- Open Access
Microscopic Mechanisms of Low Lattice Thermal Conductivity in Alloys Revealed by Neuroevolution Machine-Learning Potential
PRX Energy 5, 023013 – Published 18 June, 2026
DOI: https://doi.org/10.1103/df1n-9bll
Abstract
Understanding thermal transport in alloys is critical for the reliable thermal management of high-power electronic devices. However, theoretical predictions of lattice thermal conductivity based on the traditional Abele’s virtual crystal approximation (VCA) significantly deviate from experimental measurements, and these discrepancies have long been attributed to finite-size effects. Unlike the traditional VCA, which homogenizes atomic masses and bonding environments, we explicitly incorporate both mass disorder and interatomic force constant (IFC) disorder by directly performing Boltzmann transport equation calculations on large special quasirandom structures, aiming to uncover their impact on lattice thermal transport. Our results show that mass disorder plays a dominant role in suppressing by significantly enhancing the anharmonic scattering of low-frequency phonons, whereas the heat-carrying capacity of high-frequency phonons is completely eliminated due to substantially reduced group velocities and strong harmonic scattering. In comparison, IFC disorder mainly increases anharmonic scattering rates but has negligible influence on the group velocities of low-frequency phonons. When both disorder types are accounted for, the predicted thermal conductivities align closely with experimental observations. This indicates that the previously reported overestimations from VCA are not due to finite-size effects. We also find that the alloy scattering model based on perturbation theory significantly overestimates the harmonic scattering rates of high-frequency phonons, despite their negligible contribution to thermal conductivity. These findings highlight the necessity of atomistic disorder modeling in wide-bandgap alloys and provide critical insights for thermal design in -based electronics.
Physics Subject Headings (PhySH)
Popular Summary
Understanding the thermal transport of alloys is critical for the thermal management of high-power electronic devices. However, predictions based on the virtual crystal approximation deviate from experiments, with discrepancies long attributed to finite-size effects. In this work, the authors resolved this discrepancy by explicitly incorporating both mass disorder and interatomic force-constant (IFC) disorder into phonon transport calculations, enabling accurate thermal-conductivity predictions in close agreement with experiments. These results show that mass disorder dominates the suppression of lattice thermal conductivity by enhancing anharmonic scattering of low-frequency phonons and eliminating high-frequency contributions through reduced group velocities and strong harmonic scattering. In comparison, IFC disorder mainly increases anharmonic scattering but has little influence on low-frequency group velocities. This work clarifies the microscopic origin of low thermal conductivity in alloys and introduces a quantitative, transferable methodology for systematically separating and combining mass and IFC disorder, advancing phonon-transport studies in disordered systems.
Article Text
Supplemental Material
References (81)
- J. Piprek, Ultra-violet light-emitting diodes with quasi acceptor-free polarization doping, Opt. Quantum Electron. 44, 67 (2012).
- C.-P. Wang and Y.-R. Wu, Study of optical anisotropy in nonpolar and semipolar quantum well deep ultraviolet light emission diode, J. Appl. Phys. 112, 033104 (2012).
- I. Omura, W. Saito, T. Domon, and K. Tsuda, Gallium Nitride power HEMT for high switching frequency power electronics, in 2007 International Workshop on Physics of Semiconductor Devices (2007), p. 781.
- A. S. A. Fletcher and D. Nirmal, A survey of gallium nitride HEMT for RF and high power applications, Superlattices. Microstruct. 109, 519 (2017).
- J. Zhang and N. Tansu, Engineering of -Delta- quantum-well gain media for mid- and deep-ultraviolet lasers, IEEE Photonics J. 5, 2600209 (2013).
- S. Ali and M. Usman, Performance enhancement of ultraviolet-C laser diode, Eur. Phys. J. Plus 137, 771 (2022).
- A. G. Baca, A. M. Armstrong, B. A. Klein, A. A. Allerman, E. A. Douglas, and R. J. Kaplar, -rich based transistors, J. Vac. Sci. Technol. A 38, 020803 (2020).
