Thermal expansion and phonon anharmonicity of cuprite studied by inelastic neutron scattering and ab initio calculations

Saunders, Claire N.; Kim, D. S.; Hellman, O.; Smith, Hillary L.; Weadock, Nick J.; Omelchenko, Stefan T.; Granroth, Garrett E.; Bernal-Choban, Camille M.; Lohaus, S. H.; Abernathy, Douglas L.; Fultz, B.

doi:10.1103/PhysRevB.105.174308

Title: Thermal expansion and phonon anharmonicity of cuprite studied by inelastic neutron scattering and ab initio calculations

Journal Article · 31 May 2022 · Physical Review. B

DOI: https://doi.org/10.1103/PhysRevB.105.174308 · OSTI ID:1873803

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California Institute of Technology (CalTech), Pasadena, CA (United States)
Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)
Linkoping University (Sweden); Weizmann Institute of Science, Rehovot (Israel)
Swarthmore College, Swarthmore, PA (United States)
Univ. of Colorado, Boulder, CO (United States)
Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)

Inelastic neutron scattering measurements were performed with a time-of-flight chopper spectrometer to observe phonons in all parts of the Brillouin zone of a single crystal of cuprite Cu₂O. We reduced the experimental data to phonon dispersions in the high-symmetry directions, and changes between 10 and 300 K are reported. In this paper, we show ab initio quasiharmonic (QH) and anharmonic (AH) calculations of phonon dispersions. We performed all AH calculations with a temperature-dependent effective potential method. Both QH and AH calculations account for the small negative thermal expansion of cuprite at low temperatures. However, the measured temperature-dependent phonon behavior was predicted more accurately with the AH calculations than the QH ones. Nevertheless, at 300 K, the cubic AH used in this paper did not entirely account for the experimental phonon dispersions in cuprite.

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Research Organization:: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Basic Energy Sciences (BES)

Grant/Contract Number:: AC05-00OR22725; FG02-03ER46055

OSTI ID:: 1873803

Journal Information:: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 17 Vol. 105; ISSN 2469-9950

Publisher:: American Physical Society (APS)Copyright Statement

Country of Publication:: United States

Language:: English

References (62)

