Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Anomalous thermal transport under high pressure in boron arsenide

Abstract

High pressure represents extreme environments and provides opportunities for materials discovery1,2,3,4,5,6,7,8. Thermal transport under high hydrostatic pressure has been investigated for more than 100 years and all measurements of crystals so far have indicated a monotonically increasing lattice thermal conductivity. Here we report in situ thermal transport measurements in the newly discovered semiconductor crystal boron arsenide, and observe an anomalous pressure dependence of the thermal conductivity. We use ultrafast optics, Raman spectroscopy and inelastic X-ray scattering measurements to examine the phonon bandstructure evolution of the optical and acoustic branches, as well as thermal conductivity under varied temperatures and pressures up to 32 gigapascals. Using atomistic theory, we attribute the anomalous high-pressure behaviour to competitive heat conduction channels from interactive high-order anharmonicity physics inherent to the unique phonon bandstructure. Our study verifies ab initio theory calculations and we show that the phonon dynamics—resulting from competing three-phonon and four-phonon scattering processes—are beyond those expected from classical models and seen in common materials. This work uses high-pressure spectroscopy combined with atomistic theory as a powerful approach to probe complex phonon physics and provide fundamental insights for understanding microscopic energy transport in materials of extreme properties.

This is a preview of subscription content, access via your institution

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Fig. 1: Anomalous thermal conductivity of BAs under high pressure compared to literature studies.
Fig. 2: Experimental set-up for in situ ultrafast optical measurements under high pressure.
Fig. 3: Experimental measurements and ab initio calculations for the pressure-dependent phonon bandstructure evolution.
Fig. 4: Experimental measurements and ab initio theory for phonon dispersion and thermal conductivity as a function of pressure and temperature.

Data availability

The data that support the plots within this paper and findings of this study are available from the corresponding author upon request.

References

  1. Zhang, L., Wang, Y., Lv, J. & Ma, Y. Materials discovery at high pressures. Nat. Rev. Mater. 2, 17005 (2017).

    ADS  CAS  Google Scholar 

  2. Konôpková, Z., McWilliams, R. S., Gómez-Pérez, N. & Goncharov, A. F. Direct measurement of thermal conductivity in solid iron at planetary core conditions. Nature 534, 99–101 (2016).

    ADS  PubMed  Google Scholar 

  3. Knudson, M. D. et al. Direct observation of an abrupt insulator-to-metal transition in dense liquid deuterium. Science 348, 1455–1460 (2015).

    ADS  CAS  PubMed  Google Scholar 

  4. Pozzo, M., Davies, C., Gubbins, D. & Alfe, D. Thermal and electrical conductivity of iron at Earth’s core conditions. Nature 485, 355–358 (2012).

    ADS  CAS  PubMed  Google Scholar 

  5. Ma, Y. et al. Transparent dense sodium. Nature 458, 182–185 (2009).

    ADS  CAS  PubMed  Google Scholar 

  6. Dubrovinsky, L. et al. The most incompressible metal osmium at static pressures above 750 gigapascals. Nature 525, 226–229 (2015).

    ADS  CAS  PubMed  Google Scholar 

  7. Loubeyre, P., Occelli, F. & Dumas, P. Synchrotron infrared spectroscopic evidence of the probable transition to metal hydrogen. Nature 577, 631–635 (2020).

    ADS  CAS  PubMed  Google Scholar 

  8. Fratanduono, D. E. et al. Establishing gold and platinum standards to 1 terapascal using shockless compression. Science 372, 1063–1068 (2021).

    ADS  CAS  PubMed  Google Scholar 

  9. Bridgman, P. W. The Physics of High Pressure (MacMillan, 1931).

  10. Lawson, A. On the high temperature heat conductivity of insulators. J. Phys. Chem. Solids 3, 155–156 (1957).

    ADS  Google Scholar 

  11. Rodionov, K. P. Problem of the effect of hydrostatic pressure on the thermal conductivity of insulators. Phys. Met. Metallogr. 6, 160–164 (1958).

