The relationship between growth forms and the preferred direction of growth

THE

RELATIONSHIP THE

BETWEEN

PREFERRED A.

GROWTH

DIRECTION

ROSENBERG?:

and

OF

W.

A.

FORMS

AND

GROWTH*

TILLERt

The morphologies of the growth forms associated with the various modes of solidification of Pb crystals are okserved to be related to the crystal habit planes of Pb, and the preferred orientation exhibited in the columnar zone of an ingot of Pb is observed to related to the mode of solidification. In zone-refined lead, the mode of solidification is such as to produce a (111) preferred orientation. With the addition of 5 x lO-4 wt. per cent Ag, the mode of solidification changes and a
RELATION

ENTRE

LES

FORMES ET LA DE CROISSANCE

DIRECTION

PREFEREXTIELLE

On observe que la morphologie des formes de croissance associke aux divers modes de solidification de cristaux de Pb est en relation avec les plans d’habitat cristallins de plomb et que le mode d’orientation p&f&entielle qui apparait dans la zone basaltique d’un lingot de plomb est en relation avec le mode de solidification. Dans le plomb raffinb par la mkthode de la zone fondue, le mode de solidificat,ion est. to1 qu’il se produit une orientation pkfkentielle en (111 j. Par addition de 5 x lOY?,& en poids d’hg, IH mode de solidification est modifik et une orientation prkfbrentielle en (100) se produit. DER

ZUSAMMENHANG ZWISCHEN WACHSTUMSFORMEN BEVORZUGTEN WACHSTCMSRICHTUSG

UND

DER

Es wurde beobachtet, dass die Morphologie der Wachstumsformen, wie sie bei den verschiedenen iZrten der Kristallisation von Blei entstehen, mit den Habitus-Ebenen von Pb in Beziehung stehen, und weiterhin, dass die bevorzugte Richtung in der Zone der Stengelkristallisation eines Blei-Gusstiicks mit der Art der Erstarrung zusammenhkngt. In zonengereinigtem Blei ist die Erstarrungsart derart, dass sie eine (Ill)-Vorzugsorientierung hervorruft. Bei Zufiigen von 4 x 10ml Gew..Prozent Ag ilndcrt sich die Ersterrungsart, sodass eine (100).Vorzugsorientierung entsteht. INTRODUCTION

This article describes

a series of experiments

relate the crystal habit planes preferred orientation exhibited

PlOtelet Platelet Cjrowth buid Growth t D2ct1on DIrection .9 ~l$rface In’e,‘ace -7 , / , ,‘I _‘< 2 /‘,, ,’ i Platelets -’

that

of a metal to the by the columnar

grains of an ingot of that metal. Crystal

Wranglen’l)

habit.

has recently

Crystal

compared

the Bravais and the Kossel-Stranski theories of crystal habit; he finds their predictions to be in good agreement with each other and with experiment. According to the Bravais theory, the smaller is the reticular

4

FIG. 1. A trace of the solid-liquid parallel to the axis of growth which growth of platelets.

as illustrated

itself.

separating

solid

the crystal

and in the final crystal

surfaces of slowest perpendicular These are the close-packed the preferred result

crystal

of solidification

only

the

growth will persist.

surfaces.

The normals to

faces that are developed are tabulated

as a

in t’he second

column of Table 1 for t’he various crystal structures. Recent experiments by Rosenbergc2) on the solidification of lead crystals show that there is a relation-

The

METALLURGICA,

VOL.

interface represents

in Fig.

and liquid

edges of the platelets

attachment

1.

on a section the edgewise

The

interface

is not’ a smooth

plane

are composed

of smaller

of

atoms,

and

accounts

for

the

high

component of growth in this direction. The faces of the platelets appear to be fairly perfect, and thus have Llquld Platelet

Growih

c\

or platelike,

* Received December 10, 1956; in revised form February 20, 1957. t Westinghouse Research Laboratories, Pittsburgh 35, Pennsylvania. $ Now at the H. H. Wills Physical Laboratory, University of Bristol, England. ACTA

