Smooth Disorder Library¶
Smooth Disorder is a Python library that smoothly explains influence of structural disorder on the smoothness of vibrational density of states and interprets it in terms of disorder linewidth that decomposes diffusivity into propagation velocity and mean free path.
The library introduces three main functionalities:
calculation of Allen-Feldman (AF) conductivity and diffusivity starting from a structure’s unit cell and second order force constants,
computation of Bond-Network Entropy (BNE), which is a descriptor of disorder for network solids,
fitting of Disorder Linewidth (DL), which is a measure of scattering due to disorder and allows decomposition of diffusivity in disordered materials.
All together, these form complementary tools for connecting structural disorder to thermal transport:
Allen-Feldman conductivity is a standard expression for thermal conductivity and diffusivity for harmonic disordered solids based on atomic structure and interactions between atoms. The other tools in the library allow for more in-depth understanding of its predictions and how they depend on the degree of disorder.
Bond-Network Entropy classifies local atomic environments using H1 persistent homology barcodes and summarises their distribution with a single Shannon entropy value. Higher BNE means greater heterogeneity — more disorder.
Disorder Linewidth connects structural disorder to phonon linewidths and thermal transport. It models how disorder broadens the vibrational density of states (VDOS) via a Lorentzian spectral function ansatz, fits two physical parameters — grain-boundary size L and defect-scattering amplitude R — to the disordered VDOS using PyTorch autodiff (L-BFGS), and decomposes thermal diffusivity into propagation velocity and mean free path.
The concepts of BNE and DL relate the atomic structure to the conductivity via a set of physical relations, for more information see the package’s corresponding paper.
Warning
We encourage users to first go through the tutorials that explain the theory behind concepts used and quantities calculated by this code. If the users are interested only in executing the code, then workflows are provided that calculate both BNE and DL, use at your own risk.
Corresponding Paper: K. Iwanowski, G. Csányi, and M. Simoncelli, Physical Review X 15, 041041 (2025) — DOI: 10.1103/w4p6-b9mp
Library Authors: Kamil Iwanowski, Michele Simoncelli (Columbia University)
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Background Theory
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