Effect of Density Change on Rapid Liquid-Solid Interface Kinetics and Heat Flow
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EFFECT OF DENSITY CHANGE ON RAPID LIQUID-SOLID INTERFACE KINETICS AND HEAT FLOW Peter M. Richards Sandia National Laboratories, Albuquerque,
NM 87185-5800
ABSTRACT Consequences of the need to transport density to or from a fast-moving There can be a severe limitation of liquid-solid interface are examined. the freezing velocity and a change in the amount of heat which must be effect produces a net latent heat which can be conducted. The latter significantly different from the equilibrium value and even change sign. INTRODUCTION and melting experiments [1,2] on the rapid Pulsed laser resolidification of silicon have shown a strong asymmetry in the interface That is, for a given speeds for heterogeneous freezing and melting. IT - T I IvI is much greater for melting T > TM than for freezing T < TM Here T is the absolute temperature, T is the equilibrium (see Alg. 1). melting temperature, and v is the interface velocity, defined with the usual The algebraic convention that v > 0 is for freezing and v < 0 for melting. This cannot be explained asymmetry is strong for IT - TMI/TM less than 5%. state theory (TST) [3], which predicts a by conventional transition symmetric v near TM, as shown in Fig. 1. of TST has prompted much discussion. The apparent failure Reexamination of TST in terms of entropy limited growth [4] and a modified version [5] of TST have shown that large asymmetry can occur for large undercooling and overheating, but the theories remain symmetric for T near TM. The question can also be raised as to whether the assumption of quasiequilibrium on which TST is based remains valid for the high interface The viewpoint taken here and elsewhere [6] (referred velocities reported. to as PR) is that quasi-equilibrium and thus the fundamentals of TST remain valid, but an important ingredient, the density difference between liquid Inclusion of the density effect can produce and solid, must be considered.
a major asymmetry as seen in Fig. 1. It is well known that latent heat LH can limit the interface velocity. v cannot exceed the speed at which LH liberated on freezing is conducted Otherwise, heat would build up at the interface away from the interface. In a similar way, when a substance, such as silicon, and prevent freezing. whose liquid is denser than the solid freezes, there is "left-over" mass If it cannot be which must be transported away from the interface (Fig. 2). transported faster than v, there is a large density pile-up against which
20
T
O
Fig.
-20
1.
Interface
velocity in
silicon.
Solid curve is theory from Ref. 6,
_
dashed curve conventional Both transition state theory. curves have parameters chosen to
> -40
make maximum melting speed be 1600
1800
ITE:MI i)
Mat. Res. Soc. Symrp. Proc. Vol. 100. t1988 Materials Research Society
speed of sound and v = 15 m/s at (Ref. 1450 2. from8).Ref. Experimental pointsK are
532
0 • Fig. 2.
I
Molecular rearrangement in liquid layer for freezing with liquid d denser
than
solid.
Molecule
shown as open circle has been to liquid forced back i
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