.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "api/gallery/crystal/crystal_systems/plot_01_crystal_systems.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_crystal_crystal_systems_plot_01_crystal_systems.py>`
        to download the full example code.

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

.. _sphx_glr_api_gallery_crystal_crystal_systems_plot_01_crystal_systems.py:


Weiss's crystal systems: classifying a unit cell by its axes
=============================================================

Christian Samuel Weiss (1815) sorted crystals into *systems* by the
lengths of, and angles between, their crystallographic axes -- the idea
that survives as today's 7 crystal systems.
:func:`~chemistrykit.crystal.systems.crystal_systems.classify_crystal_system`
classifies a unit cell purely from the equalities/inequalities among its
six lattice parameters :math:`(a,b,c,\alpha,\beta,\gamma)`, and
:func:`~chemistrykit.crystal.systems.crystal_systems.unit_cell_volume`
gives the general-cell volume formula that reduces to familiar shortcuts
(:math:`abc`, :math:`\frac{\sqrt3}{2}a^2c`) in special cases.

.. GENERATED FROM PYTHON SOURCE LINES 17-30

.. code-block:: Python

    import numpy as np

    from chemistrykit.crystal.systems.crystal_systems import classify_crystal_system, unit_cell_volume

    cells = {
        "NaCl (rock salt)": (5.640, 5.640, 5.640, 90.0, 90.0, 90.0),
        "TiO2 (rutile)": (4.593, 4.593, 2.959, 90.0, 90.0, 90.0),
        "alpha-quartz": (4.913, 4.913, 5.405, 90.0, 90.0, 120.0),
        "calcite (rhombohedral setting)": (6.375, 6.375, 6.375, 46.08, 46.08, 46.08),
        "gypsum": (5.679, 15.202, 6.522, 90.0, 113.83, 90.0),
        "K2Cr2O7 (potassium dichromate)": (7.418, 7.318, 13.379, 98.6, 90.4, 95.5),
    }








.. GENERATED FROM PYTHON SOURCE LINES 31-36

.. code-block:: Python

    for name, (a, b, c, alpha, beta, gamma) in cells.items():
        system = classify_crystal_system(a, b, c, alpha, beta, gamma)
        V = unit_cell_volume(a, b, c, alpha, beta, gamma)
        print(f"{name:35s} -> {system:14s} V = {V:8.2f} A^3")





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

 .. code-block:: none

    NaCl (rock salt)                    -> cubic          V =   179.41 A^3
    TiO2 (rutile)                       -> tetragonal     V =    62.42 A^3
    alpha-quartz                        -> hexagonal      V =   112.98 A^3
    calcite (rhombohedral setting)      -> trigonal       V =   122.63 A^3
    gypsum                              -> monoclinic     V =   515.06 A^3
    K2Cr2O7 (potassium dichromate)      -> triclinic      V =   714.64 A^3




.. GENERATED FROM PYTHON SOURCE LINES 37-39

A right-angle (orthorhombic/tetragonal/cubic) cell's volume is exactly
a*b*c -- the general formula's simplest special case:

.. GENERATED FROM PYTHON SOURCE LINES 39-44

.. code-block:: Python

    V_general = unit_cell_volume(4.593, 4.593, 2.959, 90.0, 90.0, 90.0)
    V_shortcut = 4.593 * 4.593 * 2.959
    print(f"\nRutile: general formula = {V_general:.4f}, a*b*c shortcut = {V_shortcut:.4f}")
    assert np.isclose(V_general, V_shortcut)





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

 .. code-block:: none


    Rutile: general formula = 62.4220, a*b*c shortcut = 62.4220




.. GENERATED FROM PYTHON SOURCE LINES 45-47

The hexagonal shortcut (sqrt(3)/2 * a^2 * c) matches the general
formula too, for quartz's hexagonal cell:

.. GENERATED FROM PYTHON SOURCE LINES 47-52

.. code-block:: Python

    a, c = 4.913, 5.405
    V_general = unit_cell_volume(a, a, c, 90.0, 90.0, 120.0)
    V_shortcut = (np.sqrt(3.0) / 2.0) * a**2 * c
    print(f"Quartz:  general formula = {V_general:.4f}, hexagonal shortcut = {V_shortcut:.4f}")
    assert np.isclose(V_general, V_shortcut)




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

 .. code-block:: none

    Quartz:  general formula = 112.9848, hexagonal shortcut = 112.9848





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

   **Total running time of the script:** (0 minutes 0.001 seconds)


.. _sphx_glr_download_api_gallery_crystal_crystal_systems_plot_01_crystal_systems.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_crystal_systems.ipynb <plot_01_crystal_systems.ipynb>`

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

      :download:`Download Python source code: plot_01_crystal_systems.py <plot_01_crystal_systems.py>`

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

      :download:`Download zipped: plot_01_crystal_systems.zip <plot_01_crystal_systems.zip>`


.. only:: html

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

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