Hostname: page-component-586b7cd67f-dsjbd Total loading time: 0 Render date: 2024-11-26T06:24:58.870Z Has data issue: false hasContentIssue false
  • English
  • Français

Examination of a Polycrystalline Thin-Film Model to Explore the Relation between Probe Size and Structural Correlation Length in Fluctuation Electron Microscopy

Published online by Cambridge University Press:  18 January 2012

M.M.J. Treacy  and
J.M. Gibson
M.M.J. Treacy*
Affiliation:
Department of Physics, Arizona State University, Tempe, AZ 85287, USA
J.M. Gibson
Affiliation:
Department of Physics, Northeastern University, Boston, MA 02115, USA
*
Corresponding author. E-mail: [email protected]
Get access

Abstract

We examine simulated electron microdiffraction patterns from models of thin polycrystalline silicon. The models are made by a Voronoi tessellation of random points in a box. The Voronoi domains are randomly selected to contain either a randomly-oriented cubic crystalline grain or a region of continuous random network material. The microdiffraction simulations from coherent probes of different widths are computed at the ideal kinematical limit, ignoring inelastic and multiple scattering. By examining the normalized intensity variance that is obtained in fluctuation electron microscopy experiments, we confirm that intensity fluctuations increase monotonically with the percentage of crystalline grains in the material. However, anomalously high variance is observed for models that have 100% crystalline grains with no imperfections. We confirm that the reduced normalized variance, V(k,R) − 1, that is associated with four-body correlations at scattering vector k, varies inversely with specimen thickness. Further, for probe sizes R larger than the mean grain size, we confirm that the reduced normalized variance obeys the predicted form given by Gibson et al. [Ultramicroscopy, 83, 169–178 (2000)] for the kinematical coherent scattering limit.

Keywords

amorphous siliconcontinuous random networkfluctuation electron microscopypair distribution functionstructural correlation lengthsupervariance
Type
Techniques Development
Information
Microscopy and Microanalysis , Volume 18 , Issue 1 , February 2012 , pp. 241 - 253
Copyright
Copyright © Microscopy Society of America 2012

