# Generalization of soft phonon modes

## Abstract

Soft phonon modes describe a collective movement of atoms that transform a higher-symmetry crystal structure into a lower-symmetry crystal structure. Such structural transformations occur at finite temperatures, where the phonons (i.e., the low-temperature 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 higher-symmetry 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 higher-symmetry 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):
- LA-UR-17-31191

Journal ID: ISSN 2469-9950

- Grant/Contract Number:
- AC52-06NA25396

- Resource Type:
- Journal Article: Accepted Manuscript

- Journal Name:
- Physical Review B

- Additional Journal Information:
- Journal Volume: 97; Journal Issue: 13; Journal ID: ISSN 2469-9950

- 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.
```

```
@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 higher-symmetry crystal structure into a lower-symmetry crystal structure. Such structural transformations occur at finite temperatures, where the phonons (i.e., the low-temperature 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 higher-symmetry 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 higher-symmetry structure of which stabilizes with temperature.},

doi = {10.1103/PhysRevB.97.134114},

journal = {Physical Review B},

number = 13,

volume = 97,

place = {United States},

year = {Fri Apr 27 00:00:00 EDT 2018},

month = {Fri Apr 27 00:00:00 EDT 2018}

}