# The Scattering of Phonons by Infinitely Long Quantum Dislocations Segments and the Generation of Thermal Transport Anisotropy in a Solid Threaded by Many Parallel Dislocations

## Abstract

A canonical quantization procedure is applied to the interaction of elastic waves—phonons—with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach–Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly proportional to frequency. As a consequence, the thermal transport anisotropy generated on a material by the presence of a highly-oriented array of dislocations is considerably more sensitive to the frequency of each propagating mode, and, therefore, to the temperature of the material.

- Authors:

- Publication Date:

- Research Org.:
- Massachusetts Inst. of Technology (MIT), Cambridge, MA (United States)

- Sponsoring Org.:
- USDOE Office of Nuclear Energy (NE); USDOE Office of Science (SC)

- OSTI Identifier:
- 1656667

- Alternate Identifier(s):
- OSTI ID: 1802204

- Grant/Contract Number:
- SC0011090

- Resource Type:
- Published Article

- Journal Name:
- Nanomaterials

- Additional Journal Information:
- Journal Name: Nanomaterials Journal Volume: 10 Journal Issue: 9; Journal ID: ISSN 2079-4991

- Publisher:
- MDPI AG

- Country of Publication:
- Switzerland

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Chemistry; Science & Technology - Other Topics; Materials Science; Physics; thermal transport; dislocations; quantum field theory

## Citation Formats

```
Lund, Fernando, and Scheihing-Hitschfeld, Bruno. The Scattering of Phonons by Infinitely Long Quantum Dislocations Segments and the Generation of Thermal Transport Anisotropy in a Solid Threaded by Many Parallel Dislocations. Switzerland: N. p., 2020.
Web. doi:10.3390/nano10091711.
```

```
Lund, Fernando, & Scheihing-Hitschfeld, Bruno. The Scattering of Phonons by Infinitely Long Quantum Dislocations Segments and the Generation of Thermal Transport Anisotropy in a Solid Threaded by Many Parallel Dislocations. Switzerland. https://doi.org/10.3390/nano10091711
```

```
Lund, Fernando, and Scheihing-Hitschfeld, Bruno. Sat .
"The Scattering of Phonons by Infinitely Long Quantum Dislocations Segments and the Generation of Thermal Transport Anisotropy in a Solid Threaded by Many Parallel Dislocations". Switzerland. https://doi.org/10.3390/nano10091711.
```

```
@article{osti_1656667,
```

title = {The Scattering of Phonons by Infinitely Long Quantum Dislocations Segments and the Generation of Thermal Transport Anisotropy in a Solid Threaded by Many Parallel Dislocations},

author = {Lund, Fernando and Scheihing-Hitschfeld, Bruno},

abstractNote = {A canonical quantization procedure is applied to the interaction of elastic waves—phonons—with infinitely long dislocations that can oscillate about an equilibrium, straight line, configuration. The interaction is implemented through the well-known Peach–Koehler force. For small dislocation excursions away from the equilibrium position, the quantum theory can be solved to all orders in the coupling constant. We study in detail the quantum excitations of the dislocation line and its interactions with phonons. The consequences for the drag on a dislocation caused by the phonon wind are pointed out. We compute the cross-section for phonons incident on the dislocation lines for an arbitrary angle of incidence. The consequences for thermal transport are explored, and we compare our results, involving a dynamic dislocation, with those of Klemens and Carruthers, involving a static dislocation. In our case, the relaxation time is inversely proportional to frequency, rather than directly proportional to frequency. As a consequence, the thermal transport anisotropy generated on a material by the presence of a highly-oriented array of dislocations is considerably more sensitive to the frequency of each propagating mode, and, therefore, to the temperature of the material.},

doi = {10.3390/nano10091711},

journal = {Nanomaterials},

number = 9,

volume = 10,

place = {Switzerland},

year = {2020},

month = {8}

}

https://doi.org/10.3390/nano10091711