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Barkema, G.T. & Mousseau, N. (2000). High-quality continuous random networks. Phys Rev B 62, 4985–4990.CrossRefGoogle Scholar
Biswas, P., Tafen, D. & Drabold, D.A. (2005). Experimentally constrained molecular relaxation: The case of GeSe2. Phys Rev B 71, 054204.CrossRefGoogle Scholar
Bogle, S.N., Voyles, P.M., Khare, S.V. & Abelson, J.R. (2007). Quantifying nanoscale order in amorphous materials: Simulating fluctuation electron microscopy of amorphous silicon. J Phys-Condens Mat 19, 455204.CrossRefGoogle Scholar
Borisenko, K.B., Haberl, B., Liu, A.C.Y., Chen, Y., Li, G., Williams, J.S., Bradby, J.E., Cockayne, D.J.H. & Treacy, M.M.J. (2012). Medium-range order in amorphous silicon investigated by constrained structural relaxation of two-body and four-body electron diffraction data. Acta Mater 60, 359–375.CrossRefGoogle Scholar
Chen, X., Sullivan, J.P., Friedmann, T.A. & Gibson, J.M. (2004). Fluctuation microscopy studies of medium-range ordering in amorphous diamond-like carbon films. Appl Phys Lett 84, 2823–2825.CrossRefGoogle Scholar
Cheng, J.-Y., Treacy, M.M.J., Keblinski, P.J. & Gibson, J.M. (2004). Diffraction microscopy for disordered tetrahedral networks. J Appl Phys 95, 7779–7784.CrossRefGoogle Scholar
Dainty, J.C. (1975). Stellar speckle interferometry. In Laser Speckle and Related Phenomena, Dainty, J.C. (Ed.), pp. 255–280. New York: Springer-Verlag.Google Scholar
Dash, R.K., Voyles, P.M., Gibson, J.M., Treacy, M.M.J. & Keblinski, P. (2003). A quantitative measure of medium-range order in amorphous materials from transmission electron micrographs. J Phys Cond Mat 15, S2425–S2435.CrossRefGoogle Scholar
Daulton, T., Bondi, K. & Kelton, K. (2010). Nanobeam diffraction fluctuation electron microscopy technique for structural characterization of disordered materials—Application to Al88−xY7Fe5Tix metallic glasses. Ultramicroscopy 110, 1279–1289.CrossRefGoogle Scholar
Fan, L., Paterson, D., McNulty, I., Treacy, M.M.J. & Gibson, J.M. (2007). Fluctuation X-ray microscopy: A novel approach for the structural study of disordered materials. J Microsc 225, 41–48.CrossRefGoogle ScholarPubMed
Freeman, L.A., Howie, A. & Treacy, M.M.J. (1977). Bright field and hollow cone dark field electron-microscopy of palladium catalysts. J Microsc 111, 165–178.CrossRefGoogle Scholar
Gibson, J.M. & Treacy, M.M.J. (1997). Diminished medium-range order observed in annealed amorphous germanium. Phys Rev Lett 78, 1074–1077.CrossRefGoogle Scholar
Gibson, J.M., Treacy, M.M.J., Sun, T. & Zaluzec, N.J. (2010). Substantial crystalline topology in amorphous silicon. Phys Rev Lett 105, 125504.CrossRefGoogle ScholarPubMed
Gibson, J.M., Treacy, M.M.J. & Voyles, P.M. (2000). Atom pair persistence in disordered materials from fluctuation microscopy. Ultramicroscopy 83, 169–178.CrossRefGoogle ScholarPubMed
Gibson, J.M., Treacy, M.M.J., Voyles, P.M., Jin, H.-C. & Abelson, J.R. (1998). Structural disorder induced in hydrogenated amorphous silicon by light soaking. Appl Phys Lett 73, 3093–3096.CrossRefGoogle Scholar
Goodman, J.W. (1975). Some fundamental properties of speckle. In Laser Speckle and Related Phenomena, Dainty, J.C. (Ed.), pp. 60–68. New York: Springer-Verlag.Google Scholar
Hwang, J., Clausen, A.M., Cao, H. & Voyles, P.M. (2009). Reverse Monte Carlo structural model for a zirconium-based metallic glass incorporating fluctuation microscopy medium-range order data. J Mater Res 24, 3121–3129.CrossRefGoogle Scholar
Khare, S.V., Nakhmanson, S.M., Voyles, P.M., Keblinski, P. & Abelson, J.R. (2004). Evidence from atomistic simulations of fluctuation electron microscopy for preferred local orientations in amorphous silicon. Appl Phys Letts 85, 745–747.CrossRefGoogle Scholar
Lee, B.-S., Bishop, S.G. & Abelson, J.R. (2010). Fluctuation transmission electron microscopy: Detecting nanoscale order in disordered structures. Chem Phys Chem 11, 2311–2317.CrossRefGoogle ScholarPubMed
Li, J., Gu, X. & Hufnagel, T.C. (2001). Medium-range order in metallic glasses studied by fluctuation microscopy. Microsc Microanal 7(S2), 1260–1261 (CD-ROM).CrossRefGoogle Scholar
Li, J., Gu, X. & Hufnagel, T.C. (2003). Using fluctuation microscopy to characterize structural order in metallic glass. Microsc Microanal 9, 509–515.CrossRefGoogle Scholar
Liu, A.C.Y., Arenal, R., Miller, D.J., Chen, X., Johnson, J.A., Eryilmaz, O.L., Erdemir, A. & Woodford, J.B. (2007). Structural order in near-frictionless hydrogenated diamondlike carbon films probed at three length scales via transmission electron microscopy. Phys Rev B 75, 205402.CrossRefGoogle Scholar
Singh, V. (1998). Entropy-Based Parameter Estimation in Hydrology (Water Science and Technology Library). Norwell, MA: Kluwer Academic Publishers.CrossRefGoogle Scholar
Stratton, W.G., Hamann, J., Perepezko, J.H., Voyles, P.M., Khare, S.V. & Mao, X. (2005). Aluminum nanoscale order in amorphous Al92Sm8 measured by fluctuation electron microscopy. Appl Phys Lett 86, 141910.CrossRefGoogle Scholar
Stratton, W.G. & Voyles, P.M. (2008). A phenomenological model of fluctuation electron microscopy for a nanocrystal/amorphous composite. Ultramicroscopy 108, 727–736.CrossRefGoogle ScholarPubMed
Tersoff, J. (1988a). Empirical interatomic potential for silicon with improved elastic properties. Phys Rev B 38, 9902–9905.CrossRefGoogle ScholarPubMed
Tersoff, J. (1988b). New empirical-approach for the structure and energy of covalent systems. Phys Rev B 37, 6991–7000.CrossRefGoogle ScholarPubMed
Treacy, M.M.J. (2005). What is fluctuation microscopy? Microsc Today 13, 20–21.CrossRefGoogle Scholar
Treacy, M.M.J. & Gibson, J.M. (1996). Variable coherence microscopy: A rich source of structural information from disordered materials. Acta Crystallogr A 52, 212–220.CrossRefGoogle Scholar
Treacy, M.M.J. & Gibson, J.M. (1997). Statistics of partial coherence in dark-field images of amorphous materials. Inst Phys Conf Ser 153, 433–436.Google Scholar
Treacy, M.M.J., Gibson, J.M., Fan, L., Paterson, D.J. & McNulty, I. (2005). Fluctuation microscopy: A probe of medium range order. Rep Progr Phys 68, 2899–2944.CrossRefGoogle Scholar
Treacy, M.M.J., Gibson, J.M. & Keblinski, P.J. (1998). Paracrystallites found in evaporated amorphous tetrahedral semiconductors. J Non-Crystallogr Solids 231, 99–110.CrossRefGoogle Scholar
Voyles, P.M. & Abelson, J.R. (2003). Medium-range order in amorphous silicon measured by fluctuation electron microscopy. Solar Energy Mater Solar Cells 78, 85–113.CrossRefGoogle Scholar
Voyles, P.M., Gerbi, J.E., Treacy, M.M.J., Gibson, J.M. & Abelson, J.R. (2001a). Increased medium-range order in amorphous silicon with increased substrate temperature. Phys Rev Lett 86, 5514–5518.CrossRefGoogle Scholar
Voyles, P.M., Zotov, N., Nakhmanson, S.M., Drabold, D.A., Gibson, J.M., Treacy, M.M.J. & Keblinski, P. (2001b). Structure and physical properties of paracrystalline atomistic models of amorphous silicon. J Appl Phys 90, 4437–4451.CrossRefGoogle Scholar
Wen, J., Cheng, Y.Q., Wang, J.Q. & Ma, E. (2009). Distinguishing medium-range order in metallic glasses using fluctuation electron microscopy: A theoretical study using atomic models. J Appl Phys 105, 043519.CrossRefGoogle Scholar
Zhao, G., Buseck, P.R., Rougée, A. & Treacy, M.M.J. (2009). Medium-range order in molecular materials: Fluctuation electron microscopy for detecting fullerenes in disordered carbons. Ultramicroscopy 109, 177–188.CrossRefGoogle ScholarPubMed
Zhao, G., Treacy, M.M.J. & Buseck, P.R. (2010). Fluctuation electron microscopy of medium-range order in ion-irradiated zircon. Philos Mag 90, 4661–4677.CrossRefGoogle Scholar