MEASUREMENTS OF CELL AND PRIMARY DENDRITE ARM SPACINGS IN DIRECTIONALLY SOLIDIFIED

ALUMIN~UM ALLOYS

D. G. MCCARTNEY and J. D. HUNT

Department of Metallurgy and !Science of Materials, University of Oxford, Oxford, U.K.

(Rcceired 16 February 1981)

Abstract-Ceil and primary dendrite arm spacings have been measured in AI-& and Al-Mg-Si alloys directionally solidified at steady state over a very large range of growth conditions. The Al-Mg-Si alloys have been chosen so as to minimize gravitational fluid flow in the liquid. A spacing parameter, 1, has been correlated with the liquid temperature gradient G L, the growth velocity, V and the bulk alloy composition, C,.

It has been found that for dendrites in the ALMg-Si system j. = 272G;o.S V-o.8 Cafe

where C&r is the atom fraction of Si in the alloy. It has also been observed that there is a discontinuous change in the spacing relationship, as measured

by L, when the growth morphology changes from cellular to dendritic, Cells were found to form a roughly hexagonal array whereas dendrites adopted a much less regular pattern. This discontinuous change in I is explained by considering how the nature of an array affects its average nearest neighbour spacing I*.

RCsum&-Nous avons mesure les espacements des cellules et des bras des dendrites primaires dans des alliages Al-t3 et Al-Mg-Si 8 ~Iidifi~tion orient& en regime permanent, pour me gamme t&s &endue de conditions de croissance. Nous avons choisi le systeme Al-Mg-Si afin de minimiser ICcoulement gravitationnel dans le liquide. Nous avons corr& un parametre despacement avec le gradient de temperature du liquide GL, la vitesse de croissance V et la composition massive de lalliage C, .

Dans le cas des dendrites du sy&me Al-Mg-Si 1 f 272Gie.5 V-.~s Cakes

oil CmsI est la tencur atomique de lailiage en silicium. Nous avons egalement observe un changement discontinu darts lespacement mesure par 2, lorsque ia

morphologje de la croissance de cellulaim devient dendritique: Les cellulcs forment grossi&ement des hexagones alors que les dendrites adoptent une configuration beaucoup moins r#gttliere. Nous expli- quons ce changement discontinu de L en considCrant comment la nature dun arrangement affecte lespaccment moyen P des premiers voisins.

Zusammanfaaaung-Die Abstiinde von Zellen und prim&en Dettdriten wurden in Ai-Cu- und ACMg- SiLegierungen gemessen; die Legierungen waren unter stationiiren Bedingungen crstarrt in einem groBen Bereich von Wachstumsbedingungen. Die Al-Mg-Si-Lcgierungen wurden gewghlt, urn ~a~~tions~in~e Bewegnngen in der Riissigkeit zu ~~i~er~. Ein A~~ds~ra~t~ d wurde mit dem Temperaturgradienten Gr, in der Fhissigkeit, der Wachstumsgeschwindigkeit V und der Legier- ungsznsammensetzung C, korreliert.

Fiir die Dendriten in dem Al-Mg-Si-System ergab sich: 2 = 272GiO.sS V-O.%3 p~32

t

wobei CIDsi den Atombruchteil des Si in dcr Legicrung bedqptet. AuDerdem wurde beobachtet, dal3 eine diskontinuierliche Anderung in der Abstandsheziehung, gemes-

sen mit .J, at&rat, wenn die W~hstumsmo~holo~e vom zeUuBiren in den dendritischen Charakter umschlug. Die ZeUen bilden eine etwa hexagonale S$uktur, wohingegen die Dendriten eine vie1 regello- sere Struktur einnehmen. Diese diskontinuierliche Anderung in wird erkltirt, indem die Beeinflussung des mittleren Abstandes ntichster Nachbarn I* durch die Strukturart betrachtet wird.

INTRODUCTION gradient and growth velocity have not been measured There has been considerable experimental work in the inde~ndendy and instead the spacing of the primary past number of years on the measurement of cell and arms has been correlated with a parameter such as primary dendrite arm spacings in a variety of alloy frtning rate or cooling rate [l-3,5]. Of the work h systems [l-11]. Much of this has, however, been car- which the primary spacings have been correlated with ried out under conditions in which the temperature gradient and velocity separately much has been car-

1851

1852 MCCARTNEY AND HUNT: DIRECTIONALLY SOLIDiFIED ALUMINIUM ALLOYS

-crucible value. That is in a two component system

~=(~)c~~(~)~~

z flow of solute

/rich liquid.

