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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
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Z,em
10
8
6, t==
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1100
00
2
Z,em
5.3 - - - - - - - - - - = ~ - - - - -
- - - - - - - -1413 --------------
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rr
< ~ ~ k k k ~ * ' . , . . _ . . , . _ ~ ~ •
I ;
,, Jt
, , t ' . r , r , , , _ ~ . c _ r , , C < t - i : ; < k ' ~ ~ ~ ~
4-
4 . . . _ ~
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1
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••
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9
'._
f
't
t
I
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./
i
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..
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,.,
• •
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t I
t
<
I • '
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.......
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.... .
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-+
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-+
,,.
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... ~ ~ ~ ~ ~ ~ - - ~ · · - ·
.. ·
..
- : : 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
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I ' I I ' ' ' ' , I
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f • \ f • f •
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f • • •
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j
~ r ; ; i _ . u u = - - - - - ; = ; J : . J . l l f \ 1 , ~ . • • 1 •
1
• • · · · · iSoO ' . , .
:
:( ':
.:
·,,::::
'.:.:.:::
.
:
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I ' . 0 ~ : :
1: ~ : : : : : : : : : : : : :
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'
' . . . . . . ' . ' . . . . . . . .
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4.91. : ' . : : :
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: . .
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: ·. .
- - 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.
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phase formation
in weightless
ness. -
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1979 - 256
p. (in Russian).
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microgravity
on the homogeneity
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Results
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ET
RAS Surface. X-rays,
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