.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/volcanology/plot_06_goldschmidt_ionic_substitution.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_06_goldschmidt_ionic_substitution.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_06_goldschmidt_ionic_substitution.py:


Goldschmidt's geochemical rules (1937)
======================================

Victor Goldschmidt classified the elements by where they go in the Earth and
stated the rules for which ions replace one another in a crystal: ions of the
same charge whose radii differ by less than about 15% substitute freely. Blundy
and Wood (1994) made the rule quantitative: the partition coefficient falls off
on both sides of the radius that fits the site, as the strain energy of the
lattice grows.

.. GENERATED FROM PYTHON SOURCE LINES 12-36



.. image-sg:: /api/gallery/volcanology/images/sphx_glr_plot_06_goldschmidt_ionic_substitution_001.png
   :alt: Size decides substitution
   :srcset: /api/gallery/volcanology/images/sphx_glr_plot_06_goldschmidt_ionic_substitution_001.png
   :class: sphx-glr-single-img





.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from earthsciencekit.volcanology import lattice_strain_partition

    optimal, peak, modulus, temperature = 1.0e-10, 2.0, 250e9, 1500  # a clinopyroxene M2-like site
    radius = np.linspace(0.6e-10, 1.45e-10, 400)
    ions = {"Mg2+": 0.89e-10, "Fe2+": 0.92e-10, "Ca2+": 1.12e-10, "Sr2+": 1.26e-10, "Ba2+": 1.42e-10}  # 8-fold radii
    partition = lattice_strain_partition(radius, optimal, peak, modulus, temperature)
    assert np.isclose(partition.max(), peak, rtol=1e-4)
    assert lattice_strain_partition(ions["Ba2+"], optimal, peak, modulus, temperature) < 1e-3 * peak

    fig, ax = plt.subplots()
    ax.semilogy(radius * 1e10, partition)
    ax.axvspan(0.85, 1.15, color="0.9", label="within 15% of the site radius")
    for name, value in ions.items():
        d = lattice_strain_partition(value, optimal, peak, modulus, temperature)
        ax.plot(value * 1e10, d, "ko")
        ax.annotate(name, (value * 1e10, d), textcoords="offset points", xytext=(4, 4), fontsize=8)
    ax.set(xlabel="ionic radius [angstrom]", ylabel="mineral/melt partition coefficient", title="Size decides substitution", ylim=(1e-6, 5))
    ax.legend()

    plt.show()


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

   **Total running time of the script:** (0 minutes 0.191 seconds)


.. _sphx_glr_download_api_gallery_volcanology_plot_06_goldschmidt_ionic_substitution.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_06_goldschmidt_ionic_substitution.ipynb
        :alt: Launch JupyterLite
        :width: 150 px

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

      :download:`Download Jupyter notebook: plot_06_goldschmidt_ionic_substitution.ipynb <plot_06_goldschmidt_ionic_substitution.ipynb>`

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

      :download:`Download Python source code: plot_06_goldschmidt_ionic_substitution.py <plot_06_goldschmidt_ionic_substitution.py>`

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

      :download:`Download zipped: plot_06_goldschmidt_ionic_substitution.zip <plot_06_goldschmidt_ionic_substitution.zip>`


.. only:: html

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

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