/isotherm

/macroscopic S/L interface shape during growth

Fig. I. Jkiation of the macroscopic interface shape (solid line) from the shape of the isotherm (dotted line) due to fluid flow. Dense solute rich liquid flows in the directions

shown by the arrows.

ried out over relatively small ranges of velocity, gradient and composition, and/or in systems in which convective mixing may have been an important factor [4, G-11]*

It is sometimes assumed that one method of elimin- ating gravitational convection in the melt is to main- tain a negative vertical density gradient in the inter- dendrite liquid by solidifying vertically upwards in a system in which the solute being rejected at the inter- face is denser than the bulk liquid. Burden et al. Cl23 have shown, however, that this is not so. If at any stage the macroscopic interface shape becomes slightly non-planar the densest solute flows into the retarded region and the resulting increase in solute content will cause it to drop still further behind forrn- ing a steeple as shown in Fig 1,

Preliminary experiments on an Al-6 wt.% Cu alloy showed that specimens solidified at growth rates of less than 8 x 10-3mms- with a temperature gradient of 6 K mm- exhibited severe macroscopic interface curvature indicating significant fluid flow. This curvature was not the result of changes in the heat flow pattern since pure Al and an Al-01 speci- men of eutectic composition solidified with near planar interfaces indicating that the isotherms of the system were also of this near planar shape.

In a dendritic specimen the liquid composition between the dendrites varies with temperature as it does along the liquidus line of the phase diagram, and it has been suggested [13] that the average liquid composition just ahead of the dendrites varies in a similar way. Thus one method of eliminating or at least reducing flow in this region is to reduce the density change along the liquidus line, dp/dl; where p is the density and T the temperature, to a very low

to make

tend towards zero, where Ca is the alloy composition and m is the liquidus slope. Previous work [I21 has shown that it is very difficult to find a two component system where the temperature density change is sufficiently accurately balanced by the composition density change to eliminate the flow.

It has, however, been possible to eliminate the flow in a tin based system where zinc is the main alloying element by adding small amounts of lead. A tin alloy containing 0.19 at .% Pb and 3.85 at. Y. Zn showed no fluid flow, a Sn-3.85 at.%Zn alloy showed the characteristic macrosegregation of a system where the liquid gets lighter on cooling, whereas a Sn-3.37 at.% Zn-0.35 at .% Pb alloy showed the characteristics of a system where the liquid becomes denser [I45 A tern- ary alurn~i~ based alloy was developed having similar properties. Increasing amounts of magnesium were added to an aluminium-silicon alloy until the steeple effect was just eliminated. It was found that provided the atomic ratio of Mg to Si was kept con- stant in alloys of different total solute content flow did not appear to occur. The Al-Mg-Si system whose phase diagram is shown in Fig 2 is suitable for other reasons as welL The Al-Si and A?-Mg bmaries have similar liquidus and solidus slopes. The ternary alloys might thus be expected to behave as pseudo-binaries, with the solid-liquid tie lines lying along the lines of constant Mg to Si ratio and freeze in a similar fashion to simple binary alloys in which aluminium is reject- ing a single solute.

The main object of this work was thus to measure primary arm spacings over a wide range of growth velocity, temperature gradient, and alloy composition in the Al-Mg-Si system, under conditions in which solute diffusion was the dominant mechanism of mass transfer.

EXPERIMENTAL METHOD

Apparatus

The aluminium alloy specimens contained in graphite crucibles were directionally solidified in three different types of furnace arrangements in order to cover the required ranges of growth velocity and temperature gradient.

Low temperature gradients of between 0.2 and 1.5K mm- at growth rates ranging from 4 x 10-s to lo- mm s-i were obtained by using a thermal valve furnace [16] which is shown schematically in Fig. 3. The alloy was contained in a graphite crucible of 9.0mm O.D. and 300mm total length which was drilled out to a depth of 180mm with an I.D. of 7.3 mm. The furnace consisted of three separate heat- ing zones each of which was controlled independently, and the crucible was held in a fixed position. The

MCCARTNEY AND HUNT: DIRECTIONALLY SOLIDIFIED ALUMINIUM ALLOYS 1853

Al b At % Si

Fig. 2. Al rich corner of the Al-Mg-Si phasq diagram showing eutcctic valleys (solid lines) and isotherms on the liquidus surface (dotted lines). Taken from reference [16].

middle zone was kept as near as possible (within about one degree) to the temperature of the freezing interface, and the top and bottom zones were con- trolled by thermocouples inserted in the specimen. Temperature measurements in the specimen were made using four transverse Pt/Pt, 13%Rh thermo- couples placed 10 mm apart, made from 0.15 mm dia. wire and insulated from the specimen using alumina tubing of 0.2 mn I.D. 0.5 mm O.D. By feeding linearly increasing D.C. voltages into the top and bottom zone thermocouple circuits, the temperature of both ends of the specimen could be made to decrease linearly and a constant growth rate and temperature gradient could be obtained. The temperature vs time trace for each of the four thermocouples was recorded in turn, enabling the growth velocity and temperature gradient to be measured and their linearity checked. The specimen was then rapidly quenched into a water bath after it had grown approximately 10 mm past the fourth measuring thermocouple. Only specimens in which the velocity and temperature gradient changed by less than 5% were used for spacing measurements.