    Google Scholar 

  12. Klemens, K. P. Pressure dependence of the thermal conductivity of non-metals. In Proc. Ninth Conf. Thermal Conductivity 533–534 (United States Atomic Energy Commission, 1969).

  13. Slack, G. A. In Proc. Int Conf. Phonon Scattering in Solids 24 (Centre d’Etudes Nucleaires de Saclay, 1972).

  14. Ziman, J. M. Electrons and Phonons: The Theory of Transport Phenomena in Solids (Oxford Univ. Press, 1960).

  15. Leibfried, G. & Schlömann, E. Thermal conductivity of dielectric solids by a variational technique. Nachr. Akad. Wiss. Gött. Math.-Phys. Kl. 2A 23, 1366–1370 (1954).

  16. Anderson, O. L. The Debye temperature of vitreous silica. J. Phys. Chem. Solids 12, 41–52 (1959).

    ADS  CAS  Google Scholar 

  17. Steigmeier, E. F. & Kudman, I. Thermal conductivity of III–V compounds at high temperatures. Phys. Rev. 132, 508–512 (1963).

    Google Scholar 

  18. Billard, D. & Cabannes, F. La conductivité thermique de réseau aux hautes températures. High Temp. High Press. 3, 201 (1971).

    CAS  Google Scholar 

  19. Wolf, G. H. & Jeanloz, R. Vibrational properties of model monatomic crystals under pressure. Phys. Rev. B 32, 7798–7810 (1985).

    Google Scholar 

  20. Slack, G. A. The thermal conductivity of nonmetallic crystals. Solid State Phys. 34, 1–71 (1979).

    CAS  Google Scholar 

  21. Gerlich, D. & Andersson, P. Temperature and pressure effects on the thermal conductivity and heat capacity of CsCl, CsBr and CsI. J. Phys. C: Solid State Phys. 15, 5211–5222 (1982).

    Google Scholar 

  22. Hakansson, B. & Andersson, P. Thermal conductivity and heat capacity of solid NaCl and NaI under pressure. J. Phys. Chem. Solids 47, 355–362 (1986).

    ADS  Google Scholar 

  23. Xiong, X., Ragasa, E. J., Chernatynskiy, A., Tang, D. & Phillpot, S. R. Lattice thermal conductivity of quartz at high pressure and temperature from the Boltzmann transport equation. J. Appl. Phys. 126, 215106 (2019).

    ADS  Google Scholar 

  24. Hsieh, W. P., Chen, B., Li, J., Keblinski, P. & Cahill, D. G. Pressure tuning of the thermal conductivity of the layered muscovite crystal. Phys. Rev. B 80, 180302 (2009).

    ADS  Google Scholar 

  25. Chen, B., Hsieh, W. P., Cahill, D. G., Trinkle, D. R. & Li, J. Thermal conductivity of compressed H2O to 22 GPa: a test of the Leibfried–Schlömann equation. Phys. Rev. B 83, 132301 (2011).

    ADS  Google Scholar 

  26. Ohta, K. et al. Lattice thermal conductivity of MgSiO3 perovskite and post-perovskite at the core–mantle boundary. Earth Planet. Sci. Lett. 349, 109–115 (2012).

    ADS  Google Scholar 

  27. Broido, D. A., Lindsay, L. & Ward, A. Thermal conductivity of diamond under extreme pressure: a first-principles study. Phys. Rev. B 86, 115203 (2012).

    ADS  Google Scholar 

  28. Dalton, D. A., Hsieh, W. P., Hohensee, G. T., Cahill, D. G. & Goncharov, A. F. Effect of mass disorder on the lattice thermal conductivity of MgO periclase under pressure. Sci. Rep. 3, 2400 (2013).

    PubMed  PubMed Central  Google Scholar 

  29. Mukhopadhyay, S. & Stewart, D. A. Polar effects on the thermal conductivity of cubic boron nitride under pressure. Phys. Rev. Lett. 113, 25901 (2014).

    ADS  CAS  Google Scholar 

  30. Sun, Z., Yuan, K., Zhang, X. & Tang, D. Pressure tuning of the thermal conductivity of gallium arsenide from first-principles calculations. Phys. Chem. Chem. Phys. 20, 30331–30339 (2018).

