Origin of spiral eutectic structures

ORIGIN

OF SPIRAL

EUTECTIC

R. L. FULLMAN

STRUCTURES*

and D. L. WOODt

Eutectic structures in which the two phases appear as intertwined spirals been observed in zinc-magnesium and aluminum-thorium alloys. The spatial structure in zinc-magnesium alloys is a spiral cone. A theory of the solidification for formation of this type structure is advanced based on a particular type difference in growth rates of the two phases. L’ORIGINE

DES

STRUCTURES

EUTECTIQUES,

in cross section have form of the eutectic conditions necessary of anisotropy in the

SPIRALIFORMES

On a observe dans des alliages zinc-magnesium et aluminium-thorium, des structures eutectiques dans lesquelles les deux phases apparaissent, dans une coupe transversale, en forme de spirales entrelackes. Dans l’espace la structure eutectique dans les alliages zinc-magnesium est en forme d’une helicdide conique. On propose une theorie des conditions necessaires lors de la solidification pour former ce type de structure. Cette thdorie est bas6e sur l’anisotropie de la difference entre les vitesses de croissance des deux phases. DER

URSPRUNG

DER

EUTEKTISCHEN

SPIRALSTRUKTUREN

In Zink-Magnesium und Aluminium-Thorium Legierungen wurden eutektische Strukturen beobachtet, in denen die beiden Phasen als verschlungene Spiralen im Schnitt erschienen. Die raumliche Form der eutektischen Strukturen der Zink-Magnesium Legierungen ist ein Spiralkegel. Es wird eine Theorie der Erstarrungsbedingungen, die fiir die Bildung einer derartigen Struktur erforderlich sind, dargelegt. Diese Theorie grtindet sich auf eine bestimmte Form der Anisotropie in der Differenz der Wachstumsgeschwindigkeiten der beiden Phasen.

Scheil [l] and Buckle [2] have published illustrations of eutectic structures in which the polished and etched cross section reveals the two phases wrapped around each other in the form of spirals. The structures were found in the zinc-magnesium [l] and aluminum-thorium [2] systems. This paper reports the results of an investigation of the spatial arrangement of the phases in eutectic spirals of an alloy of zinc plus 3 per cent magnesium. A theory of the prerequisites for the formation of spiral eutectic structures is advanced.

Experimental

Procedure

Small heats of the alloy were melted in air, and cast into simple ingots suitable for metallographic preparation. A wide range of cooling rates was obtained by varying the casting conditions (i.e., from extremely rapid cooling obtained by casting onto a large cold brass block, to extremely slow cooling obtained by allowing the heat to cool in a small furnace). Cross sections were prepared for metallographic examination by mechanical polishing and were etched with 1 per cent Nital. Specimens showing well-developed spiral structures were used to investigate the spatial arrangement of the phases. A “Knoop” micro-hardness indentation was made on the surface of each specimen to be investigated. Since the long axis of the “Knoop” diamond indenter has a base angle of 172 degrees, the depth polished away is equal to *Received October 13, 1953. tGenera1 Electric Research Laboratory, ACTA

METALLURGICA,

VOL.

Schenectady,

2, MAR.

1954

N.Y.

0.0306 times the change observed in the indentation length. The indentation was photographed at a magnification of 250X, and one or more spirals were photographed at a magnification of 2000X. The specimen was then repolished and etched, and the same spirals were photographed, along with the indentation as shown in Figure 1. Alternate polishing and photographing were continued until a considerable depth of the specimen had been examined. When an indentation had shrunk to near zero size, a new indentation was placed on the specimen, and both indentations were photographed so as to provide continuity in the record of the depth removed by polishing.

