Generalization of soft phonon modes
Abstract
Soft phonon modes describe a collective movement of atoms that transform a highersymmetry crystal structure into a lowersymmetry crystal structure. Such structural transformations occur at finite temperatures, where the phonons (i.e., the lowtemperature vibrational modes) and the static perfect crystal structures provide an incomplete picture of the dynamics. In this paper, principal vibrational modes (PVMs) are introduced as descriptors of the dynamics of a material system with $N$ atoms. The PVMs represent the independent collective movements of the atoms at a given temperature. Molecular dynamics (MD) simulations, here in the form of quantum MD using density functional theory calculations, provide both the data describing the atomic motion and the data used to construct the PVMs. The leading mode, $${\mathrm{PVM}}_{0}$$, represents the $3N$dimensional direction in which the system moves with greatest amplitude. For structural phase transitions, $${\mathrm{PVM}}_{0}$$ serves as a generalization of soft phonon modes. At low temperatures, $${\mathrm{PVM}}_{0}$$ reproduces the soft phonon mode in systems where one phonon dominates the phase transformation. In general, multiple phonon modes combine to describe a transformation, in which case $${\mathrm{PVM}}_{0}$$ culls these phonon modes. Moreover, while soft phonon modes arise in the highersymmetry crystal structure, $${\mathrm{PVM}}_{0}$$ can be equally well calculated on either side of the structural phase transition. Finally, two applications demonstrate these properties: first, transitions into and out of bcc titanium, and, second, the two crystal structures proposed for the $${\beta}$$ phase of uranium, the highersymmetry structure of which stabilizes with temperature.
 Authors:

 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Publication Date:
 Research Org.:
 Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
 Sponsoring Org.:
 USDOE; New Mexico Small Business Assistance Program (NMSBA) (United States)
 OSTI Identifier:
 1441318
 Alternate Identifier(s):
 OSTI ID: 1434984
 Report Number(s):
 LAUR1731191
Journal ID: ISSN 24699950; TRN: US1900897
 Grant/Contract Number:
 AC5206NA25396
 Resource Type:
 Accepted Manuscript
 Journal Name:
 Physical Review B
 Additional Journal Information:
 Journal Volume: 97; Journal Issue: 13; Journal ID: ISSN 24699950
 Publisher:
 American Physical Society (APS)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; molecular dynamics; principle vibrational modes; materials
Citation Formats
Rudin, Sven P. Generalization of soft phonon modes. United States: N. p., 2018.
Web. doi:10.1103/PhysRevB.97.134114.
Rudin, Sven P. Generalization of soft phonon modes. United States. doi:10.1103/PhysRevB.97.134114.
Rudin, Sven P. Fri .
"Generalization of soft phonon modes". United States. doi:10.1103/PhysRevB.97.134114. https://www.osti.gov/servlets/purl/1441318.
@article{osti_1441318,
title = {Generalization of soft phonon modes},
author = {Rudin, Sven P.},
abstractNote = {Soft phonon modes describe a collective movement of atoms that transform a highersymmetry crystal structure into a lowersymmetry crystal structure. Such structural transformations occur at finite temperatures, where the phonons (i.e., the lowtemperature vibrational modes) and the static perfect crystal structures provide an incomplete picture of the dynamics. In this paper, principal vibrational modes (PVMs) are introduced as descriptors of the dynamics of a material system with $N$ atoms. The PVMs represent the independent collective movements of the atoms at a given temperature. Molecular dynamics (MD) simulations, here in the form of quantum MD using density functional theory calculations, provide both the data describing the atomic motion and the data used to construct the PVMs. The leading mode, ${\mathrm{PVM}}_{0}$, represents the $3N$dimensional direction in which the system moves with greatest amplitude. For structural phase transitions, ${\mathrm{PVM}}_{0}$ serves as a generalization of soft phonon modes. At low temperatures, ${\mathrm{PVM}}_{0}$ reproduces the soft phonon mode in systems where one phonon dominates the phase transformation. In general, multiple phonon modes combine to describe a transformation, in which case ${\mathrm{PVM}}_{0}$ culls these phonon modes. Moreover, while soft phonon modes arise in the highersymmetry crystal structure, ${\mathrm{PVM}}_{0}$ can be equally well calculated on either side of the structural phase transition. Finally, two applications demonstrate these properties: first, transitions into and out of bcc titanium, and, second, the two crystal structures proposed for the ${\beta}$ phase of uranium, the highersymmetry structure of which stabilizes with temperature.},
doi = {10.1103/PhysRevB.97.134114},
journal = {Physical Review B},
number = 13,
volume = 97,
place = {United States},
year = {2018},
month = {4}
}
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