Mode-Resolved Bulk Data

The material underlying the structure is described by the following mode-resolved quantities:

Property [symbol]	Shape	Units
scattering_time [\(\tau]\)	\(N\)	s
heat_capacity [\(C]\)	\(N\)	Jm \(^{-3}\) K \(^{-1}\)
group_velocity [\(\mathbf{v}\)]	\(N\times 3\)	ms \(^{-1}\)

where \(N=N_q\times N_b\), with \(N_q\) and \(N_b\) being the number of wave-vectors and polarization, respectively. The bulk thermal conductivity tensor is given by

\[\kappa^{\alpha\beta}=\sum_\mu C_\mu \tau_\mu v_\mu^\alpha v_\mu^\beta.\]

The (specific) heat capacity is defined by

\[C_\mu = \frac{k_B}{N_q\mathcal{V}} \left[\frac{\eta_\mu}{\sinh(\eta_\mu)}\right]^2\]

with \(\eta_\mu = \hbar \omega_\mu/(2 k_b T)\). Note that the presence of \(N_q\) in the heat capacity is not standard but introduced here for convenience.

The material data is stored as a sqlite3 database (with .db extension), which can be conveniently handled by sqlitedict. With your material file, say foo.db, is in the current directory, you can load it with

from openbte import load_rta

rta_data = load_rta('foo',source='local')

The above code is nothing than a wrapper to the sqlite3’s loader. Note that there is also a minimal database of precomputed materials. Currently, it includes silicon at room temperature, computed with AlmaBTE.

from openbte import load_rta

rta_data = load_rta('Si_rta',source='database')

To save your own material data, you can also use a wrapper

import openbte.utils

#C = ...
#v   = ...
#tau = ...

utils.save('rta',{'scattering_time':tau,'heat_capacity':C,'group_velocity':v}

You can double-check the consistency of your data by comparing the resulting thermal conductivity with the expected one

import numpy as np
#C = ...
#v   = ...
#tau = ...
#kappa = ... #Expected thermal conductivity tensor

print(np.allclose(np.einsum('u,ui,uj,u->ij',C,v,v,tau)-kappa))