Where heat flows and where to change it: gauge-free sensitivity maps of thermal conductivity in disordered solids
Abstract
Designing materials for thermal management requires knowing where heat flows, not only how much. Within harmonic (Allen−−Feldman) theory we develop two local descriptions and test them on amorphous silicon. The first, a projection of the conductivity κ onto atoms, depends on how the potential energy is divided among atoms (a "gauge"); we find the dependence moderate, 23% of the map's spatial standard deviation at single sites and 9.5% over regions of radius 0.4 nm, apart from a uniform offset of 0.8% of κ. The second avoids the division altogether. It is the exact response of κ to the mass of each atom and the stiffness of each bond, it obeys an Euler sum rule, and it contains the heat-flow map as one of three exact terms. In amorphous and paracrystalline silicon, with ACE, GAP-18 and Keating force constants, the two maps are anti-correlated: where little heat flows a heavier atom lowers κ, and where much heat flows it tends to raise it. The explanation is local softness. The harmonic vibrational amplitude of each atom predicts both maps, and at room temperature the anti-correlation largely disappears at fixed amplitude, in a 32,768-atom replica as well; below about 100 K a component remains that softness does not capture. Thus soft regions, which carry little heat, act through the mixing of vibrational modes about 1−−2 meV apart. In paracrystalline silicon the grains conduct more heat per atom, while the disordered matrix controls the response. Exact recalculations show that the response map guides the placement of dispersed substituents and locates the region that limits transport across an amorphous/crystalline interface.
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BibTeX
@misc{drabold2026where,
title = {{Where heat flows and where to change it: gauge-free sensitivity maps of thermal conductivity in disordered solids}},
author = {D. A. Drabold and C. Ugwumadu},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.06958},
eprint = {2611.06958},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.06958},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Where heat flows and where to change it: gauge-free sensitivity maps of thermal conductivity in disordered solids
AU - D. A. Drabold
AU - C. Ugwumadu
PY - 2026
DA - 2026/11/03
PB - arXiv
DO - 10.48550/arxiv.2611.06958
UR - https://arxiv.org/abs/2611.06958
AB - Designing materials for thermal management requires knowing where heat flows, not only how much. Within harmonic (Allen−−Feldman) theory we develop two local descriptions and test them on amorphous silicon. The first, a projection of the conductivity κ onto atoms, depends on how the potential energy is divided among atoms (a "gauge"); we find the dependence moderate, 23% of the map's spatial standard deviation at single sites and 9.5% over regions of radius 0.4 nm, apart from a uniform offset of 0.8% of κ. The second avoids the division altogether. It is the exact response of κ to the mass of each atom and the stiffness of each bond, it obeys an Euler sum rule, and it contains the heat-flow map as one of three exact terms. In amorphous and paracrystalline silicon, with ACE, GAP-18 and Keating force constants, the two maps are anti-correlated: where little heat flows a heavier atom lowers κ, and where much heat flows it tends to raise it. The explanation is local softness. The harmonic vibrational amplitude of each atom predicts both maps, and at room temperature the anti-correlation largely disappears at fixed amplitude, in a 32,768-atom replica as well; below about 100 K a component remains that softness does not capture. Thus soft regions, which carry little heat, act through the mixing of vibrational modes about 1−−2 meV apart. In paracrystalline silicon the grains conduct more heat per atom, while the disordered matrix controls the response. Exact recalculations show that the response map guides the placement of dispersed substituents and locates the region that limits transport across an amorphous/crystalline interface.
ER -