- D. Q. Tran, R. D. Carrascon, M. Iwaya, B. Monemar, V. Darakchieva, and P. P. Paskov, Thermal conductivity of () epitaxial layers, Phys. Rev. Mater. 6, 104602 (2022).
- T.-L. Luo, Y.-F. Ding, B.-J. Wei, J.-Y. Du, X.-Y. Shen, G.-M. Zhu, and B.-W. Li, Phononic thermal conduction and thermal regulation in low-dimensional micro-nano scale systems: Nonequilibrium statistical physics problems from chip heat dissipation, Acta Phys. Sin. 72, 234401 (2023).
- Z. Qi, W. Shen, R. Li, X. Sun, L. Li, Q. Wang, G. Wu, and K. Liang, /diamond interface nanoengineering for reducing thermal boundary resistance by molecular dynamics simulations, Appl. Surf. Sci. 615, 156419 (2023).
- A. Chen, D. Wei, J. Xu, A. Li, H. Wang, Z. Qin, and G. Qin, Alloying reversed anisotropy of thermal transport in bulk , J. Phys. Chem. Lett. 14, 9746 (2023).
- W. Liu and A. A. Balandin, Temperature dependence of thermal conductivity of thin films measured by the differential technique, Appl. Phys. Lett. 85, 5230 (2004).
- W. Liu and A. A. Balandin, Thermal conduction in alloys and thin films, J. Appl. Phys. 97, 073710 (2005).
- D. Q. Tran, R. Delgado-Carrascon, J. F. Muth, T. Paskova, M. Nawaz, V. Darakchieva, and P. P. Paskov, Phonon-boundary scattering and thermal transport in : Effect of layer thickness, Appl. Phys. Lett. 117, 252102 (2020).
- D. G. Cahill, Thermal conductivity measurement from 30 to 750 K: The method, Rev. Sci. Instrum. 61, 802 (1990).
- J. Ma, W. Li, and X. Luo, Intrinsic thermal conductivities and size effect of alloys of wurtzite , , and from first-principles, J. Appl. Phys. 119, 125702 (2016).
- B. Abeles, Lattice thermal conductivity of disordered semiconductor alloys at high temperatures, Phys. Rev. 131, 1906 (1963).
- J. Garg, N. Bonini, B. Kozinsky, and N. Marzari, Role of disorder and anharmonicity in the thermal conductivity of silicon-germanium alloys: A first-principles study, Phys. Rev. Lett. 106, 045901 (2011).
- T. Dao-Sheng, H. Yu-Chao, Z. Yan-Guang, and C. Bing-Yang, Thermal conductivity modeling of films, Acta Phys. Sin. 70, 045101 (2021).
- G. Yang, Y.-B. Liu, L. Yang, and B.-Y. Cao, Machine-learned atomic cluster expansion potentials for fast and quantum-accurate thermal simulations of wurtzite , J. Appl. Phys. 135, 085105 (2024).
- A. Ward, D. A. Broido, D. A. Stewart, and G. Deinzer, Ab initio theory of the lattice thermal conductivity in diamond, Phys. Rev. B 80, 125203 (2009).
- R. Drautz, Atomic cluster expansion for accurate and transferable interatomic potentials, Phys. Rev. B 99, 014104 (2019).
- Z. Fan, Y. Wang, P. Ying, K. Song, J. Wang, Y. Wang, Z. Zeng, K. Xu, E. Lindgren, J. M. Rahm, A. J. Gabourie, J. Liu, H. Dong, J. Wu, Y. Chen, Z. Zhong, J. Sun, P. Erhart, Y. Su, and T. Ala-Nissila, GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations, J. Chem. Phys. 157, 114801 (2022).
- Z. Fan, Z. Zeng, C. Zhang, Y. Wang, K. Song, H. Dong, Y. Chen, and T. Ala-Nissila, Neuroevolution machine learning potentials: Combining high accuracy and low cost in atomistic simulations and application to heat transport, Phys. Rev. B 104, 104309 (2021).
- Z. Fan, Improving the accuracy of the neuroevolution machine learning potential for multi-component systems, J. Phys.: Condens. Matter 34, 125902 (2022).
