Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements
Abstract
The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the N-body distribution of atomic displacements, ρN. We calculate the information-theoretic entropy from the expectation value of lnρN. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye–Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. We apply this approach to elemental body-centered cubic sodium and face-centered cubic aluminum, showing good agreement with experimental values above the Debye temperatures of the metals. Below the Debye temperatures, we extract an effective vibrational density of states from eigenvalues of the covariance matrix, and then evaluate the entropy quantum mechanically, again yielding good agreement with experiment down to low temperatures. Our method readily generalizes to complex solids, as we demonstrate for a high entropy alloy. Further, our method applies in cases where the quasiharmonic approximation fails, as we demonstrate by calculating the HCP/BCC transition in Ti.
- Publication Date:
- Research Org.:
- Carnegie Mellon Univ., Pittsburgh, PA (United States)
- Sponsoring Org.:
- USDOE Office of Science (SC)
- OSTI Identifier:
- 1865698
- Alternate Identifier(s):
- OSTI ID: 1865900
- Grant/Contract Number:
- SC0014506; AC02-05CH11231
- Resource Type:
- Published Article
- Journal Name:
- Entropy
- Additional Journal Information:
- Journal Name: Entropy Journal Volume: 24 Journal Issue: 5; Journal ID: ISSN 1099-4300
- Publisher:
- MDPI AG
- Country of Publication:
- Switzerland
- Language:
- English
- Subject:
- 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; ab initio; vibrational entropy; information theory
Citation Formats
Huang, Yang, and Widom, Michael. Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements. Switzerland: N. p., 2022.
Web. doi:10.3390/e24050618.
Huang, Yang, & Widom, Michael. Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements. Switzerland. https://doi.org/10.3390/e24050618
Huang, Yang, and Widom, Michael. Thu .
"Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements". Switzerland. https://doi.org/10.3390/e24050618.
@article{osti_1865698,
title = {Vibrational Entropy of Crystalline Solids from Covariance of Atomic Displacements},
author = {Huang, Yang and Widom, Michael},
abstractNote = {The vibrational entropy of a solid at finite temperature is investigated from the perspective of information theory. Ab initio molecular dynamics (AIMD) simulations generate ensembles of atomic configurations at finite temperature from which we obtain the N-body distribution of atomic displacements, ρN. We calculate the information-theoretic entropy from the expectation value of lnρN. At a first level of approximation, treating individual atomic displacements independently, our method may be applied using Debye–Waller B-factors, allowing diffraction experiments to obtain an upper bound on the thermodynamic entropy. At the next level of approximation we correct the overestimation through inclusion of displacement covariances. We apply this approach to elemental body-centered cubic sodium and face-centered cubic aluminum, showing good agreement with experimental values above the Debye temperatures of the metals. Below the Debye temperatures, we extract an effective vibrational density of states from eigenvalues of the covariance matrix, and then evaluate the entropy quantum mechanically, again yielding good agreement with experiment down to low temperatures. Our method readily generalizes to complex solids, as we demonstrate for a high entropy alloy. Further, our method applies in cases where the quasiharmonic approximation fails, as we demonstrate by calculating the HCP/BCC transition in Ti.},
doi = {10.3390/e24050618},
journal = {Entropy},
number = 5,
volume = 24,
place = {Switzerland},
year = {Thu Apr 28 00:00:00 EDT 2022},
month = {Thu Apr 28 00:00:00 EDT 2022}
}
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