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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. S. R. Elliott, “The structure of amorphous hydrogenated silicon and its alloys: A review,” Adv. Phys.38(1), 1–88 (1989).
    [CrossRef]
  2. 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 B238(1–4), 196–199 (2005).
    [CrossRef]
  3. W. D. Luedtke and U. Landman, “Preparation, structure, dynamics, and energetics of amorphous silicon: A molecular-dynamics study,” Phys. Rev. B Condens. Matter40(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. Cells78(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. Matter4, 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 A207(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).
    [CrossRef] [PubMed]
  9. 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]
  10. M. Treacy and J. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta. Crystallogr., Sect. A52(2), 212–220 (1996).
    [CrossRef]
  11. M. Treacy, J. Gibson, and P. Keblinski, “Paracrystallites found in evaporated amorphous tetrahedral semiconductors,” J. Non-Cryst. Solids231(1–2), 99–110 (1998).
    [CrossRef]
  12. J. Gibson and M. Treacy, “Diminished medium-range order observed in annealed amorphous germanium,” Phys. Rev. Lett.78(6), 1074–1077 (1997).
    [CrossRef]
  13. 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]
  14. 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]
  15. 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]
  16. 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]
  17. 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]
  18. 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 Films519(12), 4078–4081 (2011).
    [CrossRef]
  19. 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]
  20. J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science312(5772), 416–419 (2006).
    [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]
  22. 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,” Ultramicroscopy110(10), 1273–1278 (2010).
    [CrossRef]
  23. 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]
  24. J. M. Cowley, “Electron nanodiffraction methods for measuring medium-range order,” Ultramicroscopy90(2–3), 197–206 (2002).
    [CrossRef] [PubMed]
  25. 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).
  26. R. Hegerl and W. Hoppe, “Dynamic theory of crystalline structure analysis by electron diffraction in inhomogeneous primary wave field,” Ber. Bunsenges. Phys. Chem74(11), 1148 (1970).
    [CrossRef]
  27. H. N. Chapman, “Phase-retrieval X-ray microscopy by Wigner-distribution deconvolution,” Ultramicroscopy66(3–4), 153–172 (1996).
    [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]
  29. 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]
  30. 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,” Ultramicroscopy111(8), 1184–1188 (2011).
    [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,” Ultramicroscopy83(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 B349(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

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

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 Films519(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,” Ultramicroscopy111(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

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,” Ultramicroscopy110(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 A207(3), 544–547 (2010).
[CrossRef]

2009

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

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

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

J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science312(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

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 B238(1–4), 196–199 (2005).
[CrossRef]

2004

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 B349(1–4), 281–295 (2004).
[CrossRef]

2003

P. M. Voyles and J. R. Abelson, “Medium-range order in amorphous silicon measured by fluctuation electron microscopy,” Sol. Energy Mater. Sol. Cells78(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

J. M. Cowley, “Electron nanodiffraction methods for measuring medium-range order,” Ultramicroscopy90(2–3), 197–206 (2002).
[CrossRef] [PubMed]

2000

J. M. Gibson, M. M. Treacy, and P. M. Voyles, “Atom pair persistence in disordered materials from fluctuation microscopy,” Ultramicroscopy83(3–4), 169–178 (2000).
[CrossRef] [PubMed]

1998

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. Solids231(1–2), 99–110 (1998).
[CrossRef]

1997

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

1996

M. Treacy and J. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta. Crystallogr., Sect. A52(2), 212–220 (1996).
[CrossRef]

H. N. Chapman, “Phase-retrieval X-ray microscopy by Wigner-distribution deconvolution,” Ultramicroscopy66(3–4), 153–172 (1996).
[CrossRef]

1992

S. R. Elliott, “The origin of the first sharp diffraction peak in the structure factor of covalent glasses and liquids,” J. Phys. Condens. Matter4, 7661 (1992).