Experimental

Observations

It was found that well-developed spiral structures were produced over a wide range of cooling rates. At the fastest cooling rates used, the microstructure revealed small spiral segments, but the numerous eutectic colonies impinged before any attained sufficient size for a spiral of several turns. At the slowest cooling rates used, the phases were distributed in a typical spheroidized structure. A 5-minute anneal at about 15°C below the eutectic temperature caused similar spheroidization of the structure of a sample that had a well-developed spiral structure before annealing. Hence the formation of the spiral morphology does not appear to require any special range of cooling rates, except for limitations imposed by high nucleation rate: growth-rate ratios at high cooling rates, or spheroid-

PLATE I. Figure l-Top, two cross sections of same area of zinc plus 37s magnesium alloy, 1000X. Bottom, “Knoop” microhardness mdentation corresponding to the cross sections above, 200X. Figure 2-Typical microstructure of zinc plus 3y0 magnesium alloy. As cast. 750X. Figure 3-Double sprral structure. Zinc plus 3% magnesium. 1500 X. Figure 7Nearly axial cross section of zinc plus 370 magnesium eutectic colony. 250 X .

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FULLMAN

AND

WOOD:

SPIRAL

ization at low cooling rates. Most of the spirals were single, as shown in Figure 2, but occasional closed loops or double spirals, as shown in Figure 3, were found. The spirals had approximately regular spirals were hexagonal form, and neighboring usually of nearly identical orientation. On repolishing samples to investigate the spatial arrangement of the phases, it was found that the spiral centers wound farther around or unwound as material was removed. One spiral was found that unwound at first, and then wound up as more material was removed. The general shape to be inferred from this observation is that of a spiral cone, as shown in Figure 4. As the cone widens out,

EUTECTIC

STRUCTURES

191

spiral center turns times the spacing of the spiral turns measures the distance that the cone opens or closes in a given distance along the axis. Hence, if the shape is actually a regular cone, a graph of spiral revolutions times spiral spacing versus the 7 SPIRAL 6 0

SPACING,

MICRONS 1.4 0

0

1.3

DEPTH,

d

MICRONS

FIGURE 5. Analysis of spatial form of spiral eutectic colonies in zinc plus 3% magnesium.

FIGURB 4.

Schematic diagram of spiral cone morphology.

distance polished should consist of two straight lines of equal slope but opposite sign. The slope of the lines is equal to the half-angle of the cone. Data

the spiral winds farther around, filling in the center of the figure. Hence, unwinding of the spiral center is observed if the direction of polishing is toward the center of the cone, and winding of the spiral center is observed if the direction-of polishing is away from the cone center. The spiral center first unwinds and then winds if the initial direction of polishing is toward the cone center and polishing is continued beyond the cone center.* The product of number of revohttions that the *The alloys studied contained primary dendrites, and most of the spiral cones ap ared to start from dendrites. Hence only one half of the r*cYe eal double cone was observed in most of the spirals investigated. Nucleation from a common dendrite is no doubt responsible for the similar orientations of neighboring spirals, apparent in Figures 1, 2 and 3.

FIGURE 6. Schematic diagram of axial cross section through a spiral cone.

192

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METALLURGICA,

from 12 spiral eutectic colonies are plotted in this manner in Figure 5. The cone angle is about 17 degrees, and is independent of the spacing of the spiral turns, within experimental scatter. A longitudinal section through a spiral cone would appear as shown in Figure 6, if the section were exactly along the cone axis. The discontinuities of alternate branches would disappear if the section were off the cone axis. The appearance of these discontinuous branches over a considerable distance in the photomicrograph of Figure 7 indicates that the section is nearly parallel to the cone axis. Hence the observed angle between branches of the cone is approximately equal to the true cone angle. The angle found is again 17”.

Theory of Formation of Spiral Eutectic Structures In order to understand the attributes of a eutectic system necessary for the formation of spiral eutectic structures, it is convenient to consider first the behavior of a hypothetical eutectic system of two-dimensional crystals. Typical eutectic solidification would consist of the growth of adjacent rods of the two phases, as shown in the upper part of Figure 8. The composition of liquid

VOL.

