# Features

ShengBTE solves the full linearized Boltzmann transport equation for phonons using an iterative method. This goes far beyond the widely used relaxation-time approximation (RTA); the difference can be important in materials where "normal" (quasimomentum-conserving) three-phonon processes play a relevant role. By using inputs coming from ab-initio calculations, ShengBTE yields results with predictive power without the need for fitting to experiment.

Two kinds of system can currently be studied: bulk crystalline materials and nanowires thereof. The dominant phonon scattering mechanism in the former are three-phonon processes and isotopic disorder. Both are implemented in ShengBTE:

**Isotopic scattering**: Implemented using Tamura's formula. The projected vibrational density of states appearing in the formula is computed using a locally adaptive broadening algorithm.**Three-phonon processes**: Three-phonon scattering amplitudes are computed from a set of 3rd-order derivatives of the energy. A crucial point is enforcing conservation of energy so that only allowed processes are considered. In contrast with other approaches to the problem, in ShengBTE this problem is solved using a locally adaptive, parameter-free method.

As regards nanowires, an efficient and accurate approximation developed by some of the **authors** is implemented to solve the Boltzmann transport equation in the presence of boundaries.

Thanks to a general implementation of symmetries based on **spglib**, ShengBTE is able to deal with arbitrary three-dimensional lattices. Symmetry is used to dramatically reduce the complexity of the calculation.

In addition to the thermal conductivity tensor, ShengBTE outputs the following quantities:

Phonon frequencies at the sampled q-points.

Phonon group velocities.

Lattice specific heat.

Nanograined thermal-conductivity per unit mean free path.

Fraction of three-phonon processed allowed by conservation of energy, sometimes called three-phonon phase space.

Mode contributions to the three-phonon phase space.

Vibrational density of states: total and projected.

Per-mode contributions to the thermal conductivity.

Cumulative thermal conductivity: contribution to this quantity by phonons with mean free paths smaller than a threshold.

Scattering rates: total, RTA values, isotopic and anharmonic contributions.

Thermal conductivity of nanowires cut along arbitrary crystallographic directions of the bulk.

Total and mode Grüneisen parameters.

The number of 3rd-order derivatives of the energy needed to accurately describe three-phonon scattering can easily run into the hundreds of thousands. Their direct calculation using a real-space supercell approach can thus be prohibitively expensive. By harnessing the symmetries of the system, thirdorder.py can typically reduce the problem to a few hundreds of DFT runs. This means third-order calculations will still be the most computationally-expensive part of the process, but it becomes tractable for single compounds or even for moderately-sized libraries.

Both ShengBTE and thirdorder.py have user-friendly interfaces. The code needs to be compiled only once and parameters are provided through the command line or in configuration files. The packages are **fully documented**, and their **code** is available under the terms of the GPL.

See **the ShengBTE article** for the full details of the calculation and relevant references.