- L. Dai, M. Li, and Y. Hu, Machine learning for thermal transport and phonon high-order anharmonicity in high thermal conductivity materials: A case study in boron arsenide, Phys. Rev. Mater. 9, 045403 (2025).
- I. S. Novikov, K. Gubaev, E. V. Podryabinkin, and A. V. Shapeev, The MLIP package: Moment tensor potentials with MPI and active learning, Mach. Learn.: Sci. Technol. 2, 025002 (2021).
- J. Tiwari and T. Feng, Accurate prediction of thermal conductivity of at ultrahigh temperatures, Phys. Rev. B 109, 075201 (2024).
- L. Zhang, J. Han, H. Wang, R. Car, and W. E, Deep potential molecular dynamics: A scalable model with the accuracy of quantum mechanics, Phys. Rev. Lett. 120, 143001 (2018).
- H. Dong, Z. Li, B. Sun, Y. Zhou, L. Liu, and J.-Y. Yang, Thermal transport in disordered wurtzite alloys using machine learning interatomic potentials, Mater. Today Commun. 39, 109213 (2024).
- Z. Sun, X. Sun, Z. Qi, Q. Wang, R. Li, L. Li, G. Wu, W. Shen, and S. Liu, Investigating thermal transport across the /diamond interface via the machine learning potential, Diamond Relat. Mater. 147, 111303 (2024).
- K. Song et al., General-purpose machine-learned potential for 16 elemental metals and their alloys, Nat. Commun. 15, 10208 (2024).
- G. Kresse and J. Furthmüller, Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set, Phys. Rev. B 54, 11169 (1996).
- P. E. Blöchl, Projector augmented-wave method, Phys. Rev. B 50, 17953 (1994).
- G. Kresse and D. Joubert, From ultrasoft pseudopotentials to the projector augmented-wave method, Phys. Rev. B 59, 1758 (1999).
- J. P. Perdew, K. Burke, and M. Ernzerhof, Generalized gradient approximation made simple, Phys. Rev. Lett. 77, 3865 (1996).
- H. J. Monkhorst and J. D. Pack, Special points for Brillouin-zone integrations, Phys. Rev. B 13, 5188 (1976).
- X. Z. Shi, C. Y. He, C. J. Pickard, C. Tang, and J. X. Zhong, Stochastic generation of complex crystal structures combining group and graph theory with application to carbon, Phys. Rev. B 97, 014104 (2018).
- A. Jain, S. P. Ong, G. Hautier, W. Chen, W. D. Richards, S. Dacek, S. Cholia, D. Gunter, D. Skinner, G. Ceder, and K. A. Persson, Commentary: The Materials Project: A materials genome approach to accelerating materials innovation, APL Mater. 1, 011002 (2013).
- W. Li, J. Carrete, N. A. Katcho, and N. Mingo, ShengBTE: A solver of the Boltzmann transport equation for phonons, Comput. Phys. Commun. 185, 1747 (2014).
- Z. Han, X. Yang, W. Li, T. Feng, and X. Ruan, FourPhonon: An extension module to ShengBTE for computing four-phonon scattering rates and thermal conductivity, Comput. Phys. Commun. 270, 108179 (2022).
- S. Grimme, J. Antony, S. Ehrlich, and H. Krieg, A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu, J. Chem. Phys. 132, 154104 (2010).
- S. Grimme, S. Ehrlich, and L. Goerigk, Effect of the damping function in dispersion corrected density functional theory, J. Comput. Chem. 32, 1456 (2011).
- A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015).
- A. Sztein, J. Haberstroh, J. E. Bowers, S. P. DenBaars, and S. Nakamura, Calculated thermoelectric properties of , , and , J. Appl. Phys. 113, 183707 (2013).
- A. Zunger, S. H. Wei, L. G. Ferreira, and J. E. Bernard, Special quasirandom structures, Phys. Rev. Lett. 65, 353 (1990).
