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THE EFFECT OF VIBRATIONAL

CONVECTION

DURING

DIRECTIONAL

SOLIDIFICATION UNDER

MICROGRAVITY

0

Fedorov

1

 

V

Demcenko

2

1

Space Research Institute of NAS and SSA of Ukraine SRI NAS

U-SSAU)

2

Paton Electric Welding Institu te

of

NAS

of

Ukraine

Space materials science is one of the priorities of

different national

and

international space programs,

in particular, in the research

on

the International

Space Station. So, great interest is connected with

obtaining materials in space conditions using melt

solidification methods . However, the development of

space technologies

of

practical impor tance meet seri

ous difficulties associated with a lack of understand

ing of the hydrodynamic processes in weightlessness,

which determines the complex physical and

chemi

cal properties of crystalline materials.

Numerous studies

of

solidification in space con

ditions showed that in contrast to terrestrial condi

tions, the relative contribution

of

surface and bulk

processes significantly changes [1-3]. The physical

processes

of

heat and mass transfer in microgravity

(including the role of g-jitter)

is

far from complete

clarity, especially for important practical technology

for producing crystals from the melt. Some authors

consider that this factor

is

responsible for the diffi

culty

of

obtaining crystals with the desired structure

and properties [2]. At the same time insignificant in

fluence

of

residual heat and mass transfer processes

on the microgravity environment established in

other

research, [4].

The

idea

of

the impact on crystallizing

melt by low friquency vibration includes not only the

possibility to suppress unwanted microaccelerations

(g-jitter),

but

also to actively influence the structure

of

the crystallization front. This approach is

one

of

the most effective ways to influence the quality

of

materials produced in flight conditions. Note that

the interest in the problem

is

not limi ted to space ap

plications. Fundamentally important to ascertain the

conditions of effective use of vibration exposure as

solidification process control technology.

The

subject of this work is the effect of vibrations

on the thermal and hydrodynamic processes dur

ing crystal growth using Bridgman and floating zone

techniques, which have

the

greatest prospect of prac

tical application in space.

In

the present approach

we consider the gravitational convection, Marangoni

convection (essential with a free surface [5]), as well

as the vibrational effect

on

the melt for some special

cases. The results of simulation were compared with

some experimental

data

obtained by the authors us

ing a transparent model substance - succinonitrile

(Bridgman method),

and

silicon (floating zone

method). Substances used, process parameters and

characteristics of the experimental units correspond

the

equipment

developed for onboard research and

serve as a basis for selecting

optimum

conditions vi

bration exposure as a factor affecting the solidifica

tion pattern. The direction of imposing vibrations

coincide with the axis of the crystal, the frequency

are presented by the harmonic Jaw, and the force of

gravity was varied by changing its absolute value.

Schemes of relevant processes are shown in Fig. I.

In the first method (Fig. 1, a), molten zone

is

formed in the initial sample I) using a heater (2).

The melt (3) which

is

moving along with the heater

provides the workpiece melt ing and subsequent melt

crystallization. In the Bridgeman method (Fig. I, b),

melting and crystallization were carried out using the

unit, which consists

of

heater (5), refrigerator (8) and

the heat-insulating layer (7). The unit was moved at a

predetermined speed v along the outer surface of the

ampoule 4, in which the sample

is

placed.

athematical model

considered axisymmetric ap

proximation

of

joint convective-conductive energy

transfer in the system crystal - melt. In the Bridg

man

scheme only the heat transfer through the gas

gap (6) was taken into account. Heat transfer coef

ficient was calculated as the reciprocal

of

the thermal

resistance of

the gas gap; on the border with the insu

lator,

it

was assumed zero.

Zone

melting process was

carried out in a vacuum chamber, and surface tension

forces maintained the molten zone; electron-beam

heater as a source

of

energy was used (experimental

studies

of

heat flux distribution discussed in [61 . The

heat exchange with the environmental the end sur

faces

of

the sample was neglected. At the crystalliza

tion and melting fronts perfect contact between the

131

•

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•

c

~ . .

