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:
objectQuasiharmonic approximation.
- Parameters:
energies (list) – list of DFT energies in eV
volumes (list) – list of volumes in Ang^3
structure (Structure) – pymatgen structure object
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
- gruneisen_parameter(temperature, volume)[source]
- Slater-gamma formulation(the default):
- gruneisen parameter = - 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.
Compute the vibrational Helmholtz free energy, A_vib.
- Compute the Gibbs free energy as a function of volume, temperature
and pressure, G(V,T,P).
- Perform an equation of state fit to get the functional form of
Gibbs free energy:G(V, T, P).
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