A thermodynamic explanation of the Invar effect

S. H. Lohaus; M. Heine; P. Guzman; C. M. Bernal-Choban; C. N. Saunders; G. Shen; O. Hellman; D. Broido; B. Fultz

doi:10.1038/s41567-023-02142-z

A thermodynamic explanation of the Invar effect

S. H. Lohaus, M. Heine, P. Guzman, C. M. Bernal-Choban, C. N. Saunders, G. Shen, O. Hellman, D. Broido, B. Fultz

Department of Molecular Chemistry and Materials Science Perlman

Research output: Contribution to journal › Article › peer-review

19 Citations (Scopus)

Abstract

The anomalously low thermal expansion of Fe-Ni Invar has long been associated with magnetism, but to date, the microscopic underpinnings of the Invar behaviour have eluded both theory and experiment. Here we present nuclear resonant X-ray scattering measurements of the phonon and magnetic entropies under pressure. By applying a thermodynamic Maxwell relation to these data, we obtain the separate phonon and magnetic contributions to thermal expansion. We find that the Invar behaviour stems from a competition between phonons and spins. In particular, the phonon contribution to thermal expansion cancels the magnetic contribution over the 0-3 GPa pressure range of Invar behaviour. At pressures above 3 GPa, the cancellation is lost, but our analysis reproduces the positive thermal expansion measured separately by synchrotron X-ray diffractometry. Ab initio calculations informed by experimental data show that spin-phonon interactions improve the accuracy of this cancellation over the range of Invar behaviour. Spin-phonon interactions also explain how different phonon modes have different energy shifts with pressure.The iron-nickel alloy Invar has an extremely small coefficient of thermal expansion that has been difficult to explain theoretically. A study of Invar under pressure now suggests that there is a cancellation of phonon and spin contributions to expansion.

Original language	English
Pages (from-to)	1642-1648
Number of pages	7
Journal	Nature Physics
Volume	19
Issue number	11
Early online date	27 Jul 2023
DOIs	https://doi.org/10.1038/s41567-023-02142-z
Publication status	Published - Nov 2023

Funding

This work was supported by the National Science Foundation under grant no. 1904714 (S.H.L., P.G., C.M.B-C., C.N.S. and B.F.). Work at Boston College was supported by the US Department of Energy (DOE), Office of Science, Basic Energy Sciences, under award no. DE-SC0021071 (M.H. and D.B.). O.H. acknowledges support from the Swedish Research Council (VR) program 2020-04630. M.H. and D.B. acknowledge the Boston College Linux clusters for their computational resources and support. Calculations were also performed in part using MATLAB. This research used resources of the APS, a US DOE Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under contract no. DE-AC02-06CH11357 (S.H.L., P.G., C.M.B-C., G.S. and B.F.). HPCAT operations are supported by DOE-NNSA’s Office of Experimental Sciences. Use of the COMPRES-GSECARS gas-loading system was supported by COMPRES under NSF Cooperative Agreement EAR-1606856 and by GSECARS through NSF grant EAR-1634415 and DOE grant DE-FG02-94ER14466. This research also used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory (S.H.L., C.M.B-C. and B.F.). We thank D. Rhiger for informing us of his dissertation research, C. Li for assistance with the pressure cells and J. A. Kornfield for use of the DSC. We also acknowledge the help from the beamline scientists at the APS (E. E. Alp, J. Zhao, B. Lavina and M. Hu) and D. Abernathy at Oak Ridge National Laboratory. Author contributions - S.H.L. designed and performed the experiments, analysed the data and compiled the paper. M.H. performed and analysed the calculations. P.G. and C.M.B-C. helped execute the beamline experiments at the APS. C.N.S. analysed the neutron scattering data. The remote XRD experiments were locally handled by G.S. O.H. developed and supervised the computational analyses. D.B. conceptualized and supervised the computational efforts. B.F. conceptualized and supervised the study. S.H.L., M.H., D.B. and B.F. wrote the paper, with contributions from all authors.

All Science Journal Classification (ASJC) codes

General Physics and Astronomy

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10.1038/s41567-023-02142-z

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abstract = "The anomalously low thermal expansion of Fe-Ni Invar has long been associated with magnetism, but to date, the microscopic underpinnings of the Invar behaviour have eluded both theory and experiment. Here we present nuclear resonant X-ray scattering measurements of the phonon and magnetic entropies under pressure. By applying a thermodynamic Maxwell relation to these data, we obtain the separate phonon and magnetic contributions to thermal expansion. We find that the Invar behaviour stems from a competition between phonons and spins. In particular, the phonon contribution to thermal expansion cancels the magnetic contribution over the 0-3 GPa pressure range of Invar behaviour. At pressures above 3 GPa, the cancellation is lost, but our analysis reproduces the positive thermal expansion measured separately by synchrotron X-ray diffractometry. Ab initio calculations informed by experimental data show that spin-phonon interactions improve the accuracy of this cancellation over the range of Invar behaviour. Spin-phonon interactions also explain how different phonon modes have different energy shifts with pressure.The iron-nickel alloy Invar has an extremely small coefficient of thermal expansion that has been difficult to explain theoretically. A study of Invar under pressure now suggests that there is a cancellation of phonon and spin contributions to expansion.",

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AU - Broido, D.

AU - Fultz, B.

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A thermodynamic explanation of the Invar effect

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