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

Adam M R De Graff, Michael Thorpe

Research output: Contribution to journalArticlepeer-review

25 Scopus citations


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 languageEnglish (US)
Pages (from-to)22-31
Number of pages10
JournalActa Crystallographica Section A: Foundations of Crystallography
Issue number1
StatePublished - Jan 11 2010


  • 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


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