I

1

0 B

- > - - - -

:=:=:=:=:=:=:=:r::::::::::::::::

:-:-:-:-:-:-:-: -:-:-:-:-:-:-:-:

::::::::::::::;::::=:=:=::::::::

-   -

4

5

6

~ ~ i f ; : ~ t ~ l ~

v

t

3

9

7

3

,

-:--::_::::=:=:= £=:=:=:=:=:=:=:

I

I

10

a

R

p

b

8

Fig 1 Crystal growth using floating zone (a)

and

Bridgman (b) techniques. 1 - crys

tal,

2 -

heater,

3 -

melt,

4 - ampoule, 5 -

heater,

6 -

gaseous gap, 7 - insulator,

8 -

refrigerator,

9 -

melt

liquid and solid phases is supposed the latent heat

was neglected).

Hydrodynamic processes in the melt are described

by the

Navier-Stokes

equations in

the

Boussinesq

approximation. The vibration of surface conside red

harmonic

oscillations ( g

1

t)

A

sin

2mut),

w -

fre

quency, A

-

amplitude of vibrational acceleration);

the vibration and

background

gravity was

considered

operating along

the

axis

of

the crystal.

he

results of numerical experiments

oating

zone

method

Thermal and

hydrodynamic

processes under zone

melting studied for

the

silicon

sample R = 1 mm

and

=

100

mm) and

pulling velocity of broach

annular electron

beam heater in

the

range

of 1 -

1

µm/s.

The distribution of the

heat

flux density

on the surface of the

sample

was set in accordance

with

the

experimental data [7]

obtained

by the split

anode.

Numerical

study found that the height of

melted

zone

determined

by

the

power

of

electron

beam heating and practically

does

not depend on the

pulling velocity. This fact might

be

explained by small

values of

the

thermal Peclet number. The calculated

height of

the

melt zone

on

the lateral surface of

the

sample

is

1

mm,

which is within 5 with

the

value

measured experimentally. Fig. 2 and 3 show

the

tem

perature field and velocity pattern

of

the melt in qua-

si-stationary state for silicon single crystal grown by

floating-zone method in terrestrial

conditions

and in

reduced

gravity. Motion

of

the melt

is

formed mainly

under

the

influence of buoyancy force: on the

free

surface there

is the

ascending stream which unfolds

in radial

direction near

the

front

of

melting, forming

a toroidal vortex (shown schematically by large ar

rows), with

the

center shifted to

the

front

of

melting.

The highest flow rate

(3

cm/sec) was observed on the

free surface in the area of maximum heat flow, and at

the axial portions of the melt (because of the sample

cylindricity).

The flow of liquid silicon under reduced gravity is

governed by competitive interaction of thermo-grav

itational and thermo-capillary forces, resulting in

secondary vortex formation in the molten zone near

the

crystallization front.

At

reduced

gravity

the

speed

of

the

melt flow de

creases

by

two orders

of magnitude, the

height of the

molten zone reduced by 5 and a convex crystal

lization front formed.

We considered

two specific cases:

1

the result

ing

acceleration g t)

(superposition

of

background

acceleration

of

gravity and vibration acceleration)

in one

period

of vibration possess

the

same sign as

the background

acceleration; 2)

g(t)

changes the

sign(vibration of high intensity). It

is

reasonable to

introduce the constant

of the

hydrodynamic process

32

Z,cm

1

8

2

0

a

Rg 2

floating

Rg 4

T

streamlin

lization

7.5 mm,

g•

whic

flow

fro

cal evalL

fromg

0

introduc

value

of

vibratior

Tg, vibra1

in

hydro

suit,

the

flow is r

increase

of strear

( > IO

f

so that t

saved

air

8/8/2019 The Effect of Vibrational Convection

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Z,em

10

8

6, t==

UUU====j

4

1100

00

2

Z,em

5.3 - - - - - - - - - - = ~ - - - - -

- - - - - - - -1413 --------------

5.2

•

rr

< ~ ~ k k k ~ * ' . , . . _ . . , . _ ~ ~ •

I ;

,, Jt

, , t ' . r , r , , , _ ~ . c _ r , , C < t - i : ; < k ' ~ ~ ~ ~

4-

4 . . . _ ~

J

1

' ; ; , · ~ · J < i , ¥ M ' « ' K l f k ' < - f < / _ ~ . _ . . _ ...

••

..

,. ,. ;; £ ,..

' ...... k -- .... :

. _ .

