### Abstract

We develop a general theory to calculate the vibrational response functions for disordered solids (such as glasses and disordered crystalline alloys) in the presence of long-range Coulomb forces. The longitudinal l() and transverse t() dielectric functions are shown to be related by l()/=2-/t(), where is the high-frequency electronic response. The Lyddane-Sachs-Teller relation is generalized for use in such systems. We derive sum rules involving moments that should be useful in interpreting experimental data. A general formulation is also set up for the density of states (2) and the neutron scattering law S(k,). These general results are illustrated by calculating these response functions for a model AX2 glass that roughly corresponds to vitreous silica. A periodic random network with 1536 ions in each supercell is constructed. The response functions are found using the equation-of-motion method with the Coulomb sums included explicitly using the Ewald method. The (bare) transverse response shows a rather broad optic peak whereas the longitudinal response (which is sensitive to the depolarizing field) has a sharper response at a higher frequency.

Original language | English (US) |
---|---|

Pages (from-to) | 8490-8505 |

Number of pages | 16 |

Journal | Physical Review B |

Volume | 33 |

Issue number | 12 |

DOIs | |

State | Published - 1986 |

Externally published | Yes |

### Fingerprint

### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physical Review B*,

*33*(12), 8490-8505. https://doi.org/10.1103/PhysRevB.33.8490

**Coulomb effects in disordered solids.** / Thorpe, Michael; De Leeuw, S. W.

Research output: Contribution to journal › Article

*Physical Review B*, vol. 33, no. 12, pp. 8490-8505. https://doi.org/10.1103/PhysRevB.33.8490

}

TY - JOUR

T1 - Coulomb effects in disordered solids

AU - Thorpe, Michael

AU - De Leeuw, S. W.

PY - 1986

Y1 - 1986

N2 - We develop a general theory to calculate the vibrational response functions for disordered solids (such as glasses and disordered crystalline alloys) in the presence of long-range Coulomb forces. The longitudinal l() and transverse t() dielectric functions are shown to be related by l()/=2-/t(), where is the high-frequency electronic response. The Lyddane-Sachs-Teller relation is generalized for use in such systems. We derive sum rules involving moments that should be useful in interpreting experimental data. A general formulation is also set up for the density of states (2) and the neutron scattering law S(k,). These general results are illustrated by calculating these response functions for a model AX2 glass that roughly corresponds to vitreous silica. A periodic random network with 1536 ions in each supercell is constructed. The response functions are found using the equation-of-motion method with the Coulomb sums included explicitly using the Ewald method. The (bare) transverse response shows a rather broad optic peak whereas the longitudinal response (which is sensitive to the depolarizing field) has a sharper response at a higher frequency.

AB - We develop a general theory to calculate the vibrational response functions for disordered solids (such as glasses and disordered crystalline alloys) in the presence of long-range Coulomb forces. The longitudinal l() and transverse t() dielectric functions are shown to be related by l()/=2-/t(), where is the high-frequency electronic response. The Lyddane-Sachs-Teller relation is generalized for use in such systems. We derive sum rules involving moments that should be useful in interpreting experimental data. A general formulation is also set up for the density of states (2) and the neutron scattering law S(k,). These general results are illustrated by calculating these response functions for a model AX2 glass that roughly corresponds to vitreous silica. A periodic random network with 1536 ions in each supercell is constructed. The response functions are found using the equation-of-motion method with the Coulomb sums included explicitly using the Ewald method. The (bare) transverse response shows a rather broad optic peak whereas the longitudinal response (which is sensitive to the depolarizing field) has a sharper response at a higher frequency.

UR - http://www.scopus.com/inward/record.url?scp=0004838306&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0004838306&partnerID=8YFLogxK

U2 - 10.1103/PhysRevB.33.8490

DO - 10.1103/PhysRevB.33.8490

M3 - Article

AN - SCOPUS:0004838306

VL - 33

SP - 8490

EP - 8505

JO - Physical Review B-Condensed Matter

JF - Physical Review B-Condensed Matter

SN - 0163-1829

IS - 12

ER -