# Nucleation and Spinodal Decomposition in Ternary-Component Alloys

## Summary (1 min read)

### 1. Introduction

- Alloys are composite materials which are formed by mixing a number of pure metals together at a high temperature and then rapidly quenching or cooling the mixture to form a solid.
- These pattern formations can be divided into two classes: Nucleation and Spinodal Decomposition.
- This behavior is modelled mathematically by the Cahn-Moral equation.
- G represents the set of all possible states or average mass concentrations of the ternary alloy, this follows from the conservation of mass.
- In their research the authors used two nonlinearities.

### 3. Results and Discussion

- For each of their nonlinearities the authors created Matlab code which shows which regions on the Gibbs simplex have no, one or two positive eigenvalues.
- In the pictures below the Gibbs simplex is projected onto the plane.
- The red area represents the nucleation region where there are no positive eigenvalues.
- To reach the non-trivial nucleation branches the authors had to begin in the spinodal region.
- 3.2.1. Tracing the quadratic nonlinearity.

### 4. Conclusions and Future Work

- The authors would like to successfully trace alpha back into the nucleation region from several branches at the same λ value and compare bubble formations.
- The authors hope to eventually find which bubble formations are possible at each value of λ for each nonlinearity.
- The authors third partner James O’Beirne will be investigating a sixth degree polynomial nonlinearity and comparing the results with their investigations.
- Eventually the research should be expanded to two and three dimensions to see if be used.
- Both of these extensions though requiring more computing power, will make the model considerably more reliable.

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##### References

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### "Nucleation and Spinodal Decompositi..." refers background in this paper

...The Gibbs triangle for the quadratic nonlinearity is shown on the left, and the triangle for the logarithmic nonlinearity is depicted on the right Both of the nonlinearities have been investigated previously in both the one and two dimensional cases [3],[4],[2]....

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^{1}, Hanein H. Edrees

^{2}, Joseph J. Price

^{2}, Evelyn Sander

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17 citations

### "Nucleation and Spinodal Decompositi..." refers background in this paper

...Otherwise it lies in the spinodal region [2]....

[...]

...The Gibbs triangle for the quadratic nonlinearity is shown on the left, and the triangle for the logarithmic nonlinearity is depicted on the right Both of the nonlinearities have been investigated previously in both the one and two dimensional cases [3],[4],[2]....

[...]

17 citations

### "Nucleation and Spinodal Decompositi..." refers background or methods in this paper

...Given a state (ū, v̄, w̄) ∈ G, the stability of that particular state is given by computing the eigenvalues of Jf (ū, v̄, w̄), where Jf is the Jacobian of f(u) [4]....

[...]

...The Gibbs triangle for the quadratic nonlinearity is shown on the left, and the triangle for the logarithmic nonlinearity is depicted on the right Both of the nonlinearities have been investigated previously in both the one and two dimensional cases [3],[4],[2]....

[...]