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.. _dcdft tut:
Calculating Delta-values
========================
In this tutorial we compare the equation-of-state (EOS) calculated for 7 FCC
metals using values from :class:`~ase.calculators.emt.EMT`, WIEN2k and
experiment. Each EOS is described by three parameters:
* volume per atom
* bulk-modulus
* pressure derivative of bulk-modulus
Differences between two EOS'es can be measured by a single `\Delta` value
defined as:
.. math::
\sqrt{\frac{\int_{V_a}^{V_b}
(E_1(V) - E_2(V))^2 dV}
{V_b - V_a}},
where `E_n(V)` is the energy per atom as a function of volume.
The `\Delta` value can be calculated using the
:func:`ase.utils.deltacodesdft.delta` function:
.. autofunction:: ase.utils.deltacodesdft.delta
.. seealso::
* Collection of ground-state elemental crystals: :ref:`dcdft`
* Equation-of-state module: :mod:`ase.eos`
We get the WIEN2k and experimental numbers from the :ref:`dcdft` ASE-collection
and we calculate the EMT EOS using this script:
.. literalinclude:: calculate.py
And fit to a Birch-Murnaghan EOS:
.. literalinclude:: fit.py
Result for Pt:
.. image:: Pt.png
Volumes in Ang^3:
.. csv-table::
:file: volume.csv
Bulk moduli in GPa:
.. csv-table::
:file: B.csv
Pressure derivative of bulk-moduli:
.. csv-table::
:file: Bp.csv
Now, we can calculate `\Delta` between EMT and WIEN2k for Pt:
>>> from ase.utils.deltacodesdft import delta
>>> from ase.units import kJ
>>> delta(15.08, 278.67 * 1e-24 * kJ, 5.31,
... 15.64, 248.71 * 1e-24 * kJ, 5.46)
0.03205389052984122
Here are all the values (in meV/atom) calculated with the script below:
.. csv-table::
:file: delta.csv
.. literalinclude:: tables.py
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