B

steps as shown in Fig. 2. This gives many sites for the

has shown that the freezing of zone-refined lead occurs of a lamellar,

.

advancing normal to itself, but is a corrugated surface advancing in t,he direction of the edges of the platelets.

ship betwetln the crystal habit’ of lead and the structure of the interface between the solid and the liquid. He by the edgewise extension

_’

Crystal

structure,

from

Site

SolId

density of a surface, the faster will it grow normal to The fastest growing surfaces will soon disappear

, -Corner

5, OCTOBER

1957

SolId FIG. 565

2. Magnified diagram of platelets showing small steps on the edges and relatively perfect faces.

566

ACTA

METALLURGICA,

VOL.

5,

1957

of Boundary

D~rectm

-Gram Formation

C

step

lnterfoce

/ Sohd

FIG. 4. Interface step between two crystals which leads to the encroachment of B by A.

poured Fro.

n

3. Platelet structure seen on the decanted of a Pb bicrystal.

negligible

tion.

component

interface

mold.

of growth in the normal direc-

Fig. 3 shows the interface of a bicrystal.

In one

crystal, the platelets are intersecting

t’he surface at a

very

ot,her, they

small

making

angle,

a steep

whereas angle

in the

with

the interface

difficult to see at this magnification. platelets

are nearly always

however,

occasionally

observed. agreement

a.re are

The faces of the

one of the (111) planes;

a different

The order of observed

platelet systems is {ill},

and

{loo},

platelet

(llO), (311).

with the order of preference

planes in t’he habit theories.

system

occurrence

Therefore,

is

of the

This is in for crystal

one can say

that the crystal habit theory, although meant to apply to equilibrium

forms, gives the orientation

of the platelet form in lead. change The

A growth form may be defined as a unit

its essential

platelet

of the face

which seems to be the basic growth

of solid having a particular morphology geometric

will be referred

which does not

features

as it grows.

to as the primary

or

basic growth form, rather than the basic growth unit, because it has been observed that it develops from the building up of layers of solid which are not necessarily parallel to the platelet face.

Rosenberg@)

have shown that this type of growth

and Grafc3)

form may be

observed in most metals, and that it appears to be the simplest type of growth form. Preferred

orientation.

