openmaterials.ai / codes / kALDo

kALDo: phonon transport in crystals and glasses from the same force constants

An anharmonic lattice dynamics code that solves the phonon Boltzmann equation for crystals and the quasi-harmonic Green-Kubo equations for disordered solids in one Python workflow.

What it is and how it works

One theory for order and disorder

Second and third order force constants feed both the Boltzmann equation, solved by RTA, iteration or inversion, and the quasi-harmonic Green-Kubo method for glasses and alloys beyond 1e4 atoms (Barbalinardo 2020).

Three BTE solvers

RTA, self-consistent iteration and direct inversion of the scattering matrix, quantum or classical statistics. RTA undershoots silicon by about 5% (Barbalinardo 2020).

QHGK for disordered solids

A real-space Green-Kubo sum over mode pairs with generalized velocities and lifetimes. It reduces to RTA in crystals and to Allen-Feldman with a fixed bandwidth.

Tensor algebra on GPU or CPU

The projection of the cubic potential on phonon modes runs as 2Nk(3N) tensor products of size (Nk 3N)^2, in NumPy and TensorFlow on CPU or GPU (Barbalinardo 2020).

Force constants from any code

Finite differences through any ASE calculator (DFT, tight binding, force fields), a native LAMMPS interface in USER-PHONON, or compressed-sensing fits from hiPhive.

Unfolding for large cells

When the cell exceeds twice the interaction range, kALDo computes forces inside the cell and unfolds them by periodic boundary conditions, cutting Nreplicas N atoms to N.

What people do with it

Convergence of kappa in a carbon nanotube

For a (10,0) nanotube the BTE gives 9960 W/m/K with quantum statistics and 3190 classical at 300 K. The longest mean free path is 6 mm, so kappa converges only past 1 mm (Barbalinardo 2021). Barbalinardo 2021

Diffuson coherence in amorphous silicon

In a 4096-atom Stillinger-Weber a-Si model, kALDo gave the QHGK conductivity set against a coherence model in which diffuson clusters propagate up to a micron (Zhang 2022). Zhang 2022

AlN-SiC interface seen by EELS

Vibrational EELS resolves a temperature drop within about 2 nm of the interface. kALDo on a NEP force calculator gave the phonon eigenvectors for the modal analysis of NEMD cells (Liu 2025). Liu 2025

How it is used

  1. Force constants

    ForceConstants(calculator=...): .second and .third by finite differences through ASE.

  2. Phonons

    Phonons(temperature=...): frequencies, velocities, phase space, bandwidths, heat capacity.

  3. Conductivity

    Conductivity(method='rta', 'inverse' or 'qhgk'): conductivity, mean_free_path.

  4. Modal analysis

    Cumulative kappa against frequency or mean free path, participation_ratio, diffusivity.