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Diffuse Inelastic Neutron Scattering from Anharmonic Vibrations in Cuprite
Authors:
C. N. Saunders,
V. V. Ladygin,
D. S. Kim,
C. M. Bernal-Choban,
S. H. Lohaus,
G. E. Granroth,
D. L. Abernathy,
B. Fultz
Abstract:
Atomic vibrational dynamics in cuprite, Cu2O, was studied by inelastic neutron scattering and molecular dynamics (MD) simulations from 10 K to 900 K. Above 300 K, a diffuse inelastic intensity (DII) appeared, obscuring the high-energy phonon modes. Classical MD simulations with a machine learning interatomic potential reproduced general features of the DII, especially with a Langevin thermostat. T…
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Atomic vibrational dynamics in cuprite, Cu2O, was studied by inelastic neutron scattering and molecular dynamics (MD) simulations from 10 K to 900 K. Above 300 K, a diffuse inelastic intensity (DII) appeared, obscuring the high-energy phonon modes. Classical MD simulations with a machine learning interatomic potential reproduced general features of the DII, especially with a Langevin thermostat. The DII originates from random phase shifts of vibrating O-atoms that have anharmonic interactions with neighboring Cu-atoms.
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Submitted 1 September, 2023;
originally announced September 2023.
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Prediction and Observation of Intermodulation Sidebands from Anharmonic Phonons
Authors:
Y. Shen,
C. N. Saunders,
C. M. Bernal,
D. L. Abernathy,
T. J. Williams,
M. E. Manley,
B. Fultz
Abstract:
A quantum Langevin model, similar to models used recently for optomechanics, was used to predict intermodulation phonon sidebands (IPS). Ab initio calculations of anharmonic phonons in rocksalt NaBr showed these spectral features as "many-body effects". Modern inelastic neutron scattering measurements on a crystal of NaBr at 300K revealed diffuse intensity at high phonon energy from a predicted up…
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A quantum Langevin model, similar to models used recently for optomechanics, was used to predict intermodulation phonon sidebands (IPS). Ab initio calculations of anharmonic phonons in rocksalt NaBr showed these spectral features as "many-body effects". Modern inelastic neutron scattering measurements on a crystal of NaBr at 300K revealed diffuse intensity at high phonon energy from a predicted upper IPS. The transverse optical (TO) part of the new features originates from phonon intermodulation between the transverse acoustic (TA) and TO phonons. The longitudinal optical (LO) spectral features originate from three-phonon coupling between the TA modes and the TO lattice modes. The partner lower IPS proves to be an "intrinsic localized mode". Interactions with the thermal bath broaden and redistribute the spectral weight of the IPS pair. These sidebands are a probe of anharmonicity and quantum noise, which originate from interactions between the phonons in NaBr.
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Submitted 9 January, 2021; v1 submitted 9 November, 2020;
originally announced November 2020.
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The Anharmonic Origin of the Giant Thermal Expansion of NaBr
Authors:
Y. Shen,
C. N. Saunders,
C. M. Bernal,
D. L. Abernathy,
M. E. Manley,
B. Fultz
Abstract:
All phonons in a single crystal of NaBr were measured by inelastic neutron scattering at temperatures of 10, 300 and 700 K. Even at 300 K the phonons, especially the longitudinal-optical (LO) phonons, showed large shifts in frequencies, and showed large broadenings in energy owing to anharmonicity. Ab initio computations were first performed with the quasiharmonic approximation (QHA), in which the…
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All phonons in a single crystal of NaBr were measured by inelastic neutron scattering at temperatures of 10, 300 and 700 K. Even at 300 K the phonons, especially the longitudinal-optical (LO) phonons, showed large shifts in frequencies, and showed large broadenings in energy owing to anharmonicity. Ab initio computations were first performed with the quasiharmonic approximation (QHA), in which the phonon frequencies depend only on $V$, and on $T$ only insofar as it alters $V$ by thermal expansion. This QHA was an unqualified failure for predicting the temperature dependence of phonon frequencies, even 300 K, and the thermal expansion was in error by a factor of four. Ab initio computations that included both anharmonicity and quasiharmonicity successfully predicted both the temperature dependence of phonons and the large thermal expansion of NaBr. The frequencies of LO phonon modes decrease significantly with temperature owing to the real part of the phonon self-energy from explicit anhamonicity, originating from the cubic anharmonicity of nearest-neighbor Na-Br bonds. Anharmonicity is not a correction to the QHA predictions of thermal expansion and thermal phonon shifts, but dominates the behavior.
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Submitted 6 September, 2019;
originally announced September 2019.
