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.