### Abstract

The lattice statics Green’s function describes the linear response of displacement to the application of a force on a crystal lattice. From a macroscopie point of view, the crystal lattice behaves like an anisotropic elastic body. Therefore, the lattice statics Green’s function must approach the elastic Green’s function for large distances from the point at which the force is applied. The lattice used in calculating the lattice Green’s function should have the elastic constants corresponding to the crystal and a symmetrical stress tensor in the continuum elastic limit. In order to satisfy these conditions, three-body forces are introduced. The Green’s function for the infinite lattice with short-range atomic interaction is calculated immediately by translational symmetry. The Green’s function for the defective lattice is derived from the Dyson equation. The definitive Green’s function for the semi-infinite lattice is presented.

Original language | English |
---|---|

Pages (from-to) | 431-449 |

Number of pages | 19 |

Journal | Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties |

Volume | 74 |

Issue number | 2 |

DOIs | |

Publication status | Published - Aug 1996 |

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### All Science Journal Classification (ASJC) codes

- Electronic, Optical and Magnetic Materials
- Materials Science(all)
- Condensed Matter Physics
- Physics and Astronomy (miscellaneous)
- Metals and Alloys

### Cite this

*Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties*,

*74*(2), 431-449. https://doi.org/10.1080/01418619608242153

**Lattice statics green’s function for a semi-infinite crystal.** / Ohsawa, K.; Kuramoto, E.; Suzuki, T.

Research output: Contribution to journal › Article

*Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties*, vol. 74, no. 2, pp. 431-449. https://doi.org/10.1080/01418619608242153

}

TY - JOUR

T1 - Lattice statics green’s function for a semi-infinite crystal

AU - Ohsawa, K.

AU - Kuramoto, E.

AU - Suzuki, T.

PY - 1996/8

Y1 - 1996/8

N2 - The lattice statics Green’s function describes the linear response of displacement to the application of a force on a crystal lattice. From a macroscopie point of view, the crystal lattice behaves like an anisotropic elastic body. Therefore, the lattice statics Green’s function must approach the elastic Green’s function for large distances from the point at which the force is applied. The lattice used in calculating the lattice Green’s function should have the elastic constants corresponding to the crystal and a symmetrical stress tensor in the continuum elastic limit. In order to satisfy these conditions, three-body forces are introduced. The Green’s function for the infinite lattice with short-range atomic interaction is calculated immediately by translational symmetry. The Green’s function for the defective lattice is derived from the Dyson equation. The definitive Green’s function for the semi-infinite lattice is presented.

AB - The lattice statics Green’s function describes the linear response of displacement to the application of a force on a crystal lattice. From a macroscopie point of view, the crystal lattice behaves like an anisotropic elastic body. Therefore, the lattice statics Green’s function must approach the elastic Green’s function for large distances from the point at which the force is applied. The lattice used in calculating the lattice Green’s function should have the elastic constants corresponding to the crystal and a symmetrical stress tensor in the continuum elastic limit. In order to satisfy these conditions, three-body forces are introduced. The Green’s function for the infinite lattice with short-range atomic interaction is calculated immediately by translational symmetry. The Green’s function for the defective lattice is derived from the Dyson equation. The definitive Green’s function for the semi-infinite lattice is presented.

UR - http://www.scopus.com/inward/record.url?scp=0030208719&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0030208719&partnerID=8YFLogxK

U2 - 10.1080/01418619608242153

DO - 10.1080/01418619608242153

M3 - Article

AN - SCOPUS:0030208719

VL - 74

SP - 431

EP - 449

JO - Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties

JF - Philosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties

SN - 0141-8610

IS - 2

ER -