Phase Separation and Cahn Hilliard Equation
Phase separation describes the change of an alloy from a uniform mixed state
to that of a spatially separated multi-phase structure. This change takes
place when the temperature is rapidly reduced below a critical temperature.
The mathematical model is due to Cahn and Hilliard.
For further information about phase separation in a binary alloy, ie. the
two-phase structure, you may want to take a look at the
brief summary of the mathematical and thermodynamical
background. A more comprehensive description can be found in
"Thomas Blesgen, Axel Rotthäuser: Phasentrennung in binären
Mischungen (Diplomarbeit)".
If you have any questions, especially about the following images and how
GRAPE has been used to create them, feel free to contact
blesgen@geo.uni-bonn.de
(Thomas Blesgen) or
axel@iam.uni-bonn.de
(Axel Rotthäuser).
Two Phases in Two Space Dimensions:
The development in time from a mixed state to a separated two-phase structure
is shown. The two colors, green and red, indicate which of the two phases
is dominant. By taking into account the actual value of the dominant phase,
the blurred phase transitions and the intensity of the colors
give an impression of how far the separation has already taken place.
Three Phases in Two Space Dimensions:
The development in time from a mixed state to a separated three-phase structure
is shown. The three colors, green, red and blue, indicate which of the three
phases is dominant. By taking into account the actual value of the dominant
phase, the blurred phase transitions and the intensity of the colors
give an impression of how far the separation has already taken place.
Two Phases in Three Space Dimensions:
The development in time from a mixed state to a separated two-phase structure
is shown. One phase is represented by the golden colored volume, the other
phase is kept invisible as it is just the complement. The surface of the
volume indicates the region of phase transition. To give an impression on
how far the separation has already taken place, the isolines on the boundary
of the cube refer to the actual values of the concentration. The steep
gradients in the last images (isolines are close in the area of phase
transition) give proof of a truly separated state.
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axel@iam.uni-bonn.de -
March 11, 1996