    CAS  PubMed  Google Scholar 

  31. Lindsay, L., Broido, D. A. & Reinecke, T. L. First-principles determination of ultrahigh thermal conductivity of boron arsenide: a competitor for diamond? Phys. Rev. Lett. 111, 25901 (2013).

    ADS  CAS  Google Scholar 

  32. Kang, J. S., Li, M., Wu, H., Nguyen, H. & Hu, Y. Experimental observation of high thermal conductivity in boron arsenide. Science 361, 575–578 (2018).

    ADS  CAS  PubMed  Google Scholar 

  33. Li, S. et al. High thermal conductivity in cubic boron arsenide crystals. Science 361, 579–581 (2018).

    ADS  CAS  PubMed  Google Scholar 

  34. Tian, F. et al. Unusual high thermal conductivity in boron arsenide bulk crystals. Science 361, 582–585 (2018).

    ADS  CAS  PubMed  Google Scholar 

  35. Kang, J. S. et al. Integration of boron arsenide cooling substrates into gallium nitride devices. Nat. Electron. 4, 416–423 (2021).

    CAS  Google Scholar 

  36. Cui, Y., Qin, Z., Wu, H., Li, M. & Hu, Y. Flexible thermal interface based on self-assembled boron arsenide for high-performance thermal management. Nat. Commun. 12, 1284 (2021).

    ADS  CAS  PubMed  PubMed Central  Google Scholar 

  37. Ravichandran, N. K. & Broido, D. Non-monotonic pressure dependence of the thermal conductivity of boron arsenide. Nat. Commun. 10, 827 (2019).

    PubMed  PubMed Central  Google Scholar 

  38. Kang, J. S., Li, M., Wu, H., Nguyen, H. & Hu, Y. Basic physical properties of cubic boron arsenide. Appl. Phys. Lett. 115, 122103 (2019).

    ADS  Google Scholar 

  39. Kang, J. S., Wu, H., Li, M. & Hu, Y. Intrinsic low thermal conductivity and phonon renormalization due to strong anharmonicity of single-crystal tin selenide. Nano Lett. 19, 4941–4948 (2019).

    ADS  CAS  PubMed  Google Scholar 

  40. Maradudin, A. A. & Fein, A. E. Scattering of neutrons by an anharmonic crystal. Phys. Rev. 128, 2589–2608 (1962).

    ADS  CAS  Google Scholar 

  41. Lindsay, L. & Broido, D. A. Three-phonon phase space and lattice thermal conductivity in semiconductors. J. Phys. Condens. Matter 20, 165209 (2008).

    ADS  Google Scholar 

  42. Feng, T., Lindsay, L. & Ruan, X. Four-phonon scattering significantly reduces intrinsic thermal conductivity of solids. Phys. Rev. B 96, 161201 (2017).

    ADS  Google Scholar 

  43. Lindsay, L., Broido, D. A., Carrete, J., Mingo, N. & Reinecke, T. L. Anomalous pressure dependence of thermal conductivities of large mass ratio compounds. Phys. Rev. B 91, 121202 (2015).

    ADS  Google Scholar 

  44. Mao, H. K., Xu, J. A. & Bell, P. M. Calibration of the ruby pressure gauge to 800 kbar under quasi‐hydrostatic conditions. J. Geophys. Res. Solid Earth 91, 4673–4676 (1986).

    CAS  Google Scholar 

  45. Kunz, M. et al. A beamline for high-pressure studies at the Advanced Light Source with a superconducting bending magnet as the source. J. Synchrotron Rad. 12, 650–658 (2005).

    Google Scholar 

  46. Said, A. H. et al. High-energy-resolution inelastic X-ray scattering spectrometer at beamline 30-ID of the advanced photon source. J. Synchrotron Rad. 27, 827–835 (2020).

    CAS  Google Scholar 

  47. Toellner, T. S., Alatas, A. & Said, A. H. Six‐reflection meV‐monochromator for synchrotron radiation. J. Synchrotron Rad. 18, 605–611 (2011).