Lattice Vibrations of Cu2O at the Long Wave Limit Carabatos, C. physica status solidi (b), Vol. 37, Issue 2 https://doi.org/10.1002/pssb.19700370228	journal	January 1970
The elastic constants of cuprous oxide Hallberg, J.; Hanson, R. C. physica status solidi (b), Vol. 42, Issue 1 https://doi.org/10.1002/pssb.19700420131	journal	January 1970
Light Scattering and Infrared Absorption in Cuprous Oxide Reydellet, J.; Balkanski, M.; Trivich, D. Physica Status Solidi (b), Vol. 52, Issue 1 https://doi.org/10.1002/pssb.2220520120	journal	July 1972
The long wave modes of the Cu2O lattice Huang, Kun Zeitschrift f�r Physik, Vol. 171, Issue 1 https://doi.org/10.1007/BF01379349	journal	February 1963
Neutron powder diffraction study of the thermal expansion of cuprite Sch�fer, W.; Kirfel, A. Applied Physics A: Materials Science & Processing, Vol. 74, Issue 0 https://doi.org/10.1007/s003390201601	journal	December 2002
First order Raman spectrum of Cu2O Balkanski, M.; Nusimovici, M. A.; Reydellet, J. Solid State Communications, Vol. 7, Issue 11 https://doi.org/10.1016/0038-1098(69)90768-6	journal	June 1969
Surface damage effects on allowed and forbidden phonon raman scattering in cuprous oxide Compaan, A. Solid State Communications, Vol. 16, Issue 3 https://doi.org/10.1016/0038-1098(75)90171-4	journal	February 1975
Efficiency of ab-initio total energy calculations for metals and semiconductors using a plane-wave basis set Kresse, G.; Furthmüller, J. Computational Materials Science, Vol. 6, Issue 1, p. 15-50 https://doi.org/10.1016/0927-0256(96)00008-0	journal	July 1996
The dielectric and lattice vibrational spectrum of cuprous oxide Dawson, P.; Hargreave, M. M.; Wilkinson, G. R. Journal of Physics and Chemistry of Solids, Vol. 34, Issue 12 https://doi.org/10.1016/S0022-3697(73)80067-8	journal	December 1973
The thermal behaviour of cuprite: An XRD–EXAFS combined approach Dapiaggi, M.; Tiano, W.; Artioli, G. Nuclear Instruments and Methods in Physics Research Section B: Beam Interactions with Materials and Atoms, Vol. 200 https://doi.org/10.1016/S0168-583X(02)01682-8	journal	January 2003
Mantid—Data analysis and visualization package for neutron scattering and μ SR experiments 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 https://doi.org/10.1016/j.nima.2014.07.029	journal	November 2014
The Spallation Neutron Source in Oak Ridge: A powerful tool for materials research Mason, T. E.; Abernathy, D.; Anderson, I. Physica B: Condensed Matter, Vol. 385-386 https://doi.org/10.1016/j.physb.2006.05.281	journal	November 2006
First principles phonon calculations in materials science Togo, Atsushi; Tanaka, Isao Scripta Materialia, Vol. 108 https://doi.org/10.1016/j.scriptamat.2015.07.021	journal	November 2015
Cu and Cu-Based Nanoparticles: Synthesis and Applications in Catalysis Gawande, Manoj B.; Goswami, Anandarup; Felpin, François-Xavier Chemical Reviews, Vol. 116, Issue 6 https://doi.org/10.1021/acs.chemrev.5b00482	journal	March 2016
Ferromagnetism of Single-Crystalline Cu ₂ O Induced through Poly( N -vinyl-2-pyrrolidone) Interaction Triggering d-Orbital Alteration Kim, Do Yoon; Kim, Chang Woo; Sohn, Jong Hwa The Journal of Physical Chemistry C, Vol. 119, Issue 23 https://doi.org/10.1021/acs.jpcc.5b02762	journal	June 2015
Thermoelectric Properties of p-Type Cu ₂ O, CuO, and NiO from Hybrid Density Functional Theory Linnera, Jarno; Sansone, Giuseppe; Maschio, Lorenzo The Journal of Physical Chemistry C, Vol. 122, Issue 27 https://doi.org/10.1021/acs.jpcc.8b04281	journal	June 2018
Direct observation of d-orbital holes and Cu–Cu bonding in Cu2O Zuo, J. M.; Kim, M.; O'Keeffe, M. Nature, Vol. 401, Issue 6748 https://doi.org/10.1038/43403	journal	September 1999
Cu2O nanocubes with mixed oxidation-state facets for (photo)catalytic hydrogenation of carbon dioxide Wan, Lili; Zhou, Qixing; Wang, Xin Nature Catalysis, Vol. 2, Issue 10 https://doi.org/10.1038/s41929-019-0338-z	journal	September 2019
LATTICE DYNAMICS OF CUPRITE (Cu ₂ O) Kugel, G. E.; Carabatos, C.; Kress, W. Le Journal de Physique Colloques, Vol. 42, Issue C6 https://doi.org/10.1051/jphyscol:19816262	journal	December 1981
Infrared Optical Properties of Cuprous Oxide O'Keeffe, Michael The Journal of Chemical Physics, Vol. 39, Issue 7 https://doi.org/10.1063/1.1734530	journal	October 1963
