.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_05_bowen_reaction_series.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_api_gallery_volcanology_plot_05_bowen_reaction_series.py>`
        to download the full example code or to run this example in your browser via JupyterLite.

.. rst-class:: sphx-glr-example-title

.. _sphx_glr_api_gallery_volcanology_plot_05_bowen_reaction_series.py:


Bowen's reaction series (1928)
==============================

Norman Bowen's experiments showed that a basaltic melt crystallizes minerals
in a fixed order and that crystals either keep reacting with the melt or are
removed from it. Removing them (fractional crystallization) lets the residual
melt evolve far towards granite; keeping them in equilibrium limits how far it
can go. Trace elements show the difference most clearly: an element the
crystals reject is enriched without limit by fractionation, but at most
``1 / D`` by equilibrium crystallization.

.. GENERATED FROM PYTHON SOURCE LINES 13-31



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_05_bowen_reaction_series_001.png
   :alt: Removing crystals drives the melt further
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_05_bowen_reaction_series_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.volcanology import equilibrium_crystallization_melt, fractional_crystallization_melt

    melt = np.linspace(1, 0.01, 300)
    fig, ax = plt.subplots()
    for partition, label in [(0.1, "incompatible, D = 0.1"), (5.0, "compatible (Ni in olivine), D = 5")]:
        ax.semilogy(melt, fractional_crystallization_melt(1, melt, partition), label=f"fractional, {label}")
        ax.semilogy(melt, equilibrium_crystallization_melt(1, melt, partition), "--", label=f"equilibrium, {label}")
    assert np.isclose(equilibrium_crystallization_melt(1, 0, 0.1), 10)
    assert fractional_crystallization_melt(1, 0.01, 0.1) > 60
    ax.invert_xaxis()
    ax.set(xlabel="fraction of melt remaining", ylabel="concentration / initial", title="Removing crystals drives the melt further")
    ax.legend(fontsize=8)

    plt.show()


.. rst-class:: sphx-glr-timing

   **Total running time of the script:** (0 minutes 0.133 seconds)


.. _sphx_glr_download_api_gallery_volcanology_plot_05_bowen_reaction_series.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

    .. container:: lite-badge

      .. image:: images/jupyterlite_badge_logo.svg
        :target: ../../../lite/lab/index.html?path=api/gallery/volcanology/plot_05_bowen_reaction_series.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

    .. container:: sphx-glr-download sphx-glr-download-jupyter

      :download:`Download Jupyter notebook: plot_05_bowen_reaction_series.ipynb <plot_05_bowen_reaction_series.ipynb>`

    .. container:: sphx-glr-download sphx-glr-download-python

      :download:`Download Python source code: plot_05_bowen_reaction_series.py <plot_05_bowen_reaction_series.py>`

    .. container:: sphx-glr-download sphx-glr-download-zip

      :download:`Download zipped: plot_05_bowen_reaction_series.zip <plot_05_bowen_reaction_series.zip>`


.. only:: html

 .. rst-class:: sphx-glr-signature

    `Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_