.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/surface/tpd/plot_01_redhead_tpd.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

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

        :ref:`Go to the end <sphx_glr_download_api_gallery_surface_tpd_plot_01_redhead_tpd.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_surface_tpd_plot_01_redhead_tpd.py:


Redhead's analysis of temperature-programmed desorption
==========================================================

In a TPD experiment a covered surface is heated at a steady rate
:math:`\beta` while the desorbing gas is recorded, and each binding state
shows up as a peak. :func:`~chemistrykit.surface.systems.tpd.simulate_tpd`
integrates the Polanyi-Wigner rate equation to produce these spectra.
Redhead (1962) turned a first-order peak temperature :math:`T_p` into a
desorption energy:
:math:`E_d = RT_p[\ln(\nu T_p/\beta) - 3.64]`
(:func:`~chemistrykit.surface.systems.tpd.redhead_desorption_energy`).
Below, the formula is checked against the exact peak condition
(:func:`~chemistrykit.surface.systems.tpd.first_order_peak_temperature`).
First-order peaks shift with heating rate but not with coverage, while
second-order peaks move to lower temperature as the coverage rises.

.. GENERATED FROM PYTHON SOURCE LINES 20-34

.. code-block:: Python

    import matplotlib.pyplot as plt

    from chemistrykit.surface.systems.tpd import first_order_peak_temperature, redhead_desorption_energy, simulate_tpd

    Ed, nu = 110.0e3, 1.0e13  # J/mol, 1/s
    for beta in [1.0, 10.0, 100.0]:
        res = simulate_tpd(Ed, nu, beta, T_start=250.0, T_end=650.0)
        Ed_redhead = redhead_desorption_energy(res.peak_temperature, nu, beta)
        print(
            f"beta = {beta:5.1f} K/s: T_p = {res.peak_temperature:.2f} K "
            f"(exact {first_order_peak_temperature(Ed, nu, beta):.2f} K), "
            f"Redhead E_d = {Ed_redhead / 1e3:.2f} kJ/mol (true {Ed / 1e3:.0f})"
        )





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

 .. code-block:: none

    beta =   1.0 K/s: T_p = 407.53 K (exact 407.53 K), Redhead E_d = 109.46 kJ/mol (true 110)
    beta =  10.0 K/s: T_p = 436.65 K (exact 436.65 K), Redhead E_d = 109.17 kJ/mol (true 110)
    beta = 100.0 K/s: T_p = 470.08 K (exact 470.08 K), Redhead E_d = 108.82 kJ/mol (true 110)




.. GENERATED FROM PYTHON SOURCE LINES 35-57

.. code-block:: Python

    fig, axes = plt.subplots(1, 3, figsize=(15, 4))
    for beta in [1.0, 10.0, 100.0]:
        res = simulate_tpd(Ed, nu, beta, T_start=250.0, T_end=650.0)
        axes[0].plot(res.T, res.desorption_rate * beta, label=rf"$\beta$ = {beta:g} K/s")
    axes[0].set_xlabel("T (K)")
    axes[0].set_ylabel(r"desorption rate $-d\theta/dt$ (1/s)")
    axes[0].set_title("First order: peak shifts with heating rate")
    axes[0].legend()

    for theta0 in [0.25, 0.5, 1.0]:
        res = simulate_tpd(Ed, nu, 10.0, theta0=theta0, T_start=250.0, T_end=650.0)
        axes[1].plot(res.T, res.desorption_rate, label=rf"$\theta_0$ = {theta0}")
        res2 = simulate_tpd(Ed, nu, 10.0, theta0=theta0, order=2, T_start=250.0, T_end=650.0)
        axes[2].plot(res2.T, res2.desorption_rate, label=rf"$\theta_0$ = {theta0}")
    axes[1].set_title("First order: peak fixed as coverage varies")
    axes[2].set_title("Second order: peak moves down as coverage rises")
    for ax in axes[1:]:
        ax.set_xlabel("T (K)")
        ax.set_ylabel(r"$-d\theta/dT$ (1/K)")
        ax.legend()
    plt.tight_layout()
    plt.show()



.. image-sg:: /api/gallery/surface/tpd/images/sphx_glr_plot_01_redhead_tpd_001.png
   :alt: First order: peak shifts with heating rate, First order: peak fixed as coverage varies, Second order: peak moves down as coverage rises
   :srcset: /api/gallery/surface/tpd/images/sphx_glr_plot_01_redhead_tpd_001.png
   :class: sphx-glr-single-img






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

   **Total running time of the script:** (0 minutes 0.134 seconds)


.. _sphx_glr_download_api_gallery_surface_tpd_plot_01_redhead_tpd.py:

.. only:: html

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

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

      :download:`Download Jupyter notebook: plot_01_redhead_tpd.ipynb <plot_01_redhead_tpd.ipynb>`

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

      :download:`Download Python source code: plot_01_redhead_tpd.py <plot_01_redhead_tpd.py>`

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

      :download:`Download zipped: plot_01_redhead_tpd.zip <plot_01_redhead_tpd.zip>`


.. only:: html

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

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