    CAS  Google Scholar 

  48. Rivers, M. et al. The COMPRES/GSECARS gas-loading system for diamond anvil cells at the Advanced Photon Source. High Press. Res. 28, 273–292 (2008).

    ADS  CAS  Google Scholar 

  49. Hu, Y., Zeng, L., Minnich, A. J., Dresselhaus, M. S. & Chen, G. Spectral mapping of thermal conductivity through nanoscale ballistic transport. Nat. Nanotechnol. 10, 701–706 (2015).

    ADS  CAS  PubMed  Google Scholar 

  50. Kang, J. S., Ke, M. & Hu, Y. Ionic intercalation in two-dimensional van der Waals materials: in situ characterization and electrochemical control of the anisotropic thermal conductivity of black phosphorus. Nano Lett. 17, 1431–1438 (2017).

    ADS  CAS  PubMed  Google Scholar 

  51. Kang, J. S., Wu, H. & Hu, Y. Thermal properties and phonon spectral characterization of synthetic boron phosphide for high thermal conductivity applications. Nano Lett. 17, 7507–7514 (2017).

    ADS  CAS  PubMed  Google Scholar 

  52. Li, M., Kang, J. S. & Hu, Y. Anisotropic thermal conductivity measurement using a new asymmetric-beam time-domain thermoreflectance (AB-TDTR) method. Rev. Sci. Instrum. 89, 084901 (2018).

    ADS  PubMed  Google Scholar 

  53. Li, M. et al. Anisotropic thermal boundary resistance across 2D black phosphorus: experiment and atomistic modeling of interfacial energy transport. Adv. Mater. 31, 1901021 (2019).

    Google Scholar 

  54. Thomsen, C., Grahn, H. T., Maris, H. J. & Tauc, J. Surface generation and detection of phonons by picosecond light pulses. Phys. Rev. B 34, 4129–4138 (1986).

    Google Scholar 

  55. Lin, H., Stoner, R. J., Maris, H. J. & Tauc, J. Phonon attenuation and velocity measurements in transparent materials by picosecond acoustic interferometry. J. Appl. Phys. 69, 3816–3822 (1991).

    ADS  CAS  Google Scholar 

  56. Wright, O. B. Thickness and sound velocity measurement in thin transparent films with laser picosecond acoustics. J. Appl. Phys. 71, 1617–1629 (1992).

    ADS  Google Scholar 

  57. Perrin, B., Rossignol, C., Bonello, B. & Jeannet, J. C. Interferometric detection in picosecond ultrasonics. Physica B 263, 571–573 (1999).

    ADS  Google Scholar 

  58. O’Hara, K. E., Hu, X. & Cahill, D. G. Characterization of nanostructured metal films by picosecond acoustics and interferometry. J. Appl. Phys. 90, 4852–4858 (2001).

    ADS  Google Scholar 

  59. Ma, W., Miao, T., Zhang, X., Kohno, M. & Takata, Y. Comprehensive study of thermal transport and coherent acoustic-phonon wave propagation in thin metal film–substrate by applying picosecond laser pump–probe method. J. Phys. Chem. C 119, 5152–5159 (2015).

    CAS  Google Scholar 

  60. Feng, T. & Ruan, X. Quantum mechanical prediction of four-phonon scattering rates and reduced thermal conductivity of solids. Phys. Rev. B 93, 045202 (2016); erratum 97, 079901 (2018).

    ADS  Google Scholar 

  61. Fan, H., Wu, H., Lindsay, L. & Hu, Y. Ab initio investigation of single-layer high thermal conductivity boron compounds. Phys. Rev. B 100, 85420 (2019).

    ADS  CAS  Google Scholar 

  62. Wu, H., Fan, H. & Hu, Y. Ab initio determination of ultrahigh thermal conductivity in ternary compounds. Phys. Rev. B 103, L041203 (2021).

    ADS  CAS  Google Scholar 

  63. Baroni, S., de Gironcoli, S., Dal Corso, A. & Giannozzi, P. Phonons and related crystal properties from density-functional perturbation theory. Rev. Mod. Phys. 73, 515–562 (2001).

