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Published August 1, 2014 | Submitted + Supplemental Material + Published
Journal Article Open

Nonharmonic phonons in α-iron at high temperatures


Phonon densities of states (DOS) of bcc α−^(57)Fe were measured from room temperature through the 1044 K Curie transition and the 1185 K fcc γ-Fe phase transition using nuclear resonant inelastic x-ray scattering. At higher temperatures all phonons shift to lower energies (soften) with thermal expansion, but the low transverse modes soften especially rapidly above 700 K, showing strongly nonharmonic behavior that persists through the magnetic transition. Interatomic force constants for the bcc phase were obtained by iteratively fitting a Born–von Kármán model to the experimental phonon spectra using a genetic algorithm optimization. The second-nearest-neighbor fitted axial force constants weakened significantly at elevated temperatures. An unusually large nonharmonic behavior is reported, which increases the vibrational entropy and accounts for a contribution of 35 meV/atom in the free energy at high temperatures. The nonharmonic contribution to the vibrational entropy follows the thermal trend of the magnetic entropy, and may be coupled to magnetic excitations. A small change in vibrational entropy across the α−γ structural phase transformation is also reported.

Additional Information

© 2014 American Physical Society. Published 20 August 2014. Received 19 April 2014. Revised 7 July 2014. This work benefited from important discussions with Drs. W. Sturhahn, F. Körmann, B. Grabowski, T. Hickel, and J. Neugebauer. This work was supported by the Department of Energy through the Carnegie-DOE Alliance Center, funded by the Department of Energy through the Stewardship Sciences Academic Alliance Program. This work benefited from DANSE software developed under NSF Grant No.DMR-0520547. Portions of this work were performed at HPCAT (Sector 16),Advanced Photon Source (APS),Argonne National Laboratory. HPCAT operations are supported by DOE-NNSA under Award No. DE-NA0001974 and DOEBES under Award No. DE-FG02-99ER45775, with partial instrumentation funding by NSF. The Advanced Photon Source is a U.S. Department of Energy (DOE) Office of Science User Facility operated for the DOE Office of Science by Argonne National Laboratory under Contract No. DEAC02-06CH11357.

Attached Files

Published - PhysRevB.90.064303.pdf

Submitted - 1404.4998v2.pdf

Supplemental Material - DispersionFits_BestFits_2NNFixedMink_Final_Concave_20140703_SS_AnharmonicBranchSmag.pdf

Supplemental Material - HighTFe_2x0_Supplemental.bbl

Supplemental Material - HighTFe_2x0_Supplemental.pdf

Supplemental Material - HighTFe_2x0_Supplemental.tex


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August 20, 2023
October 18, 2023