Kinetics of Rapid Solidification
last updated 1/12/98
Kinetics of Rapid Solidification
last updated 1/12/98
In solidification the phase selection, growth velocity, chemical composition,
long-range order and microstructure of a growing phase are functions of
the local conditions at the crystal/melt interface, e.g. temperature, composition,
orientation, curvature, crystal structure. The objective of our research
is to illuminate how atomic structure and the kinetics of atom movements
lead to these functions. We have taken several steps toward predictive
capability for the production of materials under solidification processing
and other nonequilibrium conditions.
The modeling of an alloy solidification process typically assumes local
equilibrium at the crystal/melt interface. Local equilibrium is not
maintained during rapid solidification, for which models of nonequilibrium
interface kinetics abound but good measurements have been lacking.
Rapid solidification following pulsed laser melting is a well-controlled
experimental technique for investigating the kinetics of solidification
far from local equilibrium. Pulsed laser irradiation creates on the surface
of the sample a short-lived liquid layer that resolidifies, due to the
high thermal gradients, at speeds measured to be as high as 15 m/sec in
Si and 100 m/sec in pure elemental metals. With a spatially uniform pulsed
excimer laser we constrain melting and solidification to occur in a one-dimensional
geometry, permitting simple but accurate calculations and even measurements
of important quantities such as interface positions and velocities, and
temperature and solute depth profiles, which are usually only estimated
in rapid solidification processing and other "rapid quenching" techniques.
In Fig.
1 (a) shows the interface position vs. time, (b) shows the initial
(ion-implanted) solute depth profile, and subsequent frames show snapshots
of the profile during rapid solidification displaying solute partitioning
at the interface, during an experiment to measure the nonequilibrium partition
coefficient k, the ratio of solute concentration in the solid at
the interface to that in the melt at the interface [1]. The predicted final
profile is calculated for a variety of k values and compared to
the measured final profile; the best fit determines k.
By making nanosecond-resolved measurements of the transverse electrical
resistance of a thin film on an insulating substrate [2] , as shown in
Fig. 2, we have measured solid/liquid interface velocities in silicon during
the rapid melting (10-100 m/s) and subsequent solidification (1-10 m/s)
induced by pulsed laser melting. This "transient conductance" measurement
exploits the thirty-fold increase in electrical conductivity that accompanies
the melting of Si. Even though the resistivity change attending the melting
of a metal is much less than that in the melting of Si, we have successfully
adapted this method [3] to the determination of interface velocities in
pulsed laser melting of metallic alloys [4,5] .
Fig.
2. Transient conductance measurement and equivalent DC circuit.
Knowledge of resistivities of individual phases permits us to determine
the instantaneous melt depth from a measurement of the instantaneous film
resistance.
When a rapid phase transformation occurs, the interface velocity v
is the single most important variable to characterize in the process. Many
other phenomena such as the interfacial undercooling, the extension of
solubility, and the stability of a planar interface are explicit functions
of v. The ability
to measure it, rather than merely to estimate it from heat flow calculations,
has been a significant step forward in quantifying these phenomena, permitting
the correct theoretical ideas to be separated from the incorrect. We have
been applying this method to rapid alloy solidification following pulsed
laser melting in order to provide an accurate characterization of phase,
composition, and microstructure selection. It has contributed substantially
to the development of a fundamental understanding of the principles of
nonequilibrium processing. We have further refined this technique so that
we can measure the temperature of this rapidly moving interface [7-9],
as shown in Fig. 3.
Fig.
3Measurement of velocity-undercooling function. Top circuit
measures interface velocity as in Fig. 2. This is built on top of a thin
Pt layer which never melts, the resistance of which tells us the temperature
of the Pt layer. Because this is quite close to the interface and because
we know exactly where and at what rate the latent heat is being dumped,
we can calculate the correction (DTcorr)
fairly well, permitting a determination of the temperature of the interface
itself, or its undercooling (DTu).
Details about our accomplishments can be found in a recent
review article [6] which can be downloaded in pdf format
Currently, Paul Sanders, Michael
Aziz, and Frans
Spaepen are trying to apply the transient conductance technique
and the time-resolved temperature-measurement technique, to measure the
temperature of homogeneous crystal nucleation from undercooled liquid silicon.
Such a measurement is needed to resolve a controversy in the interpretation
of other nucleation experiments.
These techniques can also be used to measure liquid-phase diffusivities
[10]. They are particularly useful for high melting-point materials, where
the diffusivity is notoriously difficult to measure by any other means.
References :
1. R. Reitano, P.M. Smith and M.J. Aziz, "Solute Trapping of Group III, IV and V Elements in Silicon by Aperiodic Stepwise Growth Mechanism", J. Appl. Phys. 76, 1518 (1994).2. M.O. Thompson, G.J. Galvin, J.W. Mayer, P.S. Peercy and R.B. Hammond, Appl. Phys. Lett. 42, 445 (1983).
3. J.Y. Tsao, S.T. Picraux, P.S. Peercy and M.O. Thompson, Appl. Phys. Lett. 48, 278 (1986).
5. P.M. Smith and M.J. Aziz, "Solute Trapping in Aluminum Alloys", Acta Metall. Mater. 42, 3515 (1994).