The free growth of dendrites in a uniformly supercooled solution was examined using cine photography with a Schlieren optical system. Crystals were grown in the bulk of the solution from a centrally located capillary tube, nucleated at the interface with a liquid nitrogen cooled wire. Crystals propagated along the tube, the slower growing orientations eliminated, and emerged at the tip, usually growing parallel to the tube direction. For both sodium sulfate decahydrate from its solution and ice from sodium chloride solution, growth rate and fineness of dendrites increased with supercooling. In sodium sulfate, upward convection of the less dense depleted solution occurs; downward convection was observed for the rejected, more concentrated sodium chloride solution. In both cases, there was a spatial and temporal delay in the release of the convective plume from the moving dendrite tip. The role of this convection on the growth characteristics and the production of secondary crystals is examined. A proposed low-g experiment to examine differences in growth rate, crystal texture, and secondary nucleation in a reduced convective regime where molecular diffusion is the dominant transfer process is discussed

Hallett, J.

Wedum, E.

English

NASA Technical Reports Server

'32077
76
INFLUENCE OF CONVECTION ON FREE GROWTH OF DENDRITE CRYSTALS FROM SOLUTION
0. Hallett and E.
The free growth of dendrites in a uniformly supercooled solution has
been examined using cine photography with a Schlieren optical system. Crystals
were grown in the bulk of the solution from a centrally located capillary tube,
nucleated at the interface with a liquid nitrogen cooled wire. Crystals pro-
pagated along the tube, the slower growing orientations eliminated, and emerged,
at the tip, usually growing parallel to the tube direction. For both sodium
sulfate decahydrate from its solution and ice from sodium chloride solution,
growth rate and fineness of dendrites increased with supercooling. In sodium
sulfate, upward convection of the less dense depleted solution occurs; downward
convection was observed for the rejected, more concentrated sodium chloride
solution. In both cases, there was a spatial and temporal delay in the re-
lease of the convective plume from the moving dendrite tip. The role of this
convection on the growth Characteristics and the production of secondary crystals
is examined. A proposed low-g experiment will examine differences in growth
rate, crystal texture and secondary nucleation in a reduced convective regime
where molecular diffusion is the dominant transfer process.
Atmospheric Sciences Center, Desert Research Institute, Reno, Nevada 89507
211
https://ntrs.nasa.gov/search.jsp?R=19820024201 2020-03-21T06:22:03+00:00Z
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INFLUENCE OF CONVECTION ON FREE GROWTH OF DENDRITE CRYSTALS FROM SOLUTION
by
J. Hallett and E. Wedum^
INTRODUCTION
The growth morphology of a crystal is known to depend in a complex
way on the environmental conditions: supersaturation or supercooling, physical
properties of the fluid, Prandtl and Sherwood number, and the bulk fluid flow
around the crystal. These parameters influence the growth of the crystal
through heat and mass transport processes, and, most important from the view-
point of growth rate and crystal habit, through the kinetic processes taking
place at the crystal interface. Plane faces appear when layer growth takes
place in Tow index direction in regions of modest supersaturation, with layers
originating either from defects or on crystal edges protruding further into the
diffusion field and- subje *. to surface nucleation. Skeletal crystals form
when these layers fail to reach the crystal center before nucleation of further
layers,
Experimental studies aimed at investigating the nature of these de-
pendencies and the molecular detail of the growth mechanism necessarily aim
for an idealization experiment to reduce the number of physical variables.
For very small growth rates, an isothermal experiment is a practical idealiza-
tion; rapid stirring prevents local density differentials. For more rapid
growth rates, an adiabatic idealization is practical, with crystals growing
freely into an infinite, constant condition environment. This latter case is
relevant to more extreme growth conditions with large driving force:for growth,
In all cases, it is necessary to avoid the presence of extraneous surfaces
which give, spurious heat transfer or nucleation.
Atmospheric Sciences Center, Desert Research Institute, Reno, Nevada 89507
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A second feature of crystal growth, especially in the case of these
higher driving forces, is the occurrence of secondary crystallization - that
is, of the formation of crystals of orientations other than that of an initial
single crystal, a phenomenon which gives a differing crystal texture and im-
purity distribution following complete solidification.
In assessing the role of these different parameters, there are several
aspects of the crystal growth to be considered. The habit, the ratio of growth
velocity in different low index planes, the absolute growth rate in these di-
rections, the tendency to skeletal growth, and the occurrence of secondary
crystals are all important both from the viewpoint of understanding the growth
mechanism and from the viewpoint of crystal growth technology.