Design and operation of the wide angular-range chopper spectrometer ARCS at the Spallation Neutron Source Abernathy, D. L.; Stone, M. B.; Loguillo, M. J. Review of Scientific Instruments, Vol. 83, Issue 1 https://doi.org/10.1063/1.3680104	journal	January 2012
Phonons, nature of bonding, and their relation to anomalous thermal expansion behavior of M ₂ O (M = Au, Ag, Cu) Gupta, M. K.; Mittal, R.; Chaplot, S. L. Journal of Applied Physics, Vol. 115, Issue 9 https://doi.org/10.1063/1.4867437	journal	March 2014
Design and operating characteristic of a vacuum furnace for time-of-flight inelastic neutron scattering measurements Niedziela, J. L.; Mills, R.; Loguillo, M. J. Review of Scientific Instruments, Vol. 88, Issue 10 https://doi.org/10.1063/1.5007089	journal	October 2017
Thermal expansion in insulating solids from first principles Ritz, Ethan T.; Li, Sabrina J.; Benedek, Nicole A. Journal of Applied Physics, Vol. 126, Issue 17 https://doi.org/10.1063/1.5125779	journal	November 2019
Negative thermal expansion of Cu ₂ O studied by quasi-harmonic approximation and cubic force-constant method Linnera, Jarno; Erba, Alessandro; Karttunen, Antti J. The Journal of Chemical Physics, Vol. 151, Issue 18 https://doi.org/10.1063/1.5126931	journal	November 2019
Nuclear quantum effect with pure anharmonicity and the anomalous thermal expansion of silicon Kim, D. S.; Hellman, O.; Herriman, J. Proceedings of the National Academy of Sciences, Vol. 115, Issue 9 https://doi.org/10.1073/pnas.1707745115	journal	February 2018
Neutron scattering lengths and cross sections Sears, Varley F. Neutron News, Vol. 3, Issue 3 https://doi.org/10.1080/10448639208218770	journal	January 1992
XXXVI. On unilateral conductivity Schuster, Arthur The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Vol. 48, Issue 318 https://doi.org/10.1080/14786447408641116	journal	October 1874
Thermal expansion of cuprous oxide at low temperatures White, G. K. Journal of Physics C: Solid State Physics, Vol. 11, Issue 11 https://doi.org/10.1088/0022-3719/11/11/009	journal	June 1978
Symmetry of Excitons in Cu 2 O Elliott, R. J. Physical Review, Vol. 124, Issue 2 https://doi.org/10.1103/PhysRev.124.340	journal	October 1961
Scattering of Neutrons by an Anharmonic Crystal Maradudin, A. A.; Fein, A. E. Physical Review, Vol. 128, Issue 6 https://doi.org/10.1103/PhysRev.128.2589	journal	December 1962
Far-Infrared Properties of Cuprous Oxide Heltemes, E. C. Physical Review, Vol. 141, Issue 2 https://doi.org/10.1103/PhysRev.141.803	journal	January 1966
Study of photoluminescence in Cu 2 O Petroff, Y.; Yu, P. Y.; Shen, Y. R. Physical Review B, Vol. 12, Issue 6 https://doi.org/10.1103/PhysRevB.12.2488	journal	September 1975
Study of phonon dispersion relations in cuprous oxide by inelastic neutron scattering Beg, M. M.; Shapiro, S. M. Physical Review B, Vol. 13, Issue 4 https://doi.org/10.1103/PhysRevB.13.1728	journal	February 1976
High-pressure x-ray study of Cu 2 O and Ag 2 O Werner, A.; Hochheimer, H. D. Physical Review B, Vol. 25, Issue 9 https://doi.org/10.1103/PhysRevB.25.5929	journal	May 1982
Raman scattering and photoluminescence in Cu 2 O under hydrostatic pressure Reimann, K.; Syassen, K. Physical Review B, Vol. 39, Issue 15 https://doi.org/10.1103/PhysRevB.39.11113	journal	May 1989
Ab initiomolecular dynamics for liquid metals Kresse, G.; Hafner, J. Physical Review B, Vol. 47, Issue 1, p. 558-561 https://doi.org/10.1103/PhysRevB.47.558	journal	January 1993
Ab initio molecular-dynamics simulation of the liquid-metal–amorphous-semiconductor transition in germanium Kresse, G.; Hafner, J. Physical Review B, Vol. 49, Issue 20, p. 14251-14269 https://doi.org/10.1103/PhysRevB.49.14251	journal	May 1994
Efficient iterative schemes for ab initio total-energy calculations using a plane-wave basis set Kresse, G.; Furthmüller, J. Physical Review B, Vol. 54, Issue 16, p. 11169-11186 https://doi.org/10.1103/PhysRevB.54.11169	journal	October 1996
From ultrasoft pseudopotentials to the projector augmented-wave method Kresse, G.; Joubert, D. Physical Review B, Vol. 59, Issue 3, p. 1758-1775 https://doi.org/10.1103/PhysRevB.59.1758	journal	January 1999
Raman Scattering, Luminescence, and Exciton-Phonon Coupling in Cu 2 O Compaan, A.; Cummins, H. Z. Physical Review B, Vol. 6, Issue 12 https://doi.org/10.1103/PhysRevB.6.4753	journal	December 1972
Negative thermal expansion and local dynamics in Cu 2 O and Ag 2 O Sanson, A.; Rocca, F.; Dalba, G. Physical Review B, Vol. 73, Issue 21 https://doi.org/10.1103/PhysRevB.73.214305	journal	June 2006
