Abstract

Characterization of microscopic structural order and in particular medium range order (MRO) in amorphous materials is challenging. A new technique is demonstrated that allows analysis of MRO using X-rays. Diffraction data were collected from a sample consisting of densely packed polystyrene-latex micro-spheres. Ptychography is used to reconstruct the sample transmission function and fluctuation microscopy applied to characterize structural order producing a detailed `fluctuation map' allowing analysis of the sample at two distinct length scales. Independent verification is provided via X-ray diffractometry. Simulations of dense random packing of spheres have also been used to explore the origin of the structural order measured.

© 2013 Optical Society of America

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    [Crossref]
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    [Crossref]
  3. W. D. Luedtke and U. Landman, “Preparation, structure, dynamics, and energetics of amorphous silicon: A molecular-dynamics study,” Phys. Rev. B Condens. Matter 40(2), 1164–1174 (1989).
    [Crossref] [PubMed]
  4. P. M. Voyles and J. R. Abelson, “Medium-range order in amorphous silicon measured by fluctuation electron microscopy,” Sol. Energy Mater. Sol. Cells 78(1–4), 85–113 (2003).
    [Crossref]
  5. S. R. Elliott, “The origin of the first sharp diffraction peak in the structure factor of covalent glasses and liquids,” J. Phys. Condens. Matter 4, 7661 (1992).
  6. S. Muthmann, F. Köhler, R. Carius, and A. Gordijn, “Structural order on different length scales in amorphous silicon investigated by Raman spectroscopy,” Phys. Status Solidi A 207(3), 544–547 (2010).
    [Crossref]
  7. J. J. Turner, X. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray diffraction microscopy of magnetic structures,” Phys. Rev. Lett. 107(3), 033904 (2011).
    [Crossref] [PubMed]
  8. P. Wochner, C. Gutt, T. Autenrieth, T. Demmer, V. Bugaev, A. D. Ortiz, A. Duri, F. Zontone, G. Grübel, and H. Dosch, “X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter,” Proc. Natl. Acad. Sci. U.S.A. 106(28), 11511–11514 (2009).
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    [Crossref]
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    [Crossref] [PubMed]
  21. J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
    [Crossref]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref]
  28. J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
  31. C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
    [Crossref] [PubMed]
  32. J. M. Gibson, M. M. Treacy, and P. M. Voyles, “Atom pair persistence in disordered materials from fluctuation microscopy,” Ultramicroscopy 83(3–4), 169–178 (2000).
    [Crossref] [PubMed]
  33. G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
    [Crossref] [PubMed]
  34. H. M. Quiney, A. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
    [Crossref]
  35. M. Skoge, A. Donev, F. H. Stillinger, and S. Torquato, “Packing hyperspheres in high-dimensional Euclidean spaces,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(4), 041127 (2006).
    [Crossref] [PubMed]
  36. B. D. Lubachevsky and F. H. Stillinger, “Geometric properties of random disk packings,” J. Stat. Phys. 60(5–6), 561–583 (1990).
    [Crossref]
  37. A. Nikulin, A. Darahanau, R. Horney, and T. Ishikawa, “High-resolution X-ray diffraction imaging of non-Bragg diffracting materials using phase retrieval X-ray diffractometry (PRXRD) technique,” Physica B 349(1–4), 281–295 (2004).
    [Crossref]
  38. Y. Jiao, F. H. Stillinger, and S. Torquato, “A superior descriptor of random textures and its predictive capacity,” Proc. Natl. Acad. Sci. U.S.A. 106(42), 17634–17639 (2009).
    [Crossref] [PubMed]
  39. R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor,” Proc. Natl. Acad. Sci. U.S.A. 110(33), 13250–13254 (2013).
    [Crossref] [PubMed]

2013 (1)

R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor,” Proc. Natl. Acad. Sci. U.S.A. 110(33), 13250–13254 (2013).
[Crossref] [PubMed]

2011 (5)

J. J. Turner, X. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray diffraction microscopy of magnetic structures,” Phys. Rev. Lett. 107(3), 033904 (2011).
[Crossref] [PubMed]

I. Tamáska, G. Dobrik, P. Nemes-Incze, K. Kertész, E. Horváth, G. Márk, T. Jászi, P. Neumann, Z. Horváth, and L. Biró, “Bioinspired photonic nanoarchitectures from graphitic thin films,” Thin Solid Films 519(12), 4078–4081 (2011).
[Crossref]

J. Hwang and P. M. Voyles, “Variable resolution fluctuation electron microscopy on Cu-Zr metallic glass using a wide range of coherent stem probe size,” Microsc. Microanal. 17(1), 67–74 (2011).
[Crossref] [PubMed]

