.. _concepts.lattice:

==================
Crystal Lattice
==================

.. sample('EuPtIn4_eh1_ver', a=4.542, b=16.955, c=7.389)

Record a sample's crystalline :index:`lattice` parameters: :math:`a, b, c,
\alpha, \beta, \gamma`. Information for a crystal lattice is stored in an
instance of :class:`hklpy2.blocks.lattice.Lattice()`.  This class will examine
the lattice parameters and report the crystal system.  If the parameters do not
match any of these crystal systems, an exception will be raised.

A lattice is stored as part of the :ref:`sample <concepts.sample>`.

.. rubric:: Examples of the Seven 3-D Crystal Systems (highest to lowest symmetry)

=============== =================================== = === === ===== ====== =====
system          command                             a b   c   alpha beta   gamma
=============== =================================== = === === ===== ====== =====
cubic           ``Lattice(5.)``                     5 *5* *5* *90*  *90*   *90*
hexagonal       ``Lattice(4., c=3., gamma=120)``    4 *4* 3   *90*  *90*   120
rhombohedral    ``Lattice(4., alpha=80.2)``         4 *4* *4* 80.2  *80.2* *80.2*
tetragonal      ``Lattice(4, c=3)``                 4 *4* 3   *90*  *90*   *90*
orthorhombic    ``Lattice(4, 5, 3)``                4 5   3   *90*  *90*   *90*
monoclinic      ``Lattice(4, 5, 3, beta=75)``       4 5   3   *90*  75     *90*
triclinic       ``Lattice(4, 5, 3, 75., 85., 95.)`` 4 5   3   75    85     95
=============== =================================== = === === ===== ====== =====

Default values are *italicized*.  It is not necessary to supply the default parameters.

:see: https://dictionary.iucr.org/Crystal_system
:see: https://en.wikipedia.org/wiki/Crystal_system

.. rubric:: EXAMPLES

It is not necessary to enter any of the default information for any lattice
(such as the 90 degree angles for an orthorhombic crystals).

.. code-block:: Python
    :linenos:

    >>> from hklpy2 import Lattice
    >>> Lattice(5.)
    Lattice(a=5.0, b=5.0, c=5.0, alpha=90.0, beta=90.0, gamma=90.0)

    >>> Lattice(4., c=3., gamma=120)
    Lattice(a=4.0, b=4.0, c=3.0, alpha=90.0, beta=90.0, gamma=120)

    >>> Lattice(4., alpha=80.2)
    Lattice(a=4.0, b=4.0, c=4.0, alpha=80.2, beta=80.2, gamma=80.2)

    >>> Lattice(4, c=3)
    Lattice(a=4, b=4, c=3, alpha=90.0, beta=90.0, gamma=90.0)

    >>> Lattice(4, 5, 3)
    Lattice(a=4, b=5, c=3, alpha=90.0, beta=90.0, gamma=90.0)

    >>> Lattice(4, 5, 3, beta=75)
    Lattice(a=4, b=5, c=3, alpha=90.0, beta=75, gamma=90.0)

    >>> Lattice(4, 5, 3, 75., 85., 95.)
    Lattice(a=4, b=5, c=3, alpha=75.0, beta=85.0, gamma=95.0)

.. seealso:: :ref:`glossary`