.. _sphx_glr_api_gallery_crystal_defects:

Point defects
---------------

Frenkel and Schottky point-defect concentrations vs. temperature, from
Boltzmann-factor equilibrium.


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  <div id='sg-tag-list' class='sphx-glr-tag-list'></div>


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    <div class="sphx-glr-thumbnails">

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    <div class="sphx-glr-thumbcontainer" tooltip="Frenkel (1926) argued that at any T&gt;0 some ions leave their sites for interstitial gaps, because the configurational entropy gained outweighs the enthalpy cost at low concentration. The equilibrium number is n_F=\sqrt{NN_i}\exp(-\Delta H_F/2k_BT) (~chemistrykit.crystal.systems.defects.frenkel_defect_concentration). AgCl, where small Ag+ ions readily occupy interstitial sites, is the textbook Frenkel-dominated solid (\Delta H_F\approx1.4 eV).">

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  .. image:: /api/gallery/crystal/defects/images/thumb/sphx_glr_plot_01_frenkel_defects_thumb.png
    :alt:

  :doc:`/api/gallery/crystal/defects/plot_01_frenkel_defects`

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      <div class="sphx-glr-thumbnail-title">Frenkel defects: vacancy-interstitial pairs in silver chloride</div>
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    <div class="sphx-glr-thumbcontainer" tooltip="Wagner and Schottky (1930) identified the second point-defect mechanism of ionic crystals: a cation and an anion leave the bulk together, keeping the crystal neutral and leaving a vacancy pair behind. The equilibrium number is n_S=N\exp(-\Delta H_S/2k_BT) (~chemistrykit.crystal.systems.defects.schottky_defect_concentration). In NaCl, the classic Schottky-dominated solid, \Delta H_S\approx2.3 eV.">

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  .. image:: /api/gallery/crystal/defects/images/thumb/sphx_glr_plot_02_schottky_defects_thumb.png
    :alt:

  :doc:`/api/gallery/crystal/defects/plot_02_schottky_defects`

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      <div class="sphx-glr-thumbnail-title">Schottky defects: paired cation and anion vacancies in rock salt</div>
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.. toctree::
   :hidden:

   /api/gallery/crystal/defects/plot_01_frenkel_defects
   /api/gallery/crystal/defects/plot_02_schottky_defects