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
[Crossref] [PubMed]

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
[Crossref] [PubMed]

2010 (2)

S. N. Bogle, L. N. Nittala, R. D. Twesten, P. M. Voyles, and J. R. Abelson, “Size analysis of nanoscale order in amorphous materials by variable-resolution fluctuation electron microscopy,” Ultramicroscopy 110(10), 1273–1278 (2010).
[Crossref]

S. Muthmann, F. Köhler, R. Carius, and A. Gordijn, “Structural order on different length scales in amorphous silicon investigated by Raman spectroscopy,” Phys. Status Solidi A 207(3), 544–547 (2010).
[Crossref]

2009 (3)

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 80(5), 051903 (2009).
[Crossref] [PubMed]

P. Wochner, C. Gutt, T. Autenrieth, T. Demmer, V. Bugaev, A. D. Ortiz, A. Duri, F. Zontone, G. Grübel, and H. Dosch, “X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter,” Proc. Natl. Acad. Sci. U.S.A. 106(28), 11511–11514 (2009).
[Crossref] [PubMed]

Y. Jiao, F. H. Stillinger, and S. Torquato, “A superior descriptor of random textures and its predictive capacity,” Proc. Natl. Acad. Sci. U.S.A. 106(42), 17634–17639 (2009).
[Crossref] [PubMed]

2008 (1)

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4(5), 394–398 (2008).
[Crossref]

2007 (3)

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Y. Takahashi, Y. Nishino, T. Ishikawa, and E. Matsubara, “Approach for three-dimensional observation of mesoscopic precipitates in alloys by coherent x-ray diffraction microscopy,” Appl. Phys. Lett. 90(18), 184105 (2007).
[Crossref]

L. Fan, D. Paterson, I. McNulty, M. M. Treacy, and J. M. Gibson, “Fluctuation X-ray microscopy: a novel approach for the structural study of disordered materials,” J. Microsc. 225(1), 41–48 (2007).
[Crossref] [PubMed]

2006 (4)

J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science 312(5772), 416–419 (2006).
[Crossref] [PubMed]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[Crossref] [PubMed]

H. M. Quiney, A. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

M. Skoge, A. Donev, F. H. Stillinger, and S. Torquato, “Packing hyperspheres in high-dimensional Euclidean spaces,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(4), 041127 (2006).
[Crossref] [PubMed]

2005 (2)

M. Treacy, J. Gibson, L. Fan, D. Paterson, and I. McNulty, “Fluctuation microscopy: a probe of medium range order,” Rep. Prog. Phys. 68(12), 2899–2944 (2005).
[Crossref]

L. Fan, I. McNulty, D. Paterson, M. M. J. Treacy, and J. M. Gibson, “Fluctuation microscopy – a tool for examining medium-range order in noncrystalline systems,” Nucl. Instrum. Methods B 238(1–4), 196–199 (2005).
[Crossref]

2004 (2)

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

A. Nikulin, A. Darahanau, R. Horney, and T. Ishikawa, “High-resolution X-ray diffraction imaging of non-Bragg diffracting materials using phase retrieval X-ray diffractometry (PRXRD) technique,” Physica B 349(1–4), 281–295 (2004).
[Crossref]

2003 (2)

P. M. Voyles and J. R. Abelson, “Medium-range order in amorphous silicon measured by fluctuation electron microscopy,” Sol. Energy Mater. Sol. Cells 78(1–4), 85–113 (2003).
[Crossref]

P. Gerbi, M. Voyles, M. M. J. Treacy, J. M. Gibson, and J. R. Abelson, “Increasing medium-range order in amorphous silicon with low-energy ion bombardment,” Appl. Phys. Lett. 82(21), 3665–3667 (2003).
[Crossref]

2002 (1)

J. M. Cowley, “Electron nanodiffraction methods for measuring medium-range order,” Ultramicroscopy 90(2–3), 197–206 (2002).
[Crossref] [PubMed]

2000 (1)

J. M. Gibson, M. M. Treacy, and P. M. Voyles, “Atom pair persistence in disordered materials from fluctuation microscopy,” Ultramicroscopy 83(3–4), 169–178 (2000).
[Crossref] [PubMed]

1998 (2)

J. Gibson, M. Treacy, P. Voyles, H. Jin, and J. Abelson, “Structural disorder induced in hydrogenated amorphous silicon by light soaking,” Appl. Phys. Lett. 73(21), 3093–3095 (1998).
[Crossref]

M. Treacy, J. Gibson, and P. Keblinski, “Paracrystallites found in evaporated amorphous tetrahedral semiconductors,” J. Non-Cryst. Solids 231(1–2), 99–110 (1998).
[Crossref]