. _ . _ ..

i ·;

t

I ;· • , " '

t

~ . :

-

,,,,. ; . . . . . . . . . . . . . . . . . . ._

~ ' f t J ~ ' ~ · , , . , · J . J t / . ' ' ' L

9

  '._

f

't

t

I

f

./

i

I

t

1 1 { 1 • •

..

• • •

r t ., 1 J f •

,.,

• •

~ · ~ 1' \

t I

t

<

I • '

f A

I l ~ i ~ ~ ~ · ~ · , , · ~ , , ~ · ·

5 . 0 i ~ ~ ~ · ~ · 1 · ' \ .. , ~ ,

.......

..,,.. ,.

\ ~ ~ · 1 , - 4 1 4 , ' : . t ,

. . . . . - ~ ' ~ ' ~

.... .

• "' - ~ . . . '::..-.,,,.

...... .... .

..,.. ....

-+

....

-+

,,.

"

... ~ ~ ~ ~ ~ ~ - - ~ · · - ·

.. ·

..

- : : i . . - : a ' - : i a ' - ; l o . ~ ~ ~ - - ? ~ . . . , . _ , . ~ _ , , . _ , , . , . . _,. ,

4.9

. . . . . . .

4.

8

1413------------------------

0

0.5 0.0 0.1 0.2 0.3 0.4 r,

err

a b

Ftg 2. The temperature

field (a)

and

flow of the melt (b) in

floating-zone method for single crystal grown in terrestrial

conditions

Z,em

~ ~ 5.3 - - - - - - - - - - - - ~ - -

---- -

.

·-,,.. ... --.. .

1413 - - ~ ••••

~ •• •

:

I . : : : : · ) ? ( = ~ : : : · · •

... ~ ~ :

..

· . · . : ~

5.2- , , , , , , , • , , • , , • , • • ' • • • •' ' ' :

I

: : : : : : . :

....

: : . : : . ; , < A ~ . : :

f I

t j

I 1 I I

j

I ' I I ' ' ' ' , I

#

f • \ f • f •

j

f • • •

f ' • '

j

~ r ; ; i _ . u u = - - - - - ; = ; J : . J . l l f \ 1 , ~ . • • 1 •

1

• • · · · · iSoO ' . , .

:

:( ':

.:

·,,::::

'.:.:.:::

.

:

..

"

' I '

-

I ' . 0 ~ : :

1: ~ : : : : : : : : : : : : :

~ : : : : : : : ~ : : :

..

'

' . . . . . . ' . ' . . . . . . . .

' • ' I ' ' I ' ' ' • •

..,

.. •

I • • ' ,

' . .

..

' . .

._. . . . . .

4.91. : ' . : : :

. . .

: . .

:-;

: ·. .

- - 1413 - -

~

~ ~ ~

4.8

·····.

0 0.5 0.0 0.1

0.2 0.3 0.4

r,

err

a

b

Ftg

3.

Thermal state of the sample (a) and melt flow pa ttern

(b) for growing a silicon crystal

under

low gravity

l JJJJJll J \

J

l

J

1 1

J

1 1

l

I

\

l i j l l l

~ / \

l.

\ . \ J \ \ ~ ~

\

J

\

. ..

..

~ -. . -.,.

'-,.. . . ~ _ . r l

· .....   ' - . . - . . . . . . . - . . . . . . . - - - ~ ~ r

- .

. .

-- --   ·

--.---....

........

Ftg 4 The velocity field (a) and

streamlines (b)

near

the crystal

lization front (ampoule radius of

7.5

mm,

Bridgeman

method,

suc-

cinonitrile)

---- --

-

..

-

-

--

 

..

--

a

'g'

which

mean the time

required for adjustment

of

flow from one steady state to another. For numeri

cal evaluation of the value ofTg the acceleration pulse

from g

0

= I · I 0-

3

cm/c

2

up to g

0

= 5 · I

o-

3

cm/c

2

was

introduced. Calculations for floating zone give the

value of the constant about

one

second. In the case of

vibration with the period of one cycle comparable to

g

vibration disturbances lead

to

a significant change

in hydrodynamic flow in the molten zone. As the re

sult, the direction

of

melt circulation of the vortex

flow is reversed during

one

period of vibration.

The

increase in amplitude does not change the structure

of streams. In contrast, at high frequency vibration

( >

I 0

Hz) bipolar vibration acceleration averaged,

so that the structure and intensity

of

convective flows

saved almost the same as in the absence of vibration.

