directions at right angles to those adopted in flakes-although the actual kinetics of molecular attachment may still involve an extension of basal planes from defects in the close packed faces.( 50, 112,111) (viii) Since the modified structures are different, the improved ductilities must arise in rather different ways. ACKNOWLEDGEMENTS

The author is indebted to Dr. V. de L. Davies and Dr. L. F. Mondolfo and particularly to Dr. M. G. Day for kindly supplying photographs from their work.

76

PROGRESS IN MATERIALS SCIENCE REFERENCES

(i) ZENER, C., Trans. Amer. Inst. Min. (Metal) Engrs., 167 (1946) 550. (2) TILLER, W. A., Liquid Metals and Solidification, American Society for Metals, Cleveland, Ohio (1958). (3) JACKSON, K. A. and HUNT, J. D., Trans. Met. Soe. A.LM.E., 236 (1966) 1129. (4) HANSEN, M., The Constitution of Binary Alloys, McGraw-Hill (1958). (5) ELLIOTr, R. P., Ibid., Supplement (1965). (6) DUWEZ, P., WILLENS, R. H. and KLEMENT, W., J. Appl. Phys., 31 (1960) 1137. (7) KLEMENT, W., WILLENS, R. H. and DUWEZ, P., Nature, 187 (1960) 869. (8) THALL, B. M. and CHALMERS, B., J. Inst. Metals, 78 (1949) 79. (o) PACZ, A., U.S. Patent No. 1387900 (1921). (lO) DAVIES, V. dE L. and WEST, J. M., J. Inst. Metals, 92 (1963-64) 208. (11) BOTSCHWAR, A. A., Ref. Underwood, E. E., J. Metals, 17 (1962) 914. 02) WAGNER,R. S. and ELLIS, W. C., Trans. Met. Soc. A.LM.E., 223 (1965) 1053. (13) CHADWICK, G. A., Progress in Materials Science, 12(2) (1963) 99. (14) SUNDQUIST,I . E. and MONDOLFO, L. F., Trans. Met. Soc, A.I.M.E., 221 (1961) 157. (15) SUNDQUIST, B. E. and MONDOLEO, L. F., Ibid., 221 (1961) 607. c161SUNDQUIST, B. E., BRUSCATO, R. and MONDOLFO, L. F., J. Inst. Metals, 91 (1962-63) 204 (17) MONDOLEO, L. F., J. Australian Inst. Metals, 10 (1965) 169. (18) CROSLEY, P. B. and MONDOLEO, L. F., Modern Castings, 49 (1966) 63. (19) HOLLOMAN, J. H. and TURNaULL, D., Trans. Met. Soc. A.LM.E., 191 (1951) 803. (20) HOPKINS, R. H. and KRAFT, R. W., Trans. Met. Soc. A.1.M.E., 242 (1968) 1627. (~1) DOUBLE, D. D., TRUELOVE, P. and HELLAWEtL, A., J. Crystal Growth, 2 (1968) 181. (22) TAMMAN, G. and BOTSCrtWAR, A. A., Z. Anorg. Chemie, 157 (1926) 26. (83) K6FLER, A., Z. Metallkunde, 41 (1950) 22. (24) SCHEIL, E., Arch. Eisenhiittenwesen, 8 (1934) 565. (85) SCHEIL, E., Z. Metallkunde, 37 (1946) 1. (23) HUNT, J. D. and JACKSON, K. A., Trans. Met. Soc. A.LM.E., 239 (1967) 864. (27) MOLLARD, F. R. and FLEMINGS, M. C., Trans. Met. Soc. A.LM.E., 239 (1967) 1526, 1534. (28) BELL, J. A. E. and WINEGARD,W. C., J. Inst. Metals, 93 (1965) 318. (20) COOKSEY, D. J. S., DAY, M. G. and HELLAWELL, A., International Conference on Crystal Growth, J. Phys. Chem. Solids (Suppl.) 1967. (ao) DAY, M. G. and HELLAWELL, A., Proc. Roy. Soc. A, 305 (1968) 473. (31) JACKSON, K. A., Trans. Met. Soc. A.I.M.E., 242 (1968) 1275. (32) CLINE, H. E., Trans. Met. Soc. A.I.M.E., 242 (1968) 1613. (33) JORDAN, R. M. Communication. (34) KERR, H. W., Ph.D. Thesis, Toronto University (1966). (as) WHELAN, E. P. and HAWORTrI, C. W., J. Australian Inst. Metals, 12 (1967) 77. (36) HUNT, J. D. and JACKSON, K. A., Trans. Met. Soc. A.LM.E., 236 (1966) 843. (z7) HErLAWELL, A., Trans. Met. Soe. A.LM.E., 239 (1967) 1049. (as) MEUSSNER, R. A., U.S. Naval Res. Lab. Rep. No. 5341 (1959). (39) GURTLER, G., Z. Metallkunde, 44 (1953) 503. c49) RaIN~, F.N. and TIMPE, W. F. B. Z. Metallkunde, 48 (1957) 109. (41) COOKSEY, O. J. S., MUNSON, O., WILKINSON, M. P. and HELLAWELL, A., Phil. Mag., 10 (1964) 745. (42) O'HARA, S. and HELLAWELL, A., Scripta Met., 2 (1968) 107. (43) TURNBULL, D., J. Chem. Phys., 18 (1950) 769. (44) JACKSON, K. A., Liquid Metals and Solidification, American Society of Metals, Cleveland, Ohio (1958). (45) BURTON, F., CABRERA, N. and FRANK, F. C., Phil. Trans. Roy. Soe. A 243 (1951) 299. (46) CHADWICK, G. A., The Solidification of Metals, p. 49 Iron & Steel Inst. (1968). (47) HUNT, J. D., Ibid., p. 125. (4s) HULME, K. F. and MULLIN, J. B., J. Phys, Chem. Solids, 17 (1960) 1. ~49)HUNT, J. D. and HURLE, D. T. J., Trans. Met. Soe. A.LM.E., 242 (•968) 1043. (59) FRANK, F. C., Discussions Faraday Soe., 5 (1949) 48. (sx) WAGNER, R. S., Aeta Met., 8 (1960) 57. (52) HAMILTON, D. R. and SEIDENSTICKER, R. G., J. Appl. Phys., 31 (1960) 1165.