1997 (1)

J. Gibson and M. Treacy, “Diminished medium-range order observed in annealed amorphous germanium,” Phys. Rev. Lett. 78(6), 1074–1077 (1997).
[Crossref]

1996 (2)

M. Treacy and J. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta. Crystallogr., Sect. A 52(2), 212–220 (1996).
[Crossref]

H. N. Chapman, “Phase-retrieval X-ray microscopy by Wigner-distribution deconvolution,” Ultramicroscopy 66(3–4), 153–172 (1996).
[Crossref]

1992 (1)

S. R. Elliott, “The origin of the first sharp diffraction peak in the structure factor of covalent glasses and liquids,” J. Phys. Condens. Matter 4, 7661 (1992).

1990 (1)

B. D. Lubachevsky and F. H. Stillinger, “Geometric properties of random disk packings,” J. Stat. Phys. 60(5–6), 561–583 (1990).
[Crossref]

1989 (2)

W. D. Luedtke and U. Landman, “Preparation, structure, dynamics, and energetics of amorphous silicon: A molecular-dynamics study,” Phys. Rev. B Condens. Matter 40(2), 1164–1174 (1989).
[Crossref] [PubMed]

S. R. Elliott, “The structure of amorphous hydrogenated silicon and its alloys: A review,” Adv. Phys. 38(1), 1–88 (1989).
[Crossref]

1970 (1)

R. Hegerl and W. Hoppe, “Dynamic theory of crystalline structure analysis by electron diffraction in inhomogeneous primary wave field,” Ber. Bunsenges. Phys. Chem 74(11), 1148 (1970).
[Crossref]

Abbey, B.

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4(5), 394–398 (2008).
[Crossref]

Abelson, J.

J. Gibson, M. Treacy, P. Voyles, H. Jin, and J. Abelson, “Structural disorder induced in hydrogenated amorphous silicon by light soaking,” Appl. Phys. Lett. 73(21), 3093–3095 (1998).
[Crossref]

Abelson, J. R.

S. N. Bogle, L. N. Nittala, R. D. Twesten, P. M. Voyles, and J. R. Abelson, “Size analysis of nanoscale order in amorphous materials by variable-resolution fluctuation electron microscopy,” Ultramicroscopy 110(10), 1273–1278 (2010).
[Crossref]

P. Gerbi, M. Voyles, M. M. J. Treacy, J. M. Gibson, and J. R. Abelson, “Increasing medium-range order in amorphous silicon with low-energy ion bombardment,” Appl. Phys. Lett. 82(21), 3665–3667 (2003).
[Crossref]

P. M. Voyles and J. R. Abelson, “Medium-range order in amorphous silicon measured by fluctuation electron microscopy,” Sol. Energy Mater. Sol. Cells 78(1–4), 85–113 (2003).
[Crossref]

Autenrieth, T.

P. Wochner, C. Gutt, T. Autenrieth, T. Demmer, V. Bugaev, A. D. Ortiz, A. Duri, F. Zontone, G. Grübel, and H. Dosch, “X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter,” Proc. Natl. Acad. Sci. U.S.A. 106(28), 11511–11514 (2009).
[Crossref] [PubMed]

Balaur, E.

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
[Crossref] [PubMed]

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
[Crossref] [PubMed]

Bálint, Z.

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 80(5), 051903 (2009).
[Crossref] [PubMed]

Biró, L.

I. Tamáska, G. Dobrik, P. Nemes-Incze, K. Kertész, E. Horváth, G. Márk, T. Jászi, P. Neumann, Z. Horváth, and L. Biró, “Bioinspired photonic nanoarchitectures from graphitic thin films,” Thin Solid Films 519(12), 4078–4081 (2011).
[Crossref]

Biró, L. P.

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 80(5), 051903 (2009).
[Crossref] [PubMed]

Bogle, S. N.

S. N. Bogle, L. N. Nittala, R. D. Twesten, P. M. Voyles, and J. R. Abelson, “Size analysis of nanoscale order in amorphous materials by variable-resolution fluctuation electron microscopy,” Ultramicroscopy 110(10), 1273–1278 (2010).
[Crossref]

Bugaev, V.

P. Wochner, C. Gutt, T. Autenrieth, T. Demmer, V. Bugaev, A. D. Ortiz, A. Duri, F. Zontone, G. Grübel, and H. Dosch, “X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter,” Proc. Natl. Acad. Sci. U.S.A. 106(28), 11511–11514 (2009).
[Crossref] [PubMed]

Bunk, O.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

Cadenazzi, G. A.

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
[Crossref] [PubMed]

Cai, Z.

H. M. Quiney, A. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

Carius, R.

S. Muthmann, F. Köhler, R. Carius, and A. Gordijn, “Structural order on different length scales in amorphous silicon investigated by Raman spectroscopy,” Phys. Status Solidi A 207(3), 544–547 (2010).
[Crossref]

Carvalho, T.

R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor,” Proc. Natl. Acad. Sci. U.S.A. 110(33), 13250–13254 (2013).
[Crossref] [PubMed]

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Y. Takahashi, Y. Nishino, T. Ishikawa, and E. Matsubara, “Approach for three-dimensional observation of mesoscopic precipitates in alloys by coherent x-ray diffraction microscopy,” Appl. Phys. Lett. 90(18), 184105 (2007).
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C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
[Crossref] [PubMed]

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[Crossref] [PubMed]

J. J. Turner, X. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray diffraction microscopy of magnetic structures,” Phys. Rev. Lett. 107(3), 033904 (2011).
[Crossref] [PubMed]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4(5), 394–398 (2008).
[Crossref]

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[Crossref] [PubMed]

M. Treacy, J. Gibson, L. Fan, D. Paterson, and I. McNulty, “Fluctuation microscopy: a probe of medium range order,” Rep. Prog. Phys. 68(12), 2899–2944 (2005).
[Crossref]

L. Fan, I. McNulty, D. Paterson, M. M. J. Treacy, and J. M. Gibson, “Fluctuation microscopy – a tool for examining medium-range order in noncrystalline systems,” Nucl. Instrum. Methods B 238(1–4), 196–199 (2005).
[Crossref]

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R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor,” Proc. Natl. Acad. Sci. U.S.A. 110(33), 13250–13254 (2013).
[Crossref] [PubMed]

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S. Muthmann, F. Köhler, R. Carius, and A. Gordijn, “Structural order on different length scales in amorphous silicon investigated by Raman spectroscopy,” Phys. Status Solidi A 207(3), 544–547 (2010).
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I. Tamáska, G. Dobrik, P. Nemes-Incze, K. Kertész, E. Horváth, G. Márk, T. Jászi, P. Neumann, Z. Horváth, and L. Biró, “Bioinspired photonic nanoarchitectures from graphitic thin films,” Thin Solid Films 519(12), 4078–4081 (2011).
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Neumann, P.

I. Tamáska, G. Dobrik, P. Nemes-Incze, K. Kertész, E. Horváth, G. Márk, T. Jászi, P. Neumann, Z. Horváth, and L. Biró, “Bioinspired photonic nanoarchitectures from graphitic thin films,” Thin Solid Films 519(12), 4078–4081 (2011).
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Y. Takahashi, Y. Nishino, T. Ishikawa, and E. Matsubara, “Approach for three-dimensional observation of mesoscopic precipitates in alloys by coherent x-ray diffraction microscopy,” Appl. Phys. Lett. 90(18), 184105 (2007).
[Crossref]

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S. N. Bogle, L. N. Nittala, R. D. Twesten, P. M. Voyles, and J. R. Abelson, “Size analysis of nanoscale order in amorphous materials by variable-resolution fluctuation electron microscopy,” Ultramicroscopy 110(10), 1273–1278 (2010).
[Crossref]

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C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
[Crossref] [PubMed]

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
[Crossref] [PubMed]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4(5), 394–398 (2008).
[Crossref]

H. M. Quiney, A. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[Crossref] [PubMed]

Ortiz, A. D.

P. Wochner, C. Gutt, T. Autenrieth, T. Demmer, V. Bugaev, A. D. Ortiz, A. Duri, F. Zontone, G. Grübel, and H. Dosch, “X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter,” Proc. Natl. Acad. Sci. U.S.A. 106(28), 11511–11514 (2009).
[Crossref] [PubMed]

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J. J. Turner, X. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray diffraction microscopy of magnetic structures,” Phys. Rev. Lett. 107(3), 033904 (2011).
[Crossref] [PubMed]

Paterson, D.

L. Fan, D. Paterson, I. McNulty, M. M. Treacy, and J. M. Gibson, “Fluctuation X-ray microscopy: a novel approach for the structural study of disordered materials,” J. Microsc. 225(1), 41–48 (2007).
[Crossref] [PubMed]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[Crossref] [PubMed]

H. M. Quiney, A. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

M. Treacy, J. Gibson, L. Fan, D. Paterson, and I. McNulty, “Fluctuation microscopy: a probe of medium range order,” Rep. Prog. Phys. 68(12), 2899–2944 (2005).
[Crossref]

L. Fan, I. McNulty, D. Paterson, M. M. J. Treacy, and J. M. Gibson, “Fluctuation microscopy – a tool for examining medium-range order in noncrystalline systems,” Nucl. Instrum. Methods B 238(1–4), 196–199 (2005).
[Crossref]

Peele, A.