When

a liquid

metal

~~

~~~_~

_~~ .~ ~-~

Face-centered cubic Body-centered cubic Hexagonal C.P. Body-centered tetragons1

(1) Preferred casting orientation

is

a cold mold,

oriented

Some

of

a chill

(2) Preferred habit orientation

(109) (190) (lOlO>

(111)

(116)

(100)

j$::{

zone of very fine

grains appears at the edge of the the

grains,

on

growing

inwards,

survive, but most do not.

The surviving grains become columnar in shape and exhibit a preferred orientation

with respect to the long axis of the grain. ferred orient)ations of the columnar crysballographic

structures

The pre-

grains for several

are t’abulated

in column

one of Table 1. In general, the arguments casting orientation

used to account

have depended

for the

on the existence of

an interface step between crystals of different orientation as shown in Fig. 4.

The grain in advance

a component, of growth in the lateral direction,

has

and is

thus able to encroach on the retarded grain and crowd it out of the specimen. phenomenon

Tammannt4)

explained

on the basis of the anisotropy

of the material.

Grains

maximum

velocity

‘linear

the direction

in which

this

of growth

the direction

of growth”

of

is parallel to

of heat flow will grow faster, and hence

fart’her, into the melt. However, in an ingot, growth velocity of a grain is determined by

the the

difference in heat flow down the temperature gradients in the liquid and solid at the interface. Therefore, if two grains of dissimilar orientation are growing side by side, one cannot grow faster than another unless it has a greater thermal conductivity flow.

The

depend

essentially

conductivity his

considerations upon

of

in the direction of heat Tammann,

an anistropy

therefore, of

with crystallographicdirection.

considerations

may

account

tions made upon anisotropic

TABLE 1. Preferred orientation

Crystal structure

into

randomly

for

materials,

thermal Although

the

observa-

they do not

adequately explain the phenomenon of preferred orientation in cubic materials. Chalmers(5) has tried to account for the preferred orientation of cubic materials by assuming that interfaces of different orientation are in equilibrium with the liquid at different temperatures. This allows one grain to be growing in advance of another

of different

orientation

freezing at the same velocity.

even

though

it is

ROSENBERG

The preferred orientation

of the columnar

always the same as the dendrite materials,

and therefore

TILLER:

AND

OF

GROWTH

grains is

orientation

it has generally

DIRECTION

r2

567 In. Dm Pvrex Tube

in these been

con-

sidered that the preferred direction of growth of the columnar grains is a fundamental characteristic of the pure metal.

It will be shown later that the assumption

is in error and that the (100) preferred orientation

of

lead, as a representative of the f.c.c. crystal structure, is due to the presence of solute in the melt. It can be seen from the platelet growth experiments that the crystal habit theories predict the orientation of the primary

growth

casting orientation growth

of

the

relationship

form.

Since

the preferred

must in some way be related to the

platelets,

one

would

expect

some

between the plane of the primary growth

form and the preferred casting direction. should expect a relationship growth form and the growth

In fact, one

between the primary of dendrites. Finally,

one might ask, since a (1111 platelet system is so prominent in the growth of lead, then why is it not prominent

in the preferred

orientation

of pure lead?

The present work was designed to shed some light’ on t.his problem (1) The

by studying:

preferred

orientation

of zone-refined

lead

and lead with alloy additions. (2) The relationship

between

form and the “cellular” additions.

This

the primary

growth

growth form caused by alloy

growth

form

is shown

in Fig.

10.

FIG. 5. Mold design for unidirectional solidification.

almost ilat over t’he entire 2 in. cross-section showed

that the growth

Optical inspection

was indeed

which

unidirectional.

of the interface showed the grain

size to range from 1 to 10 mm2.

Of these grains, 90

per cent showed

structure

strong platelet

platelets intersecting

the interface

that their orientation major

platelet

with the

at small angles so

was within a few degrees of a

system.

On etching

