### Abstract

Liquids are in thermal equilibrium and have a non-zero structure factor = = in the long-wavelength limit where is the number density, is the temperature, is the scattering vector and is the isothermal compressibility. The first part of this result involving the number (or density) fluctuations is a purely geometrical result and does not involve any assumptions about thermal equilibrium or ergodicity, so is obeyed by all materials. From a large computer model of amorphous silicon, local number fluctuations extrapolate to give = 0.035 0.001. The same computation on a large model of vitreous silica using only the silicon atoms and rescaling the distances gives = , which suggests that this numerical result is robust and perhaps similar for all amorphous tetrahedral networks. For vitreous silica, it is found that = , close to the experimental value of = obtained recently by small-angle neutron scattering. Further experimental and modeling studies are needed to determine the relationship between the fictive temperature and structure.

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

Pages (from-to) | 22-31 |

Number of pages | 10 |

Journal | Acta Crystallographica Section A: Foundations of Crystallography |

Volume | 66 |

Issue number | 1 |

DOIs | |

State | Published - 2010 |

### Fingerprint

### Keywords

- Amorphous silicon
- Computer model
- Density fluctuations
- Long-wavelength
- Neutron scattering
- Silicon dioxide
- Structure factor
- Vitreous silica
- X-ray scattering

### ASJC Scopus subject areas

- Structural Biology

### Cite this

*Acta Crystallographica Section A: Foundations of Crystallography*,

*66*(1), 22-31. https://doi.org/10.1107/S0108767309045206

**The long-wavelength limit of the structure factor of amorphous silicon and vitreous silica.** / De Graff, Adam M R; Thorpe, Michael.

Research output: Contribution to journal › Article

*Acta Crystallographica Section A: Foundations of Crystallography*, vol. 66, no. 1, pp. 22-31. https://doi.org/10.1107/S0108767309045206

}

TY - JOUR

T1 - The long-wavelength limit of the structure factor of amorphous silicon and vitreous silica

AU - De Graff, Adam M R

AU - Thorpe, Michael

PY - 2010

Y1 - 2010

N2 - Liquids are in thermal equilibrium and have a non-zero structure factor = = in the long-wavelength limit where is the number density, is the temperature, is the scattering vector and is the isothermal compressibility. The first part of this result involving the number (or density) fluctuations is a purely geometrical result and does not involve any assumptions about thermal equilibrium or ergodicity, so is obeyed by all materials. From a large computer model of amorphous silicon, local number fluctuations extrapolate to give = 0.035 0.001. The same computation on a large model of vitreous silica using only the silicon atoms and rescaling the distances gives = , which suggests that this numerical result is robust and perhaps similar for all amorphous tetrahedral networks. For vitreous silica, it is found that = , close to the experimental value of = obtained recently by small-angle neutron scattering. Further experimental and modeling studies are needed to determine the relationship between the fictive temperature and structure.

AB - Liquids are in thermal equilibrium and have a non-zero structure factor = = in the long-wavelength limit where is the number density, is the temperature, is the scattering vector and is the isothermal compressibility. The first part of this result involving the number (or density) fluctuations is a purely geometrical result and does not involve any assumptions about thermal equilibrium or ergodicity, so is obeyed by all materials. From a large computer model of amorphous silicon, local number fluctuations extrapolate to give = 0.035 0.001. The same computation on a large model of vitreous silica using only the silicon atoms and rescaling the distances gives = , which suggests that this numerical result is robust and perhaps similar for all amorphous tetrahedral networks. For vitreous silica, it is found that = , close to the experimental value of = obtained recently by small-angle neutron scattering. Further experimental and modeling studies are needed to determine the relationship between the fictive temperature and structure.

KW - Amorphous silicon

KW - Computer model

KW - Density fluctuations

KW - Long-wavelength

KW - Neutron scattering

KW - Silicon dioxide

KW - Structure factor

KW - Vitreous silica

KW - X-ray scattering

UR - http://www.scopus.com/inward/record.url?scp=73449085128&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=73449085128&partnerID=8YFLogxK

U2 - 10.1107/S0108767309045206

DO - 10.1107/S0108767309045206

M3 - Article

C2 - 20029130

AN - SCOPUS:73449085128

VL - 66

SP - 22

EP - 31

JO - Acta Crystallographica Section A: Foundations and Advances

JF - Acta Crystallographica Section A: Foundations and Advances

SN - 0108-7673

IS - 1

ER -