Final Project Prompt In engineering applications, materials used are rarely of a singular composition. More often than not, alloys are employed in order to utilize thermal-mechanical strength in combination that one element cannot.
computer science
Description
Final Project Prompt In engineering applications, materials used are rarely of a singular composition. More often than not, alloys are employed in order to utilize thermal-mechanical strength in combination that one element cannot. An example of alloying used in everyday application would be stainless steel, which consist of carbon, iron, and chromium. Such an alloy has the mechanical strength of carbon, thermal conductivity of steel, and oxidation/corrosion resistance of chromium. Alloying of materials can be simulated using a theory of mixture known as the Phase Field model. For this project, we will employ Phase Field modeling to a Spinodal Alloying Decomposition as the mixture evolves over time 1.
Phase Field Theory
In Phase Field, the boundary between two mixture (known as the Phase Boundary) is
modeled closely, in order the simulate its evolution and growth. Let us define the phase
order parameter as φ. Initially, two distinct material phases are mixed via a random distribution. Here, one material would be categorized as one phase (φ = 1) while then other an
entirely different phase (φ = −1). It is easy to see that the phase order can be a function
of position and time, i.e. φ = φ(x, y, t).
where a and b are phase potential coefficients and γ is an phase boundary penalty constant. If we apply physical intuition, e.g. φ is the measure of particle number and F is
the energy f particular configuration of φ, then the variation in F with respect to φ can be
defined as the chemical potential of the system (Eq 2)
