Cahn-Hilliard Phase Decomposition

Microscale and Nanoscale Applications :
Cahn-Hilliard phase decomposition can model such disparate phenomena as:

* Tin-Lead solder aging
* Void lattice formation in irradiated semiconductors
* Self-assembly of thin film patterns

Free Energy Formulation :
Cahn-Hilliard systems model material separation and interface evolution by racking flow driven by configurational and interfacial free energy minimization.


Cahn-Hilliard Equation :
Adding a material-dependent mobility coefficient defines the concentration flux.



Weak Cahn-Hilliard Equation :
Taking a weighted residual and integrating by parts twice,


Gives a functional defined on in case of constant Mc.

Phase Separation :

* Random perturbations in initial conditions rapidly segregate into two distinct phases, divided by a labyrinth of sharp interfaces.
* Rapid anti-diffusionary process.


Spinodal Decomposition :

* Over long timescales, single-phase regions coalesce.
* Motion into curvature vector resembles surface tension.
* Patterning may occur when additional stress, surface tropisms are applied.


3D Phase Separation :

* Qualitatively similar.
* Topologically very different.
* Much more computationally intensive.

Thin Film Patterning :

* Electrostatic or chemical surface treatment attracts one material component preferentially.
* A spatially varying bias is added to the configurational free energy.

Effects of Bias Strength :
Low surface potential energy biases are overwhelmed by random noise.

Higher surface potential energy biases form patterns with decreasing defect density


Source : www.cfdlab.ae.utexas.edu/~roystgnr/usnccm9.pdf