the sample,

the

bottom surface showed ten times as many crystallites as the interface, and t#heouter walls showed many long crystallite

boundaries

extending

the sample to the interface.

from t’he bottom

of

Therefore, it appears that

growth

no grains existed in the ingot ot’her than those which

form and the “dendrite” growth form. The experimental techniques used in this investi-

grains in this layer about 90 per cent had been crowded

(3) The relationship

gation

between

have all been described

the primary

elsewhere,(2p 6~‘) and

will be referred to as needed to discuss the experimental observations.

Most of the observations

were made on

interfaces which were produced by rapidly decanting the liquid from the solid during growth.c7)

Preferred

orientation.

A

quantity

(250 cm3)

of

lead was melted in a clean beaker in air

under a reducing

flame.

on the lower surface,

out by the surviving interface

grains.

boundary

migration

orientation

The lead was then poured

The appearance

had occurred.

Laue photographs

positions

of the interface.

of the of grain

To determine

of the grains in the interface,

reflection

plotted

and of the original

showed that only a small amount

large size were X-rayed

OBSERVATIONS

zone-refined

nucleated

were taken

X-ray

at random

In all, 15 crystallites

against

the upper through

part

of the Cu;

the water

chamber.

hot water

on the st’ereographic

triangle

of a standard (111)

was

The lead was

superheated about lOO”C, and as it was poured into the mold, cold water was injected into the chamber to rapidly chill the Cu. On striking the cold Cu plate, Pb crystals nucleated and began to freeze upwards. After about 2 in. of solid had formed, the remaining liquid metal was rapidly decanted from the solid by an abrupt inverting of the crucible.

It was observed that the interface was

of

and the results are shown

into a mold designed for unidirectional freezing (Fig. 5). The mold was first pre-heated by directing a flame flowing

the back

FIG. 6. Stereographic projection of crystallite orientation from zone-refined Pb ingot.

solute coIlcel~tra,tion is sufficient to produce a eelluls~ int,erface. Deueloprn~ent Pb + 0.0001%

of

the cellular

pwct?i

form.

Sererd

photomicrographs were taken of the interfaces during various st’ages of cellular growth to show how the

Ag

complex

pyramidal

growt,h

form

of’ the

“cellnlar

interface”

mode of growth, is developed from the basic growth form : i.c ., a particular (11 I> platelet syst,em of the ‘@ane Fig (&A)

int,erface” mode of growth.

9 shows

t4la.t the elongated

gonal cell boundaries, of the individual

of cr_wta~llite orienFIG. 7. Stereographic pmjertion tnt,ion from Pb _I- 0.0001 wt. per cent Ag ingot,. (100)

proj&ion

in Fig.

6.

these grooves

preferred orientation

The

of t,he grains in this ingot was found to be the (Ill) orientation. A second test wa,s carried out in an ident’ical manner with the addition the Pb.

of lo-*

This particular

wt. per cent Ag present in amount

of Ag was chosen

since it was not enough to change the mode of solidification to “cellular,”

butt it wa.s enough I,0 have some

effect upon the solidi~e~tion t,hc interface beginning

showed

to become

unstable

onset of cellular growth. X-rayed

process.

Inspection

that t,he crgstallites with

About

respect

in Fig.

solute concentrat’ion,

the grains exhibited

random

of

distribution

to the

26 crystallites

and the results plotted

orientation,

of

were just were

7. For this an almost

with

a slight

preference for the (loo} direction. A third test, was carried out in an identical manner with the lead cont,aining 5 x IO-* wt.. per cent Ag. This

amonnt

interface

of Ag

was added

would be produced.

this expectat,ion:

a cellular

all the crystallit,es exhibited

stages of cell development, X-rayed

so that

The results con~rmed various

Again 15 crystallites

were

aald the results plott,ed in Fig. S. It can be

seen that the (100) orientation

is preferred

when the

cell

boundaries

which form prior to the f~~rrn~~ti~~n of the hexado so i>y a grooving of &he edge

platelets

produces

(R-B).

shows that when the elongated regular

The

are formed

of the edge of the platelets

hexagonal formed

sides.

The

of

Fig. 10

cells break down into

cells, the cell boundaries

grooving

stacking

t,he I)ounda,ry A-A.

outer

two

