.. only:: html

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

        Click :ref:`here <sphx_glr_download_examples_2D_simulation(crystalline)_plot_3_SAS_Rb2CrO4.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_2D_simulation(crystalline)_plot_3_SAS_Rb2CrO4.py:


Rb2CrO4, 87Rb (I=3/2) SAS
^^^^^^^^^^^^^^^^^^^^^^^^^

87Rb (I=3/2) Switched-angle spinning (SAS) simulation.

The following is a switched-angle spinning (SAS) simulation of
:math:`\text{Rb}_2\text{CrO}_4`. While :math:`\text{Rb}_2\text{CrO}_4` has two
rubidium sites, the site with the smaller quadrupolar interaction was selectively
observed and reported by Shore `et. al.` [#f1]_. The following is the simulation
based on the published tensor parameters.


.. code-block:: python

    import matplotlib as mpl
    import matplotlib.pyplot as plt
    import mrsimulator.signal_processing as sp
    import mrsimulator.signal_processing.apodization as apo
    from mrsimulator import Simulator, SpinSystem, Site
    from mrsimulator.methods import Method2D

    # global plot configuration
    font = {"size": 9}
    mpl.rc("font", **font)
    mpl.rcParams["figure.figsize"] = [4.25, 3.0]








Generate the site and spin system objects.


.. code-block:: python

    site = Site(
        isotope="87Rb",
        isotropic_chemical_shift=-7,  # in ppm
        shielding_symmetric={"zeta": 110, "eta": 0},
        quadrupolar={
            "Cq": 3.5e6,  # in Hz
            "eta": 0.3,
            "alpha": 0,  # in rads
            "beta": 70 * 3.14159 / 180,  # in rads
            "gamma": 0,  # in rads
        },
    )
    spin_system = SpinSystem(sites=[site])








Use the generic 2D method, `Method2D`, to simulate a SAS spectrum by customizing the
method parameters, as shown below. Note, the Method2D method simulates an infinite
spinning speed spectrum.


.. code-block:: python

    sas = Method2D(
        channels=["87Rb"],
        magnetic_flux_density=4.2,  # in T
        spectral_dimensions=[
            {
                "count": 256,
                "spectral_width": 1.5e4,  # in Hz
                "reference_offset": -5e3,  # in Hz
                "label": "70.12 dimension",
                "events": [{"rotor_angle": 70.12 * 3.14159 / 180}],  # in radians
            },
            {
                "count": 512,
                "spectral_width": 15e3,  # in Hz
                "reference_offset": -7e3,  # in Hz
                "label": "MAS dimension",
                "events": [{"rotor_angle": 54.74 * 3.14159 / 180}],  # in radians
            },
        ],
    )








Create the Simulator object, add the method and spin system objects, and
run the simulation.


.. code-block:: python

    sim = Simulator()
    sim.spin_systems = [spin_system]  # add the spin systems
    sim.methods = [sas]  # add the method.

    # Configure the simulator object. For non-coincidental tensors, set the value of the
    # `integration_volume` attribute to `hemisphere`.
    sim.config.integration_volume = "hemisphere"
    sim.run()








The plot of the simulation.


.. code-block:: python

    data = sim.methods[0].simulation
    ax = plt.subplot(projection="csdm")
    cb = ax.imshow(data / data.max(), aspect="auto", cmap="gist_ncar_r")
    plt.colorbar(cb)
    ax.invert_xaxis()
    plt.tight_layout()
    plt.show()




.. image:: /examples/2D_simulation(crystalline)/images/sphx_glr_plot_3_SAS_Rb2CrO4_001.png
    :alt: plot 3 SAS Rb2CrO4
    :class: sphx-glr-single-img





Add post-simulation signal processing.


.. code-block:: python

    processor = sp.SignalProcessor(
        operations=[
            # Gaussian convolution along both dimensions.
            sp.IFFT(dim_index=(0, 1)),
            apo.Gaussian(FWHM="0.2 kHz", dim_index=0),
            apo.Gaussian(FWHM="0.2 kHz", dim_index=1),
            sp.FFT(dim_index=(0, 1)),
        ]
    )
    processed_data = processor.apply_operations(data=data)
    processed_data /= processed_data.max()








The plot of the simulation after signal processing.


.. code-block:: python

    ax = plt.subplot(projection="csdm")
    cb = ax.imshow(processed_data.real, cmap="gist_ncar_r", aspect="auto")
    plt.colorbar(cb)
    ax.invert_xaxis()
    plt.tight_layout()
    plt.show()




.. image:: /examples/2D_simulation(crystalline)/images/sphx_glr_plot_3_SAS_Rb2CrO4_002.png
    :alt: plot 3 SAS Rb2CrO4
    :class: sphx-glr-single-img





.. [#f1] Shore, J.S., Wang, S.H., Taylor, R.E., Bell, A.T., Pines, A. Determination of
      quadrupolar and chemical shielding tensors using solid-state two-dimensional NMR
      spectroscopy, J. Chem. Phys. (1996)  **105** *21*, 9412.
      `DOI: 10.1063/1.472776 <https://doi.org/10.1063/1.472776>`_


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

   **Total running time of the script:** ( 0 minutes  0.585 seconds)


.. _sphx_glr_download_examples_2D_simulation(crystalline)_plot_3_SAS_Rb2CrO4.py:


.. only :: html

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