2,

1954

spiral, subsequent nucleation of another crystal on the lateral liquid-solid interface could lead to the formation of a double spiral. In most real (three-dimensional) eutectic systems, the faster-growing phase grows around the slower growing phase in all directions, so that the slower growing phase is surrounded and isolated from the liquid, without formation of a spiral. If the difference in growth rates is approximately isotropic, the slower-growing phase will be roughly spherical. If the difference in growth rates is small in a single direction, the isolated phase will be in the form of rods, while if the difference is large in a single direction plates will be formed. A conical spiral eutectic morphology can be produced if the anisotropy in growth rates is so large that the growth-rate difference changes in sign as well as magnitude as a function of direction. Consider the hypothetical growth rate plot shown in Figure 9. In this idealized model it is assumed

FIGURE 9. Hypothetical growth rate anisotropy for formation of spiral cone eutectic structure.

FIGURE8. Schematicgrowth of rods during solidification

of a hypothetical

two-dimensional

eutectic

alloy.

ahead of the rapid-growth directions of each rod is shifted toward the composition of the other phase. As a result, the liquid at the ends of the slowergrowing beta-rod is more supercooled with respect to growth of phase alpha than is the liquid at the ends of the alpha-rod. Hence the faster-growing phase tends to grow around the slower-growing phase, as shown in the lower part of Figure 8. Continued growth of the pair of two-dimensional rods would then lead to formation of a spiral unless there were no error of closure of the loop formed. If a complete loop were formed, repeated alternate nucleation of alpha- and beta-crystals at the liquid-solid interface could lead to the formation of a series of rings. If the closure error were larger than that required for the development of a single

required

that the growth-rate difference is a function only of the angle 4 from some crystallographic direction. For the situation considered, beta-crystals grow faster than alpha-crystals for all values of 4 from 0 to 41, and alpha grows faster at larger values of 4. If contiguous crystals were growing from the melt, the growth-rate anisotropy shown in Figure 9 would cause phase alpha to grow around phase beta in all directions in the plane 4 = 90”, while phase beta would grow around phase alpha in the direction 4 = O”, leading to the configuration shown in Figure 10. But as phase beta grows around phase alpha the direction of the growing edge changes from 4 = 0 to larger values of 4. When the direction of the edge reaches $1, the growth rates become equal and the two phases grow out as a cone with half-angle &. The cone axis is the direction C#J = 0”. Since with this configuration there is no opportunity for the faster-growing phase to surround the slower-growing phase, the arguments

FULLMAN

AND

WOOD:

SPIRAL

predicting spiral morphology in a hypothetical two-dimensional eutectic system are not invalidated. Only growth directions between & and 90 degrees are operative, so that G,-Gb ranges from zero to a maximum positive value in the plane $S = 90”. The result is a spiral cone morphology, as shown in Figure 4. The growth rates of real crystals do not depend on only a single orientation parameter c$, as has been assumed above. The growth rates of the two crystal types can be described as functions of 4 and an angle 8 measured in the plane perpendicular to the spiral axis. Then for each value of B a plot

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193

of 8 there will be a value &(e) at which the growthrate difference is zero, but the angle +r and the growth rate at which this occurs will depend on the value of 8 chosen. Since the longitudinal growth of the spiral colony involves only directions for which the two growth rates are equal, it behaves like a single phase, and only the slowest growth rate operates. Hence the group of crystallographically equivalent directions +1(e) which have the smallest growth rate are the only active growth directions, and the spiral is faceted.

Conclusions The spatial form of eutectic colonies that appear as spirals in cross sections of zinc + 3 per cent magnesium alloy has been analyzed. The colonies have the form of spiral cones with hexagonal faceting and a cone angle of 17 degrees. The formation of eutectic colonies with this morphology can be rationalized on the basis of a particular type of anisotropy in growth rates of the two phases.

Acknowledgement

FIGURE10. Elementary growth form leading to formation of spiral cone eutectic morphology.

The authors wish to express their appreciation to Miss D. Kontoleon for assistance in the preparation of the several hundred photomicrographs required in this investigation.

References of the growth-rate difference as a function of 4 may be drawn, similar to Figure 9. For each value

1. k

HEIL, E. Z. fiir Metallkunde, 37 (1946) 1. 2. BUCKLE,H. Z. fiir Metallkunde, 37 (1946) 43.