Phase Field of Modeling Solidification of Single Component Materials

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Phase Field of Modeling Solidification of Single
Component Materials

• R. Edwin García
• redwing_at_purdue.edu

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The Cahn-Hilliard Equation
(for conserved quantities)
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The Allen-Cahn Equation
(for non-conserved quantities)
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Thermodynamics of Solidification
(A very-very brief remainder)
L
liquid
solid
Tm
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Hidden Thermodynamic Variables
1
0
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Extending the Phase Field to Solidification
Define thermodynamic order parameter that
quantifies the amount of transformed stuff.
liquid
degree of disorder
solid
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Single-Component Systems
Free Energy Construction
and a penalty for isothermally transforming from
solid to liquid
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Single-Component Systems
Free Energy Construction
(order parameter contribution)
liquid
solid
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Single-Component Systems
Free Energy Construction
(volume fraction, coupling term)
liquid
solid
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Assembling the Free Energy Function
can be set to zero, if solid component A is taken
as the reference state
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Trends in the Free Energy
liquid
solid
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Isothermal Solidification
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Thermal Contribution to the Model
Recall that Ficks Law for heat transfer is still
valid!
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Fitting Experimental Data to the Model