,•

'

<

'

,.)

··-

--

• >

·..________.,,,, ..-;

b

Bridgman Technique

Bridgman

method scheme

(Fig. I, b) corre

sponds

to the

laboratory

ground

installation, which

is

under

development for flight experiment. Gravi

tational convection in the melt is due

to

the radial

temperature gradient [8]. The attention was primar

ily paid

to the

melt streams

near the

crystallization

front because they

determine

morphological stability.

For

precise description

of

flow pattern of the liquid

phase,

we

extracted the certain melt fragment near

crystallization front (Fig.

I). Under

buoyancy forces

in the liquid phase, global vortex is formed;

near

the

wall of heater the

melt rises

to

the top

of

the

ampoule

and in the axial part of the ampoule formed descend

ing flow directed

to

the crystallization front (Fig. 4,

133

•

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•

g (t)

jHmmnnmnn I

0

5s

10 s

15 s

20 s

Fig. 5. Temperature fields in the melt under intense vibration

succinonitrile (t

=

0

corresponds to the

steady state after 6000

s exposure without vibration)

a).

As

the result of flow braking near the front weak

intensive unsteady vortices appeared. (Fig. 4, b).

Identified in simulation processes

unsteady

sec

ondary vortices mentioned above were directly ob

served in the

experimental

Bridgman

setup

[6] To do

this, markers

Lycopodium

spores) inserted

to

melt

succinonitrile, whose motion was fixed and recor

dered. Observed

thus

markers can be divided into two

groups. In

the

first,

the

trajectories

of

particle

motion

consistent with the

circulation

of he

melt

in the glob

al vortex. The second group

of markers

that localized

near crystallization

front

oscillates, that may

indicate

the

existence

of

secondary

vortices

predicted

by

nu

merical simulation. Simplified

experimental scheme

does

not

allow

to

get quantitative

data on

flow rates,

but the nature of the

particle motion

in

front qualita

tively

indicates

unsteady nature of

the

melt near the

front

and

the

existence

of several circulation

circuits

near the crystallization front.

Consider

the

effects of vibration

on

the hydrody

namics of the

melt in

the

Bridgman scheme

at ter

restrial conditions A< go In

the

presence of

vibration

the melt

flow

localized

near the wall

of

the ampoule

and flow rate in the axial zone significantly weak

ened.

With

this circumstance

apparently connected

disappearance

of

oscillating

secondary vortices

near

the

crystallization front, which arise in the

absence

of vibration.

This

effect is observed in the frequency

range cu= 10-50 Hz.

The other

situation

occurs

when the low-frequen

cy vibration oflarge amplitude accelerations A >

g

0

).

Under

these conditions Rayleigh-Taylor instability of

melt

flow appears,

which

is a consequence of alter

nating of

total

acceleration.

As

illustration the

results

of numerical calcula

tions Fig. 5 shows the temperature fields almost cor

respond to the lines of current) under the following

conditions of vibration g t) = Asign 2rrwt), A

=

9.8

m/s

2

,

= 0.05.

The

results of

calculations show

that the sensitiv

ity of hydrodynamic processes

to

vibration are es

sentially different for the two characteristic bands:

1) the total acceleration g t) is of constant sign A <

<g

0

);

2) g t)

changes

sign for

one

period of vibration

A> go).

In

the

first range of

amplitudes

numerical experi

ment

demonstrates the

effect

of

suppressing

the

un

steady vortices for

both

methods

of

crystal growth. In

Bridgman installation in the absence of vibration un

steady

secondary

vortices arises

near

the crystalliza

tion

front. Qualitatively,

the same

result is discussed

in [9]

to

the same experimental conditions and

us

ing

the

same system

succinonitrile

-acetone. The

authors obtained a local vortex

rotating

in the direc

tion counter

to

the direction

of rotation

of

the

global

vortex. Imposition

of torsion vibrations

led to the

partition

of the vortex into two

to equalize

the

con

centration in homogeneity along the crystallization

front. In our case, the

imposition

of axial vibrations

of small amplitude contributed to the disappearance

of secondary vortices in the scheme of Bridgman. A

similar

effect is found in the numerical experiment

for the floating zone

method

when

under

vibration

exposure additional vortex near the crystallization

melting) front suppressed, Fig. 4. This effect

is

ob

served in both

schemes experiment

despite the differ

ent relative

positioning

of the axis of symmetry and

the global flow

direction of

vibration.

