.. _sphx_glr_api_gallery_crystal_lattice_energy:

Lattice energy
----------------

The Born-Lande and Kapustinskii equations for ionic-crystal lattice
energy, and the Shannon ionic radii the Kapustinskii equation uses.


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


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

.. thumbnail-parent-div-open

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    <div class="sphx-glr-thumbcontainer" tooltip="Born and Lande (1918) balanced the Madelung attraction -A/r against a short-range repulsion B/r^n; setting dU/dr=0 at the observed spacing r_0 gives U=-\frac{N_AM|z_+z_-|e^2}{4\pi\varepsilon_0r_0}(1-\frac{1}{n}), which BornLandeLatticeEnergy evaluates. This example shows the energy curve for NaCl and compares the equation with Born-Haber values for six rock-salt halides.">

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  .. image:: /api/gallery/crystal/lattice_energy/images/thumb/sphx_glr_plot_01_born_lande_thumb.png
    :alt:

  :doc:`/api/gallery/crystal/lattice_energy/plot_01_born_lande`

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      <div class="sphx-glr-thumbnail-title">Born-Lande equation: lattice energies of the alkali halides</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Kapustinskii (1956) replaced the structure-specific Madelung constant with a near-universal constant per ion, so KapustinskiiLatticeEnergy needs only the number of ions per formula unit, the charges, and the ionic radii. On rock-salt halides it tracks the structure-based Born-Lande value; it also handles salts of other structures (fluorite CaF2) where no Madelung constant is supplied at all.">

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  .. image:: /api/gallery/crystal/lattice_energy/images/thumb/sphx_glr_plot_02_kapustinskii_thumb.png
    :alt:

  :doc:`/api/gallery/crystal/lattice_energy/plot_02_kapustinskii`

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      <div class="sphx-glr-thumbnail-title">Kapustinskii equation: lattice energy without a crystal structure</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Shannon (1976) fitted one self-consistent radius per ion (for a given coordination number) so that cation-anion distances in thousands of crystals are reproduced by simple sums r_++r_-. SHANNON_IONIC_RADII_PM holds the 6-coordinate values; here their sums are checked against measured rock-salt nearest-neighbor distances, and their periodic trends are plotted.">

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  .. image:: /api/gallery/crystal/lattice_energy/images/thumb/sphx_glr_plot_03_shannon_ionic_radii_thumb.png
    :alt:

  :doc:`/api/gallery/crystal/lattice_energy/plot_03_shannon_ionic_radii`

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      <div class="sphx-glr-thumbnail-title">Shannon's effective ionic radii: additivity and periodic trends</div>
    </div>


.. thumbnail-parent-div-close

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    </div>


.. toctree::
   :hidden:

   /api/gallery/crystal/lattice_energy/plot_01_born_lande
   /api/gallery/crystal/lattice_energy/plot_02_kapustinskii
   /api/gallery/crystal/lattice_energy/plot_03_shannon_ionic_radii