:orphan:

.. _user-guide_conventions_bravais-lattices:

****************
Bravais lattices
****************

Wulfric implements two conventions for the definition of the high-symmetry points in
reciprocal space and recommended k-paths

*   "HPKOT" as defined in [1]_

    In this work authors defined a set of high-symmetry points in
    reciprocal space and recommended k-paths for each "extended Bravais lattice symbol".
    Therefore, we provide in total 29 examples for each extended Bravais lattice symbol.

*   "SC" as in [2]_

    In this work authors defined a set of high-symmetry points in
    reciprocal space and recommended k-paths for each variation of Bravais lattice.
    We provide examples for each of 25 lattice variations.

Below is the table that summarizes lattice variations and extended lattice symbols for
each of the 14 Bravais lattices.



=============================== =============================================================================== ==============================================================================
Bravais lattice                 HPKOT                                                                           SC
=============================== =============================================================================== ==============================================================================
Cubic (cP)                      :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_01_cP1.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_01_CUB.py`
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_02_cP2.py`
Face-centered cubic (cF)        :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_03_cF1.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_02_FCC.py`
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_04_cF2.py`
Body-centered cubic (cI)        :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_05_cI1.py`  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_03_BCC.py`
Tetragonal (tP)                 :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_06_tP1.py`  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_04_TET.py`
Body-centered tetragonal (tI)   :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_07_tI1.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_05_BCT1.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_08_tI2.py`  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_06_BCT2.py`
Orthorhombic (oP)               :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_09_oP1.py`  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_07_ORC.py`
Face-centered orthorhombic (oF) :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_10_oF1.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_08_ORCF1.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_11_oF2.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_09_ORCF2.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_12_oF3.py`  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_10_ORCF3.py`
Body-centered orthorhombic (oI) :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_13_oI1.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_11_ORCI.py`
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_14_oI2.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_15_oI3.py`
Base-centered orthorhombic (oS) :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_16_oC1.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_12_ORCC.py`
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_17_oC2.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_18_oA1.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_19_oA2.py`
Hexagonal (hP)                  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_20_hP1.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_13_HEX.py`
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_21_hP2.py`
Rhombohedral (hR)               :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_22_hR1.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_14_RHL1.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_23_hR2.py`  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_15_RHL2.py`
Monoclinic (mP)                 :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_24_mP1.py`  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_16_MCL.py`
Base-centered monoclinic (mS)   :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_25_mC1.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_17_MCLC1.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_26_mC2.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_18_MCLC2.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_27_mC3.py`  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_19_MCLC3.py`,
                                                                                                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_20_MCLC4.py`,
                                                                                                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_21_MCLC5.py`
Triclinic (aP)                  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_28_aP2.py`, :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_22_TRI1a.py`,
                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_1_hpkot_plot_29_aP3.py`  :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_23_TRI2a.py`,
                                                                                                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_24_TRI1b.py`,
                                                                                                                :ref:`sphx_glr_user-guide_conventions_bravais-lattices_2_sc_plot_25_TRI2b.py`,
=============================== =============================================================================== ==============================================================================


.. [1] Hinuma, Y., Pizzi, G., Kumagai, Y., Oba, F. and Tanaka, I., 2017.
        Band structure diagram paths based on crystallography.
        Computational Materials Science, 128, pp.140-184.
.. [2] Setyawan, W. and Curtarolo, S., 2010.
        High-throughput electronic band structure calculations: Challenges and tools.
        Computational materials science, 49(2), pp. 299-312.

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Hinuma, Pizzi, Kumagai, Oba, Tanaka (HPKOT)
===========================================

.. admonition:: Reference

    |POSCAR|_ files with the crystal structure for these examples are taken from the
    |seekpath|_ repository with the permission of its authors. We refer you to
    |seekpath|_ for the original copies of the files and the license for those. To read
    more about the extended Bravais lattice symbols, chosen high-symmetry points and
    k-paths we refer you to the |HPKOT-paper|_.


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Setyawan and Curtarolo (SC)
===========================

In the examples of SC convention we use cells as defined in
:py:func:`wulfric.cell.sc_get_example` with one artificial atom
``dict(positions=[[0, 0, 0]], spglib_types=[1])``.


