凝固枝晶文檔

Formation

Of

DendritesWhen

regual

cells,such

as

those

of

Figs.3-2

and

3-9,

formand

grow

at

relativelylowrates,they

grow

perpendicular

toThe

liquid-solid

interface

regardless

of

crystal

orientation.When,however,growth

rate

is

increased,crystallographiceffects

bagin

to

exert

an

influence

and

the

cell-growthdirection

deviates

toward

the

preferred

crystallographicgrowth

direction

(for

example,<100>

for

cubicmetals).sim-ultaneously,

the

cross

section

of

the

cell

generally

beginsto

deviate

from

its

previously

circular

geometry

owing

toeffects

of

crystallography.This

structure

has

been

describ-ed

variously

as

a

flanged

structure,or

maltesscross,in

cu-bic

materials;it

is

shown

In

Fig.

3-17.As

growth

rate

increasestill

further,

the

cros

strycture

first

becomes

more

apparentand

then

serrations

begin

to

appear

in

the

flanges

of

the

crossthat

is,secondary

dendrite

arms

become

discernible.32-35The

point

at

which

the

cellular

structure

in

Fig.3-17a

becomes

dendritic

is

a

matter

of

terminology,employed

in

the

liteature

is

not

consistent

.Some

writers

prefer

to

think

of

the

stcture

as

dendritic

when

it

is

growing

in

or

near

its

crystallogphic

orientation,as

in

Fig.3-17b.Others

prefer

to

describe

itdendritic

only

when

secondary

branches

can

be

discerned,

as

in

Fig.3-17d.The

latter

terminology

is

employed

in

this

text.Figure

3-18,which

depicts

a

transparent

organic

liquid,shows

one

example

of

solidification

where

secondary

arms

arejust

discernible.Closely

comparablestructureshave

describefor

a

large

number

of

metal

alloys,including

Pb-Sb

alloys

(Morris

and

Winegard,34)

and

aluminum

alloys(Biloni

et

al.36).

Figur3-19

shows

a

rangeof

structures

in

Fe-10%

Ni

alloy

from

cellu-lar

to

dendritic.

These

structures

were

obtained

in

a

unidireconally

solidified

ingot,

and

so

rate

of

heat

removed

decreasedwith

the

squareof

the

distance

from

the

chill,

the

strycture

icellular

although

the

shape

of

the

cross

section

of

the

cells

iseen

to

be

influenced

by

crystallographic

effects.

At

greaterstances

from

the

chill,

the

cross

section

becomes

flanged

andsecondarydendrite

arms

become

visible.another

point

on

the

terminology

of

dendritic

structures

wibecome

more

important

in

later

chapters

when

we

describemore

important

in

later

chapters

when

we

describe

more

co-mplex

dendritic

structures:the

differerce

between

a

dendriteand

a

dendrite

arm.the

central

portion

of

the

structure

in

Fig.-17d

which

isgrowingin

approximately

the

heat-flow

directionis

termed

a

primary

dendrite

arm;

the

rodlike

protrusions

per-pendicular

to

the

primary

dendrite

arm

are

secondary

den-drite

arms.In

Fig.3-18

and

the

upper

part

of

Fig.3-19,many

such

primary

and

secondary

dendrite

arm

are

seen.All

the

pr-imary

dendrite

arms

in

these

two

figures

have

grown

from

thesame

nucleus

and

have

nearly

the

same

crystallographic

ori-entation.They

are

thus

a

part

of

the

sane

grain,

or,in

the

ter-minology

of

this

text,

the

same

dendrite.Cellular-dendritic

TransitionQuantiative

description

of

effects

of

solidificationvariablethe

cell-dendrite

transition

is

one

that

has

eluded

investigatin

spite

of

many

studies

conducted

over

the

last

15

years.12

16

3237

Qualitatively,

secondary

arms

form

because

the

approxima-tely

paraboloidal

interface

of

the

cell

tip

becomes

unstable

Thdriving

force

for

the

instability

is

constitutional

supercoolithe

liquid

just

back

from

the

cell

(dendrite)

tips.One

would

thefore

expect

that

this

instability

should

depend

approximatelyon

the

same

variables

that

enter

into

the

constitutional

supercooling

theory

for

breakdown

of

a

plane

interface.

Experimenta-lists

who

have

studied

the

problem

have

plotted

their

date

invarious

ways,generally

as

a

function

of

G/R1/2,

where

G

is

thethermal

gradient

in

the

vicinity

of

the

cell

tips;

Fig.3-20

isexample

from

the

work

of

Plaskett

and

Winegard,32

As

Davies38

has

pointed