https://github.com/tkphd/ternary-phase-diagram

Derivation and construction of a thermodynamic phase diagram for ternary alloy systems with 2 or 3 phases
https://github.com/tkphd/ternary-phase-diagram

constrained-optimization lagrange-multipliers materials-science phase-diagram phase-field thermodynamics

Last synced: 3 months ago
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Derivation and construction of a thermodynamic phase diagram for ternary alloy systems with 2 or 3 phases

• Host: GitHub
• URL: https://github.com/tkphd/ternary-phase-diagram
• Owner: tkphd
• Created: 2019-03-21T00:04:23.000Z (almost 6 years ago)
• Default Branch: main
• Last Pushed: 2020-06-16T14:57:07.000Z (over 4 years ago)
• Last Synced: 2023-03-27T15:56:11.538Z (almost 2 years ago)
• Topics: constrained-optimization, lagrange-multipliers, materials-science, phase-diagram, phase-field, thermodynamics
• Language: Python
• Size: 389 KB
• Stars: 11
• Watchers: 4
• Forks: 3
• Open Issues: 0
• Metadata Files:
  • Readme: README.md

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README

        
# ternary-phase-diagram

This repository presents the math and code required to construct the

thermodynamic phase diagram for a ternary alloy system containing two or three

phases.

![example-diagram](example-diagram.png)

*A ternary phase diagram, for example.*

A Makefile is provided to build both the documentation and a shared library

required to efficiently crunch the numbers. The

[derivation](ternary-diagram.tex) is written in LaTeX, while the

[implementation](phase-diagram.py) is in Python.

## Dependencies

- To use the Makefile, you will need [make](https://www.gnu.org/software/make/).

- To build the derivation, you will need a LaTeX distribution.

- To build the shared library, you will need a scientific Python distribution

  (*e.g.*, [Anaconda](https://store.continuum.io/cshop/anaconda/),

  [Canopy](https://enthought.com/products/canopy/),

  [Python(x,y)](https://python-xy.github.io/)) and

  [SymPy](https://www.sympy.org), which is available from

  [GitHub](https://github.com/sympy/sympy) or

  [PyPI](https://pypi.org/project/sympy/) (`pip install sympy`).

## Usage

With these dependencies met, you can regenerate the example phase diagram with

```bash

  $ make

```

This triggers a three-stage process:

1. Evaluate [free-energies.py](free-energies.py) to write three paraboloid

   free energies (one per phase) to C expressions:

    ```bash

    $ python free-energies.py

    ```

2. Compile the C expressions to a shared library:

    ```bash

    $ gcc -Wall -fPIC -shared paraboloids.c -o paraboloids.so

    ```

3. Execute [phase-diagram.py](phase-diagram.py) to draw the pretty picture:

    ```bash

    $ python phase-diagram.py

    ```

To rebuild the documentation, simply

```bash

  $ make docs

```

## Reuse

To make this code your own, edit [free-energies.py](free-energies.py) and refine

(or redefine) the three pure-phase free energy expressions: `GA`, `GB`, and

`GC`. Perhaps start with increasing curvatures, or change `skew` to change the

amount of "squish" along the $x_1 = x_2$ line. If you change the arguments

required to evaluate a function, you will also need to modify

[pyCinterface.py](pyCinterface.py) accordingly. When you're done, simply

```bash

  $ make

```

If things aren't making sense, it might make sense to visualize your free

energy landscape. The utility file [ternary-landscape.py](ternary-landscape.py)

will convert your free energy landscape to a grayscale contour plot. Run

```bash

  $ python ternary-landscape.py

```