Anharmonic phonons, thermal expansion, and nuclear quantum effects in Zn

V. V. Ladygin; F. Knoop; C. M. Bernal-Choban; G. E. Granroth; B. Fultz

doi:10.1103/pr3j-jwd5

Anharmonic phonons, thermal expansion, and nuclear quantum effects in Zn

V. V. Ladygin
, F. Knoop
, C. M. Bernal-Choban
, G. E. Granroth
, B. Fultz

Direct Geometry

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

Abstract

The anharmonic behavior of phonons and thermal expansion of hexagonal zinc were studied from 15 to 690 K by inelastic neutron scattering (INS) and ab initio simulations. Phonon spectra were measured for Q-points covering the full Brillouin zone, giving the phonon density of states (DOS) and dispersions along high-symmetry directions. The dispersions were sharp at 15 K, but diffuse intensity was observed at energies above them. The dispersions broadened with temperature T and the diffuse intensity became stronger. This diffuse intensity appeared in all INS measurements and simulations, except for classical molecular dynamics at 15 K. The temperature-dependent effective potential (TDEP) method, which included the nuclear quantum effect from zero-point vibrational dynamics, was used to calculate the free energy and thermal expansion. For T<100K nuclear quantum effects were essential for obtaining the correct negative thermal expansion, and path integral molecular dynamics (PIMD) was particularly effective for obtaining the negative thermal expansion in the basal plane. A Heisenberg-Langevin model for interacting phonons coupled to a thermal bath was able to reproduce the shape and intensity of the diffuse spectral features.

Original language	English
Article number	125001
Journal	Physical Review Materials
Volume	9
Issue number	12
DOIs	https://doi.org/10.1103/pr3j-jwd5
State	Published - Dec 2025

Funding

The authors thank S. Lohaus for assisting in experimental data collection, and C. N. Saunders for discussions about experimental data reduction. This research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. XRD measurements were performed at the Center for Nanophase Materials Sciences (CNMS), a U.S. Department of Energy Office of Science User Facility operated by Oak Ridge National Laboratory, under the CNMS user program. F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630. Some computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at NSC and PDC, partially funded by the Swedish Research Council through Grant Agreement No. 2022-06725. V.L. and F.K. acknowledge Olle Hellman and Alos Castellano for fruitful discussions. We acknowledge Dr. Jong Keum for performing the cryogenic X-ray diffraction (XRD) measurements. This work used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. This work was supported by the DOE Office of Science, BES, under Contract No. DE-FG02-03ER46055. The authors thank S. Lohaus for assisting in experimental data collection, and C. N. Saunders for discussions about experimental data reduction. This research used resources at the Spallation Neutron Source, a DOE Office of Science User Facility operated by the Oak Ridge National Laboratory. XRD measurements were performed at the Center for Nanophase Materials Sciences (CNMS), a U.S. Department of Energy Office of Science User Facility operated by Oak Ridge National Laboratory, under the CNMS user program. F.K. acknowledges support from the Swedish Research Council (VR) program 2020-04630. Some computations were enabled by resources provided by the National Academic Infrastructure for Supercomputing in Sweden (NAISS) at NSC and PDC, partially funded by the Swedish Research Council through Grant Agreement No. 2022-06725. V.L. and F.K. acknowledge Olle Hellman and Aloïs Castellano for fruitful discussions. We acknowledge Dr. Jong Keum for performing the cryogenic X-ray diffraction (XRD) measurements. This work used resources of the National Energy Research Scientific Computing Center (NERSC), a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231. This work was supported by the DOE Office of Science, BES, under Contract No. DE-FG02-03ER46055.

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title = "Anharmonic phonons, thermal expansion, and nuclear quantum effects in Zn",

abstract = "The anharmonic behavior of phonons and thermal expansion of hexagonal zinc were studied from 15 to 690 K by inelastic neutron scattering (INS) and ab initio simulations. Phonon spectra were measured for Q-points covering the full Brillouin zone, giving the phonon density of states (DOS) and dispersions along high-symmetry directions. The dispersions were sharp at 15 K, but diffuse intensity was observed at energies above them. The dispersions broadened with temperature T and the diffuse intensity became stronger. This diffuse intensity appeared in all INS measurements and simulations, except for classical molecular dynamics at 15 K. The temperature-dependent effective potential (TDEP) method, which included the nuclear quantum effect from zero-point vibrational dynamics, was used to calculate the free energy and thermal expansion. For T<100K nuclear quantum effects were essential for obtaining the correct negative thermal expansion, and path integral molecular dynamics (PIMD) was particularly effective for obtaining the negative thermal expansion in the basal plane. A Heisenberg-Langevin model for interacting phonons coupled to a thermal bath was able to reproduce the shape and intensity of the diffuse spectral features.",

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N2 - The anharmonic behavior of phonons and thermal expansion of hexagonal zinc were studied from 15 to 690 K by inelastic neutron scattering (INS) and ab initio simulations. Phonon spectra were measured for Q-points covering the full Brillouin zone, giving the phonon density of states (DOS) and dispersions along high-symmetry directions. The dispersions were sharp at 15 K, but diffuse intensity was observed at energies above them. The dispersions broadened with temperature T and the diffuse intensity became stronger. This diffuse intensity appeared in all INS measurements and simulations, except for classical molecular dynamics at 15 K. The temperature-dependent effective potential (TDEP) method, which included the nuclear quantum effect from zero-point vibrational dynamics, was used to calculate the free energy and thermal expansion. For T<100K nuclear quantum effects were essential for obtaining the correct negative thermal expansion, and path integral molecular dynamics (PIMD) was particularly effective for obtaining the negative thermal expansion in the basal plane. A Heisenberg-Langevin model for interacting phonons coupled to a thermal bath was able to reproduce the shape and intensity of the diffuse spectral features.

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Anharmonic phonons, thermal expansion, and nuclear quantum effects in Zn

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