.. _sphx_glr_api_gallery_crystal_crystal_chemistry:

Crystal chemistry
-------------------

Rules of thumb from ionic radii: Pauling's radius-ratio rule for
coordination numbers and Goldschmidt's tolerance factor for perovskites.


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    <div class="sphx-glr-thumbcontainer" tooltip="Pauling&#x27;s first rule (1929): each cation is surrounded by a polyhedron of anions whose size is fixed by the radius ratio r_+/r_-. A polyhedron is stable only while the anions still touch the cation, which sets the limits \sqrt2-1=0.414 (octahedral), \sqrt3-1=0.732 (cubic), and so on. radius_ratio_coordination applies the rule; here it is tested against observed structures.">

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  .. image:: /api/gallery/crystal/crystal_chemistry/images/thumb/sphx_glr_plot_01_pauling_radius_ratio_thumb.png
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  :doc:`/api/gallery/crystal/crystal_chemistry/plot_01_pauling_radius_ratio`

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      <div class="sphx-glr-thumbnail-title">Pauling's radius-ratio rule: predicting coordination numbers</div>
    </div>


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    <div class="sphx-glr-thumbcontainer" tooltip="Goldschmidt (1926) noted that in an ideal cubic ABX_3 perovskite the A-X distance equals \sqrt2 times the B-X distance, so hard spheres fit exactly when t=(r_A+r_X)/[\sqrt2(r_B+r_X)]=1 (~chemistrykit.crystal.systems.crystal_chemistry.goldschmidt_tolerance_factor). Titanates with A-cations of different sizes span the range from tilted to cubic to ferroelectrically distorted.">

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  .. image:: /api/gallery/crystal/crystal_chemistry/images/thumb/sphx_glr_plot_02_goldschmidt_tolerance_factor_thumb.png
    :alt:

  :doc:`/api/gallery/crystal/crystal_chemistry/plot_02_goldschmidt_tolerance_factor`

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      <div class="sphx-glr-thumbnail-title">Goldschmidt's tolerance factor: which perovskites are cubic</div>
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    </div>


.. toctree::
   :hidden:

   /api/gallery/crystal/crystal_chemistry/plot_01_pauling_radius_ratio
   /api/gallery/crystal/crystal_chemistry/plot_02_goldschmidt_tolerance_factor