Intermediate temperature gradients of between 2.5 and lOKmm- at growth rates ranging from 4 x lo- 3 to 1 mm s- were obtained using a Bridg- man type of furnace arrangement which is shown in Fig. 4. The furnace temperature was controlled by a thermocouple placed between the heating element and the alumina tube. Improved stability was achieved for low velocity runs by filling the interior of the furnace tube with an insulating material; a 13 mm diameter hole being left down the centre. The alloy was contained in a graphite crucible 6.3 mn O.D., 4.3 mn I.D., and 220mm long held in a stainless steel

rod. Unidirectional growth was achieved by with- drawing the specimen at a constant rate into a water bath contained in a water-cooled brass jacket which was inserted into the hot zone of the furnace. Prelimi- nary experiments were carried out to check that the withdrawal rate was qua1 to the growth rate of the interface over the entire range of growth conditions.

control thermocouple.

top furnace.

_ _._tirmocouDle

iiikple.

Fig. 3. Sectional view of the thermal valve furnace.

minsulation.

Fig. 4. Sectional view of intermediate temperature gradient furnace.

The temperature of the specimen was recorded using a single transverse pt/Pt, 13% Rh thermocouple of the same size as before, and from the temperature versus time trace the temperature gradient in the liquid at the growth front was measured. The specimen was rapidly quenched into water after it had grown at least 10mm past the thermocouple and after at least 50 mm of steady state growth had taken place.

The arrangement of the high temperature gradient furnace was essentially the same as that shown in Fig. 4 except that the water bath was replaced by a liquid metal coolant (LMC) which was held at 65C by pumping hot water around the water jacket. Using this apparatus gradients of up to 20 K mm- at velo- cities ranging from lo- to 1 mm s- were obtained.

Alloy Preparation

Al-Cu alloys were prepared by melting together the required amounts of 99.99%Al and 99.99x01 in a vacuum, mixing well and charging the molten alloy directly into the graphite crucible already in position in the unidirectional growth apparatus and held at a sufficiently high temperature to prevent the molten charge solidifying. By filling the graphite crucibles in this way macrosegregation, which would otherwise occur due to the freezing and remelting of the alloy, is avoided.

Liquid temperature

1 Growth gradient Irm Morphology Rate mm s-l K mm-

128 D 1.0 3.40 76

:: 1.0 11.0

72 1.0 12.1 66

:: 1.0 15.5

158 5 x 10-l 4.85 118 D 5 x 10-l 8.70 96 5 x 10-I 13.9

475 :: 5 x 10-z 2.05 310 D 5 x 10-z 5.50 280 D 5 x 10-f 7.90 200 D 5 x lo-* 11.8 175 D 5 x 10-f 16.7 471 D 1.67 x IO-* 3.67 415 D 1.67 x IO- 4.86 349 D 1.67 x IO-* 6.70 251

: 1.67 x IO-* 13.0

398 4.3 x lo- 4.2 380 C 4.3 x lo- 6.0 355 C 4.3 x 1o-3 8.4

The morphology is indicated as dendritic (D) or cellular

Al-Mg-Si alloys were prepared from 9.990/,Al 99.99/,Si and an Al-Mg alloy containing a known amount of Mg (usually about 4 wt.%). The melting and charging technique was identical to that for the Al-Cu alloy. 0.

water bath.

1854 MrCARTNEY AND HUNT: DIRECTIONALLY SOLIDIFIED ALUMINIUM ALLOYS

The master alloy was prepared by melting 99.99%Al in a vacuum furnace, carefully adding 99.99% Mg in such a way as to prevent any loss by oxidation, mixing the molten alloy well and then prq- ducing a rapidly solidified cast rod of 10.5 mm diam- eter and 150 mm long. Slices of this cast rod were chemically analyzed using atomic absorption spectro- photometry. Slices taken from either end were found to be of slightly different composition from those taken from the central 140 mm of the rod which were of uniform composition and within 5% of the made up composition. Thus 1Omm were discarded from each end of the master alloy rod and only the central 130 mm was used in making up the Al-Mg-Si alloys.

Measurement of primary spacings

The quenched unidirectionally grown specimens were removed from their graphite crucibles and a longitudinal section which included the quenched interface was cut from the solidified rod. This was ground and polished to reveal the quenched interface and a transverse section which contained the quenched interface was then prepared. This was care- fully ground from the quenched liquid side until the tips of the primary arms just became visible. This ensured that the primary spacing at the growth front was measured rather than the final spacing obtained after coarsening. These spacings have been shown to be very different in cellular specimens [a].

