Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor

Ruobing Xie, Gabrielle G. Long, Steven J. Weigand, Simon C. Moss, Tobi Carvalho, Sjoerd Roorda, Miroslav Hejna, Salvatore Torquato, Paul J. Steinhardt

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65 Scopus citations


We report the results of highly sensitive transmission X-ray scattering measurements performed at the Advanced Photon Source, Argonne National Laboratory, on nearly fully dense high-purity amorphous-silicon (a-Si) samples for the purpose of determining their degree of hyperuniformity. A perfectly hyperuniform structure has complete suppression of infinite-wavelength density fluctuations, or, equivalently, the structure factor S(q→0) = 0; the smaller the value of S(0), the higher the degree of hyperuniformity. Annealing was observed to increase the degree of hyperuniformity in a-Si where we found S(0) = 0.0075 (±0.0005), which is significantly below the computationally determined lower bound recently suggested by de Graff and Thorpe [de Graff AMR, Thorpe MF (2010) Acta Crystallogr A 66(Pt 1):22-31] based on studies of continuous randomnetwork models, but consistent with the recently proposed nearly hyperuniform network picture of a-Si. Increasing hyperuniformity is correlated with narrowing of the first diffraction peak and extension of the range of oscillations in the pair distribution function.

Original languageEnglish (US)
Pages (from-to)13250-13254
Number of pages5
JournalProceedings of the National Academy of Sciences of the United States of America
Issue number33
StatePublished - Aug 13 2013

All Science Journal Classification (ASJC) codes

  • General


  • Disordered solid
  • Glass


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