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Title: Nonharmonic contributions to the high-temperature phonon thermodynamics of Cr

Abstract

Here, phonon densities of states (DOSs) of body-centered cubic chromium were measured by time-of-flight inelastic neutron scattering at temperatures up to 1493 K. Density functional theory calculations with both quasiharmonic (QH) and anharmonic (AH) methods were performed at temperatures above the Néel temperature. Features in the phonon DOSs decrease in energy (soften) substantially with temperature. A Born–von Kármán analysis using fits to the experimental DOSs reveals a softening of almost 17% of the high-transverse phonon branch between 330 and 1493 K. The low-transverse branch changes by approximately half this amount. The AH calculations capture the observed behavior of the two transverse phonon branches, but the QH calculations give some inverted trends. Vibrational entropies from phonons and electrons are obtained, and their sum is in excellent agreement with the entropy of chromium obtained by calorimetry, indicating that above 330 K, no explicit temperature-dependent magnetic contributions are necessary.

Authors:
ORCiD logo [1]; ORCiD logo [2]; ORCiD logo [1]; ORCiD logo [3];  [4]; ORCiD logo [5]; ORCiD logo [1]
  1. California Institute of Technology (CalTech), Pasadena, CA (United States)
  2. Swarthmore College, Swarthmore, PA (United States)
  3. Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
  4. California Institute of Technology (CalTech), Pasadena, CA (United States). Jet Propulsion Lab. (JPL)
  5. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
Publication Date:
Research Org.:
Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES)
OSTI Identifier:
1960678
Grant/Contract Number:  
AC05-00OR22725
Resource Type:
Accepted Manuscript
Journal Name:
Physical Review. B
Additional Journal Information:
Journal Volume: 107; Journal Issue: 5; Journal ID: ISSN 2469-9950
Publisher:
American Physical Society (APS)
Country of Publication:
United States
Language:
English
Subject:
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY

Citation Formats

Bernal-Choban, C. M., Smith, H. L., Saunders, C. N., Kim, D. S., Mauger, L., Abernathy, D. L., and Fultz, B. Nonharmonic contributions to the high-temperature phonon thermodynamics of Cr. United States: N. p., 2023. Web. doi:10.1103/physrevb.107.054312.
Bernal-Choban, C. M., Smith, H. L., Saunders, C. N., Kim, D. S., Mauger, L., Abernathy, D. L., & Fultz, B. Nonharmonic contributions to the high-temperature phonon thermodynamics of Cr. United States. https://doi.org/10.1103/physrevb.107.054312
Bernal-Choban, C. M., Smith, H. L., Saunders, C. N., Kim, D. S., Mauger, L., Abernathy, D. L., and Fultz, B. Mon . "Nonharmonic contributions to the high-temperature phonon thermodynamics of Cr". United States. https://doi.org/10.1103/physrevb.107.054312. https://www.osti.gov/servlets/purl/1960678.
@article{osti_1960678,
title = {Nonharmonic contributions to the high-temperature phonon thermodynamics of Cr},
author = {Bernal-Choban, C. M. and Smith, H. L. and Saunders, C. N. and Kim, D. S. and Mauger, L. and Abernathy, D. L. and Fultz, B.},
abstractNote = {Here, phonon densities of states (DOSs) of body-centered cubic chromium were measured by time-of-flight inelastic neutron scattering at temperatures up to 1493 K. Density functional theory calculations with both quasiharmonic (QH) and anharmonic (AH) methods were performed at temperatures above the Néel temperature. Features in the phonon DOSs decrease in energy (soften) substantially with temperature. A Born–von Kármán analysis using fits to the experimental DOSs reveals a softening of almost 17% of the high-transverse phonon branch between 330 and 1493 K. The low-transverse branch changes by approximately half this amount. The AH calculations capture the observed behavior of the two transverse phonon branches, but the QH calculations give some inverted trends. Vibrational entropies from phonons and electrons are obtained, and their sum is in excellent agreement with the entropy of chromium obtained by calorimetry, indicating that above 330 K, no explicit temperature-dependent magnetic contributions are necessary.},
doi = {10.1103/physrevb.107.054312},
journal = {Physical Review. B},
number = 5,
volume = 107,
place = {United States},
year = {Mon Feb 27 00:00:00 EST 2023},
month = {Mon Feb 27 00:00:00 EST 2023}
}

Works referenced in this record:

Generalized Gradient Approximation Made Simple
journal, October 1996

  • Perdew, John P.; Burke, Kieron; Ernzerhof, Matthias
  • Physical Review Letters, Vol. 77, Issue 18, p. 3865-3868
  • DOI: 10.1103/PhysRevLett.77.3865

On the evaluation of phonon widths and shifts
journal, January 1962

  • Maradudin, A. A.; Fein, A. E.; Vineyard, G. H.
  • physica status solidi (b), Vol. 2, Issue 11
  • DOI: 10.1002/pssb.19620021106