Inelastic neutron scattering and lattice dynamical calculation of negative thermal expansion compounds Cu 2 O and Ag 2 O Mittal, R.; Chaplot, S. L.; Mishra, S. K. Physical Review B, Vol. 75, Issue 17 https://doi.org/10.1103/PhysRevB.75.174303	journal	May 2007
Phonons in aluminum at high temperatures studied by inelastic neutron scattering Kresch, M.; Lucas, M.; Delaire, O. Physical Review B, Vol. 77, Issue 2 https://doi.org/10.1103/PhysRevB.77.024301	journal	January 2008
Ab initio lattice dynamics and thermal expansion of Cu 2 O Bohnen, Klaus-Peter; Heid, Rolf; Pintschovius, Lothar Physical Review B, Vol. 80, Issue 13 https://doi.org/10.1103/PhysRevB.80.134304	journal	October 2009
Lattice dynamics of anharmonic solids from first principles Hellman, O.; Abrikosov, I. A.; Simak, S. I. Physical Review B, Vol. 84, Issue 18 https://doi.org/10.1103/PhysRevB.84.180301	journal	November 2011
Importance of reference Hamiltonians containing exact exchange for accurate one-shot G W calculations of Cu 2 O Isseroff, Leah Y.; Carter, Emily A. Physical Review B, Vol. 85, Issue 23 https://doi.org/10.1103/PhysRevB.85.235142	journal	June 2012
Temperature dependent effective potential method for accurate free energy calculations of solids Hellman, Olle; Steneteg, Peter; Abrikosov, I. A. Physical Review B, Vol. 87, Issue 10 https://doi.org/10.1103/PhysRevB.87.104111	journal	March 2013
Temperature-dependent effective third-order interatomic force constants from first principles Hellman, Olle; Abrikosov, I. A. Physical Review B, Vol. 88, Issue 14 https://doi.org/10.1103/PhysRevB.88.144301	journal	October 2013
Framework flexibility and the negative thermal expansion mechanism of copper(I) oxide Cu 2 O Rimmer, Leila H. N.; Dove, Martin T.; Winkler, Björn Physical Review B, Vol. 89, Issue 21 https://doi.org/10.1103/PhysRevB.89.214115	journal	June 2014
Strongly Constrained and Appropriately Normed Semilocal Density Functional Sun, Jianwei; Ruzsinszky, Adrienn; Perdew, John P. Physical Review Letters, Vol. 115, Issue 3 https://doi.org/10.1103/PhysRevLett.115.036402	journal	July 2015
Anharmonic Origin of the Giant Thermal Expansion of NaBr Shen, Y.; Saunders, C. N.; Bernal, C. M. Physical Review Letters, Vol. 125, Issue 8 https://doi.org/10.1103/PhysRevLett.125.085504	journal	August 2020
Resonance Raman Scattering at the Forbidden Yellow Exciton in Cu 2 O Yu, P. Y.; Shen, Y. R.; Petroff, Y. Physical Review Letters, Vol. 30, Issue 7 https://doi.org/10.1103/PhysRevLett.30.283	journal	February 1973
The Copper Oxide Rectifier Brattain, Walter H. Reviews of Modern Physics, Vol. 23, Issue 3 https://doi.org/10.1103/RevModPhys.23.203	journal	July 1951
Thermal expansion in cuprite-type structures from 10 K to decomposition temperature: Cu ₂ O and Ag ₂ O Tiano, Walter; Dapiaggi, Monica; Artioli, Gilberto Journal of Applied Crystallography, Vol. 36, Issue 6 https://doi.org/10.1107/S0021889803020818	journal	November 2003
UB matrix implementation for inelastic neutron scattering experiments Lumsden, M. D.; Robertson, J. L.; Yethiraj, M. Journal of Applied Crystallography, Vol. 38, Issue 3 https://doi.org/10.1107/S0021889805004875	journal	May 2005
Raman Effect in Cuprous Oxide Compared with Infrared Absorption Taylor, J. C. W.; Weichman, F. L. Canadian Journal of Physics, Vol. 49, Issue 5 https://doi.org/10.1139/p71-078	journal	March 1971
Statistical Physics of Crystals and Liquids Wallace, Duane C. world Scientific https://doi.org/10.1142/5060	book	January 2003
Theory of thermal expansion: Quasi-harmonic approximation and corrections from quasi-particle renormalization Allen, Philip B. Modern Physics Letters B, Vol. 34, Issue 02 https://doi.org/10.1142/S0217984920500256	journal	December 2019
Multiphonon: Phonon Density of States tools for Inelastic Neutron Scattering Powder Data Y. Y. Lin, Jiao; Islam, Fahima; Kresh, Max The Journal of Open Source Software, Vol. 3, Issue 21 https://doi.org/10.21105/joss.00440	journal	January 2018
Synthesis of Cu2O/CuO Nanocrystals and Their Application to H2S Sensing Mikami, Kazuki; Kido, Yuta; Akaishi, Yuji Sensors, Vol. 19, Issue 1 https://doi.org/10.3390/s19010211	journal	January 2019
Copper (I) oxide (Cu_{2) based solar cells - a review} Abdu, Y.; Musa, Ao Bayero Journal of Pure and Applied Sciences, Vol. 2, Issue 2 https://doi.org/10.4314/bajopas.v2i2.63717	journal	February 2011