1990

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

1989

W. D. Luedtke and U. Landman, “Preparation, structure, dynamics, and energetics of amorphous silicon: A molecular-dynamics study,” Phys. Rev. B Condens. Matter40(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

R. Hegerl and W. Hoppe, “Dynamic theory of crystalline structure analysis by electron diffraction in inhomogeneous primary wave field,” Ber. Bunsenges. Phys. Chem74(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,” Ultramicroscopy110(10), 1273–1278 (2010).
[CrossRef]

P. M. Voyles and J. R. Abelson, “Medium-range order in amorphous silicon measured by fluctuation electron microscopy,” Sol. Energy Mater. Sol. Cells78(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]

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,” Ultramicroscopy111(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 Films519(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,” Ultramicroscopy110(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,” Ultramicroscopy111(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 A207(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]

Chapman, H. N.

H. N. Chapman, “Phase-retrieval X-ray microscopy by Wigner-distribution deconvolution,” Ultramicroscopy66(3–4), 153–172 (1996).
[CrossRef]

Chen, J. H.

J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science312(5772), 416–419 (2006).
[CrossRef] [PubMed]

Clark, J. N.

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,” Ultramicroscopy111(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]

Costan, E.

J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science312(5772), 416–419 (2006).
[CrossRef] [PubMed]

Cowley, J. M.

J. M. Cowley, “Electron nanodiffraction methods for measuring medium-range order,” Ultramicroscopy90(2–3), 197–206 (2002).
[CrossRef] [PubMed]

Cullis, A. G.

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]

Curwood, E. K.

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,” Ultramicroscopy111(8), 1184–1188 (2011).
[CrossRef] [PubMed]

Darahanau, A.

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 B349(1–4), 281–295 (2004).
[CrossRef]

David, C.

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]

De Jonge, M.

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]

de Jonge, M. D.

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]

Demmer, 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]

Dhal, B. B.

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]

Dobrik, G.

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 Films519(12), 4078–4081 (2011).
[CrossRef]

Dobson, B. R.

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]

Donev, A.

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]

Dosch, H.

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]

Duri, A.

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]

Elliott, S. R.

S. R. Elliott, “The origin of the first sharp diffraction peak in the structure factor of covalent glasses and liquids,” J. Phys. Condens. Matter4, 7661 (1992).

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

Fan, L.

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]

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 B238(1–4), 196–199 (2005).
[CrossRef]

Faulkner, H. M.

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

Fischer, P.

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]

Gambino, R.

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]

Gerbi, P.

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]

Gibson, J.

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]

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. Solids231(1–2), 99–110 (1998).
[CrossRef]

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

M. Treacy and J. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta. Crystallogr., Sect. A52(2), 212–220 (1996).
[CrossRef]

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).

Gibson, J. 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]

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 B238(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]

J. M. Gibson, M. M. Treacy, and P. M. Voyles, “Atom pair persistence in disordered materials from fluctuation microscopy,” Ultramicroscopy83(3–4), 169–178 (2000).
[CrossRef] [PubMed]

Gordijn, A.

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 A207(3), 544–547 (2010).
[CrossRef]

Grübel, G.

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]

Gutt, C.

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]

Hegerl, R.

R. Hegerl and W. Hoppe, “Dynamic theory of crystalline structure analysis by electron diffraction in inhomogeneous primary wave field,” Ber. Bunsenges. Phys. Chem74(11), 1148 (1970).
[CrossRef]

Hejna, M.

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]

Henderson, C. 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,” Ultramicroscopy111(8), 1184–1188 (2011).
[CrossRef] [PubMed]

Hoppe, W.

R. Hegerl and W. Hoppe, “Dynamic theory of crystalline structure analysis by electron diffraction in inhomogeneous primary wave field,” Ber. Bunsenges. Phys. Chem74(11), 1148 (1970).
[CrossRef]

Horney, R.

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 B349(1–4), 281–295 (2004).
[CrossRef]

Horváth, E.

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 Films519(12), 4078–4081 (2011).
[CrossRef]

Horváth, Z.