- M. Ångqvist, W. A. Muñoz, J. M. Rahm, E. Fransson, C. Durniak, P. Rozyczko, T. H. Rod, and P. Erhart, ICET – A Python library for constructing and sampling alloy cluster expansions, Adv. Theory Simul. 2, 1900015 (2019).
- See Supplemental Material at http://link.aps.org/supplemental/10.1103/df1n-9bll for additional results and validations, including convergence tests of lattice thermal conductivity with respect to -point sampling, supercell size, and the sampling method; validation of the NEP model against DFT for crystalline phases, heterostructures, and out-of-sample alloy compositions; representative SQS configurations of alloys used in this work; and a comparison of anharmonic scattering rates of the alloy at different temperatures.
- W. Li, L. Lindsay, D. A. Broido, D. A. Stewart, and N. Mingo, Thermal conductivity of bulk and nanowire alloys from first principles, Phys. Rev. B 86, 174307 (2012).
- S.-I. Tamura, Isotope scattering of dispersive phonons in , Phys. Rev. B 27, 858 (1983).
- A. Katre, J. Carrete, B. Dongre, G. K. H. Madsen, and N. Mingo, Exceptionally strong phonon scattering by B substitution in cubic , Phys. Rev. Lett. 119, 075902 (2017).
- Z. Fan, H. Dong, A. Harju, and T. Ala-Nissila, Homogeneous nonequilibrium molecular dynamics method for heat transport and spectral decomposition with many-body potentials, Phys. Rev. B 99, 064308 (2019).
- D. J. Evans, Homogeneous nemd algorithm for thermal conductivity—Application of non-canonical linear response theory, Phys. Lett. A 91, 457 (1982).
- K. K. Mandadapu, R. E. Jones, and P. Papadopoulos, A homogeneous nonequilibrium molecular dynamics method for calculating thermal conductivity with a three-body potential, J. Chem. Phys. 130, 204106 (2009).
- T. Ruf, J. Serrano, M. Cardona, P. Pavone, M. Pabst, M. Krisch, M. D’Astuto, T. Suski, I. Grzegory, and M. Leszczynski, Phonon dispersion curves in wurtzite-structure determined by inelastic X-ray scattering, Phys. Rev. Lett. 86, 906 (2001).
- M. Schwoerer-Böhning, A. T. Macrander, M. Pabst, and P. Pavone, Phonons in wurtzite aluminum nitride, Phys. Status Solidi (b) 215, 177 (1999).
- J. M. Zhang, T. Ruf, M. Cardona, O. Ambacher, M. Stutzmann, J. M. Wagner, and F. Bechstedt, Raman spectra of isotopic , Phys. Rev. B 56, 14399 (1997).
- Z. Cheng, Y. R. Koh, A. Mamun, J. Shi, T. Bai, K. Huynh, L. Yates, Z. Liu, R. Li, E. Lee, M. E. Liao, Y. Wang, H. M. Yu, M. Kushimoto, T. Luo, M. S. Goorsky, P. E. Hopkins, H. Amano, A. Khan, and S. Graham, Experimental observation of high intrinsic thermal conductivity of , Phys. Rev. Mater. 4, 044602 (2020).
- A. V. Inyushkin, A. N. Taldenkov, D. A. Chernodubov, E. N. Mokhov, S. S. Nagalyuk, V. G. Ralchenko, and A. A. Khomich, On the thermal conductivity of single crystal , J. Appl. Phys. 127, 205109 (2020).
- L. Lindsay, D. A. Broido, and T. L. Reinecke, Thermal conductivity and large isotope effect in from first principles, Phys. Rev. Lett. 109, 095901 (2012).
- G. A. Slack, R. A. Tanzilli, R. O. Pohl, and J. W. Vandersande, The intrinsic thermal conductivity of , J. Phys. Chem. Solids 48, 641 (1987).
- Q. Zheng, C. Li, A. Rai, J. H. Leach, D. A. Broido, and D. G. Cahill, Thermal conductivity of , , and from 150 K to 850 K, Phys. Rev. Mater. 3, 014601 (2019).