G R O W T H AND S T R U C T U R E OF EUTECTIC SILICON

77

(53) GWYER, A. G. C. and PHILLIPS, H. W. L., J. Inst. Metals', 36 (1926) 283. (54) EDWARDS, J. D., Chem. Met. Eng., 28 (1923) 165. (~5) DIx, E. H. and HEATH, A. C., Trans. ,4.LM.E., 78 (1928) 164. ~56~CRAIGHEAD,C. M., CAWTHORNE, E. W. and JAErEE, R. 1., Trans. ,4.I.M.E., 203 (1955) 81. (57) GAYLER, M. L. V., J. Inst. Metals, 38 (1927) 157. (58) SCHEUER, E., J. Inst. Metals, 78 (1950-51) 727. (59) WILLEV, L. A., Trans. ,4.LM.E., 206 (1956) 263. (60) OTANI, B., J. Inst. Metals, 36 (1926) 243. (61) PATTERSON, W., Giesserei, 26 (1939) 451. (62) GURTLER, G. and SCHULZ, E., Giesserei, 26 (1939) 536. (6z) PLUMB, R. C. and LEWIS, J. E., J. Inst. Metals', 86 (1957) 393. (04) KIM, C. B. and HEINE, R. W., J. Inst. Metals, 92 (1963-64) 367. (~5) DAY, M. G., J. Metals', 21 (4) (1969) 3l. (66) SINC~ER,A. R. E. and COTTRELL, S. A., J. Inst. Metals, 73 (1947) 31. (67) STRAUMANIS, M. and BRAKSS,N., Z. Phys. Chem. B, 38 (1937) 140. (68) DAY, M. G., to be published Institute of Metals 1970. (60) KLEMM, H., Praktische Metallographies, 5 (1968) 662. (70) DAY, M. G., The Soh'dification of Metals, p. 177 Iron & Steel Inst. (1968). (71) CHADWICK, G. A., Liquids, Elsevier (1965). (72) WALTON D., TILLER, W. A., RUTTER, J. W. and WINEGARD,W. C., J. Metals 7 (1955) 1023. (7a) MORRIS, L. R., Communication. (74) ELLIS, W. C., Trans. Met. Soc. ,4.I.M.E., 188 (1950) 886. (7~) DA'¢, M. G., Oxford University, D.Phil. thesis (1967). (76) CHAMBERLAIN,J. H., Oxford University, Pt. II thesis (1969). (77) BARDESLEY,W., BOULTON,J. S. and HURLE, D. T. J., Solid State Electronics, 5 (1962) 395. (78) MULLER, A. and WILHELM, M., Z. Naturforschung, 22 (1967) 264. (79) M~tLLER, A. and WILHELM, M., J. Phys. Chem. Solids', 28 (1967) 219. (8o) SMITH, R. W., The Solidification of Metals, p. 224 Iron & Steel Inst. (1968). (81.) DAVIES, V. dE L. and WEST, J. M., J. Inst. Metals, 92 (1963-64) 175. (82) EDWARDS,J. D., FRARY, F. C. and CHURCHILL, H. V., U.S. Patent No. 1410461 (1920). (83) DAY, M. G. and