An area counting method was used to obtain a measure of the cell/dendrite primary spacings. A spao ing parameter, 2, was calculated by counting the number of primary arm centres, N, inside a known

Table 1. Measurements of primary arm spacing parameter, 5 in Al-6 wt.% Cu specimens

MCCARTNEY AND HUNT: DIRECTIONALLY SOLIDIFIED ALUMINIUM ALLOYS 1855

Table 2. Measurements of primary arm spacing parameter, i, in Al-O.63 at.% Mg-1.39 at.% Si specimens

I Growth rate Liquid temperature /tn1 mms- gradient K mm-

444 1.73 x 10-z 4.10 439 1.73 x 10-l 5.20 320 1.73 x 1o-z 9.40 320 1.73 x 10-z 9.70 290 1.73 x 10-2 11.7 390 3.30 x 10-l 4.20 231 5 x 10-Z 9.20 302 6.67 x IO-* 4.80 176 6.67 x lo-* 14.2 300 10-l 3.95 151 10-l 14.7 140 10-l 17.0 198 5 x 10-l 3.74 87 5 x 10-l 14.7

210 1.0 2.92 70 1.0 15.5

870 1.18 x lo-* 1.64 630 10-I 1.10

1034 1.45 x 10-z 1.12 1270 7.70 x lo- 1.14 860 3.67 x 1O-2 0.92 800 6.45 x 1O-2 0.84

1055 1.08 x 10-l 0.45

All specimens had dendritic morphologies.

Table 3. Measurements of primary arm spacing parameter d in Al-O.15 at.% Mg-0.33 at.% Si specimens.

Liquid temperature

1 Growth rate gradient Itm Morphology mm s-l K mm-

126 133 220 340 616 434 895 614 532 380 612 48.0 60.5 76.4 55.3 72.1 99.0

158 66.0 89.7 C 85.0

154 175 M 98.0 C

154 C 130 C 173 C

D 1.83 x 1O-2 0.76 M 5 x 10-l 11.0

5 x 10-l 3.15 5 x 10-l 2.30

10-l 2.35 1.05 x 10-l 1.08 1.50 x 10-l 0.35 6.91 x lo- 0.92 4.60 x 10-2 0.30 3.33 x 10-2 0.66 3.85 x lo- 0.81 3.17 x 10-z 1.67

5 x 10-l 8.82 5 x 10-l 6.05

10-l 18.5 10-l 11.0 10-l 4.20 10-l 6.3

3.33 x 10-2 18.0 3.33 x 10-2 10.0 3.33 x 10-2 9.65 3.33 x 10-2 5.55 3.33 x 10-2 4.43 1.67 x lo- 11.0 1.67 x 1O-2 5.48 8.3 x 1O-3 8.43 8.3 x lo- 4.40

Morphologies are indicated as cellular (C), Dendritic (D) where K is a constant and there is a standard error in or mixed (M) both exponents of f0.02. The primary spacings in

Table 4. Measurements of primary arm spacing parameter, 1. in alloys of various total solute contents with a constant

atomic ratio of Mg to Si equal to 0.45.

Liquid temperature

i C,Si Growth rate gradient /tm at./, mms- K mm-

145 0.35 lo- 5.85 190 0.83 10-l 5.80 239 I .39 10-l 6.05 275 2.61 10-l 5.50 338 4.68 10-l 6.23

C,Si is the atomic percent silicon in the alloys.

area, A, at four different locations on the transverse section and setting 1 equal to &%. Each measure- ment given in Tables 14 is the average value of JX/N taken over the different locations. The error bars on all the graphs were obtained by plotting the smallest and largest values of I measured on a par- ticular transverse section.

RESULTS

Since a significant amount of work was carried out on both the Al-& and Al-Mg-Si systems the results are presented separately.

Al-6wt.% Cu

The measurements of the primary spacing par- ameter, k on A1-6 wt.% Cu are listed in Table 1 and presented graphically in Fig. 5 in which log 1 is plotted against log GL for various different growth velocities Y

All the closed points represent specimens which solidified dendritically with macroscopically planar solid-liquid interfaces. The open points represent those specimens which solidified with a cellular morphology and with macroscopically curved solid liquid interfaces. A longitudinal section through the quenched interface of such a specimen is shown in Fig. 6. Electron microproble analysis of this specimen revealed that the composition of the quenched liquid 20 mm from the interface was uniform and equal to the made up composition of 6wtP/,Cu. The compo- sition of the quenched liquid was also analyzed just ahead of the leading part of the macroscopic interface and down the right hand side of the specimen. Ahead of the leading edge it was found to contain 6.5 wt.%Cu whereas down the side the Cu content rose to approximately 11.5 Wt.% Cu, indicating severe segregation due to gravitational fluid flow.