    ADS  CAS  Google Scholar 

  64. Li, M., Dai, L. & Hu, Y. Machine learning for harnessing thermal energy: from materials discovery to system optimization. ACS Energy Lett. 7, 3204–3226 (2022).

    CAS  Google Scholar 

  65. Srivastava, G. P. The Physics of Phonons (Taylor & Francis, 1990).

  66. Hohenberg, P. & Kohn, W. Inhomogeneous electron gas. Phys. Rev. 136, B864–B871 (1964).

    ADS  MathSciNet  Google Scholar 

  67. Kohn, W. & Sham, L. J. Self-consistent equations including exchange and correlation effects. Phys. Rev. 140, A1133–A1138 (1965).

    ADS  MathSciNet  Google Scholar 

  68. Giannozzi, P. et al. QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J. Phys. Condens. Matter 21, 395502 (2009).

    PubMed  Google Scholar 

  69. Giannozzi, P. et al. Advanced capabilities for materials modelling with Quantum ESPRESSO. J. Phys. Condens. Matter 29, 465901 (2017).

    CAS  PubMed  Google Scholar 

  70. Tadano, T., Gohda, Y. & Tsuneyuki, S. Anharmonic force constants extracted from first-principles molecular dynamics: applications to heat transfer simulations. J. Phys. Condens. Matter 26, 225402 (2014).

    CAS  PubMed  Google Scholar 

Download references

Acknowledgements

We thank B. Kalkan, K. Armstrong and B. Lavina for technical help and discussion. Y.H. acknowledges support from a CAREER Award from the National Science Foundation (NSF) under grant no. DMR-1753393, an Alfred P. Sloan Research Fellowship under grant no. FG-2019-11788, and the Vernroy Makoto Watanabe Excellence in Research Award. This work used computational and storage services associated with the Hoffman 2 Shared Cluster provided by UCLA Institute for Digital Research and Education’s Research Technology Group, and the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number ACI-1548562. This research used resources at the US Department of Energy (DOE) Office of Science user facility, including the Advanced Photon Source by Argonne National Laboratory under contract no. DE-AC02-06CH11357 and the Advanced Light Source by Lawrence Berkeley National Laboratory under contract no. DE-AC02-05CH1123.

Author information

Authors and Affiliations

Authors

Contributions

Y.H. proposed and directed the research. S.L., Z.Q. and M.L. performed the experiments. H.W. performed the theory calculations. M.K. helped with the XRD study. A.A. helped with the IXS study. A.K. helped with technical discussions. The manuscript was prepared by S.L., Z.Q., H.W., M.L. and Y.H. with input from all co-authors.

Corresponding author

Correspondence to Yongjie Hu.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature thanks Yee Kan Koh and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Additional information

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Extended data figures and tables

Extended Data Fig. 1 Synchrotron X-ray diffraction (XRD) measurement of BAs and its pressure-dependent lattice constant.

a, Synchrotron XRD patterns of BAs measured at different pressures (~0–32.6 GPa), verifying the cubic phase of BAs under all high pressures without phase transition. b, Experimentally measured pressure-dependent lattice constant of BAs (circles), in comparison with the ab initio calculation (line).

Extended Data Fig. 2 Synchrotron single-crystal X-ray diffraction measurement.

Example diffraction image of BAs in which all peaks are indexed to the cubic phase.

Extended Data Fig. 3 Inelastic X-ray scattering (IXS) spectrum measurement of BAs crystal.

Shown in figure are scattering peaks that determine the phonon frequency for scattering vector Q at (3.5 2.5 2.5).

Extended Data Fig. 4 Brillouin scattering oscillation signals measured on a BAs sample.

Fast Fourier transform result of Brillouin scattering data (inset) determines the Brillouin frequency.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Li, S., Qin, Z., Wu, H. et al. Anomalous thermal transport under high pressure in boron arsenide. Nature (2022). https://doi.org/10.1038/s41586-022-05381-x

Download citation

  • Received:

  • Accepted:

  • Published:

  • DOI: https://doi.org/10.1038/s41586-022-05381-x

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing