title: Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor.
abstract: 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 random network 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.
authors.affiliation: X-Ray Science Division, Argonne National Laboratory, Argonne, IL 60439, USA.
authors.forename: Ruobing
authors.initials: R
authors.lastname: Xie
authors.forename: Gabrielle G
authors.initials: GG
authors.lastname: Long
authors.forename: Steven J
authors.initials: SJ
authors.lastname: Weigand
authors.forename: Simon C
authors.initials: SC
authors.lastname: Moss
authors.forename: Tobi
authors.initials: T
authors.lastname: Carvalho
authors.forename: Sjoerd
authors.initials: S
authors.lastname: Roorda
authors.forename: Miroslav
authors.initials: M
authors.lastname: Hejna
authors.forename: Salvatore
authors.initials: S
authors.lastname: Torquato
authors.forename: Paul J
authors.initials: PJ
authors.lastname: Steinhardt
mesh_terms: D008854:Microscopy, Electron; D008956:Models, Chemical; D012825:Silicon / Q000737:chemistry*; D014961:X-Ray Diffraction / Q000379:methods
chemical_list: D012825:Silicon
keywords: disordered solid; glass
references.citation: Acta Crystallogr A. 2010 Jan;66(Pt 1):22-31
references.pmid: 20029130
references.citation: Phys Rev Lett. 2005 Aug 26;95(9):090604
references.pmid: 16197201
references.citation: Proc Natl Acad Sci U S A. 2009 Jul 14;106(28):11511-4
references.pmid: 20716512
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2011 May;83(5 Pt 1):051309
references.pmid: 21728527
references.citation: Phys Rev E Stat Nonlin Soft Matter Phys. 2003 Oct;68(4 Pt 1):041113
references.pmid: 14682929
references.citation: Phys Rev B Condens Matter. 1995 Aug 15;52(8):5685-5689
references.pmid: 9981754
references.citation: Phys Rev Lett. 2010 Sep 17;105(12):125504
references.pmid: 20867656
references.citation: Phys Rev B Condens Matter. 1992 Apr 15;45(15):8355-8358
references.pmid: 10000669
references.citation: Proc Natl Acad Sci U S A. 2009 Dec 8;106(49):20658-63
references.pmid: 19918087
references.citation: Phys Rev B Condens Matter. 1994 May 15;49(20):14322-14330
references.pmid: 10010513
references.citation: Phys Rev Lett. 2012 Jun 22;108(25):255501
references.pmid: 23004617
references.citation: Science. 2012 Feb 24;335(6071):950-3
references.pmid: 22363003
references.citation: Phys Rev Lett. 1989 Apr 17;62(16):1880-1883
references.pmid: 10039794
references.citation: Phys Rev Lett. 1991 Aug 5;67(6):711-714
references.pmid: 10044969