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 Films519(12), 4078–4081 (2011).
[CrossRef]

Huang, X.

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]

Hurst, A. C.

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]

Hwang, J.

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]

Ishikawa, T.

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]

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 B349(1–4), 281–295 (2004).
[CrossRef]

Jászi, T.

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 Films519(12), 4078–4081 (2011).
[CrossRef]

Jefimovs, K.

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]

Jiao, Y.

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]

Jin, H.

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]

Johnson, I.

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]

Keblinski, P.

M. Treacy, J. Gibson, and P. Keblinski, “Paracrystallites found in evaporated amorphous tetrahedral semiconductors,” J. Non-Cryst. Solids231(1–2), 99–110 (1998).
[CrossRef]

Kertész, K.

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 Films519(12), 4078–4081 (2011).
[CrossRef]

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]

Kevan, 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]

Kisslinger, K.

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]

Köhler, F.

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 A207(3), 544–547 (2010).
[CrossRef]

Krupin, O.

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]

Landman, U.

W. D. Luedtke and U. Landman, “Preparation, structure, dynamics, and energetics of amorphous silicon: A molecular-dynamics study,” Phys. Rev. B Condens. Matter40(2), 1164–1174 (1989).
[CrossRef] [PubMed]

Lima, E.

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]

Long, G. G.

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]

Lubachevsky, B. D.

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

Luedtke, W. D.

W. D. Luedtke and U. Landman, “Preparation, structure, dynamics, and energetics of amorphous silicon: A molecular-dynamics study,” Phys. Rev. B Condens. Matter40(2), 1164–1174 (1989).
[CrossRef] [PubMed]

Mangin, 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]

Márk, G.

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 Films519(12), 4078–4081 (2011).
[CrossRef]

Márk, G. I.

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]

Matsubara, E.

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]

McNulty, I.

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,” Ultramicroscopy111(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]

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]

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]

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 B238(1–4), 196–199 (2005).
[CrossRef]

Moss, S. C.

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]

Muthmann, S.

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 A207(3), 544–547 (2010).
[CrossRef]

Nemes-Incze, 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 Films519(12), 4078–4081 (2011).
[CrossRef]

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 Films519(12), 4078–4081 (2011).
[CrossRef]

Nikulin, A.

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 B349(1–4), 281–295 (2004).
[CrossRef]

Nishino, Y.

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]

Nittala, L. 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,” Ultramicroscopy110(10), 1273–1278 (2010).
[CrossRef]

Nugent, K. 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]

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,” Ultramicroscopy111(8), 1184–1188 (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]

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]

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]

Parks, D.

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]

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 B238(1–4), 196–199 (2005).
[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]

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, 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,” Ultramicroscopy111(8), 1184–1188 (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).
[CrossRef] [PubMed]

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,” Ultramicroscopy111(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.

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]

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,” Ultramicroscopy111(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).
[CrossRef] [PubMed]

Skoge, M.

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]

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,” Ultramicroscopy111(8), 1184–1188 (2011).
[CrossRef] [PubMed]

Stillinger, F. H.

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]

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]

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

Takahashi, Y.

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]

Tamáska, I.

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 Films519(12), 4078–4081 (2011).
[CrossRef]

Torquato, 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]

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]

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]

Tran, C. Q.

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]

Treacy, M.

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]

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. Solids231(1–2), 99–110 (1998).
[CrossRef]

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

M. Treacy and J. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta. Crystallogr., Sect. A52(2), 212–220 (1996).
[CrossRef]

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,” Ultramicroscopy83(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 B238(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]

Twesten, R. D.

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,” Ultramicroscopy110(10), 1273–1278 (2010).
[CrossRef]

van Huis, M. A.

J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science312(5772), 416–419 (2006).
[CrossRef] [PubMed]

Vértesy, 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]

Vine, D. 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,” Ultramicroscopy111(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]

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]

Voyles, P.