by 8 ret’arding of a section

by in

on four of t)he boundaries of platelet

zLre edge.

Fig. 11 shows the a,ppea,rance of the platelets during cellular growth specimen

observed

grown

on the upper surface

in a horiz~)ntai

t,inuity of plat;elet growth is visible.

Some

of a con-

across the cell l~ound~ries

As t,he growth conditions cells projected

boat..

were changed so t,hat the

fart’her int,o the liquid, it was observed

that a second platelet system, which appears to be a (100) @em,

was also operating

to provide

growth.

This is shown in Fig. 12. Fig. 13 shows a cellular interface exhibiting

at least one major platelet system and

several other platelet which appear

minor

The cells composing

systems compared

systems course

system.

of Fig. 14 contain

syst.ems and the begin-

Fig. 15 shows three (111) plat*elet

on a cell. of these

t,o the {Ill>

the interface

two ~-ell-de~~eloped platelet nings of another.

(indicat,ed by arrows)

It was observed

observations

that

throughout

the

the presence

of

solute, and part,icularly the presence of cells had a large influence upon increasing the frequency of t’he minor platelet systems.

of occurrence

This is especially

true

for the (100) systems which appeared very freqncntlp under these conditions. ?Yhen crystals of lead

containing

concentrations

using the t,hermal valet

were grown

higher

t,echIliq~le of Tiller a,nd Kutt~er(F) it became

alloy

increas-

ingly apparent to t,he unaided eye that certain regions were growing in advance of others on the intcrfacc. When t,he cryst,ai was etched in 10 per ceI& nitric acid, it was observed t,hat’ a single retarded region r’~~presentcd a single grain. The boundary separating the

I+‘rc-:.8. ?bw3ographic projection of crystallite orientation from Pb _1-0.0005 at. per cent Ag ingot.

elevated and the depressed regions coincided exactly with the grain boundaries of the grains. A photomicrograph of the specimen in the unctohed st:Lte is

FIG:. 9. Decanted intorfare (H-R) and elongated crll

FIG. 10. Decanted

showing platelet structure boundaries (A-A). 500 x

interface showing platelet on a rellulnr interface.

structure

FIG. 11. Upper surface of a crystal showing trace of the decanted int,erface. The platelets comprising the cells are clearly visihlc as they intersect the upper surface. 210 X.

FIG. 12. Decanted

cellular interfare exhibiting platelet SystCnIS. 100 ”

FIG. 13. Decanted

cellular interface platelet s?_strms.

FIG.

two

exhibiting

several

14. Decanted cellular interface exhibiting platelet s~stc~ms. “50 ,’ .

sevrral

570

ACTA

METALLURGICA,

VOL.

5,

1957

shown in Fig. 16. The specimen after etching is shown in Fig. 17. It can be seen that the orientation depressed

of the

region (light) differs from the main orien-

tation (dark). This effect first became noticeable to the unaided eye at solute concentrations of 0.15 wt. per cent, Sn in Pb and greatly increased

as t)he solute concentration

increased.

shown in Fig. 16 contained

The specimen

0.75 wt. per cent Sn and the interface

present’ed a

depressed region which was 0.03 cm below the surface of the main crystal. observed compared

The depressed

crystallites

were

to dways exhibit, an enlarged cell size to the crystallites in advance which

exhibited a much smaller cell size, X-rays showed that FIG. 15. Decanted cellular interface exhibiting { 11I} platelet systems. 2.50x .

three

the depressed

crystal

always

had orientations

in the cent,er of t’he stereographic (100)

projection,

and t’he crystals

orient,ations near a (100) pole.

lying

triangle of a standard in advance

had

This would lead to a

pronounced (100) preferred orientation in the columna,r zone of an ingot of this alloy. Development

of the dendritic growth form.

A series

of experiments were carried out to observe therelationship between t,he basic growth form and the dendritic growth form that develops with its supercooled A crystal

when a solid is in contact

melt.

of zone-refined

lead in which

platelet system was intersecting

a {ill}

the upper surface at, a

small angle was grown in a horizontal

boat.

surface of the melt ahead of the interface

The top

was super-

cooled by lightly playing an air jet on the liquid just ahead of the interface dendrites FIG. 16. Decanted interface of Pb + 0.75 wt. per cent Sn sample exhibiting a region depressed 0.03 cm below the rest’ of sample.