A best fit double linear regression analysis on all the data at 1.67 x lo- mm s-l and above shows that

~ = K Gi0.55 V-o.28

1856 MCCARTNEY AND HUNT: DIRECTIONALLY SOLIDIFIED ALUMINIUM ALLOYS

Lyok) AL-6wt/oCu

2.7 -

2-b -

2.5 -

2.4 -

2.3 -

2.1 -

2.0 -

I I I 1 I I I I 1 I -I 0.2 03 0.1 05 0.6 0.7 08 09 1.0 14 1.2 1.3

h(GJ Fig. 5. Plot of log 1 vs log GL for Al-6 wt.% Cu at various different growth velocities, I! Closed points represent dendritic specimens. Open points represent cellular specimens solidified at V = 4.3 x lo-

mms-. Lines of slope -0.5 are drawn through the dendritic points.

Fig. 6. Longitudinal section showing the quenched inter- face of an AI-6 wt.,, IO- mm s-I

Cu specimen with Y = 4.3 x and GL = 5.5 K mm-. Magnification =

23 x .

specimens grown at 4.3 x lo-mms- are smaller than would be predicted from the above equation (as can be seen from Fig. 5) and are almost independent of gradient. It would seem that this is most probably due to the convective flow which is observed to occur and is discussed further later.

Al-Mg-Si

In order to reduce the macroscopic interface curva- ture due to fluid flow (see Fig. 1) it is necessary to eliminate, or reduce to a small value, density changes with composition and temperature ahead of the den- drite tips and in the interdendritic liquid. This can be done by choosing a ternary alloy containing one sol- ute element which is denser than the solvent and one which is less dense. If the composition of an alloy is adjusted there will be one particular atomic ratio of Mg to Si which just eliminates density changes with composition and temperature along the liquidus. A series of unidirection growth experiments was carried out at a growth rate of 4.3 x lo- mms- with a temperature gradient of 5.5 K mm- in order to de- termine the Mg to Si ratio which produced a minimal amount of fluid flow (as assessed by the macroscopic interface curvature of a quenched specimen).

A number of alloy specimens each containing a known amount of solute but with different Mg to Si ratios weie directionally frozen at steady state for ap- proximately 50mm and rapidly quenched. A longi- tudinal section containing the quenched interface was then examined and its macroscopic curvature com-

MCCARTNEY AND HUNT: DIRECTIONALLY SOLIDIFIED ALUMINIUM ALLOYS 1857

(b) Fig. 7. (a) Longitudinal section showing the quenched interface of an Al-Cu eutectic specimen. V = 4.3 x 10-3nuns;GL = 6.8 Kmm-. Magnification = 23 x . @) L.ongitudinal section showing the quenched inte~a~ofanAl=0.61at.~M~l.3Qat.~gis~men. V=4.3 x 10-mns-; GL=5.5Kmm-.

Magnification = 23 x .

pared with that of the freezing isotherm for an Al-Cu eutectic specimen under the same conditions. When the liquid at the dendrite tips is much denser than that of the bulk liquid severe macroscopic curvature develops (as shown in Fig. 6 for Al-6 wtp/,Cu) whereas if it is only slightly denser the macroscopic curvature is greatly reduced. It was found that an alloy containing 1.39 at.% Si and 0.63 at.% Mg (a Mg to Si ratio of 0.45) exhibited only a small deviation from the isotherm shape indicating a minimal amount of fluid flow due to the liquid at the dendrite tips being only slightly denser than the bulk liquid. Figures 7(a) and (b) compare the quenched interfaces of an Al-Cu eutectic and Al-O.63 at.% Mg-1.39 at.% Si solidified under the conditions described above.

The Al-Mg-Si phase diagram is shown in Fig. 2. It is apparent that because of the similar slopes of the binary Al-MB and Al-Si liquidus lines, the ternary alloy of the above composition might be expected to behave like a pseudo-binary system. Hence all alloys subsequently used were made up to lie in this pseudo- binary system (that is with a Mg to Si ratio of 0.45) and none appeared to exhibit fluid flow.

The measurements of the spacing parameter, J,, in Al-Mg-Si alloys of two different compositions are listed in Tables 2 and 3 and the growth morphology is also indicated. From the results obtained for the alloy containing 0.63 at.% Mg, 1.39 at .% Si it is possible to relate I for dendrites to GL and V using a double linear regression analysis on the 23 data points. It is found that

L = 346 (3EO.S6 y-O.28

with a standard error in both exponents of f0.02. By carrying out a similar analysis for the specimens

containing 0.15 at .% Mg 0.33 at.% Si and using 10 data points from fully dendritic specimens we find that

2 = lgl Gi0.54 V-O.8

with a standard error of f0.03 in the GL exponent and i-0.02 in the V exponent.