H. M. Quiney, A. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

Peele, A. G.

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
[Crossref] [PubMed]

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
[Crossref] [PubMed]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4(5), 394–398 (2008).
[Crossref]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[Crossref] [PubMed]

Pfeifer, M. A.

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
[Crossref] [PubMed]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4(5), 394–398 (2008).
[Crossref]

Pfeiffer, F.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
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Putkunz, C. T.

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
[Crossref] [PubMed]

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
[Crossref] [PubMed]

Quiney, H. M.

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[Crossref] [PubMed]

H. M. Quiney, A. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
[Crossref]

Rodenburg, J. M.

J. M. Rodenburg, A. C. Hurst, A. G. Cullis, B. R. Dobson, F. Pfeiffer, O. Bunk, C. David, K. Jefimovs, and I. Johnson, “Hard-x-ray lensless imaging of extended objects,” Phys. Rev. Lett. 98(3), 034801 (2007).
[Crossref] [PubMed]

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
[Crossref]

Roorda, S.

R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor,” Proc. Natl. Acad. Sci. U.S.A. 110(33), 13250–13254 (2013).
[Crossref] [PubMed]

Roy, S.

J. J. Turner, X. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray diffraction microscopy of magnetic structures,” Phys. Rev. Lett. 107(3), 033904 (2011).
[Crossref] [PubMed]

Scholten, R. E.

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
[Crossref] [PubMed]

Seu, K. A.

J. J. Turner, X. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray diffraction microscopy of magnetic structures,” Phys. Rev. Lett. 107(3), 033904 (2011).
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M. Skoge, A. Donev, F. H. Stillinger, and S. Torquato, “Packing hyperspheres in high-dimensional Euclidean spaces,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(4), 041127 (2006).
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Steinhardt, P. J.

R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor,” Proc. Natl. Acad. Sci. U.S.A. 110(33), 13250–13254 (2013).
[Crossref] [PubMed]

Stewart, R. J.

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
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Y. Jiao, F. H. Stillinger, and S. Torquato, “A superior descriptor of random textures and its predictive capacity,” Proc. Natl. Acad. Sci. U.S.A. 106(42), 17634–17639 (2009).
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M. Skoge, A. Donev, F. H. Stillinger, and S. Torquato, “Packing hyperspheres in high-dimensional Euclidean spaces,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(4), 041127 (2006).
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B. D. Lubachevsky and F. H. Stillinger, “Geometric properties of random disk packings,” J. Stat. Phys. 60(5–6), 561–583 (1990).
[Crossref]

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Y. Takahashi, Y. Nishino, T. Ishikawa, and E. Matsubara, “Approach for three-dimensional observation of mesoscopic precipitates in alloys by coherent x-ray diffraction microscopy,” Appl. Phys. Lett. 90(18), 184105 (2007).
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I. Tamáska, G. Dobrik, P. Nemes-Incze, K. Kertész, E. Horváth, G. Márk, T. Jászi, P. Neumann, Z. Horváth, and L. Biró, “Bioinspired photonic nanoarchitectures from graphitic thin films,” Thin Solid Films 519(12), 4078–4081 (2011).
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R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor,” Proc. Natl. Acad. Sci. U.S.A. 110(33), 13250–13254 (2013).
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Y. Jiao, F. H. Stillinger, and S. Torquato, “A superior descriptor of random textures and its predictive capacity,” Proc. Natl. Acad. Sci. U.S.A. 106(42), 17634–17639 (2009).
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M. Skoge, A. Donev, F. H. Stillinger, and S. Torquato, “Packing hyperspheres in high-dimensional Euclidean spaces,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 74(4), 041127 (2006).
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G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
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M. Treacy, J. Gibson, L. Fan, D. Paterson, and I. McNulty, “Fluctuation microscopy: a probe of medium range order,” Rep. Prog. Phys. 68(12), 2899–2944 (2005).
[Crossref]

M. Treacy, J. Gibson, and P. Keblinski, “Paracrystallites found in evaporated amorphous tetrahedral semiconductors,” J. Non-Cryst. Solids 231(1–2), 99–110 (1998).
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J. Gibson, M. Treacy, P. Voyles, H. Jin, and J. Abelson, “Structural disorder induced in hydrogenated amorphous silicon by light soaking,” Appl. Phys. Lett. 73(21), 3093–3095 (1998).
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J. Gibson and M. Treacy, “Diminished medium-range order observed in annealed amorphous germanium,” Phys. Rev. Lett. 78(6), 1074–1077 (1997).
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M. Treacy and J. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta. Crystallogr., Sect. A 52(2), 212–220 (1996).
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J. Gibson and M. Treacy, “Defocus as an ineffective means of changing spot size for fluctuation microscopy,” J. Phys. Conf. Ser.186(1), 012053 (2009).