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Entropic elasticity and negative thermal expansion in a simple cubic crystal
Authors:
David Wendt,
Emil Bozin,
Joerg Neuefeind,
Katharine Page,
Wei Ku,
Limin Wang,
Brent Fultz,
Alexei Tkachenko,
Igor Zaliznyak
Abstract:
While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely-jointed chain. The origin of NTE in solids has been widely believed to be different. Our neutron scattering study of a simple cubic NTE material, ScF3, overturns this consensus. We observe th…
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While most solids expand when heated, some materials show the opposite behavior: negative thermal expansion (NTE). In polymers and biomolecules, NTE originates from the entropic elasticity of an ideal, freely-jointed chain. The origin of NTE in solids has been widely believed to be different. Our neutron scattering study of a simple cubic NTE material, ScF3, overturns this consensus. We observe that the correlation in the positions of the neighboring fluorine atoms rapidly fades on warming, indicating an uncorrelated thermal motion constrained by the rigid Sc-F bonds. This leads us to a quantitative theory of NTE in terms of entropic elasticity of a floppy network crystal, which is in remarkable agreement with experimental results. We thus reveal the formidable universality of the NTE phenomenon in soft and hard matter.
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Submitted 12 June, 2019;
originally announced June 2019.
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A nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon
Authors:
D. S. Kim,
O. Hellman,
J. Herriman,
H. L. Smith,
J. Y. Y. Lin,
N. Shulumba,
J. L. Niedziela,
C. W. Li,
D. L. Abernathy,
B. Fultz
Abstract:
Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well-understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron…
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Despite the widespread use of silicon in modern technology, its peculiar thermal expansion is not well-understood. Adapting harmonic phonons to the specific volume at temperature, the quasiharmonic approximation, has become accepted for simulating the thermal expansion, but has given ambiguous interpretations for microscopic mechanisms. To test atomistic mechanisms, we performed inelastic neutron scattering experiments from 100-1500K on a single-crystal of silicon to measure the changes in phonon frequencies. Our state-of-the-art ab initio calculations, which fully account for phonon anharmonicity and nuclear quantum effects, reproduced the measured shifts of individual phonons with temperature, whereas quasiharmonic shifts were mostly of the wrong sign. Surprisingly, the accepted quasiharmonic model was found to predict the thermal expansion owing to a fortuitous cancellation of contributions from individual phonons.
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Submitted 6 February, 2018; v1 submitted 27 October, 2016;
originally announced October 2016.
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Phonon quarticity induced by changes in phonon-tracked hybridization during lattice expansion and its stabilization of rutile TiO$_2$
Authors:
Tian Lan,
C. W. Li,
O. Hellman,
D. Kim,
J. A. Muñoz,
H. Smith,
D. L. Abernathy,
B. Fultz
Abstract:
Although the rutile structure of TiO$_2$ is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000\,K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density o…
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Although the rutile structure of TiO$_2$ is stable at high temperatures, the conventional quasiharmonic approximation predicts that several acoustic phonons decrease anomalously to zero frequency with thermal expansion, incorrectly predicting a structural collapse at temperatures well below 1000\,K. Inelastic neutron scattering was used to measure the temperature dependence of the phonon density of states (DOS) of rutile TiO$_2$ from 300 to 1373\,K. Surprisingly, these anomalous acoustic phonons were found to increase in frequency with temperature. First-principles calculations showed that with lattice expansion, the potentials for the anomalous acoustic phonons transform from quadratic to quartic, stabilizing the rutile phase at high temperatures. In these modes, the vibrational displacements of adjacent Ti and O atoms cause variations in hybridization of $3d$ electrons of Ti and $2p$ electrons of O atoms. With thermal expansion, the energy variation in this "phonon-tracked hybridization" flattens the bottom of the interatomic potential well between Ti and O atoms, and induces a quarticity in the phonon potential.
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Submitted 16 August, 2015; v1 submitted 16 February, 2015;
originally announced February 2015.
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Nonharmonic Phonons in $α$-Iron at High Temperatures
Authors:
L. Mauger,
M. S. Lucas,
J. A. Muñoz,
S. J. Tracy,
M. Kresch,
Yuming Xiao,
Paul Chow,
B. Fultz
Abstract:
Phonon densities of states (DOS) of bcc $α$-$^{57}$Fe were measured from room temperature through the 1044K Curie transition and the 1185K 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 700K, showing strongly nonhar…
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Phonon densities of states (DOS) of bcc $α$-$^{57}$Fe were measured from room temperature through the 1044K Curie transition and the 1185K 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 700K, 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.
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Submitted 23 April, 2014; v1 submitted 19 April, 2014;
originally announced April 2014.