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    <div class="sphx-glr-thumbcontainer" tooltip="Face-centered cubic cell is defined by single parameter a.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_02_FCC_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_02_FCC`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">FCC</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Body-centered cubic cell is defined by single parameter a.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_03_BCC_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_03_BCC`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">BCC</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Tetragonal cell is defined by two parameters a and c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_04_TET_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_04_TET`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">TET</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Body-centered tetragonal cell is defined by two parameters a and c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_05_BCT1_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_05_BCT1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">BCT1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Body-centered tetragonal cell is defined by two parameters a and c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_06_BCT2_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_06_BCT2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">BCT2</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Orthorhombic cell is defined by three parameters a, b and c with a &lt; b &lt; c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_07_ORC_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_07_ORC`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ORC</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Face-centred orthorhombic cell is defined by three parameters a, b and c with a &lt; b &lt; c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_08_ORCF1_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_08_ORCF1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ORCF1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Face-centred orthorhombic cell is defined by three parameters a, b and c with a &lt; b &lt; c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_09_ORCF2_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_09_ORCF2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ORCF2</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Face-centred orthorhombic cell is defined by three parameters a, b and c with a &lt; b &lt; c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_10_ORCF3_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_10_ORCF3`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ORCF3</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Body-centered orthorhombic cell is defined by three parameters a, b and c with a &lt; b &lt; c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_11_ORCI_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_11_ORCI`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ORCI</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Base-centered orthorhombic cell is defined by three parameters a, b and c with a &lt; b &lt; c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_12_ORCC_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_12_ORCC`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">ORCC</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Hexagonal cell is defined by two parameters a and c.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_13_HEX_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_13_HEX`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">HEX</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Rhombohedral cell is defined by two parameters a and \alpha.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_14_RHL1_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_14_RHL1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">RHL1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Rhombohedral cell is defined by two parameters a and \alpha.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_15_RHL2_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_15_RHL2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">RHL2</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Monoclinic cell is defined by four parameters a, b, c and \alpha with b \le c, \alpha &lt; 90^{\circ}.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_16_MCL_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_16_MCL`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MCL</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Base-centered monoclinic cell is defined by four parameters a, b, c and \alpha with b \le c, \alpha &lt; 90^{\circ}.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_17_MCLC1_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_17_MCLC1`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MCLC1</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Base-centered monoclinic cell is defined by four parameters a, b, c and \alpha with b \le c, \alpha &lt; 90^{\circ}.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_18_MCLC2_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_18_MCLC2`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MCLC2</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Base-centered monoclinic cell is defined by four parameters a, b, c and \alpha with b \le c, \alpha &lt; 90^{\circ}.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_19_MCLC3_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_19_MCLC3`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MCLC3</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Base-centered monoclinic cell is defined by four parameters a, b, c and \alpha with b \le c, \alpha &lt; 90^{\circ}.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_20_MCLC4_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_20_MCLC4`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MCLC4</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Base-centered monoclinic cell is defined by four parameters a, b, c and \alpha with b \le c, \alpha &lt; 90^{\circ}.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_21_MCLC5_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_21_MCLC5`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">MCLC5</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Triclinic cell is defined by six parameters a, b, c and \alpha, \beta, \gamma.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_22_TRI1a_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_22_TRI1a`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">TRI1a</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Triclinic cell is defined by six parameters a, b, c and \alpha, \beta, \gamma.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_23_TRI2a_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_23_TRI2a`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">TRI2a</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Triclinic cell is defined by six parameters a, b, c and \alpha, \beta, \gamma.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_24_TRI1b_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_24_TRI1b`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">TRI1b</div>
    </div>


.. raw:: html

    <div class="sphx-glr-thumbcontainer" tooltip="Triclinic cell is defined by six parameters a, b, c and \alpha, \beta, \gamma.">

.. only:: html

  .. image:: /user-guide/conventions/bravais-lattices/2_sc/images/thumb/sphx_glr_plot_25_TRI2b_thumb.png
    :alt:

  :doc:`/user-guide/conventions/bravais-lattices/2_sc/plot_25_TRI2b`

.. raw:: html

      <div class="sphx-glr-thumbnail-title">TRI2b</div>
    </div>


.. thumbnail-parent-div-close

.. raw:: html

    </div>


.. toctree::
   :hidden:
   :includehidden:


   /user-guide/conventions/bravais-lattices/1_hpkot/index.rst
   /user-guide/conventions/bravais-lattices/2_sc/index.rst


.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-gallery

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

      :download:`Download all examples in Python source code: bravais-lattices_python.zip </user-guide/conventions/bravais-lattices/bravais-lattices_python.zip>`

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

      :download:`Download all examples in Jupyter notebooks: bravais-lattices_jupyter.zip </user-guide/conventions/bravais-lattices/bravais-lattices_jupyter.zip>`


.. only:: html

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

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