Treacy, M. M.

L. Fan, D. Paterson, I. McNulty, M. M. Treacy, and J. M. Gibson, “Fluctuation X-ray microscopy: a novel approach for the structural study of disordered materials,” J. Microsc. 225(1), 41–48 (2007).
[Crossref] [PubMed]

J. M. Gibson, M. M. Treacy, and P. M. Voyles, “Atom pair persistence in disordered materials from fluctuation microscopy,” Ultramicroscopy 83(3–4), 169–178 (2000).
[Crossref] [PubMed]

Treacy, M. M. J.

L. Fan, I. McNulty, D. Paterson, M. M. J. Treacy, and J. M. Gibson, “Fluctuation microscopy – a tool for examining medium-range order in noncrystalline systems,” Nucl. Instrum. Methods B 238(1–4), 196–199 (2005).
[Crossref]

P. Gerbi, M. Voyles, M. M. J. Treacy, J. M. Gibson, and J. R. Abelson, “Increasing medium-range order in amorphous silicon with low-energy ion bombardment,” Appl. Phys. Lett. 82(21), 3665–3667 (2003).
[Crossref]

Turner, J. J.

J. J. Turner, X. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray diffraction microscopy of magnetic structures,” Phys. Rev. Lett. 107(3), 033904 (2011).
[Crossref] [PubMed]

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S. N. Bogle, L. N. Nittala, R. D. Twesten, P. M. Voyles, and J. R. Abelson, “Size analysis of nanoscale order in amorphous materials by variable-resolution fluctuation electron microscopy,” Ultramicroscopy 110(10), 1273–1278 (2010).
[Crossref]

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J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science 312(5772), 416–419 (2006).
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G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 80(5), 051903 (2009).
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C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
[Crossref] [PubMed]

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
[Crossref] [PubMed]

Voyles, M.

P. Gerbi, M. Voyles, M. M. J. Treacy, J. M. Gibson, and J. R. Abelson, “Increasing medium-range order in amorphous silicon with low-energy ion bombardment,” Appl. Phys. Lett. 82(21), 3665–3667 (2003).
[Crossref]

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J. Gibson, M. Treacy, P. Voyles, H. Jin, and J. Abelson, “Structural disorder induced in hydrogenated amorphous silicon by light soaking,” Appl. Phys. Lett. 73(21), 3093–3095 (1998).
[Crossref]

Voyles, P. M.

J. Hwang and P. M. Voyles, “Variable resolution fluctuation electron microscopy on Cu-Zr metallic glass using a wide range of coherent stem probe size,” Microsc. Microanal. 17(1), 67–74 (2011).
[Crossref] [PubMed]

S. N. Bogle, L. N. Nittala, R. D. Twesten, P. M. Voyles, and J. R. Abelson, “Size analysis of nanoscale order in amorphous materials by variable-resolution fluctuation electron microscopy,” Ultramicroscopy 110(10), 1273–1278 (2010).
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P. M. Voyles and J. R. Abelson, “Medium-range order in amorphous silicon measured by fluctuation electron microscopy,” Sol. Energy Mater. Sol. Cells 78(1–4), 85–113 (2003).
[Crossref]

J. M. Gibson, M. M. Treacy, and P. M. Voyles, “Atom pair persistence in disordered materials from fluctuation microscopy,” Ultramicroscopy 83(3–4), 169–178 (2000).
[Crossref] [PubMed]

Weigand, S. J.

R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor,” Proc. Natl. Acad. Sci. U.S.A. 110(33), 13250–13254 (2013).
[Crossref] [PubMed]

Williams, G. J.

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, E. Balaur, G. A. Cadenazzi, E. K. Curwood, C. A. Henderson, R. E. Scholten, R. J. Stewart, I. McNulty, K. A. Nugent, and A. G. Peele, “Mapping granular structure in the biological adhesive of Phragmatopoma californica using phase diverse coherent diffractive imaging,” Ultramicroscopy 111(8), 1184–1188 (2011).
[Crossref] [PubMed]

C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
[Crossref] [PubMed]

B. Abbey, K. A. Nugent, G. J. Williams, J. N. Clark, A. G. Peele, M. A. Pfeifer, M. De Jonge, and I. McNulty, “Keyhole coherent diffractive imaging,” Nat. Phys. 4(5), 394–398 (2008).
[Crossref]

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
[Crossref] [PubMed]

Wochner, P.

