.. DO NOT EDIT.
.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
.. "examples_generated/tutorials/eos_01.py"
.. LINE NUMBERS ARE GIVEN BELOW.

.. only:: html

    .. note::
        :class: sphx-glr-download-link-note

        :ref:`Go to the end <sphx_glr_download_examples_generated_tutorials_eos_01.py>`
        to download the full example code.

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

.. _sphx_glr_examples_generated_tutorials_eos_01.py:


.. _eos_example:

==========================================
EOS: Introduction to the Equation of state
==========================================

The equation of states (EOS) can be used to compute the
minimum lattice constants for a bulk material.
In the following, we demonstrate how the ASE Equation
of state function can be used to compute the
minimum energy lattice constant and pressure
for FCC silver.

First, do a bulk calculation for different lattice constants:

.. GENERATED FROM PYTHON SOURCE LINES 20-41

.. code-block:: Python

    import numpy as np

    from ase import Atoms
    from ase.calculators.emt import EMT
    from ase.eos import EquationOfState
    from ase.io import read
    from ase.io.trajectory import Trajectory
    from ase.units import kJ

    a = 4.0  # approximate lattice constant
    b = a / 2
    ag = Atoms(
        'Ag', cell=[(0, b, b), (b, 0, b), (b, b, 0)], pbc=1, calculator=EMT()
    )  # use EMT potential
    cell = ag.get_cell()
    traj = Trajectory('Ag.traj', 'w')
    for x in np.linspace(0.95, 1.05, 5):
        ag.set_cell(cell * x, scale_atoms=True)
        ag.get_potential_energy()
        traj.write(ag)








.. GENERATED FROM PYTHON SOURCE LINES 42-45

This writes a trajectory file containing five configurations of FCC silver
for five different lattice constants. Now, analyse the result with
the :class:`~ase.eos.EquationOfState` class:

.. GENERATED FROM PYTHON SOURCE LINES 45-55

.. code-block:: Python


    configs = read('Ag.traj@0:5')  # read 5 configurations
    # Extract volumes and energies:
    volumes = [ag.get_volume() for ag in configs]
    energies = [ag.get_potential_energy() for ag in configs]
    eos = EquationOfState(volumes, energies)
    v0, e0, B = eos.fit()
    print(B / kJ * 1.0e24, 'GPa')
    eos.plot('Ag-eos.png')




.. image-sg:: /examples_generated/tutorials/images/sphx_glr_eos_01_001.png
   :alt: sj: E: -0.000 eV, V: 16.781 Å$^3$, B: 100.142 GPa
   :srcset: /examples_generated/tutorials/images/sphx_glr_eos_01_001.png
   :class: sphx-glr-single-img


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

 .. code-block:: none

    100.14189241973199 GPa

    <Axes: title={'center': 'sj: E: -0.000 eV, V: 16.781 Å$^3$, B: 100.142 GPa'}, xlabel='volume [Å$^3$]', ylabel='energy [eV]'>



.. GENERATED FROM PYTHON SOURCE LINES 56-59

A quicker way to do this analysis is to use the :mod:`ase.gui` tool::

    $   ase gui Ag.traj

.. GENERATED FROM PYTHON SOURCE LINES 61-62

And then choose :menuselection:`Tools --> Bulk modulus`.


.. _sphx_glr_download_examples_generated_tutorials_eos_01.py:

.. only:: html

  .. container:: sphx-glr-footer sphx-glr-footer-example

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

      :download:`Download Jupyter notebook: eos_01.ipynb <eos_01.ipynb>`

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

      :download:`Download Python source code: eos_01.py <eos_01.py>`

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

      :download:`Download zipped: eos_01.zip <eos_01.zip>`


.. only:: html

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

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