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

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.