Phonons API Reference¶

Building the phonons object is the intermediate step between finishing your Finite Difference object, and initializing the Conductivity object.

Attributes¶

class kaldo.phonons.Phonons(**kwargs)[source]¶

The Phonons object exposes all the phononic properties of a system. It’s can be fed into a Conductivity object and must be built with a ForceConstant object.

Parameters:

forceconstants (ForceConstants) – contains all the information about the system and the derivatives of the potential.
is_classic (bool) – specifies if the system is classic, $True$ or quantum, $False$ Default is $False$
kpts – defines the number of k points to use to create the k mesh Default is (1, 1, 1)
temperature (float) – defines the temperature of the simulation. Units: K.
min_frequency (float, optional) – ignores all phonons with frequency below $min_frequency$ THz, Default is $None$
max_frequency (float, optional) – ignores all phonons with frequency above $max_frequency$ THz Default is $None$
third_bandwidth (float, optional) – Defines the width of the energy conservation smearing in the phonons scattering calculation. If $None$ the width is calculated dynamically. Otherwise the input value corresponds to the width. Units: THz.
broadening_shape (string, optional) – Defines the algorithm to use for the broadening of the conservation of the energy for third irder interactions. Available broadenings are $gauss$ , $lorentz$ and $triangle$ . Default is $gauss$ .
folder (string, optional) – Specifies where to store the data files. Default is $output$ .
storage ( $default$ , $formatted$ , $numpy$ , $memory$ , $hdf5$ , optional) – Defines the storing strategy used to store the observables. The $default$ strategy stores formatted output and numpy arrays. $memory$ storage doesn’t generate any output.
grid_type ('F' or 'C, optional) – Specify if to use ‘C” style atoms replica grid of fortran style ‘F’, Default ‘C’
is_balanced (Enforce detailed balance when calculating anharmonic properties,) – Default: False

Return type:

Phonons Object

Attributes:

bandwidth: Calculate the phonons bandwidth, the inverse of the lifetime, for each k point in k_points and each mode.
eigenvalues: Calculates the eigenvalues of the dynamical matrix in Thz^2.
eigenvectors: Calculates the eigenvectors of the dynamical matrix.
frequency: Calculate phonons frequency
heat_capacity: Calculate the heat capacity for each k point in k_points and each mode.
heat_capacity_2d: Calculate the generalized 2d heat capacity for each k point in k_points and each mode.
omega: Calculates the angular frequencies from the diagonalized dynamical matrix.
participation_ratio: Calculates the participation ratio of each normal mode.
phase_space: Calculate the 3-phonons-processes phase_space, for each k point in k_points and each mode.
physical_mode: Calculate physical modes.
population: Calculate the phonons population for each k point in k_points and each mode.
velocity: Calculates the velocity using Hellmann-Feynman theorem.

property bandwidth¶

Calculate the phonons bandwidth, the inverse of the lifetime, for each k point in k_points and each mode.

Returns:: bandwidth – bandwidth for each k point and each mode
Return type:: np.array(n_k_points, n_modes)

property eigenvalues¶

Calculates the eigenvalues of the dynamical matrix in Thz^2.

Returns:: eigenvalues – (n_phonons) Eigenvalues of the dynamical matrix
Return type:: np array

property eigenvectors¶

Calculates the eigenvectors of the dynamical matrix.

Returns:: eigenvectors – (n_phonons, n_phonons) Eigenvectors of the dynamical matrix
Return type:: np array

property frequency¶: Calculate phonons frequency :returns: frequency – (n_k_points, n_modes) frequency in THz :rtype: np array

property heat_capacity¶

Calculate the heat capacity for each k point in k_points and each mode. If classical, it returns the Boltzmann constant in J/K. If quantum it returns the derivative of the Bose-Einstein weighted by each phonons energy. .. math:

c_\mu = k_B \frac{\nu_\mu^2}{ \tilde T^2} n_\mu (n_\mu + 1)

where the frequency $\nu$ and the temperature $\tilde T$ are in THz.

Returns:: c_v – heat capacity in J/K for each k point and each mode
Return type:: np.array(n_k_points, n_modes)

property heat_capacity_2d¶

Calculate the generalized 2d heat capacity for each k point in k_points and each mode. If classical, it returns the Boltzmann constant in W/m/K.

Returns:: heat_capacity_2d – heat capacity in W/m/K for each k point and each modes couple.
Return type:: np.array(n_k_points, n_modes, n_modes)

property omega¶

Calculates the angular frequencies from the diagonalized dynamical matrix.

Returns:: frequency – (n_k_points, n_modes) frequency in rad
Return type:: np array

property participation_ratio¶: Calculates the participation ratio of each normal mode. Participation ratio’s represent the fraction of atoms that are displaced meaning a value of 1 corresponds to translation. Defined by equations in DOI: 10.1103/PhysRevB.53.11469 :returns: participation_ratio – (n_k_points, n_modes) atomic participation :rtype: np array

property phase_space¶

Calculate the 3-phonons-processes phase_space, for each k point in k_points and each mode.

Returns:: phase_space – phase_space for each k point and each mode
Return type:: np.array(n_k_points, n_modes)

property physical_mode¶: Calculate physical modes. Non physical modes are the first 3 modes of q=(0, 0, 0) and, if defined, all the modes outside the frequency range min_frequency and max_frequency. :returns: physical_mode – (n_k_points, n_modes) bool :rtype: np array

property population¶

Calculate the phonons population for each k point in k_points and each mode. If classical, it returns the temperature divided by each frequency, using equipartition theorem. If quantum it returns the Bose-Einstein distribution

Returns:: population – population for each k point and each mode
Return type:: np.array(n_k_points, n_modes)

property velocity¶

Calculates the velocity using Hellmann-Feynman theorem.

Returns:: velocity – (n_k_points, n_unit_cell * 3, 3) velocity in 100m/s or A/ps
Return type:: np array