P. Wochner, C. Gutt, T. Autenrieth, T. Demmer, V. Bugaev, A. D. Ortiz, A. Duri, F. Zontone, G. Grübel, and H. Dosch, “X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter,” Proc. Natl. Acad. Sci. U.S.A. 106(28), 11511–11514 (2009).
[Crossref] [PubMed]

Xie, R.

R. Xie, G. G. Long, S. J. Weigand, S. C. Moss, T. Carvalho, S. Roorda, M. Hejna, S. Torquato, and P. J. Steinhardt, “Hyperuniformity in amorphous silicon based on the measurement of the infinite-wavelength limit of the structure factor,” Proc. Natl. Acad. Sci. U.S.A. 110(33), 13250–13254 (2013).
[Crossref] [PubMed]

Xu, Q.

J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science 312(5772), 416–419 (2006).
[Crossref] [PubMed]

Zandbergen, H. W.

J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science 312(5772), 416–419 (2006).
[Crossref] [PubMed]

Zontone, F.

P. Wochner, C. Gutt, T. Autenrieth, T. Demmer, V. Bugaev, A. D. Ortiz, A. Duri, F. Zontone, G. Grübel, and H. Dosch, “X-ray cross correlation analysis uncovers hidden local symmetries in disordered matter,” Proc. Natl. Acad. Sci. U.S.A. 106(28), 11511–11514 (2009).
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M. Treacy and J. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta. Crystallogr., Sect. A 52(2), 212–220 (1996).
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S. R. Elliott, “The structure of amorphous hydrogenated silicon and its alloys: A review,” Adv. Phys. 38(1), 1–88 (1989).
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Y. Takahashi, Y. Nishino, T. Ishikawa, and E. Matsubara, “Approach for three-dimensional observation of mesoscopic precipitates in alloys by coherent x-ray diffraction microscopy,” Appl. Phys. Lett. 90(18), 184105 (2007).
[Crossref]

J. Gibson, M. Treacy, P. Voyles, H. Jin, and J. Abelson, “Structural disorder induced in hydrogenated amorphous silicon by light soaking,” Appl. Phys. Lett. 73(21), 3093–3095 (1998).
[Crossref]

P. Gerbi, M. Voyles, M. M. J. Treacy, J. M. Gibson, and J. R. Abelson, “Increasing medium-range order in amorphous silicon with low-energy ion bombardment,” Appl. Phys. Lett. 82(21), 3665–3667 (2003).
[Crossref]

J. M. Rodenburg and H. M. Faulkner, “A phase retrieval algorithm for shifting illumination,” Appl. Phys. Lett. 85(20), 4795–4797 (2004).
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L. Fan, D. Paterson, I. McNulty, M. M. Treacy, and J. M. Gibson, “Fluctuation X-ray microscopy: a novel approach for the structural study of disordered materials,” J. Microsc. 225(1), 41–48 (2007).
[Crossref] [PubMed]

J. Non-Cryst. Solids (1)

M. Treacy, J. Gibson, and P. Keblinski, “Paracrystallites found in evaporated amorphous tetrahedral semiconductors,” J. Non-Cryst. Solids 231(1–2), 99–110 (1998).
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S. R. Elliott, “The origin of the first sharp diffraction peak in the structure factor of covalent glasses and liquids,” J. Phys. Condens. Matter 4, 7661 (1992).

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B. D. Lubachevsky and F. H. Stillinger, “Geometric properties of random disk packings,” J. Stat. Phys. 60(5–6), 561–583 (1990).
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Microsc. Microanal. (1)

J. Hwang and P. M. Voyles, “Variable resolution fluctuation electron microscopy on Cu-Zr metallic glass using a wide range of coherent stem probe size,” Microsc. Microanal. 17(1), 67–74 (2011).
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Nat. Phys. (2)

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H. M. Quiney, A. Peele, Z. Cai, D. Paterson, and K. A. Nugent, “Diffractive imaging of highly focused X-ray fields,” Nat. Phys. 2(2), 101–104 (2006).
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Nucl. Instrum. Methods B (1)

L. Fan, I. McNulty, D. Paterson, M. M. J. Treacy, and J. M. Gibson, “Fluctuation microscopy – a tool for examining medium-range order in noncrystalline systems,” Nucl. Instrum. Methods B 238(1–4), 196–199 (2005).
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Phys. Rev. B Condens. Matter (1)

