# Anharmonicity and necessity of phonon eigenvectors in the phonon normal mode analysis

## Abstract

It is well known that phonon frequencies can shift from their harmonic values when elevated to a finite temperature due to the anharmonicity of interatomic potential. Here, we show that phonon eigenvectors also have shifts, but only for compound materials in which each atom has at least two types of anharmonic interactions with other atoms. Using PbTe as the model material, we show that the shifts in some phonon modes may reach as much as 50% at 800 K. Phonon eigenvectors are used in normal mode analysis (NMA) to predict phonon relaxation times and thermal conductivity. We show, from both analytical derivations and numerical simulations, that the eigenvectors are unnecessary in frequency-domain NMA, which gives a critical revision of previous knowledge. This simplification makes the calculation in frequency-domain NMA more convenient since no separate lattice dynamics calculations are needed. On the other hand, we expect our finding of anharmonic eigenvectors may make difference in time-domain NMA and other areas, like wave-packet analysis.

- Authors:

- School of Mechanical Engineering and the Birck Nanotechnology Center, Purdue University, West Lafayette, Indiana 47907-2088 (United States)

- Publication Date:

- OSTI Identifier:
- 22410227

- Resource Type:
- Journal Article

- Journal Name:
- Journal of Applied Physics

- Additional Journal Information:
- Journal Volume: 117; Journal Issue: 19; Other Information: (c) 2015 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0021-8979

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; COMPUTERIZED SIMULATION; EIGENVECTORS; INTERATOMIC FORCES; LEAD TELLURIDES; NORMAL-MODE ANALYSIS; PHONONS; POTENTIALS; THERMAL CONDUCTIVITY; WAVE PACKETS

### Citation Formats

```
Feng, Tianli, Qiu, Bo, and Ruan, Xiulin, E-mail: ruan@purdue.edu.
```*Anharmonicity and necessity of phonon eigenvectors in the phonon normal mode analysis*. United States: N. p., 2015.
Web. doi:10.1063/1.4921108.

```
Feng, Tianli, Qiu, Bo, & Ruan, Xiulin, E-mail: ruan@purdue.edu.
```*Anharmonicity and necessity of phonon eigenvectors in the phonon normal mode analysis*. United States. doi:10.1063/1.4921108.

```
Feng, Tianli, Qiu, Bo, and Ruan, Xiulin, E-mail: ruan@purdue.edu. Thu .
"Anharmonicity and necessity of phonon eigenvectors in the phonon normal mode analysis". United States. doi:10.1063/1.4921108.
```

```
@article{osti_22410227,
```

title = {Anharmonicity and necessity of phonon eigenvectors in the phonon normal mode analysis},

author = {Feng, Tianli and Qiu, Bo and Ruan, Xiulin, E-mail: ruan@purdue.edu},

abstractNote = {It is well known that phonon frequencies can shift from their harmonic values when elevated to a finite temperature due to the anharmonicity of interatomic potential. Here, we show that phonon eigenvectors also have shifts, but only for compound materials in which each atom has at least two types of anharmonic interactions with other atoms. Using PbTe as the model material, we show that the shifts in some phonon modes may reach as much as 50% at 800 K. Phonon eigenvectors are used in normal mode analysis (NMA) to predict phonon relaxation times and thermal conductivity. We show, from both analytical derivations and numerical simulations, that the eigenvectors are unnecessary in frequency-domain NMA, which gives a critical revision of previous knowledge. This simplification makes the calculation in frequency-domain NMA more convenient since no separate lattice dynamics calculations are needed. On the other hand, we expect our finding of anharmonic eigenvectors may make difference in time-domain NMA and other areas, like wave-packet analysis.},

doi = {10.1063/1.4921108},

journal = {Journal of Applied Physics},

issn = {0021-8979},

number = 19,

volume = 117,

place = {United States},

year = {2015},

month = {5}

}