By considering the 9 data points from cellular specimens with the same ~m~sition and applying a similar analysis we find that

J. = 145 GLO 46 v-0.20

1858 MCCARTNEY AND HUNT: DIRECIIONALLY SOLIDIFIED ALUMINWM ALLOYS

t WX)

f-----. dendrites

Fig. 8. Plot of log A vs log (C, Y.) for cells and dendrites. Circles represent dendritic specimens, squares are for cellular ones. &St fit lines are drawn through the points and a line of slope -0.5 is indicated for

comparative purposes.

with standard errors of f0.04 and 20.03 in the Cr. and V exponents respectively.

One way of representing these results graphically is by plotting log (It) against log (GL Vi*) and this is done in Fig 8 for dendrites grown at both tempo- sitions and for cells produced from the alloy of lower solute content. The error bars indicated were obtained as previously described, best fit lines are drawn through the data points, and a line of slope -0.5 is included for comparative purposes.

It can be seen from Fig. 8 that although the spacing of cells and dendrites grown from alloys of the same composition follow a similar functional dependence on Gt and V over the range considered, the two best fit lines are displaced from one another. This effect is better illustrated by Plotting log (2) vs log (GL) for four different growth velocities as shown in Fig. 9. Lines of slope -0.5 are drawn through both the cellu- lar and dendritic points, and the error bars have been obtained as previously described. For each growth rate the two lines are displaced relative to one another and specimens of mixed morphology lie on neither line. (Specimens are defined as being of mixed morphology when a transverse section con- tains primary stalks both with and without sidearms). It would thus seem that this effect is in some way related to the transition from dendritic to cellular growth.

These results clearly show that there is a break going from a cellular to a dendritic structure when the spacing is measured as *1= @j%. There has been some doubt about this in the past 163.

in order to determine the composition dependence of the primary dendrite arm spacing parameter 1, a

number of specimens of &&rent totat solute contents but with the same atomic ratio of Mg to Si were solidified at the same growth rate at gradients of ap proximately 6.0 K mm- * and the results are listed in Table 4. The actual spacings were then corrected for the small differences in actual gradient from one specimen. to another assuming a Gii* relationship before being plotted graphically.

Figure 10 is a plot of log (A) vs log (Cas& where Cmsi is the atomic percent of silicon in the alloy, for a constant growth rate and temperature gradient+ The error bars were determined as before and a best fit line of slope 0.32 k 0.04 is drawn through the points. A line of slope +0.33 is included for comparative purposes.

SUNNY OF RESULI3

The extensive data on Al-h4gSi alloys direction- ally solidified at steady state vertically upwards and stable against fluid flow give the following main results:

(i) 1 == 346 GLO*ss Y-oP2s for dendrites grown from alloys of composition Al-O.61 at.% Mg-1.39 at.% Si with a standard error &0.02 in both exponents.

(ii) A = 181 Gi** Y-o.zs for dendrites grown from alloys of composition Al - 0.15 at.% Mg - 0.33 at.%Si with standard errors of f0.03 and f0.02 in the GL and V exponents respectively.

1 = 145 GL0*46 V-o*2o for cells grown from the same composition with standard errors of &0.04 and f 0.02 respectively.

MCCARTNEY AND HUNT: DIRECTIONALLY SOLlDlFIED ALUMINIUM ALLOYS 1859

Dendrites f :,a&ufvs.

+ v =3.3&&n/$.

f v =ti?n*

4 v=W&ulvs.

Fig. 9. Plot of log 1 vs log GL for cells and dendrites grown from Al-O.15 at.% Mg-0.33 at.% Si at four different growth rates.

(iii) At a f&d grow&h rate of 10-t mms-t and corrected for small deviations of Gt from the nominal temperature gradient of approximately 6.0 K mm- value. the composition dependence of the primary dendrite (iv) By combining the results on Al-Mg-Si arm spacing is given by 1 a (C,S1)0~32*0~04. Where dendrites from (i) (ii) and (iii) above we obtain a Cmsi is the atomic percent of silicon in the alloy, the combined relationship which is given by Mg to Si ratio has been fixed at 0.45 and d has been 1 = 272 G;O.ss V-0.28 -0,32.

+-O-45 l -036 I -0.26 I -096-046 t 1 I I , I t I I I 0 *O-l0 l 0-x + 0-u * OIL

Log(&&if

Fig. 10. Plot of log I vs log (CT,,,) at a constant temperature gradient (6 K mm-), growth rate (lo- mm s- *), and atomic ratio of Mg to Si (0.45). A best fit line is drawn through the points and one of

slope 0.33 is included for comparison.