In the second case, when the vibration amplitude

exceeds

the

amplitude

of the background

effects of

acceleration

A

> g

0

) ,

the pattern changes signifi

cantly. Differences in the melt flow

pattern

for the

techniques under consideration both in the presence

of vibration impact

and without

them) are associated

with different thermal conditions in the liquid phase.

In the scheme of Bridgman the

melt

temperature

increases

monotonically

along

the axial coordinate

from the crystallization temperature

to the

tempera

ture

of the

heater, keeping unchanged

the

sign of the

temperature gradient. In

the

floating

zone

method,

the

thermal

center

of the melt

is

symmetric with

respect

to melting and

solidification fronts. Conse-

134

quen

occu

insta

tion

mine

u

melt

ity

a

to c

Thus

isles

T

demc

press

Th es

distri

st rue

distri

is

a

ture

rial

keep

three

the a

subst

I

tiona

trolli1

of

gn

along

veale

man

tic

ba

2

ofsm

it was

flows

ofob

3

and

bility

meth

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quently, when A >

g

0

 

and

low

frequency

vibration

occurs in the Bridgman scheme the

Rayleigh-Taylor

instability

of melt

flow

appeared,

and

the configura

tion and the dynamics of the global vortex

is

deter

mined

by

vibration

exposure.

Under the same conditions, the

circulation

of the

melt in the

floating

zone

method

of preserving stabil

ity

and the impact

of

vibration

perturbations

limited

to changes

the

direction

of

rotation

of the vortex.

Thus,

in this range of vibration

floating

zone method

is

less sensitive to vibration perturbations.

The

experimental

techniques

under discussion

demonstrated the applicability of vibration to sup

press

irregular

flow near the crystallization

front.

These kinds of flows affect not only the

macroscopic

distribution of impurities, and microsegregation

structure as well. It

is

known

that the intentional

distribution of

impurities

before

crystallization

front

is

a powerful way to control the

structure

and struc

ture-

sensitive

properties

of

the

crystalline

mate

rial [1

O] Subsequent

steps in this

direction

suggest

keeping variability direction of microgravity vector,

three-dimensional

modeling

and

comparison, with

the actual pattern on the solidification of transparent

substances.

Conclusions

1

Vibration

influence on the melt during direc

tional

solidification

can

be an

effective

means ofcon

trolling

the solidification structure at different

levels

of

gravitational conve ction. f vibration is imposed

along

the

axis

of

growing, numerical simulation re

vealed

significant

features of the melt flow for

Bridg

man and

floating

zone techniques in two

characteris

tic bands of

vibration action.

2 Upon application of low-frequency oscillations

of

small

amplitude

A <g

0

)

along the

axis of

growing

it was

found the suppression of the

secondary

vortex

flows

near the crystallization front

in

both methods

of

obtaining

crystals.

3.

When alternating vibration exposure A > g

0

)

and low

frequency vibration Rayleigh-Taylor insta

bility in

melt

flow is occurred when

using Bridgman

method.

35

4. The same conditions

in the floating

zone method

are characterized by steady melt

flow

and the

effects

of vibration

are

reduced

only

to

change

the direction

of melt

flow.

Low

sensitivity

to the

Rayleigh-Taylor

instability

is due to

the

symmetry

of

the

temperature

field

of the melt along the

axial

coordinate.

REFERENCES

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in weightless

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p. (in Russian).

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microgravity

on the homogeneity

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methods.

Results

and

perspectives of research in IM

ET

RAS Surface. X-rays,

synchrotrons and neutron re

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Paton B.E., Asnis E.A., Zabo/otin S.P. et al. Processing

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14-16.

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Fedyushkin A., Bourago N., Po/ezhaev

V.

Lharikov

E. The

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on hydrodynamics and heat-mass

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crystal

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Journal

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Crystal

Growth. - 2005. - Y 275. - P 1557-1563.

6

Ovsiyenko D.E., Fedorov O.P., Temkin D.E., Chemerinsky

G.P. Interaction

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particles

with crystals growing

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(in Russian).

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E. V.

Avetisov l.H., Skorenko

A. V

et al.

Prepara

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space

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by direction

al solidification

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impact

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the

Russian

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