Plotting Ternary Phase Diagrams and Using Triangular Axes
=========================================================

Often in thermodynamics, it is useful to use a two dimensional plot to
express equilibria in a three component system with fixed potentials.
The ``ternplot`` API provides a straightforward way to calculate
equilibria and generate ternary phase diagrams. Alternatively, if you
already have an equilibrium calculation, you can directly import and use
``eqplot``.

ternplot
--------

Here we will use the ternplot API to plot an isothermal section of the
Al-Cu-Y system from the thermodynamic database found at the `NIST
CALPHAD assessments <http://hdl.handle.net/11115/101>`__ assessed by
Zhang et al. `Calphad 35
(2011) <https://doi.org/10.1016/j.calphad.2011.09.008>`__.

.. code:: ipython3

    %matplotlib inline
    from pycalphad import Database, ternplot
    from pycalphad import variables as v
    
    db_al_cu_y = Database('Al-Cu-Y.tdb')
    comps = ['AL', 'CU', 'Y', 'VA']
    phases = list(db_al_cu_y.phases.keys())
    conds = {v.T: 830, v.P:101325, v.X('AL'): (0,1,0.015), v.X('Y'): (0,1,0.015)}
    
    %time ternplot(db_al_cu_y, comps, phases, conds, x=v.X('AL'), y=v.X('Y'))


.. parsed-literal::

    Wall time: 5min 56s
    



.. parsed-literal::

    <TriangularAxesSubplot:title={'center':'Al-Cu-Y'}, xlabel='X(AL)', ylabel='X(Y)'>




.. image:: TernaryExamples_files%5CTernaryExamples_2_2.png


triangular projection
---------------------

Importing the ``pycalphad.plot.triangular`` module automatically
registers a ``'triangular'`` projection in matplotlib for you to use in
custom plots, such as liquidus projections or contour plots of custom
property models.

Here we will use pycalphad to calculate the mixing enthalpy of the FCC
phase in our Al-Cu-Y system. Then we will the triangular projection to
plot the calculated points as a colored scatterplot on the triangular
axes.

.. code:: ipython3

    import matplotlib.pyplot as plt
    from pycalphad.plot import triangular
    from pycalphad import calculate
    
    # some sample data, these could be from an equilibrium calculation or a property model.
    # here we are calculating the mixing enthlapy of the FCC_A1 phase at 830K. 
    c = calculate(db_al_cu_y, comps, 'FCC_A1', output='HM_MIX', T=830, P=101325, pdens=5000)
    
    # Here we are getting the values from our plot. 
    xs = c.X.values[0, 0, 0, :, 0]  # 1D array of Al compositions
    ys = c.X.values[0, 0, 0, :, 1]  # 1D array of Cu compositions
    zs = c.HM_MIX.values[0, 0, 0, :]  # 1D array of mixing enthalpies at these compositions
    
    # when we imported the pycalphad.plot.triangular module, it made the 'triangular' projection available for us to use.
    fig = plt.figure()
    ax = fig.add_subplot(projection='triangular')
    ax.scatter(xs, ys, c=zs, 
               cmap='coolwarm', 
               linewidth=0.0)
    
    # label the figure
    ax.set_xlabel('X (AL)')
    ax.set_ylabel('X (CU)')
    ax.yaxis.label.set_rotation(60)  # rotate ylabel
    ax.yaxis.set_label_coords(x=0.12, y=0.5)  # move the label to a pleasing position
    ax.set_title('AL-CU-Y HM_MIX at 830K')
    
    # set up the colorbar
    cm = plt.cm.ScalarMappable(cmap='coolwarm')
    cm.set_array(zs)
    fig.colorbar(cm);



.. image:: TernaryExamples_files%5CTernaryExamples_4_0.png