From the viewpoint of the utility of a low-g environment, there are
two aspects of growth selected for study here which are very difficult to
investigate in 1-g situations. With dendrites in free growth, the growth rate
and dendrite dimension are determined by thejambient supercooling. In 1-g
and in an unstirred environment, the release! of latent heat and/or depletion
of the nearby solution lead to density differences which give rise to local
i " • . '
convection. The question arises as to the importance of this self-induced con-
vection on the growth of the dendrite; first^ is there an enhancement of dendrite
i - '' ' ~ .
growth because of the motion (it is known that externally imposed motion en-
hances growth rate), and second is this motibn responsible for any secondary
i
crystal nucleation. These questions are relevent for growth in an environment
I • •
initially at rest with respect to the growing crystal, and not set in motion
i . •
on the scale of the containing tank. The following experiments were designed
to investigate the physical processes occurring in 1-g growth and serve as a .
basis for assessing the presence of self-induced natural convection by direct
' • • . ' . . • r . '
comparison with an identical experiment in Ibw-g.
' • • ' ! - ' ' " . . . . • • . . • '
213 ! • ' ' ".-••: '
ORIGINAL PAGEJS
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From the viewpoint of ease of study, the crystallization of sodium
sulfate decahydrate from supersaturated solution was chosen. A liter of near
saturated solution can readily be supercooled as much as IOC; it is transparent
and ideal for optical studies in a convenient range of temperatures, the
saturated solution crystallizing at 32.5C. Studies were also carried out of
ice cryatallizing in sea water (approximately 0.4 M Nad). The solution was
contained in a tank with plate glass viewing windows, dimensions 7 in x 7 in
high x 1.5 in thick. It was thermostated to j^0.2C with a similar vertical
and horizontal uniformity. An L-shaped Teflon capillary tube was located at
the side of the tank (Fig. 1). This arrangement allowed crystallization to be
initiated in the bulk of the liquid. A liquid nitrogen-cooled wire was in-
serted into the capillary; nucleation occurred at the cold spot and crystals
grew inside the Teflon tube. The slower growing directions were eliminated,
and a fast growth dendrite would usually emerge from the open end to grow
horizontally into the liqi'd. The whole system was inserted into a Schlieren
optical system, with the results recorded on still or movie film (Fig. 2).
This technique is similar to that employed for the studies of sodium chlorate
crystals by Chen et al. (1). Sodium sulfate solution crystallizing to deca-
hydrate gave upward convection of diluted solution; sodium chloride solution
crystallizing to ice and rejecting the solute gave a denser solution with down-
ward convection (Fig. 3a,b). In both cases, crystallization velocity increased
with supercooling. At large supercooling (> IOC for ^ SO* and > 5C for ice)
with velocities * cm s , the crystal growth kept ahead of any convection and
no effects were visible. Very low growth velocities (R < 0.01 cm/sec) at
AT < 3C for Na2S04 and AT < 0,25C for ice, were complicated by thermal inter-
actions with the walls of the tank. This gives a range of supercooling of about
8 C for Na?SO. and 4 C for ice over which data could be obtained where differences
214
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Figure 3 Crystallization of NaaSO^lOHaO from solution and ice in sea-water.
Both pictures were taken with Tr-X film utilizing the tank and
'Schlieren system shown in Figs, 1 and 2. The plume from growing
NazSfVlOHpO dendrites (3a) convects upward at 'vO.E cm s"' (2.7 M,
AT = 5,5 C], The plume from the ice dendrites (3b) convects down-
ward at *vfl,01 cm s"l (AT = 0.5 C), Scale divisions on the right are
1 cm.
217
ORIGINAL PAGE
BLACK AND WHITE PHOTOGRAPH
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are expected because of natural convection. Within this range, it was neces-
sary to examine the growth only during the period that the convection had not
set up a general circulation in the tank - some 2 to 30 s.
RESULTS
For dendrites of both sodium sulfate decahydrate and ice, a convective
plume was evident coming from just behind the advancing tip. A starting plume
began as growing crystals emerged from the capillary, with velocity ~0.2 cm s"
for sodium sulfate and 0.01 cm s" for ice in sea-water (Fig. 4). As this
moved away from the tip, the Na2$04 plume retained shape similarity with re-
spect to the tip and became approximately parabolic, as can be seen from Fig. 3
for both ice and sodium sulfate. There is a spatial delay in the visible plume
detaching from the dendrite, which increases with the crystal growth velocity
(Fig, 5). To a first approximation, the time for detachment is independent of
the growth velocity and is 10 s for sodium sulfate and 20 s for ice. There is
an asymmetry in the growth velocity of dendrites with direction which is a com-
plicated function of both crystal habit and convection velocity. In Na^SO.
solution (Fig 3a), dendrites will grow more slowly into the disturbed solution
with the fastest growing crystal being horizontal, while the ice crystal is
distinctly inhibited in the convecting region (3b). Growth of dendrites into
