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

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_gallery_analytical_scattering.py>`
        to download the full example code.

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

.. _sphx_glr_gallery_analytical_scattering.py:


Scattering Example: Percus Yevick Structure Factor and Phase Function
=====================================================================

Example of Percus Yevick structure factor computation for a polydisperse
mixture and corresponding phase function calculation.

.. GENERATED FROM PYTHON SOURCE LINES 9-66

.. code-block:: Python


    import matplotlib.pyplot as plt
    import numpy as np

    from PackLab import analytical, samplers, scattering
    from PackLab.units import ureg

    sampler = samplers.NormalRadiusSampler(
        mean=100 * ureg.nanometer,
        standard_deviation=10 * ureg.nanometer,
        bins=10
    )

    particle_radii, number_fractions = sampler.to_bins()

    py_domain = analytical.PercusYevickDomain(
        size=100 * ureg.micrometer,
        radii=particle_radii,
        volume_fraction=0.24,
        number_fractions=number_fractions,
    )

    py_domain.print_bins()

    distances = np.linspace(
        py_domain.radii.min() * 2,
        py_domain.radii.max() * 10,
        400,
    )
    solver = analytical.PercusYevickSolver(
        densities=py_domain.particle_densities_per_radius,
        radii=py_domain.radii,
        wavenumber="auto",
    )

    py_result = solver.compute(distances=distances)

    fig, ax = plt.subplots(1, 1, figsize=(12, 8))

    K = len(particle_radii)
    for i in range(K):
        for j in range(K):
            _ = ax.plot(
                py_result.distances.to("micrometer"),
                py_result.g[i, j],
                linewidth=1.5,
                label=f"{i}-{j}",
            )


    ax.set_xlabel("r")
    ax.set_ylabel(r"$g_{ij}(r)$")
    ax.set_title("Partial pair correlation: RSA vs Percus Yevick")
    _ = ax.legend()
    plt.show()





.. image-sg:: /gallery/analytical/images/sphx_glr_scattering_001.png
   :alt: Partial pair correlation: RSA vs Percus Yevick
   :srcset: /gallery/analytical/images/sphx_glr_scattering_001.png
   :class: sphx-glr-single-img





.. GENERATED FROM PYTHON SOURCE LINES 67-69

Calculate and plot the scattering phase function
-------------------------------------------------

.. GENERATED FROM PYTHON SOURCE LINES 69-98

.. code-block:: Python


    datas = scattering.compute_scattering_amplitudes(
        wavelength=150 * ureg.nanometer,
        diameters=py_result.radii,
        material=1.45,
        medium=1.0,
        phi=np.linspace(-np.pi / 2, np.pi / 2, 400) * ureg.radian,
        polarization=0 * ureg.degree,
    )

    datas.process()


    phi, theta, phase_function = datas.get_phase_function(
        densities=py_result.densities,
        H=py_result.H,
        wavenumber=py_result.wavenumber,
        theta_points=150
    )


    _ = scattering.plottings.plot_phase_function_3d(
        phi=phi,
        theta=theta,
        phase_function=phase_function.to('1 / meter').magnitude,
        mode="spherical"
    )

    plt.show()



.. image-sg:: /gallery/analytical/images/sphx_glr_scattering_002.png
   :alt: Phase function mapped on sphere (radius proportional to P)
   :srcset: /gallery/analytical/images/sphx_glr_scattering_002.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 18.452 seconds)


.. _sphx_glr_download_gallery_analytical_scattering.py:

.. only:: html

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

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

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

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

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

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

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


.. only:: html

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

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