pymatgen.analysis.eos module

This module implements various equation of states.

Note: Most of the code were initially adapted from ASE and deltafactor by @gmatteo but has since undergone major refactoring.

class Birch(volumes, energies)

Bases: EOSBase

Birch EOS.

Parameters:

• volumes (list/numpy.array) – volumes in Ang^3

• energies (list/numpy.array) – energy in eV

class BirchMurnaghan(volumes, energies)

Bases: EOSBase

BirchMurnaghan EOS

Parameters:

• volumes (list/numpy.array) – volumes in Ang^3

• energies (list/numpy.array) – energy in eV

class DeltaFactor(volumes, energies)

Bases: PolynomialEOS

Fitting a polynomial EOS using delta factor.

Parameters:

• volumes (list/numpy.array) – volumes in Ang^3

• energies (list/numpy.array) – energy in eV

fit(order=3)

Overridden since this eos works with volume**(2/3) instead of volume.

class EOS(eos_name='murnaghan')

Bases: object

Convenient wrapper. Retained in its original state to ensure backward compatibility.

Fit equation of state for bulk systems.

The following equations are supported:

murnaghan: PRB 28, 5480 (1983)

birch: Intermetallic compounds: Principles and Practice, Vol I:
    Principles. pages 195-210

birch_murnaghan: PRB 70, 224107

pourier_tarantola: PRB 70, 224107

vinet: PRB 70, 224107

deltafactor

numerical_eos: 10.1103/PhysRevB.90.174107.

Usage:

eos = EOS(eos_name='murnaghan')
eos_fit = eos.fit(volumes, energies)
eos_fit.plot()

Parameters:

eos_name (str) – Type of EOS to fit.

MODELS = {'birch': <class 'pymatgen.analysis.eos.Birch'>, 'birch_murnaghan': <class 'pymatgen.analysis.eos.BirchMurnaghan'>, 'deltafactor': <class 'pymatgen.analysis.eos.DeltaFactor'>, 'murnaghan': <class 'pymatgen.analysis.eos.Murnaghan'>, 'numerical_eos': <class 'pymatgen.analysis.eos.NumericalEOS'>, 'pourier_tarantola': <class 'pymatgen.analysis.eos.PourierTarantola'>, 'vinet': <class 'pymatgen.analysis.eos.Vinet'>}

fit(volumes, energies)

Fit energies as function of volumes.

Parameters:

• volumes (list/np.array) –

• energies (list/np.array) –

Returns:

EOSBase object

Return type:

EOSBase

class EOSBase(volumes, energies)

Bases: object

Abstract class that must be subclassed by all equation of state implementations.

Parameters:

• volumes (list/numpy.array) – volumes in Ang^3

• energies (list/numpy.array) – energy in eV

property b0

Returns the bulk modulus. Note: the units for the bulk modulus: unit of energy/unit of volume^3.

property b0_GPa

Returns the bulk modulus in GPa. Note: This assumes that the energy and volumes are in eV and Ang^3

respectively

property b1

Returns the derivative of bulk modulus wrt pressure(dimensionless)

property e0

Returns the min energy.

fit()

Do the fitting. Does least square fitting. If you want to use custom fitting, must override this.

func(volume)

The equation of state function with the parameters other than volume set to the ones obtained from fitting.

Parameters:

volume (list/numpy.array) –

Returns:

numpy.array

plot(width=8, height=None, plt=None, dpi=None, **kwargs)

Plot the equation of state.

Parameters:

• width (float) – Width of plot in inches. Defaults to 8in.

• height (float) – Height of plot in inches. Defaults to width * golden ratio.

• plt (matplotlib.pyplot) – If plt is supplied, changes will be made to an existing plot. Otherwise, a new plot will be created.

• dpi –

• kwargs (dict) – additional args fed to pyplot.plot. supported keys: style, color, text, label

Returns:

Matplotlib plot object.

plot_ax(ax=None, fontsize=12, **kwargs)

Plot the equation of state on axis ax

Parameters:

• ax – matplotlib Axes or None if a new figure should be created.

• fontsize – Legend fontsize.

• color (str) – plot color.

• label (str) – Plot label

• text (str) – Legend text (options)

Returns:

Matplotlib figure object.

Keyword arguments controlling the display of the figure:

kwargs	Meaning
title	Title of the plot (Default: None).
show	True to show the figure (default: True).
savefig	“abc.png” or “abc.eps” to save the figure to a file.
size_kwargs	Dictionary with options passed to fig.set_size_inches e.g. size_kwargs=dict(w=3, h=4)
tight_layout	True to call fig.tight_layout (default: False)
ax_grid	True (False) to add (remove) grid from all axes in fig. Default: None i.e. fig is left unchanged.
ax_annotate	Add labels to subplots e.g. (a), (b). Default: False
fig_close	Close figure. Default: False.

property results

Returns a summary dict.

Returns:

dict

property v0

Returns the minimum or the reference volume in Ang^3.

exception EOSError

Bases: Exception

Error class for EOS fitting.

class Murnaghan(volumes, energies)

Bases: EOSBase

Murnaghan EOS.

Parameters:

• volumes (list/numpy.array) – volumes in Ang^3

• energies (list/numpy.array) – energy in eV

class NumericalEOS(volumes, energies)

Bases: PolynomialEOS

A numerical EOS.

Parameters:

• volumes (list/numpy.array) – volumes in Ang^3

• energies (list/numpy.array) – energy in eV

fit(min_ndata_factor=3, max_poly_order_factor=5, min_poly_order=2)

Fit the input data to the ‘numerical eos’, the equation of state employed in the quasiharmonic Debye model described in the paper: 10.1103/PhysRevB.90.174107.

credits: Cormac Toher

Parameters:

• min_ndata_factor (int) –

  parameter that controls the minimum number of data points that will be used for fitting. minimum number of data points =

  total data points-2*min_ndata_factor

• max_poly_order_factor (int) –

  parameter that limits the max order of the polynomial used for fitting. max_poly_order = number of data points used for fitting -

  max_poly_order_factor

• min_poly_order (int) – minimum order of the polynomial to be considered for fitting.

class PolynomialEOS(volumes, energies)

Bases: EOSBase

Derives from EOSBase. Polynomial based equations of states must subclass this.

Parameters:

• volumes (list/numpy.array) – volumes in Ang^3

• energies (list/numpy.array) – energy in eV

fit(order)

Do polynomial fitting and set the parameters. Uses numpy polyfit.

Parameters:

order (int) – order of the fit polynomial

class PourierTarantola(volumes, energies)

Bases: EOSBase

PourierTarantola EOS

Parameters:

• volumes (list/numpy.array) – volumes in Ang^3

• energies (list/numpy.array) – energy in eV

class Vinet(volumes, energies)

Bases: EOSBase

Vinet EOS.

Parameters:

• volumes (list/numpy.array) – volumes in Ang^3

• energies (list/numpy.array) – energy in eV