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Anharmonic lattice dynamics of Ag$_2$O studied by inelastic neutron scattering and first principles molecular dynamics simulations
Authors:
Tian Lan,
Chen W. Li,
J. L. Niedziela,
Hillary Smith,
Douglas L. Abernathy,
George R. Rossman,
Brent Fultz
Abstract:
Inelastic neutron scattering measurements on silver oxide (Ag$_2$O) with the cuprite structure were performed at temperatures from 40 to 400\,K, and Fourier transform far-infrared spectra were measured from 100 to 300\,K. The measured phonon densities of states and the infrared spectra showed unusually large energy shifts with temperature, and large linewidth broadenings. First principles molecula…
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Inelastic neutron scattering measurements on silver oxide (Ag$_2$O) with the cuprite structure were performed at temperatures from 40 to 400\,K, and Fourier transform far-infrared spectra were measured from 100 to 300\,K. The measured phonon densities of states and the infrared spectra showed unusually large energy shifts with temperature, and large linewidth broadenings. First principles molecular dynamics (MD) calculations were performed at various temperatures, successfully accounting for the negative thermal expansion (NTE) and local dynamics. Using the Fourier-transformed velocity autocorrelation method, the MD calculations reproduced the large anharmonic effects of Ag$_2$O, and were in excellent agreement with the neutron scattering data. The quasiharmonic approximation (QHA) was less successful in accounting for much of the phonon behavior. The QHA could account for some of the NTE below 250 K, although not at higher temperatures. Strong anharmonic effects were found for both phonons and for the NTE. The lifetime broadenings of Ag$_2$O were explained by anharmonic perturbation theory, which showed rich interactions between the Ag-dominated modes and the O-dominated modes in both up- and down-conversion processes.
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Submitted 3 March, 2014; v1 submitted 14 February, 2014;
originally announced February 2014.
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Phonon Density of States of LaFeAsO1-xFx
Authors:
A. D. Christianson,
M. D. Lumsden,
O. Delaire,
M. B. Stone,
D. L. Abernathy,
M. A. McGuire,
A. S. Sefat,
R. Jin,
B. C. Sales,
D. Mandrus,
E. D. Mun,
P. C. Canfield,
J. Y. Y. Lin,
M. Lucas,
M. Kresch,
J. B. Keith,
B. Fultz,
E. A. Goremychkin,
R. J. McQueeney
Abstract:
We have studied the phonon density of states (PDOS) in LaFeAsO1-xFx with inelastic neutron scattering methods. The PDOS of the parent compound(x=0) is very similar to the PDOS of samples optimally doped with fluorine to achieve the maximum Tc (x~0.1). Good agreement is found between the experimental PDOS and first-principle calculations with the exception of a small difference in Fe mode frequen…
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We have studied the phonon density of states (PDOS) in LaFeAsO1-xFx with inelastic neutron scattering methods. The PDOS of the parent compound(x=0) is very similar to the PDOS of samples optimally doped with fluorine to achieve the maximum Tc (x~0.1). Good agreement is found between the experimental PDOS and first-principle calculations with the exception of a small difference in Fe mode frequencies. The PDOS reported here is not consistent with conventional electron-phonon mediated superconductivity.
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Submitted 22 July, 2008;
originally announced July 2008.
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White Lines and 3d-Occupancy for the 3d Transition-Metal Oxides
Authors:
J. Graetz,
C. C. Ahn,
H. Ouyang,
P. Rez,
B. Fultz
Abstract:
Electron energy-loss spectrometry was employed to measure the white lines at the L23 absorption edges of the 3d transition-metal oxides and lithium transition-metal oxides. The white-line ratio (L3/L2) was found to increase between d^0 and d^5 and decrease between d^5 and d^10, consistent with previous results for the transition metals and their oxides. The intensities of the white lines, normal…
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Electron energy-loss spectrometry was employed to measure the white lines at the L23 absorption edges of the 3d transition-metal oxides and lithium transition-metal oxides. The white-line ratio (L3/L2) was found to increase between d^0 and d^5 and decrease between d^5 and d^10, consistent with previous results for the transition metals and their oxides. The intensities of the white lines, normalized to the post-edge background, are linear for the 3d transition-metal oxides and lithium transition-metal oxides. An empirical correlation between normalized white-line intensity and 3d occupancy is established. It provides a method for measuring changes in the 3d-state occupancy. As an example, this empirical relationship is used to measure changes in the transition-metal valences of Li_{1-x}Ni_{0.8}Co_{0.2}O_2 in the range of 0 < x < 0.64. In these experiments the 3d occupancy of the nickel ion decreased upon lithium deintercalation, while the cobalt valence remained constant.
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Submitted 23 June, 2004;
originally announced June 2004.