simulation.rst

Simulations

Simulating diffraction patterns

Contents

• :ref:`powdersim`
• :ref:`electrostatic`

Polycrystalline Diffraction Simulation

The simplest diffraction simulation available in scikit-ued is polycrystalline diffraction simulation.

All you need is a :class:`Crystal` object and a range of scattering length, defined from scattering angles s as s = \sin{\theta}/\lambda:

import matplotlib.pyplot as plt
import numpy as np
from skued import powdersim
from skued import Crystal
graphite = Crystal.from_database('C')

q = np.linspace(1, 10, 1024)
diff = powdersim(graphite, q)

plt.figure()
plt.plot(q, diff/diff.max())

After plot formatting:

.. plot::

        import matplotlib.pyplot as plt
        import numpy as np
        from skued import Crystal
        graphite = Crystal.from_database('C')
        from skued import powdersim
        q = np.linspace(1, 10, 1024)
        diff = powdersim(graphite, q)
        plt.figure()
        plt.plot(q, diff/diff.max())
        plt.xlim([q.min(), q.max()])
        plt.xlabel('$q (1/\AA)$')
        plt.ylabel('Diffracted intensity (A.u.)')
        plt.title('Polycrystalline graphite diffraction')

Electrostatic Potential Simulation

The scattering potential of electrons is the crystal electrostatic potential; hence computing such potential is a useful tool.

To compute the electrostatic potential for an infinite crystal on an arbitrary 3D mesh, take a look at :func:`electrostatic`:

from skued import Crystal
from skued import electrostatic

graphite = Crystal.from_database('C')

extent = np.linspace(-10, 10, 256)
xx, yy, zz = np.meshgrid(extent, extent, extent)
potential = electrostatic(graphite, xx, yy, zz)

Another possibility is to calculate the electrostatic potential for an infinite slab in the x-y plane, but finite in z-direction, using :func:`pelectrostatic` (p for projected):

from skued import pelectrostatic

extent = np.linspace(-5, 5, 256)
xx, yy= np.meshgrid(extent, extent)
potential = pelectrostatic(graphite, xx, yy)

After plot formatting:

.. plot::

    import matplotlib.pyplot as plt
    import numpy as np
    from skued import Crystal
    from skued import pelectrostatic

    extent = np.linspace(-5, 5, 256)
    xx, yy = np.meshgrid(extent, extent)

    potential = pelectrostatic(Crystal.from_database('C'), xx, yy)

    fig = plt.figure()
    ax = fig.add_subplot(111)
    ax.xaxis.set_visible(False)
    ax.yaxis.set_visible(False)
    ax.set_title('Electrostatic potential of graphite')
    im = ax.imshow(potential)
    cbar = plt.colorbar(im)
    cbar.set_label('Electrostatic potential ($V \cdot \AA$)')

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