undisturbed fluid is aided by convection as can be clearly seen in these figures.
For sodium sulfate, secondary nuclea.tion of crystals occurs for super-r
coolings between 3 and 6C. These small crystals rise with the buoyant fluid,
grow, and produce yet more crystals as they fall out. For ice, larger crystals
occasionally break away at supercooling >1 C to give other orientations. Ice.
being less dense than the solution, rises - decahydrate being more dense finally
sinks relative to the fluid motion. In each case, the crystals move into fresh
218
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219
GR2GSSAL ***
OF POOR Qb&
Figure 5. Spatial delay in the separation of the plume from the crystal in-
creases with Increased velocity, a and b are 3.0 M NaSCL
dendrites with V = 0.02 cm/sec, spatial delay = 0.16 cm and V =
0,2 cm/sec, delay = 1.7 cm. c and d are 28% salinity sea water
dendrites with V = 0.008 cm/sec, delay = 0.16 cm and V = 0.025 cm/
sec, delay = 0.5 cm.
220
environmental fluid. As supercooling is increased, the morphology of the
dendrites change, the branches becoming finer and apparently more fragile.
DISCUSSION
Cbnvective flow is sufficiently slow that the regime is laminar for all
situations examined, with Re < 20. The convective velocity is consistent with
the expected density differences. It increases as Apn (n £ 1 to a first approx-
imation). The growth velocity of the dendrites on the other hand increases as
Apm (m 2-3 to a first approximation) so that beyond a critical excess the growth
is sufficiently rapid to mitigate any effect of 1-g convection. An estimate of
Grashoff number (Gr) is difficult, since the dimension to be taken as relevant
for convection is not obvious, and the physical properties of the fluids, under
the experimental conditions are not known very precisely; a crude estimateJs
in the range 500 to 5000. A reduction of gravity by 10 would reduce Gr in
proportion, with a corresponding overall reduction in mass heat transfer and
velocity.
The role of increasing fineness of dendrites with supercooling is to be
i • ' . •'
assessed in terms of their likelihood of breaking in the local flow or self-
induced buoyancy (O'Hara and Tiller) (2). One might expect their strength to
increase as d (d = diameter) with both buoyancy forces and drag force increasing
2 ' • ' ' • ' •
approximately d , so finer dendrites; would be more likely to fracture. On the
other hand, finer dendrites might be expected to contain fewer defects; there
is probably an optimum size for maximum fracture probability.
The lag of convection in detaching from a growing dendrite is to be
interpreted in terms of a sufficient dimension being required to enable the
buoyant fluid to separate - to be interpreted analytically in terms of a criti-
cal Rayleigh number. The possibility exists that there is a convective plume
ahead_of_the visible pljjme_whi^h_c^nnot be detected by the Schlj.eren technique.^
221
This is limited by the optical path difference caused by the width of the
convective plume (^ mm), and the refractive index differential (^ 10" ).
- 2 - 1This gives an order of magnitude refractive index gradient of 10 cm
overall; the detail of the local gradient is somewhat masked by the nature
of the path length integration accomplished by the Schlieren system.
CONCLUSION
The optical technique used in this experiment gives immediate quali -
tative information on the nature of the induced fluid flow around free growing
dendrites. In the two systems investigated, new crystal orientations appear.
In sodium sulfate this occurs only beyond a critical supercooling, and can be
hypothesized as being associated with local shear resulting from natural con-
vection. In the case of ice, new orientations apparently result from buoyant
displacement of the larger crystals, A better understanding of these physical
mechanisms will come from ~*u-Jies over a wider range of environmental conditions
than has been attempted so far. In particular, a Tow-g experiment in which
convective velocities are substantially reduced should yield a comparison situa-
tion in which no secondary crystals are produced and where growth velocities
are uninfluenced by the fluid flow; in this case the optical system should
yield detail of the molecular diffusion properties in a stationary environment
around the growing dendrite. A candidate material for a study is sodium ace-
tate - a trihydrate with a convenient melting temperature of 58 C.
The comparison study will give a better understanding of the mechanism
of dendrite growth and its application in higher velocity crystallization,
situations which often occur in metals (3) and solutions.
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ACKNOWLEDGEMENT
This work was supported in part by NSF Grant #AER75-19601, RANN and
NSF Grant #ATM77-07995, Atmospheric Sciences Section of the National Science
Foundation, Washington, DC.
223
REFERENCES
1. P. S. Chen, P. J. Shlichta, W. R. Wilcox and R. A. Lefever, to appear
in J. Crystal Growth, (1979).
2. S. O'Hara and W. A. Tiller, Trans. Metal!. Soc. A. S. M. E., 239, 497-
501, (1967). "^
3. P. G. Grodzka and C. S. Griner, AIAA 15th Aerospace Sciences Meeting,
Los Angeles, CA, January 24-26, 1977.
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224


Influence of convection on free growth of dendrite crystals from solution

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