Response of MnBi-Bi Eutectic to Freezing Rate Changes
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RESPONSE OF MnBi-Bi EUTECTIC TO FREEZING RATE CHANGES
M. NAIR*, T-W. FU, W. R. WILCOX, K. DODDI AND P. S. RAVISHANKAR** Department of Chemical Engineering, Clarkson College of Technology, York 13676, USA
Potsdam, New
and D. LARSON Grumman Aerospace Corporation,
Bethpage,
New York 11714,
USA
ABSTRACT Previously we reported on a theoretical treatment of the influence on freezing rate of sudden changes in translation rate in the Bridgman-Stockbarger technique (11. This has now been extended to consideration of a linear ramped translation rate and an oscillatory freezing rate. Oscillations above a few hertz are found to be highly damped in small diameter apparatus. An experimental test was made of the theoretical predictions for a sudden change of translation rate. MnBi-Bi eutectic was solidified with current induced interface demarcation. The experimental results correspond reasonably well with theory if the silica ampoule wall is assumed either (1) to contribute only a resistance to heat exchange of sample with the furnace wall, or (2) to transmit heat effectively in the axial direction by radiation. In an attempt to explain the fact that a finer microstructure is obtained in space, MnBi-Bi microstructure is being determined when the freezing rate is rapidly increased or decreased. Preliminary results indicate that fiber branching does not occur as readily as does fiber termination.
INTRODUCTION Previously we determined that the solidification velocity V vs. time t behavior caused by a sudden change in translation velocity from V 1 to V2 is given by V-s 62-6 -tV2-VI =e , where B = -2 (1) V2 -V1 2-61 ' 62-11 6 is the interface position relative to the apparatus of translation, and subscripts 1 and 2 denote initial values [1]. We found that B is insensitive to V 1 and cooler temperature settings for a constant difference Present address: EPA, State Government of Delaware, Present address: Exxon R&D, Linden, New Jersey.
**
measured in the direction and final steady state V2 , and to heater and between the two. A Dover,
Delaware 19901
534
1.1
1
1
1
•-. 0 1 0.9-/ w C" 07 0.75
0
: 0.6 -
LIJ
o.
r=oi
I 0
0.
0
0.2-
Te=2
-
i
m min
•
0
0
2
4
8 6 Time (min.)
10
Figure 1. Freezing velocity acceleration for translation velocity increased linearly for 5 minutes; for different values of relaxation time T = I/B.
535 correlation for B (and hence for 62 - 6 1) was derived: k£ Bk.5 B 3.55C
where k p
its
is
9
Hkm exp (-(1.12 PP yb
7k + vWi
0.0771 + 1.69IHm + 0.0181W )J b
the thermal conductivity of the liquid, C
density,
number, hh is
R the radius of the sample,
Hkm = Vhhh
is
its
heat capacity,
R/k£ is
the heat transfer coefficient in the heater, hc is
cooler, Wb = AHf/Cpk(Th-Tc)
is
the Weber number, AHf is
(2)
a log mean Biot that in
the
the latent heat of fu-
sion, Th the temperature of the heater, Tc that of the cooler, I = b/R, and 2b is
the width of the insulation.
THEORY FOR SINUSOIDAL AND LINEAR RAMP TRANSLATIONS In control theory, an exponential response to
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