186@ MCCARTNEY AND HUNT: DIRE~lONALLY SOLIDIFIED ALUMINIUM ALLOYS

DISCUSSION

Comparison with theoretical models

The problem to be modelled is the growth of an array of dendrites in a positive temperature gradient. Most of the detailed theoretical treatments of dendri- tic solidification have considered the growth of an isolated dendrite into an undercooled bath [17-231, and are not readiIy appli~ble to the growth of an array. The most complete treatments of the array problem to date which relate dendrite spacings to growth variables are those due to Hunt [24] and Kutz and Fisher [25].

Both predict a primary spacing relationship of the form

;, = K G-o.5 y-0.2$ Cto.25 m

where G is the temperature gradient, I/ is the growth velocity and Ic is a constant for a binary alloy whose solute content is C, providing the critical conditions for plane front breakdown are sufficiently exceeded.

It is clear that our results on primary dendrite spao ings are in good agreement with the G and V expo- nents predicted by these models, although agreement with the composition exponent is less good. A more detailed comparison is to be made in due course when the constants needed in the analyses have been obtained from work presently being carried out.

Both models indicate a change in the alone relationship when the growth rate is no longer much greater than that which would just produce planar front growth, and the predictions of the two models are shown in Fig. 11 using data from reference [25J for an Al-2 wt .% Cu alloy. Figure 11 illustrates the variation of primary spacing with growth rate (at a constant gradient) predicted by the two models. KUR

x

and Fishers model [25] predicts that at sufficiently low growth rates the cell spacing initially becomes larger than that which would be expected by extra- polating the dendrite measurements at higher veloci- ties. Our results provide no evidence for this and we have found, to the contrary, that the spacing par- ameter, j,, for cells is less than would be predicted from the ~asuremen~ on dendrites grown from alloys of the same ~m~sition.

Other more approximate models have been put forward by other workers[26-295, but our results, obtained over wide ranges of GL and K show signifi- cant discrepancies from the predicted exponents.

Cellular-dendritic transition

Figure 8 illustrates the discontinuous nature of the relationship between the spacing parameter 11 and (G Y) for cells and dendrites grown from alloys of the same ~m~sition. The graph of log I vs log GL for various different growth rates shown in Fig. 9 indicates that for both oells and dendrites I = KGE where a is approximately 0.5 for both 8;rowth forms, that K is smaller for cells than for dendrites and that the change in K is associated with a change in mor- phology both of the primary stalks and of the array adopted by the growing primary arms. (Those speci- mens defined as mixed contain primary arms both with and without secondary arms.)

As was mentioned earlier, the spacing parameter 1 is defined as J&%. The actual spa&g in a regular array depends on the form of the array. If we define the nearest neighbour spacing as 1+ then for a hexa- gonal array we find that ,I: = 1.075 &@I. For a square array 12 = J7ii. For a completely random array of points it has been shown [30] that the aver- age nearest neighbour distance is given by 5+ = 0.5

8 VCS Al-Zwt%Cu.

io*

Fig. Ii. I as a function of Y in an Al-2 wt.% Cu alloy at a temperature gradient of IOK mm- as predicted by the models of Hunt (241 and Kurz and Fisher [25] (Iabelled Hand K-F respectively). The data is taken from Ref. [253, and V,, is the constitotiona1 supercooling velocity for planar front growth.

MCCARTNEY AND HUNT: DIRECTIONALLY SOLlDlFIED ALUMINHJM ALLOYS 1861

h is defined as J1AIN) where N is the number of primary arm centres in an area A

SQUARE ARRAY l . . l

AL ARRAY

. . l

.

X-l;,-?KiZ

$= ,.OKiW$

Fig. 12. Schematic representatious of three different arrays of points. k$ is the nearest aeighbour spacing for a cubic array, 4 is for a hexagonal array, I$ is the average nearest neighbour spacing for a random array. N is the number of

points in an area A.

@R. These three cases are illustrated schematically in Fig. 12. The above expressions can all be written in the form d* = B,/&@ where B depends on the nature of the array.

It was observed that the c&~lar structure had a well defined hexagonaI array whereas the dendritic structure was much iess regular. These two cases are illustrated by the micrographs of Figs 13(a) and (b). Essentially the dendrites form a regular rectangular/ square pattern over small regions but there appears to be little long range order. There is also considerable evidence from the results of other workers [4,31 f that these types of patterns arc generally observed.

It could be argued that what is important in an analysis of the growth is the average nearest neigh- bour distance since this is the term which d&es the diffusion distance. Thus when comparing results on cells and dendrites the parameter rt*, defined as the average nearest neighbour distance, should perhaps be used.

For the hexagonal array of cells B = 1.075. The value of B necessary to bring the dendrite measure- ments in Fig. 8 into the same fine as that for cells, thus leading to no discontinuity in A*, is approxi- mately 0.8. It can be seen that this value of B for dendrites lies between the value of B for completely random and the regular square array.

