.. only:: html

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

        Click :ref:`here <sphx_glr_download_examples_1D_simulation(macro_amorphous)_plot_6_extended_czjzek.py>`     to download the full example code or to run this example in your browser via Binder
    .. rst-class:: sphx-glr-example-title

    .. _sphx_glr_examples_1D_simulation(macro_amorphous)_plot_6_extended_czjzek.py:


Extended Czjzek distribution (Shielding and Quadrupolar)
========================================================

In this example, we illustrate the simulation of spectrum originating from an
extended Czjzek distribution of traceless symmetric tensors. We show two cases, an
extended Czjzek distribution of the shielding and quadrupolar tensor parameters,
respectively.

Import the required modules.


.. code-block:: python

    import matplotlib as mpl
    import matplotlib.pyplot as plt
    import numpy as np
    from mrsimulator import Simulator
    from mrsimulator.methods import BlochDecaySpectrum, BlochDecayCentralTransitionSpectrum
    from mrsimulator.models import ExtCzjzekDistribution
    from mrsimulator.utils.collection import single_site_system_generator

    # pre config the figures
    mpl.rcParams["figure.figsize"] = [4.25, 3.0]








Symmetric shielding tensor
--------------------------

Create the extended Czjzek distribution
'''''''''''''''''''''''''''''''''''''''

First, create a distribution of the zeta and eta parameters of the shielding tensors
using the :ref:`extended_czjzek_distribution` model as follows,


.. code-block:: python


    # The range of zeta and eta coordinates over which the distribution is sampled.
    z_lim = np.arange(100) * 0.4 + 40  # in ppm
    e_lim = np.arange(21) / 20

    dominant = {"zeta": 60, "eta": 0.3}
    z_dist, e_dist, amp = ExtCzjzekDistribution(dominant, eps=0.14).pdf(pos=[z_lim, e_lim])








The following is the plot of the extended Czjzek distribution.


.. code-block:: python

    plt.contourf(z_dist, e_dist, amp, levels=10)
    plt.xlabel(r"$\zeta$ / ppm")
    plt.ylabel(r"$\eta$")
    plt.tight_layout()
    plt.show()




.. image:: /examples/1D_simulation(macro_amorphous)/images/sphx_glr_plot_6_extended_czjzek_001.png
    :alt: plot 6 extended czjzek
    :class: sphx-glr-single-img





Simulate the spectrum
'''''''''''''''''''''

Create the spin systems from the above :math:`\zeta` and :math:`\eta` parameters.


.. code-block:: python

    systems = single_site_system_generator(
        isotopes="13C", shielding_symmetric={"zeta": z_dist, "eta": e_dist}, abundance=amp
    )
    print(len(systems))





.. rst-class:: sphx-glr-script-out

 Out:

 .. code-block:: none

    838




Create a simulator object and add the above system.


.. code-block:: python

    sim = Simulator()
    sim.spin_systems = systems  # add the systems
    sim.methods = [BlochDecaySpectrum(channels=["13C"])]  # add the method
    sim.run()








The following is the static spectrum arising from a Czjzek distribution of the
second-rank traceless shielding tensors.


.. code-block:: python

    plt.figure(figsize=(4.25, 3.0))
    ax = plt.gca(projection="csdm")
    ax.plot(sim.methods[0].simulation, color="black", linewidth=1)
    plt.tight_layout()
    plt.show()




.. image:: /examples/1D_simulation(macro_amorphous)/images/sphx_glr_plot_6_extended_czjzek_002.png
    :alt: plot 6 extended czjzek
    :class: sphx-glr-single-img





Quadrupolar tensor
------------------

Create the extended Czjzek distribution
'''''''''''''''''''''''''''''''''''''''

Similarly, you may also create an extended Czjzek distribution of the electric field
gradient (EFG) tensor parameters.


.. code-block:: python


    # The range of Cq and eta coordinates over which the distribution is sampled.
    cq_lim = np.arange(100) * 0.1  # assumed in MHz
    e_lim = np.arange(21) / 20

    dominant = {"Cq": 6.1, "eta": 0.1}
    cq_dist, e_dist, amp = ExtCzjzekDistribution(dominant, eps=0.25).pdf(
        pos=[cq_lim, e_lim]
    )








The following is the plot of the extended Czjzek distribution.


.. code-block:: python

    plt.contourf(cq_dist, e_dist, amp, levels=10)
    plt.xlabel(r"$C_q$ / MHz")
    plt.ylabel(r"$\eta$")
    plt.tight_layout()
    plt.show()




.. image:: /examples/1D_simulation(macro_amorphous)/images/sphx_glr_plot_6_extended_czjzek_003.png
    :alt: plot 6 extended czjzek
    :class: sphx-glr-single-img





Simulate the spectrum
'''''''''''''''''''''
**Static spectrum**
Create the spin systems.


.. code-block:: python

    systems = single_site_system_generator(
        isotopes="71Ga", quadrupolar={"Cq": cq_dist * 1e6, "eta": e_dist}, abundance=amp
    )








Create a simulator object and add the above system.


.. code-block:: python

    sim = Simulator()
    sim.spin_systems = systems  # add the systems
    sim.methods = [
        BlochDecayCentralTransitionSpectrum(
            channels=["71Ga"],
            magnetic_flux_density=9.4,  # in T
            spectral_dimensions=[{"count": 2048, "spectral_width": 2e5}],
        )
    ]  # add the method
    sim.run()








The following is a static spectrum arising from an extended Czjzek distribution of
the second-rank traceless EFG tensors.


.. code-block:: python

    plt.figure(figsize=(4.25, 3.0))
    ax = plt.gca(projection="csdm")
    ax.plot(sim.methods[0].simulation, color="black", linewidth=1)
    ax.invert_xaxis()
    plt.tight_layout()
    plt.show()




.. image:: /examples/1D_simulation(macro_amorphous)/images/sphx_glr_plot_6_extended_czjzek_004.png
    :alt: plot 6 extended czjzek
    :class: sphx-glr-single-img





**MAS spectrum**


.. code-block:: python

    sim.methods = [
        BlochDecayCentralTransitionSpectrum(
            channels=["71Ga"],
            magnetic_flux_density=9.4,  # in T
            rotor_frequency=25000,  # in Hz
            spectral_dimensions=[
                {"count": 2048, "spectral_width": 2e5, "reference_offset": -1e4}
            ],
        )
    ]  # add the method
    sim.config.number_of_sidebands = 16
    sim.run()








The following is the MAS spectrum arising from an extended Czjzek distribution of the
second-rank traceless EFG tensors.


.. code-block:: python

    plt.figure(figsize=(4.25, 3.0))
    ax = plt.gca(projection="csdm")
    ax.plot(sim.methods[0].simulation, color="black", linewidth=1)
    ax.invert_xaxis()
    plt.tight_layout()
    plt.show()



.. image:: /examples/1D_simulation(macro_amorphous)/images/sphx_glr_plot_6_extended_czjzek_005.png
    :alt: plot 6 extended czjzek
    :class: sphx-glr-single-img






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

   **Total running time of the script:** ( 0 minutes  8.447 seconds)


.. _sphx_glr_download_examples_1D_simulation(macro_amorphous)_plot_6_extended_czjzek.py:


.. only :: html

 .. container:: sphx-glr-footer
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