st#udied.

and the development

It was observed

that

of the traces

other platelet systems began to appear (at, A-A) interface

was

containing

transformed

from

dendrit’ic project’ions.

a

plane

of

as the to

one

Fig. 18 shows the

curving of the dendrit’e spine as the dendrite becomes fully developed. The actual dendrites supercooled

structures extending decanting

which

melt are revealed

are growing

into the

as three-dimensional

ahead of the interface by rapidly

the liquid from the solid.

The relationship

between bhe (11 I} platelets and the dendrites is clearly shown by the end-on view of a dendrite tip in Fig. 19. The

four

forming

complementary

(ill>

pla)nes are

t*he bulk of the tip of the dendrite.

clearly Several

features are worth noting. The platelets are being nucleated independently approximately in the center of each face. The platelets then spread out from this nucleation site in all directions. The

FIG. 17. Sample of Fig. 16 etched to show that depressed region was a single grain.

the

boundaries of the faces are approximately triangular and an apex of the triangle in each case is directed towards the tip of the dendrite. This direction is, of course, a (211) direction.

ROSENBERG

The essential morphology completely extreme dendrites.

TILLER:

AND

of the dendrite

DIRECTION

OF

GROWTH

571

is more

illust,rated with Figs. 20 and 21. These are magni~cat,ion

phot,ographs

of the

t,ips of

These figures show that t,he (111) platelets

ext,end to t,he very tip of the dendrite and provide the bulk of the solid which forms the dendrites even in this region. Fig. 20 shows however, a few extremely fa.int plattelets eent,ered aboutS a (100) pole and at least one other set of still fainter platelets probably

a (311)

pole.

The

about what is

fa’ct that

under

the

FIG. 19. Decanted interfwe showing a dendrite tip on which four symmetrically-located {ill; platelet systems are operating. 60 x

Fro. 20. Dendrite tip showing the four {ll 1) plat,elet systems extending almost to t’he tip. At the tip, a series of faint concentric rings reveal the presence of a 100 platelet system. 900 x

F’IQ. 18. Upper surface ofa pure load crystal, exhibiting the platelet traces during the development of a dendrite interface (.4bove *4-A). 20 x

circumstances of dendritic growth, the (100) platelets are approximately the same intensity as the (311) plat’eiets is indicative of the minor role pIayed by the (100) platelet,s in dendritic growt.h, if tohey pIay a role at all. It should be pointed out that the (100) platelets are extremely difficult to find, in fact in the ea,rly stages of dendritic growth or growth of dendrites under small supercoolings, a (loo} platelet system is never present.

Fra. 21. Photomicrograph of dendrite tip under oil immersion reveals only four (111) platelet systems and not the (100). 1000 x.

DISCUSSION

orientation.

Prc$‘~red

zonk-reined extension

the

It has been seen that when

lead is ma,de to solidify, of a single family

it does so by the

of {Ill>

platelets.

The

particular plat,elet, system that operates appears to be the one most nearly normal to the axis of heat flow. This mode of solidfication, which has been defined here as the “basic growt,h form,” casting orientation t,o substantiate previous

leads to a, preferred

in t,he ( 11 I! dire&ion.

the hypothesis

This serves

simultaneous

operation

of

these

four

platelet

systems willbe such that for each of the platelet planes a (211) direction dendrite.

will point, t~owards the pea,k of the

From these considerahions

one may conclude

that

t,he dendrite axis, in Pb, as a reprrsent,ative of all f.c.c. metals, is the result of enclosing a certain direct,ion by t,he four symmetrically which

are

locat*ed Cl 1 I> platelet syst,ems

t’he fundamental

growth

forms.

The

that the results of the

dendrit,e axis is in the (100) direction only beca,use this

work on t’he preferred direction of growth of

is the direction bounded by four (11 l} platelet systems having a (211) axis pointing towards the peak of the

Pb and probably an impurity

all f.c.c. met’als can be attributed

to

effect,

dendrit,e.

The effect of adding impurit,ies to the melt is such as to eliminate the (11 I > preferred orientation completely

random

orientation

giving a

if the level of solute

is below that required for the formahion of “cells.” the concentration