- H. Shibata, Y. Waseda, H. Ohta, K. Kiyomi, K. Shimoyama, K. Fujito, H. Nagaoka, Y. Kagamitani, R. Simura, and T. Fukuda, High thermal conductivity of gallium nitride () crystals grown by HVPE process, Mater. Trans. 48, 2782 (2007).
- L. Lindsay, D. A. Broido, and T. L. Reinecke, Ab initio thermal transport in compound semiconductors, Phys. Rev. B 87, 165201 (2013).
- W. Li and N. Mingo, Thermal conductivity of bulk and nanowire , , and polymorphs from first principles, J. Appl. Phys. 114, 183505 (2013).
- R. Wu, R. Hu, and X. Luo, First-principle-based full-dispersion Monte Carlo simulation of the anisotropic phonon transport in the wurtzite thin film, J. Appl. Phys. 119, 145706 (2016).
- J. Garg, T. Luo, and G. Chen, Spectral concentration of thermal conductivity in —A first-principles study, Appl. Phys. Lett. 112, 252101 (2018).
- B. C. Daly, H. J. Maris, A. V. Nurmikko, M. Kuball, and J. Han, Optical pump-and-probe measurement of the thermal conductivity of nitride thin films, J. Appl. Phys. 92, 3820 (2002).
- A. Filatova-Zalewska, Z. Litwicki, T. Suski, and A. Jeżowski, Thermal conductivity of thin films of gallium nitride, doped with aluminium, measured with method, Solid State Sci. 101, 106105 (2020).
- P. F. de Aguiar, B. Bourguignon, M. S. Khots, D. L. Massart, and R. Phan-Than-Luu, D-optimal designs, Chemometr. Intell. Lab. Syst. 30, 199 (1995).
- E. Podryabinkin, K. Garifullin, A. Shapeev, and I. Novikov, MLIP-3: Active learning on atomic environments with moment tensor potentials, J. Chem. Phys. 159, 084112 (2023).
- S. A. Goreinov, I. V. Oseledets, D. V. Savostyanov, E. E. Tyrtyshnikov, and N. L. Zamarashkin, How to find a good submatrix, in Matrix Methods: Theory, Algorithms and Applications (World Scientific, Singapore, 2010), p. 247.
- https://github.com/psn417/nep_extrapolation.
- L. Zhang, H. Yan, G. Zhu, S. Liu, Z. Gan, and Z. Zhang, Effect of substrate surface on deposition of : A molecular dynamics simulation, Crystals 8, 279 (2018).
- D.-S. Tang and B.-Y. Cao, Phonon thermal transport and its tunability in for near-junction thermal management of electronics: A review, Int. J. Heat Mass Transf. 200, 123497 (2023).
- A. Katre, J. Carrete, B. Dongre, G. K. H. Madsen, and N. Mingo, Exceptionally strong phonon scattering by B substitution in cubic , Phys. Rev. Lett. 119, 075902 (2017).
- G. Pang, F. Meng, Y. Chen, A. Katre, J. Carrete, B. Dongre, G. K. Madsen, N. Mingo, and W. Li, Thermal conductivity reduction in highly-doped cubic by phonon-defect and phonon-electron scattering, Mater. Today Phys. 41, 101346 (2024).
- A. Kundu, N. Mingo, D. A. Broido, and D. A. Stewart, Role of light and heavy embedded nanoparticles on the thermal conductivity of alloys, Phys. Rev. B 84, 125426 (2011).
- H. Wu, Z. Qin, S. Li, L. Lindsay, and Y. Hu, Nonperturbative determination of isotope-induced anomalous vibrational physics, Phys. Rev. B 108, L140302 (2023).
- M. Li, K. Pan, Y. Ge, K. Huynh, M. S. Goorsky, T. S. Fisher, and Y. Hu, Wafer-scale bonded – with high interface thermal conductance, Appl. Phys. Lett. 125, 032104 (2024).
- E. Fransson, M. Slabanja, P. Erhart, and G. Wahnström, Dynasor—A tool for extracting dynamical structure factors and current correlation functions from molecular dynamics simulations, Adv. Theory Simul. 4, 2000240 (2021).