It is concluded therefore that the discontinuity in % = JAjiij can be a result of the form of the array and a value of B z 0.8 leads to no discontinuity in rl* which is the average nearest neighbour distance.

Discussion o~prL,~io#s experimental work

There has been considerable experimental work on the measurement of primary arm spacings and most of this has been reviewed by Hunt [24] and Klaren, et al. [ll J. It is of interest, however, to compare our results with the most recent work. This was carried out by Klaren et al. [ll J on Pb-Sn and Pb-Au alloys. The bulk of their results were obtained on lead-tin alloys containing between 10 and 50 wt .% Sn.

As they pointed out the tin which is being rejected is lighter than the bulk liquid and since the specimens were frozen vertically upwards this means that the density of the interdendritic liquid increases in the vertical direction giving an unstable hydrodynamic situation, It seems possible therefore that in these experiments con~ion currents occur in the liquid, that these interact with the solute diffusion process and affect the dendrite spacings. One would thus expect little agreement between either their results and those obtained in alloys in which a denser solute is being rejected at the interface or the predictions of a diffusion controlled model. Moreover as the growth velocity is decreased convection will become relatively more important in inserting solute and it is not unexpected that a critical velocity is observed below which the spacing becomes independent of velocity. Presumably at this stage convection has become the dominant mass transfer mechanism.

Burden and Hunt [32] have in fact observed the significant effect of convection on the dendrite spac- ings in the ammonium chforidewater system. They found that ammonium chtoride dendrites grown verti- cally downwards had a much coarser spacing than those grown vertically upwards. In the former case the interdendritic density gradient was stable whereas in the latter case it was potentially unstable.

The results of Klaren at al. [l l] on Pb-Au also need to be treated with caution in that although there is a stable vertical interdendritic density gradient, ffuid flow of the type observed by Burden et al. [12] (and described in the In~~uction) may still be occur- ring. This type of flow becomes serious when there is a large density difference between the solute and soi- vent atoms, and when there is a large solute boundary layer ahead of the dendrite type. Various workers [15,33,34] have found that this boundary layer depends on G/V where G is the temperature gradient and V the growth rate.

Pb-Au is a system in which the liquid densities differ considerably (liquid density of Pb = 10.68 x lo3 kg/m3 [35]; liquid density of Au = 17.36 x lo3 kg/m3 [35]) and so under conditions of high gradient and IOW velocity significant fluid flow might be expected and could account for the existence of a critical vel-

1862 MCCARTNEY AND HUNT: DIRECTIONALLY SOLiDPIED ALUMINJUM ALLOYS

Fig. 13. (a) Cell

ocity below which th independent of rate.

In conclusion then must be treated wit1 bility of tluid flow liquid.

(a)

ular array in an Al-O.15 at.% Mg-0.33 at.% Si alloy. Magnification = 90x array in an Al-O.63 at.% Mg-l.39at./0 Si alloy. Magnification = 75 x .

be dendrite spacing is apparently SUMMARY AND Cf3 INCLUSIONS

the results of Kiaren et nl. [ 11 J Experimental results have been obtained h caution because of the possi- alloys of various compositions in the ACMg-S in the bulk and interdendritic tern which exhibit little fluid flop w in the interden

or bulk liquid, These have been obtained over a

: . (b) Dendritic

i sys-

dritic wide

MCCARTNEY AND HUNT: DIRECTIONALLY SOLIDIFIED ALUMINIUM ALLOYS 1863

range of liquid temperature gradient, GL, growth vel- ocity, V and alloy composition, C,. The parameter A, which is a measure of the primary arm spacing has been related to GL, V and C, using linear regression analyses. It has been found that for dendrites the relationship is of the form

where K is a constant and C,Si is the atomic percent of silicon in the alloy. This shows good preliminary agreement with the models presented by Hunt [24], and Kurz and Fisher [25].

It has also been observed that the spacing relation- ship for cells and dendrites, for specimens grown from alloys of the same composition, is discontinuous when ,I is taken as a measure of the primary arm spacing.

If, however, the average nearest neighbour spacing, A*, is taken to be the important parameter in assess- ing cellular or dendritic growth instead of 1 (which simply equals m) then the discontinuous change in I can be explained in terms of the different arrays adopted by cells and dendrites. It has been shown that A* = Bm where the value of B depends on the array. To eliminate a discontinuity in A* a value of B for dendrites of 0.8 is required and this value is between that for a square array and a completely random array.

Acknowledgements-The authors would like to thank Pro- fessor Sir Peter Hirsch F.R.S. for the provision of labora- tory facilities which has made this work possible. One of us (D. G. McC.) would like to acknowledge financial support from the Department of Education for Northern Ireland.

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