Thermal expansion of Chromium (Cr) to melting temperature
journal, December 1997


Mantid—Data analysis and visualization package for neutron scattering and μ SR experiments
journal, November 2014

  • Arnold, O.; Bilheux, J. C.; Borreguero, J. M.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 764
  • DOI: 10.1016/j.nima.2014.07.029

Generalized Gradient Approximation Made Simple [Phys. Rev. Lett. 77, 3865 (1996)]
journal, February 1997


Projector augmented-wave method
journal, December 1994


Magnetic excitations in chromium. II
journal, March 1985


Anharmonic Origin of the Giant Thermal Expansion of NaBr
journal, August 2020


Characterization of the high-pressure and high-temperature phase diagram and equation of state of chromium
journal, April 2022


Special points for Brillouin-zone integrations
journal, June 1976

  • Monkhorst, Hendrik J.; Pack, James D.
  • Physical Review B, Vol. 13, Issue 12, p. 5188-5192
  • DOI: 10.1103/PhysRevB.13.5188

Phonon anharmonicity in silicon from 100 to 1500 K
journal, January 2015


Thermodynamic properties of chromium
journal, July 1985

  • Andersson, J. -O.
  • International Journal of Thermophysics, Vol. 6, Issue 4
  • DOI: 10.1007/BF00500271

Anharmonicity measure for materials
journal, August 2020


Nonharmonic phonons in α -iron at high temperatures
journal, August 2014


Thermodynamic modeling of chromium: strong and weak magnetic coupling
journal, September 2013


Temperature-dependent renormalization of magnetic interactions by thermal, magnetic, and lattice disorder from first principles
journal, May 2021


Thermodynamic re-assessment of pure chromium using modified segmented regression model
journal, June 2020


Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set
journal, October 1996


First principles phonon calculations in materials science
journal, November 2015


From ultrasoft pseudopotentials to the projector augmented-wave method
journal, January 1999


Magnetic ground state of Cr in density-functional theory
journal, May 2002


Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium
journal, May 1994


Extended anharmonic collapse of phonon dispersions in SnS and SnSe
journal, September 2020


Electronic, quasiharmonic, and anharmonic entropies of transition metals
journal, September 1992


Thermal expansivities, thermal conductivities, and densities of vanadium, titanium, chromium and some vanadium-base alloys
journal, September 1969


Design and operation of the wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source
journal, January 2012

  • Abernathy, D. L.; Stone, M. B.; Loguillo, M. J.
  • Review of Scientific Instruments, Vol. 83, Issue 1
  • DOI: 10.1063/1.3680104

Multiphonon: Phonon Density of States tools for Inelastic Neutron Scattering Powder Data
journal, January 2018

  • Y. Y. Lin, Jiao; Islam, Fahima; Kresh, Max
  • The Journal of Open Source Software, Vol. 3, Issue 21
  • DOI: 10.21105/joss.00440

Vibrational thermodynamics of materials
journal, May 2010


The role of harmonics in the first order antiferromagnetic to paramagnetic transition in chromium
journal, August 1974


Lattice dynamics of anharmonic solids from first principles
journal, November 2011


Thermal expansion and phonon anharmonicity of cuprite studied by inelastic neutron scattering and ab initio calculations
journal, May 2022


Crystallography, thermodynamics and phase transitions in refractory binary alloys
journal, November 2020


Ab initiomolecular dynamics for liquid metals
journal, January 1993


Measurement of strong phonon softening in Cr with and without Fermi-surface nesting by inelastic x-ray scattering
journal, November 2010


Phase Equilibria and Thermodynamic Properties in the Fe-Cr System
journal, May 2010

  • Xiong, Wei; Selleby, Malin; Chen, Qing
  • Critical Reviews in Solid State and Materials Sciences, Vol. 35, Issue 2
  • DOI: 10.1080/10408431003788472

Design and operating characteristic of a vacuum furnace for time-of-flight inelastic neutron scattering measurements
journal, October 2017

  • Niedziela, J. L.; Mills, R.; Loguillo, M. J.
  • Review of Scientific Instruments, Vol. 88, Issue 10
  • DOI: 10.1063/1.5007089

Corrections to the electronic heat capacity of metals due to finite lifetimes of the conduction electrons
journal, November 1986

  • Thiessen, M.
  • International Journal of Thermophysics, Vol. 7, Issue 6
  • DOI: 10.1007/BF00503974

Temperature dependence of the lattice dynamics of chromium
journal, February 1993


Investigations of Paramagnetic Neutron Scattering from Chromium
journal, September 1962


Vibrational free energy and phase stability of paramagnetic and antiferromagnetic CrN from ab initio molecular dynamics
journal, May 2014


Spin fluctuations in paramagnetic chromium determined from entropy considerations
journal, June 1993


MCViNE – An object oriented Monte Carlo neutron ray tracing simulation package
journal, February 2016

  • Lin, Jiao Y. Y.; Smith, Hillary L.; Granroth, Garrett E.
  • Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipment, Vol. 810
  • DOI: 10.1016/j.nima.2015.11.118