of impurities

cause constitutional

If

present is sufficient to

supercooling,

then the mode

of

For

zone-refined

between

Pb,

the crystal

orientation. direction

a relationship

habit

does

exist

plane and the preferred

They are the (111) plane and the (111) respect#ively.

This

preferred

orientation

exists because the mode of solidifi(~ation is t~he edge-

solidi~cat.ion changes from the “basic growth form” to the “cellular grorvt,h form.” The development of

wise extension

t’he cellular int,erface is such a,s t,o give rise to a (100)

duces a~ plane (corrugated)

preferred casting orient’ation.

addition of a small amount of sohrte csn eliminate this

The

theoretical

directions

explanation

of

these

preferred

of growth has been treated by Tiller.(R)

~?~~~,l~~r ~~~w~~.qform. It has been observed t-he cell bound&es

begin to form,

well developed,

t.hat as

t,hey do so by a

13uring this reached sppear.

As the cells become more

they project

development,

farther into the liquid. a contour

of surface

is

at m-hich other platelet, syst’ems begin to The new platelet systems that become

prominent

preferred orientation.

in growth are other (11 I} platelet systems.

form is modified

families

of conjugate

(1 II> platelet

these conditions, a (100)preferred Under

conditions

finally 4, conjug& conjugate

1, then

2, 3, and

(111) platelet

systems.

The four

(111) platelet

axis pointing

each have a (211)

t#owards the pea’k of the tetrahedron

which they form. ~~~?~~r~ticgrowth born. drvclopment

systems

When

one

considers

t,he

of dendrites in pure metals, it appears to

growth

which

in pure PI),

“cellular”

growt,h form.

like

the

The tip of the dendrite

is a

is much

coInpound

growt,h form made up from four ~onju~te

plabelet systems, each growing on scparat,e tetrahedral faces of the dendrite tip. The dendrite is

1f Ill]

which have their preferred

a single platelet

from

Under

orientation develops.

of dendritic

develops

of 1, 2, 3, or 4

syst,ems.

form

than t,he same contour

wit,h only

Thr

a growth

growing in the (loo}

The cell develops

front.

to the cellular

growt,h form which ma.y be composed

It can be hypothesised that the new platelet, sy&ems form because they provide a surface of lower energy system.

solidification

With a further increase of solute

content,, the growth

change in t,he contour of the particular platelet system of which they are composed.

of a single pla~telet system which pro-

direct,ion bounded

direction

only because this is the

by the four (1111 platJelet systems axis of growth

pointing

towards the peak of the dendrite. It, seems very likely that t,he possible

platelet

systems and their order of occurrence

for a part,icular

crystal structure will be those predicted by the crystal habit theories for equilibrium growth forms. It, is also very likely t.hat, any observed

growth form of these

systems is merely a complex st’ru&urc composed of, and

occur by a similar process to t,hat already outlined for

bound

the development of corrugations. For Pb it would appear that a dendrite growing into an absolutely

growth forms observed as a result of solidification from the melt is small compared to vapor deposition, or electrolytic deposition. This is probably related to the different, kinet,ics of formation of t,he growth forms for

supercooled liquid must develop from a one platelet t.ypc substrat,e ~interfa~e) t80 the fully developed dendrite by the successive operation of t,wo, then ibree, arid finally four conjugate {Ill} platelet systems. A preferential growth direction in the (111) plane is a [211] direct,ion, so that the growth form developed by

by, the basic growth

forms.

The number

of

the different processes. It seems very likely also, that t,he preferred casting orientation of the va,rious crystal struct,ures tabulated in Table 1 will be given by column 2 if t,he metals are very pure.

ROSENBERG

AND

TILLER:

REFERENCES 1. 2. 3. 4.

G. A. L. G.

WRANCLEN Acta Chem. Stand. 9, 661 (1955). Ph.D. thesis,U. of Toronto (1956). ROSENBERG GRAF 2. Metdk. 42, 336, (1951). TAMMANN 2. Met&k. 21, 375 (1923).

DIRECTIOS

OF

GROW’TH

553

5. B. CHALMERS Tmm. Amer. Inst. Nin. (Metall). Dngrs. 200, 519 (1954). 6. W. A. TILLER acd J. W. RTITTER Crmad. J. Phys. 34, 96 (1956). 7. C.ELBA~M~~~R.CHALMERS Cnnad.J.P~/ys.33,196(1955). 8. W. A. TILLEI~ To be published.