Conductivity¶

The conductivity class is used to calculate the thermal conductivity in one of the four frameworks outline in the theory portion. When building a conductivity class object, be sure to include a phonon object and select a framework for calculation.

API Reference¶

class kaldo.conductivity.Conductivity(phonons: Phonons, *, method: str = 'rta', diffusivity_bandwidth: float | None = None, diffusivity_threshold: float | None = None, diffusivity_shape: str = 'lorentz', is_diffusivity_including_antiresonant: bool = False, tolerance: int | None = None, n_iterations: int | None = None, length: tuple[int, int, int] = (None, None, None), finite_length_method: str = 'ms', storage: str = 'formatted', **kwargs)[source]¶

The conductivity object is responsible for mean free path and conductivity calculations. It takes a phonons object as a required argument.

Parameters:¶

phonons : Phonons¶

Contains all the information about the calculated phononic properties of the system

method : 'rta', 'sc', 'qhgk', 'inverse'¶

Specifies the method used to calculate the conductivity. 'rta' is relaxation time approximation; 'sc' is self-consistent; 'qhgk' is Quasi-Harmonic Green Kubo; 'inverse' is inversion of the scattering matrix for mean free path.

diffusivity_bandwidth : float, optional¶

(QHGK) Specifies the bandwidth to use in the calculation of the flux operator in the Allen-Feldman model of the thermal conductivity in amorphous systems. Units: rad/ps

diffusivity_threshold : float, optional¶

(QHGK) This option is off by default. In such case the flux operator in the QHGK and AF models is calculated

diffusivity_shape : string, optional¶

(QHGK) Defines the algorithm to use to calculate the diffusivity. Available broadenings are 'gauss', 'lorentz' and 'triangle'. Default is 'lorentz'.

is_diffusivity_including_antiresonant : bool, optional¶

(QHGK) Defines if you want to include or not anti-resonant terms in diffusivity calculations. Default is False.

tolerance : int¶

(Self-consistent) In the self consistent conductivity calculation, it specifies the difference in W/m/K between n and n+1 step, to set as exit/convergence condition.

n_iterations : int¶

(Self-consistent) Specifies the max number of iterations to set as exit condition in the self consistent conductivity calculation

length: tuple[int, int, int] = (None, None, None)¶

(Finite Size) Specifies the length to use in x, y, z to calculate the finite size conductivity. 0 or None values corresponds to the infinity length limit.

finite_length_method : 'ms', 'ballistic'¶

(Finite Size) Specifies how to calculate the finite size conductivity. ‘ms’ is the Mckelvey-Schockley method. ‘ballistic’ is the ballistic limit.

storage : 'formatted', 'hdf5', 'numpy', 'memory', optional¶

Defines the type of storage used for the simulation. Default is 'formatted'

Returns:¶

An instance of the Conductivity class.

Return type:¶

Conductivity

Examples

Here’s an example to calculate the inverse conductivity on the phonons object and tracing over the phonons modes

` Conductivity(phonons=phonons, method='inverse', storage='memory').conductivity.sum(axis=0)) `

property conductivity : Any¶

Calculate the thermal conductivity per mode in W/m/K

Returns:¶

conductivity – (n_k_points, n_modes, 3, 3) float

Return type:¶

np array

property mean_free_path : Any¶

Calculate the mean_free_path per mode in A

Returns:¶

mfp – (n_k_points, n_modes) float

Return type:¶

np array

property diffusivity¶

Calculate the diffusivity, for each k point in k_points and each mode.

Returns:¶

diffusivity – diffusivity in mm^2/s

Return type:¶

np.array(n_k_points, n_modes)

calculate_scattering_matrix(is_including_diagonal, is_rescaling_omega, is_rescaling_population)[source]¶

Calculate the scattering matrix for phonons.

calculate_mfp_inverse()[source]¶

This method calculates the inverse of the mean free path for each phonon. The matrix returns k vectors for each mode and has units of inverse Angstroms.

Returns:¶

lambda – (n_k_points, n_modes)

Return type:¶

np array

calculate_conductivity_full(is_using_gamma_tensor_evects=False)[source]¶

This calculates the conductivity using the full solution of the space-dependent Boltzmann Transport Equation.

Returns:¶

conductivity_per_mode – (n_k_points, n_modes, 3)

Return type:¶

np array