W. D. Luedtke and U. Landman, “Preparation, structure, dynamics, and energetics of amorphous silicon: A molecular-dynamics study,” Phys. Rev. B Condens. Matter 40(2), 1164–1174 (1989).
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Phys. Rev. E Stat. Nonlinear Soft Matter Phys. (2)

G. I. Márk, Z. Vértesy, K. Kertész, Z. Bálint, and L. P. Biró, “Order-disorder effects in structure and color relation of photonic-crystal-type nanostructures in butterfly wing scales,” Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 80(5), 051903 (2009).
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Phys. Rev. Lett. (5)

G. J. Williams, H. M. Quiney, B. B. Dhal, C. Q. Tran, K. A. Nugent, A. G. Peele, D. Paterson, and M. D. de Jonge, “Fresnel coherent diffractive imaging,” Phys. Rev. Lett. 97(2), 025506 (2006).
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J. J. Turner, X. Huang, O. Krupin, K. A. Seu, D. Parks, S. Kevan, E. Lima, K. Kisslinger, I. McNulty, R. Gambino, S. Mangin, S. Roy, and P. Fischer, “X-ray diffraction microscopy of magnetic structures,” Phys. Rev. Lett. 107(3), 033904 (2011).
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C. T. Putkunz, J. N. Clark, D. J. Vine, G. J. Williams, M. A. Pfeifer, E. Balaur, I. McNulty, K. A. Nugent, and A. G. Peele, “Phase-diverse coherent diffractive imaging: High sensitivity with low dose,” Phys. Rev. Lett. 106(1), 013903 (2011).
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Physica B (1)

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Proc. Natl. Acad. Sci. U.S.A. (3)

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Science (1)

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Other (2)

J. Gibson and M. Treacy, “Defocus as an ineffective means of changing spot size for fluctuation microscopy,” J. Phys. Conf. Ser.186(1), 012053 (2009).

H. Noh, S. F. Liew, V. Saranathan, R. O. Prum, E. R. Dufresne, S. G. Mochrie, and H. Cao, “Double scattering of light from biophotonic nanostructures with short-range order,” Quantum Electronics and Laser Science Conference (Optical Society of America, 2010).
[Crossref]

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Figures (5)

Fig. 1
Fig. 1

Electron microscope image of section of sample of 350 nm polystyrene-latex spheres dried to form a film on a SiN membrane.

Fig. 2
Fig. 2

Reconstruction of the extended polystyrene sphere sample using the ptychographic method described in the text. The amplitude (Fig. 2(a)) and phase (Fig. 2(b)) are shown. The scale bars indicate a length of 10 µm.

Fig. 3
Fig. 3

Results of PFM analysis of polystyrene sphere sample, (a) shows a fluctuation map describing the behaviour of the variance as a function of both scattering vector, q (x axis), and probe beam diameter, R (y axis). The peak seen at q = (4.8 ± 0.2) × 10−4 Å−1 (indicated by an arrow) corresponds to short range order in the material at 260 ± 9 nm. Peaks at q = (4.8 ± 0.2) × 10−4 Å−1, q = (7.3 ± 0.6) × 10−4 Å−1 and q = (9.3 ± 0.6) × 10−4 Å−1 indicate the strong SRO present within the sample, (b) shows the variation of the variance along the line indicated by the arrow in (a), the increase at 4.94 × 10−4 ± 0.05 μm (shown by the red line) indicates the presence of MRO within the sample, with a corresponding increase in the variance along q = (7.3 ± 0.6) × 10−4 Å−1 (shown by the green line) and q = (9.3 ± 0.6) × 10−4 Å−1 (shown by the blue line).

Fig. 4
Fig. 4

2D simulation with a packing fraction of 0.8 in which the boundary between three `domains' of order can be seen.

Fig. 5
Fig. 5

X-ray diffractometry data collected at the Photon Factory, Japan using 8.05 keV X-rays. The first oscillation of the XRD diffraction data located q = 0.4 × 10−3 Å−1 indicates structure within the sample at 265 nm, consistent with the PFM, SEM and simulation data.

Equations (7)

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V(q,R)= I (q,R,r) 2 r I (q,R,r) 2 r 2 1
Ψ detector ( k xi , k yi ) = P( r ) ×( ψ ESW ).
I( k xi , k yi ) = Ψ * detector ( k xi , k yi ) Ψ detector ( k xi , k yi )
I t ( r ) = i=1 N I( k xi , k yi ) ,
I t 2 ( r ) = i=1 N I 2 ( k xi , k yi ) ,
I(r) = 1 N I t (r)
V(r)= I 2 (r) I(r) 2 1

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