pymatgen.analysis.quasiharmonic module

This module implements the Quasi-harmonic Debye approximation that can be used to compute thermal properties.

See the following papers for more info:

class QuasiharmonicDebyeApprox(energies, volumes, structure, t_min=300.0, t_step=100, t_max=300.0, eos='vinet', pressure=0.0, poisson=0.25, use_mie_gruneisen=False, anharmonic_contribution=False)[source]

Bases: object

Parameters
  • energies (list) – list of DFT energies in eV

  • volumes (list) – list of volumes in Ang^3

  • structure (Structure) –

  • t_min (float) – min temperature

  • t_step (float) – temperature step

  • t_max (float) – max temperature

  • eos (str) –

    equation of state used for fitting the energies and the volumes. options supported by pymatgen: “quadratic”, “murnaghan”, “birch”,

    ”birch_murnaghan”, “pourier_tarantola”, “vinet”, “deltafactor”, “numerical_eos”

  • pressure (float) – in GPa, optional.

  • poisson (float) – poisson ratio.

  • use_mie_gruneisen (bool) – whether or not to use the mie-gruneisen formulation to compute the gruneisen parameter. The default is the slater-gamma formulation.

  • anharmonic_contribution (bool) – whether or not to consider the anharmonic contribution to the Debye temperature. Cannot be used with use_mie_gruneisen. Defaults to False.

static debye_integral(y)[source]

Debye integral. Eq(5) in doi.org/10.1016/j.comphy.2003.12.001

Parameters

y (float) – debye temperature/T, upper limit

Returns

unitless

Return type

float

debye_temperature(volume)[source]

Calculates the debye temperature. Eq(6) in doi.org/10.1016/j.comphy.2003.12.001. Thanks to Joey.

Eq(6) above is equivalent to Eq(3) in doi.org/10.1103/PhysRevB.37.790 which does not consider anharmonic effects. Eq(20) in the same paper and Eq(18) in doi.org/10.1016/j.commatsci.2009.12.006 both consider anharmonic contributions to the Debye temperature through the Gruneisen parameter at 0K (Gruneisen constant).

The anharmonic contribution is toggled by setting the anharmonic_contribution to True or False in the QuasiharmonicDebyeApprox constructor.

Parameters

volume (float) – in Ang^3

Returns

debye temperature in K

Return type

float

get_summary_dict()[source]

Returns a dict with a summary of the computed properties.

gruneisen_parameter(temperature, volume)[source]
Slater-gamma formulation(the default):
gruneisen paramter = - d log(theta)/ d log(V)

= - ( 1/6 + 0.5 d log(B)/ d log(V) ) = - (1/6 + 0.5 V/B dB/dV),

where dB/dV = d^2E/dV^2 + V * d^3E/dV^3

Mie-gruneisen formulation:

Eq(31) in doi.org/10.1016/j.comphy.2003.12.001 Eq(7) in Blanco et. al. Joumal of Molecular Structure (Theochem)

368 (1996) 245-255

Also se J.P. Poirier, Introduction to the Physics of the Earth’s

Interior, 2nd ed. (Cambridge University Press, Cambridge, 2000) Eq(3.53)

Parameters
  • temperature (float) – temperature in K

  • volume (float) – in Ang^3

Returns

unitless

Return type

float

optimize_gibbs_free_energy()[source]

Evaluate the gibbs free energy as a function of V, T and P i.e G(V, T, P), minimize G(V, T, P) wrt V for each T and store the optimum values.

Note: The data points for which the equation of state fitting fails

are skipped.

optimizer(temperature)[source]

Evaluate G(V, T, P) at the given temperature(and pressure) and minimize it wrt V.

  1. Compute the vibrational helmholtz free energy, A_vib.

  2. Compute the gibbs free energy as a function of volume, temperature

    and pressure, G(V,T,P).

  3. Preform an equation of state fit to get the functional form of

    gibbs free energy:G(V, T, P).

  4. Finally G(V, P, T) is minimized with respect to V.

Parameters

temperature (float) – temperature in K

Returns

G_opt(V_opt, T, P) in eV and V_opt in Ang^3.

Return type

float, float

thermal_conductivity(temperature, volume)[source]

Eq(17) in 10.1103/PhysRevB.90.174107

Parameters
  • temperature (float) – temperature in K

  • volume (float) – in Ang^3

Returns

thermal conductivity in W/K/m

Return type

float

vibrational_free_energy(temperature, volume)[source]

Vibrational Helmholtz free energy, A_vib(V, T). Eq(4) in doi.org/10.1016/j.comphy.2003.12.001

Parameters
  • temperature (float) – temperature in K

  • volume (float) –

Returns

vibrational free energy in eV

Return type

float

vibrational_internal_energy(temperature, volume)[source]

Vibrational internal energy, U_vib(V, T). Eq(4) in doi.org/10.1016/j.comphy.2003.12.001

Parameters
  • temperature (float) – temperature in K

  • volume (float) – in Ang^3

Returns

vibrational internal energy in eV

Return type

float