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,” Ultramicroscopy110(10), 1273–1278 (2010).
[CrossRef]

P. M. Voyles and J. R. Abelson, “Medium-range order in amorphous silicon measured by fluctuation electron microscopy,” Sol. Energy Mater. Sol. Cells78(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,” Ultramicroscopy83(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, 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,” Ultramicroscopy111(8), 1184–1188 (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,” Science312(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,” Science312(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).
[CrossRef] [PubMed]

Acta. Crystallogr., Sect. A

M. Treacy and J. Gibson, “Variable coherence microscopy: a rich source of structural information from disordered materials,” Acta. Crystallogr., Sect. A52(2), 212–220 (1996).
[CrossRef]

Adv. Phys.

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

Appl. Phys. Lett.

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).
[CrossRef]

Ber. Bunsenges. Phys. Chem

R. Hegerl and W. Hoppe, “Dynamic theory of crystalline structure analysis by electron diffraction in inhomogeneous primary wave field,” Ber. Bunsenges. Phys. Chem74(11), 1148 (1970).
[CrossRef]

J. Microsc.

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

M. Treacy, J. Gibson, and P. Keblinski, “Paracrystallites found in evaporated amorphous tetrahedral semiconductors,” J. Non-Cryst. Solids231(1–2), 99–110 (1998).
[CrossRef]

J. Phys. Condens. Matter

S. R. Elliott, “The origin of the first sharp diffraction peak in the structure factor of covalent glasses and liquids,” J. Phys. Condens. Matter4, 7661 (1992).

J. Stat. Phys.

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

Microsc. Microanal.

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]

Nat. Phys.

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]

Nucl. Instrum. Methods B

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 B238(1–4), 196–199 (2005).
[CrossRef]

Phys. Rev. B Condens. Matter

W. D. Luedtke and U. Landman, “Preparation, structure, dynamics, and energetics of amorphous silicon: A molecular-dynamics study,” Phys. Rev. B Condens. Matter40(2), 1164–1174 (1989).
[CrossRef] [PubMed]

Phys. Rev. E Stat. Nonlinear Soft Matter Phys.

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]

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]

Phys. Rev. Lett.

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]

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

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]

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]

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]

Phys. Status Solidi A

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 A207(3), 544–547 (2010).
[CrossRef]

Physica B

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 B349(1–4), 281–295 (2004).
[CrossRef]

Proc. Natl. Acad. Sci. U.S.A.

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]

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]

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]

Rep. Prog. Phys.

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]

Science

J. H. Chen, E. Costan, M. A. van Huis, Q. Xu, and H. W. Zandbergen, “Atomic pillar-based nanoprecipitates strengthen AlMgSi alloys,” Science312(5772), 416–419 (2006).
[CrossRef] [PubMed]

Sol. Energy Mater. Sol. Cells

P. M. Voyles and J. R. Abelson, “Medium-range order in amorphous silicon measured by fluctuation electron microscopy,” Sol. Energy Mater. Sol. Cells78(1–4), 85–113 (2003).
[CrossRef]

Thin Solid Films

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 Films519(12), 4078–4081 (2011).
[CrossRef]

Ultramicroscopy

H. N. Chapman, “Phase-retrieval X-ray microscopy by Wigner-distribution deconvolution,” Ultramicroscopy66(3–4), 153–172 (1996).
[CrossRef]

J. M. Cowley, “Electron nanodiffraction methods for measuring medium-range order,” Ultramicroscopy90(2–3), 197–206 (2002).
[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,” Ultramicroscopy110(10), 1273–1278 (2010).
[CrossRef]

J. M. Gibson, M. M. Treacy, and P. M. Voyles, “Atom pair persistence in disordered materials from fluctuation microscopy,” Ultramicroscopy83(3–4), 169–178 (2000).
[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,” Ultramicroscopy111(8), 1184–1188 (2011).
[CrossRef] [PubMed]

Other

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]

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


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)

Equations on this page are rendered with MathJax. Learn more.

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

Metrics