Crystal growth from liquid phase & accommodation factor
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Transcript of Crystal growth from liquid phase & accommodation factor
Crystal Growth From Liquid Phase
The movement of the boundary separating a liquid from a crystalline phase, under a temperature gradient normal to the boundary, may be considered the resultant of two different atomic movements.
Cont’d…
At the interface , those atoms that leave the liquid and join the solid determine a rate of attachment.
At the interface, those atoms that leave the solid and join the liquid determine a rate of detachment.
This point of view shows that the movement of interface is a two dimensional diffusion problem in which
Cont’d…
Where Rf & Rm are the rates of attachment and detachment, Rfo and Rmo are approximate constants, Qf and Qm are activation energies, and R and T have their usual significance.
Cont’d…
The activation energy Qf represents the energy to take an atom that lies on the liquid side of the boundary to the saddle point, as shown in the figure (1).
The activation energy Qm represents the energy to take an atom that lies on the solid side of the boundary to the saddle point, as shown in the figure (1).
Cont’d…
In figure (1) , the potential energy wells shown on each side of saddle point differ by the latent heat of fusion.
An atom in the solid possesses a lower energy than one in the liquid, but it should be noted that it also possesses a lower entropy.
Fig. 1 The Relationship between the activation energies for
Attachment and Detachment
Cont’d…
The rates of attachment, Rf, and detachment, Rm, may be expressed as
1. Atoms per second crossing the boundary
2. Velocities of the boundary in centimeters per second.
Cont’d…
The constants Rfo & Rmo depends on a number of factors that can be estimated for “Copper” by Chalmers as shown in
figure (2). It shows the curves for freezing rate & melting
rate as a function of temperature. There is an equilibrium freezing or melting point
at which curves diverge sharply on either side.
Fig. 2 The rates of freezing and meltingFor “Cu”
Cont’d…
The difference in individual rates determine the actual rate with which interface moves.
It is clear from figure (2), at equilibrium point interface is stable.
When the temperature decreases from equilibrium point, rate of freezing becomes dominant resulted in the movement of interface towards the liquid phase and vice versa.
Accommodation Factor
It is a chance of an atom in a given phase, either in liquid or solid, can find a position on the other side of the boundary where it can attach itself.
It determines the magnitude of constants (Rfo & Rmo).
It is independent of the chemical nature of liquid as the liquid phases of metals have very similar structures.
Cont’d…
On the contrary, it varies with the nature of solid having different crystalline structures and indices of crystalline plane that faces the liquid phase.
The less close-packed the planes, the easier it is for liquid atoms to attach themselves to the crystal.
Cont’d…
This fact is shown in the figure (3-A)
& (3-B) representing a FCC structure, which shows the atomic arrangements on {111} & {100} surfaces.
Cont’d… The growth velocity for a given amount of
supercooling is higher for less close-packed {100} plane than close-packed {111} plane because former contains holes or pockets for accommodation of liquid atoms.
Low atomic density planes of a crystal grow themselves out of existence, leaving behind only close-packed surface
as shown in figure (4).