HELLAWELL, A., J. Inst. Metals, 95 (1967) 377. (84) SCHULTZ, E., Z. Metallkunde, 39 (1948) 123. (85) NOWOTNY, H. and SCHEIL, E., Z. Metallkunde, 38 (1947) 76. (88) RANSLEY, C. E. and NEUFELD, H., J. Inst. Metals, 78 (1950) 25. (87) DAy, M. G., Nature, 219 (1968) 1357. (88) OBINATA, Z. and KOMATSU, N., Sci. Rep. Tohoku Univ. ,4, 9 (1957) 107. (89) MASCRI~,C., Proc. Inst. Brit. Found., 46 (1953) 227. (90) SCHEUER, E., Met. Ind., 49 (1936) 553. (91) SCH.~EER, R. and KLEMM, W., Z. ,4norA. Chemie., 312 (1961) 214. (9~) WITIE, J. and SCHNERINt3, H. G., Ibid., 327 (1964) 260. (93) MONDOLEO, L. F., J. Inst. Metals, 78 (1950-51) 733. (94) SCHEIL, E. and ZIMMERMAN,R., Z. Metallkunde, 40 (1949) 24. (95) SCHEIL, E., Z. Metallkunde, 40 (1949) 246. (96) CURRAN, J. J., Chem. & Met. Eng., 27 (1922) 360. (97) GUILLET, L., Rev. Met., 19 (1922) 303. (98) JEEFRIES, Z., Chem. & Met. Eng., 26 (1922) 750. (99) MASON, B. J., Physics of Clouds, Oxford University Press (1957). (lOO) RIEGGER, O. K. and VAN VLACK, L. H., Trans. ,4.I.M.E., 218 (1960) 933. (i.oi) TSAMURA,Y., Nippon Kinzoku Gakkai-Si, 21 0957) 69. (lo2) HAWORTH, C. W. and WHELAN, E. P., J. Australian Inst. Met., 10 (1965) 84. (lo8) EDWARDS, J. B., HUCKE, E. E. and MARTIN, J. J., Met. Rev., 120 (1968) 1. (lo4) GURTLER, G. and SCHULZ, E., Giesserie, 26 (1939) 537. (io5) GRAND, M. L., Fonderie, 2625 0951). (lo6) LOHBERG, K. and SCHULZ, E., Z. Metallkunde, 43 (1952) 501. (lo7) KROLL, W. J., J. Inst. Metals, 78 (1950-51) 733. (1.o8) CIBULA, A., J. Inst. Metals, 76 (1949-50) 321. (1.oo) MORROGH, H. and WILLIAMS, W. J., J. Iron & Steel Inst., 158 (1947) 306.

78

PROGRESS OF MATERIALS SCIENCE

(l.t0) LAKELAND,K. D., J. Brit. Cast. Iron Res. Assn., 12 (1964) 634. (~.lx) DOUBLE,D. D. and HELLAWELL,A., Acta Met., 17 (1969) 1071. ~z) MINKOFF, I. and NIXON, W. C., J, AppL Physics, 37 (1966) 4848. (~ts) SYLWESTROWICZ,W. D., Phil. Mag., 7 (1962) 1825. tl!.,t) HANNEMANN,H. and SCHR.~DER,A., Terniire Legierlungen des Aluminiums, Dusseldorf (1952).

Manuscript submitted July 1969