Shelby R. Turner1,2,3, Stéphane Pailhès3, Frédéric Bourdarot4, Jacques Ollivier1, Yvan Sidis5, John-Paul Castellan5,6, Jean-Marc Zanotti5, Quentin Berrod7, Florence Porcher5, Alexei Bosak8, Michael Feuerbacher9, Helmut Schober1, Marc de Boissieu2, and Valentina M. Giordano3
1 Institut Laue-Langevin, F-38042 Grenoble cedex, France
2 Université Grenoble Alpes, CNRS, Grenoble-INP, SIMaP, F-38000 Grenoble, France
3 Institute of Light and Matter, UMR5306 Université Lyon 1-CNRS, Université de Lyon, F-69622 Villeurbanne cedex, France
4 Université Grenoble Alpes, CEA, IRIG, MEM, MDN, F-38000 Grenoble cedex, France
5 Université Paris-Saclay, CNRS, CEA, Laboratoire Léon Brillouin, F-91191 Gif-sur-Yvette, France
6 Institut für Festkörperphysik, Karlsruher Institut für Technologie, D-76021 Karlsruhe, Germany
7 Université Grenoble Alpes, CEA, CNRS, IRIG-SyMMES, F-38000 Grenoble cedex, France
8 European Synchrotron Radiation Facility, BP 220, F-38043 Grenoble cedex, France
9 Peter Grünberg Institut PGI-5 and ER-C, FZ Jülich GmbH, D-52425 Jülich, Germany
See the full published paper : Nature Communications (10.1038/s41467-022-35125-4, 2022).
Understanding thermal transport in materials is one of the major challenges today, fundamental for engineering new materials efficient for thermal management and energy harvesting. A good understanding of heat transport mechanisms is now achieved for crystals on one side and disordered materials (glasses) on the other. In order to achieve such understanding, it has been fundamental not only to develop more advanced theoretical models, but especially to validate them with experimental data. The key quantities to calculate and measure are the individual properties of phonons in the entire Brillouin zone, energies and lifetime. These can be accessed by inelastic neutron scattering techniques, which can be complemented by X-ray inelastic scattering when samples are very small. In this work we have applied such techniques for understanding phonon dynamics and thermal transport in a new class of alloys, which lies between ordered and disordered materials: high entropy alloys (HEAs). Here the elements composing the alloy are present in the same proportions and randomly occupy the atomic sites of a simple unit cell (Figure 1). As a consequence, despite the long range order typical of a crystal, there is a large short range chemical disorder, which leads to remarkable mechanical and thermal properties1,2. Several kinds of disorder are present: atomic size, mass, force-constants, the same that we find in a glass, where atoms are also spatially disordered and not sitting on regular, periodic positions as in the HEA (topological disorder).
Figure 1. Crystalline structure of the HEA: 16 unit cells are represented, of a face centred cubic structure where the atomic sites are randomly occupied by one of the 5 elements, represented with different colours.
In these alloys, the thermal conductivity has been found to be much lower than in simple crystals and very weakly temperature dependent, as in glasses3,4. In this article the authors have tried to unveil the microscopic mechanisms leading to a glass-like thermal transport and identify the position of HEAs with respect to crystals and glasses.
This has been possible thanks to the availability of a large single crystal of the 5-elements HEA Fe20Co20Cr20Mn20Ni20, allowing to perform inelastic neutron scattering (INS) experiments to investigate the phonon dynamics. INS measurements were performed on (IN5, IN6)@ILL and 1T@LLB. Specifically, the authors have measured the phonon density of states but as well the individual dispersions of the transverse acoustic modes along different high symmetry directions. These data have been complemented by inelastic X-ray scattering (IXS) measurements of the longitudinal modes, so that the full phonon spectrum has been measured for the first time in a HEA.
The authors have shown that the heat waves propagate well until sub-nanometric wavelengths and an energy of several tens of meV, like in a simple, ordered, crystal. Moreover, their dispersions are very similar to the ones of the simple elements and binary alloys of the elements composing it (see Figure 2). Still, the analysis of the phonon energy width (or lifetime) revealed that they are much more attenuated due to the disorder, which explains the lower thermal conductivity. The attenuation is mostly due to the disorder of the force constants5, usually absent in crystals but dominant in glasses. Still, attenuation remains weaker than in disordered materials, so that phonons can propagate until the wavelength becomes comparable to the interatomic distance.
This work has allowed the authors to identify HEAs as a new family of materials with its own dynamics, lying at the frontier between crystals and glasses. Moreover, their findings point to a new strategy of thermal material’s engineering: increasing the force constant disorder by choosing more dissimilar elements for obtaining an even lower thermal conductivity.
Figure 2. Resulting phonon dispersions obtained from INS (1T@LLB) and IXS (ID28@ESRF) measured along two high symmetry directions at room and low temperature, compared with literature data for Ni (solid gray line) and the binary Fe-Ni alloy (dot-dashed gray line).
1 B. Cantor, I. Chang, P. Knight, and A. Vincent, Mat. Sci. Eng. A 375-377, 213 (2004).
2 M. Gao, J.-W. Yeh, P. Liaw, and Y. Zhang, eds., High–Entropy Alloys (Springer-Verlag GmbH, 2016).
3 M.-H. Tsai, Physical properties of high entropy alloys, Entropy 15, 5338 (2013)
4 Z. Fan, H. Wang, Y. Wu, X. Liu, and Z. Lu, , Materials Research Letters 5, 187 (2016).
5 S. Mu, R. J. Olsen, B. Dutta, L. Lindsay, G. D. Samolyuk, T. Berlijn, E. D. Specht, K. Jin, H. Bei, T. Hickel, B. C. Larson, and G. M. Stocks, npj Computational Materials 6, 4 (2020).