55 lines
2.0 KiB
ReStructuredText
55 lines
2.0 KiB
ReStructuredText
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Let's raise the temperature
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In this tutorial we will learn how to introduce lattice vibrations in the calculation. Indeed, vibrational
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damping can greatly change the result of a calculation since it adds incoherence that will damp the modulations
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of the signal.
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This was experimentally shown back to 1986 for example by R. Trehan and S. Fadley (see reference below). In their
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work, they performed azimutal scans of a copper(001) surface at 2 different polar angles: one at grazing incidence
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and one at 45° for incresing temperatures from 298K to roughly 1000K.
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For each azimutal scan, they looked at the *anisotropy* of the signal, that is:
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:math:`\frac{\Delta I}{I_{max}}`
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This value is representative of how clear are the modulations of the signal. As it was shown by their
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experiments, this anisotropy decreases when the temperature is increased due to the increased disorder
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in the structure coming from thermal agitation. They also showed that this variation in anisotropy is more
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pronounced for grazing incidence angles. This is related to the fact that surface atoms are expected to
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vibrate more than bulk ones. They also proposed single scattering calculations that reproduced well these
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results.
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We propose here to reproduce this kind of calculation to introduce the parameters that control the
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vibrational damping.
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.. figure:: fig1.png
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:align: center
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:width: 80%
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Azimutal scans for Cu(2p) at grazing incidence and at 45°.
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.. figure:: fig2.png
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:align: center
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:width: 80%
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Variation of anisotropy as a function of temperature and polar angle.
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.. literalinclude:: Cu_temperature.py
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:linenos:
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Here is the full script used to generate those data (:download:`download <Cu_temperature.py>`)
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.. seealso::
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Temperature dependence x-ray photoelectron diffraction from copper: Surface and bulk effects
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R. Trehan & C. S. Fadley, Phys. Rev. B **34** (10) p1654 (1986)
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`[doi] <https://doi.org/10.1103/PhysRevB.34.6784>`__
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